diff --git a/build/source/engine/soilLiqFlx.f90 b/build/source/engine/soilLiqFlx.f90
index 520e9c37626e7f5288faae9c5b7bd7fb1ad5eb3f..e65e45812c5b781fccc1c08b5bad158b5498f936 100644
--- a/build/source/engine/soilLiqFlx.f90
+++ b/build/source/engine/soilLiqFlx.f90
@@ -766,7 +766,7 @@ subroutine soilLiqFlx(&
! (use un-perturbed value)
case default
- s calarHydCondTrial = mLayerHydCond(nSoil) ! hydraulic conductivity at the mid-point of the lowest unsaturated soil layer (m s-1)
+ scalarHydCondTrial = mLayerHydCond(nSoil) ! hydraulic conductivity at the mid-point of the lowest unsaturated soil layer (m s-1)
end select ! (re-computing hydraulic conductivity)
diff --git a/build/source/engine/vegNrgFlux.f90 b/build/source/engine/vegNrgFlux.f90
index 63b68b1b8c1ddee21dc7b7bc8929d0eef6e84290..1d42ffab9058f81d632dde5e099e302bf43abdef 100644
--- a/build/source/engine/vegNrgFlux.f90
+++ b/build/source/engine/vegNrgFlux.f90
@@ -20,1941 +20,1848 @@
module vegNrgFlux_module
- ! data types
- USE nrtype
-
- ! derived types to define the data structures
- USE data_types,only:&
- var_i, & ! data vector (i4b)
- var_d, & ! data vector (rkind)
- var_ilength, & ! data vector with variable length dimension (i4b)
- var_dlength, & ! data vector with variable length dimension (rkind)
- model_options ! defines the model decisions
-
- ! indices that define elements of the data structures
- USE var_lookup,only:iLookTYPE ! named variables for structure elements
- USE var_lookup,only:iLookPROG ! named variables for structure elements
- USE var_lookup,only:iLookDIAG ! named variables for structure elements
- USE var_lookup,only:iLookFLUX ! named variables for structure elements
- USE var_lookup,only:iLookFORCE ! named variables for structure elements
- USE var_lookup,only:iLookPARAM ! named variables for structure elements
- USE var_lookup,only:iLookINDEX ! named variables for structure elements
- USE var_lookup,only:iLookBVAR ! named variables for structure elements
- USE var_lookup,only:iLookDECISIONS ! named variables for elements of the decision structure
-
- ! constants
- USE multiconst,only:gravity ! acceleration of gravity (m s-2)
- USE multiconst,only:vkc ! von Karman's constant (-)
- USE multiconst,only:w_ratio ! molecular ratio water to dry air (-)
- USE multiconst,only:R_wv ! gas constant for water vapor (Pa K-1 m3 kg-1; J kg-1 K-1)
- USE multiconst,only:Cp_air ! specific heat of air (J kg-1 K-1)
- USE multiconst,only:Cp_ice ! specific heat of ice (J kg-1 K-1)
- USE multiconst,only:Cp_soil ! specific heat of soil (J kg-1 K-1)
- USE multiconst,only:Cp_water ! specific heat of liquid water (J kg-1 K-1)
- USE multiconst,only:Tfreeze ! temperature at freezing (K)
- USE multiconst,only:LH_fus ! latent heat of fusion (J kg-1)
- USE multiconst,only:LH_vap ! latent heat of vaporization (J kg-1)
- USE multiconst,only:LH_sub ! latent heat of sublimation (J kg-1)
- USE multiconst,only:sb ! Stefan Boltzman constant (W m-2 K-4)
- USE multiconst,only:iden_air ! intrinsic density of air (kg m-3)
- USE multiconst,only:iden_ice ! intrinsic density of ice (kg m-3)
- USE multiconst,only:iden_water ! intrinsic density of liquid water (kg m-3)
-
- ! look-up values for method used to compute derivative
- USE mDecisions_module,only: &
- numerical, & ! numerical solution
- analytical ! analytical solution
-
- ! look-up values for choice of boundary conditions for thermodynamics
- USE mDecisions_module,only: &
- prescribedTemp, & ! prescribed temperature
- energyFlux, & ! energy flux
- zeroFlux ! zero flux
-
- ! look-up values for the choice of parameterization for vegetation roughness length and displacement height
- USE mDecisions_module,only: &
- Raupach_BLM1994, & ! Raupach (BLM 1994) "Simplified expressions..."
- CM_QJRMS1988, & ! Choudhury and Monteith (QJRMS 1988) "A four layer model for the heat budget..."
- vegTypeTable ! constant parameters dependent on the vegetation type
-
- ! look-up values for the choice of parameterization for canopy emissivity
- USE mDecisions_module,only: &
- simplExp, & ! simple exponential function
- difTrans ! parameterized as a function of diffuse transmissivity
-
- ! look-up values for the choice of canopy wind profile
- USE mDecisions_module,only: &
- exponential, & ! exponential wind profile extends to the surface
- logBelowCanopy ! logarithmic profile below the vegetation canopy
-
- ! look-up values for choice of stability function
- USE mDecisions_module,only: &
- standard, & ! standard MO similarity, a la Anderson (1976)
- louisInversePower, & ! Louis (1979) inverse power function
- mahrtExponential ! Mahrt (1987) exponential
-
- ! look-up values for the choice of groundwater representation (local-column, or single-basin)
- USE mDecisions_module,only: &
- localColumn, & ! separate groundwater representation in each local soil column
- singleBasin ! single groundwater store over the entire basin
-
- ! -------------------------------------------------------------------------------------------------
- ! privacy
- implicit none
- private
- public::vegNrgFlux
- public::wettedFrac
- ! dimensions
- integer(i4b),parameter :: nBands=2 ! number of spectral bands for shortwave radiation
- ! named variables
- integer(i4b),parameter :: ist = 1 ! Surface type: IST=1 => soil; IST=2 => lake
- integer(i4b),parameter :: isc = 4 ! Soil color type
- integer(i4b),parameter :: ice = 0 ! Surface type: ICE=0 => soil; ICE=1 => sea-ice
- ! spatial indices
- integer(i4b),parameter :: iLoc = 1 ! i-location
- integer(i4b),parameter :: jLoc = 1 ! j-location
- ! algorithmic parameters
- real(rkind),parameter :: missingValue=-9999._rkind ! missing value, used when diagnostic or state variables are undefined
- real(rkind),parameter :: verySmall=1.e-6_rkind ! used as an additive constant to check if substantial difference among real numbers
- real(rkind),parameter :: tinyVal=epsilon(1._rkind) ! used as an additive constant to check if substantial difference among real numbers
- real(rkind),parameter :: mpe=1.e-6_rkind ! prevents overflow error if division by zero
- real(rkind),parameter :: dx=1.e-11_rkind ! finite difference increment
- ! control
- logical(lgt) :: printflag ! flag to turn on printing
- contains
-
- ! *******************************************************************************************************
- ! public subroutine vegNrgFlux: muster program to compute energy fluxes at vegetation and ground surfaces
- ! *******************************************************************************************************
- subroutine vegNrgFlux(&
- ! input: model control
- firstSubStep, & ! intent(in): flag to indicate if we are processing the first sub-step
- firstFluxCall, & ! intent(in): flag to indicate if we are processing the first flux call
- computeVegFlux, & ! intent(in): flag to indicate if we need to compute fluxes over vegetation
- requireLWBal, & ! intent(in): flag to indicate if we need longwave to be balanced
-
- ! input: model state variables
- upperBoundTemp, & ! intent(in): temperature of the upper boundary (K) --> NOTE: use air temperature
- canairTempTrial, & ! intent(in): trial value of the canopy air space temperature (K)
- canopyTempTrial, & ! intent(in): trial value of canopy temperature (K)
- groundTempTrial, & ! intent(in): trial value of ground temperature (K)
- canopyIceTrial, & ! intent(in): trial value of mass of ice on the vegetation canopy (kg m-2)
- canopyLiqTrial, & ! intent(in): trial value of mass of liquid water on the vegetation canopy (kg m-2)
-
- ! input: model derivatives
- dCanLiq_dTcanopy, & ! intent(in): derivative in canopy liquid w.r.t. canopy temperature (kg m-2 K-1)
-
- ! input/output: data structures
- type_data, & ! intent(in): type of vegetation and soil
- forc_data, & ! intent(in): model forcing data
- mpar_data, & ! intent(in): model parameters
- indx_data, & ! intent(in): state vector geometry
- prog_data, & ! intent(in): model prognostic variables for a local HRU
- diag_data, & ! intent(inout): model diagnostic variables for a local HRU
- flux_data, & ! intent(inout): model fluxes for a local HRU
- bvar_data, & ! intent(in): model variables for the local basin
- model_decisions, & ! intent(in): model decisions
-
- ! output: liquid water fluxes associated with evaporation/transpiration (needed for coupling)
- returnCanopyTranspiration, & ! intent(out): canopy transpiration (kg m-2 s-1)
- returnCanopyEvaporation, & ! intent(out): canopy evaporation/condensation (kg m-2 s-1)
- returnGroundEvaporation, & ! intent(out): ground evaporation/condensation -- below canopy or non-vegetated (kg m-2 s-1)
-
- ! output: fluxes
- canairNetFlux, & ! intent(out): net energy flux for the canopy air space (W m-2)
- canopyNetFlux, & ! intent(out): net energy flux for the vegetation canopy (W m-2)
- groundNetFlux, & ! intent(out): net energy flux for the ground surface (W m-2)
-
- ! output: energy flux derivatives
- dCanairNetFlux_dCanairTemp, & ! intent(out): derivative in net canopy air space flux w.r.t. canopy air temperature (W m-2 K-1)
- dCanairNetFlux_dCanopyTemp, & ! intent(out): derivative in net canopy air space flux w.r.t. canopy temperature (W m-2 K-1)
- dCanairNetFlux_dGroundTemp, & ! intent(out): derivative in net canopy air space flux w.r.t. ground temperature (W m-2 K-1)
- dCanopyNetFlux_dCanairTemp, & ! intent(out): derivative in net canopy flux w.r.t. canopy air temperature (W m-2 K-1)
- dCanopyNetFlux_dCanopyTemp, & ! intent(out): derivative in net canopy flux w.r.t. canopy temperature (W m-2 K-1)
- dCanopyNetFlux_dGroundTemp, & ! intent(out): derivative in net canopy flux w.r.t. ground temperature (W m-2 K-1)
- dGroundNetFlux_dCanairTemp, & ! intent(out): derivative in net ground flux w.r.t. canopy air temperature (W m-2 K-1)
- dGroundNetFlux_dCanopyTemp, & ! intent(out): derivative in net ground flux w.r.t. canopy temperature (W m-2 K-1)
- dGroundNetFlux_dGroundTemp, & ! intent(out): derivative in net ground flux w.r.t. ground temperature (W m-2 K-1)
-
- ! output liquid water flux derivarives (canopy evap)
- dCanopyEvaporation_dCanWat, & ! intent(out): derivative in canopy evaporation w.r.t. canopy total water content (s-1)
- dCanopyEvaporation_dTCanair, & ! intent(out): derivative in canopy evaporation w.r.t. canopy air temperature (kg m-2 s-1 K-1)
- dCanopyEvaporation_dTCanopy, & ! intent(out): derivative in canopy evaporation w.r.t. canopy temperature (kg m-2 s-1 K-1)
- dCanopyEvaporation_dTGround, & ! intent(out): derivative in canopy evaporation w.r.t. ground temperature (kg m-2 s-1 K-1)
-
- ! output: liquid water flux derivarives (ground evap)
- dGroundEvaporation_dCanWat, & ! intent(out): derivative in ground evaporation w.r.t. canopy total water content (s-1)
- dGroundEvaporation_dTCanair, & ! intent(out): derivative in ground evaporation w.r.t. canopy air temperature (kg m-2 s-1 K-1)
- dGroundEvaporation_dTCanopy, & ! intent(out): derivative in ground evaporation w.r.t. canopy temperature (kg m-2 s-1 K-1)
- dGroundEvaporation_dTGround, & ! intent(out): derivative in ground evaporation w.r.t. ground temperature (kg m-2 s-1 K-1)
-
- ! output: transpiration derivatives
- dCanopyTrans_dCanWat, & ! intent(out): derivative in canopy transpiration w.r.t. canopy total water content (s-1)
- dCanopyTrans_dTCanair, & ! intent(out): derivative in canopy transpiration w.r.t. canopy air temperature (kg m-2 s-1 K-1)
- dCanopyTrans_dTCanopy, & ! intent(out): derivative in canopy transpiration w.r.t. canopy temperature (kg m-2 s-1 K-1)
- dCanopyTrans_dTGround, & ! intent(out): derivative in canopy transpiration w.r.t. ground temperature (kg m-2 s-1 K-1)
-
- ! output: cross derivative terms
- dCanopyNetFlux_dCanWat, & ! intent(out): derivative in net canopy fluxes w.r.t. canopy total water content (J kg-1 s-1)
- dGroundNetFlux_dCanWat, & ! intent(out): derivative in net ground fluxes w.r.t. canopy total water content (J kg-1 s-1)
-
- ! output: error control
- err,message) ! intent(out): error control
-
- ! utilities
- USE expIntegral_module,only:expInt ! function to calculate the exponential integral
- ! conversion functions
- USE conv_funcs_module,only:satVapPress ! function to compute the saturated vapor pressure (Pa)
- USE conv_funcs_module,only:getLatentHeatValue ! function to identify latent heat of vaporization/sublimation (J kg-1)
- ! stomatal resistance
- USE stomResist_module,only:stomResist ! subroutine to calculate stomatal resistance
- ! phase changes
- USE snow_utils_module,only:fracliquid ! compute fraction of liquid water at a given temperature
-
- ! compute energy and mass fluxes for vegetation
- implicit none
-
- ! ---------------------------------------------------------------------------------------
- ! * dummy variables
- ! ---------------------------------------------------------------------------------------
- ! input: model control
- logical(lgt),intent(in) :: firstSubStep ! flag to indicate if we are processing the first sub-step
- logical(lgt),intent(in) :: firstFluxCall ! flag to indicate if we are processing the first flux call
- logical(lgt),intent(in) :: computeVegFlux ! flag to indicate if computing fluxes over vegetation
- logical(lgt),intent(in) :: requireLWBal ! flag to indicate if we need longwave to be balanced
- ! input: model state variables
- real(rkind),intent(in) :: upperBoundTemp ! temperature of the upper boundary (K) --> NOTE: use air temperature
- real(rkind),intent(in) :: canairTempTrial ! trial value of canopy air space temperature (K)
- real(rkind),intent(in) :: canopyTempTrial ! trial value of canopy temperature (K)
- real(rkind),intent(in) :: groundTempTrial ! trial value of ground temperature (K)
- real(rkind),intent(in) :: canopyIceTrial ! trial value of mass of ice on the vegetation canopy (kg m-2)
- real(rkind),intent(in) :: canopyLiqTrial ! trial value of mass of liquid water on the vegetation canopy (kg m-2)
-
- ! input: model derivatives
- real(rkind),intent(in) :: dCanLiq_dTcanopy ! intent(in): derivative in canopy liquid w.r.t. canopy temperature (kg m-2 K-1)
-
- ! input/output: data structures
- type(var_i),intent(in) :: type_data ! type of vegetation and soil
- type(var_d),intent(in) :: forc_data ! model forcing data
- type(var_dlength),intent(in) :: mpar_data ! model parameters
- type(var_ilength),intent(in) :: indx_data ! state vector geometry
- type(var_dlength),intent(in) :: prog_data ! prognostic variables for a local HRU
- type(var_dlength),intent(inout) :: diag_data ! diagnostic variables for a local HRU
- type(var_dlength),intent(inout) :: flux_data ! model fluxes for a local HRU
- type(var_dlength),intent(in) :: bvar_data ! model variables for the local basin
- type(model_options),intent(in) :: model_decisions(:) ! model decisions
-
- ! output: liquid water fluxes associated with evaporation/transpiration (needed for coupling)
- real(rkind),intent(out) :: returnCanopyTranspiration ! canopy transpiration (kg m-2 s-1)
- real(rkind),intent(out) :: returnCanopyEvaporation ! canopy evaporation/condensation (kg m-2 s-1)
- real(rkind),intent(out) :: returnGroundEvaporation ! ground evaporation/condensation -- below canopy or non-vegetated (kg m-2 s-1)
-
- ! output: fluxes
- real(rkind),intent(out) :: canairNetFlux ! net energy flux for the canopy air space (W m-2)
- real(rkind),intent(out) :: canopyNetFlux ! net energy flux for the vegetation canopy (W m-2)
- real(rkind),intent(out) :: groundNetFlux ! net energy flux for the ground surface (W m-2)
-
- ! output: energy flux derivatives
- real(rkind),intent(out) :: dCanairNetFlux_dCanairTemp ! derivative in net canopy air space flux w.r.t. canopy air temperature (W m-2 K-1)
- real(rkind),intent(out) :: dCanairNetFlux_dCanopyTemp ! derivative in net canopy air space flux w.r.t. canopy temperature (W m-2 K-1)
- real(rkind),intent(out) :: dCanairNetFlux_dGroundTemp ! derivative in net canopy air space flux w.r.t. ground temperature (W m-2 K-1)
- real(rkind),intent(out) :: dCanopyNetFlux_dCanairTemp ! derivative in net canopy flux w.r.t. canopy air temperature (W m-2 K-1)
- real(rkind),intent(out) :: dCanopyNetFlux_dCanopyTemp ! derivative in net canopy flux w.r.t. canopy temperature (W m-2 K-1)
- real(rkind),intent(out) :: dCanopyNetFlux_dGroundTemp ! derivative in net canopy flux w.r.t. ground temperature (W m-2 K-1)
- real(rkind),intent(out) :: dGroundNetFlux_dCanairTemp ! derivative in net ground flux w.r.t. canopy air temperature (W m-2 K-1)
- real(rkind),intent(out) :: dGroundNetFlux_dCanopyTemp ! derivative in net ground flux w.r.t. canopy temperature (W m-2 K-1)
- real(rkind),intent(out) :: dGroundNetFlux_dGroundTemp ! derivative in net ground flux w.r.t. ground temperature (W m-2 K-1)
-
- ! output: liquid flux derivatives (canopy evap)
- real(rkind),intent(out) :: dCanopyEvaporation_dCanWat ! derivative in canopy evaporation w.r.t. canopy total water content (s-1)
- real(rkind),intent(out) :: dCanopyEvaporation_dTCanair ! derivative in canopy evaporation w.r.t. canopy air temperature (kg m-2 s-1 K-1)
- real(rkind),intent(out) :: dCanopyEvaporation_dTCanopy ! derivative in canopy evaporation w.r.t. canopy temperature (kg m-2 s-1 K-1)
- real(rkind),intent(out) :: dCanopyEvaporation_dTGround ! derivative in canopy evaporation w.r.t. ground temperature (kg m-2 s-1 K-1)
-
- ! output: liquid flux derivatives (ground evap)
- real(rkind),intent(out) :: dGroundEvaporation_dCanWat ! derivative in ground evaporation w.r.t. canopy total water content (s-1)
- real(rkind),intent(out) :: dGroundEvaporation_dTCanair ! derivative in ground evaporation w.r.t. canopy air temperature (kg m-2 s-1 K-1)
- real(rkind),intent(out) :: dGroundEvaporation_dTCanopy ! derivative in ground evaporation w.r.t. canopy temperature (kg m-2 s-1 K-1)
- real(rkind),intent(out) :: dGroundEvaporation_dTGround ! derivative in ground evaporation w.r.t. ground temperature (kg m-2 s-1 K-1)
-
- ! output: transpiration derivatives
- real(rkind),intent(out) :: dCanopyTrans_dCanWat ! intent(out): derivative in canopy transpiration w.r.t. canopy total water content (s-1)
- real(rkind),intent(out) :: dCanopyTrans_dTCanair ! intent(out): derivative in canopy transpiration w.r.t. canopy air temperature (kg m-2 s-1 K-1)
- real(rkind),intent(out) :: dCanopyTrans_dTCanopy ! intent(out): derivative in canopy transpiration w.r.t. canopy temperature (kg m-2 s-1 K-1)
- real(rkind),intent(out) :: dCanopyTrans_dTGround ! intent(out): derivative in canopy transpiration w.r.t. ground temperature (kg m-2 s-1 K-1)
-
- ! output: cross derivative terms
- real(rkind),intent(out) :: dCanopyNetFlux_dCanWat ! derivative in net canopy fluxes w.r.t. canopy total water content (J kg-1 s-1)
- real(rkind),intent(out) :: dGroundNetFlux_dCanWat ! derivative in net ground fluxes w.r.t. canopy total water content (J kg-1 s-1)
-
- ! output: error control
- integer(i4b),intent(out) :: err ! error code
- character(*),intent(out) :: message ! error message
-
- ! ---------------------------------------------------------------------------------------
- ! * local variables
- ! ---------------------------------------------------------------------------------------
- ! local (general)
- character(LEN=256) :: cmessage ! error message of downwind routine
- real(rkind) :: VAI ! vegetation area index (m2 m-2)
- real(rkind) :: exposedVAI ! exposed vegetation area index (m2 m-2)
- real(rkind) :: totalCanopyWater ! total water on the vegetation canopy (kg m-2)
- real(rkind) :: scalarAquiferStorage ! aquifer storage (m)
-
- ! local (compute numerical derivatives)
- integer(i4b),parameter :: unperturbed=1 ! named variable to identify the case of unperturbed state variables
- integer(i4b),parameter :: perturbStateGround=2 ! named variable to identify the case where we perturb the ground temperature
- integer(i4b),parameter :: perturbStateCanopy=3 ! named variable to identify the case where we perturb the canopy temperature
- integer(i4b),parameter :: perturbStateCanair=4 ! named variable to identify the case where we perturb the canopy air temperature
- integer(i4b),parameter :: perturbStateCanWat=5 ! named variable to identify the case where we perturb the canopy total water content
- integer(i4b) :: itry ! index of flux evaluation
- integer(i4b) :: nFlux ! number of flux evaluations
- real(rkind) :: groundTemp ! value of ground temperature used in flux calculations (may be perturbed)
- real(rkind) :: canopyTemp ! value of canopy temperature used in flux calculations (may be perturbed)
- real(rkind) :: canairTemp ! value of canopy air temperature used in flux calculations (may be perturbed)
- real(rkind) :: canopyWat ! value of canopy total water used in flux calculations (may be perturbed)
- real(rkind) :: canopyLiq ! value of canopy liquid water used in flux calculations (may be perturbed)
- real(rkind) :: canopyIce ! value of canopy ice used in flux calculations (may be perturbed)
- real(rkind) :: try0,try1 ! trial values to evaluate specific derivatives (testing only)
-
- ! local (saturation vapor pressure of veg)
- real(rkind) :: TV_celcius ! vegetaion temperature (C)
- real(rkind) :: TG_celcius ! ground temperature (C)
- real(rkind) :: dSVPCanopy_dCanopyTemp ! derivative in canopy saturated vapor pressure w.r.t. vegetation temperature (Pa/K)
- real(rkind) :: dSVPGround_dGroundTemp ! derivative in ground saturated vapor pressure w.r.t. ground temperature (Pa/K)
-
- ! local (wetted canopy area)
- real(rkind) :: fracLiquidCanopy ! fraction of liquid water in the canopy (-)
- real(rkind) :: canopyWetFraction ! trial value of the canopy wetted fraction (-)
- real(rkind) :: dCanopyWetFraction_dWat ! derivative in wetted fraction w.r.t. canopy total water (kg-1 m2)
- real(rkind) :: dCanopyWetFraction_dT ! derivative in wetted fraction w.r.t. canopy temperature (K-1)
-
- ! local (longwave radiation)
- real(rkind) :: expi ! exponential integral
- real(rkind) :: scaleLAI ! scaled LAI (computing diffuse transmissivity)
- real(rkind) :: diffuseTrans ! diffuse transmissivity (-)
- real(rkind) :: groundEmissivity ! emissivity of the ground surface (-)
- real(rkind),parameter :: vegEmissivity=0.98_rkind ! emissivity of vegetation (0.9665 in JULES) (-)
- real(rkind),parameter :: soilEmissivity=0.98_rkind ! emmisivity of the soil (0.9665 in JULES) (-)
- real(rkind),parameter :: snowEmissivity=0.99_rkind ! emissivity of snow (-)
- real(rkind) :: dLWNetCanopy_dTCanopy ! derivative in net canopy radiation w.r.t. canopy temperature (W m-2 K-1)
- real(rkind) :: dLWNetGround_dTGround ! derivative in net ground radiation w.r.t. ground temperature (W m-2 K-1)
- real(rkind) :: dLWNetCanopy_dTGround ! derivative in net canopy radiation w.r.t. ground temperature (W m-2 K-1)
- real(rkind) :: dLWNetGround_dTCanopy ! derivative in net ground radiation w.r.t. canopy temperature (W m-2 K-1)
-
- ! local (aerodynamic resistance)
- real(rkind) :: scalarCanopyStabilityCorrection_old ! stability correction for the canopy (-)
- real(rkind) :: scalarGroundStabilityCorrection_old ! stability correction for the ground surface (-)
-
- ! local (turbulent heat transfer)
- real(rkind) :: z0Ground ! roughness length of the ground (ground below the canopy or non-vegetated surface) (m)
- real(rkind) :: soilEvapFactor ! soil water control on evaporation from non-vegetated surfaces
- real(rkind) :: soilRelHumidity_noSnow ! relative humidity in the soil pores [0-1]
- real(rkind) :: scalarLeafConductance ! leaf conductance (m s-1)
- real(rkind) :: scalarCanopyConductance ! canopy conductance (m s-1)
- real(rkind) :: scalarGroundConductanceSH ! ground conductance for sensible heat (m s-1)
- real(rkind) :: scalarGroundConductanceLH ! ground conductance for latent heat -- includes soil resistance (m s-1)
- real(rkind) :: scalarEvapConductance ! conductance for evaporation (m s-1)
- real(rkind) :: scalarTransConductance ! conductance for transpiration (m s-1)
- real(rkind) :: scalarTotalConductanceSH ! total conductance for sensible heat (m s-1)
- real(rkind) :: scalarTotalConductanceLH ! total conductance for latent heat (m s-1)
- real(rkind) :: dGroundResistance_dTGround ! derivative in ground resistance w.r.t. ground temperature (s m-1 K-1)
- real(rkind) :: dGroundResistance_dTCanopy ! derivative in ground resistance w.r.t. canopy temperature (s m-1 K-1)
- real(rkind) :: dGroundResistance_dTCanair ! derivative in ground resistance w.r.t. canopy air temperature (s m-1 K-1)
- real(rkind) :: dCanopyResistance_dTCanopy ! derivative in canopy resistance w.r.t. canopy temperature (s m-1 K-1)
- real(rkind) :: dCanopyResistance_dTCanair ! derivative in canopy resistance w.r.t. canopy air temperature (s m-1 K-1)
- real(rkind) :: turbFluxCanair ! total turbulent heat fluxes exchanged at the canopy air space (W m-2)
- real(rkind) :: turbFluxCanopy ! total turbulent heat fluxes from the canopy to the canopy air space (W m-2)
- real(rkind) :: turbFluxGround ! total turbulent heat fluxes from the ground to the canopy air space (W m-2)
-
- ! local (turbulent heat transfer -- compute numerical derivatives)
- ! (temporary scalar resistances when states are perturbed)
- real(rkind) :: trialLeafResistance ! mean leaf boundary layer resistance per unit leaf area (s m-1)
- real(rkind) :: trialGroundResistance ! below canopy aerodynamic resistance (s m-1)
- real(rkind) :: trialCanopyResistance ! above canopy aerodynamic resistance (s m-1)
- real(rkind) :: notUsed_RiBulkCanopy ! bulk Richardson number for the canopy (-)
- real(rkind) :: notUsed_RiBulkGround ! bulk Richardson number for the ground surface (-)
- real(rkind) :: notUsed_z0Canopy ! roughness length of the vegetation canopy (m)
- real(rkind) :: notUsed_WindReductionFactor ! canopy wind reduction factor (-)
- real(rkind) :: notUsed_ZeroPlaneDisplacement ! zero plane displacement (m)
- real(rkind) :: notUsed_scalarCanopyStabilityCorrection ! stability correction for the canopy (-)
- real(rkind) :: notUsed_scalarGroundStabilityCorrection ! stability correction for the ground surface (-)
- real(rkind) :: notUsed_EddyDiffusCanopyTop ! eddy diffusivity for heat at the top of the canopy (m2 s-1)
- real(rkind) :: notUsed_FrictionVelocity ! friction velocity (m s-1)
- real(rkind) :: notUsed_WindspdCanopyTop ! windspeed at the top of the canopy (m s-1)
- real(rkind) :: notUsed_WindspdCanopyBottom ! windspeed at the height of the bottom of the canopy (m s-1)
- real(rkind) :: notUsed_dGroundResistance_dTGround ! derivative in ground resistance w.r.t. ground temperature (s m-1 K-1)
- real(rkind) :: notUsed_dGroundResistance_dTCanopy ! derivative in ground resistance w.r.t. canopy temperature (s m-1 K-1)
- real(rkind) :: notUsed_dGroundResistance_dTCanair ! derivative in ground resistance w.r.t. canopy air temperature (s m-1 K-1)
- real(rkind) :: notUsed_dCanopyResistance_dTCanopy ! derivative in canopy resistance w.r.t. canopy temperature (s m-1 K-1)
- real(rkind) :: notUsed_dCanopyResistance_dTCanair ! derivative in canopy resistance w.r.t. canopy air temperature (s m-1 K-1)
-
- ! (fluxes after perturbations in model states -- canopy air space)
- real(rkind) :: turbFluxCanair_dStateCanair ! turbulent exchange from the canopy air space to the atmosphere, after canopy air temperature is perturbed (W m-2)
- real(rkind) :: turbFluxCanair_dStateCanopy ! turbulent exchange from the canopy air space to the atmosphere, after canopy temperature is perturbed (W m-2)
- real(rkind) :: turbFluxCanair_dStateGround ! turbulent exchange from the canopy air space to the atmosphere, after ground temperature is perturbed (W m-2)
- real(rkind) :: turbFluxCanair_dStateCanWat ! turbulent exchange from the canopy air space to the atmosphere, after canopy total water content is perturbed (W m-2)
- ! (fluxes after perturbations in model states -- vegetation canopy)
- real(rkind) :: turbFluxCanopy_dStateCanair ! total turbulent heat fluxes from the canopy to the canopy air space, after canopy air temperature is perturbed (W m-2)
- real(rkind) :: turbFluxCanopy_dStateCanopy ! total turbulent heat fluxes from the canopy to the canopy air space, after canopy temperature is perturbed (W m-2)
- real(rkind) :: turbFluxCanopy_dStateGround ! total turbulent heat fluxes from the canopy to the canopy air space, after ground temperature is perturbed (W m-2)
- real(rkind) :: turbFluxCanopy_dStateCanWat ! total turbulent heat fluxes from the canopy to the canopy air space, after canopy total water content is perturbed (W m-2)
-
- ! (fluxes after perturbations in model states -- ground surface)
- real(rkind) :: turbFluxGround_dStateCanair ! total turbulent heat fluxes from the ground to the canopy air space, after canopy air temperature is perturbed (W m-2)
- real(rkind) :: turbFluxGround_dStateCanopy ! total turbulent heat fluxes from the ground to the canopy air space, after canopy temperature is perturbed (W m-2)
- real(rkind) :: turbFluxGround_dStateGround ! total turbulent heat fluxes from the ground to the canopy air space, after ground temperature is perturbed (W m-2)
- real(rkind) :: turbFluxGround_dStateCanWat ! total turbulent heat fluxes from the ground to the canopy air space, after canopy total water content is perturbed (W m-2)
-
- ! (fluxes after perturbations in model states -- canopy evaporation)
- real(rkind) :: latHeatCanEvap_dStateCanair ! canopy evaporation after canopy air temperature is perturbed (W m-2)
- real(rkind) :: latHeatCanEvap_dStateCanopy ! canopy evaporation after canopy temperature is perturbed (W m-2)
- real(rkind) :: latHeatCanEvap_dStateGround ! canopy evaporation after ground temperature is perturbed (W m-2)
- real(rkind) :: latHeatCanEvap_dStateCanWat ! canopy evaporation after canopy total water content is perturbed (W m-2)
-
- ! (flux derivatives -- canopy air space)
- real(rkind) :: dTurbFluxCanair_dTCanair ! derivative in net canopy air space fluxes w.r.t. canopy air temperature (W m-2 K-1)
- real(rkind) :: dTurbFluxCanair_dTCanopy ! derivative in net canopy air space fluxes w.r.t. canopy temperature (W m-2 K-1)
- real(rkind) :: dTurbFluxCanair_dTGround ! derivative in net canopy air space fluxes w.r.t. ground temperature (W m-2 K-1)
- real(rkind) :: dTurbFluxCanair_dCanWat ! derivative in net canopy air space fluxes w.r.t. canopy total water content (J kg-1 s-1)
-
- ! (flux derivatives -- vegetation canopy)
- real(rkind) :: dTurbFluxCanopy_dTCanair ! derivative in net canopy turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
- real(rkind) :: dTurbFluxCanopy_dTCanopy ! derivative in net canopy turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
- real(rkind) :: dTurbFluxCanopy_dTGround ! derivative in net canopy turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
- real(rkind) :: dTurbFluxCanopy_dCanWat ! derivative in net canopy turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
-
- ! (flux derivatives -- ground surface)
- real(rkind) :: dTurbFluxGround_dTCanair ! derivative in net ground turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
- real(rkind) :: dTurbFluxGround_dTCanopy ! derivative in net ground turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
- real(rkind) :: dTurbFluxGround_dTGround ! derivative in net ground turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
- real(rkind) :: dTurbFluxGround_dCanWat ! derivative in net ground turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
-
- ! (liquid water flux derivatives -- canopy evap)
- real(rkind) :: dLatHeatCanopyEvap_dCanWat ! derivative in latent heat of canopy evaporation w.r.t. canopy total water content (W kg-1)
- real(rkind) :: dLatHeatCanopyEvap_dTCanair ! derivative in latent heat of canopy evaporation w.r.t. canopy air temperature (W m-2 K-1)
- real(rkind) :: dLatHeatCanopyEvap_dTCanopy ! derivative in latent heat of canopy evaporation w.r.t. canopy temperature (W m-2 K-1)
- real(rkind) :: dLatHeatCanopyEvap_dTGround ! derivative in latent heat of canopy evaporation w.r.t. ground temperature (W m-2 K-1)
-
- ! (liquid water flux derivatives -- ground evap)
- real(rkind) :: dLatHeatGroundEvap_dCanWat ! derivative in latent heat of ground evaporation w.r.t. canopy total water content (J kg-1 s-1)
- real(rkind) :: dLatHeatGroundEvap_dTCanair ! derivative in latent heat of ground evaporation w.r.t. canopy air temperature (W m-2 K-1)
- real(rkind) :: dLatHeatGroundEvap_dTCanopy ! derivative in latent heat of ground evaporation w.r.t. canopy temperature (W m-2 K-1)
- real(rkind) :: dLatHeatGroundEvap_dTGround ! derivative in latent heat of ground evaporation w.r.t. ground temperature (W m-2 K-1)
-
- ! output: latent heat flux derivatives (canopy trans)
- real(rkind) :: dLatHeatCanopyTrans_dCanWat ! derivative in the latent heat of canopy transpiration w.r.t. canopy total water (J kg-1 s-1)
- real(rkind) :: dLatHeatCanopyTrans_dTCanair ! derivative in the latent heat of canopy transpiration w.r.t. canopy air temperature
- real(rkind) :: dLatHeatCanopyTrans_dTCanopy ! derivative in the latent heat of canopy transpiration w.r.t. canopy temperature
- real(rkind) :: dLatHeatCanopyTrans_dTGround ! derivative in the latent heat of canopy transpiration w.r.t. ground temperature
-
- ! ---------------------------------------------------------------------------------------
- ! point to variables in the data structure
- ! ---------------------------------------------------------------------------------------
- associate(&
-
- ! input: model decisions
- ix_bcUpprTdyn => model_decisions(iLookDECISIONS%bcUpprTdyn)%iDecision, & ! intent(in): [i4b] choice of upper boundary condition for thermodynamics
- ixDerivMethod => model_decisions(iLookDECISIONS%fDerivMeth)%iDecision, & ! intent(in): [i4b] choice of method to compute derivatives
- ix_veg_traits => model_decisions(iLookDECISIONS%veg_traits)%iDecision, & ! intent(in): [i4b] choice of parameterization for vegetation roughness length and displacement height
- ix_canopyEmis => model_decisions(iLookDECISIONS%canopyEmis)%iDecision, & ! intent(in): [i4b] choice of parameterization for canopy emissivity
- ix_windPrfile => model_decisions(iLookDECISIONS%windPrfile)%iDecision, & ! intent(in): [i4b] choice of canopy wind profile
- ix_astability => model_decisions(iLookDECISIONS%astability)%iDecision, & ! intent(in): [i4b] choice of stability function
- ix_soilStress => model_decisions(iLookDECISIONS%soilStress)%iDecision, & ! intent(in): [i4b] choice of function for the soil moisture control on stomatal resistance
- ix_groundwatr => model_decisions(iLookDECISIONS%groundwatr)%iDecision, & ! intent(in): [i4b] choice of groundwater parameterization
- ix_stomResist => model_decisions(iLookDECISIONS%stomResist)%iDecision, & ! intent(in): [i4b] choice of function for stomatal resistance
- ix_spatial_gw => model_decisions(iLookDECISIONS%spatial_gw)%iDecision, & ! intent(in): [i4b] choice of groundwater representation (local, basin)
-
- ! input: layer geometry
- nSnow => indx_data%var(iLookINDEX%nSnow)%dat(1), & ! intent(in): [i4b] number of snow layers
- nSoil => indx_data%var(iLookINDEX%nSoil)%dat(1), & ! intent(in): [i4b] number of soil layers
- nLayers => indx_data%var(iLookINDEX%nLayers)%dat(1), & ! intent(in): [i4b] total number of layers
-
- ! input: physical attributes
- vegTypeIndex => type_data%var(iLookTYPE%vegTypeIndex), & ! intent(in): [i4b] vegetation type index
- soilTypeIndex => type_data%var(iLookTYPE%soilTypeIndex), & ! intent(in): [i4b] soil type index
-
- ! input: vegetation parameters
- heightCanopyTop => mpar_data%var(iLookPARAM%heightCanopyTop)%dat(1), & ! intent(in): [dp] height at the top of the vegetation canopy (m)
- heightCanopyBottom => mpar_data%var(iLookPARAM%heightCanopyBottom)%dat(1), & ! intent(in): [dp] height at the bottom of the vegetation canopy (m)
- canopyWettingFactor => mpar_data%var(iLookPARAM%canopyWettingFactor)%dat(1), & ! intent(in): [dp] maximum wetted fraction of the canopy (-)
- canopyWettingExp => mpar_data%var(iLookPARAM%canopyWettingExp)%dat(1), & ! intent(in): [dp] exponent in canopy wetting function (-)
- scalarCanopyIceMax => diag_data%var(iLookDIAG%scalarCanopyIceMax)%dat(1), & ! intent(in): [dp] maximum interception storage capacity for ice (kg m-2)
- scalarCanopyLiqMax => diag_data%var(iLookDIAG%scalarCanopyLiqMax)%dat(1), & ! intent(in): [dp] maximum interception storage capacity for liquid water (kg m-2)
-
- ! input: vegetation phenology
- scalarLAI => diag_data%var(iLookDIAG%scalarLAI)%dat(1), & ! intent(in): [dp] one-sided leaf area index (m2 m-2)
- scalarSAI => diag_data%var(iLookDIAG%scalarSAI)%dat(1), & ! intent(in): [dp] one-sided stem area index (m2 m-2)
- scalarExposedLAI => diag_data%var(iLookDIAG%scalarExposedLAI)%dat(1), & ! intent(in): [dp] exposed leaf area index after burial by snow (m2 m-2)
- scalarExposedSAI => diag_data%var(iLookDIAG%scalarExposedSAI)%dat(1), & ! intent(in): [dp] exposed stem area index after burial by snow (m2 m-2)
- scalarGrowingSeasonIndex => diag_data%var(iLookDIAG%scalarGrowingSeasonIndex)%dat(1), & ! intent(in): [dp] growing season index (0=off, 1=on)
- scalarFoliageNitrogenFactor => diag_data%var(iLookDIAG%scalarFoliageNitrogenFactor)%dat(1), & ! intent(in): [dp] foliage nitrogen concentration (1.0 = saturated)
-
- ! input: aerodynamic resistance parameters
- z0Snow => mpar_data%var(iLookPARAM%z0Snow)%dat(1), & ! intent(in): [dp] roughness length of snow (m)
- z0Soil => mpar_data%var(iLookPARAM%z0Soil)%dat(1), & ! intent(in): [dp] roughness length of soil (m)
- z0CanopyParam => mpar_data%var(iLookPARAM%z0Canopy)%dat(1), & ! intent(in): [dp] roughness length of the canopy (m)
- zpdFraction => mpar_data%var(iLookPARAM%zpdFraction)%dat(1), & ! intent(in): [dp] zero plane displacement / canopy height (-)
- critRichNumber => mpar_data%var(iLookPARAM%critRichNumber)%dat(1), & ! intent(in): [dp] critical value for the bulk Richardson number where turbulence ceases (-)
- Louis79_bparam => mpar_data%var(iLookPARAM%Louis79_bparam)%dat(1), & ! intent(in): [dp] parameter in Louis (1979) stability function
- Louis79_cStar => mpar_data%var(iLookPARAM%Louis79_cStar)%dat(1), & ! intent(in): [dp] parameter in Louis (1979) stability function
- Mahrt87_eScale => mpar_data%var(iLookPARAM%Mahrt87_eScale)%dat(1), & ! intent(in): [dp] exponential scaling factor in the Mahrt (1987) stability function
- windReductionParam => mpar_data%var(iLookPARAM%windReductionParam)%dat(1), & ! intent(in): [dp] canopy wind reduction parameter (-)
- leafExchangeCoeff => mpar_data%var(iLookPARAM%leafExchangeCoeff)%dat(1), & ! intent(in): [dp] turbulent exchange coeff between canopy surface and canopy air ( m s-(1/2) )
- leafDimension => mpar_data%var(iLookPARAM%leafDimension)%dat(1), & ! intent(in): [dp] characteristic leaf dimension (m)
-
- ! input: soil stress parameters
- theta_sat => mpar_data%var(iLookPARAM%theta_sat)%dat(1), & ! intent(in): [dp] soil porosity (-)
- theta_res => mpar_data%var(iLookPARAM%theta_res)%dat(1), & ! intent(in): [dp] residual volumetric liquid water content (-)
- plantWiltPsi => mpar_data%var(iLookPARAM%plantWiltPsi)%dat(1), & ! intent(in): [dp] matric head at wilting point (m)
- soilStressParam => mpar_data%var(iLookPARAM%soilStressParam)%dat(1), & ! intent(in): [dp] parameter in the exponential soil stress function (-)
- critSoilWilting => mpar_data%var(iLookPARAM%critSoilWilting)%dat(1), & ! intent(in): [dp] critical vol. liq. water content when plants are wilting (-)
- critSoilTranspire => mpar_data%var(iLookPARAM%critSoilTranspire)%dat(1), & ! intent(in): [dp] critical vol. liq. water content when transpiration is limited (-)
- critAquiferTranspire => mpar_data%var(iLookPARAM%critAquiferTranspire)%dat(1), & ! intent(in): [dp] critical aquifer storage value when transpiration is limited (m)
- minStomatalResistance => mpar_data%var(iLookPARAM%minStomatalResistance)%dat(1), & ! intent(in): [dp] mimimum stomatal resistance (s m-1)
-
- ! snow parameters
- snowfrz_scale => mpar_data%var(iLookPARAM%snowfrz_scale)%dat(1), & ! intent(in): [dp] scaling parameter for the snow freezing curve (K-1)
-
- ! input: forcing at the upper boundary
- mHeight => diag_data%var(iLookDIAG%scalarAdjMeasHeight)%dat(1), & ! intent(in): [dp] measurement height (m)
- airtemp => forc_data%var(iLookFORCE%airtemp), & ! intent(in): [dp] air temperature at some height above the surface (K)
- windspd => forc_data%var(iLookFORCE%windspd), & ! intent(in): [dp] wind speed at some height above the surface (m s-1)
- airpres => forc_data%var(iLookFORCE%airpres), & ! intent(in): [dp] air pressure at some height above the surface (Pa)
- LWRadAtm => forc_data%var(iLookFORCE%LWRadAtm), & ! intent(in): [dp] downwelling longwave radiation at the upper boundary (W m-2)
- scalarVPair => diag_data%var(iLookDIAG%scalarVPair)%dat(1), & ! intent(in): [dp] vapor pressure at some height above the surface (Pa)
- scalarO2air => diag_data%var(iLookDIAG%scalarO2air)%dat(1), & ! intent(in): [dp] atmospheric o2 concentration (Pa)
- scalarCO2air => diag_data%var(iLookDIAG%scalarCO2air)%dat(1), & ! intent(in): [dp] atmospheric co2 concentration (Pa)
- scalarTwetbulb => diag_data%var(iLookDIAG%scalarTwetbulb)%dat(1), & ! intent(in): [dp] wetbulb temperature (K)
- scalarRainfall => flux_data%var(iLookFLUX%scalarRainfall)%dat(1), & ! intent(in): [dp] computed rainfall rate (kg m-2 s-1)
- scalarSnowfall => flux_data%var(iLookFLUX%scalarSnowfall)%dat(1), & ! intent(in): [dp] computed snowfall rate (kg m-2 s-1)
- scalarThroughfallRain => flux_data%var(iLookFLUX%scalarThroughfallRain)%dat(1), & ! intent(in): [dp] rainfall through the vegetation canopy (kg m-2 s-1)
- scalarThroughfallSnow => flux_data%var(iLookFLUX%scalarThroughfallSnow)%dat(1), & ! intent(in): [dp] snowfall through the vegetation canopy (kg m-2 s-1)
-
- ! input: water storage
- ! NOTE: soil stress only computed at the start of the substep (firstFluxCall=.true.)
- scalarSWE => prog_data%var(iLookPROG%scalarSWE)%dat(1), & ! intent(in): [dp] snow water equivalent on the ground (kg m-2)
- scalarSnowDepth => prog_data%var(iLookPROG%scalarSnowDepth)%dat(1), & ! intent(in): [dp] snow depth on the ground surface (m)
- mLayerVolFracLiq => prog_data%var(iLookPROG%mLayerVolFracLiq)%dat, & ! intent(in): [dp(:)] volumetric fraction of liquid water in each layer (-)
- mLayerMatricHead => prog_data%var(iLookPROG%mLayerMatricHead)%dat, & ! intent(in): [dp(:)] matric head in each soil layer (m)
- localAquiferStorage => prog_data%var(iLookPROG%scalarAquiferStorage)%dat(1), & ! intent(in): [dp] aquifer storage for the local column (m)
- basinAquiferStorage => bvar_data%var(iLookBVAR%basin__AquiferStorage)%dat(1), & ! intent(in): [dp] aquifer storage for the single basin (m)
-
- ! input: shortwave radiation fluxes
- scalarCanopySunlitLAI => diag_data%var(iLookDIAG%scalarCanopySunlitLAI)%dat(1), & ! intent(in): [dp] sunlit leaf area (-)
- scalarCanopyShadedLAI => diag_data%var(iLookDIAG%scalarCanopyShadedLAI)%dat(1), & ! intent(in): [dp] shaded leaf area (-)
- scalarCanopySunlitPAR => flux_data%var(iLookFLUX%scalarCanopySunlitPAR)%dat(1), & ! intent(in): [dp] average absorbed par for sunlit leaves (w m-2)
- scalarCanopyShadedPAR => flux_data%var(iLookFLUX%scalarCanopyShadedPAR)%dat(1), & ! intent(in): [dp] average absorbed par for shaded leaves (w m-2)
- scalarCanopyAbsorbedSolar => flux_data%var(iLookFLUX%scalarCanopyAbsorbedSolar)%dat(1), & ! intent(in): [dp] solar radiation absorbed by canopy (W m-2)
- scalarGroundAbsorbedSolar => flux_data%var(iLookFLUX%scalarGroundAbsorbedSolar)%dat(1), & ! intent(in): [dp] solar radiation absorbed by ground (W m-2)
-
- ! output: fraction of wetted canopy area and fraction of snow on the ground
- scalarCanopyWetFraction => diag_data%var(iLookDIAG%scalarCanopyWetFraction)%dat(1), & ! intent(out): [dp] fraction of canopy that is wet
- scalarGroundSnowFraction => diag_data%var(iLookDIAG%scalarGroundSnowFraction)%dat(1), & ! intent(out): [dp] fraction of ground covered with snow (-)
-
- ! output: longwave radiation fluxes
- scalarCanopyEmissivity => diag_data%var(iLookDIAG%scalarCanopyEmissivity)%dat(1), & ! intent(out): [dp] effective emissivity of the canopy (-)
- scalarLWRadCanopy => flux_data%var(iLookFLUX%scalarLWRadCanopy)%dat(1), & ! intent(out): [dp] longwave radiation emitted from the canopy (W m-2)
- scalarLWRadGround => flux_data%var(iLookFLUX%scalarLWRadGround)%dat(1), & ! intent(out): [dp] longwave radiation emitted at the ground surface (W m-2)
- scalarLWRadUbound2Canopy => flux_data%var(iLookFLUX%scalarLWRadUbound2Canopy)%dat(1), & ! intent(out): [dp] downward atmospheric longwave radiation absorbed by the canopy (W m-2)
- scalarLWRadUbound2Ground => flux_data%var(iLookFLUX%scalarLWRadUbound2Ground)%dat(1), & ! intent(out): [dp] downward atmospheric longwave radiation absorbed by the ground (W m-2)
- scalarLWRadUbound2Ubound => flux_data%var(iLookFLUX%scalarLWRadUbound2Ubound)%dat(1), & ! intent(out): [dp] atmospheric radiation reflected by the ground and lost thru upper boundary (W m-2)
- scalarLWRadCanopy2Ubound => flux_data%var(iLookFLUX%scalarLWRadCanopy2Ubound)%dat(1), & ! intent(out): [dp] longwave radiation emitted from canopy lost thru upper boundary (W m-2)
- scalarLWRadCanopy2Ground => flux_data%var(iLookFLUX%scalarLWRadCanopy2Ground)%dat(1), & ! intent(out): [dp] longwave radiation emitted from canopy absorbed by the ground (W m-2)
- scalarLWRadCanopy2Canopy => flux_data%var(iLookFLUX%scalarLWRadCanopy2Canopy)%dat(1), & ! intent(out): [dp] canopy longwave reflected from ground and absorbed by the canopy (W m-2)
- scalarLWRadGround2Ubound => flux_data%var(iLookFLUX%scalarLWRadGround2Ubound)%dat(1), & ! intent(out): [dp] longwave radiation emitted from ground lost thru upper boundary (W m-2)
- scalarLWRadGround2Canopy => flux_data%var(iLookFLUX%scalarLWRadGround2Canopy)%dat(1), & ! intent(out): [dp] longwave radiation emitted from ground and absorbed by the canopy (W m-2)
- scalarLWNetCanopy => flux_data%var(iLookFLUX%scalarLWNetCanopy)%dat(1), & ! intent(out): [dp] net longwave radiation at the canopy (W m-2)
- scalarLWNetGround => flux_data%var(iLookFLUX%scalarLWNetGround)%dat(1), & ! intent(out): [dp] net longwave radiation at the ground surface (W m-2)
- scalarLWNetUbound => flux_data%var(iLookFLUX%scalarLWNetUbound)%dat(1), & ! intent(out): [dp] net longwave radiation at the upper boundary (W m-2)
-
- ! output: aerodynamic resistance
- scalarZ0Canopy => diag_data%var(iLookDIAG%scalarZ0Canopy)%dat(1), & ! intent(out): [dp] roughness length of the canopy (m)
- scalarWindReductionFactor => diag_data%var(iLookDIAG%scalarWindReductionFactor)%dat(1), & ! intent(out): [dp] canopy wind reduction factor (-)
- scalarZeroPlaneDisplacement => diag_data%var(iLookDIAG%scalarZeroPlaneDisplacement)%dat(1), & ! intent(out): [dp] zero plane displacement (m)
- scalarRiBulkCanopy => diag_data%var(iLookDIAG%scalarRiBulkCanopy)%dat(1), & ! intent(out): [dp] bulk Richardson number for the canopy (-)
- scalarRiBulkGround => diag_data%var(iLookDIAG%scalarRiBulkGround)%dat(1), & ! intent(out): [dp] bulk Richardson number for the ground surface (-)
- scalarEddyDiffusCanopyTop => flux_data%var(iLookFLUX%scalarEddyDiffusCanopyTop)%dat(1), & ! intent(out): [dp] eddy diffusivity for heat at the top of the canopy (m2 s-1)
- scalarFrictionVelocity => flux_data%var(iLookFLUX%scalarFrictionVelocity)%dat(1), & ! intent(out): [dp] friction velocity (m s-1)
- scalarWindspdCanopyTop => flux_data%var(iLookFLUX%scalarWindspdCanopyTop)%dat(1), & ! intent(out): [dp] windspeed at the top of the canopy (m s-1)
- scalarWindspdCanopyBottom => flux_data%var(iLookFLUX%scalarWindspdCanopyBottom)%dat(1), & ! intent(out): [dp] windspeed at the height of the bottom of the canopy (m s-1)
- scalarLeafResistance => flux_data%var(iLookFLUX%scalarLeafResistance)%dat(1), & ! intent(out): [dp] mean leaf boundary layer resistance per unit leaf area (s m-1)
- scalarGroundResistance => flux_data%var(iLookFLUX%scalarGroundResistance)%dat(1), & ! intent(out): [dp] below canopy aerodynamic resistance (s m-1)
- scalarCanopyResistance => flux_data%var(iLookFLUX%scalarCanopyResistance)%dat(1), & ! intent(out): [dp] above canopy aerodynamic resistance (s m-1)
-
- ! input/output: soil resistance -- intent(in) and intent(inout) because only called at the first flux call
- mLayerRootDensity => diag_data%var(iLookDIAG%mLayerRootDensity)%dat, & ! intent(in): [dp] root density in each layer (-)
- scalarAquiferRootFrac => diag_data%var(iLookDIAG%scalarAquiferRootFrac)%dat(1), & ! intent(in): [dp] fraction of roots below the lowest soil layer (-)
- scalarTranspireLim => diag_data%var(iLookDIAG%scalarTranspireLim)%dat(1), & ! intent(inout): [dp] weighted average of the transpiration limiting factor (-)
- mLayerTranspireLim => diag_data%var(iLookDIAG%mLayerTranspireLim)%dat, & ! intent(inout): [dp] transpiration limiting factor in each layer (-)
- scalarTranspireLimAqfr => diag_data%var(iLookDIAG%scalarTranspireLimAqfr)%dat(1), & ! intent(inout): [dp] transpiration limiting factor for the aquifer (-)
- scalarSoilRelHumidity => diag_data%var(iLookDIAG%scalarSoilRelHumidity)%dat(1), & ! intent(inout): [dp] relative humidity in the soil pores [0-1]
- scalarSoilResistance => flux_data%var(iLookFLUX%scalarSoilResistance)%dat(1), & ! intent(inout): [dp] resistance from the soil (s m-1)
-
- ! input/output: stomatal resistance -- intent(inout) because only called at the first flux call
- scalarStomResistSunlit => flux_data%var(iLookFLUX%scalarStomResistSunlit)%dat(1), & ! intent(inout): [dp] stomatal resistance for sunlit leaves (s m-1)
- scalarStomResistShaded => flux_data%var(iLookFLUX%scalarStomResistShaded)%dat(1), & ! intent(inout): [dp] stomatal resistance for shaded leaves (s m-1)
- scalarPhotosynthesisSunlit => flux_data%var(iLookFLUX%scalarPhotosynthesisSunlit)%dat(1), & ! intent(inout): [dp] sunlit photosynthesis (umolco2 m-2 s-1)
- scalarPhotosynthesisShaded => flux_data%var(iLookFLUX%scalarPhotosynthesisShaded)%dat(1), & ! intent(inout): [dp] shaded photosynthesis (umolco2 m-2 s-1)
-
- ! output: turbulent heat fluxes
- scalarLatHeatSubVapCanopy => diag_data%var(iLookDIAG%scalarLatHeatSubVapCanopy)%dat(1), & ! intent(inout): [dp] latent heat of sublimation/vaporization for the vegetation canopy (J kg-1)
- scalarLatHeatSubVapGround => diag_data%var(iLookDIAG%scalarLatHeatSubVapGround)%dat(1), & ! intent(inout): [dp] latent heat of sublimation/vaporization for the ground surface (J kg-1)
- scalarSatVP_canopyTemp => diag_data%var(iLookDIAG%scalarSatVP_CanopyTemp)%dat(1), & ! intent(out): [dp] saturation vapor pressure at the temperature of the vegetation canopy (Pa)
- scalarSatVP_groundTemp => diag_data%var(iLookDIAG%scalarSatVP_GroundTemp)%dat(1), & ! intent(out): [dp] saturation vapor pressure at the temperature of the ground surface (Pa)
- scalarSenHeatTotal => flux_data%var(iLookFLUX%scalarSenHeatTotal)%dat(1), & ! intent(out): [dp] sensible heat from the canopy air space to the atmosphere (W m-2)
- scalarSenHeatCanopy => flux_data%var(iLookFLUX%scalarSenHeatCanopy)%dat(1), & ! intent(out): [dp] sensible heat flux from the canopy to the canopy air space (W m-2)
- scalarSenHeatGround => flux_data%var(iLookFLUX%scalarSenHeatGround)%dat(1), & ! intent(out): [dp] sensible heat flux from ground surface below vegetation (W m-2)
- scalarLatHeatTotal => flux_data%var(iLookFLUX%scalarLatHeatTotal)%dat(1), & ! intent(out): [dp] latent heat from the canopy air space to the atmosphere (W m-2)
- scalarLatHeatCanopyEvap => flux_data%var(iLookFLUX%scalarLatHeatCanopyEvap)%dat(1), & ! intent(out): [dp] latent heat flux for evaporation from the canopy to the canopy air space (W m-2)
- scalarLatHeatCanopyTrans => flux_data%var(iLookFLUX%scalarLatHeatCanopyTrans)%dat(1), & ! intent(out): [dp] latent heat flux for transpiration from the canopy to the canopy air space (W m-2)
- scalarLatHeatGround => flux_data%var(iLookFLUX%scalarLatHeatGround)%dat(1), & ! intent(out): [dp] latent heat flux from ground surface below vegetation (W m-2)
-
- ! output: advective heat fluxes
- scalarCanopyAdvectiveHeatFlux => flux_data%var(iLookFLUX%scalarCanopyAdvectiveHeatFlux)%dat(1), & ! intent(out): [dp] heat advected to the canopy surface with rain + snow (W m-2)
- scalarGroundAdvectiveHeatFlux => flux_data%var(iLookFLUX%scalarGroundAdvectiveHeatFlux)%dat(1), & ! intent(out): [dp] heat advected to the ground surface with throughfall (W m-2)
-
- ! output: mass fluxes
- scalarCanopySublimation => flux_data%var(iLookFLUX%scalarCanopySublimation)%dat(1), & ! intent(out): [dp] canopy sublimation/frost (kg m-2 s-1)
- scalarSnowSublimation => flux_data%var(iLookFLUX%scalarSnowSublimation)%dat(1), & ! intent(out): [dp] snow sublimation/frost -- below canopy or non-vegetated (kg m-2 s-1)
-
- ! input/output: canopy air space variables
- scalarVP_CanopyAir => diag_data%var(iLookDIAG%scalarVP_CanopyAir)%dat(1), & ! intent(inout): [dp] vapor pressure of the canopy air space (Pa)
- scalarCanopyStabilityCorrection => diag_data%var(iLookDIAG%scalarCanopyStabilityCorrection)%dat(1),& ! intent(inout): [dp] stability correction for the canopy (-)
- scalarGroundStabilityCorrection => diag_data%var(iLookDIAG%scalarGroundStabilityCorrection)%dat(1),& ! intent(inout): [dp] stability correction for the ground surface (-)
-
- ! output: liquid water fluxes
- scalarCanopyTranspiration => flux_data%var(iLookFLUX%scalarCanopyTranspiration)%dat(1), & ! intent(out): [dp] canopy transpiration (kg m-2 s-1)
- scalarCanopyEvaporation => flux_data%var(iLookFLUX%scalarCanopyEvaporation)%dat(1), & ! intent(out): [dp] canopy evaporation/condensation (kg m-2 s-1)
- scalarGroundEvaporation => flux_data%var(iLookFLUX%scalarGroundEvaporation)%dat(1), & ! intent(out): [dp] ground evaporation/condensation -- below canopy or non-vegetated (kg m-2 s-1)
-
- ! output: derived fluxes
- scalarTotalET => flux_data%var(iLookFLUX%scalarTotalET)%dat(1), & ! intent(out): [dp] total ET (kg m-2 s-1)
- scalarNetRadiation => flux_data%var(iLookFLUX%scalarNetRadiation)%dat(1) & ! intent(out): [dp] net radiation (W m-2)
- )
- ! ---------------------------------------------------------------------------------------
- ! initialize error control
- err=0; message="vegNrgFlux/"
-
- ! initialize printflag
- printflag = .false.
-
- ! identify the type of boundary condition for thermodynamics
- select case(ix_bcUpprTdyn)
-
+! data types
+USE nrtype
+
+! derived types to define the data structures
+USE data_types,only:&
+ var_i, & ! data vector (i4b)
+ var_d, & ! data vector (rkind)
+ var_ilength, & ! data vector with variable length dimension (i4b)
+ var_dlength, & ! data vector with variable length dimension (rkind)
+ model_options ! defines the model decisions
+
+! indices that define elements of the data structures
+USE var_lookup,only:iLookTYPE ! named variables for structure elements
+USE var_lookup,only:iLookPROG ! named variables for structure elements
+USE var_lookup,only:iLookDIAG ! named variables for structure elements
+USE var_lookup,only:iLookFLUX ! named variables for structure elements
+USE var_lookup,only:iLookFORCE ! named variables for structure elements
+USE var_lookup,only:iLookPARAM ! named variables for structure elements
+USE var_lookup,only:iLookINDEX ! named variables for structure elements
+USE var_lookup,only:iLookBVAR ! named variables for structure elements
+USE var_lookup,only:iLookDECISIONS ! named variables for elements of the decision structure
+
+! constants
+USE multiconst,only:gravity ! acceleration of gravity (m s-2)
+USE multiconst,only:vkc ! von Karman's constant (-)
+USE multiconst,only:w_ratio ! molecular ratio water to dry air (-)
+USE multiconst,only:R_wv ! gas constant for water vapor (Pa K-1 m3 kg-1; J kg-1 K-1)
+USE multiconst,only:Cp_air ! specific heat of air (J kg-1 K-1)
+USE multiconst,only:Cp_ice ! specific heat of ice (J kg-1 K-1)
+USE multiconst,only:Cp_soil ! specific heat of soil (J kg-1 K-1)
+USE multiconst,only:Cp_water ! specific heat of liquid water (J kg-1 K-1)
+USE multiconst,only:Tfreeze ! temperature at freezing (K)
+USE multiconst,only:LH_fus ! latent heat of fusion (J kg-1)
+USE multiconst,only:LH_vap ! latent heat of vaporization (J kg-1)
+USE multiconst,only:LH_sub ! latent heat of sublimation (J kg-1)
+USE multiconst,only:sb ! Stefan Boltzman constant (W m-2 K-4)
+USE multiconst,only:iden_air ! intrinsic density of air (kg m-3)
+USE multiconst,only:iden_ice ! intrinsic density of ice (kg m-3)
+USE multiconst,only:iden_water ! intrinsic density of liquid water (kg m-3)
+
+! look-up values for method used to compute derivative
+USE mDecisions_module,only: &
+ numerical, & ! numerical solution
+ analytical ! analytical solution
+
+! look-up values for choice of boundary conditions for thermodynamics
+USE mDecisions_module,only: &
+ prescribedTemp, & ! prescribed temperature
+ energyFlux, & ! energy flux
+ zeroFlux ! zero flux
+
+! look-up values for the choice of parameterization for vegetation roughness length and displacement height
+USE mDecisions_module,only: &
+ Raupach_BLM1994, & ! Raupach (BLM 1994) "Simplified expressions..."
+ CM_QJRMS1988, & ! Choudhury and Monteith (QJRMS 1988) "A four layer model for the heat budget..."
+ vegTypeTable ! constant parameters dependent on the vegetation type
+
+! look-up values for the choice of parameterization for canopy emissivity
+USE mDecisions_module,only: &
+ simplExp, & ! simple exponential function
+ difTrans ! parameterized as a function of diffuse transmissivity
+
+! look-up values for the choice of canopy wind profile
+USE mDecisions_module,only: &
+ exponential, & ! exponential wind profile extends to the surface
+ logBelowCanopy ! logarithmic profile below the vegetation canopy
+
+! look-up values for choice of stability function
+USE mDecisions_module,only: &
+ standard, & ! standard MO similarity, a la Anderson (1976)
+ louisInversePower, & ! Louis (1979) inverse power function
+ mahrtExponential ! Mahrt (1987) exponential
+
+! look-up values for the choice of groundwater representation (local-column, or single-basin)
+USE mDecisions_module,only: &
+ localColumn, & ! separate groundwater representation in each local soil column
+ singleBasin ! single groundwater store over the entire basin
+
+! -------------------------------------------------------------------------------------------------
+! privacy
+implicit none
+private
+public::vegNrgFlux
+public::wettedFrac
+! dimensions
+integer(i4b),parameter :: nBands=2 ! number of spectral bands for shortwave radiation
+! named variables
+integer(i4b),parameter :: ist = 1 ! Surface type: IST=1 => soil; IST=2 => lake
+integer(i4b),parameter :: isc = 4 ! Soil color type
+integer(i4b),parameter :: ice = 0 ! Surface type: ICE=0 => soil; ICE=1 => sea-ice
+! spatial indices
+integer(i4b),parameter :: iLoc = 1 ! i-location
+integer(i4b),parameter :: jLoc = 1 ! j-location
+! algorithmic parameters
+real(rkind),parameter :: missingValue=-9999._rkind ! missing value, used when diagnostic or state variables are undefined
+real(rkind),parameter :: verySmall=1.e-6_rkind ! used as an additive constant to check if substantial difference among real numbers
+real(rkind),parameter :: tinyVal=epsilon(1._rkind) ! used as an additive constant to check if substantial difference among real numbers
+real(rkind),parameter :: mpe=1.e-6_rkind ! prevents overflow error if division by zero
+real(rkind),parameter :: dx=1.e-11_rkind ! finite difference increment
+! control
+logical(lgt) :: printflag ! flag to turn on printing
+contains
+
+! *******************************************************************************************************
+! public subroutine vegNrgFlux: muster program to compute energy fluxes at vegetation and ground surfaces
+! *******************************************************************************************************
+subroutine vegNrgFlux(&
+ ! input: model control
+ firstSubStep, & ! intent(in): flag to indicate if we are processing the first sub-step
+ firstFluxCall, & ! intent(in): flag to indicate if we are processing the first flux call
+ computeVegFlux, & ! intent(in): flag to indicate if we need to compute fluxes over vegetation
+ insideIDA, & ! intent(in): flag to indicate inside Sundials Solver (do not require longwave to be balanced)
+
+ ! input: model state variables
+ upperBoundTemp, & ! intent(in): temperature of the upper boundary (K) --> NOTE: use air temperature
+ canairTempTrial, & ! intent(in): trial value of the canopy air space temperature (K)
+ canopyTempTrial, & ! intent(in): trial value of canopy temperature (K)
+ groundTempTrial, & ! intent(in): trial value of ground temperature (K)
+ canopyIceTrial, & ! intent(in): trial value of mass of ice on the vegetation canopy (kg m-2)
+ canopyLiqTrial, & ! intent(in): trial value of mass of liquid water on the vegetation canopy (kg m-2)
+
+ ! input: model derivatives
+ dCanLiq_dTcanopy, & ! intent(in): derivative in canopy liquid w.r.t. canopy temperature (kg m-2 K-1)
+
+ ! input/output: data structures
+ type_data, & ! intent(in): type of vegetation and soil
+ forc_data, & ! intent(in): model forcing data
+ mpar_data, & ! intent(in): model parameters
+ indx_data, & ! intent(in): state vector geometry
+ prog_data, & ! intent(in): model prognostic variables for a local HRU
+ diag_data, & ! intent(inout): model diagnostic variables for a local HRU
+ flux_data, & ! intent(inout): model fluxes for a local HRU
+ bvar_data, & ! intent(in): model variables for the local basin
+ model_decisions, & ! intent(in): model decisions
+
+ ! output: liquid water fluxes associated with evaporation/transpiration (needed for coupling)
+ returnCanopyTranspiration, & ! intent(out): canopy transpiration (kg m-2 s-1)
+ returnCanopyEvaporation, & ! intent(out): canopy evaporation/condensation (kg m-2 s-1)
+ returnGroundEvaporation, & ! intent(out): ground evaporation/condensation -- below canopy or non-vegetated (kg m-2 s-1)
+
+ ! output: fluxes
+ canairNetFlux, & ! intent(out): net energy flux for the canopy air space (W m-2)
+ canopyNetFlux, & ! intent(out): net energy flux for the vegetation canopy (W m-2)
+ groundNetFlux, & ! intent(out): net energy flux for the ground surface (W m-2)
+
+ ! output: energy flux derivatives
+ dCanairNetFlux_dCanairTemp, & ! intent(out): derivative in net canopy air space flux w.r.t. canopy air temperature (W m-2 K-1)
+ dCanairNetFlux_dCanopyTemp, & ! intent(out): derivative in net canopy air space flux w.r.t. canopy temperature (W m-2 K-1)
+ dCanairNetFlux_dGroundTemp, & ! intent(out): derivative in net canopy air space flux w.r.t. ground temperature (W m-2 K-1)
+ dCanopyNetFlux_dCanairTemp, & ! intent(out): derivative in net canopy flux w.r.t. canopy air temperature (W m-2 K-1)
+ dCanopyNetFlux_dCanopyTemp, & ! intent(out): derivative in net canopy flux w.r.t. canopy temperature (W m-2 K-1)
+ dCanopyNetFlux_dGroundTemp, & ! intent(out): derivative in net canopy flux w.r.t. ground temperature (W m-2 K-1)
+ dGroundNetFlux_dCanairTemp, & ! intent(out): derivative in net ground flux w.r.t. canopy air temperature (W m-2 K-1)
+ dGroundNetFlux_dCanopyTemp, & ! intent(out): derivative in net ground flux w.r.t. canopy temperature (W m-2 K-1)
+ dGroundNetFlux_dGroundTemp, & ! intent(out): derivative in net ground flux w.r.t. ground temperature (W m-2 K-1)
+
+ ! output liquid water flux derivarives (canopy evap)
+ dCanopyEvaporation_dCanWat, & ! intent(out): derivative in canopy evaporation w.r.t. canopy total water content (s-1)
+ dCanopyEvaporation_dTCanair, & ! intent(out): derivative in canopy evaporation w.r.t. canopy air temperature (kg m-2 s-1 K-1)
+ dCanopyEvaporation_dTCanopy, & ! intent(out): derivative in canopy evaporation w.r.t. canopy temperature (kg m-2 s-1 K-1)
+ dCanopyEvaporation_dTGround, & ! intent(out): derivative in canopy evaporation w.r.t. ground temperature (kg m-2 s-1 K-1)
+
+ ! output: liquid water flux derivarives (ground evap)
+ dGroundEvaporation_dCanWat, & ! intent(out): derivative in ground evaporation w.r.t. canopy total water content (s-1)
+ dGroundEvaporation_dTCanair, & ! intent(out): derivative in ground evaporation w.r.t. canopy air temperature (kg m-2 s-1 K-1)
+ dGroundEvaporation_dTCanopy, & ! intent(out): derivative in ground evaporation w.r.t. canopy temperature (kg m-2 s-1 K-1)
+ dGroundEvaporation_dTGround, & ! intent(out): derivative in ground evaporation w.r.t. ground temperature (kg m-2 s-1 K-1)
+
+ ! output: transpiration derivatives
+ dCanopyTrans_dCanWat, & ! intent(out): derivative in canopy transpiration w.r.t. canopy total water content (s-1)
+ dCanopyTrans_dTCanair, & ! intent(out): derivative in canopy transpiration w.r.t. canopy air temperature (kg m-2 s-1 K-1)
+ dCanopyTrans_dTCanopy, & ! intent(out): derivative in canopy transpiration w.r.t. canopy temperature (kg m-2 s-1 K-1)
+ dCanopyTrans_dTGround, & ! intent(out): derivative in canopy transpiration w.r.t. ground temperature (kg m-2 s-1 K-1)
+
+ ! output: cross derivative terms
+ dCanopyNetFlux_dCanWat, & ! intent(out): derivative in net canopy fluxes w.r.t. canopy total water content (J kg-1 s-1)
+ dGroundNetFlux_dCanWat, & ! intent(out): derivative in net ground fluxes w.r.t. canopy total water content (J kg-1 s-1)
+
+ ! output: error control
+ err,message) ! intent(out): error control
+
+ ! utilities
+ USE expIntegral_module,only:expInt ! function to calculate the exponential integral
+ ! conversion functions
+ USE conv_funcs_module,only:satVapPress ! function to compute the saturated vapor pressure (Pa)
+ USE conv_funcs_module,only:getLatentHeatValue ! function to identify latent heat of vaporization/sublimation (J kg-1)
+ ! stomatal resistance
+ USE stomResist_module,only:stomResist ! subroutine to calculate stomatal resistance
+ ! phase changes
+ USE snow_utils_module,only:fracliquid ! compute fraction of liquid water at a given temperature
+
+ ! compute energy and mass fluxes for vegetation
+ implicit none
+
+ ! ---------------------------------------------------------------------------------------
+ ! * dummy variables
+ ! ---------------------------------------------------------------------------------------
+ ! input: model control
+ logical(lgt),intent(in) :: firstSubStep ! flag to indicate if we are processing the first sub-step
+ logical(lgt),intent(in) :: firstFluxCall ! flag to indicate if we are processing the first flux call
+ logical(lgt),intent(in) :: computeVegFlux ! flag to indicate if computing fluxes over vegetation
+ logical(lgt),intent(in) :: insideIDA ! flag if inside Sundials solver
+ ! input: model state variables
+ real(rkind),intent(in) :: upperBoundTemp ! temperature of the upper boundary (K) --> NOTE: use air temperature
+ real(rkind),intent(in) :: canairTempTrial ! trial value of canopy air space temperature (K)
+ real(rkind),intent(in) :: canopyTempTrial ! trial value of canopy temperature (K)
+ real(rkind),intent(in) :: groundTempTrial ! trial value of ground temperature (K)
+ real(rkind),intent(in) :: canopyIceTrial ! trial value of mass of ice on the vegetation canopy (kg m-2)
+ real(rkind),intent(in) :: canopyLiqTrial ! trial value of mass of liquid water on the vegetation canopy (kg m-2)
+
+ ! input: model derivatives
+ real(rkind),intent(in) :: dCanLiq_dTcanopy ! intent(in): derivative in canopy liquid w.r.t. canopy temperature (kg m-2 K-1)
+
+ ! input/output: data structures
+ type(var_i),intent(in) :: type_data ! type of vegetation and soil
+ type(var_d),intent(in) :: forc_data ! model forcing data
+ type(var_dlength),intent(in) :: mpar_data ! model parameters
+ type(var_ilength),intent(in) :: indx_data ! state vector geometry
+ type(var_dlength),intent(in) :: prog_data ! prognostic variables for a local HRU
+ type(var_dlength),intent(inout) :: diag_data ! diagnostic variables for a local HRU
+ type(var_dlength),intent(inout) :: flux_data ! model fluxes for a local HRU
+ type(var_dlength),intent(in) :: bvar_data ! model variables for the local basin
+ type(model_options),intent(in) :: model_decisions(:) ! model decisions
+
+ ! output: liquid water fluxes associated with evaporation/transpiration (needed for coupling)
+ real(rkind),intent(out) :: returnCanopyTranspiration ! canopy transpiration (kg m-2 s-1)
+ real(rkind),intent(out) :: returnCanopyEvaporation ! canopy evaporation/condensation (kg m-2 s-1)
+ real(rkind),intent(out) :: returnGroundEvaporation ! ground evaporation/condensation -- below canopy or non-vegetated (kg m-2 s-1)
+
+ ! output: fluxes
+ real(rkind),intent(out) :: canairNetFlux ! net energy flux for the canopy air space (W m-2)
+ real(rkind),intent(out) :: canopyNetFlux ! net energy flux for the vegetation canopy (W m-2)
+ real(rkind),intent(out) :: groundNetFlux ! net energy flux for the ground surface (W m-2)
+
+ ! output: energy flux derivatives
+ real(rkind),intent(out) :: dCanairNetFlux_dCanairTemp ! derivative in net canopy air space flux w.r.t. canopy air temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dCanairNetFlux_dCanopyTemp ! derivative in net canopy air space flux w.r.t. canopy temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dCanairNetFlux_dGroundTemp ! derivative in net canopy air space flux w.r.t. ground temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dCanopyNetFlux_dCanairTemp ! derivative in net canopy flux w.r.t. canopy air temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dCanopyNetFlux_dCanopyTemp ! derivative in net canopy flux w.r.t. canopy temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dCanopyNetFlux_dGroundTemp ! derivative in net canopy flux w.r.t. ground temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dGroundNetFlux_dCanairTemp ! derivative in net ground flux w.r.t. canopy air temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dGroundNetFlux_dCanopyTemp ! derivative in net ground flux w.r.t. canopy temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dGroundNetFlux_dGroundTemp ! derivative in net ground flux w.r.t. ground temperature (W m-2 K-1)
+
+ ! output: liquid flux derivatives (canopy evap)
+ real(rkind),intent(out) :: dCanopyEvaporation_dCanWat ! derivative in canopy evaporation w.r.t. canopy total water content (s-1)
+ real(rkind),intent(out) :: dCanopyEvaporation_dTCanair ! derivative in canopy evaporation w.r.t. canopy air temperature (kg m-2 s-1 K-1)
+ real(rkind),intent(out) :: dCanopyEvaporation_dTCanopy ! derivative in canopy evaporation w.r.t. canopy temperature (kg m-2 s-1 K-1)
+ real(rkind),intent(out) :: dCanopyEvaporation_dTGround ! derivative in canopy evaporation w.r.t. ground temperature (kg m-2 s-1 K-1)
+
+ ! output: liquid flux derivatives (ground evap)
+ real(rkind),intent(out) :: dGroundEvaporation_dCanWat ! derivative in ground evaporation w.r.t. canopy total water content (s-1)
+ real(rkind),intent(out) :: dGroundEvaporation_dTCanair ! derivative in ground evaporation w.r.t. canopy air temperature (kg m-2 s-1 K-1)
+ real(rkind),intent(out) :: dGroundEvaporation_dTCanopy ! derivative in ground evaporation w.r.t. canopy temperature (kg m-2 s-1 K-1)
+ real(rkind),intent(out) :: dGroundEvaporation_dTGround ! derivative in ground evaporation w.r.t. ground temperature (kg m-2 s-1 K-1)
+
+ ! output: transpiration derivatives
+ real(rkind),intent(out) :: dCanopyTrans_dCanWat ! intent(out): derivative in canopy transpiration w.r.t. canopy total water content (s-1)
+ real(rkind),intent(out) :: dCanopyTrans_dTCanair ! intent(out): derivative in canopy transpiration w.r.t. canopy air temperature (kg m-2 s-1 K-1)
+ real(rkind),intent(out) :: dCanopyTrans_dTCanopy ! intent(out): derivative in canopy transpiration w.r.t. canopy temperature (kg m-2 s-1 K-1)
+ real(rkind),intent(out) :: dCanopyTrans_dTGround ! intent(out): derivative in canopy transpiration w.r.t. ground temperature (kg m-2 s-1 K-1)
+
+ ! output: cross derivative terms
+ real(rkind),intent(out) :: dCanopyNetFlux_dCanWat ! derivative in net canopy fluxes w.r.t. canopy total water content (J kg-1 s-1)
+ real(rkind),intent(out) :: dGroundNetFlux_dCanWat ! derivative in net ground fluxes w.r.t. canopy total water content (J kg-1 s-1)
+
+ ! output: error control
+ integer(i4b),intent(out) :: err ! error code
+ character(*),intent(out) :: message ! error message
+
+ ! ---------------------------------------------------------------------------------------
+ ! * local variables
+ ! ---------------------------------------------------------------------------------------
+ ! local (general)
+ character(LEN=256) :: cmessage ! error message of downwind routine
+ real(rkind) :: VAI ! vegetation area index (m2 m-2)
+ real(rkind) :: exposedVAI ! exposed vegetation area index (m2 m-2)
+ real(rkind) :: totalCanopyWater ! total water on the vegetation canopy (kg m-2)
+ real(rkind) :: scalarAquiferStorage ! aquifer storage (m)
+
+ ! local (compute numerical derivatives)
+ integer(i4b),parameter :: unperturbed=1 ! named variable to identify the case of unperturbed state variables
+ integer(i4b),parameter :: perturbStateGround=2 ! named variable to identify the case where we perturb the ground temperature
+ integer(i4b),parameter :: perturbStateCanopy=3 ! named variable to identify the case where we perturb the canopy temperature
+ integer(i4b),parameter :: perturbStateCanair=4 ! named variable to identify the case where we perturb the canopy air temperature
+ integer(i4b),parameter :: perturbStateCanWat=5 ! named variable to identify the case where we perturb the canopy total water content
+ integer(i4b) :: itry ! index of flux evaluation
+ integer(i4b) :: nFlux ! number of flux evaluations
+ real(rkind) :: groundTemp ! value of ground temperature used in flux calculations (may be perturbed)
+ real(rkind) :: canopyTemp ! value of canopy temperature used in flux calculations (may be perturbed)
+ real(rkind) :: canairTemp ! value of canopy air temperature used in flux calculations (may be perturbed)
+ real(rkind) :: canopyWat ! value of canopy total water used in flux calculations (may be perturbed)
+ real(rkind) :: canopyLiq ! value of canopy liquid water used in flux calculations (may be perturbed)
+ real(rkind) :: canopyIce ! value of canopy ice used in flux calculations (may be perturbed)
+ real(rkind) :: try0,try1 ! trial values to evaluate specific derivatives (testing only)
+
+ ! local (saturation vapor pressure of veg)
+ real(rkind) :: TV_celcius ! vegetaion temperature (C)
+ real(rkind) :: TG_celcius ! ground temperature (C)
+ real(rkind) :: dSVPCanopy_dCanopyTemp ! derivative in canopy saturated vapor pressure w.r.t. vegetation temperature (Pa/K)
+ real(rkind) :: dSVPGround_dGroundTemp ! derivative in ground saturated vapor pressure w.r.t. ground temperature (Pa/K)
+
+ ! local (wetted canopy area)
+ real(rkind) :: fracLiquidCanopy ! fraction of liquid water in the canopy (-)
+ real(rkind) :: canopyWetFraction ! trial value of the canopy wetted fraction (-)
+ real(rkind) :: dCanopyWetFraction_dWat ! derivative in wetted fraction w.r.t. canopy total water (kg-1 m2)
+ real(rkind) :: dCanopyWetFraction_dT ! derivative in wetted fraction w.r.t. canopy temperature (K-1)
+
+ ! local (longwave radiation)
+ real(rkind) :: expi ! exponential integral
+ real(rkind) :: scaleLAI ! scaled LAI (computing diffuse transmissivity)
+ real(rkind) :: diffuseTrans ! diffuse transmissivity (-)
+ real(rkind) :: groundEmissivity ! emissivity of the ground surface (-)
+ real(rkind),parameter :: vegEmissivity=0.98_rkind ! emissivity of vegetation (0.9665 in JULES) (-)
+ real(rkind),parameter :: soilEmissivity=0.98_rkind ! emmisivity of the soil (0.9665 in JULES) (-)
+ real(rkind),parameter :: snowEmissivity=0.99_rkind ! emissivity of snow (-)
+ real(rkind) :: dLWNetCanopy_dTCanopy ! derivative in net canopy radiation w.r.t. canopy temperature (W m-2 K-1)
+ real(rkind) :: dLWNetGround_dTGround ! derivative in net ground radiation w.r.t. ground temperature (W m-2 K-1)
+ real(rkind) :: dLWNetCanopy_dTGround ! derivative in net canopy radiation w.r.t. ground temperature (W m-2 K-1)
+ real(rkind) :: dLWNetGround_dTCanopy ! derivative in net ground radiation w.r.t. canopy temperature (W m-2 K-1)
+
+ ! local (aerodynamic resistance)
+ real(rkind) :: scalarCanopyStabilityCorrection_old ! stability correction for the canopy (-)
+ real(rkind) :: scalarGroundStabilityCorrection_old ! stability correction for the ground surface (-)
+
+ ! local (turbulent heat transfer)
+ real(rkind) :: z0Ground ! roughness length of the ground (ground below the canopy or non-vegetated surface) (m)
+ real(rkind) :: soilEvapFactor ! soil water control on evaporation from non-vegetated surfaces
+ real(rkind) :: soilRelHumidity_noSnow ! relative humidity in the soil pores [0-1]
+ real(rkind) :: scalarLeafConductance ! leaf conductance (m s-1)
+ real(rkind) :: scalarCanopyConductance ! canopy conductance (m s-1)
+ real(rkind) :: scalarGroundConductanceSH ! ground conductance for sensible heat (m s-1)
+ real(rkind) :: scalarGroundConductanceLH ! ground conductance for latent heat -- includes soil resistance (m s-1)
+ real(rkind) :: scalarEvapConductance ! conductance for evaporation (m s-1)
+ real(rkind) :: scalarTransConductance ! conductance for transpiration (m s-1)
+ real(rkind) :: scalarTotalConductanceSH ! total conductance for sensible heat (m s-1)
+ real(rkind) :: scalarTotalConductanceLH ! total conductance for latent heat (m s-1)
+ real(rkind) :: dGroundResistance_dTGround ! derivative in ground resistance w.r.t. ground temperature (s m-1 K-1)
+ real(rkind) :: dGroundResistance_dTCanopy ! derivative in ground resistance w.r.t. canopy temperature (s m-1 K-1)
+ real(rkind) :: dGroundResistance_dTCanair ! derivative in ground resistance w.r.t. canopy air temperature (s m-1 K-1)
+ real(rkind) :: dCanopyResistance_dTCanopy ! derivative in canopy resistance w.r.t. canopy temperature (s m-1 K-1)
+ real(rkind) :: dCanopyResistance_dTCanair ! derivative in canopy resistance w.r.t. canopy air temperature (s m-1 K-1)
+ real(rkind) :: turbFluxCanair ! total turbulent heat fluxes exchanged at the canopy air space (W m-2)
+ real(rkind) :: turbFluxCanopy ! total turbulent heat fluxes from the canopy to the canopy air space (W m-2)
+ real(rkind) :: turbFluxGround ! total turbulent heat fluxes from the ground to the canopy air space (W m-2)
+
+ ! local (turbulent heat transfer -- compute numerical derivatives)
+ ! (temporary scalar resistances when states are perturbed)
+ real(rkind) :: trialLeafResistance ! mean leaf boundary layer resistance per unit leaf area (s m-1)
+ real(rkind) :: trialGroundResistance ! below canopy aerodynamic resistance (s m-1)
+ real(rkind) :: trialCanopyResistance ! above canopy aerodynamic resistance (s m-1)
+ real(rkind) :: notUsed_RiBulkCanopy ! bulk Richardson number for the canopy (-)
+ real(rkind) :: notUsed_RiBulkGround ! bulk Richardson number for the ground surface (-)
+ real(rkind) :: notUsed_z0Canopy ! roughness length of the vegetation canopy (m)
+ real(rkind) :: notUsed_WindReductionFactor ! canopy wind reduction factor (-)
+ real(rkind) :: notUsed_ZeroPlaneDisplacement ! zero plane displacement (m)
+ real(rkind) :: notUsed_scalarCanopyStabilityCorrection ! stability correction for the canopy (-)
+ real(rkind) :: notUsed_scalarGroundStabilityCorrection ! stability correction for the ground surface (-)
+ real(rkind) :: notUsed_EddyDiffusCanopyTop ! eddy diffusivity for heat at the top of the canopy (m2 s-1)
+ real(rkind) :: notUsed_FrictionVelocity ! friction velocity (m s-1)
+ real(rkind) :: notUsed_WindspdCanopyTop ! windspeed at the top of the canopy (m s-1)
+ real(rkind) :: notUsed_WindspdCanopyBottom ! windspeed at the height of the bottom of the canopy (m s-1)
+ real(rkind) :: notUsed_dGroundResistance_dTGround ! derivative in ground resistance w.r.t. ground temperature (s m-1 K-1)
+ real(rkind) :: notUsed_dGroundResistance_dTCanopy ! derivative in ground resistance w.r.t. canopy temperature (s m-1 K-1)
+ real(rkind) :: notUsed_dGroundResistance_dTCanair ! derivative in ground resistance w.r.t. canopy air temperature (s m-1 K-1)
+ real(rkind) :: notUsed_dCanopyResistance_dTCanopy ! derivative in canopy resistance w.r.t. canopy temperature (s m-1 K-1)
+ real(rkind) :: notUsed_dCanopyResistance_dTCanair ! derivative in canopy resistance w.r.t. canopy air temperature (s m-1 K-1)
+
+ ! (fluxes after perturbations in model states -- canopy air space)
+ real(rkind) :: turbFluxCanair_dStateCanair ! turbulent exchange from the canopy air space to the atmosphere, after canopy air temperature is perturbed (W m-2)
+ real(rkind) :: turbFluxCanair_dStateCanopy ! turbulent exchange from the canopy air space to the atmosphere, after canopy temperature is perturbed (W m-2)
+ real(rkind) :: turbFluxCanair_dStateGround ! turbulent exchange from the canopy air space to the atmosphere, after ground temperature is perturbed (W m-2)
+ real(rkind) :: turbFluxCanair_dStateCanWat ! turbulent exchange from the canopy air space to the atmosphere, after canopy total water content is perturbed (W m-2)
+ ! (fluxes after perturbations in model states -- vegetation canopy)
+ real(rkind) :: turbFluxCanopy_dStateCanair ! total turbulent heat fluxes from the canopy to the canopy air space, after canopy air temperature is perturbed (W m-2)
+ real(rkind) :: turbFluxCanopy_dStateCanopy ! total turbulent heat fluxes from the canopy to the canopy air space, after canopy temperature is perturbed (W m-2)
+ real(rkind) :: turbFluxCanopy_dStateGround ! total turbulent heat fluxes from the canopy to the canopy air space, after ground temperature is perturbed (W m-2)
+ real(rkind) :: turbFluxCanopy_dStateCanWat ! total turbulent heat fluxes from the canopy to the canopy air space, after canopy total water content is perturbed (W m-2)
+
+ ! (fluxes after perturbations in model states -- ground surface)
+ real(rkind) :: turbFluxGround_dStateCanair ! total turbulent heat fluxes from the ground to the canopy air space, after canopy air temperature is perturbed (W m-2)
+ real(rkind) :: turbFluxGround_dStateCanopy ! total turbulent heat fluxes from the ground to the canopy air space, after canopy temperature is perturbed (W m-2)
+ real(rkind) :: turbFluxGround_dStateGround ! total turbulent heat fluxes from the ground to the canopy air space, after ground temperature is perturbed (W m-2)
+ real(rkind) :: turbFluxGround_dStateCanWat ! total turbulent heat fluxes from the ground to the canopy air space, after canopy total water content is perturbed (W m-2)
+
+ ! (fluxes after perturbations in model states -- canopy evaporation)
+ real(rkind) :: latHeatCanEvap_dStateCanair ! canopy evaporation after canopy air temperature is perturbed (W m-2)
+ real(rkind) :: latHeatCanEvap_dStateCanopy ! canopy evaporation after canopy temperature is perturbed (W m-2)
+ real(rkind) :: latHeatCanEvap_dStateGround ! canopy evaporation after ground temperature is perturbed (W m-2)
+ real(rkind) :: latHeatCanEvap_dStateCanWat ! canopy evaporation after canopy total water content is perturbed (W m-2)
+
+ ! (flux derivatives -- canopy air space)
+ real(rkind) :: dTurbFluxCanair_dTCanair ! derivative in net canopy air space fluxes w.r.t. canopy air temperature (W m-2 K-1)
+ real(rkind) :: dTurbFluxCanair_dTCanopy ! derivative in net canopy air space fluxes w.r.t. canopy temperature (W m-2 K-1)
+ real(rkind) :: dTurbFluxCanair_dTGround ! derivative in net canopy air space fluxes w.r.t. ground temperature (W m-2 K-1)
+ real(rkind) :: dTurbFluxCanair_dCanWat ! derivative in net canopy air space fluxes w.r.t. canopy total water content (J kg-1 s-1)
+
+ ! (flux derivatives -- vegetation canopy)
+ real(rkind) :: dTurbFluxCanopy_dTCanair ! derivative in net canopy turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
+ real(rkind) :: dTurbFluxCanopy_dTCanopy ! derivative in net canopy turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
+ real(rkind) :: dTurbFluxCanopy_dTGround ! derivative in net canopy turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
+ real(rkind) :: dTurbFluxCanopy_dCanWat ! derivative in net canopy turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
+
+ ! (flux derivatives -- ground surface)
+ real(rkind) :: dTurbFluxGround_dTCanair ! derivative in net ground turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
+ real(rkind) :: dTurbFluxGround_dTCanopy ! derivative in net ground turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
+ real(rkind) :: dTurbFluxGround_dTGround ! derivative in net ground turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
+ real(rkind) :: dTurbFluxGround_dCanWat ! derivative in net ground turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
+
+ ! (liquid water flux derivatives -- canopy evap)
+ real(rkind) :: dLatHeatCanopyEvap_dCanWat ! derivative in latent heat of canopy evaporation w.r.t. canopy total water content (W kg-1)
+ real(rkind) :: dLatHeatCanopyEvap_dTCanair ! derivative in latent heat of canopy evaporation w.r.t. canopy air temperature (W m-2 K-1)
+ real(rkind) :: dLatHeatCanopyEvap_dTCanopy ! derivative in latent heat of canopy evaporation w.r.t. canopy temperature (W m-2 K-1)
+ real(rkind) :: dLatHeatCanopyEvap_dTGround ! derivative in latent heat of canopy evaporation w.r.t. ground temperature (W m-2 K-1)
+
+ ! (liquid water flux derivatives -- ground evap)
+ real(rkind) :: dLatHeatGroundEvap_dCanWat ! derivative in latent heat of ground evaporation w.r.t. canopy total water content (J kg-1 s-1)
+ real(rkind) :: dLatHeatGroundEvap_dTCanair ! derivative in latent heat of ground evaporation w.r.t. canopy air temperature (W m-2 K-1)
+ real(rkind) :: dLatHeatGroundEvap_dTCanopy ! derivative in latent heat of ground evaporation w.r.t. canopy temperature (W m-2 K-1)
+ real(rkind) :: dLatHeatGroundEvap_dTGround ! derivative in latent heat of ground evaporation w.r.t. ground temperature (W m-2 K-1)
+
+ ! output: latent heat flux derivatives (canopy trans)
+ real(rkind) :: dLatHeatCanopyTrans_dCanWat ! derivative in the latent heat of canopy transpiration w.r.t. canopy total water (J kg-1 s-1)
+ real(rkind) :: dLatHeatCanopyTrans_dTCanair ! derivative in the latent heat of canopy transpiration w.r.t. canopy air temperature
+ real(rkind) :: dLatHeatCanopyTrans_dTCanopy ! derivative in the latent heat of canopy transpiration w.r.t. canopy temperature
+ real(rkind) :: dLatHeatCanopyTrans_dTGround ! derivative in the latent heat of canopy transpiration w.r.t. ground temperature
+
+ ! ---------------------------------------------------------------------------------------
+ ! point to variables in the data structure
+ ! ---------------------------------------------------------------------------------------
+ associate(&
+
+ ! input: model decisions
+ ix_bcUpprTdyn => model_decisions(iLookDECISIONS%bcUpprTdyn)%iDecision, & ! intent(in): [i4b] choice of upper boundary condition for thermodynamics
+ ixDerivMethod => model_decisions(iLookDECISIONS%fDerivMeth)%iDecision, & ! intent(in): [i4b] choice of method to compute derivatives
+ ix_veg_traits => model_decisions(iLookDECISIONS%veg_traits)%iDecision, & ! intent(in): [i4b] choice of parameterization for vegetation roughness length and displacement height
+ ix_canopyEmis => model_decisions(iLookDECISIONS%canopyEmis)%iDecision, & ! intent(in): [i4b] choice of parameterization for canopy emissivity
+ ix_windPrfile => model_decisions(iLookDECISIONS%windPrfile)%iDecision, & ! intent(in): [i4b] choice of canopy wind profile
+ ix_astability => model_decisions(iLookDECISIONS%astability)%iDecision, & ! intent(in): [i4b] choice of stability function
+ ix_soilStress => model_decisions(iLookDECISIONS%soilStress)%iDecision, & ! intent(in): [i4b] choice of function for the soil moisture control on stomatal resistance
+ ix_groundwatr => model_decisions(iLookDECISIONS%groundwatr)%iDecision, & ! intent(in): [i4b] choice of groundwater parameterization
+ ix_stomResist => model_decisions(iLookDECISIONS%stomResist)%iDecision, & ! intent(in): [i4b] choice of function for stomatal resistance
+ ix_spatial_gw => model_decisions(iLookDECISIONS%spatial_gw)%iDecision, & ! intent(in): [i4b] choice of groundwater representation (local, basin)
+
+ ! input: layer geometry
+ nSnow => indx_data%var(iLookINDEX%nSnow)%dat(1), & ! intent(in): [i4b] number of snow layers
+ nSoil => indx_data%var(iLookINDEX%nSoil)%dat(1), & ! intent(in): [i4b] number of soil layers
+ nLayers => indx_data%var(iLookINDEX%nLayers)%dat(1), & ! intent(in): [i4b] total number of layers
+
+ ! input: physical attributes
+ vegTypeIndex => type_data%var(iLookTYPE%vegTypeIndex), & ! intent(in): [i4b] vegetation type index
+ soilTypeIndex => type_data%var(iLookTYPE%soilTypeIndex), & ! intent(in): [i4b] soil type index
+
+ ! input: vegetation parameters
+ heightCanopyTop => mpar_data%var(iLookPARAM%heightCanopyTop)%dat(1), & ! intent(in): [dp] height at the top of the vegetation canopy (m)
+ heightCanopyBottom => mpar_data%var(iLookPARAM%heightCanopyBottom)%dat(1), & ! intent(in): [dp] height at the bottom of the vegetation canopy (m)
+ canopyWettingFactor => mpar_data%var(iLookPARAM%canopyWettingFactor)%dat(1), & ! intent(in): [dp] maximum wetted fraction of the canopy (-)
+ canopyWettingExp => mpar_data%var(iLookPARAM%canopyWettingExp)%dat(1), & ! intent(in): [dp] exponent in canopy wetting function (-)
+ scalarCanopyIceMax => diag_data%var(iLookDIAG%scalarCanopyIceMax)%dat(1), & ! intent(in): [dp] maximum interception storage capacity for ice (kg m-2)
+ scalarCanopyLiqMax => diag_data%var(iLookDIAG%scalarCanopyLiqMax)%dat(1), & ! intent(in): [dp] maximum interception storage capacity for liquid water (kg m-2)
+
+ ! input: vegetation phenology
+ scalarLAI => diag_data%var(iLookDIAG%scalarLAI)%dat(1), & ! intent(in): [dp] one-sided leaf area index (m2 m-2)
+ scalarSAI => diag_data%var(iLookDIAG%scalarSAI)%dat(1), & ! intent(in): [dp] one-sided stem area index (m2 m-2)
+ scalarExposedLAI => diag_data%var(iLookDIAG%scalarExposedLAI)%dat(1), & ! intent(in): [dp] exposed leaf area index after burial by snow (m2 m-2)
+ scalarExposedSAI => diag_data%var(iLookDIAG%scalarExposedSAI)%dat(1), & ! intent(in): [dp] exposed stem area index after burial by snow (m2 m-2)
+ scalarGrowingSeasonIndex => diag_data%var(iLookDIAG%scalarGrowingSeasonIndex)%dat(1), & ! intent(in): [dp] growing season index (0=off, 1=on)
+ scalarFoliageNitrogenFactor => diag_data%var(iLookDIAG%scalarFoliageNitrogenFactor)%dat(1), & ! intent(in): [dp] foliage nitrogen concentration (1.0 = saturated)
+
+ ! input: aerodynamic resistance parameters
+ z0Snow => mpar_data%var(iLookPARAM%z0Snow)%dat(1), & ! intent(in): [dp] roughness length of snow (m)
+ z0Soil => mpar_data%var(iLookPARAM%z0Soil)%dat(1), & ! intent(in): [dp] roughness length of soil (m)
+ z0CanopyParam => mpar_data%var(iLookPARAM%z0Canopy)%dat(1), & ! intent(in): [dp] roughness length of the canopy (m)
+ zpdFraction => mpar_data%var(iLookPARAM%zpdFraction)%dat(1), & ! intent(in): [dp] zero plane displacement / canopy height (-)
+ critRichNumber => mpar_data%var(iLookPARAM%critRichNumber)%dat(1), & ! intent(in): [dp] critical value for the bulk Richardson number where turbulence ceases (-)
+ Louis79_bparam => mpar_data%var(iLookPARAM%Louis79_bparam)%dat(1), & ! intent(in): [dp] parameter in Louis (1979) stability function
+ Louis79_cStar => mpar_data%var(iLookPARAM%Louis79_cStar)%dat(1), & ! intent(in): [dp] parameter in Louis (1979) stability function
+ Mahrt87_eScale => mpar_data%var(iLookPARAM%Mahrt87_eScale)%dat(1), & ! intent(in): [dp] exponential scaling factor in the Mahrt (1987) stability function
+ windReductionParam => mpar_data%var(iLookPARAM%windReductionParam)%dat(1), & ! intent(in): [dp] canopy wind reduction parameter (-)
+ leafExchangeCoeff => mpar_data%var(iLookPARAM%leafExchangeCoeff)%dat(1), & ! intent(in): [dp] turbulent exchange coeff between canopy surface and canopy air ( m s-(1/2) )
+ leafDimension => mpar_data%var(iLookPARAM%leafDimension)%dat(1), & ! intent(in): [dp] characteristic leaf dimension (m)
+
+ ! input: soil stress parameters
+ theta_sat => mpar_data%var(iLookPARAM%theta_sat)%dat(1), & ! intent(in): [dp] soil porosity (-)
+ theta_res => mpar_data%var(iLookPARAM%theta_res)%dat(1), & ! intent(in): [dp] residual volumetric liquid water content (-)
+ plantWiltPsi => mpar_data%var(iLookPARAM%plantWiltPsi)%dat(1), & ! intent(in): [dp] matric head at wilting point (m)
+ soilStressParam => mpar_data%var(iLookPARAM%soilStressParam)%dat(1), & ! intent(in): [dp] parameter in the exponential soil stress function (-)
+ critSoilWilting => mpar_data%var(iLookPARAM%critSoilWilting)%dat(1), & ! intent(in): [dp] critical vol. liq. water content when plants are wilting (-)
+ critSoilTranspire => mpar_data%var(iLookPARAM%critSoilTranspire)%dat(1), & ! intent(in): [dp] critical vol. liq. water content when transpiration is limited (-)
+ critAquiferTranspire => mpar_data%var(iLookPARAM%critAquiferTranspire)%dat(1), & ! intent(in): [dp] critical aquifer storage value when transpiration is limited (m)
+ minStomatalResistance => mpar_data%var(iLookPARAM%minStomatalResistance)%dat(1), & ! intent(in): [dp] mimimum stomatal resistance (s m-1)
+
+ ! snow parameters
+ snowfrz_scale => mpar_data%var(iLookPARAM%snowfrz_scale)%dat(1), & ! intent(in): [dp] scaling parameter for the snow freezing curve (K-1)
+
+ ! input: forcing at the upper boundary
+ mHeight => diag_data%var(iLookDIAG%scalarAdjMeasHeight)%dat(1), & ! intent(in): [dp] measurement height (m)
+ airtemp => forc_data%var(iLookFORCE%airtemp), & ! intent(in): [dp] air temperature at some height above the surface (K)
+ windspd => forc_data%var(iLookFORCE%windspd), & ! intent(in): [dp] wind speed at some height above the surface (m s-1)
+ airpres => forc_data%var(iLookFORCE%airpres), & ! intent(in): [dp] air pressure at some height above the surface (Pa)
+ LWRadAtm => forc_data%var(iLookFORCE%LWRadAtm), & ! intent(in): [dp] downwelling longwave radiation at the upper boundary (W m-2)
+ scalarVPair => diag_data%var(iLookDIAG%scalarVPair)%dat(1), & ! intent(in): [dp] vapor pressure at some height above the surface (Pa)
+ scalarO2air => diag_data%var(iLookDIAG%scalarO2air)%dat(1), & ! intent(in): [dp] atmospheric o2 concentration (Pa)
+ scalarCO2air => diag_data%var(iLookDIAG%scalarCO2air)%dat(1), & ! intent(in): [dp] atmospheric co2 concentration (Pa)
+ scalarTwetbulb => diag_data%var(iLookDIAG%scalarTwetbulb)%dat(1), & ! intent(in): [dp] wetbulb temperature (K)
+ scalarRainfall => flux_data%var(iLookFLUX%scalarRainfall)%dat(1), & ! intent(in): [dp] computed rainfall rate (kg m-2 s-1)
+ scalarSnowfall => flux_data%var(iLookFLUX%scalarSnowfall)%dat(1), & ! intent(in): [dp] computed snowfall rate (kg m-2 s-1)
+ scalarThroughfallRain => flux_data%var(iLookFLUX%scalarThroughfallRain)%dat(1), & ! intent(in): [dp] rainfall through the vegetation canopy (kg m-2 s-1)
+ scalarThroughfallSnow => flux_data%var(iLookFLUX%scalarThroughfallSnow)%dat(1), & ! intent(in): [dp] snowfall through the vegetation canopy (kg m-2 s-1)
+
+ ! input: water storage
+ ! NOTE: soil stress only computed at the start of the substep (firstFluxCall=.true.)
+ scalarSWE => prog_data%var(iLookPROG%scalarSWE)%dat(1), & ! intent(in): [dp] snow water equivalent on the ground (kg m-2)
+ scalarSnowDepth => prog_data%var(iLookPROG%scalarSnowDepth)%dat(1), & ! intent(in): [dp] snow depth on the ground surface (m)
+ mLayerVolFracLiq => prog_data%var(iLookPROG%mLayerVolFracLiq)%dat, & ! intent(in): [dp(:)] volumetric fraction of liquid water in each layer (-)
+ mLayerMatricHead => prog_data%var(iLookPROG%mLayerMatricHead)%dat, & ! intent(in): [dp(:)] matric head in each soil layer (m)
+ localAquiferStorage => prog_data%var(iLookPROG%scalarAquiferStorage)%dat(1), & ! intent(in): [dp] aquifer storage for the local column (m)
+ basinAquiferStorage => bvar_data%var(iLookBVAR%basin__AquiferStorage)%dat(1), & ! intent(in): [dp] aquifer storage for the single basin (m)
+
+ ! input: shortwave radiation fluxes
+ scalarCanopySunlitLAI => diag_data%var(iLookDIAG%scalarCanopySunlitLAI)%dat(1), & ! intent(in): [dp] sunlit leaf area (-)
+ scalarCanopyShadedLAI => diag_data%var(iLookDIAG%scalarCanopyShadedLAI)%dat(1), & ! intent(in): [dp] shaded leaf area (-)
+ scalarCanopySunlitPAR => flux_data%var(iLookFLUX%scalarCanopySunlitPAR)%dat(1), & ! intent(in): [dp] average absorbed par for sunlit leaves (w m-2)
+ scalarCanopyShadedPAR => flux_data%var(iLookFLUX%scalarCanopyShadedPAR)%dat(1), & ! intent(in): [dp] average absorbed par for shaded leaves (w m-2)
+ scalarCanopyAbsorbedSolar => flux_data%var(iLookFLUX%scalarCanopyAbsorbedSolar)%dat(1), & ! intent(in): [dp] solar radiation absorbed by canopy (W m-2)
+ scalarGroundAbsorbedSolar => flux_data%var(iLookFLUX%scalarGroundAbsorbedSolar)%dat(1), & ! intent(in): [dp] solar radiation absorbed by ground (W m-2)
+
+ ! output: fraction of wetted canopy area and fraction of snow on the ground
+ scalarCanopyWetFraction => diag_data%var(iLookDIAG%scalarCanopyWetFraction)%dat(1), & ! intent(out): [dp] fraction of canopy that is wet
+ scalarGroundSnowFraction => diag_data%var(iLookDIAG%scalarGroundSnowFraction)%dat(1), & ! intent(out): [dp] fraction of ground covered with snow (-)
+
+ ! output: longwave radiation fluxes
+ scalarCanopyEmissivity => diag_data%var(iLookDIAG%scalarCanopyEmissivity)%dat(1), & ! intent(out): [dp] effective emissivity of the canopy (-)
+ scalarLWRadCanopy => flux_data%var(iLookFLUX%scalarLWRadCanopy)%dat(1), & ! intent(out): [dp] longwave radiation emitted from the canopy (W m-2)
+ scalarLWRadGround => flux_data%var(iLookFLUX%scalarLWRadGround)%dat(1), & ! intent(out): [dp] longwave radiation emitted at the ground surface (W m-2)
+ scalarLWRadUbound2Canopy => flux_data%var(iLookFLUX%scalarLWRadUbound2Canopy)%dat(1), & ! intent(out): [dp] downward atmospheric longwave radiation absorbed by the canopy (W m-2)
+ scalarLWRadUbound2Ground => flux_data%var(iLookFLUX%scalarLWRadUbound2Ground)%dat(1), & ! intent(out): [dp] downward atmospheric longwave radiation absorbed by the ground (W m-2)
+ scalarLWRadUbound2Ubound => flux_data%var(iLookFLUX%scalarLWRadUbound2Ubound)%dat(1), & ! intent(out): [dp] atmospheric radiation reflected by the ground and lost thru upper boundary (W m-2)
+ scalarLWRadCanopy2Ubound => flux_data%var(iLookFLUX%scalarLWRadCanopy2Ubound)%dat(1), & ! intent(out): [dp] longwave radiation emitted from canopy lost thru upper boundary (W m-2)
+ scalarLWRadCanopy2Ground => flux_data%var(iLookFLUX%scalarLWRadCanopy2Ground)%dat(1), & ! intent(out): [dp] longwave radiation emitted from canopy absorbed by the ground (W m-2)
+ scalarLWRadCanopy2Canopy => flux_data%var(iLookFLUX%scalarLWRadCanopy2Canopy)%dat(1), & ! intent(out): [dp] canopy longwave reflected from ground and absorbed by the canopy (W m-2)
+ scalarLWRadGround2Ubound => flux_data%var(iLookFLUX%scalarLWRadGround2Ubound)%dat(1), & ! intent(out): [dp] longwave radiation emitted from ground lost thru upper boundary (W m-2)
+ scalarLWRadGround2Canopy => flux_data%var(iLookFLUX%scalarLWRadGround2Canopy)%dat(1), & ! intent(out): [dp] longwave radiation emitted from ground and absorbed by the canopy (W m-2)
+ scalarLWNetCanopy => flux_data%var(iLookFLUX%scalarLWNetCanopy)%dat(1), & ! intent(out): [dp] net longwave radiation at the canopy (W m-2)
+ scalarLWNetGround => flux_data%var(iLookFLUX%scalarLWNetGround)%dat(1), & ! intent(out): [dp] net longwave radiation at the ground surface (W m-2)
+ scalarLWNetUbound => flux_data%var(iLookFLUX%scalarLWNetUbound)%dat(1), & ! intent(out): [dp] net longwave radiation at the upper boundary (W m-2)
+
+ ! output: aerodynamic resistance
+ scalarZ0Canopy => diag_data%var(iLookDIAG%scalarZ0Canopy)%dat(1), & ! intent(out): [dp] roughness length of the canopy (m)
+ scalarWindReductionFactor => diag_data%var(iLookDIAG%scalarWindReductionFactor)%dat(1), & ! intent(out): [dp] canopy wind reduction factor (-)
+ scalarZeroPlaneDisplacement => diag_data%var(iLookDIAG%scalarZeroPlaneDisplacement)%dat(1), & ! intent(out): [dp] zero plane displacement (m)
+ scalarRiBulkCanopy => diag_data%var(iLookDIAG%scalarRiBulkCanopy)%dat(1), & ! intent(out): [dp] bulk Richardson number for the canopy (-)
+ scalarRiBulkGround => diag_data%var(iLookDIAG%scalarRiBulkGround)%dat(1), & ! intent(out): [dp] bulk Richardson number for the ground surface (-)
+ scalarEddyDiffusCanopyTop => flux_data%var(iLookFLUX%scalarEddyDiffusCanopyTop)%dat(1), & ! intent(out): [dp] eddy diffusivity for heat at the top of the canopy (m2 s-1)
+ scalarFrictionVelocity => flux_data%var(iLookFLUX%scalarFrictionVelocity)%dat(1), & ! intent(out): [dp] friction velocity (m s-1)
+ scalarWindspdCanopyTop => flux_data%var(iLookFLUX%scalarWindspdCanopyTop)%dat(1), & ! intent(out): [dp] windspeed at the top of the canopy (m s-1)
+ scalarWindspdCanopyBottom => flux_data%var(iLookFLUX%scalarWindspdCanopyBottom)%dat(1), & ! intent(out): [dp] windspeed at the height of the bottom of the canopy (m s-1)
+ scalarLeafResistance => flux_data%var(iLookFLUX%scalarLeafResistance)%dat(1), & ! intent(out): [dp] mean leaf boundary layer resistance per unit leaf area (s m-1)
+ scalarGroundResistance => flux_data%var(iLookFLUX%scalarGroundResistance)%dat(1), & ! intent(out): [dp] below canopy aerodynamic resistance (s m-1)
+ scalarCanopyResistance => flux_data%var(iLookFLUX%scalarCanopyResistance)%dat(1), & ! intent(out): [dp] above canopy aerodynamic resistance (s m-1)
+
+ ! input/output: soil resistance -- intent(in) and intent(inout) because only called at the first flux call
+ mLayerRootDensity => diag_data%var(iLookDIAG%mLayerRootDensity)%dat, & ! intent(in): [dp] root density in each layer (-)
+ scalarAquiferRootFrac => diag_data%var(iLookDIAG%scalarAquiferRootFrac)%dat(1), & ! intent(in): [dp] fraction of roots below the lowest soil layer (-)
+ scalarTranspireLim => diag_data%var(iLookDIAG%scalarTranspireLim)%dat(1), & ! intent(inout): [dp] weighted average of the transpiration limiting factor (-)
+ mLayerTranspireLim => diag_data%var(iLookDIAG%mLayerTranspireLim)%dat, & ! intent(inout): [dp] transpiration limiting factor in each layer (-)
+ scalarTranspireLimAqfr => diag_data%var(iLookDIAG%scalarTranspireLimAqfr)%dat(1), & ! intent(inout): [dp] transpiration limiting factor for the aquifer (-)
+ scalarSoilRelHumidity => diag_data%var(iLookDIAG%scalarSoilRelHumidity)%dat(1), & ! intent(inout): [dp] relative humidity in the soil pores [0-1]
+ scalarSoilResistance => flux_data%var(iLookFLUX%scalarSoilResistance)%dat(1), & ! intent(inout): [dp] resistance from the soil (s m-1)
+
+ ! input/output: stomatal resistance -- intent(inout) because only called at the first flux call
+ scalarStomResistSunlit => flux_data%var(iLookFLUX%scalarStomResistSunlit)%dat(1), & ! intent(inout): [dp] stomatal resistance for sunlit leaves (s m-1)
+ scalarStomResistShaded => flux_data%var(iLookFLUX%scalarStomResistShaded)%dat(1), & ! intent(inout): [dp] stomatal resistance for shaded leaves (s m-1)
+ scalarPhotosynthesisSunlit => flux_data%var(iLookFLUX%scalarPhotosynthesisSunlit)%dat(1), & ! intent(inout): [dp] sunlit photosynthesis (umolco2 m-2 s-1)
+ scalarPhotosynthesisShaded => flux_data%var(iLookFLUX%scalarPhotosynthesisShaded)%dat(1), & ! intent(inout): [dp] shaded photosynthesis (umolco2 m-2 s-1)
+
+ ! output: turbulent heat fluxes
+ scalarLatHeatSubVapCanopy => diag_data%var(iLookDIAG%scalarLatHeatSubVapCanopy)%dat(1), & ! intent(inout): [dp] latent heat of sublimation/vaporization for the vegetation canopy (J kg-1)
+ scalarLatHeatSubVapGround => diag_data%var(iLookDIAG%scalarLatHeatSubVapGround)%dat(1), & ! intent(inout): [dp] latent heat of sublimation/vaporization for the ground surface (J kg-1)
+ scalarSatVP_canopyTemp => diag_data%var(iLookDIAG%scalarSatVP_CanopyTemp)%dat(1), & ! intent(out): [dp] saturation vapor pressure at the temperature of the vegetation canopy (Pa)
+ scalarSatVP_groundTemp => diag_data%var(iLookDIAG%scalarSatVP_GroundTemp)%dat(1), & ! intent(out): [dp] saturation vapor pressure at the temperature of the ground surface (Pa)
+ scalarSenHeatTotal => flux_data%var(iLookFLUX%scalarSenHeatTotal)%dat(1), & ! intent(out): [dp] sensible heat from the canopy air space to the atmosphere (W m-2)
+ scalarSenHeatCanopy => flux_data%var(iLookFLUX%scalarSenHeatCanopy)%dat(1), & ! intent(out): [dp] sensible heat flux from the canopy to the canopy air space (W m-2)
+ scalarSenHeatGround => flux_data%var(iLookFLUX%scalarSenHeatGround)%dat(1), & ! intent(out): [dp] sensible heat flux from ground surface below vegetation (W m-2)
+ scalarLatHeatTotal => flux_data%var(iLookFLUX%scalarLatHeatTotal)%dat(1), & ! intent(out): [dp] latent heat from the canopy air space to the atmosphere (W m-2)
+ scalarLatHeatCanopyEvap => flux_data%var(iLookFLUX%scalarLatHeatCanopyEvap)%dat(1), & ! intent(out): [dp] latent heat flux for evaporation from the canopy to the canopy air space (W m-2)
+ scalarLatHeatCanopyTrans => flux_data%var(iLookFLUX%scalarLatHeatCanopyTrans)%dat(1), & ! intent(out): [dp] latent heat flux for transpiration from the canopy to the canopy air space (W m-2)
+ scalarLatHeatGround => flux_data%var(iLookFLUX%scalarLatHeatGround)%dat(1), & ! intent(out): [dp] latent heat flux from ground surface below vegetation (W m-2)
+
+ ! output: advective heat fluxes
+ scalarCanopyAdvectiveHeatFlux => flux_data%var(iLookFLUX%scalarCanopyAdvectiveHeatFlux)%dat(1), & ! intent(out): [dp] heat advected to the canopy surface with rain + snow (W m-2)
+ scalarGroundAdvectiveHeatFlux => flux_data%var(iLookFLUX%scalarGroundAdvectiveHeatFlux)%dat(1), & ! intent(out): [dp] heat advected to the ground surface with throughfall (W m-2)
+
+ ! output: mass fluxes
+ scalarCanopySublimation => flux_data%var(iLookFLUX%scalarCanopySublimation)%dat(1), & ! intent(out): [dp] canopy sublimation/frost (kg m-2 s-1)
+ scalarSnowSublimation => flux_data%var(iLookFLUX%scalarSnowSublimation)%dat(1), & ! intent(out): [dp] snow sublimation/frost -- below canopy or non-vegetated (kg m-2 s-1)
+
+ ! input/output: canopy air space variables
+ scalarVP_CanopyAir => diag_data%var(iLookDIAG%scalarVP_CanopyAir)%dat(1), & ! intent(inout): [dp] vapor pressure of the canopy air space (Pa)
+ scalarCanopyStabilityCorrection => diag_data%var(iLookDIAG%scalarCanopyStabilityCorrection)%dat(1),& ! intent(inout): [dp] stability correction for the canopy (-)
+ scalarGroundStabilityCorrection => diag_data%var(iLookDIAG%scalarGroundStabilityCorrection)%dat(1),& ! intent(inout): [dp] stability correction for the ground surface (-)
+
+ ! output: liquid water fluxes
+ scalarCanopyTranspiration => flux_data%var(iLookFLUX%scalarCanopyTranspiration)%dat(1), & ! intent(out): [dp] canopy transpiration (kg m-2 s-1)
+ scalarCanopyEvaporation => flux_data%var(iLookFLUX%scalarCanopyEvaporation)%dat(1), & ! intent(out): [dp] canopy evaporation/condensation (kg m-2 s-1)
+ scalarGroundEvaporation => flux_data%var(iLookFLUX%scalarGroundEvaporation)%dat(1), & ! intent(out): [dp] ground evaporation/condensation -- below canopy or non-vegetated (kg m-2 s-1)
+
+ ! output: derived fluxes
+ scalarTotalET => flux_data%var(iLookFLUX%scalarTotalET)%dat(1), & ! intent(out): [dp] total ET (kg m-2 s-1)
+ scalarNetRadiation => flux_data%var(iLookFLUX%scalarNetRadiation)%dat(1) & ! intent(out): [dp] net radiation (W m-2)
+ )
+ ! ---------------------------------------------------------------------------------------
+ ! initialize error control
+ err=0; message="vegNrgFlux/"
+
+ ! initialize printflag
+ printflag = .false.
+
+ ! identify the type of boundary condition for thermodynamics
+ select case(ix_bcUpprTdyn)
+
! *****
! (1) DIRICHLET OR ZERO FLUX BOUNDARY CONDITION...
! ************************************************
-
+
! NOTE: Vegetation fluxes are not computed in this case
-
+
! ** prescribed temperature or zero flux at the upper boundary of the snow-soil system
case(prescribedTemp,zeroFlux)
-
- ! derived fluxes
- scalarTotalET = 0._rkind ! total ET (kg m-2 s-1)
- scalarNetRadiation = 0._rkind ! net radiation (W m-2)
- ! liquid water fluxes associated with evaporation/transpiration
- scalarCanopyTranspiration = 0._rkind ! canopy transpiration (kg m-2 s-1)
- scalarCanopyEvaporation = 0._rkind ! canopy evaporation/condensation (kg m-2 s-1)
- scalarGroundEvaporation = 0._rkind ! ground evaporation/condensation -- below canopy or non-vegetated (kg m-2 s-1)
- ! solid water fluxes associated with sublimation/frost
- scalarCanopySublimation = 0._rkind ! sublimation from the vegetation canopy ((kg m-2 s-1)
- scalarSnowSublimation = 0._rkind ! sublimation from the snow surface ((kg m-2 s-1)
- ! set canopy fluxes to zero (no canopy)
- canairNetFlux = 0._rkind ! net energy flux for the canopy air space (W m-2)
- canopyNetFlux = 0._rkind ! net energy flux for the vegetation canopy (W m-2)
- ! set canopy derivatives to zero
- dCanairNetFlux_dCanairTemp = 0._rkind ! derivative in net canopy air space flux w.r.t. canopy air temperature (W m-2 K-1)
- dCanairNetFlux_dCanopyTemp = 0._rkind ! derivative in net canopy air space flux w.r.t. canopy temperature (W m-2 K-1)
- dCanairNetFlux_dGroundTemp = 0._rkind ! derivative in net canopy air space flux w.r.t. ground temperature (W m-2 K-1)
- dCanopyNetFlux_dCanairTemp = 0._rkind ! derivative in net canopy flux w.r.t. canopy air temperature (W m-2 K-1)
- dCanopyNetFlux_dCanopyTemp = 0._rkind ! derivative in net canopy flux w.r.t. canopy temperature (W m-2 K-1)
- dCanopyNetFlux_dGroundTemp = 0._rkind ! derivative in net canopy flux w.r.t. ground temperature (W m-2 K-1)
- dGroundNetFlux_dCanairTemp = 0._rkind ! derivative in net ground flux w.r.t. canopy air temperature (W m-2 K-1)
- dGroundNetFlux_dCanopyTemp = 0._rkind ! derivative in net ground flux w.r.t. canopy temperature (W m-2 K-1)
- ! set liquid flux derivatives to zero (canopy evap)
- dCanopyEvaporation_dCanWat = 0._rkind ! derivative in canopy evaporation w.r.t. canopy total water content (s-1)
- dCanopyEvaporation_dTCanair= 0._rkind ! derivative in canopy evaporation w.r.t. canopy air temperature (kg m-2 s-1 K-1)
- dCanopyEvaporation_dTCanopy= 0._rkind ! derivative in canopy evaporation w.r.t. canopy temperature (kg m-2 s-1 K-1)
- dCanopyEvaporation_dTGround= 0._rkind ! derivative in canopy evaporation w.r.t. ground temperature (kg m-2 s-1 K-1)
- ! set liquid flux derivatives to zero (ground evap)
- dGroundEvaporation_dCanWat = 0._rkind ! derivative in ground evaporation w.r.t. canopy total water content (s-1)
- dGroundEvaporation_dTCanair= 0._rkind ! derivative in ground evaporation w.r.t. canopy air temperature (kg m-2 s-1 K-1)
- dGroundEvaporation_dTCanopy= 0._rkind ! derivative in ground evaporation w.r.t. canopy temperature (kg m-2 s-1 K-1)
- dGroundEvaporation_dTGround= 0._rkind ! derivative in ground evaporation w.r.t. ground temperature (kg m-2 s-1 K-1)
- ! set transpiration derivatives to zero
- dCanopyTrans_dCanWat = 0._rkind ! derivative in canopy transpiration w.r.t. canopy total water content (s-1)
- dCanopyTrans_dTCanair= 0._rkind ! derivative in canopy transpiration w.r.t. canopy air temperature (kg m-2 s-1 K-1)
- dCanopyTrans_dTCanopy= 0._rkind ! derivative in canopy transpiration w.r.t. canopy temperature (kg m-2 s-1 K-1)
- dCanopyTrans_dTGround= 0._rkind ! derivative in canopy transpiration w.r.t. ground temperature (kg m-2 s-1 K-1)
-
- ! compute fluxes and derivatives -- separate approach for prescribed temperature and zero flux,
- if(ix_bcUpprTdyn == prescribedTemp)then
- ! compute ground net flux (W m-2)
- groundNetFlux = -diag_data%var(iLookDIAG%iLayerThermalC)%dat(0)*(groundTempTrial - upperBoundTemp)/(prog_data%var(iLookPROG%mLayerDepth)%dat(1)*0.5_rkind)
- ! compute derivative in net ground flux w.r.t. ground temperature (W m-2 K-1) inside soil and snow (ssd) energy flux routine
- ! dGroundNetFlux_dGroundTemp = missingValue
- elseif(ix_bcUpprTdyn == zeroFlux)then
- groundNetFlux = 0._rkind
- ! dGroundNetFlux_dGroundTemp = missingValue
- else
- err=20; message=trim(message)//'unable to identify upper boundary condition for thermodynamics: expect the case to be prescribedTemp or zeroFlux'; return
- end if
-
- ! *****
- ! (2) NEUMANN BOUNDARY CONDITION...
- ! *********************************
-
- ! NOTE 1: This is the main routine for calculating vegetation fluxes
- ! NOTE 2: This routine also calculates surface fluxes for the case where vegetation is buried with snow (or bare soil)
-
- ! *******************************************************************************************************************************************************************
- ! *******************************************************************************************************************************************************************
- ! ***** PRELIMINARIES **********************************************************************************************************************************************
- ! *******************************************************************************************************************************************************************
- ! *******************************************************************************************************************************************************************
-
+
+ ! derived fluxes
+ scalarTotalET = 0._rkind ! total ET (kg m-2 s-1)
+ scalarNetRadiation = 0._rkind ! net radiation (W m-2)
+ ! liquid water fluxes associated with evaporation/transpiration
+ scalarCanopyTranspiration = 0._rkind ! canopy transpiration (kg m-2 s-1)
+ scalarCanopyEvaporation = 0._rkind ! canopy evaporation/condensation (kg m-2 s-1)
+ scalarGroundEvaporation = 0._rkind ! ground evaporation/condensation -- below canopy or non-vegetated (kg m-2 s-1)
+ ! solid water fluxes associated with sublimation/frost
+ scalarCanopySublimation = 0._rkind ! sublimation from the vegetation canopy ((kg m-2 s-1)
+ scalarSnowSublimation = 0._rkind ! sublimation from the snow surface ((kg m-2 s-1)
+ ! set canopy fluxes to zero (no canopy)
+ canairNetFlux = 0._rkind ! net energy flux for the canopy air space (W m-2)
+ canopyNetFlux = 0._rkind ! net energy flux for the vegetation canopy (W m-2)
+ ! set canopy derivatives to zero
+ dCanairNetFlux_dCanairTemp = 0._rkind ! derivative in net canopy air space flux w.r.t. canopy air temperature (W m-2 K-1)
+ dCanairNetFlux_dCanopyTemp = 0._rkind ! derivative in net canopy air space flux w.r.t. canopy temperature (W m-2 K-1)
+ dCanairNetFlux_dGroundTemp = 0._rkind ! derivative in net canopy air space flux w.r.t. ground temperature (W m-2 K-1)
+ dCanopyNetFlux_dCanairTemp = 0._rkind ! derivative in net canopy flux w.r.t. canopy air temperature (W m-2 K-1)
+ dCanopyNetFlux_dCanopyTemp = 0._rkind ! derivative in net canopy flux w.r.t. canopy temperature (W m-2 K-1)
+ dCanopyNetFlux_dGroundTemp = 0._rkind ! derivative in net canopy flux w.r.t. ground temperature (W m-2 K-1)
+ dGroundNetFlux_dCanairTemp = 0._rkind ! derivative in net ground flux w.r.t. canopy air temperature (W m-2 K-1)
+ dGroundNetFlux_dCanopyTemp = 0._rkind ! derivative in net ground flux w.r.t. canopy temperature (W m-2 K-1)
+ ! set liquid flux derivatives to zero (canopy evap)
+ dCanopyEvaporation_dCanWat = 0._rkind ! derivative in canopy evaporation w.r.t. canopy total water content (s-1)
+ dCanopyEvaporation_dTCanair= 0._rkind ! derivative in canopy evaporation w.r.t. canopy air temperature (kg m-2 s-1 K-1)
+ dCanopyEvaporation_dTCanopy= 0._rkind ! derivative in canopy evaporation w.r.t. canopy temperature (kg m-2 s-1 K-1)
+ dCanopyEvaporation_dTGround= 0._rkind ! derivative in canopy evaporation w.r.t. ground temperature (kg m-2 s-1 K-1)
+ ! set liquid flux derivatives to zero (ground evap)
+ dGroundEvaporation_dCanWat = 0._rkind ! derivative in ground evaporation w.r.t. canopy total water content (s-1)
+ dGroundEvaporation_dTCanair= 0._rkind ! derivative in ground evaporation w.r.t. canopy air temperature (kg m-2 s-1 K-1)
+ dGroundEvaporation_dTCanopy= 0._rkind ! derivative in ground evaporation w.r.t. canopy temperature (kg m-2 s-1 K-1)
+ dGroundEvaporation_dTGround= 0._rkind ! derivative in ground evaporation w.r.t. ground temperature (kg m-2 s-1 K-1)
+ ! set transpiration derivatives to zero
+ dCanopyTrans_dCanWat = 0._rkind ! derivative in canopy transpiration w.r.t. canopy total water content (s-1)
+ dCanopyTrans_dTCanair= 0._rkind ! derivative in canopy transpiration w.r.t. canopy air temperature (kg m-2 s-1 K-1)
+ dCanopyTrans_dTCanopy= 0._rkind ! derivative in canopy transpiration w.r.t. canopy temperature (kg m-2 s-1 K-1)
+ dCanopyTrans_dTGround= 0._rkind ! derivative in canopy transpiration w.r.t. ground temperature (kg m-2 s-1 K-1)
+
+ ! compute fluxes and derivatives -- separate approach for prescribed temperature and zero flux,
+ if(ix_bcUpprTdyn == prescribedTemp)then
+ ! compute ground net flux (W m-2)
+ groundNetFlux = -diag_data%var(iLookDIAG%iLayerThermalC)%dat(0)*(groundTempTrial - upperBoundTemp)/(prog_data%var(iLookPROG%mLayerDepth)%dat(1)*0.5_rkind)
+ ! compute derivative in net ground flux w.r.t. ground temperature (W m-2 K-1) inside soil and snow (ssd) energy flux routine
+ ! dGroundNetFlux_dGroundTemp = missingValue
+ elseif(ix_bcUpprTdyn == zeroFlux)then
+ groundNetFlux = 0._rkind
+ ! dGroundNetFlux_dGroundTemp = missingValue
+ else
+ err=20; message=trim(message)//'unable to identify upper boundary condition for thermodynamics: expect the case to be prescribedTemp or zeroFlux'; return
+ end if
+
+ ! *****
+ ! (2) NEUMANN BOUNDARY CONDITION...
+ ! *********************************
+
+ ! NOTE 1: This is the main routine for calculating vegetation fluxes
+ ! NOTE 2: This routine also calculates surface fluxes for the case where vegetation is buried with snow (or bare soil)
+
+ ! *******************************************************************************************************************************************************************
+ ! *******************************************************************************************************************************************************************
+ ! ***** PRELIMINARIES **********************************************************************************************************************************************
+ ! *******************************************************************************************************************************************************************
+ ! *******************************************************************************************************************************************************************
+
! * flux boundary condition
case(energyFlux)
-
- ! identify the appropriate groundwater variable
- select case(ix_spatial_gw)
- case(singleBasin); scalarAquiferStorage = basinAquiferStorage
- case(localColumn); scalarAquiferStorage = localAquiferStorage
- case default; err=20; message=trim(message)//'unable to identify spatial representation of groundwater'; return
- end select ! (modify the groundwater representation for this single-column implementation)
-
- ! set canopy stability corrections to the previous values
- scalarCanopyStabilityCorrection_old = scalarCanopyStabilityCorrection ! stability correction for the canopy (-)
- scalarGroundStabilityCorrection_old = scalarGroundStabilityCorrection ! stability correction for the ground surface (-)
-
- ! initialize variables to compute stomatal resistance
- if(firstFluxCall .and. firstSubStep)then
- ! vapor pressure in the canopy air space initialized as vapor pressure of air above the vegetation canopy
- ! NOTE: this is needed for the stomatal resistance calculations
- if(scalarVP_CanopyAir < 0._rkind)then
- scalarVP_CanopyAir = scalarVPair - 1._rkind ! "small" offset used to assist in checking initial derivative calculations
+
+ ! identify the appropriate groundwater variable
+ select case(ix_spatial_gw)
+ case(singleBasin); scalarAquiferStorage = basinAquiferStorage
+ case(localColumn); scalarAquiferStorage = localAquiferStorage
+ case default; err=20; message=trim(message)//'unable to identify spatial representation of groundwater'; return
+ end select ! (modify the groundwater representation for this single-column implementation)
+
+ ! set canopy stability corrections to the previous values
+ scalarCanopyStabilityCorrection_old = scalarCanopyStabilityCorrection ! stability correction for the canopy (-)
+ scalarGroundStabilityCorrection_old = scalarGroundStabilityCorrection ! stability correction for the ground surface (-)
+
+ ! initialize variables to compute stomatal resistance
+ if(firstFluxCall .and. firstSubStep)then
+ ! vapor pressure in the canopy air space initialized as vapor pressure of air above the vegetation canopy
+ ! NOTE: this is needed for the stomatal resistance calculations
+ if(scalarVP_CanopyAir < 0._rkind)then
+ scalarVP_CanopyAir = scalarVPair - 1._rkind ! "small" offset used to assist in checking initial derivative calculations
+ end if
end if
- end if
-
- ! set latent heat of sublimation/vaporization for canopy and ground surface (Pa/K)
- ! NOTE: variables are constant over the substep, to simplify relating energy and mass fluxes
- if(firstFluxCall)then
- scalarLatHeatSubVapCanopy = getLatentHeatValue(canopyTempTrial)
- ! case when there is snow on the ground (EXCLUDE "snow without a layer" -- in this case, evaporate from the soil)
- if(nSnow > 0)then
- if(groundTempTrial > Tfreeze)then; err=20; message=trim(message)//'do not expect ground temperature > 0 when snow is on the ground'; return; end if
- scalarLatHeatSubVapGround = LH_sub ! sublimation from snow
- scalarGroundSnowFraction = 1._rkind
- ! case when the ground is snow-free
- else
- scalarLatHeatSubVapGround = LH_vap ! evaporation of water in the soil pores: this occurs even if frozen because of super-cooled water
- scalarGroundSnowFraction = 0._rkind
- end if ! (if there is snow on the ground)
- end if ! (if the first flux call)
- !write(*,'(a,1x,10(f30.10,1x))') 'groundTempTrial, scalarLatHeatSubVapGround = ', groundTempTrial, scalarLatHeatSubVapGround
-
- ! compute the roughness length of the ground (ground below the canopy or non-vegetated surface)
- z0Ground = z0soil*(1._rkind - scalarGroundSnowFraction) + z0Snow*scalarGroundSnowFraction ! roughness length (m)
-
- ! compute the total vegetation area index (leaf plus stem)
- VAI = scalarLAI + scalarSAI ! vegetation area index
- exposedVAI = scalarExposedLAI + scalarExposedSAI ! exposed vegetation area index
-
- ! compute emissivity of the canopy (-)
- if(computeVegFlux)then
- select case(ix_canopyEmis)
- ! *** simple exponential function
- case(simplExp)
- scalarCanopyEmissivity = 1._rkind - exp(-exposedVAI) ! effective emissivity of the canopy (-)
- ! *** canopy emissivity parameterized as a function of diffuse transmissivity
- case(difTrans)
- ! compute the exponential integral
- scaleLAI = 0.5_rkind*exposedVAI
- expi = expInt(scaleLAI)
- ! compute diffuse transmissivity (-)
- diffuseTrans = (1._rkind - scaleLAI)*exp(-scaleLAI) + (scaleLAI**2._rkind)*expi
- ! compute the canopy emissivity
- scalarCanopyEmissivity = (1._rkind - diffuseTrans)*vegEmissivity
- ! *** check we found the correct option
- case default
- err=20; message=trim(message)//'unable to identify option for canopy emissivity'; return
- end select
- end if
-
- ! ensure canopy longwave fluxes are zero when not computing canopy fluxes
- if(.not.computeVegFlux) scalarCanopyEmissivity=0._rkind
-
- ! compute emissivity of the ground surface (-)
- groundEmissivity = scalarGroundSnowFraction*snowEmissivity + (1._rkind - scalarGroundSnowFraction)*soilEmissivity ! emissivity of the ground surface (-)
-
- ! compute the fraction of canopy that is wet
- ! NOTE: we either sublimate or evaporate over the entire substep
- if(computeVegFlux)then
-
- ! compute the fraction of liquid water in the canopy (-)
- totalCanopyWater = canopyLiqTrial + canopyIceTrial
- if(totalCanopyWater > tiny(1.0_rkind))then
- fracLiquidCanopy = canopyLiqTrial / (canopyLiqTrial + canopyIceTrial)
- else
- fracLiquidCanopy = 0._rkind
+
+ ! set latent heat of sublimation/vaporization for canopy and ground surface (Pa/K)
+ ! NOTE: variables are constant over the substep, to simplify relating energy and mass fluxes
+ if(firstFluxCall)then
+ scalarLatHeatSubVapCanopy = getLatentHeatValue(canopyTempTrial)
+ ! case when there is snow on the ground (EXCLUDE "snow without a layer" -- in this case, evaporate from the soil)
+ if(nSnow > 0)then
+ if(groundTempTrial > Tfreeze)then; err=20; message=trim(message)//'do not expect ground temperature > 0 when snow is on the ground'; return; end if
+ scalarLatHeatSubVapGround = LH_sub ! sublimation from snow
+ scalarGroundSnowFraction = 1._rkind
+ ! case when the ground is snow-free
+ else
+ scalarLatHeatSubVapGround = LH_vap ! evaporation of water in the soil pores: this occurs even if frozen because of super-cooled water
+ scalarGroundSnowFraction = 0._rkind
+ end if ! (if there is snow on the ground)
+ end if ! (if the first flux call)
+
+ ! compute the roughness length of the ground (ground below the canopy or non-vegetated surface)
+ z0Ground = z0soil*(1._rkind - scalarGroundSnowFraction) + z0Snow*scalarGroundSnowFraction ! roughness length (m)
+
+ ! compute the total vegetation area index (leaf plus stem)
+ VAI = scalarLAI + scalarSAI ! vegetation area index
+ exposedVAI = scalarExposedLAI + scalarExposedSAI ! exposed vegetation area index
+
+ ! compute emissivity of the canopy (-)
+ if(computeVegFlux)then
+ select case(ix_canopyEmis)
+ ! *** simple exponential function
+ case(simplExp)
+ scalarCanopyEmissivity = 1._rkind - exp(-exposedVAI) ! effective emissivity of the canopy (-)
+ ! *** canopy emissivity parameterized as a function of diffuse transmissivity
+ case(difTrans)
+ ! compute the exponential integral
+ scaleLAI = 0.5_rkind*exposedVAI
+ expi = expInt(scaleLAI)
+ ! compute diffuse transmissivity (-)
+ diffuseTrans = (1._rkind - scaleLAI)*exp(-scaleLAI) + (scaleLAI**2._rkind)*expi
+ ! compute the canopy emissivity
+ scalarCanopyEmissivity = (1._rkind - diffuseTrans)*vegEmissivity
+ ! *** check we found the correct option
+ case default
+ err=20; message=trim(message)//'unable to identify option for canopy emissivity'; return
+ end select
end if
-
- ! get wetted fraction and derivatives
- call wettedFrac(&
- ! input
- .true., & ! flag to denote if derivative is desired
- (ixDerivMethod == numerical), & ! flag to denote that numerical derivatives are required (otherwise, analytical derivatives are calculated)
- (scalarLatHeatSubVapCanopy > LH_vap+verySmall), & ! flag to denote if the canopy is frozen
- dCanLiq_dTcanopy, & ! derivative in canopy liquid w.r.t. canopy temperature (kg m-2 K-1)
- fracLiquidCanopy, & ! fraction of liquid water on the canopy (-)
- canopyLiqTrial, & ! canopy liquid water (kg m-2)
- canopyIceTrial, & ! canopy ice (kg m-2)
- scalarCanopyLiqMax, & ! maximum canopy liquid water (kg m-2)
- scalarCanopyIceMax, & ! maximum canopy ice content (kg m-2)
- canopyWettingFactor, & ! maximum wetted fraction of the canopy (-)
- canopyWettingExp, & ! exponent in canopy wetting function (-)
- ! output
- scalarCanopyWetFraction, & ! canopy wetted fraction (-)
- dCanopyWetFraction_dWat, & ! derivative in wetted fraction w.r.t. canopy total water (kg-1 m2)
- dCanopyWetFraction_dT, & ! derivative in wetted fraction w.r.t. canopy temperature (K-1)
- err,cmessage)
- if(err/=0)then; message=trim(message)//trim(cmessage); return; end if
-
- else
- scalarCanopyWetFraction = 0._rkind ! canopy wetted fraction (-)
- dCanopyWetFraction_dWat = 0._rkind ! derivative in wetted fraction w.r.t. canopy total water (kg-1 m2)
- dCanopyWetFraction_dT = 0._rkind ! derivative in wetted fraction w.r.t. canopy temperature (K-1)
- end if
- !write(*,'(a,1x,L1,1x,f25.15,1x))') 'computeVegFlux, scalarCanopyWetFraction = ', computeVegFlux, scalarCanopyWetFraction
- !print*, 'dCanopyWetFraction_dWat = ', dCanopyWetFraction_dWat
- !print*, 'dCanopyWetFraction_dT = ', dCanopyWetFraction_dT
- !print*, 'canopyLiqTrial = ', canopyLiqTrial
- !print*, 'canopyIceTrial = ', canopyIceTrial
- !print*, 'scalarCanopyLiqMax = ', scalarCanopyLiqMax
- !print*, 'scalarCanopyIceMax = ', scalarCanopyIceMax
-
- ! *******************************************************************************************************************************************************************
- ! *******************************************************************************************************************************************************************
- ! ***** AERODYNAMIC RESISTANCE *****************************************************************************************************************************************
- ! *******************************************************************************************************************************************************************
- ! *******************************************************************************************************************************************************************
-
- ! NOTE: compute for all iterations
-
- ! compute aerodynamic resistances
- ! Refs: Choudhury and Monteith (4-layer model for heat budget of homogenous surfaces; QJRMS, 1988)
- ! Niu and Yang (Canopy effects on snow processes; JGR, 2004)
- ! Mahat et al. (Below-canopy turbulence in a snowmelt model, WRR, 2012)
- call aeroResist(&
- ! input: model control
- computeVegFlux, & ! intent(in): logical flag to compute vegetation fluxes (.false. if veg buried by snow)
- (ixDerivMethod == analytical), & ! intent(in): logical flag if would like to compute analytical derivaties
- ix_veg_traits, & ! intent(in): choice of parameterization for vegetation roughness length and displacement height
- ix_windPrfile, & ! intent(in): choice of canopy wind profile
- ix_astability, & ! intent(in): choice of stability function
- ! input: above-canopy forcing data
- mHeight, & ! intent(in): measurement height (m)
- airtemp, & ! intent(in): air temperature at some height above the surface (K)
- windspd, & ! intent(in): wind speed at some height above the surface (m s-1)
- ! input: canopy and ground temperature
- canairTempTrial, & ! intent(in): temperature of the canopy air space (K)
- groundTempTrial, & ! intent(in): temperature of the ground surface (K)
- ! input: diagnostic variables
- exposedVAI, & ! intent(in): exposed vegetation area index -- leaf plus stem (m2 m-2)
- scalarSnowDepth, & ! intent(in): snow depth (m)
- ! input: parameters
- z0Ground, & ! intent(in): roughness length of the ground (below canopy or non-vegetated surface [snow]) (m)
- z0CanopyParam, & ! intent(in): roughness length of the canopy (m)
- zpdFraction, & ! intent(in): zero plane displacement / canopy height (-)
- critRichNumber, & ! intent(in): critical value for the bulk Richardson number where turbulence ceases (-)
- Louis79_bparam, & ! intent(in): parameter in Louis (1979) stability function
- Mahrt87_eScale, & ! intent(in): exponential scaling factor in the Mahrt (1987) stability function
- windReductionParam, & ! intent(in): canopy wind reduction parameter (-)
- leafExchangeCoeff, & ! intent(in): turbulent exchange coeff between canopy surface and canopy air ( m s-(1/2) )
- leafDimension, & ! intent(in): characteristic leaf dimension (m)
- heightCanopyTop, & ! intent(in): height at the top of the vegetation canopy (m)
- heightCanopyBottom, & ! intent(in): height at the bottom of the vegetation canopy (m)
- ! output: stability corrections
- scalarRiBulkCanopy, & ! intent(out): bulk Richardson number for the canopy (-)
- scalarRiBulkGround, & ! intent(out): bulk Richardson number for the ground surface (-)
- scalarCanopyStabilityCorrection, & ! intent(out): stability correction for the canopy (-)
- scalarGroundStabilityCorrection, & ! intent(out): stability correction for the ground surface (-)
- ! output: scalar resistances
- scalarZ0Canopy, & ! intent(out): roughness length of the canopy (m)
- scalarWindReductionFactor, & ! intent(out): canopy wind reduction factor (-)
- scalarZeroPlaneDisplacement, & ! intent(out): zero plane displacement (m)
- scalarEddyDiffusCanopyTop, & ! intent(out): eddy diffusivity for heat at the top of the canopy (m2 s-1)
- scalarFrictionVelocity, & ! intent(out): friction velocity (m s-1)
- scalarWindspdCanopyTop, & ! intent(out): windspeed at the top of the canopy (m s-1)
- scalarWindspdCanopyBottom, & ! intent(out): windspeed at the height of the bottom of the canopy (m s-1)
- scalarLeafResistance, & ! intent(out): mean leaf boundary layer resistance per unit leaf area (s m-1)
- scalarGroundResistance, & ! intent(out): below canopy aerodynamic resistance (s m-1)
- scalarCanopyResistance, & ! intent(out): above canopy aerodynamic resistance (s m-1)
- ! output: derivatives in scalar resistances
- dGroundResistance_dTGround, & ! intent(out): derivative in ground resistance w.r.t. ground temperature (s m-1 K-1)
- dGroundResistance_dTCanopy, & ! intent(out): derivative in ground resistance w.r.t. canopy temperature (s m-1 K-1)
- dGroundResistance_dTCanair, & ! intent(out): derivative in ground resistance w.r.t. canopy air temperature (s m-1 K-1)
- dCanopyResistance_dTCanopy, & ! intent(out): derivative in canopy resistance w.r.t. canopy temperature (s m-1 K-1)
- dCanopyResistance_dTCanair, & ! intent(out): derivative in canopy resistance w.r.t. canopy air temperature (s m-1 K-1)
- ! output: error control
- err,cmessage ) ! intent(out): error control
- if(err/=0)then; message=trim(message)//trim(cmessage); return; end if
- !print*, scalarLeafResistance, & ! mean leaf boundary layer resistance per unit leaf area (s m-1)
- ! scalarGroundResistance, & ! below canopy aerodynamic resistance (s m-1)
- ! scalarCanopyResistance, & ! above canopy aerodynamic resistance (s m-1)
- ! '(leaf, ground, canopy)'
-
- ! *******************************************************************************************************************************************************************
- ! *******************************************************************************************************************************************************************
- ! ***** STOMATAL RESISTANCE *****************************************************************************************************************************************
- ! *******************************************************************************************************************************************************************
- ! *******************************************************************************************************************************************************************
-
- ! stomatal resistance is constant over the SUBSTEP
- ! NOTE: This is a simplification, as stomatal resistance does depend on canopy temperature
- ! This "short-cut" made because:
- ! (1) computations are expensive;
- ! (2) derivative calculations are rather complex (iterations within the Ball-Berry routine); and
- ! (3) stomatal resistance does not change rapidly
- if(firstFluxCall)then
-
- ! compute the saturation vapor pressure for vegetation temperature
- TV_celcius = canopyTempTrial - Tfreeze
- call satVapPress(TV_celcius, scalarSatVP_CanopyTemp, dSVPCanopy_dCanopyTemp)
-
- ! compute soil moisture factor controlling stomatal resistance
- call soilResist(&
- ! input (model decisions)
- ix_soilStress, & ! intent(in): choice of function for the soil moisture control on stomatal resistance
- ix_groundwatr, & ! intent(in): groundwater parameterization
- ! input (state variables)
- mLayerMatricHead(1:nSoil), & ! intent(in): matric head in each soil layer (m)
- mLayerVolFracLiq(nSnow+1:nLayers), & ! intent(in): volumetric fraction of liquid water in each soil layer (-)
- scalarAquiferStorage, & ! intent(in): aquifer storage (m)
- ! input (diagnostic variables)
- mLayerRootDensity(1:nSoil), & ! intent(in): root density in each layer (-)
- scalarAquiferRootFrac, & ! intent(in): fraction of roots below the lowest soil layer (-)
- ! input (parameters)
- plantWiltPsi, & ! intent(in): matric head at wilting point (m)
- soilStressParam, & ! intent(in): parameter in the exponential soil stress function (-)
- critSoilWilting, & ! intent(in): critical vol. liq. water content when plants are wilting (-)
- critSoilTranspire, & ! intent(in): critical vol. liq. water content when transpiration is limited (-)
- critAquiferTranspire, & ! intent(in): critical aquifer storage value when transpiration is limited (m)
- ! output
- scalarTranspireLim, & ! intent(out): weighted average of the transpiration limiting factor (-)
- mLayerTranspireLim(1:nSoil), & ! intent(out): transpiration limiting factor in each layer (-)
- scalarTranspireLimAqfr, & ! intent(out): transpiration limiting factor for the aquifer (-)
- err,cmessage ) ! intent(out): error control
- if(err/=0)then; message=trim(message)//trim(cmessage); return; end if
- !print*, 'weighted average of the soil moiture factor controlling stomatal resistance (-) = ', scalarTranspireLim
-
- !write(*,'(a,1x,10(f20.10,1x))') 'canopyTempTrial, scalarSatVP_CanopyTemp, scalarVP_CanopyAir = ', &
- ! canopyTempTrial, scalarSatVP_CanopyTemp, scalarVP_CanopyAir
-
- ! compute stomatal resistance
- call stomResist(&
- ! input (state and diagnostic variables)
- canopyTempTrial, & ! intent(in): temperature of the vegetation canopy (K)
- scalarSatVP_CanopyTemp, & ! intent(in): saturation vapor pressure at the temperature of the veg canopy (Pa)
- scalarVP_CanopyAir, & ! intent(in): canopy air vapor pressure (Pa)
- ! input: data structures
- type_data, & ! intent(in): type of vegetation and soil
- forc_data, & ! intent(in): model forcing data
- mpar_data, & ! intent(in): model parameters
- model_decisions, & ! intent(in): model decisions
- ! input-output: data structures
- diag_data, & ! intent(inout): model diagnostic variables for a local HRU
- flux_data, & ! intent(inout): model fluxes for a local HRU
- ! output: error control
- err,cmessage ) ! intent(out): error control
- if(err/=0)then; message=trim(message)//trim(cmessage); return; end if
-
- end if ! (if the first flux call in a given sub-step)
-
-
- ! *******************************************************************************************************************************************************************
- ! *******************************************************************************************************************************************************************
- ! ***** LONGWAVE RADIATION *****************************************************************************************************************************************
- ! *******************************************************************************************************************************************************************
- ! *******************************************************************************************************************************************************************
-
- ! compute canopy longwave radiation balance
- call longwaveBal(&
- ! input: model control
- ixDerivMethod, & ! intent(in): method used to calculate flux derivatives
- computeVegFlux, & ! intent(in): flag to compute fluxes over vegetation
- requireLWBal, & ! intent(in): flag to indicate if we need longwave to be balanced
- ! input: canopy and ground temperature
- canopyTempTrial, & ! intent(in): temperature of the vegetation canopy (K)
- groundTempTrial, & ! intent(in): temperature of the ground surface (K)
- ! input: canopy and ground emissivity
- scalarCanopyEmissivity, & ! intent(in): canopy emissivity (-)
- groundEmissivity, & ! intent(in): ground emissivity (-)
- ! input: forcing
- LWRadAtm, & ! intent(in): downwelling longwave radiation at the upper boundary (W m-2)
- ! output: emitted radiation from the canopy and ground
- scalarLWRadCanopy, & ! intent(out): longwave radiation emitted from the canopy (W m-2)
- scalarLWRadGround, & ! intent(out): longwave radiation emitted at the ground surface (W m-2)
- ! output: individual fluxes
- scalarLWRadUbound2Canopy, & ! intent(out): downward atmospheric longwave radiation absorbed by the canopy (W m-2)
- scalarLWRadUbound2Ground, & ! intent(out): downward atmospheric longwave radiation absorbed by the ground (W m-2)
- scalarLWRadUbound2Ubound, & ! intent(out): atmospheric radiation reflected by the ground and lost thru upper boundary (W m-2)
- scalarLWRadCanopy2Ubound, & ! intent(out): longwave radiation emitted from canopy lost thru upper boundary (W m-2)
- scalarLWRadCanopy2Ground, & ! intent(out): longwave radiation emitted from canopy absorbed by the ground (W m-2)
- scalarLWRadCanopy2Canopy, & ! intent(out): canopy longwave reflected from ground and absorbed by the canopy (W m-2)
- scalarLWRadGround2Ubound, & ! intent(out): longwave radiation emitted from ground lost thru upper boundary (W m-2)
- scalarLWRadGround2Canopy, & ! intent(out): longwave radiation emitted from ground and absorbed by the canopy (W m-2)
- ! output: net fluxes
- scalarLWNetCanopy, & ! intent(out): net longwave radiation at the canopy (W m-2)
- scalarLWNetGround, & ! intent(out): net longwave radiation at the ground surface (W m-2)
- scalarLWNetUbound, & ! intent(out): net longwave radiation at the upper boundary (W m-2)
- ! output: flux derivatives
- dLWNetCanopy_dTCanopy, & ! intent(out): derivative in net canopy radiation w.r.t. canopy temperature (W m-2 K-1)
- dLWNetGround_dTGround, & ! intent(out): derivative in net ground radiation w.r.t. ground temperature (W m-2 K-1)
- dLWNetCanopy_dTGround, & ! intent(out): derivative in net canopy radiation w.r.t. ground temperature (W m-2 K-1)
- dLWNetGround_dTCanopy, & ! intent(out): derivative in net ground radiation w.r.t. canopy temperature (W m-2 K-1)
- ! output: error control
- err,cmessage ) ! intent(out): error control
- if(err/=0)then; message=trim(message)//trim(cmessage); return; end if
- !print*, 'dLWNetCanopy_dTGround = ', dLWNetCanopy_dTGround
-
-
- ! *******************************************************************************************************************************************************************
- ! *******************************************************************************************************************************************************************
- ! ***** TURBULENT HEAT FLUXES **************************************************************************************************************************************
- ! *******************************************************************************************************************************************************************
- ! *******************************************************************************************************************************************************************
-
- ! check the need to compute numerical derivatives
- if(ixDerivMethod == numerical)then
- nFlux=5 ! compute the derivatives using one-sided finite differences
- else
- nFlux=1 ! compute analytical derivatives
- end if
-
- ! either one or multiple flux calls, depending on if using analytical or numerical derivatives
- do itry=nFlux,1,-1 ! (work backwards to ensure all computed fluxes come from the un-perturbed case)
-
- ! -------------------------------------------------------------------------------------
- ! state perturbations for numerical deriavtives with one-sided finite differences
- ! note: no perturbations performed using analytical derivatives (nFlux=1)
- ! -------------------------------------------------------------------------------------
-
- ! initialize for unperturbed state
- canopyWetFraction = scalarCanopyWetFraction
-
- ! identify the type of perturbation
- select case(itry)
-
- ! un-perturbed case
- case(unperturbed)
- groundTemp = groundTempTrial
- canopyTemp = canopyTempTrial
- canairTemp = canairTempTrial
- canopyWat = totalCanopyWater
-
- ! perturb ground temperature
- case(perturbStateGround)
- groundTemp = groundTempTrial + dx
- canopyTemp = canopyTempTrial
- canairTemp = canairTempTrial
- canopyWat = totalCanopyWater
-
- ! perturb canopy temperature
- case(perturbStateCanopy)
- groundTemp = groundTempTrial
- canopyTemp = canopyTempTrial + dx
- canairTemp = canairTempTrial
- canopyWat = totalCanopyWater
-
- ! perturb canopy air temperature
- case(perturbStateCanair)
- groundTemp = groundTempTrial
- canopyTemp = canopyTempTrial
- canairTemp = canairTempTrial + dx
- canopyWat = totalCanopyWater
-
- ! perturb canopy total water content
- case(perturbStateCanWat)
- groundTemp = groundTempTrial
- canopyTemp = canopyTempTrial
- canairTemp = canairTempTrial
- canopyWat = totalCanopyWater + dx
-
- ! check for an unknown perturbation
- case default; err=10; message=trim(message)//"unknown perturbation"; return
-
- end select ! (type of perturbation)
-
- ! perturbations in canopy total water content affect canopy wetted fraction
- if(itry == perturbStateCanopy .OR. itry == perturbStateCanWat)then
-
- ! recalculate liquid and ice from total water
- fracLiquidCanopy = fracliquid(canopyTemp,snowfrz_scale)
- canopyLiq = fracLiquidCanopy*canopyWat
- canopyIce = (1._rkind - fracLiquidCanopy)*canopyWat
-
- if(computeVegFlux)then
+
+ ! ensure canopy longwave fluxes are zero when not computing canopy fluxes
+ if(.not.computeVegFlux) scalarCanopyEmissivity=0._rkind
+
+ ! compute emissivity of the ground surface (-)
+ groundEmissivity = scalarGroundSnowFraction*snowEmissivity + (1._rkind - scalarGroundSnowFraction)*soilEmissivity ! emissivity of the ground surface (-)
+
+ ! compute the fraction of canopy that is wet
+ ! NOTE: we either sublimate or evaporate over the entire substep
+ if(computeVegFlux)then
+
+ ! compute the fraction of liquid water in the canopy (-)
+ totalCanopyWater = canopyLiqTrial + canopyIceTrial
+ if(totalCanopyWater > tiny(1.0_rkind))then
+ fracLiquidCanopy = canopyLiqTrial / (canopyLiqTrial + canopyIceTrial)
+ else
+ fracLiquidCanopy = 0._rkind
+ end if
+
+ ! get wetted fraction and derivatives
call wettedFrac(&
! input
- .false., & ! flag to denote if derivative is desired
+ .true., & ! flag to denote if derivative is desired
(ixDerivMethod == numerical), & ! flag to denote that numerical derivatives are required (otherwise, analytical derivatives are calculated)
(scalarLatHeatSubVapCanopy > LH_vap+verySmall), & ! flag to denote if the canopy is frozen
dCanLiq_dTcanopy, & ! derivative in canopy liquid w.r.t. canopy temperature (kg m-2 K-1)
fracLiquidCanopy, & ! fraction of liquid water on the canopy (-)
- canopyLiq, & ! canopy liquid water (kg m-2)
- canopyIce, & ! canopy ice (kg m-2)
+ canopyLiqTrial, & ! canopy liquid water (kg m-2)
+ canopyIceTrial, & ! canopy ice (kg m-2)
scalarCanopyLiqMax, & ! maximum canopy liquid water (kg m-2)
scalarCanopyIceMax, & ! maximum canopy ice content (kg m-2)
canopyWettingFactor, & ! maximum wetted fraction of the canopy (-)
canopyWettingExp, & ! exponent in canopy wetting function (-)
! output
- canopyWetFraction, & ! canopy wetted fraction (-)
- dCanopyWetFraction_dWat, & ! derivative in wetted fraction w.r.t. canopy liquid water (kg-1 m2)
+ scalarCanopyWetFraction, & ! canopy wetted fraction (-)
+ dCanopyWetFraction_dWat, & ! derivative in wetted fraction w.r.t. canopy total water (kg-1 m2)
dCanopyWetFraction_dT, & ! derivative in wetted fraction w.r.t. canopy temperature (K-1)
err,cmessage)
if(err/=0)then; message=trim(message)//trim(cmessage); return; end if
-
- else
- canopyWetFraction = 0._rkind
- end if ! (desired computing vegetation flux)
-
- end if ! (re-computing wetted fraction for perturbed cases)
- !print*, 'wetted fraction derivative = ', (canopyWetFraction - scalarCanopyWetFraction)/dx
- !pause
-
- ! compute the saturation vapor pressure for vegetation temperature
- ! NOTE: saturated vapor pressure derivatives don't seem that accurate....
- TV_celcius = canopyTemp - Tfreeze
- call satVapPress(TV_celcius, scalarSatVP_CanopyTemp, dSVPCanopy_dCanopyTemp)
-
- ! compute the saturation vapor pressure for ground temperature
- ! NOTE: saturated vapor pressure derivatives don't seem that accurate....
- TG_celcius = groundTemp - Tfreeze
- call satVapPress(TG_celcius, scalarSatVP_GroundTemp, dSVPGround_dGroundTemp)
-
- ! -------------------------------------------------------------------------------------
- ! calculation block (unperturbed fluxes returned [computed last])
- ! -------------------------------------------------------------------------------------
-
- ! re-compute aerodynamic resistances for perturbed cases
- ! NOTE: unperturbed fluxes computed earlier, and not over-written
- if(itry /= unperturbed)then
- call aeroResist(&
- ! input: model control
- computeVegFlux, & ! intent(in): logical flag to compute vegetation fluxes (.false. if veg buried by snow)
- .false., & ! intent(in): logical flag if would like to compute analytical derivaties
- ix_veg_traits, & ! intent(in): choice of parameterization for vegetation roughness length and displacement height
- ix_windPrfile, & ! intent(in): choice of canopy wind profile
- ix_astability, & ! intent(in): choice of stability function
- ! input: above-canopy forcing data
- mHeight, & ! intent(in): measurement height (m)
- airtemp, & ! intent(in): air temperature at some height above the surface (K)
- windspd, & ! intent(in): wind speed at some height above the surface (m s-1)
- ! input: temperature (canopy, ground, canopy air space)
- canairTemp, & ! intent(in): temperature of the canopy air space (K)
- groundTemp, & ! intent(in): ground temperature (K)
- ! input: diagnostic variables
- exposedVAI, & ! intent(in): exposed vegetation area index -- leaf plus stem (m2 m-2)
- scalarSnowDepth, & ! intent(in): snow depth (m)
- ! input: parameters
- z0Ground, & ! intent(in): roughness length of the ground (below canopy or non-vegetated surface [snow]) (m)
- z0CanopyParam, & ! intent(in): roughness length of the canopy (m)
- zpdFraction, & ! intent(in): zero plane displacement / canopy height (-)
- critRichNumber, & ! intent(in): critical value for the bulk Richardson number where turbulence ceases (-)
- Louis79_bparam, & ! intent(in): parameter in Louis (1979) stability function
- Mahrt87_eScale, & ! intent(in): exponential scaling factor in the Mahrt (1987) stability function
- windReductionParam, & ! intent(in): canopy wind reduction parameter (-)
- leafExchangeCoeff, & ! intent(in): turbulent exchange coeff between canopy surface and canopy air ( m s-(1/2) )
- leafDimension, & ! intent(in): characteristic leaf dimension (m)
- heightCanopyTop, & ! intent(in): height at the top of the vegetation canopy (m)
- heightCanopyBottom, & ! intent(in): height at the bottom of the vegetation canopy (m)
- ! output: stability corrections
- notUsed_RiBulkCanopy, & ! intent(out): bulk Richardson number for the canopy (-)
- notUsed_RiBulkGround, & ! intent(out): bulk Richardson number for the ground surface (-)
- notUsed_scalarCanopyStabilityCorrection, & ! intent(out): stability correction for the canopy (-)
- notUsed_scalarGroundStabilityCorrection, & ! intent(out): stability correction for the ground surface (-)
- ! output: scalar resistances
- notUsed_z0Canopy, & ! intent(out): roughness length of the canopy (m)
- notUsed_WindReductionFactor, & ! intent(out): canopy wind reduction factor (-)
- notUsed_ZeroPlaneDisplacement, & ! intent(out): zero plane displacement (m)
- notUsed_EddyDiffusCanopyTop, & ! intent(out): eddy diffusivity for heat at the top of the canopy (m2 s-1)
- notUsed_FrictionVelocity, & ! intent(out): friction velocity (m s-1)
- notUsed_WindspdCanopyTop, & ! intent(out): windspeed at the top of the canopy (m s-1)
- notUsed_WindspdCanopyBottom, & ! intent(out): windspeed at the height of the bottom of the canopy (m s-1)
- trialLeafResistance, & ! intent(out): mean leaf boundary layer resistance per unit leaf area (s m-1)
- trialGroundResistance, & ! intent(out): below canopy aerodynamic resistance (s m-1)
- trialCanopyResistance, & ! intent(out): above canopy aerodynamic resistance (s m-1)
- ! output: derivatives in scalar resistances
- notUsed_dGroundResistance_dTGround, & ! intent(out): derivative in ground resistance w.r.t. ground temperature (s m-1 K-1)
- notUsed_dGroundResistance_dTCanopy, & ! intent(out): derivative in ground resistance w.r.t. canopy temperature (s m-1 K-1)
- notUsed_dGroundResistance_dTCanair, & ! intent(out): derivative in ground resistance w.r.t. canopy air temperature (s m-1 K-1)
- notUsed_dCanopyResistance_dTCanopy, & ! intent(out): derivative in canopy resistance w.r.t. canopy temperature (s m-1 K-1)
- notUsed_dCanopyResistance_dTCanair, & ! intent(out): derivative in canopy resistance w.r.t. canopy air temperature (s m-1 K-1)
- ! output: error control
- err,cmessage ) ! intent(out): error control
- if(err/=0)then; message=trim(message)//trim(cmessage); return; end if
-
-
- ! assign scalar resistances for un-perturbed cases
+
else
- trialLeafResistance = scalarLeafResistance
- trialGroundResistance = scalarGroundResistance
- trialCanopyResistance = scalarCanopyResistance
-
- end if ! (re-computing resistances for perturbed cases)
- !print*, 'trialLeafResistance = ', trialLeafResistance
- !print*, 'trialGroundResistance = ', trialGroundResistance
- !print*, 'trialCanopyResistance = ', trialCanopyResistance
-
- ! compute the relative humidity in the top soil layer and the resistance at the ground surface
- ! NOTE: computations are based on start-of-step values, so only compute for the first flux call
- if(firstFluxCall)then
- ! (soil water evaporation factor [0-1])
- soilEvapFactor = mLayerVolFracLiq(nSnow+1)/(theta_sat - theta_res)
- ! (resistance from the soil [s m-1])
- scalarSoilResistance = scalarGroundSnowFraction*1._rkind + (1._rkind - scalarGroundSnowFraction)*EXP(8.25_rkind - 4.225_rkind*soilEvapFactor) ! Sellers (1992)
- !scalarSoilResistance = scalarGroundSnowFraction*0._rkind + (1._rkind - scalarGroundSnowFraction)*exp(8.25_rkind - 6.0_rkind*soilEvapFactor) ! Niu adjustment to decrease resitance for wet soil
- ! (relative humidity in the soil pores [0-1])
- if(mLayerMatricHead(1) > -1.e+6_rkind)then ! avoid problems with numerical precision when soil is very dry
- soilRelHumidity_noSnow = exp( (mLayerMatricHead(1)*gravity) / (groundTemp*R_wv) )
- else
- soilRelHumidity_noSnow = 0._rkind
- end if ! (if matric head is very low)
- scalarSoilRelHumidity = scalarGroundSnowFraction*1._rkind + (1._rkind - scalarGroundSnowFraction)*soilRelHumidity_noSnow
- !print*, 'mLayerMatricHead(1), scalarSoilRelHumidity = ', mLayerMatricHead(1), scalarSoilRelHumidity
- end if ! (if the first flux call)
-
- ! compute turbulent heat fluxes
- call turbFluxes(&
+ scalarCanopyWetFraction = 0._rkind ! canopy wetted fraction (-)
+ dCanopyWetFraction_dWat = 0._rkind ! derivative in wetted fraction w.r.t. canopy total water (kg-1 m2)
+ dCanopyWetFraction_dT = 0._rkind ! derivative in wetted fraction w.r.t. canopy temperature (K-1)
+ end if
+
+ ! *******************************************************************************************************************************************************************
+ ! *******************************************************************************************************************************************************************
+ ! ***** AERODYNAMIC RESISTANCE *****************************************************************************************************************************************
+ ! *******************************************************************************************************************************************************************
+ ! *******************************************************************************************************************************************************************
+
+ ! NOTE: compute for all iterations
+
+ ! compute aerodynamic resistances
+ ! Refs: Choudhury and Monteith (4-layer model for heat budget of homogenous surfaces; QJRMS, 1988)
+ ! Niu and Yang (Canopy effects on snow processes; JGR, 2004)
+ ! Mahat et al. (Below-canopy turbulence in a snowmelt model, WRR, 2012)
+ call aeroResist(&
! input: model control
- computeVegFlux, & ! intent(in): logical flag to compute vegetation fluxes (.false. if veg buried by snow)
- ixDerivMethod, & ! intent(in): method used to calculate flux derivatives
+ computeVegFlux, & ! intent(in): logical flag to compute vegetation fluxes (.false. if veg buried by snow)
+ (ixDerivMethod == analytical), & ! intent(in): logical flag if would like to compute analytical derivaties
+ ix_veg_traits, & ! intent(in): choice of parameterization for vegetation roughness length and displacement height
+ ix_windPrfile, & ! intent(in): choice of canopy wind profile
+ ix_astability, & ! intent(in): choice of stability function
! input: above-canopy forcing data
- airtemp, & ! intent(in): air temperature at some height above the surface (K)
- airpres, & ! intent(in): air pressure of the air above the vegetation canopy (Pa)
- scalarVPair, & ! intent(in): vapor pressure of the air above the vegetation canopy (Pa)
- ! input: latent heat of sublimation/vaporization
- scalarLatHeatSubVapCanopy, & ! intent(in): latent heat of sublimation/vaporization for the vegetation canopy (J kg-1)
- scalarLatHeatSubVapGround, & ! intent(in): latent heat of sublimation/vaporization for the ground surface (J kg-1)
- ! input: canopy/ground temperature and saturated vapor pressure
- canairTemp, & ! intent(in): temperature of the canopy air space (K)
- canopyTemp, & ! intent(in): canopy temperature (K)
- groundTemp, & ! intent(in): ground temperature (K)
- scalarSatVP_CanopyTemp, & ! intent(in): saturation vapor pressure at the temperature of the veg canopy (Pa)
- scalarSatVP_GroundTemp, & ! intent(in): saturation vapor pressure at the temperature of the ground (Pa)
- dSVPCanopy_dCanopyTemp, & ! intent(in): derivative in canopy saturation vapor pressure w.r.t. canopy temperature (Pa K-1)
- dSVPGround_dGroundTemp, & ! intent(in): derivative in ground saturation vapor pressure w.r.t. ground temperature (Pa K-1)
+ mHeight, & ! intent(in): measurement height (m)
+ airtemp, & ! intent(in): air temperature at some height above the surface (K)
+ windspd, & ! intent(in): wind speed at some height above the surface (m s-1)
+ ! input: canopy and ground temperature
+ canairTempTrial, & ! intent(in): temperature of the canopy air space (K)
+ groundTempTrial, & ! intent(in): temperature of the ground surface (K)
! input: diagnostic variables
- exposedVAI, & ! intent(in): exposed vegetation area index -- leaf plus stem (m2 m-2)
- canopyWetFraction, & ! intent(in): trial value for the fraction of canopy that is wet [0-1]
- dCanopyWetFraction_dWat, & ! intent(in): derivative in the canopy wetted fraction w.r.t. total water content (kg-1 m-2)
- dCanopyWetFraction_dT, & ! intent(in): derivative in wetted fraction w.r.t. canopy temperature (K-1)
- scalarCanopySunlitLAI, & ! intent(in): sunlit leaf area (-)
- scalarCanopyShadedLAI, & ! intent(in): shaded leaf area (-)
- scalarSoilRelHumidity, & ! intent(in): relative humidity in the soil pores [0-1]
- scalarSoilResistance, & ! intent(in): resistance from the soil (s m-1)
- trialLeafResistance, & ! intent(in): mean leaf boundary layer resistance per unit leaf area (s m-1)
- trialGroundResistance, & ! intent(in): below canopy aerodynamic resistance (s m-1)
- trialCanopyResistance, & ! intent(in): above canopy aerodynamic resistance (s m-1)
- scalarStomResistSunlit, & ! intent(in): stomatal resistance for sunlit leaves (s m-1)
- scalarStomResistShaded, & ! intent(in): stomatal resistance for shaded leaves (s m-1)
- ! input: derivatives in scalar resistances
- dGroundResistance_dTGround, & ! intent(in): derivative in ground resistance w.r.t. ground temperature (s m-1 K-1)
- dGroundResistance_dTCanopy, & ! intent(in): derivative in ground resistance w.r.t. canopy temperature (s m-1 K-1)
- dGroundResistance_dTCanair, & ! intent(in): derivative in ground resistance w.r.t. canopy air temperature (s m-1 K-1)
- dCanopyResistance_dTCanopy, & ! intent(in): derivative in canopy resistance w.r.t. canopy temperature (s m-1 K-1)
- dCanopyResistance_dTCanair, & ! intent(in): derivative in canopy resistance w.r.t. canopy air temperature (s m-1 K-1)
- ! output: conductances (used to check derivative calculations)
- scalarLeafConductance, & ! intent(out): leaf conductance (m s-1)
- scalarCanopyConductance, & ! intent(out): canopy conductance (m s-1)
- scalarGroundConductanceSH, & ! intent(out): ground conductance for sensible heat (m s-1)
- scalarGroundConductanceLH, & ! intent(out): ground conductance for latent heat -- includes soil resistance (m s-1)
- scalarEvapConductance, & ! intent(out): conductance for evaporation (m s-1)
- scalarTransConductance, & ! intent(out): conductance for transpiration (m s-1)
- scalarTotalConductanceSH, & ! intent(out): total conductance for sensible heat (m s-1)
- scalarTotalConductanceLH, & ! intent(out): total conductance for latent heat (m s-1)
- ! output: canopy air space variables
- scalarVP_CanopyAir, & ! intent(out): vapor pressure of the canopy air space (Pa)
- ! output: fluxes from the vegetation canopy
- scalarSenHeatCanopy, & ! intent(out): sensible heat flux from the canopy to the canopy air space (W m-2)
- scalarLatHeatCanopyEvap, & ! intent(out): latent heat flux associated with evaporation from the canopy to the canopy air space (W m-2)
- scalarLatHeatCanopyTrans, & ! intent(out): latent heat flux associated with transpiration from the canopy to the canopy air space (W m-2)
- ! output: fluxes from non-vegetated surfaces (ground surface below vegetation, bare ground, or snow covered vegetation)
- scalarSenHeatGround, & ! intent(out): sensible heat flux from ground surface below vegetation, bare ground, or snow covered vegetation (W m-2)
- scalarLatHeatGround, & ! intent(out): latent heat flux from ground surface below vegetation, bare ground, or snow covered vegetation (W m-2)
- ! output: total heat fluxes to the atmosphere
- scalarSenHeatTotal, & ! intent(out): total sensible heat flux to the atmosphere (W m-2)
- scalarLatHeatTotal, & ! intent(out): total latent heat flux to the atmosphere (W m-2)
- ! output: net fluxes
- turbFluxCanair, & ! intent(out): net turbulent heat fluxes at the canopy air space (W m-2)
- turbFluxCanopy, & ! intent(out): net turbulent heat fluxes at the canopy (W m-2)
- turbFluxGround, & ! intent(out): net turbulent heat fluxes at the ground surface (W m-2)
- ! output: energy flux derivatives
- dTurbFluxCanair_dTCanair, & ! intent(out): derivative in net canopy air space fluxes w.r.t. canopy air temperature (W m-2 K-1)
- dTurbFluxCanair_dTCanopy, & ! intent(out): derivative in net canopy air space fluxes w.r.t. canopy temperature (W m-2 K-1)
- dTurbFluxCanair_dTGround, & ! intent(out): derivative in net canopy air space fluxes w.r.t. ground temperature (W m-2 K-1)
- dTurbFluxCanopy_dTCanair, & ! intent(out): derivative in net canopy turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
- dTurbFluxCanopy_dTCanopy, & ! intent(out): derivative in net canopy turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
- dTurbFluxCanopy_dTGround, & ! intent(out): derivative in net canopy turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
- dTurbFluxGround_dTCanair, & ! intent(out): derivative in net ground turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
- dTurbFluxGround_dTCanopy, & ! intent(out): derivative in net ground turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
- dTurbFluxGround_dTGround, & ! intent(out): derivative in net ground turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
- ! output: liquid flux derivatives (canopy evap)
- dLatHeatCanopyEvap_dCanWat, & ! intent(out): derivative in latent heat of canopy evaporation w.r.t. canopy total water content (W kg-1)
- dLatHeatCanopyEvap_dTCanair, & ! intent(out): derivative in latent heat of canopy evaporation w.r.t. canopy air temperature (W m-2 K-1)
- dLatHeatCanopyEvap_dTCanopy, & ! intent(out): derivative in latent heat of canopy evaporation w.r.t. canopy temperature (W m-2 K-1)
- dLatHeatCanopyEvap_dTGround, & ! intent(out): derivative in latent heat of canopy evaporation w.r.t. ground temperature (W m-2 K-1)
- ! output: liquid flux derivatives (ground evap)
- dLatHeatGroundEvap_dCanWat, & ! intent(out): derivative in latent heat of ground evaporation w.r.t. canopy total water content (J kg-1 s-1)
- dLatHeatGroundEvap_dTCanair, & ! intent(out): derivative in latent heat of ground evaporation w.r.t. canopy air temperature
- dLatHeatGroundEvap_dTCanopy, & ! intent(out): derivative in latent heat of ground evaporation w.r.t. canopy temperature
- dLatHeatGroundEvap_dTGround, & ! intent(out): derivative in latent heat of ground evaporation w.r.t. ground temperature
- ! output: latent heat flux derivatives (canopy trans)
- dLatHeatCanopyTrans_dCanWat, & ! intent(out): derivative in the latent heat of canopy transpiration w.r.t. canopy total water (J kg-1 s-1)
- dLatHeatCanopyTrans_dTCanair, & ! intent(out): derivative in the latent heat of canopy transpiration w.r.t. canopy air temperature
- dLatHeatCanopyTrans_dTCanopy, & ! intent(out): derivative in the latent heat of canopy transpiration w.r.t. canopy temperature
- dLatHeatCanopyTrans_dTGround, & ! intent(out): derivative in the latent heat of canopy transpiration w.r.t. ground temperature
- ! output: cross derivatives
- dTurbFluxCanair_dCanWat, & ! intent(out): derivative in net canopy air space fluxes w.r.t. canopy total water content (J kg-1 s-1)
- dTurbFluxCanopy_dCanWat, & ! intent(out): derivative in net canopy turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
- dTurbFluxGround_dCanWat, & ! intent(out): derivative in net ground turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
+ exposedVAI, & ! intent(in): exposed vegetation area index -- leaf plus stem (m2 m-2)
+ scalarSnowDepth, & ! intent(in): snow depth (m)
+ ! input: parameters
+ z0Ground, & ! intent(in): roughness length of the ground (below canopy or non-vegetated surface [snow]) (m)
+ z0CanopyParam, & ! intent(in): roughness length of the canopy (m)
+ zpdFraction, & ! intent(in): zero plane displacement / canopy height (-)
+ critRichNumber, & ! intent(in): critical value for the bulk Richardson number where turbulence ceases (-)
+ Louis79_bparam, & ! intent(in): parameter in Louis (1979) stability function
+ Mahrt87_eScale, & ! intent(in): exponential scaling factor in the Mahrt (1987) stability function
+ windReductionParam, & ! intent(in): canopy wind reduction parameter (-)
+ leafExchangeCoeff, & ! intent(in): turbulent exchange coeff between canopy surface and canopy air ( m s-(1/2) )
+ leafDimension, & ! intent(in): characteristic leaf dimension (m)
+ heightCanopyTop, & ! intent(in): height at the top of the vegetation canopy (m)
+ heightCanopyBottom, & ! intent(in): height at the bottom of the vegetation canopy (m)
+ ! output: stability corrections
+ scalarRiBulkCanopy, & ! intent(out): bulk Richardson number for the canopy (-)
+ scalarRiBulkGround, & ! intent(out): bulk Richardson number for the ground surface (-)
+ scalarCanopyStabilityCorrection, & ! intent(out): stability correction for the canopy (-)
+ scalarGroundStabilityCorrection, & ! intent(out): stability correction for the ground surface (-)
+ ! output: scalar resistances
+ scalarZ0Canopy, & ! intent(out): roughness length of the canopy (m)
+ scalarWindReductionFactor, & ! intent(out): canopy wind reduction factor (-)
+ scalarZeroPlaneDisplacement, & ! intent(out): zero plane displacement (m)
+ scalarEddyDiffusCanopyTop, & ! intent(out): eddy diffusivity for heat at the top of the canopy (m2 s-1)
+ scalarFrictionVelocity, & ! intent(out): friction velocity (m s-1)
+ scalarWindspdCanopyTop, & ! intent(out): windspeed at the top of the canopy (m s-1)
+ scalarWindspdCanopyBottom, & ! intent(out): windspeed at the height of the bottom of the canopy (m s-1)
+ scalarLeafResistance, & ! intent(out): mean leaf boundary layer resistance per unit leaf area (s m-1)
+ scalarGroundResistance, & ! intent(out): below canopy aerodynamic resistance (s m-1)
+ scalarCanopyResistance, & ! intent(out): above canopy aerodynamic resistance (s m-1)
+ ! output: derivatives in scalar resistances
+ dGroundResistance_dTGround, & ! intent(out): derivative in ground resistance w.r.t. ground temperature (s m-1 K-1)
+ dGroundResistance_dTCanopy, & ! intent(out): derivative in ground resistance w.r.t. canopy temperature (s m-1 K-1)
+ dGroundResistance_dTCanair, & ! intent(out): derivative in ground resistance w.r.t. canopy air temperature (s m-1 K-1)
+ dCanopyResistance_dTCanopy, & ! intent(out): derivative in canopy resistance w.r.t. canopy temperature (s m-1 K-1)
+ dCanopyResistance_dTCanair, & ! intent(out): derivative in canopy resistance w.r.t. canopy air temperature (s m-1 K-1)
! output: error control
- err,cmessage ) ! intent(out): error control
+ err,cmessage ) ! intent(out): error control
if(err/=0)then; message=trim(message)//trim(cmessage); return; end if
-
- !write(*,'(a,f25.15)') 'scalarSenHeatTotal = ', scalarSenHeatTotal
- !write(*,'(a,f25.15)') 'scalarSenHeatCanopy = ', scalarSenHeatCanopy
- !write(*,'(a,f25.15)') 'scalarLatHeatCanopyEvap = ', scalarLatHeatCanopyEvap
- !write(*,'(a,f25.15)') 'scalarLatHeatCanopyTrans = ', scalarLatHeatCanopyTrans
-
- !print*, 'scalarSenHeatGround = ', scalarSenHeatGround
- !print*, 'scalarLatHeatGround = ', scalarLatHeatGround
-
- !notUsed_scalarCanopyStabilityCorrection ! stability correction for the canopy (-)
- !notUsed_scalarGroundStabilityCorrection ! stability correction for the ground surface (-)
- !notUsed_EddyDiffusCanopyTop ! eddy diffusivity for heat at the top of the canopy (m2 s-1)
- !notUsed_FrictionVelocity ! friction velocity (m s-1)
- !notUsed_WindspdCanopyTop ! windspeed at the top of the canopy (m s-1)
- !notUsed_WindspdCanopyBottom ! windspeed at the height of the bottom of the canopy (m s-1)
- !trialLeafResistance ! mean leaf boundary layer resistance per unit leaf area (s m-1)
- !trialGroundResistance ! below canopy aerodynamic resistance (s m-1)
- !trialCanopyResistance ! above canopy aerodynamic resistance (s m-1)
-
- ! save perturbed fluxes
+
+ ! *******************************************************************************************************************************************************************
+ ! *******************************************************************************************************************************************************************
+ ! ***** STOMATAL RESISTANCE *****************************************************************************************************************************************
+ ! *******************************************************************************************************************************************************************
+ ! *******************************************************************************************************************************************************************
+
+ ! stomatal resistance is constant over the SUBSTEP
+ ! NOTE: This is a simplification, as stomatal resistance does depend on canopy temperature
+ ! This "short-cut" made because:
+ ! (1) computations are expensive;
+ ! (2) derivative calculations are rather complex (iterations within the Ball-Berry routine); and
+ ! (3) stomatal resistance does not change rapidly
+ if(firstFluxCall)then
+
+ ! compute the saturation vapor pressure for vegetation temperature
+ TV_celcius = canopyTempTrial - Tfreeze
+ call satVapPress(TV_celcius, scalarSatVP_CanopyTemp, dSVPCanopy_dCanopyTemp)
+
+ ! compute soil moisture factor controlling stomatal resistance
+ call soilResist(&
+ ! input (model decisions)
+ ix_soilStress, & ! intent(in): choice of function for the soil moisture control on stomatal resistance
+ ix_groundwatr, & ! intent(in): groundwater parameterization
+ ! input (state variables)
+ mLayerMatricHead(1:nSoil), & ! intent(in): matric head in each soil layer (m)
+ mLayerVolFracLiq(nSnow+1:nLayers), & ! intent(in): volumetric fraction of liquid water in each soil layer (-)
+ scalarAquiferStorage, & ! intent(in): aquifer storage (m)
+ ! input (diagnostic variables)
+ mLayerRootDensity(1:nSoil), & ! intent(in): root density in each layer (-)
+ scalarAquiferRootFrac, & ! intent(in): fraction of roots below the lowest soil layer (-)
+ ! input (parameters)
+ plantWiltPsi, & ! intent(in): matric head at wilting point (m)
+ soilStressParam, & ! intent(in): parameter in the exponential soil stress function (-)
+ critSoilWilting, & ! intent(in): critical vol. liq. water content when plants are wilting (-)
+ critSoilTranspire, & ! intent(in): critical vol. liq. water content when transpiration is limited (-)
+ critAquiferTranspire, & ! intent(in): critical aquifer storage value when transpiration is limited (m)
+ ! output
+ scalarTranspireLim, & ! intent(out): weighted average of the transpiration limiting factor (-)
+ mLayerTranspireLim(1:nSoil), & ! intent(out): transpiration limiting factor in each layer (-)
+ scalarTranspireLimAqfr, & ! intent(out): transpiration limiting factor for the aquifer (-)
+ err,cmessage ) ! intent(out): error control
+ if(err/=0)then; message=trim(message)//trim(cmessage); return; end if
+
+ ! compute stomatal resistance
+ call stomResist(&
+ ! input (state and diagnostic variables)
+ canopyTempTrial, & ! intent(in): temperature of the vegetation canopy (K)
+ scalarSatVP_CanopyTemp, & ! intent(in): saturation vapor pressure at the temperature of the veg canopy (Pa)
+ scalarVP_CanopyAir, & ! intent(in): canopy air vapor pressure (Pa)
+ ! input: data structures
+ type_data, & ! intent(in): type of vegetation and soil
+ forc_data, & ! intent(in): model forcing data
+ mpar_data, & ! intent(in): model parameters
+ model_decisions, & ! intent(in): model decisions
+ ! input-output: data structures
+ diag_data, & ! intent(inout): model diagnostic variables for a local HRU
+ flux_data, & ! intent(inout): model fluxes for a local HRU
+ ! output: error control
+ err,cmessage ) ! intent(out): error control
+ if(err/=0)then; message=trim(message)//trim(cmessage); return; end if
+
+ end if ! (if the first flux call in a given sub-step)
+
+
+ ! *******************************************************************************************************************************************************************
+ ! *******************************************************************************************************************************************************************
+ ! ***** LONGWAVE RADIATION *****************************************************************************************************************************************
+ ! *******************************************************************************************************************************************************************
+ ! *******************************************************************************************************************************************************************
+
+ ! compute canopy longwave radiation balance
+ call longwaveBal(&
+ ! input: model control
+ ixDerivMethod, & ! intent(in): method used to calculate flux derivatives
+ computeVegFlux, & ! intent(in): flag to compute fluxes over vegetation
+ insideIDA, & ! intent(in): flag to indicate inside Sundials Solver (do not require longwave to be balanced)
+ ! input: canopy and ground temperature
+ canopyTempTrial, & ! intent(in): temperature of the vegetation canopy (K)
+ groundTempTrial, & ! intent(in): temperature of the ground surface (K)
+ ! input: canopy and ground emissivity
+ scalarCanopyEmissivity, & ! intent(in): canopy emissivity (-)
+ groundEmissivity, & ! intent(in): ground emissivity (-)
+ ! input: forcing
+ LWRadAtm, & ! intent(in): downwelling longwave radiation at the upper boundary (W m-2)
+ ! output: emitted radiation from the canopy and ground
+ scalarLWRadCanopy, & ! intent(out): longwave radiation emitted from the canopy (W m-2)
+ scalarLWRadGround, & ! intent(out): longwave radiation emitted at the ground surface (W m-2)
+ ! output: individual fluxes
+ scalarLWRadUbound2Canopy, & ! intent(out): downward atmospheric longwave radiation absorbed by the canopy (W m-2)
+ scalarLWRadUbound2Ground, & ! intent(out): downward atmospheric longwave radiation absorbed by the ground (W m-2)
+ scalarLWRadUbound2Ubound, & ! intent(out): atmospheric radiation reflected by the ground and lost thru upper boundary (W m-2)
+ scalarLWRadCanopy2Ubound, & ! intent(out): longwave radiation emitted from canopy lost thru upper boundary (W m-2)
+ scalarLWRadCanopy2Ground, & ! intent(out): longwave radiation emitted from canopy absorbed by the ground (W m-2)
+ scalarLWRadCanopy2Canopy, & ! intent(out): canopy longwave reflected from ground and absorbed by the canopy (W m-2)
+ scalarLWRadGround2Ubound, & ! intent(out): longwave radiation emitted from ground lost thru upper boundary (W m-2)
+ scalarLWRadGround2Canopy, & ! intent(out): longwave radiation emitted from ground and absorbed by the canopy (W m-2)
+ ! output: net fluxes
+ scalarLWNetCanopy, & ! intent(out): net longwave radiation at the canopy (W m-2)
+ scalarLWNetGround, & ! intent(out): net longwave radiation at the ground surface (W m-2)
+ scalarLWNetUbound, & ! intent(out): net longwave radiation at the upper boundary (W m-2)
+ ! output: flux derivatives
+ dLWNetCanopy_dTCanopy, & ! intent(out): derivative in net canopy radiation w.r.t. canopy temperature (W m-2 K-1)
+ dLWNetGround_dTGround, & ! intent(out): derivative in net ground radiation w.r.t. ground temperature (W m-2 K-1)
+ dLWNetCanopy_dTGround, & ! intent(out): derivative in net canopy radiation w.r.t. ground temperature (W m-2 K-1)
+ dLWNetGround_dTCanopy, & ! intent(out): derivative in net ground radiation w.r.t. canopy temperature (W m-2 K-1)
+ ! output: error control
+ err,cmessage ) ! intent(out): error control
+ if(err/=0)then; message=trim(message)//trim(cmessage); return; end if
+
+
+ ! *******************************************************************************************************************************************************************
+ ! *******************************************************************************************************************************************************************
+ ! ***** TURBULENT HEAT FLUXES **************************************************************************************************************************************
+ ! *******************************************************************************************************************************************************************
+ ! *******************************************************************************************************************************************************************
+
+ ! check the need to compute numerical derivatives
if(ixDerivMethod == numerical)then
- select case(itry) ! (select type of perturbation)
- case(unperturbed)
- try0 = turbFluxGround
- exit
- case(perturbStateCanair)
- turbFluxCanair_dStateCanair = turbFluxCanair ! turbulent exchange from the canopy air space to the atmosphere (W m-2)
- turbFluxCanopy_dStateCanair = turbFluxCanopy ! total turbulent heat fluxes from the canopy to the canopy air space (W m-2)
- turbFluxGround_dStateCanair = turbFluxGround ! total turbulent heat fluxes from the ground to the canopy air space (W m-2)
- latHeatCanEvap_dStateCanair = scalarLatHeatCanopyEvap ! perturbed value for the latent heat associated with canopy evaporation (W m-2)
- case(perturbStateCanopy)
- turbFluxCanair_dStateCanopy = turbFluxCanair ! turbulent exchange from the canopy air space to the atmosphere (W m-2)
- turbFluxCanopy_dStateCanopy = turbFluxCanopy ! total turbulent heat fluxes from the canopy to the canopy air space (W m-2)
- turbFluxGround_dStateCanopy = turbFluxGround ! total turbulent heat fluxes from the ground to the canopy air space (W m-2)
- latHeatCanEvap_dStateCanopy = scalarLatHeatCanopyEvap ! perturbed value for the latent heat associated with canopy evaporation (W m-2)
- case(perturbStateGround)
- try1 = turbFluxGround
- turbFluxCanair_dStateGround = turbFluxCanair ! turbulent exchange from the canopy air space to the atmosphere (W m-2)
- turbFluxCanopy_dStateGround = turbFluxCanopy ! total turbulent heat fluxes from the canopy to the canopy air space (W m-2)
- turbFluxGround_dStateGround = turbFluxGround ! total turbulent heat fluxes from the ground to the canopy air space (W m-2)
- latHeatCanEvap_dStateGround = scalarLatHeatCanopyEvap ! perturbed value for the latent heat associated with canopy evaporation (W m-2)
- case(perturbStateCanWat)
- turbFluxCanair_dStateCanWat = turbFluxCanair ! turbulent exchange from the canopy air space to the atmosphere (W m-2)
- turbFluxCanopy_dStateCanWat = turbFluxCanopy ! total turbulent heat fluxes from the canopy to the canopy air space (W m-2)
- turbFluxGround_dStateCanWat = turbFluxGround ! total turbulent heat fluxes from the ground to the canopy air space (W m-2)
- latHeatCanEvap_dStateCanWat = scalarLatHeatCanopyEvap ! perturbed value for the latent heat associated with canopy evaporation (W m-2)
- case default; err=10; message=trim(message)//"unknown perturbation"; return
- end select ! (type of perturbation)
- end if ! (if numerical)
-
- end do ! (looping through different flux perturbations)
-
- ! test derivative
- !if(ixDerivMethod == numerical) print*, 'try0, try1 = ', try0, try1
- !if(ixDerivMethod == numerical) print*, 'derivative = ', (ixDerivMethod == numerical), (try1 - try0)/dx
- !if(ixDerivMethod == analytical) print*, 'derivative = ', (ixDerivMethod == numerical), dTurbFluxGround_dTGround
- !pause
-
- ! compute numerical derivatives
- if(ixDerivMethod == numerical)then
- ! derivatives w.r.t. canopy air temperature
- dTurbFluxCanair_dTCanair = (turbFluxCanair_dStateCanair - turbFluxCanair) / dx ! derivative in net canopy air space fluxes w.r.t. canopy air temperature (W m-2 K-1)
- dTurbFluxCanopy_dTCanair = (turbFluxCanopy_dStateCanair - turbFluxCanopy) / dx ! derivative in net canopy turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
- dTurbFluxGround_dTCanair = (turbFluxGround_dStateCanair - turbFluxGround) / dx ! derivative in net ground turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
- dLatHeatCanopyEvap_dTCanair = (latHeatCanEvap_dStateCanair - scalarLatHeatCanopyEvap) / dx ! derivative in latent heat of canopy evaporation w.r.t. canopy air temperature (W m-2 K-1)
- ! derivatives w.r.t. canopy temperature
- dTurbFluxCanair_dTCanopy = (turbFluxCanair_dStateCanopy - turbFluxCanair) / dx ! derivative in net canopy air space fluxes w.r.t. canopy temperature (W m-2 K-1)
- dTurbFluxCanopy_dTCanopy = (turbFluxCanopy_dStateCanopy - turbFluxCanopy) / dx ! derivative in net canopy turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
- dTurbFluxGround_dTCanopy = (turbFluxGround_dStateCanopy - turbFluxGround) / dx ! derivative in net ground turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
- dLatHeatCanopyEvap_dTCanopy = (latHeatCanEvap_dStateCanopy - scalarLatHeatCanopyEvap) / dx ! derivative in latent heat of canopy evaporation w.r.t. canopy temperature (W m-2 K-1)
- ! derivatives w.r.t. ground temperature
- dTurbFluxCanair_dTGround = (turbFluxCanair_dStateGround - turbFluxCanair) / dx ! derivative in net canopy air space fluxes w.r.t. ground temperature (W m-2 K-1)
- dTurbFluxCanopy_dTGround = (turbFluxCanopy_dStateGround - turbFluxCanopy) / dx ! derivative in net canopy turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
- dTurbFluxGround_dTGround = (turbFluxGround_dStateGround - turbFluxGround) / dx ! derivative in net ground turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
- dLatHeatCanopyEvap_dTGround = (latHeatCanEvap_dStateGround - scalarLatHeatCanopyEvap) / dx ! derivative in latent heat of canopy evaporation w.r.t. ground temperature (W m-2 K-1)
- ! derivatives w.r.t. canopy total water content
- dTurbFluxCanair_dCanWat = (turbFluxCanair_dStateCanWat - turbFluxCanair) / dx ! derivative in net canopy air space fluxes w.r.t. canopy total water content (J kg-1 s-1)
- dTurbFluxCanopy_dCanWat = (turbFluxCanopy_dStateCanWat - turbFluxCanopy) / dx ! derivative in net canopy turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
- dTurbFluxGround_dCanWat = (turbFluxGround_dStateCanWat - turbFluxGround) / dx ! derivative in net ground turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
- dLatHeatCanopyEvap_dCanWat = (latHeatCanEvap_dStateCanWat - scalarLatHeatCanopyEvap) / dx ! derivative in latent heat of canopy evaporation w.r.t. canopy total water content (J kg-1 s-1)
- end if
- !if(heightCanopyBottom < scalarSnowDepth+z0Ground) pause 'bottom of the canopy is covered'
-
- ! test
- !print*, (ixDerivMethod == numerical)
- !print*, 'dTurbFluxCanair_dTCanair = ', dTurbFluxCanair_dTCanair
- !print*, 'dTurbFluxCanair_dTCanopy = ', dTurbFluxCanair_dTCanopy
- !print*, 'dTurbFluxCanair_dTGround = ', dTurbFluxCanair_dTGround
- !print*, 'dTurbFluxCanopy_dTCanair = ', dTurbFluxCanopy_dTCanair
- !print*, 'dTurbFluxCanopy_dTCanopy = ', dTurbFluxCanopy_dTCanopy
- !print*, 'dTurbFluxCanopy_dTGround = ', dTurbFluxCanopy_dTGround
- !print*, 'dTurbFluxGround_dTCanair = ', dTurbFluxGround_dTCanair
- !print*, 'dTurbFluxGround_dTCanopy = ', dTurbFluxGround_dTCanopy
- !print*, 'dTurbFluxGround_dTGround = ', dTurbFluxGround_dTGround
- !print*, 'dLatHeatCanopyEvap_dCanWat = ', dLatHeatCanopyEvap_dCanWat
- !print*, 'dLatHeatCanopyEvap_dTCanair = ', dLatHeatCanopyEvap_dTCanair
- !print*, 'dLatHeatCanopyEvap_dTCanopy = ', dLatHeatCanopyEvap_dTCanopy
- !print*, 'dLatHeatCanopyEvap_dTGround = ', dLatHeatCanopyEvap_dTGround
- !print*, 'dTurbFluxCanair_dCanWat = ', dTurbFluxCanair_dCanWat
- !print*, 'dTurbFluxCanopy_dCanWat = ', dTurbFluxCanopy_dCanWat
- !print*, 'dTurbFluxGround_dCanWat = ', dTurbFluxGround_dCanWat
- !print*, '*****'
- !pause
-
- !print*, 'scalarRainfall, scalarThroughfallRain, scalarSnowfall, scalarThroughfallSnow, canopyTempTrial, scalarTwetbulb = ', &
- ! scalarRainfall, scalarThroughfallRain, scalarSnowfall, scalarThroughfallSnow, canopyTempTrial, scalarTwetbulb
-
- ! compute the heat advected with precipitation (W m-2)
- ! NOTE: fluxes are in kg m-2 s-1, so no need to use density of water/ice here
- scalarCanopyAdvectiveHeatFlux = -Cp_water*(scalarRainfall - scalarThroughfallRain)*(canopyTempTrial - scalarTwetbulb) + &
- (-Cp_ice)*(scalarSnowfall - scalarThroughfallSnow)*(canopyTempTrial - scalarTwetbulb)
- scalarGroundAdvectiveHeatFlux = -Cp_water*scalarThroughfallRain*(groundTempTrial - scalarTwetbulb) + &
- (-Cp_ice)*scalarThroughfallSnow*(groundTempTrial - scalarTwetbulb) !+ &
- ! (-Cp_water)*scalarCanopyLiqDrainage *(groundTempTrial - canopyTempTrial) + &
- ! (-Cp_ice) *scalarCanopySnowUnloading*(groundTempTrial - canopyTempTrial)
- !print*, 'scalarRainfall, scalarThroughfallRain, scalarSnowfall, scalarThroughfallSnow = ', scalarRainfall, scalarThroughfallRain, scalarSnowfall, scalarThroughfallSnow
- !print*, 'scalarCanopyAdvectiveHeatFlux, scalarGroundAdvectiveHeatFlux = ', scalarCanopyAdvectiveHeatFlux, scalarGroundAdvectiveHeatFlux
-
- ! compute the mass flux associated with transpiration and evaporation/sublimation (J m-2 s-1 --> kg m-2 s-1)
- ! NOTE: remove water from the snow on the ground in preference to removing water from the water in soil pores
- !print*, 'scalarLatHeatCanopyTrans = ', scalarLatHeatCanopyTrans
- !print*, 'scalarLatHeatGround = ', scalarLatHeatGround
- ! (canopy transpiration/sublimation)
- if(scalarLatHeatSubVapCanopy > LH_vap+verySmall)then ! sublimation
- scalarCanopyEvaporation = 0._rkind
- scalarCanopySublimation = scalarLatHeatCanopyEvap/LH_sub
- if(scalarLatHeatCanopyTrans > 0._rkind)then ! flux directed towards the veg
- scalarCanopySublimation = scalarCanopySublimation + scalarLatHeatCanopyTrans/LH_sub ! frost
- scalarCanopyTranspiration = 0._rkind
+ nFlux=5 ! compute the derivatives using one-sided finite differences
else
- scalarCanopyTranspiration = scalarLatHeatCanopyTrans/LH_vap ! transpiration is always vapor
+ nFlux=1 ! compute analytical derivatives
end if
- ! (canopy transpiration/evaporation)
- else ! evaporation
- scalarCanopyEvaporation = scalarLatHeatCanopyEvap/LH_vap
- scalarCanopySublimation = 0._rkind
- if(scalarLatHeatCanopyTrans > 0._rkind)then ! flux directed towards the veg
- scalarCanopyEvaporation = scalarCanopyEvaporation + scalarLatHeatCanopyTrans/LH_vap
- scalarCanopyTranspiration = 0._rkind
+
+ ! either one or multiple flux calls, depending on if using analytical or numerical derivatives
+ do itry=nFlux,1,-1 ! (work backwards to ensure all computed fluxes come from the un-perturbed case)
+
+ ! -------------------------------------------------------------------------------------
+ ! state perturbations for numerical deriavtives with one-sided finite differences
+ ! note: no perturbations performed using analytical derivatives (nFlux=1)
+ ! -------------------------------------------------------------------------------------
+
+ ! initialize for unperturbed state
+ canopyWetFraction = scalarCanopyWetFraction
+
+ ! identify the type of perturbation
+ select case(itry)
+
+ ! un-perturbed case
+ case(unperturbed)
+ groundTemp = groundTempTrial
+ canopyTemp = canopyTempTrial
+ canairTemp = canairTempTrial
+ canopyWat = totalCanopyWater
+
+ ! perturb ground temperature
+ case(perturbStateGround)
+ groundTemp = groundTempTrial + dx
+ canopyTemp = canopyTempTrial
+ canairTemp = canairTempTrial
+ canopyWat = totalCanopyWater
+
+ ! perturb canopy temperature
+ case(perturbStateCanopy)
+ groundTemp = groundTempTrial
+ canopyTemp = canopyTempTrial + dx
+ canairTemp = canairTempTrial
+ canopyWat = totalCanopyWater
+
+ ! perturb canopy air temperature
+ case(perturbStateCanair)
+ groundTemp = groundTempTrial
+ canopyTemp = canopyTempTrial
+ canairTemp = canairTempTrial + dx
+ canopyWat = totalCanopyWater
+
+ ! perturb canopy total water content
+ case(perturbStateCanWat)
+ groundTemp = groundTempTrial
+ canopyTemp = canopyTempTrial
+ canairTemp = canairTempTrial
+ canopyWat = totalCanopyWater + dx
+
+ ! check for an unknown perturbation
+ case default; err=10; message=trim(message)//"unknown perturbation"; return
+
+ end select ! (type of perturbation)
+
+ ! perturbations in canopy total water content affect canopy wetted fraction
+ if(itry == perturbStateCanopy .OR. itry == perturbStateCanWat)then
+
+ ! recalculate liquid and ice from total water
+ fracLiquidCanopy = fracliquid(canopyTemp,snowfrz_scale)
+ canopyLiq = fracLiquidCanopy*canopyWat
+ canopyIce = (1._rkind - fracLiquidCanopy)*canopyWat
+
+ if(computeVegFlux)then
+ call wettedFrac(&
+ ! input
+ .false., & ! flag to denote if derivative is desired
+ (ixDerivMethod == numerical), & ! flag to denote that numerical derivatives are required (otherwise, analytical derivatives are calculated)
+ (scalarLatHeatSubVapCanopy > LH_vap+verySmall), & ! flag to denote if the canopy is frozen
+ dCanLiq_dTcanopy, & ! derivative in canopy liquid w.r.t. canopy temperature (kg m-2 K-1)
+ fracLiquidCanopy, & ! fraction of liquid water on the canopy (-)
+ canopyLiq, & ! canopy liquid water (kg m-2)
+ canopyIce, & ! canopy ice (kg m-2)
+ scalarCanopyLiqMax, & ! maximum canopy liquid water (kg m-2)
+ scalarCanopyIceMax, & ! maximum canopy ice content (kg m-2)
+ canopyWettingFactor, & ! maximum wetted fraction of the canopy (-)
+ canopyWettingExp, & ! exponent in canopy wetting function (-)
+ ! output
+ canopyWetFraction, & ! canopy wetted fraction (-)
+ dCanopyWetFraction_dWat, & ! derivative in wetted fraction w.r.t. canopy liquid water (kg-1 m2)
+ dCanopyWetFraction_dT, & ! derivative in wetted fraction w.r.t. canopy temperature (K-1)
+ err,cmessage)
+ if(err/=0)then; message=trim(message)//trim(cmessage); return; end if
+
+ else
+ canopyWetFraction = 0._rkind
+ end if ! (desired computing vegetation flux)
+
+ end if ! (re-computing wetted fraction for perturbed cases)
+
+ ! compute the saturation vapor pressure for vegetation temperature
+ ! NOTE: saturated vapor pressure derivatives don't seem that accurate....
+ TV_celcius = canopyTemp - Tfreeze
+ call satVapPress(TV_celcius, scalarSatVP_CanopyTemp, dSVPCanopy_dCanopyTemp)
+
+ ! compute the saturation vapor pressure for ground temperature
+ ! NOTE: saturated vapor pressure derivatives don't seem that accurate....
+ TG_celcius = groundTemp - Tfreeze
+ call satVapPress(TG_celcius, scalarSatVP_GroundTemp, dSVPGround_dGroundTemp)
+
+ ! -------------------------------------------------------------------------------------
+ ! calculation block (unperturbed fluxes returned [computed last])
+ ! -------------------------------------------------------------------------------------
+
+ ! re-compute aerodynamic resistances for perturbed cases
+ ! NOTE: unperturbed fluxes computed earlier, and not over-written
+ if(itry /= unperturbed)then
+ call aeroResist(&
+ ! input: model control
+ computeVegFlux, & ! intent(in): logical flag to compute vegetation fluxes (.false. if veg buried by snow)
+ .false., & ! intent(in): logical flag if would like to compute analytical derivaties
+ ix_veg_traits, & ! intent(in): choice of parameterization for vegetation roughness length and displacement height
+ ix_windPrfile, & ! intent(in): choice of canopy wind profile
+ ix_astability, & ! intent(in): choice of stability function
+ ! input: above-canopy forcing data
+ mHeight, & ! intent(in): measurement height (m)
+ airtemp, & ! intent(in): air temperature at some height above the surface (K)
+ windspd, & ! intent(in): wind speed at some height above the surface (m s-1)
+ ! input: temperature (canopy, ground, canopy air space)
+ canairTemp, & ! intent(in): temperature of the canopy air space (K)
+ groundTemp, & ! intent(in): ground temperature (K)
+ ! input: diagnostic variables
+ exposedVAI, & ! intent(in): exposed vegetation area index -- leaf plus stem (m2 m-2)
+ scalarSnowDepth, & ! intent(in): snow depth (m)
+ ! input: parameters
+ z0Ground, & ! intent(in): roughness length of the ground (below canopy or non-vegetated surface [snow]) (m)
+ z0CanopyParam, & ! intent(in): roughness length of the canopy (m)
+ zpdFraction, & ! intent(in): zero plane displacement / canopy height (-)
+ critRichNumber, & ! intent(in): critical value for the bulk Richardson number where turbulence ceases (-)
+ Louis79_bparam, & ! intent(in): parameter in Louis (1979) stability function
+ Mahrt87_eScale, & ! intent(in): exponential scaling factor in the Mahrt (1987) stability function
+ windReductionParam, & ! intent(in): canopy wind reduction parameter (-)
+ leafExchangeCoeff, & ! intent(in): turbulent exchange coeff between canopy surface and canopy air ( m s-(1/2) )
+ leafDimension, & ! intent(in): characteristic leaf dimension (m)
+ heightCanopyTop, & ! intent(in): height at the top of the vegetation canopy (m)
+ heightCanopyBottom, & ! intent(in): height at the bottom of the vegetation canopy (m)
+ ! output: stability corrections
+ notUsed_RiBulkCanopy, & ! intent(out): bulk Richardson number for the canopy (-)
+ notUsed_RiBulkGround, & ! intent(out): bulk Richardson number for the ground surface (-)
+ notUsed_scalarCanopyStabilityCorrection, & ! intent(out): stability correction for the canopy (-)
+ notUsed_scalarGroundStabilityCorrection, & ! intent(out): stability correction for the ground surface (-)
+ ! output: scalar resistances
+ notUsed_z0Canopy, & ! intent(out): roughness length of the canopy (m)
+ notUsed_WindReductionFactor, & ! intent(out): canopy wind reduction factor (-)
+ notUsed_ZeroPlaneDisplacement, & ! intent(out): zero plane displacement (m)
+ notUsed_EddyDiffusCanopyTop, & ! intent(out): eddy diffusivity for heat at the top of the canopy (m2 s-1)
+ notUsed_FrictionVelocity, & ! intent(out): friction velocity (m s-1)
+ notUsed_WindspdCanopyTop, & ! intent(out): windspeed at the top of the canopy (m s-1)
+ notUsed_WindspdCanopyBottom, & ! intent(out): windspeed at the height of the bottom of the canopy (m s-1)
+ trialLeafResistance, & ! intent(out): mean leaf boundary layer resistance per unit leaf area (s m-1)
+ trialGroundResistance, & ! intent(out): below canopy aerodynamic resistance (s m-1)
+ trialCanopyResistance, & ! intent(out): above canopy aerodynamic resistance (s m-1)
+ ! output: derivatives in scalar resistances
+ notUsed_dGroundResistance_dTGround, & ! intent(out): derivative in ground resistance w.r.t. ground temperature (s m-1 K-1)
+ notUsed_dGroundResistance_dTCanopy, & ! intent(out): derivative in ground resistance w.r.t. canopy temperature (s m-1 K-1)
+ notUsed_dGroundResistance_dTCanair, & ! intent(out): derivative in ground resistance w.r.t. canopy air temperature (s m-1 K-1)
+ notUsed_dCanopyResistance_dTCanopy, & ! intent(out): derivative in canopy resistance w.r.t. canopy temperature (s m-1 K-1)
+ notUsed_dCanopyResistance_dTCanair, & ! intent(out): derivative in canopy resistance w.r.t. canopy air temperature (s m-1 K-1)
+ ! output: error control
+ err,cmessage ) ! intent(out): error control
+ if(err/=0)then; message=trim(message)//trim(cmessage); return; end if
+
+
+ ! assign scalar resistances for un-perturbed cases
+ else
+ trialLeafResistance = scalarLeafResistance
+ trialGroundResistance = scalarGroundResistance
+ trialCanopyResistance = scalarCanopyResistance
+
+ end if ! (re-computing resistances for perturbed cases)
+
+
+ ! compute the relative humidity in the top soil layer and the resistance at the ground surface
+ ! NOTE: computations are based on start-of-step values, so only compute for the first flux call
+ if(firstFluxCall)then
+ ! (soil water evaporation factor [0-1])
+ soilEvapFactor = mLayerVolFracLiq(nSnow+1)/(theta_sat - theta_res)
+ ! (resistance from the soil [s m-1])
+ scalarSoilResistance = scalarGroundSnowFraction*1._rkind + (1._rkind - scalarGroundSnowFraction)*EXP(8.25_rkind - 4.225_rkind*soilEvapFactor) ! Sellers (1992)
+ !scalarSoilResistance = scalarGroundSnowFraction*0._rkind + (1._rkind - scalarGroundSnowFraction)*exp(8.25_rkind - 6.0_rkind*soilEvapFactor) ! Niu adjustment to decrease resitance for wet soil
+ ! (relative humidity in the soil pores [0-1])
+ if(mLayerMatricHead(1) > -1.e+6_rkind)then ! avoid problems with numerical precision when soil is very dry
+ soilRelHumidity_noSnow = exp( (mLayerMatricHead(1)*gravity) / (groundTemp*R_wv) )
+ else
+ soilRelHumidity_noSnow = 0._rkind
+ end if ! (if matric head is very low)
+ scalarSoilRelHumidity = scalarGroundSnowFraction*1._rkind + (1._rkind - scalarGroundSnowFraction)*soilRelHumidity_noSnow
+ end if ! (if the first flux call)
+
+ ! compute turbulent heat fluxes
+ call turbFluxes(&
+ ! input: model control
+ computeVegFlux, & ! intent(in): logical flag to compute vegetation fluxes (.false. if veg buried by snow)
+ ixDerivMethod, & ! intent(in): method used to calculate flux derivatives
+ ! input: above-canopy forcing data
+ airtemp, & ! intent(in): air temperature at some height above the surface (K)
+ airpres, & ! intent(in): air pressure of the air above the vegetation canopy (Pa)
+ scalarVPair, & ! intent(in): vapor pressure of the air above the vegetation canopy (Pa)
+ ! input: latent heat of sublimation/vaporization
+ scalarLatHeatSubVapCanopy, & ! intent(in): latent heat of sublimation/vaporization for the vegetation canopy (J kg-1)
+ scalarLatHeatSubVapGround, & ! intent(in): latent heat of sublimation/vaporization for the ground surface (J kg-1)
+ ! input: canopy/ground temperature and saturated vapor pressure
+ canairTemp, & ! intent(in): temperature of the canopy air space (K)
+ canopyTemp, & ! intent(in): canopy temperature (K)
+ groundTemp, & ! intent(in): ground temperature (K)
+ scalarSatVP_CanopyTemp, & ! intent(in): saturation vapor pressure at the temperature of the veg canopy (Pa)
+ scalarSatVP_GroundTemp, & ! intent(in): saturation vapor pressure at the temperature of the ground (Pa)
+ dSVPCanopy_dCanopyTemp, & ! intent(in): derivative in canopy saturation vapor pressure w.r.t. canopy temperature (Pa K-1)
+ dSVPGround_dGroundTemp, & ! intent(in): derivative in ground saturation vapor pressure w.r.t. ground temperature (Pa K-1)
+ ! input: diagnostic variables
+ exposedVAI, & ! intent(in): exposed vegetation area index -- leaf plus stem (m2 m-2)
+ canopyWetFraction, & ! intent(in): trial value for the fraction of canopy that is wet [0-1]
+ dCanopyWetFraction_dWat, & ! intent(in): derivative in the canopy wetted fraction w.r.t. total water content (kg-1 m-2)
+ dCanopyWetFraction_dT, & ! intent(in): derivative in wetted fraction w.r.t. canopy temperature (K-1)
+ scalarCanopySunlitLAI, & ! intent(in): sunlit leaf area (-)
+ scalarCanopyShadedLAI, & ! intent(in): shaded leaf area (-)
+ scalarSoilRelHumidity, & ! intent(in): relative humidity in the soil pores [0-1]
+ scalarSoilResistance, & ! intent(in): resistance from the soil (s m-1)
+ trialLeafResistance, & ! intent(in): mean leaf boundary layer resistance per unit leaf area (s m-1)
+ trialGroundResistance, & ! intent(in): below canopy aerodynamic resistance (s m-1)
+ trialCanopyResistance, & ! intent(in): above canopy aerodynamic resistance (s m-1)
+ scalarStomResistSunlit, & ! intent(in): stomatal resistance for sunlit leaves (s m-1)
+ scalarStomResistShaded, & ! intent(in): stomatal resistance for shaded leaves (s m-1)
+ ! input: derivatives in scalar resistances
+ dGroundResistance_dTGround, & ! intent(in): derivative in ground resistance w.r.t. ground temperature (s m-1 K-1)
+ dGroundResistance_dTCanopy, & ! intent(in): derivative in ground resistance w.r.t. canopy temperature (s m-1 K-1)
+ dGroundResistance_dTCanair, & ! intent(in): derivative in ground resistance w.r.t. canopy air temperature (s m-1 K-1)
+ dCanopyResistance_dTCanopy, & ! intent(in): derivative in canopy resistance w.r.t. canopy temperature (s m-1 K-1)
+ dCanopyResistance_dTCanair, & ! intent(in): derivative in canopy resistance w.r.t. canopy air temperature (s m-1 K-1)
+ ! output: conductances (used to check derivative calculations)
+ scalarLeafConductance, & ! intent(out): leaf conductance (m s-1)
+ scalarCanopyConductance, & ! intent(out): canopy conductance (m s-1)
+ scalarGroundConductanceSH, & ! intent(out): ground conductance for sensible heat (m s-1)
+ scalarGroundConductanceLH, & ! intent(out): ground conductance for latent heat -- includes soil resistance (m s-1)
+ scalarEvapConductance, & ! intent(out): conductance for evaporation (m s-1)
+ scalarTransConductance, & ! intent(out): conductance for transpiration (m s-1)
+ scalarTotalConductanceSH, & ! intent(out): total conductance for sensible heat (m s-1)
+ scalarTotalConductanceLH, & ! intent(out): total conductance for latent heat (m s-1)
+ ! output: canopy air space variables
+ scalarVP_CanopyAir, & ! intent(out): vapor pressure of the canopy air space (Pa)
+ ! output: fluxes from the vegetation canopy
+ scalarSenHeatCanopy, & ! intent(out): sensible heat flux from the canopy to the canopy air space (W m-2)
+ scalarLatHeatCanopyEvap, & ! intent(out): latent heat flux associated with evaporation from the canopy to the canopy air space (W m-2)
+ scalarLatHeatCanopyTrans, & ! intent(out): latent heat flux associated with transpiration from the canopy to the canopy air space (W m-2)
+ ! output: fluxes from non-vegetated surfaces (ground surface below vegetation, bare ground, or snow covered vegetation)
+ scalarSenHeatGround, & ! intent(out): sensible heat flux from ground surface below vegetation, bare ground, or snow covered vegetation (W m-2)
+ scalarLatHeatGround, & ! intent(out): latent heat flux from ground surface below vegetation, bare ground, or snow covered vegetation (W m-2)
+ ! output: total heat fluxes to the atmosphere
+ scalarSenHeatTotal, & ! intent(out): total sensible heat flux to the atmosphere (W m-2)
+ scalarLatHeatTotal, & ! intent(out): total latent heat flux to the atmosphere (W m-2)
+ ! output: net fluxes
+ turbFluxCanair, & ! intent(out): net turbulent heat fluxes at the canopy air space (W m-2)
+ turbFluxCanopy, & ! intent(out): net turbulent heat fluxes at the canopy (W m-2)
+ turbFluxGround, & ! intent(out): net turbulent heat fluxes at the ground surface (W m-2)
+ ! output: energy flux derivatives
+ dTurbFluxCanair_dTCanair, & ! intent(out): derivative in net canopy air space fluxes w.r.t. canopy air temperature (W m-2 K-1)
+ dTurbFluxCanair_dTCanopy, & ! intent(out): derivative in net canopy air space fluxes w.r.t. canopy temperature (W m-2 K-1)
+ dTurbFluxCanair_dTGround, & ! intent(out): derivative in net canopy air space fluxes w.r.t. ground temperature (W m-2 K-1)
+ dTurbFluxCanopy_dTCanair, & ! intent(out): derivative in net canopy turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
+ dTurbFluxCanopy_dTCanopy, & ! intent(out): derivative in net canopy turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
+ dTurbFluxCanopy_dTGround, & ! intent(out): derivative in net canopy turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
+ dTurbFluxGround_dTCanair, & ! intent(out): derivative in net ground turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
+ dTurbFluxGround_dTCanopy, & ! intent(out): derivative in net ground turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
+ dTurbFluxGround_dTGround, & ! intent(out): derivative in net ground turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
+ ! output: liquid flux derivatives (canopy evap)
+ dLatHeatCanopyEvap_dCanWat, & ! intent(out): derivative in latent heat of canopy evaporation w.r.t. canopy total water content (W kg-1)
+ dLatHeatCanopyEvap_dTCanair, & ! intent(out): derivative in latent heat of canopy evaporation w.r.t. canopy air temperature (W m-2 K-1)
+ dLatHeatCanopyEvap_dTCanopy, & ! intent(out): derivative in latent heat of canopy evaporation w.r.t. canopy temperature (W m-2 K-1)
+ dLatHeatCanopyEvap_dTGround, & ! intent(out): derivative in latent heat of canopy evaporation w.r.t. ground temperature (W m-2 K-1)
+ ! output: liquid flux derivatives (ground evap)
+ dLatHeatGroundEvap_dCanWat, & ! intent(out): derivative in latent heat of ground evaporation w.r.t. canopy total water content (J kg-1 s-1)
+ dLatHeatGroundEvap_dTCanair, & ! intent(out): derivative in latent heat of ground evaporation w.r.t. canopy air temperature
+ dLatHeatGroundEvap_dTCanopy, & ! intent(out): derivative in latent heat of ground evaporation w.r.t. canopy temperature
+ dLatHeatGroundEvap_dTGround, & ! intent(out): derivative in latent heat of ground evaporation w.r.t. ground temperature
+ ! output: latent heat flux derivatives (canopy trans)
+ dLatHeatCanopyTrans_dCanWat, & ! intent(out): derivative in the latent heat of canopy transpiration w.r.t. canopy total water (J kg-1 s-1)
+ dLatHeatCanopyTrans_dTCanair, & ! intent(out): derivative in the latent heat of canopy transpiration w.r.t. canopy air temperature
+ dLatHeatCanopyTrans_dTCanopy, & ! intent(out): derivative in the latent heat of canopy transpiration w.r.t. canopy temperature
+ dLatHeatCanopyTrans_dTGround, & ! intent(out): derivative in the latent heat of canopy transpiration w.r.t. ground temperature
+ ! output: cross derivatives
+ dTurbFluxCanair_dCanWat, & ! intent(out): derivative in net canopy air space fluxes w.r.t. canopy total water content (J kg-1 s-1)
+ dTurbFluxCanopy_dCanWat, & ! intent(out): derivative in net canopy turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
+ dTurbFluxGround_dCanWat, & ! intent(out): derivative in net ground turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
+ ! output: error control
+ err,cmessage ) ! intent(out): error control
+ if(err/=0)then; message=trim(message)//trim(cmessage); return; end if
+
+
+ !notUsed_scalarCanopyStabilityCorrection ! stability correction for the canopy (-)
+ !notUsed_scalarGroundStabilityCorrection ! stability correction for the ground surface (-)
+ !notUsed_EddyDiffusCanopyTop ! eddy diffusivity for heat at the top of the canopy (m2 s-1)
+ !notUsed_FrictionVelocity ! friction velocity (m s-1)
+ !notUsed_WindspdCanopyTop ! windspeed at the top of the canopy (m s-1)
+ !notUsed_WindspdCanopyBottom ! windspeed at the height of the bottom of the canopy (m s-1)
+ !trialLeafResistance ! mean leaf boundary layer resistance per unit leaf area (s m-1)
+ !trialGroundResistance ! below canopy aerodynamic resistance (s m-1)
+ !trialCanopyResistance ! above canopy aerodynamic resistance (s m-1)
+
+ ! save perturbed fluxes
+ if(ixDerivMethod == numerical)then
+ select case(itry) ! (select type of perturbation)
+ case(unperturbed)
+ try0 = turbFluxGround
+ exit
+ case(perturbStateCanair)
+ turbFluxCanair_dStateCanair = turbFluxCanair ! turbulent exchange from the canopy air space to the atmosphere (W m-2)
+ turbFluxCanopy_dStateCanair = turbFluxCanopy ! total turbulent heat fluxes from the canopy to the canopy air space (W m-2)
+ turbFluxGround_dStateCanair = turbFluxGround ! total turbulent heat fluxes from the ground to the canopy air space (W m-2)
+ latHeatCanEvap_dStateCanair = scalarLatHeatCanopyEvap ! perturbed value for the latent heat associated with canopy evaporation (W m-2)
+ case(perturbStateCanopy)
+ turbFluxCanair_dStateCanopy = turbFluxCanair ! turbulent exchange from the canopy air space to the atmosphere (W m-2)
+ turbFluxCanopy_dStateCanopy = turbFluxCanopy ! total turbulent heat fluxes from the canopy to the canopy air space (W m-2)
+ turbFluxGround_dStateCanopy = turbFluxGround ! total turbulent heat fluxes from the ground to the canopy air space (W m-2)
+ latHeatCanEvap_dStateCanopy = scalarLatHeatCanopyEvap ! perturbed value for the latent heat associated with canopy evaporation (W m-2)
+ case(perturbStateGround)
+ try1 = turbFluxGround
+ turbFluxCanair_dStateGround = turbFluxCanair ! turbulent exchange from the canopy air space to the atmosphere (W m-2)
+ turbFluxCanopy_dStateGround = turbFluxCanopy ! total turbulent heat fluxes from the canopy to the canopy air space (W m-2)
+ turbFluxGround_dStateGround = turbFluxGround ! total turbulent heat fluxes from the ground to the canopy air space (W m-2)
+ latHeatCanEvap_dStateGround = scalarLatHeatCanopyEvap ! perturbed value for the latent heat associated with canopy evaporation (W m-2)
+ case(perturbStateCanWat)
+ turbFluxCanair_dStateCanWat = turbFluxCanair ! turbulent exchange from the canopy air space to the atmosphere (W m-2)
+ turbFluxCanopy_dStateCanWat = turbFluxCanopy ! total turbulent heat fluxes from the canopy to the canopy air space (W m-2)
+ turbFluxGround_dStateCanWat = turbFluxGround ! total turbulent heat fluxes from the ground to the canopy air space (W m-2)
+ latHeatCanEvap_dStateCanWat = scalarLatHeatCanopyEvap ! perturbed value for the latent heat associated with canopy evaporation (W m-2)
+ case default; err=10; message=trim(message)//"unknown perturbation"; return
+ end select ! (type of perturbation)
+ end if ! (if numerical)
+
+ end do ! (looping through different flux perturbations)
+
+
+ ! compute numerical derivatives
+ if(ixDerivMethod == numerical)then
+ ! derivatives w.r.t. canopy air temperature
+ dTurbFluxCanair_dTCanair = (turbFluxCanair_dStateCanair - turbFluxCanair) / dx ! derivative in net canopy air space fluxes w.r.t. canopy air temperature (W m-2 K-1)
+ dTurbFluxCanopy_dTCanair = (turbFluxCanopy_dStateCanair - turbFluxCanopy) / dx ! derivative in net canopy turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
+ dTurbFluxGround_dTCanair = (turbFluxGround_dStateCanair - turbFluxGround) / dx ! derivative in net ground turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
+ dLatHeatCanopyEvap_dTCanair = (latHeatCanEvap_dStateCanair - scalarLatHeatCanopyEvap) / dx ! derivative in latent heat of canopy evaporation w.r.t. canopy air temperature (W m-2 K-1)
+ ! derivatives w.r.t. canopy temperature
+ dTurbFluxCanair_dTCanopy = (turbFluxCanair_dStateCanopy - turbFluxCanair) / dx ! derivative in net canopy air space fluxes w.r.t. canopy temperature (W m-2 K-1)
+ dTurbFluxCanopy_dTCanopy = (turbFluxCanopy_dStateCanopy - turbFluxCanopy) / dx ! derivative in net canopy turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
+ dTurbFluxGround_dTCanopy = (turbFluxGround_dStateCanopy - turbFluxGround) / dx ! derivative in net ground turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
+ dLatHeatCanopyEvap_dTCanopy = (latHeatCanEvap_dStateCanopy - scalarLatHeatCanopyEvap) / dx ! derivative in latent heat of canopy evaporation w.r.t. canopy temperature (W m-2 K-1)
+ ! derivatives w.r.t. ground temperature
+ dTurbFluxCanair_dTGround = (turbFluxCanair_dStateGround - turbFluxCanair) / dx ! derivative in net canopy air space fluxes w.r.t. ground temperature (W m-2 K-1)
+ dTurbFluxCanopy_dTGround = (turbFluxCanopy_dStateGround - turbFluxCanopy) / dx ! derivative in net canopy turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
+ dTurbFluxGround_dTGround = (turbFluxGround_dStateGround - turbFluxGround) / dx ! derivative in net ground turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
+ dLatHeatCanopyEvap_dTGround = (latHeatCanEvap_dStateGround - scalarLatHeatCanopyEvap) / dx ! derivative in latent heat of canopy evaporation w.r.t. ground temperature (W m-2 K-1)
+ ! derivatives w.r.t. canopy total water content
+ dTurbFluxCanair_dCanWat = (turbFluxCanair_dStateCanWat - turbFluxCanair) / dx ! derivative in net canopy air space fluxes w.r.t. canopy total water content (J kg-1 s-1)
+ dTurbFluxCanopy_dCanWat = (turbFluxCanopy_dStateCanWat - turbFluxCanopy) / dx ! derivative in net canopy turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
+ dTurbFluxGround_dCanWat = (turbFluxGround_dStateCanWat - turbFluxGround) / dx ! derivative in net ground turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
+ dLatHeatCanopyEvap_dCanWat = (latHeatCanEvap_dStateCanWat - scalarLatHeatCanopyEvap) / dx ! derivative in latent heat of canopy evaporation w.r.t. canopy total water content (J kg-1 s-1)
+ end if
+
+
+ ! compute the heat advected with precipitation (W m-2)
+ ! NOTE: fluxes are in kg m-2 s-1, so no need to use density of water/ice here
+ scalarCanopyAdvectiveHeatFlux = -Cp_water*(scalarRainfall - scalarThroughfallRain)*(canopyTempTrial - scalarTwetbulb) + &
+ (-Cp_ice)*(scalarSnowfall - scalarThroughfallSnow)*(canopyTempTrial - scalarTwetbulb)
+ scalarGroundAdvectiveHeatFlux = -Cp_water*scalarThroughfallRain*(groundTempTrial - scalarTwetbulb) + &
+ (-Cp_ice)*scalarThroughfallSnow*(groundTempTrial - scalarTwetbulb)
+
+
+ ! compute the mass flux associated with transpiration and evaporation/sublimation (J m-2 s-1 --> kg m-2 s-1)
+ ! NOTE: remove water from the snow on the ground in preference to removing water from the water in soil pores
+
+ ! (canopy transpiration/sublimation)
+ if(scalarLatHeatSubVapCanopy > LH_vap+verySmall)then ! sublimation
+ scalarCanopyEvaporation = 0._rkind
+ scalarCanopySublimation = scalarLatHeatCanopyEvap/LH_sub
+ if(scalarLatHeatCanopyTrans > 0._rkind)then ! flux directed towards the veg
+ scalarCanopySublimation = scalarCanopySublimation + scalarLatHeatCanopyTrans/LH_sub ! frost
+ scalarCanopyTranspiration = 0._rkind
+ else
+ scalarCanopyTranspiration = scalarLatHeatCanopyTrans/LH_vap ! transpiration is always vapor
+ end if
+ ! (canopy transpiration/evaporation)
+ else ! evaporation
+ scalarCanopyEvaporation = scalarLatHeatCanopyEvap/LH_vap
+ scalarCanopySublimation = 0._rkind
+ if(scalarLatHeatCanopyTrans > 0._rkind)then ! flux directed towards the veg
+ scalarCanopyEvaporation = scalarCanopyEvaporation + scalarLatHeatCanopyTrans/LH_vap
+ scalarCanopyTranspiration = 0._rkind
+ else
+ scalarCanopyTranspiration = scalarLatHeatCanopyTrans/LH_vap
+ end if
+ end if
+ ! (ground evaporation/sublimation)
+ if(scalarLatHeatSubVapGround > LH_vap+verySmall)then ! sublimation
+ ! NOTE: this should only occur when we have formed snow layers, so check
+ if(nSnow == 0)then; err=20; message=trim(message)//'only expect snow sublimation when we have formed some snow layers'; return; end if
+ scalarGroundEvaporation = 0._rkind ! ground evaporation is zero once the snowpack has formed
+ scalarSnowSublimation = scalarLatHeatGround/LH_sub
else
- scalarCanopyTranspiration = scalarLatHeatCanopyTrans/LH_vap
+ ! NOTE: this should only occur when we have no snow layers, so check
+ if(nSnow > 0)then; err=20; message=trim(message)//'only expect ground evaporation when there are no snow layers'; return; end if
+ scalarGroundEvaporation = scalarLatHeatGround/LH_vap
+ scalarSnowSublimation = 0._rkind ! no sublimation from snow if no snow layers have formed
end if
- end if
- ! (ground evaporation/sublimation)
- if(scalarLatHeatSubVapGround > LH_vap+verySmall)then ! sublimation
- ! NOTE: this should only occur when we have formed snow layers, so check
- if(nSnow == 0)then; err=20; message=trim(message)//'only expect snow sublimation when we have formed some snow layers'; return; end if
- scalarGroundEvaporation = 0._rkind ! ground evaporation is zero once the snowpack has formed
- scalarSnowSublimation = scalarLatHeatGround/LH_sub
- else
- ! NOTE: this should only occur when we have no snow layers, so check
- if(nSnow > 0)then; err=20; message=trim(message)//'only expect ground evaporation when there are no snow layers'; return; end if
- scalarGroundEvaporation = scalarLatHeatGround/LH_vap
- scalarSnowSublimation = 0._rkind ! no sublimation from snow if no snow layers have formed
- end if
- !print*, 'scalarSnowSublimation, scalarLatHeatGround = ', scalarSnowSublimation, scalarLatHeatGround
-
- !print*, 'canopyWetFraction, scalarCanopyEvaporation = ', canopyWetFraction, scalarCanopyEvaporation
-
- ! *******************************************************************************************************************************************************************
- ! *******************************************************************************************************************************************************************
- ! ***** AND STITCH EVERYTHING TOGETHER *****************************************************************************************************************************
- ! *******************************************************************************************************************************************************************
- ! *******************************************************************************************************************************************************************
-
- ! compute derived fluxes
- scalarTotalET = scalarGroundEvaporation + scalarCanopyEvaporation + scalarCanopyTranspiration
- scalarNetRadiation = scalarCanopyAbsorbedSolar + scalarLWNetCanopy + scalarGroundAbsorbedSolar + scalarLWNetGround
-
- ! compute net fluxes at the canopy and ground surface
- canairNetFlux = turbFluxCanair
- canopyNetFlux = scalarCanopyAbsorbedSolar + scalarLWNetCanopy + turbFluxCanopy + scalarCanopyAdvectiveHeatFlux
- groundNetFlux = scalarGroundAbsorbedSolar + scalarLWNetGround + turbFluxGround + scalarGroundAdvectiveHeatFlux
- !write(*,'(a,1x,10(e17.10,1x))') 'canopyNetFlux, groundNetFlux, scalarLWNetCanopy, turbFluxCanopy, turbFluxGround, scalarLWNetGround, scalarCanopyAdvectiveHeatFlux = ', &
- ! canopyNetFlux, groundNetFlux, scalarLWNetCanopy, turbFluxCanopy, turbFluxGround, scalarLWNetGround, scalarCanopyAdvectiveHeatFlux
- !write(*,'(a,1x,10(e20.14,1x))') 'groundNetFlux, scalarGroundAbsorbedSolar, scalarLWNetGround, turbFluxGround, scalarGroundAdvectiveHeatFlux = ', &
- ! groundNetFlux, scalarGroundAbsorbedSolar, scalarLWNetGround, turbFluxGround, scalarGroundAdvectiveHeatFlux
-
- ! compute the energy derivatives
- dCanairNetFlux_dCanairTemp = dTurbFluxCanair_dTCanair
- dCanairNetFlux_dCanopyTemp = dTurbFluxCanair_dTCanopy
- dCanairNetFlux_dGroundTemp = dTurbFluxCanair_dTGround
- dCanopyNetFlux_dCanairTemp = dTurbFluxCanopy_dTCanair
- dCanopyNetFlux_dCanopyTemp = dLWNetCanopy_dTCanopy + dTurbFluxCanopy_dTCanopy - Cp_water*(scalarRainfall - scalarThroughfallRain) - Cp_ice*(scalarSnowfall - scalarThroughfallSnow)
- dCanopyNetFlux_dGroundTemp = dLWNetCanopy_dTGround + dTurbFluxCanopy_dTGround
- dGroundNetFlux_dCanairTemp = dTurbFluxGround_dTCanair
- dGroundNetFlux_dCanopyTemp = dLWNetGround_dTCanopy + dTurbFluxGround_dTCanopy
- dGroundNetFlux_dGroundTemp = dLWNetGround_dTGround + dTurbFluxGround_dTGround - Cp_water*scalarThroughfallRain - Cp_ice*scalarThroughfallSnow
-
- ! check if evaporation or sublimation
- if(scalarLatHeatSubVapCanopy < LH_vap+verySmall)then ! evaporation
-
- ! compute the liquid water derivarives
- dCanopyEvaporation_dCanWat = dLatHeatCanopyEvap_dCanWat/LH_vap ! (s-1)
- dCanopyEvaporation_dTCanair = dLatHeatCanopyEvap_dTCanair/LH_vap ! (kg m-2 s-1 K-1)
- dCanopyEvaporation_dTCanopy = dLatHeatCanopyEvap_dTCanopy/LH_vap ! (kg m-2 s-1 K-1)
- dCanopyEvaporation_dTGround = dLatHeatCanopyEvap_dTGround/LH_vap ! (kg m-2 s-1 K-1)
-
- ! sublimation
- else
- dCanopyEvaporation_dCanWat = 0._rkind ! (s-1)
- dCanopyEvaporation_dTCanair = 0._rkind ! (kg m-2 s-1 K-1)
- dCanopyEvaporation_dTCanopy = 0._rkind ! (kg m-2 s-1 K-1)
- dCanopyEvaporation_dTGround = 0._rkind ! (kg m-2 s-1 K-1)
- end if
-
- ! transpiration
- if(scalarLatHeatCanopyTrans > 0._rkind)then ! flux directed towards the veg
- dCanopyTrans_dCanWat = 0._rkind
- dCanopyTrans_dTCanair= 0._rkind
- dCanopyTrans_dTCanopy= 0._rkind
- dCanopyTrans_dTGround= 0._rkind
+
+
+ ! *******************************************************************************************************************************************************************
+ ! *******************************************************************************************************************************************************************
+ ! ***** AND STITCH EVERYTHING TOGETHER *****************************************************************************************************************************
+ ! *******************************************************************************************************************************************************************
+ ! *******************************************************************************************************************************************************************
+
+ ! compute derived fluxes
+ scalarTotalET = scalarGroundEvaporation + scalarCanopyEvaporation + scalarCanopyTranspiration
+ scalarNetRadiation = scalarCanopyAbsorbedSolar + scalarLWNetCanopy + scalarGroundAbsorbedSolar + scalarLWNetGround
+
+ ! compute net fluxes at the canopy and ground surface
+ canairNetFlux = turbFluxCanair
+ canopyNetFlux = scalarCanopyAbsorbedSolar + scalarLWNetCanopy + turbFluxCanopy + scalarCanopyAdvectiveHeatFlux
+ groundNetFlux = scalarGroundAbsorbedSolar + scalarLWNetGround + turbFluxGround + scalarGroundAdvectiveHeatFlux
+
+ ! compute the energy derivatives
+ dCanairNetFlux_dCanairTemp = dTurbFluxCanair_dTCanair
+ dCanairNetFlux_dCanopyTemp = dTurbFluxCanair_dTCanopy
+ dCanairNetFlux_dGroundTemp = dTurbFluxCanair_dTGround
+ dCanopyNetFlux_dCanairTemp = dTurbFluxCanopy_dTCanair
+ dCanopyNetFlux_dCanopyTemp = dLWNetCanopy_dTCanopy + dTurbFluxCanopy_dTCanopy - Cp_water*(scalarRainfall - scalarThroughfallRain) - Cp_ice*(scalarSnowfall - scalarThroughfallSnow)
+ dCanopyNetFlux_dGroundTemp = dLWNetCanopy_dTGround + dTurbFluxCanopy_dTGround
+ dGroundNetFlux_dCanairTemp = dTurbFluxGround_dTCanair
+ dGroundNetFlux_dCanopyTemp = dLWNetGround_dTCanopy + dTurbFluxGround_dTCanopy
+ dGroundNetFlux_dGroundTemp = dLWNetGround_dTGround + dTurbFluxGround_dTGround - Cp_water*scalarThroughfallRain - Cp_ice*scalarThroughfallSnow
+
+ ! check if evaporation or sublimation
+ if(scalarLatHeatSubVapCanopy < LH_vap+verySmall)then ! evaporation
+
+ ! compute the liquid water derivarives
+ dCanopyEvaporation_dCanWat = dLatHeatCanopyEvap_dCanWat/LH_vap ! (s-1)
+ dCanopyEvaporation_dTCanair = dLatHeatCanopyEvap_dTCanair/LH_vap ! (kg m-2 s-1 K-1)
+ dCanopyEvaporation_dTCanopy = dLatHeatCanopyEvap_dTCanopy/LH_vap ! (kg m-2 s-1 K-1)
+ dCanopyEvaporation_dTGround = dLatHeatCanopyEvap_dTGround/LH_vap ! (kg m-2 s-1 K-1)
+
+ ! sublimation
else
- dCanopyTrans_dCanWat= dLatHeatCanopyTrans_dCanWat/LH_vap ! transpiration is always vapor
- dCanopyTrans_dTCanair= dLatHeatCanopyTrans_dTCanair/LH_vap
- dCanopyTrans_dTCanopy= dLatHeatCanopyTrans_dTCanopy/LH_vap
- dCanopyTrans_dTGround= dLatHeatCanopyTrans_dTGround/LH_vap
+ dCanopyEvaporation_dCanWat = 0._rkind ! (s-1)
+ dCanopyEvaporation_dTCanair = 0._rkind ! (kg m-2 s-1 K-1)
+ dCanopyEvaporation_dTCanopy = 0._rkind ! (kg m-2 s-1 K-1)
+ dCanopyEvaporation_dTGround = 0._rkind ! (kg m-2 s-1 K-1)
end if
-
-
- ! compute the liquid water derivarives (ground evap)
- dGroundEvaporation_dCanWat = dLatHeatGroundEvap_dCanWat/LH_vap ! (s-1)
- dGroundEvaporation_dTCanair = dLatHeatGroundEvap_dTCanair/LH_vap ! (kg m-2 s-1 K-1)
- dGroundEvaporation_dTCanopy = dLatHeatGroundEvap_dTCanopy/LH_vap ! (kg m-2 s-1 K-1)
- dGroundEvaporation_dTGround = dLatHeatGroundEvap_dTGround/LH_vap ! (kg m-2 s-1 K-1)
-
- ! compute the cross derivative terms (only related to turbulent fluxes; specifically canopy evaporation and transpiration)
- dCanopyNetFlux_dCanWat = dTurbFluxCanopy_dCanWat ! derivative in net canopy fluxes w.r.t. canopy total water content (J kg-1 s-1)
- dGroundNetFlux_dCanWat = dTurbFluxGround_dCanWat ! derivative in net ground fluxes w.r.t. canopy total water content (J kg-1 s-1)
-
- !print*, (ixDerivMethod == numerical)
- !print*, 'dGroundNetFlux_dCanairTemp = ', dGroundNetFlux_dCanairTemp
- !print*, 'dCanopyNetFlux_dCanopyTemp = ', dCanopyNetFlux_dCanopyTemp
- !print*, 'dGroundNetFlux_dCanopyTemp = ', dGroundNetFlux_dCanopyTemp
- !print*, 'dCanopyNetFlux_dGroundTemp = ', dCanopyNetFlux_dGroundTemp
- !print*, 'dGroundNetFlux_dGroundTemp = ', dGroundNetFlux_dGroundTemp
- !print*, 'dLWNetCanopy_dTGround = ', dLWNetCanopy_dTGround
- !print*, 'dTurbFluxCanopy_dTGround = ', dTurbFluxCanopy_dTGround
- !pause
-
+
+ ! transpiration
+ if(scalarLatHeatCanopyTrans > 0._rkind)then ! flux directed towards the veg
+ dCanopyTrans_dCanWat = 0._rkind
+ dCanopyTrans_dTCanair= 0._rkind
+ dCanopyTrans_dTCanopy= 0._rkind
+ dCanopyTrans_dTGround= 0._rkind
+ else
+ dCanopyTrans_dCanWat= dLatHeatCanopyTrans_dCanWat/LH_vap ! transpiration is always vapor
+ dCanopyTrans_dTCanair= dLatHeatCanopyTrans_dTCanair/LH_vap
+ dCanopyTrans_dTCanopy= dLatHeatCanopyTrans_dTCanopy/LH_vap
+ dCanopyTrans_dTGround= dLatHeatCanopyTrans_dTGround/LH_vap
+ end if
+
+
+ ! compute the liquid water derivarives (ground evap)
+ dGroundEvaporation_dCanWat = dLatHeatGroundEvap_dCanWat/LH_vap ! (s-1)
+ dGroundEvaporation_dTCanair = dLatHeatGroundEvap_dTCanair/LH_vap ! (kg m-2 s-1 K-1)
+ dGroundEvaporation_dTCanopy = dLatHeatGroundEvap_dTCanopy/LH_vap ! (kg m-2 s-1 K-1)
+ dGroundEvaporation_dTGround = dLatHeatGroundEvap_dTGround/LH_vap ! (kg m-2 s-1 K-1)
+
+ ! compute the cross derivative terms (only related to turbulent fluxes; specifically canopy evaporation and transpiration)
+ dCanopyNetFlux_dCanWat = dTurbFluxCanopy_dCanWat ! derivative in net canopy fluxes w.r.t. canopy total water content (J kg-1 s-1)
+ dGroundNetFlux_dCanWat = dTurbFluxGround_dCanWat ! derivative in net ground fluxes w.r.t. canopy total water content (J kg-1 s-1)
+
! * check
case default; err=10; message=trim(message)//'unable to identify upper boundary condition for thermodynamics'; return
-
- ! end case statement
- end select ! upper boundary condition for thermodynamics
-
- ! return liquid fluxes (needed for coupling)
- returnCanopyTranspiration = scalarCanopyTranspiration ! canopy transpiration (kg m-2 s-1)
- returnCanopyEvaporation = scalarCanopyEvaporation ! canopy evaporation/condensation (kg m-2 s-1)
- returnGroundEvaporation = scalarGroundEvaporation ! ground evaporation/condensation -- below canopy or non-vegetated (kg m-2 s-1)
-
- ! end associations
- end associate
-
-
- end subroutine vegNrgFlux
-
-
- ! *******************************************************************************************************
- ! public subroutine wettedFrac: compute wetted fraction of the canopy
- ! *******************************************************************************************************
- subroutine wettedFrac(&
- ! input
- deriv, & ! flag to denote if derivative is desired
- derNum, & ! flag to denote that numerical derivatives are required (otherwise, analytical derivatives are calculated)
- frozen, & ! flag to denote if the canopy is frozen
- dLiq_dT, & ! derivative in canopy liquid w.r.t. canopy temperature (kg m-2 K-1)
- fracLiq, & ! fraction of liquid water on the canopy (-)
- canopyLiq, & ! canopy liquid water (kg m-2)
- canopyIce, & ! canopy ice (kg m-2)
- canopyLiqMax, & ! maximum canopy liquid water (kg m-2)
- canopyIceMax, & ! maximum canopy ice content (kg m-2)
- canopyWettingFactor, & ! maximum wetted fraction of the canopy (-)
- canopyWettingExp, & ! exponent in canopy wetting function (-)
- ! output
- canopyWetFraction, & ! canopy wetted fraction (-)
- dCanopyWetFraction_dWat,& ! derivative in wetted fraction w.r.t. canopy total water (kg-1 m2)
- dCanopyWetFraction_dT, & ! derivative in wetted fraction w.r.t. canopy temperature (K-1)
- err,message) ! error control
- implicit none
- ! input
- logical(lgt),intent(in) :: deriv ! flag to denote if derivative is desired
- logical(lgt),intent(in) :: derNum ! flag to denote that numerical derivatives are required (otherwise, analytical derivatives are calculated)
- logical(lgt),intent(in) :: frozen ! flag to denote if the canopy is frozen
- real(rkind),intent(in) :: dLiq_dT ! derivative in canopy liquid w.r.t. canopy temperature (kg m-2 K-1)
- real(rkind),intent(in) :: fracLiq ! fraction of liquid water on the canopy (-)
- real(rkind),intent(in) :: canopyLiq ! canopy liquid water (kg m-2)
- real(rkind),intent(in) :: canopyIce ! canopy ice (kg m-2)
- real(rkind),intent(in) :: canopyLiqMax ! maximum canopy liquid water (kg m-2)
- real(rkind),intent(in) :: canopyIceMax ! maximum canopy ice content (kg m-2)
- real(rkind),intent(in) :: canopyWettingFactor ! maximum wetted fraction of the canopy (-)
- real(rkind),intent(in) :: canopyWettingExp ! exponent in canopy wetting function (-)
- ! output
- real(rkind),intent(out) :: canopyWetFraction ! canopy wetted fraction (-)
- real(rkind),intent(out) :: dCanopyWetFraction_dWat ! derivative in wetted fraction w.r.t. canopy total water (kg-1 m2)
- real(rkind),intent(out) :: dCanopyWetFraction_dT ! derivative in wetted fraction w.r.t. canopy temperature (K-1)
- ! output: error control
- integer(i4b),intent(out) :: err ! error code
- character(*),intent(out) :: message ! error message
- ! local variables
- logical(lgt),parameter :: smoothing=.true. ! flag to denote that smoothing is required
- real(rkind) :: canopyWetFractionPert ! canopy wetted fraction after state perturbations (-)
- real(rkind) :: canopyWetFractionDeriv ! derivative in wetted fraction w.r.t. canopy liquid water (kg-1 m2)
- ! -----------------------------------------------------------------------------------------------------------------------------------------------
- ! initialize error control
- err=0; message='wettedFrac/'
-
- ! compute case where the canopy is frozen
- if(frozen)then
- ! compute fraction of liquid water on the canopy
- call wetFraction((deriv .and. .not.derNum),smoothing,canopyIce,canopyIceMax,canopyWettingFactor,canopyWettingExp,canopyWetFraction,canopyWetFractionDeriv)
- ! compute numerical derivative, if derivative is desired
- if(deriv.and.derNum)then
- call wetFraction((deriv .and. .not.derNum),smoothing,canopyIce+dx,canopyIceMax,canopyWettingFactor,canopyWettingExp,canopyWetFractionPert,canopyWetFractionDeriv)
- canopyWetFractionDeriv = (canopyWetFractionPert - canopyWetFraction)/dx
- end if
- ! scale derivative by the fraction of water
- ! NOTE: dIce/dWat = (1._rkind - fracLiq), hence dWet/dWat = dIce/dWat . dWet/dLiq
- dCanopyWetFraction_dWat = canopyWetFractionDeriv*(1._rkind - fracLiq)
- dCanopyWetFraction_dT = -canopyWetFractionDeriv*dLiq_dT ! NOTE: dIce/dT = -dLiq/dT
- return
- end if
-
- ! compute fraction of liquid water on the canopy
- ! NOTE: if(.not.deriv) canopyWetFractionDeriv = 0._rkind
- call wetFraction((deriv .and. .not.derNum),smoothing,canopyLiq,canopyLiqMax,canopyWettingFactor,canopyWettingExp,canopyWetFraction,canopyWetFractionDeriv)
-
- ! compute numerical derivative
- if(deriv.and.derNum)then
- call wetFraction((deriv .and. .not.derNum),smoothing,canopyLiq+dx,canopyLiqMax,canopyWettingFactor,canopyWettingExp,canopyWetFractionPert,canopyWetFractionDeriv)
+
+ ! end case statement
+ end select ! upper boundary condition for thermodynamics
+
+ ! return liquid fluxes (needed for coupling)
+ returnCanopyTranspiration = scalarCanopyTranspiration ! canopy transpiration (kg m-2 s-1)
+ returnCanopyEvaporation = scalarCanopyEvaporation ! canopy evaporation/condensation (kg m-2 s-1)
+ returnGroundEvaporation = scalarGroundEvaporation ! ground evaporation/condensation -- below canopy or non-vegetated (kg m-2 s-1)
+
+ ! end associations
+ end associate
+
+end subroutine vegNrgFlux
+
+
+! *******************************************************************************************************
+! public subroutine wettedFrac: compute wetted fraction of the canopy
+! *******************************************************************************************************
+subroutine wettedFrac(&
+ ! input
+ deriv, & ! flag to denote if derivative is desired
+ derNum, & ! flag to denote that numerical derivatives are required (otherwise, analytical derivatives are calculated)
+ frozen, & ! flag to denote if the canopy is frozen
+ dLiq_dT, & ! derivative in canopy liquid w.r.t. canopy temperature (kg m-2 K-1)
+ fracLiq, & ! fraction of liquid water on the canopy (-)
+ canopyLiq, & ! canopy liquid water (kg m-2)
+ canopyIce, & ! canopy ice (kg m-2)
+ canopyLiqMax, & ! maximum canopy liquid water (kg m-2)
+ canopyIceMax, & ! maximum canopy ice content (kg m-2)
+ canopyWettingFactor, & ! maximum wetted fraction of the canopy (-)
+ canopyWettingExp, & ! exponent in canopy wetting function (-)
+ ! output
+ canopyWetFraction, & ! canopy wetted fraction (-)
+ dCanopyWetFraction_dWat,& ! derivative in wetted fraction w.r.t. canopy total water (kg-1 m2)
+ dCanopyWetFraction_dT, & ! derivative in wetted fraction w.r.t. canopy temperature (K-1)
+ err,message) ! error control
+ implicit none
+ ! input
+ logical(lgt),intent(in) :: deriv ! flag to denote if derivative is desired
+ logical(lgt),intent(in) :: derNum ! flag to denote that numerical derivatives are required (otherwise, analytical derivatives are calculated)
+ logical(lgt),intent(in) :: frozen ! flag to denote if the canopy is frozen
+ real(rkind),intent(in) :: dLiq_dT ! derivative in canopy liquid w.r.t. canopy temperature (kg m-2 K-1)
+ real(rkind),intent(in) :: fracLiq ! fraction of liquid water on the canopy (-)
+ real(rkind),intent(in) :: canopyLiq ! canopy liquid water (kg m-2)
+ real(rkind),intent(in) :: canopyIce ! canopy ice (kg m-2)
+ real(rkind),intent(in) :: canopyLiqMax ! maximum canopy liquid water (kg m-2)
+ real(rkind),intent(in) :: canopyIceMax ! maximum canopy ice content (kg m-2)
+ real(rkind),intent(in) :: canopyWettingFactor ! maximum wetted fraction of the canopy (-)
+ real(rkind),intent(in) :: canopyWettingExp ! exponent in canopy wetting function (-)
+ ! output
+ real(rkind),intent(out) :: canopyWetFraction ! canopy wetted fraction (-)
+ real(rkind),intent(out) :: dCanopyWetFraction_dWat ! derivative in wetted fraction w.r.t. canopy total water (kg-1 m2)
+ real(rkind),intent(out) :: dCanopyWetFraction_dT ! derivative in wetted fraction w.r.t. canopy temperature (K-1)
+ ! output: error control
+ integer(i4b),intent(out) :: err ! error code
+ character(*),intent(out) :: message ! error message
+ ! local variables
+ logical(lgt),parameter :: smoothing=.true. ! flag to denote that smoothing is required
+ real(rkind) :: canopyWetFractionPert ! canopy wetted fraction after state perturbations (-)
+ real(rkind) :: canopyWetFractionDeriv ! derivative in wetted fraction w.r.t. canopy liquid water (kg-1 m2)
+ ! -----------------------------------------------------------------------------------------------------------------------------------------------
+ ! initialize error control
+ err=0; message='wettedFrac/'
+
+ ! compute case where the canopy is frozen
+ if(frozen)then
+ ! compute fraction of liquid water on the canopy
+ call wetFraction((deriv .and. .not.derNum),smoothing,canopyIce,canopyIceMax,canopyWettingFactor,canopyWettingExp,canopyWetFraction,canopyWetFractionDeriv)
+ ! compute numerical derivative, if derivative is desired
+ if(deriv.and.derNum)then
+ call wetFraction((deriv .and. .not.derNum),smoothing,canopyIce+dx,canopyIceMax,canopyWettingFactor,canopyWettingExp,canopyWetFractionPert,canopyWetFractionDeriv)
canopyWetFractionDeriv = (canopyWetFractionPert - canopyWetFraction)/dx
- end if
-
- ! scale derivative by the fraction of water
- ! NOTE: dLiq/dWat = fracLiq, hence dWet/dWat = dLiq/dWat . dWet/dLiq
- dCanopyWetFraction_dWat = canopyWetFractionDeriv*fracLiq
- dCanopyWetFraction_dT = canopyWetFractionDeriv*dLiq_dT
-
- ! test
- !write(*,'(a,1x,2(L1,1x),10(f20.10,1x))') 'deriv, derNum, canopyWetFraction, canopyWetFractionDeriv = ', deriv, derNum, canopyWetFraction, canopyWetFractionDeriv
- !if(deriv) pause 'testing canopy wet fraction'
-
- end subroutine wettedFrac
-
-
- ! *******************************************************************************************************
- ! private subroutine wetFraction: compute fraction of canopy covered with liquid water
- ! *******************************************************************************************************
- subroutine wetFraction(derDesire,smoothing,canopyLiq,canopyMax,canopyWettingFactor,canopyWettingExp,canopyWetFraction,canopyWetFractionDeriv)
- implicit none
- ! dummy variables
- logical(lgt),intent(in) :: derDesire ! flag to denote if analytical derivatives are desired
- logical(lgt),intent(in) :: smoothing ! flag to denote if smoothing is required
- real(rkind),intent(in) :: canopyLiq ! liquid water content (kg m-2)
- real(rkind),intent(in) :: canopyMax ! liquid water content (kg m-2)
- real(rkind),intent(in) :: canopyWettingFactor ! maximum wetted fraction of the canopy (-)
- real(rkind),intent(in) :: canopyWettingExp ! exponent in canopy wetting function (-)
-
- real(rkind),intent(out) :: canopyWetFraction ! canopy wetted fraction (-)
- real(rkind),intent(out) :: canopyWetFractionDeriv ! derivative in wetted fraction w.r.t. canopy liquid water (kg-1 m2)
- ! local variables
- real(rkind) :: relativeCanopyWater ! water stored on vegetation canopy, expressed as a fraction of maximum storage (-)
- real(rkind) :: rawCanopyWetFraction ! initial value of the canopy wet fraction (before smoothing)
- real(rkind) :: rawWetFractionDeriv ! derivative in canopy wet fraction w.r.t. storage (kg-1 m2)
- real(rkind) :: smoothFunc ! smoothing function used to improve numerical stability at times with limited water storage (-)
- real(rkind) :: smoothFuncDeriv ! derivative in the smoothing function w.r.t.canopy storage (kg-1 m2)
- real(rkind) :: verySmall=epsilon(1._rkind) ! a very small number
- ! --------------------------------------------------------------------------------------------------------------
-
- ! compute relative canopy water
- relativeCanopyWater = canopyLiq/canopyMax
- !write(*,'(a,1x,e20.10,1x,2(f20.10,1x))') 'relativeCanopyWater, canopyLiq, canopyMax = ', relativeCanopyWater, canopyLiq, canopyMax
-
- ! compute an initial value of the canopy wet fraction
- ! - canopy below value where canopy is 100% wet
- if(relativeCanopyWater < 1._rkind)then
- rawCanopyWetFraction = canopyWettingFactor*(relativeCanopyWater**canopyWettingExp)
- if(derDesire .and. relativeCanopyWater>verySmall)then
- rawWetFractionDeriv = (canopyWettingFactor*canopyWettingExp/canopyMax)*relativeCanopyWater**(canopyWettingExp - 1._rkind)
- else
- rawWetFractionDeriv = 0._rkind
- end if
-
- ! - canopy is at capacity (canopyWettingFactor)
- else
- rawCanopyWetFraction = canopyWettingFactor
- rawWetFractionDeriv = 0._rkind
- end if
-
- ! smooth canopy wetted fraction
- if(smoothing)then
- call logisticSmoother(derDesire,canopyLiq,smoothFunc,smoothFuncDeriv)
- canopyWetFraction = rawCanopyWetFraction*smoothFunc ! logistic smoother
- else
- canopyWetFraction = rawCanopyWetFraction
- canopyWetFractionDeriv = rawWetFractionDeriv
- end if
-
- ! compute derivative (product rule)
- if(derDesire .and. smoothing)then ! NOTE: raw derivative is used if not smoothing
- canopyWetFractionDeriv = rawWetFractionDeriv*smoothFunc + rawCanopyWetFraction*smoothFuncDeriv
- else
- canopyWetFractionDeriv = 0._rkind
- end if
-
- end subroutine wetFraction
-
-
- ! *******************************************************************************************************
- ! private subroutine logisticSmoother: compute the smoothing function
- ! *******************************************************************************************************
- subroutine logisticSmoother(derDesire,canopyLiq,smoothFunc,smoothFuncDeriv)
- implicit none
- ! dummy variables
- logical(lgt),intent(in) :: derDesire ! flag to denote if analytical derivatives are desired
- real(rkind),intent(in) :: canopyLiq ! liquid water content (kg m-2)
- real(rkind),intent(out) :: smoothFunc ! smoothing function (-)
- real(rkind),intent(out) :: smoothFuncDeriv ! derivative in smoothing function (kg-1 m-2)
- ! local variables
- real(rkind) :: xArg ! argument used in the smoothing function (-)
- real(rkind) :: expX ! exp(-xArg) -- used multiple times
- real(rkind),parameter :: smoothThresh=0.01_rkind ! mid-point of the smoothing function (kg m-2)
- real(rkind),parameter :: smoothScale=0.001_rkind ! scaling factor for the smoothing function (kg m-2)
- real(rkind),parameter :: xLimit=50._rkind ! don't compute exponents for > xLimit
- ! --------------------------------------------------------------------------------------------------------------
- ! compute argument in the smoothing function
- xArg = (canopyLiq - smoothThresh)/smoothScale
-
- ! only compute smoothing function for small exponents
- if(xArg > -xLimit .and. xArg < xLimit)then ! avoid huge exponents
- expX = exp(-xarg) ! (also used in the derivative)
- smoothFunc = 1._rkind / (1._rkind + expX) ! (logistic smoother)
- if(derDesire)then
- smoothFuncDeriv = expX / (smoothScale * (1._rkind + expX)**2._rkind) ! (derivative in the smoothing function)
- else
- smoothFuncDeriv = 0._rkind
- end if
-
- ! outside limits: special case of smooth exponents
- else
- if(xArg < 0._rkind)then; smoothFunc = 0._rkind ! xArg < -xLimit
- else; smoothFunc = 1._rkind ! xArg > xLimit
- end if
+ end if
+ ! scale derivative by the fraction of water
+ ! NOTE: dIce/dWat = (1._rkind - fracLiq), hence dWet/dWat = dIce/dWat . dWet/dLiq
+ dCanopyWetFraction_dWat = canopyWetFractionDeriv*(1._rkind - fracLiq)
+ dCanopyWetFraction_dT = -canopyWetFractionDeriv*dLiq_dT ! NOTE: dIce/dT = -dLiq/dT
+ return
+ end if
+
+ ! compute fraction of liquid water on the canopy
+ ! NOTE: if(.not.deriv) canopyWetFractionDeriv = 0._rkind
+ call wetFraction((deriv .and. .not.derNum),smoothing,canopyLiq,canopyLiqMax,canopyWettingFactor,canopyWettingExp,canopyWetFraction,canopyWetFractionDeriv)
+
+ ! compute numerical derivative
+ if(deriv.and.derNum)then
+ call wetFraction((deriv .and. .not.derNum),smoothing,canopyLiq+dx,canopyLiqMax,canopyWettingFactor,canopyWettingExp,canopyWetFractionPert,canopyWetFractionDeriv)
+ canopyWetFractionDeriv = (canopyWetFractionPert - canopyWetFraction)/dx
+ end if
+
+ ! scale derivative by the fraction of water
+ ! NOTE: dLiq/dWat = fracLiq, hence dWet/dWat = dLiq/dWat . dWet/dLiq
+ dCanopyWetFraction_dWat = canopyWetFractionDeriv*fracLiq
+ dCanopyWetFraction_dT = canopyWetFractionDeriv*dLiq_dT
+
+end subroutine wettedFrac
+
+
+! *******************************************************************************************************
+! private subroutine wetFraction: compute fraction of canopy covered with liquid water
+! *******************************************************************************************************
+subroutine wetFraction(derDesire,smoothing,canopyLiq,canopyMax,canopyWettingFactor,canopyWettingExp,canopyWetFraction,canopyWetFractionDeriv)
+ implicit none
+ ! dummy variables
+ logical(lgt),intent(in) :: derDesire ! flag to denote if analytical derivatives are desired
+ logical(lgt),intent(in) :: smoothing ! flag to denote if smoothing is required
+ real(rkind),intent(in) :: canopyLiq ! liquid water content (kg m-2)
+ real(rkind),intent(in) :: canopyMax ! liquid water content (kg m-2)
+ real(rkind),intent(in) :: canopyWettingFactor ! maximum wetted fraction of the canopy (-)
+ real(rkind),intent(in) :: canopyWettingExp ! exponent in canopy wetting function (-)
+
+ real(rkind),intent(out) :: canopyWetFraction ! canopy wetted fraction (-)
+ real(rkind),intent(out) :: canopyWetFractionDeriv ! derivative in wetted fraction w.r.t. canopy liquid water (kg-1 m2)
+ ! local variables
+ real(rkind) :: relativeCanopyWater ! water stored on vegetation canopy, expressed as a fraction of maximum storage (-)
+ real(rkind) :: rawCanopyWetFraction ! initial value of the canopy wet fraction (before smoothing)
+ real(rkind) :: rawWetFractionDeriv ! derivative in canopy wet fraction w.r.t. storage (kg-1 m2)
+ real(rkind) :: smoothFunc ! smoothing function used to improve numerical stability at times with limited water storage (-)
+ real(rkind) :: smoothFuncDeriv ! derivative in the smoothing function w.r.t.canopy storage (kg-1 m2)
+ real(rkind) :: verySmall=epsilon(1._rkind) ! a very small number
+ ! --------------------------------------------------------------------------------------------------------------
+
+ ! compute relative canopy water
+ relativeCanopyWater = canopyLiq/canopyMax
+
+ ! compute an initial value of the canopy wet fraction
+ ! - canopy below value where canopy is 100% wet
+ if(relativeCanopyWater < 1._rkind)then
+ rawCanopyWetFraction = canopyWettingFactor*(relativeCanopyWater**canopyWettingExp)
+ if(derDesire .and. relativeCanopyWater>verySmall)then
+ rawWetFractionDeriv = (canopyWettingFactor*canopyWettingExp/canopyMax)*relativeCanopyWater**(canopyWettingExp - 1._rkind)
+ else
+ rawWetFractionDeriv = 0._rkind
+ end if
+
+ ! - canopy is at capacity (canopyWettingFactor)
+ else
+ rawCanopyWetFraction = canopyWettingFactor
+ rawWetFractionDeriv = 0._rkind
+ end if
+
+ ! smooth canopy wetted fraction
+ if(smoothing)then
+ call logisticSmoother(derDesire,canopyLiq,smoothFunc,smoothFuncDeriv)
+ canopyWetFraction = rawCanopyWetFraction*smoothFunc ! logistic smoother
+ else
+ canopyWetFraction = rawCanopyWetFraction
+ canopyWetFractionDeriv = rawWetFractionDeriv
+ end if
+
+ ! compute derivative (product rule)
+ if(derDesire .and. smoothing)then ! NOTE: raw derivative is used if not smoothing
+ canopyWetFractionDeriv = rawWetFractionDeriv*smoothFunc + rawCanopyWetFraction*smoothFuncDeriv
+ else
+ canopyWetFractionDeriv = 0._rkind
+ end if
+
+end subroutine wetFraction
+
+
+! *******************************************************************************************************
+! private subroutine logisticSmoother: compute the smoothing function
+! *******************************************************************************************************
+subroutine logisticSmoother(derDesire,canopyLiq,smoothFunc,smoothFuncDeriv)
+ implicit none
+ ! dummy variables
+ logical(lgt),intent(in) :: derDesire ! flag to denote if analytical derivatives are desired
+ real(rkind),intent(in) :: canopyLiq ! liquid water content (kg m-2)
+ real(rkind),intent(out) :: smoothFunc ! smoothing function (-)
+ real(rkind),intent(out) :: smoothFuncDeriv ! derivative in smoothing function (kg-1 m-2)
+ ! local variables
+ real(rkind) :: xArg ! argument used in the smoothing function (-)
+ real(rkind) :: expX ! exp(-xArg) -- used multiple times
+ real(rkind),parameter :: smoothThresh=0.01_rkind ! mid-point of the smoothing function (kg m-2)
+ real(rkind),parameter :: smoothScale=0.001_rkind ! scaling factor for the smoothing function (kg m-2)
+ real(rkind),parameter :: xLimit=50._rkind ! don't compute exponents for > xLimit
+ ! --------------------------------------------------------------------------------------------------------------
+ ! compute argument in the smoothing function
+ xArg = (canopyLiq - smoothThresh)/smoothScale
+
+ ! only compute smoothing function for small exponents
+ if(xArg > -xLimit .and. xArg < xLimit)then ! avoid huge exponents
+ expX = exp(-xarg) ! (also used in the derivative)
+ smoothFunc = 1._rkind / (1._rkind + expX) ! (logistic smoother)
+ if(derDesire)then
+ smoothFuncDeriv = expX / (smoothScale * (1._rkind + expX)**2._rkind) ! (derivative in the smoothing function)
+ else
smoothFuncDeriv = 0._rkind
- end if ! check for huge exponents
-
- end subroutine logisticSmoother
- ! --------------------------------------------------------------------------------------------------------------
-
-
- ! *******************************************************************************************************
- ! private subroutine longwaveBal: compute longwave radiation balance at the canopy and ground surface
- ! *******************************************************************************************************
- subroutine longwaveBal(&
- ! input: model control
- ixDerivMethod, & ! intent(in): choice of method used to compute derivative (analytical or numerical)
- computeVegFlux, & ! intent(in): flag to compute fluxes over vegetati
- requireLWBal, & ! intent(in): flag to indicate if we need longwave to be balanced
- ! input: canopy and ground temperature
- canopyTemp, & ! intent(in): canopy temperature (K)
- groundTemp, & ! intent(in): ground temperature (K)
- ! input: canopy and ground emissivity
- emc, & ! intent(in): canopy emissivity (-)
- emg, & ! intent(in): ground emissivity (-)
- ! input: forcing
- LWRadUbound, & ! intent(in): downwelling longwave radiation at the upper boundary (W m-2)
- ! output: sources
- LWRadCanopy, & ! intent(out): longwave radiation emitted from the canopy (W m-2)
- LWRadGround, & ! intent(out): longwave radiation emitted at the ground surface (W m-2)
- ! output: individual fluxes
- LWRadUbound2Canopy, & ! intent(out): downward atmospheric longwave radiation absorbed by the canopy (W m-2)
- LWRadUbound2Ground, & ! intent(out): downward atmospheric longwave radiation absorbed by the ground (W m-2)
- LWRadUbound2Ubound, & ! intent(out): atmospheric radiation reflected by the ground and lost thru upper boundary (W m-2)
- LWRadCanopy2Ubound, & ! intent(out): longwave radiation emitted from canopy lost thru upper boundary (W m-2)
- LWRadCanopy2Ground, & ! intent(out): longwave radiation emitted from canopy absorbed by the ground (W m-2)
- LWRadCanopy2Canopy, & ! intent(out): canopy longwave reflected from ground and absorbed by the canopy (W m-2)
- LWRadGround2Ubound, & ! intent(out): longwave radiation emitted from ground lost thru upper boundary (W m-2)
- LWRadGround2Canopy, & ! intent(out): longwave radiation emitted from ground and absorbed by the canopy (W m-2)
- ! output: net fluxes
- LWNetCanopy, & ! intent(out): net longwave radiation at the canopy (W m-2)
- LWNetGround, & ! intent(out): net longwave radiation at the ground surface (W m-2)
- LWNetUbound, & ! intent(out): net longwave radiation at the upper boundary (W m-2)
- ! output: flux derivatives
- dLWNetCanopy_dTCanopy, & ! intent(out): derivative in net canopy radiation w.r.t. canopy temperature (W m-2 K-1)
- dLWNetGround_dTGround, & ! intent(out): derivative in net ground radiation w.r.t. ground temperature (W m-2 K-1)
- dLWNetCanopy_dTGround, & ! intent(out): derivative in net canopy radiation w.r.t. ground temperature (W m-2 K-1)
- dLWNetGround_dTCanopy, & ! intent(out): derivative in net ground radiation w.r.t. canopy temperature (W m-2 K-1)
- ! output: error control
- err,message ) ! intent(out): error control
- ! -----------------------------------------------------------------------------------------------------------------------------------------------
- implicit none
- ! input: model control
- integer(i4b),intent(in) :: ixDerivMethod ! choice of method used to compute derivative (analytical or numerical)
- logical(lgt),intent(in) :: computeVegFlux ! flag to indicate if computing fluxes over vegetation
- logical(lgt),intent(in) :: requireLWBal ! flag to indicate if we need longwave to be balanced
- ! input: canopy and ground temperature
- real(rkind),intent(in) :: canopyTemp ! canopy temperature (K)
- real(rkind),intent(in) :: groundTemp ! ground temperature (K)
- ! input: canopy and ground emissivity
- real(rkind),intent(in) :: emc ! canopy emissivity (-)
- real(rkind),intent(in) :: emg ! ground emissivity (-)
- ! input: forcing
- real(rkind),intent(in) :: LWRadUbound ! downwelling longwave radiation at the upper boundary (W m-2)
- ! output: sources
- real(rkind),intent(out) :: LWRadCanopy ! longwave radiation emitted from the canopy (W m-2)
- real(rkind),intent(out) :: LWRadGround ! longwave radiation emitted at the ground surface (W m-2)
- ! output: individual fluxes
- real(rkind),intent(out) :: LWRadUbound2Canopy ! downward atmospheric longwave radiation absorbed by the canopy (W m-2)
- real(rkind),intent(out) :: LWRadUbound2Ground ! downward atmospheric longwave radiation absorbed by the ground (W m-2)
- real(rkind),intent(out) :: LWRadUbound2Ubound ! atmospheric radiation reflected by the ground and lost thru upper boundary (W m-2)
- real(rkind),intent(out) :: LWRadCanopy2Ubound ! longwave radiation emitted from canopy lost thru upper boundary (W m-2)
- real(rkind),intent(out) :: LWRadCanopy2Ground ! longwave radiation emitted from canopy absorbed by the ground (W m-2)
- real(rkind),intent(out) :: LWRadCanopy2Canopy ! canopy longwave reflected from ground and absorbed by the canopy (W m-2)
- real(rkind),intent(out) :: LWRadGround2Ubound ! longwave radiation emitted from ground lost thru upper boundary (W m-2)
- real(rkind),intent(out) :: LWRadGround2Canopy ! longwave radiation emitted from ground and absorbed by the canopy (W m-2)
- ! output: net fluxes
- real(rkind),intent(out) :: LWNetCanopy ! net longwave radiation at the canopy (W m-2)
- real(rkind),intent(out) :: LWNetGround ! net longwave radiation at the ground surface (W m-2)
- real(rkind),intent(out) :: LWNetUbound ! net longwave radiation at the upper boundary (W m-2)
- ! output: flux derivatives
- real(rkind),intent(out) :: dLWNetCanopy_dTCanopy ! derivative in net canopy radiation w.r.t. canopy temperature (W m-2 K-1)
- real(rkind),intent(out) :: dLWNetGround_dTGround ! derivative in net ground radiation w.r.t. ground temperature (W m-2 K-1)
- real(rkind),intent(out) :: dLWNetCanopy_dTGround ! derivative in net canopy radiation w.r.t. ground temperature (W m-2 K-1)
- real(rkind),intent(out) :: dLWNetGround_dTCanopy ! derivative in net ground radiation w.r.t. canopy temperature (W m-2 K-1)
- ! output: error control
- integer(i4b),intent(out) :: err ! error code
- character(*),intent(out) :: message ! error message
- ! -----------------------------------------------------------------------------------------------------------------------------------------------
- ! local variables
- integer(i4b),parameter :: unperturbed=1 ! named variable to identify the case of unperturbed state variables
- integer(i4b),parameter :: perturbStateCanopy=2 ! named variable to identify the case where we perturb the canopy temperature
- integer(i4b),parameter :: perturbStateGround=3 ! named variable to identify the case where we perturb the ground temperature
- integer(i4b) :: itry ! index of flux evaluation
- integer(i4b) :: nFlux ! number of flux evaluations
- real(rkind) :: TCan ! value of canopy temperature used in flux calculations (may be perturbed)
- real(rkind) :: TGnd ! value of ground temperature used in flux calculations (may be perturbed)
- real(rkind) :: fluxBalance ! check energy closure (W m-2)
- real(rkind),parameter :: fluxTolerance=1.e-10_rkind ! tolerance for energy closure (W m-2)
- real(rkind) :: dLWRadCanopy_dTCanopy ! derivative in emitted radiation at the canopy w.r.t. canopy temperature
- real(rkind) :: dLWRadGround_dTGround ! derivative in emitted radiation at the ground w.r.t. ground temperature
- real(rkind) :: LWNetCanopy_dStateCanopy ! net lw canopy flux after perturbation in canopy temperature
- real(rkind) :: LWNetGround_dStateCanopy ! net lw ground flux after perturbation in canopy temperature
- real(rkind) :: LWNetCanopy_dStateGround ! net lw canopy flux after perturbation in ground temperature
- real(rkind) :: LWNetGround_dStateGround ! net lw ground flux after perturbation in ground temperature
- ! -----------------------------------------------------------------------------------------------------------------------------------------------
- ! initialize error control
- err=0; message='longwaveBal/'
-
- ! check the need to compute numerical derivatives
- if(ixDerivMethod==numerical)then
- nFlux=3 ! compute the derivatives using one-sided finite differences
- else
- nFlux=1 ! compute analytical derivatives
- end if
-
- ! either one or multiple flux calls, depending on if using analytical or numerical derivatives
- do itry=nFlux,1,-1 ! (work backwards to ensure all computed fluxes come from the un-perturbed case)
-
- !print*, 'perturbation: ', (itry==unperturbed), (itry==perturbStateCanopy), (itry==perturbStateGround)
-
- ! -------------------------------------------------------------------------------------
- ! state perturbations for numerical deriavtives with one-sided finite differences
- ! note: no perturbations performed using analytical derivatives (nFlux=1)
- ! -------------------------------------------------------------------------------------
-
- ! identify the type of perturbation
- select case(itry)
-
- ! un-perturbed case
- case(unperturbed)
+ end if
+
+ ! outside limits: special case of smooth exponents
+ else
+ if(xArg < 0._rkind)then; smoothFunc = 0._rkind ! xArg < -xLimit
+ else; smoothFunc = 1._rkind ! xArg > xLimit
+ end if
+ smoothFuncDeriv = 0._rkind
+ end if ! check for huge exponents
+
+end subroutine logisticSmoother
+ ! --------------------------------------------------------------------------------------------------------------
+
+
+! *******************************************************************************************************
+! private subroutine longwaveBal: compute longwave radiation balance at the canopy and ground surface
+! *******************************************************************************************************
+subroutine longwaveBal(&
+ ! input: model control
+ ixDerivMethod, & ! intent(in): choice of method used to compute derivative (analytical or numerical)
+ computeVegFlux, & ! intent(in): flag to compute fluxes over vegetati
+ insideIDA, & ! intent(in): flag to indicate inside Sundials Solver (do not require longwave to be balanced)
+ ! input: canopy and ground temperature
+ canopyTemp, & ! intent(in): canopy temperature (K)
+ groundTemp, & ! intent(in): ground temperature (K)
+ ! input: canopy and ground emissivity
+ emc, & ! intent(in): canopy emissivity (-)
+ emg, & ! intent(in): ground emissivity (-)
+ ! input: forcing
+ LWRadUbound, & ! intent(in): downwelling longwave radiation at the upper boundary (W m-2)
+ ! output: sources
+ LWRadCanopy, & ! intent(out): longwave radiation emitted from the canopy (W m-2)
+ LWRadGround, & ! intent(out): longwave radiation emitted at the ground surface (W m-2)
+ ! output: individual fluxes
+ LWRadUbound2Canopy, & ! intent(out): downward atmospheric longwave radiation absorbed by the canopy (W m-2)
+ LWRadUbound2Ground, & ! intent(out): downward atmospheric longwave radiation absorbed by the ground (W m-2)
+ LWRadUbound2Ubound, & ! intent(out): atmospheric radiation reflected by the ground and lost thru upper boundary (W m-2)
+ LWRadCanopy2Ubound, & ! intent(out): longwave radiation emitted from canopy lost thru upper boundary (W m-2)
+ LWRadCanopy2Ground, & ! intent(out): longwave radiation emitted from canopy absorbed by the ground (W m-2)
+ LWRadCanopy2Canopy, & ! intent(out): canopy longwave reflected from ground and absorbed by the canopy (W m-2)
+ LWRadGround2Ubound, & ! intent(out): longwave radiation emitted from ground lost thru upper boundary (W m-2)
+ LWRadGround2Canopy, & ! intent(out): longwave radiation emitted from ground and absorbed by the canopy (W m-2)
+ ! output: net fluxes
+ LWNetCanopy, & ! intent(out): net longwave radiation at the canopy (W m-2)
+ LWNetGround, & ! intent(out): net longwave radiation at the ground surface (W m-2)
+ LWNetUbound, & ! intent(out): net longwave radiation at the upper boundary (W m-2)
+ ! output: flux derivatives
+ dLWNetCanopy_dTCanopy, & ! intent(out): derivative in net canopy radiation w.r.t. canopy temperature (W m-2 K-1)
+ dLWNetGround_dTGround, & ! intent(out): derivative in net ground radiation w.r.t. ground temperature (W m-2 K-1)
+ dLWNetCanopy_dTGround, & ! intent(out): derivative in net canopy radiation w.r.t. ground temperature (W m-2 K-1)
+ dLWNetGround_dTCanopy, & ! intent(out): derivative in net ground radiation w.r.t. canopy temperature (W m-2 K-1)
+ ! output: error control
+ err,message ) ! intent(out): error control
+ ! -----------------------------------------------------------------------------------------------------------------------------------------------
+ implicit none
+ ! input: model control
+ integer(i4b),intent(in) :: ixDerivMethod ! choice of method used to compute derivative (analytical or numerical)
+ logical(lgt),intent(in) :: computeVegFlux ! flag to indicate if computing fluxes over vegetation
+ logical(lgt),intent(in) :: insideIDA ! flag if inside Sundials solver
+ ! input: canopy and ground temperature
+ real(rkind),intent(in) :: canopyTemp ! canopy temperature (K)
+ real(rkind),intent(in) :: groundTemp ! ground temperature (K)
+ ! input: canopy and ground emissivity
+ real(rkind),intent(in) :: emc ! canopy emissivity (-)
+ real(rkind),intent(in) :: emg ! ground emissivity (-)
+ ! input: forcing
+ real(rkind),intent(in) :: LWRadUbound ! downwelling longwave radiation at the upper boundary (W m-2)
+ ! output: sources
+ real(rkind),intent(out) :: LWRadCanopy ! longwave radiation emitted from the canopy (W m-2)
+ real(rkind),intent(out) :: LWRadGround ! longwave radiation emitted at the ground surface (W m-2)
+ ! output: individual fluxes
+ real(rkind),intent(out) :: LWRadUbound2Canopy ! downward atmospheric longwave radiation absorbed by the canopy (W m-2)
+ real(rkind),intent(out) :: LWRadUbound2Ground ! downward atmospheric longwave radiation absorbed by the ground (W m-2)
+ real(rkind),intent(out) :: LWRadUbound2Ubound ! atmospheric radiation reflected by the ground and lost thru upper boundary (W m-2)
+ real(rkind),intent(out) :: LWRadCanopy2Ubound ! longwave radiation emitted from canopy lost thru upper boundary (W m-2)
+ real(rkind),intent(out) :: LWRadCanopy2Ground ! longwave radiation emitted from canopy absorbed by the ground (W m-2)
+ real(rkind),intent(out) :: LWRadCanopy2Canopy ! canopy longwave reflected from ground and absorbed by the canopy (W m-2)
+ real(rkind),intent(out) :: LWRadGround2Ubound ! longwave radiation emitted from ground lost thru upper boundary (W m-2)
+ real(rkind),intent(out) :: LWRadGround2Canopy ! longwave radiation emitted from ground and absorbed by the canopy (W m-2)
+ ! output: net fluxes
+ real(rkind),intent(out) :: LWNetCanopy ! net longwave radiation at the canopy (W m-2)
+ real(rkind),intent(out) :: LWNetGround ! net longwave radiation at the ground surface (W m-2)
+ real(rkind),intent(out) :: LWNetUbound ! net longwave radiation at the upper boundary (W m-2)
+ ! output: flux derivatives
+ real(rkind),intent(out) :: dLWNetCanopy_dTCanopy ! derivative in net canopy radiation w.r.t. canopy temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dLWNetGround_dTGround ! derivative in net ground radiation w.r.t. ground temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dLWNetCanopy_dTGround ! derivative in net canopy radiation w.r.t. ground temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dLWNetGround_dTCanopy ! derivative in net ground radiation w.r.t. canopy temperature (W m-2 K-1)
+ ! output: error control
+ integer(i4b),intent(out) :: err ! error code
+ character(*),intent(out) :: message ! error message
+ ! -----------------------------------------------------------------------------------------------------------------------------------------------
+ ! local variables
+ integer(i4b),parameter :: unperturbed=1 ! named variable to identify the case of unperturbed state variables
+ integer(i4b),parameter :: perturbStateCanopy=2 ! named variable to identify the case where we perturb the canopy temperature
+ integer(i4b),parameter :: perturbStateGround=3 ! named variable to identify the case where we perturb the ground temperature
+ integer(i4b) :: itry ! index of flux evaluation
+ integer(i4b) :: nFlux ! number of flux evaluations
+ real(rkind) :: TCan ! value of canopy temperature used in flux calculations (may be perturbed)
+ real(rkind) :: TGnd ! value of ground temperature used in flux calculations (may be perturbed)
+ real(rkind) :: fluxBalance ! check energy closure (W m-2)
+ real(rkind),parameter :: fluxTolerance=1.e-10_rkind ! tolerance for energy closure (W m-2)
+ real(rkind) :: dLWRadCanopy_dTCanopy ! derivative in emitted radiation at the canopy w.r.t. canopy temperature
+ real(rkind) :: dLWRadGround_dTGround ! derivative in emitted radiation at the ground w.r.t. ground temperature
+ real(rkind) :: LWNetCanopy_dStateCanopy ! net lw canopy flux after perturbation in canopy temperature
+ real(rkind) :: LWNetGround_dStateCanopy ! net lw ground flux after perturbation in canopy temperature
+ real(rkind) :: LWNetCanopy_dStateGround ! net lw canopy flux after perturbation in ground temperature
+ real(rkind) :: LWNetGround_dStateGround ! net lw ground flux after perturbation in ground temperature
+ ! -----------------------------------------------------------------------------------------------------------------------------------------------
+ ! initialize error control
+ err=0; message='longwaveBal/'
+
+ ! check the need to compute numerical derivatives
+ if(ixDerivMethod==numerical)then
+ nFlux=3 ! compute the derivatives using one-sided finite differences
+ else
+ nFlux=1 ! compute analytical derivatives
+ end if
+
+ ! either one or multiple flux calls, depending on if using analytical or numerical derivatives
+ do itry=nFlux,1,-1 ! (work backwards to ensure all computed fluxes come from the un-perturbed case)
+
+ ! -------------------------------------------------------------------------------------
+ ! state perturbations for numerical deriavtives with one-sided finite differences
+ ! note: no perturbations performed using analytical derivatives (nFlux=1)
+ ! -------------------------------------------------------------------------------------
+
+ ! identify the type of perturbation
+ select case(itry)
+
+ ! un-perturbed case
+ case(unperturbed)
TCan = canopyTemp
TGnd = groundTemp
-
- ! perturb canopy temperature
- case(perturbStateCanopy)
+
+ ! perturb canopy temperature
+ case(perturbStateCanopy)
TCan = canopyTemp + dx
TGnd = groundTemp
-
- ! perturb ground temperature
- case(perturbStateGround)
+
+ ! perturb ground temperature
+ case(perturbStateGround)
TCan = canopyTemp
TGnd = groundTemp + dx
-
- ! check for an unknown perturbation
- case default; err=10; message=trim(message)//"unknown perturbation"; return
-
- end select ! (type of perturbation)
-
- ! -------------------------------------------------------------------------------------
- ! calculation block (unperturbed fluxes returned [computed last])
- ! -------------------------------------------------------------------------------------
- ! NOTE: emc should be set to zero when not computing canopy fluxes
-
- ! compute longwave fluxes from canopy and the ground
- if(computeVegFlux)then
- LWRadCanopy = emc*sb*TCan**4._rkind ! longwave radiation emitted from the canopy (W m-2)
- else
- LWRadCanopy = 0._rkind
- end if
- LWRadGround = emg*sb*TGnd**4._rkind ! longwave radiation emitted at the ground surface (W m-2)
-
- ! compute fluxes originating from the atmosphere
- LWRadUbound2Canopy = (emc + (1._rkind - emc)*(1._rkind - emg)*emc)*LWRadUbound ! downward atmospheric longwave radiation absorbed by the canopy (W m-2)
- LWRadUbound2Ground = (1._rkind - emc)*emg*LWRadUbound ! downward atmospheric longwave radiation absorbed by the ground (W m-2)
- LWRadUbound2Ubound = (1._rkind - emc)*(1._rkind - emg)*(1._rkind - emc)*LWRadUbound ! atmospheric radiation reflected by the ground and lost thru upper boundary (W m-2)
-
- ! compute fluxes originating from the canopy
- LWRadCanopy2Ubound = (1._rkind + (1._rkind - emc)*(1._rkind - emg))*LWRadCanopy ! longwave radiation emitted from canopy lost thru upper boundary (W m-2)
- LWRadCanopy2Ground = emg*LWRadCanopy ! longwave radiation emitted from canopy absorbed by the ground (W m-2)
- LWRadCanopy2Canopy = emc*(1._rkind - emg)*LWRadCanopy ! canopy longwave reflected from ground and absorbed by the canopy (W m-2)
-
- ! compute fluxes originating from the ground surface
- LWRadGround2Ubound = (1._rkind - emc)*LWRadGround ! longwave radiation emitted from ground lost thru upper boundary (W m-2)
- LWRadGround2Canopy = emc*LWRadGround ! longwave radiation emitted from ground and absorbed by the canopy (W m-2)
-
- ! compute net longwave radiation (W m-2)
- LWNetCanopy = LWRadUbound2Canopy + LWRadGround2Canopy + LWRadCanopy2Canopy - 2._rkind*LWRadCanopy ! canopy
- LWNetGround = LWRadUbound2Ground + LWRadCanopy2Ground - LWRadGround ! ground surface
- LWNetUbound = LWRadUbound - LWRadUbound2Ubound - LWRadCanopy2Ubound - LWRadGround2Ubound ! upper boundary
-
- !print*, 'LWRadCanopy = ', LWRadCanopy
- !print*, 'LWRadGround = ', LWRadGround
-
- !print*, 'LWNetCanopy = ', LWNetCanopy
- !print*, 'LWNetGround = ', LWNetGround
- !print*, 'LWNetUbound = ', LWNetUbound
-
- ! check the flux balance
- if(requireLWBal)then
- fluxBalance = LWNetUbound - (LWNetCanopy + LWNetGround)
- if(abs(fluxBalance) > fluxTolerance)then
+
+ ! check for an unknown perturbation
+ case default; err=10; message=trim(message)//"unknown perturbation"; return
+
+ end select ! (type of perturbation)
+
+ ! -------------------------------------------------------------------------------------
+ ! calculation block (unperturbed fluxes returned [computed last])
+ ! -------------------------------------------------------------------------------------
+ ! NOTE: emc should be set to zero when not computing canopy fluxes
+
+ ! compute longwave fluxes from canopy and the ground
+ if(computeVegFlux)then
+ LWRadCanopy = emc*sb*TCan**4._rkind ! longwave radiation emitted from the canopy (W m-2)
+ else
+ LWRadCanopy = 0._rkind
+ end if
+ LWRadGround = emg*sb*TGnd**4._rkind ! longwave radiation emitted at the ground surface (W m-2)
+
+ ! compute fluxes originating from the atmosphere
+ LWRadUbound2Canopy = (emc + (1._rkind - emc)*(1._rkind - emg)*emc)*LWRadUbound ! downward atmospheric longwave radiation absorbed by the canopy (W m-2)
+ LWRadUbound2Ground = (1._rkind - emc)*emg*LWRadUbound ! downward atmospheric longwave radiation absorbed by the ground (W m-2)
+ LWRadUbound2Ubound = (1._rkind - emc)*(1._rkind - emg)*(1._rkind - emc)*LWRadUbound ! atmospheric radiation reflected by the ground and lost thru upper boundary (W m-2)
+
+ ! compute fluxes originating from the canopy
+ LWRadCanopy2Ubound = (1._rkind + (1._rkind - emc)*(1._rkind - emg))*LWRadCanopy ! longwave radiation emitted from canopy lost thru upper boundary (W m-2)
+ LWRadCanopy2Ground = emg*LWRadCanopy ! longwave radiation emitted from canopy absorbed by the ground (W m-2)
+ LWRadCanopy2Canopy = emc*(1._rkind - emg)*LWRadCanopy ! canopy longwave reflected from ground and absorbed by the canopy (W m-2)
+
+ ! compute fluxes originating from the ground surface
+ LWRadGround2Ubound = (1._rkind - emc)*LWRadGround ! longwave radiation emitted from ground lost thru upper boundary (W m-2)
+ LWRadGround2Canopy = emc*LWRadGround ! longwave radiation emitted from ground and absorbed by the canopy (W m-2)
+
+ ! compute net longwave radiation (W m-2)
+ LWNetCanopy = LWRadUbound2Canopy + LWRadGround2Canopy + LWRadCanopy2Canopy - 2._rkind*LWRadCanopy ! canopy
+ LWNetGround = LWRadUbound2Ground + LWRadCanopy2Ground - LWRadGround ! ground surface
+ LWNetUbound = LWRadUbound - LWRadUbound2Ubound - LWRadCanopy2Ubound - LWRadGround2Ubound ! upper boundary
+
+ ! check the flux balance
+ if(.not.insideIDA)then
+ fluxBalance = LWNetUbound - (LWNetCanopy + LWNetGround)
+ if(abs(fluxBalance) > fluxTolerance)then
print*, 'fluxBalance = ', fluxBalance
print*, 'emg, emc = ', emg, emc
print*, 'TCan, TGnd = ', TCan, TGnd
@@ -1974,239 +1881,239 @@ module vegNrgFlux_module
print*, 'LWNetUbound = ', LWNetUbound
message=trim(message)//'flux imbalance'
err=20; return
- end if
end if
-
- ! --------------------------------------------------------------------------------------
- ! save perturbed fluxes to calculate numerical derivatives (one-sided finite difference)
- ! --------------------------------------------------------------------------------------
- if(ixDerivMethod==numerical)then
- select case(itry) ! (select type of perturbation)
+ end if
+
+ ! --------------------------------------------------------------------------------------
+ ! save perturbed fluxes to calculate numerical derivatives (one-sided finite difference)
+ ! --------------------------------------------------------------------------------------
+ if(ixDerivMethod==numerical)then
+ select case(itry) ! (select type of perturbation)
case(unperturbed); exit
case(perturbStateCanopy)
- LWNetCanopy_dStateCanopy = LWNetCanopy
- LWNetGround_dStateCanopy = LWNetGround
+ LWNetCanopy_dStateCanopy = LWNetCanopy
+ LWNetGround_dStateCanopy = LWNetGround
case(perturbStateGround)
- LWNetCanopy_dStateGround = LWNetCanopy
- LWNetGround_dStateGround = LWNetGround
+ LWNetCanopy_dStateGround = LWNetCanopy
+ LWNetGround_dStateGround = LWNetGround
case default; err=10; message=trim(message)//"unknown perturbation"; return
- end select ! (type of perturbation)
- end if ! (if numerical)
-
- end do ! looping through different perturbations
-
- ! -------------------------------------------------------------------------------------
- ! compute derivatives
- ! -------------------------------------------------------------------------------------
- select case(ixDerivMethod)
-
- ! ***** analytical derivatives
- case(analytical)
- ! compute initial derivatives
- dLWRadCanopy_dTCanopy = 4._rkind*emc*sb*TCan**3._rkind
- dLWRadGround_dTGround = 4._rkind*emg*sb*TGnd**3._rkind
- ! compute analytical derivatives
- dLWNetCanopy_dTCanopy = (emc*(1._rkind - emg) - 2._rkind)*dLWRadCanopy_dTCanopy ! derivative in net canopy radiation w.r.t. canopy temperature (W m-2 K-1)
- dLWNetGround_dTGround = -dLWRadGround_dTGround ! derivative in net ground radiation w.r.t. ground temperature (W m-2 K-1)
- dLWNetCanopy_dTGround = emc*dLWRadGround_dTGround ! derivative in net canopy radiation w.r.t. ground temperature (W m-2 K-1)
- dLWNetGround_dTCanopy = emg*dLWRadCanopy_dTCanopy ! derivative in net ground radiation w.r.t. canopy temperature (W m-2 K-1)
-
- ! ***** numerical derivatives
- case(numerical)
- ! compute numerical derivatives (one-sided finite differences)
- dLWNetCanopy_dTCanopy = (LWNetCanopy_dStateCanopy - LWNetCanopy)/dx ! derivative in net canopy radiation w.r.t. canopy temperature (W m-2 K-1)
- dLWNetGround_dTGround = (LWNetGround_dStateGround - LWNetGround)/dx ! derivative in net ground radiation w.r.t. ground temperature (W m-2 K-1)
- dLWNetCanopy_dTGround = (LWNetCanopy_dStateGround - LWNetCanopy)/dx ! derivative in net canopy radiation w.r.t. ground temperature (W m-2 K-1)
- dLWNetGround_dTCanopy = (LWNetGround_dStateCanopy - LWNetGround)/dx ! derivative in net ground radiation w.r.t. canopy temperature (W m-2 K-1)
-
- ! ***** error check
- case default; err=10; message=trim(message)//"unknown method to calculate derivatives"; return
-
- end select ! (type of method to calculate derivatives)
-
- end subroutine longwaveBal
-
-
- ! *******************************************************************************************************
- ! private subroutine aeroResist: compute aerodynamic resistances
- ! *******************************************************************************************************
- subroutine aeroResist(&
- ! input: model control
- computeVegFlux, & ! intent(in): logical flag to compute vegetation fluxes (.false. if veg buried by snow)
- derivDesired, & ! intent(in): flag to indicate if analytical derivatives are desired
- ixVegTraits, & ! intent(in): choice of parameterization for vegetation roughness length and displacement height
- ixWindProfile, & ! intent(in): choice of canopy wind profile
- ixStability, & ! intent(in): choice of stability function
- ! input: above-canopy forcing data
- mHeight, & ! intent(in): measurement height (m)
- airtemp, & ! intent(in): air temperature at some height above the surface (K)
- windspd, & ! intent(in): wind speed at some height above the surface (m s-1)
- ! input: temperature (canopy, ground, canopy air space)
- canairTemp, & ! intent(in): temperature of the canopy air space (K)
- groundTemp, & ! intent(in): ground temperature (K)
- ! input: diagnostic variables
- exposedVAI, & ! intent(in): exposed vegetation area index -- leaf plus stem (m2 m-2)
- snowDepth, & ! intent(in): snow depth (m)
- ! input: parameters
- z0Ground, & ! intent(in): roughness length of the ground (below canopy or non-vegetated surface [snow]) (m)
- z0CanopyParam, & ! intent(in): roughness length of the canopy (m)
- zpdFraction, & ! intent(in): zero plane displacement / canopy height (-)
- critRichNumber, & ! intent(in): critical value for the bulk Richardson number where turbulence ceases (-)
- Louis79_bparam, & ! intent(in): parameter in Louis (1979) stability function
- Mahrt87_eScale, & ! intent(in): exponential scaling factor in the Mahrt (1987) stability function
- windReductionParam, & ! intent(in): canopy wind reduction parameter (-)
- leafExchangeCoeff, & ! intent(in): turbulent exchange coeff between canopy surface and canopy air ( m s-(1/2) )
- leafDimension, & ! intent(in): characteristic leaf dimension (m)
- heightCanopyTop, & ! intent(in): height at the top of the vegetation canopy (m)
- heightCanopyBottom, & ! intent(in): height at the bottom of the vegetation canopy (m)
- ! output: stability corrections
- RiBulkCanopy, & ! intent(out): bulk Richardson number for the canopy (-)
- RiBulkGround, & ! intent(out): bulk Richardson number for the ground surface (-)
- canopyStabilityCorrection, & ! intent(out): stability correction for the canopy (-)
- groundStabilityCorrection, & ! intent(out): stability correction for the ground surface (-)
- ! output: scalar resistances
- z0Canopy, & ! intent(out): roughness length of the canopy (m)
- windReductionFactor, & ! intent(out): canopy wind reduction factor (-)
- zeroPlaneDisplacement, & ! intent(out): zero plane displacement (m)
- eddyDiffusCanopyTop, & ! intent(out): eddy diffusivity for heat at the top of the canopy (m2 s-1)
- frictionVelocity, & ! intent(out): friction velocity (m s-1)
- windspdCanopyTop, & ! intent(out): windspeed at the top of the canopy (m s-1)
- windspdCanopyBottom, & ! intent(out): windspeed at the height of the bottom of the canopy (m s-1)
- leafResistance, & ! intent(out): mean leaf boundary layer resistance per unit leaf area (s m-1)
- groundResistance, & ! intent(out): below canopy aerodynamic resistance (s m-1)
- canopyResistance, & ! intent(out): above canopy aerodynamic resistance (s m-1)
- ! output: derivatives in scalar resistances
- dGroundResistance_dTGround, & ! intent(out): derivative in ground resistance w.r.t. ground temperature (s m-1 K-1)
- dGroundResistance_dTCanopy, & ! intent(out): derivative in ground resistance w.r.t. canopy temperature (s m-1 K-1)
- dGroundResistance_dTCanair, & ! intent(out): derivative in ground resistance w.r.t. canopy air temperature (s m-1 K-1)
- dCanopyResistance_dTCanopy, & ! intent(out): derivative in canopy resistance w.r.t. canopy temperature (s m-1 K-1)
- dCanopyResistance_dTCanair, & ! intent(out): derivative in canopy resistance w.r.t. canopy air temperature (s m-1 K-1)
- ! output: error control
- err,message ) ! intent(out): error control
- ! -----------------------------------------------------------------------------------------------------------------------------------------
- ! compute aerodynamic resistances
- ! Refs: Choudhury and Monteith (4-layer model for heat budget of homogenous surfaces; QJRMS, 1988)
- ! Niu and Yang (Canopy effects on snow processes; JGR, 2004)
- ! Mahat et al. (Below-canopy turbulence in a snowmelt model, WRR, 2012)
- implicit none
- ! input: model control
- logical(lgt),intent(in) :: computeVegFlux ! logical flag to compute vegetation fluxes (.false. if veg buried by snow)
- logical(lgt),intent(in) :: derivDesired ! logical flag to indicate if analytical derivatives are desired
- integer(i4b),intent(in) :: ixVegTraits ! choice of parameterization for vegetation roughness length and displacement height
- integer(i4b),intent(in) :: ixWindProfile ! choice of canopy wind profile
- integer(i4b),intent(in) :: ixStability ! choice of stability function
- ! input: above-canopy forcing data
- real(rkind),intent(in) :: mHeight ! measurement height (m)
- real(rkind),intent(in) :: airtemp ! air temperature at some height above the surface (K)
- real(rkind),intent(in) :: windspd ! wind speed at some height above the surface (m s-1)
- ! input: temperature (canopy, ground, canopy air space)
- real(rkind),intent(in) :: canairTemp ! temperature of the canopy air space (K)
- real(rkind),intent(in) :: groundTemp ! ground temperature (K)
- ! input: diagnostic variables
- real(rkind),intent(in) :: exposedVAI ! exposed vegetation area index -- leaf plus stem (m2 m-2)
- real(rkind),intent(in) :: snowDepth ! snow depth (m)
- ! input: parameters
- real(rkind),intent(in) :: z0Ground ! roughness length of the ground (below canopy or non-vegetated surface [snow]) (m)
- real(rkind),intent(in) :: z0CanopyParam ! roughness length of the canopy (m)
- real(rkind),intent(in) :: zpdFraction ! zero plane displacement / canopy height (-)
- real(rkind),intent(in) :: critRichNumber ! critical value for the bulk Richardson number where turbulence ceases (-)
- real(rkind),intent(in) :: Louis79_bparam ! parameter in Louis (1979) stability function
- real(rkind),intent(in) :: Mahrt87_eScale ! exponential scaling factor in the Mahrt (1987) stability function
- real(rkind),intent(in) :: windReductionParam ! canopy wind reduction parameter (-)
- real(rkind),intent(in) :: leafExchangeCoeff ! turbulent exchange coeff between canopy surface and canopy air ( m s-(1/2) )
- real(rkind),intent(in) :: leafDimension ! characteristic leaf dimension (m)
- real(rkind),intent(in) :: heightCanopyTop ! height at the top of the vegetation canopy (m)
- real(rkind),intent(in) :: heightCanopyBottom ! height at the bottom of the vegetation canopy (m)
- ! output: stability corrections
- real(rkind),intent(out) :: RiBulkCanopy ! bulk Richardson number for the canopy (-)
- real(rkind),intent(out) :: RiBulkGround ! bulk Richardson number for the ground surface (-)
- real(rkind),intent(out) :: canopyStabilityCorrection ! stability correction for the canopy (-)
- real(rkind),intent(out) :: groundStabilityCorrection ! stability correction for the ground surface (-)
- ! output: scalar resistances
- real(rkind),intent(out) :: z0Canopy ! roughness length of the vegetation canopy (m)
- real(rkind),intent(out) :: windReductionFactor ! canopy wind reduction factor (-)
- real(rkind),intent(out) :: zeroPlaneDisplacement ! zero plane displacement (m)
- real(rkind),intent(out) :: eddyDiffusCanopyTop ! eddy diffusivity for heat at the top of the canopy (m2 s-1)
- real(rkind),intent(out) :: frictionVelocity ! friction velocity (m s-1)
- real(rkind),intent(out) :: windspdCanopyTop ! windspeed at the top of the canopy (m s-1)
- real(rkind),intent(out) :: windspdCanopyBottom ! windspeed at the height of the bottom of the canopy (m s-1)
- real(rkind),intent(out) :: leafResistance ! mean leaf boundary layer resistance per unit leaf area (s m-1)
- real(rkind),intent(out) :: groundResistance ! below canopy aerodynamic resistance (s m-1)
- real(rkind),intent(out) :: canopyResistance ! above canopy aerodynamic resistance (s m-1)
- ! output: derivatives in scalar resistances
- real(rkind),intent(out) :: dGroundResistance_dTGround ! derivative in ground resistance w.r.t. ground temperature (s m-1 K-1)
- real(rkind),intent(out) :: dGroundResistance_dTCanopy ! derivative in ground resistance w.r.t. canopy temperature (s m-1 K-1)
- real(rkind),intent(out) :: dGroundResistance_dTCanair ! derivative in ground resistance w.r.t. canopy air temperature (s m-1 K-1)
- real(rkind),intent(out) :: dCanopyResistance_dTCanopy ! derivative in canopy resistance w.r.t. canopy temperature (s m-1 K-1)
- real(rkind),intent(out) :: dCanopyResistance_dTCanair ! derivative in canopy resistance w.r.t. canopy air temperature (s m-1 K-1)
- ! output: error control
- integer(i4b),intent(out) :: err ! error code
- character(*),intent(out) :: message ! error message
- ! -----------------------------------------------------------------------------------------------------------------------------------------
- ! local variables: general
- character(LEN=256) :: cmessage ! error message of downwind routine
- ! local variables: vegetation roughness and dispalcement height
- real(rkind),parameter :: oneThird=1._rkind/3._rkind ! 1/3
- real(rkind),parameter :: twoThirds=2._rkind/3._rkind ! 2/3
- real(rkind),parameter :: C_r = 0.3 ! roughness element drag coefficient (-) from Raupach (BLM, 1994)
- real(rkind),parameter :: C_s = 0.003_rkind ! substrate surface drag coefficient (-) from Raupach (BLM, 1994)
- real(rkind),parameter :: approxDragCoef_max = 0.3_rkind ! maximum value of the approximate drag coefficient (-) from Raupach (BLM, 1994)
- real(rkind),parameter :: psi_h = 0.193_rkind ! roughness sub-layer influence function (-) from Raupach (BLM, 1994)
- real(rkind),parameter :: c_d1 = 7.5_rkind ! scaling parameter used to define displacement height (-) from Raupach (BLM, 1994)
- real(rkind),parameter :: cd_CM = 0.2_rkind ! mean drag coefficient for individual leaves (-) from Choudhury and Monteith (QJRMS, 1988)
- real(rkind) :: funcLAI ! temporary variable to calculate zero plane displacement for the canopy
- real(rkind) :: fracCanopyHeight ! zero plane displacement expressed as a fraction of canopy height
- real(rkind) :: approxDragCoef ! approximate drag coefficient used in the computation of canopy roughness length (-)
- ! local variables: resistance
- real(rkind) :: canopyExNeut ! surface-atmosphere exchange coefficient under neutral conditions (-)
- real(rkind) :: groundExNeut ! surface-atmosphere exchange coefficient under neutral conditions (-)
- real(rkind) :: sfc2AtmExchangeCoeff_canopy ! surface-atmosphere exchange coefficient after stability corrections (-)
- real(rkind) :: groundResistanceNeutral ! ground resistance under neutral conditions (s m-1)
- real(rkind) :: windConvFactor_fv ! factor to convert friction velocity to wind speed at top of canopy (-)
- real(rkind) :: windConvFactor ! factor to convert wind speed at top of canopy to wind speed at a given height in the canopy (-)
- real(rkind) :: referenceHeight ! z0Canopy+zeroPlaneDisplacement (m)
- real(rkind) :: windspdRefHeight ! windspeed at the reference height (m/s)
- real(rkind) :: heightAboveGround ! height above the snow surface (m)
- real(rkind) :: heightCanopyTopAboveSnow ! height at the top of the vegetation canopy relative to snowpack (m)
- real(rkind) :: heightCanopyBottomAboveSnow ! height at the bottom of the vegetation canopy relative to snowpack (m)
- real(rkind),parameter :: xTolerance=0.1_rkind ! tolerance to handle the transition from exponential to log-below canopy
- ! local variables: derivatives
- real(rkind) :: dFV_dT ! derivative in friction velocity w.r.t. canopy air temperature
- real(rkind) :: dED_dT ! derivative in eddy diffusivity at the top of the canopy w.r.t. canopy air temperature
- real(rkind) :: dGR_dT ! derivative in neutral ground resistance w.r.t. canopy air temperature
- real(rkind) :: tmp1,tmp2 ! temporary variables used in calculation of ground resistance
- real(rkind) :: dCanopyStabilityCorrection_dRich ! derivative in stability correction w.r.t. Richardson number for the canopy (-)
- real(rkind) :: dGroundStabilityCorrection_dRich ! derivative in stability correction w.r.t. Richardson number for the ground surface (-)
- real(rkind) :: dCanopyStabilityCorrection_dAirTemp ! (not used) derivative in stability correction w.r.t. air temperature (K-1)
- real(rkind) :: dGroundStabilityCorrection_dAirTemp ! (not used) derivative in stability correction w.r.t. air temperature (K-1)
- real(rkind) :: dCanopyStabilityCorrection_dCasTemp ! derivative in canopy stability correction w.r.t. canopy air space temperature (K-1)
- real(rkind) :: dGroundStabilityCorrection_dCasTemp ! derivative in ground stability correction w.r.t. canopy air space temperature (K-1)
- real(rkind) :: dGroundStabilityCorrection_dSfcTemp ! derivative in ground stability correction w.r.t. surface temperature (K-1)
- real(rkind) :: singleLeafConductance ! leaf boundary layer conductance (m s-1)
- real(rkind) :: canopyLeafConductance ! leaf boundary layer conductance -- scaled up to the canopy (m s-1)
- real(rkind) :: leaf2CanopyScaleFactor ! factor to scale from the leaf to the canopy [m s-(1/2)]
- ! -----------------------------------------------------------------------------------------------------------------------------------------
- ! initialize error control
- err=0; message='aeroResist/'
-
- ! check that measurement height is above the top of the canopy
- if(mHeight < heightCanopyTop)then
- err=20; message=trim(message)//'measurement height is below the top of the canopy'; return
- end if
-
- ! -----------------------------------------------------------------------------------------------------------------------------------------
- ! * compute vegetation poperties (could be done at the same time as phenology.. does not have to be in the flux routine!)
- if(computeVegFlux) then ! (if vegetation is exposed)
-
- ! ***** identify zero plane displacement, roughness length, and surface temperature for the canopy (m)
- ! First, calculate new coordinate system above snow - use these to scale wind profiles and resistances
- ! NOTE: the new coordinate system makes zeroPlaneDisplacement and z0Canopy consistent
- heightCanopyTopAboveSnow = heightCanopyTop - snowDepth
- heightCanopyBottomAboveSnow = max(heightCanopyBottom - snowDepth, 0.0_rkind)
- select case(ixVegTraits)
-
- ! Raupach (BLM 1994) "Simplified expressions..."
- case(Raupach_BLM1994)
+ end select ! (type of perturbation)
+ end if ! (if numerical)
+
+ end do ! looping through different perturbations
+
+ ! -------------------------------------------------------------------------------------
+ ! compute derivatives
+ ! -------------------------------------------------------------------------------------
+ select case(ixDerivMethod)
+
+ ! ***** analytical derivatives
+ case(analytical)
+ ! compute initial derivatives
+ dLWRadCanopy_dTCanopy = 4._rkind*emc*sb*TCan**3._rkind
+ dLWRadGround_dTGround = 4._rkind*emg*sb*TGnd**3._rkind
+ ! compute analytical derivatives
+ dLWNetCanopy_dTCanopy = (emc*(1._rkind - emg) - 2._rkind)*dLWRadCanopy_dTCanopy ! derivative in net canopy radiation w.r.t. canopy temperature (W m-2 K-1)
+ dLWNetGround_dTGround = -dLWRadGround_dTGround ! derivative in net ground radiation w.r.t. ground temperature (W m-2 K-1)
+ dLWNetCanopy_dTGround = emc*dLWRadGround_dTGround ! derivative in net canopy radiation w.r.t. ground temperature (W m-2 K-1)
+ dLWNetGround_dTCanopy = emg*dLWRadCanopy_dTCanopy ! derivative in net ground radiation w.r.t. canopy temperature (W m-2 K-1)
+
+ ! ***** numerical derivatives
+ case(numerical)
+ ! compute numerical derivatives (one-sided finite differences)
+ dLWNetCanopy_dTCanopy = (LWNetCanopy_dStateCanopy - LWNetCanopy)/dx ! derivative in net canopy radiation w.r.t. canopy temperature (W m-2 K-1)
+ dLWNetGround_dTGround = (LWNetGround_dStateGround - LWNetGround)/dx ! derivative in net ground radiation w.r.t. ground temperature (W m-2 K-1)
+ dLWNetCanopy_dTGround = (LWNetCanopy_dStateGround - LWNetCanopy)/dx ! derivative in net canopy radiation w.r.t. ground temperature (W m-2 K-1)
+ dLWNetGround_dTCanopy = (LWNetGround_dStateCanopy - LWNetGround)/dx ! derivative in net ground radiation w.r.t. canopy temperature (W m-2 K-1)
+
+ ! ***** error check
+ case default; err=10; message=trim(message)//"unknown method to calculate derivatives"; return
+
+ end select ! (type of method to calculate derivatives)
+
+end subroutine longwaveBal
+
+
+! *******************************************************************************************************
+! private subroutine aeroResist: compute aerodynamic resistances
+! *******************************************************************************************************
+subroutine aeroResist(&
+ ! input: model control
+ computeVegFlux, & ! intent(in): logical flag to compute vegetation fluxes (.false. if veg buried by snow)
+ derivDesired, & ! intent(in): flag to indicate if analytical derivatives are desired
+ ixVegTraits, & ! intent(in): choice of parameterization for vegetation roughness length and displacement height
+ ixWindProfile, & ! intent(in): choice of canopy wind profile
+ ixStability, & ! intent(in): choice of stability function
+ ! input: above-canopy forcing data
+ mHeight, & ! intent(in): measurement height (m)
+ airtemp, & ! intent(in): air temperature at some height above the surface (K)
+ windspd, & ! intent(in): wind speed at some height above the surface (m s-1)
+ ! input: temperature (canopy, ground, canopy air space)
+ canairTemp, & ! intent(in): temperature of the canopy air space (K)
+ groundTemp, & ! intent(in): ground temperature (K)
+ ! input: diagnostic variables
+ exposedVAI, & ! intent(in): exposed vegetation area index -- leaf plus stem (m2 m-2)
+ snowDepth, & ! intent(in): snow depth (m)
+ ! input: parameters
+ z0Ground, & ! intent(in): roughness length of the ground (below canopy or non-vegetated surface [snow]) (m)
+ z0CanopyParam, & ! intent(in): roughness length of the canopy (m)
+ zpdFraction, & ! intent(in): zero plane displacement / canopy height (-)
+ critRichNumber, & ! intent(in): critical value for the bulk Richardson number where turbulence ceases (-)
+ Louis79_bparam, & ! intent(in): parameter in Louis (1979) stability function
+ Mahrt87_eScale, & ! intent(in): exponential scaling factor in the Mahrt (1987) stability function
+ windReductionParam, & ! intent(in): canopy wind reduction parameter (-)
+ leafExchangeCoeff, & ! intent(in): turbulent exchange coeff between canopy surface and canopy air ( m s-(1/2) )
+ leafDimension, & ! intent(in): characteristic leaf dimension (m)
+ heightCanopyTop, & ! intent(in): height at the top of the vegetation canopy (m)
+ heightCanopyBottom, & ! intent(in): height at the bottom of the vegetation canopy (m)
+ ! output: stability corrections
+ RiBulkCanopy, & ! intent(out): bulk Richardson number for the canopy (-)
+ RiBulkGround, & ! intent(out): bulk Richardson number for the ground surface (-)
+ canopyStabilityCorrection, & ! intent(out): stability correction for the canopy (-)
+ groundStabilityCorrection, & ! intent(out): stability correction for the ground surface (-)
+ ! output: scalar resistances
+ z0Canopy, & ! intent(out): roughness length of the canopy (m)
+ windReductionFactor, & ! intent(out): canopy wind reduction factor (-)
+ zeroPlaneDisplacement, & ! intent(out): zero plane displacement (m)
+ eddyDiffusCanopyTop, & ! intent(out): eddy diffusivity for heat at the top of the canopy (m2 s-1)
+ frictionVelocity, & ! intent(out): friction velocity (m s-1)
+ windspdCanopyTop, & ! intent(out): windspeed at the top of the canopy (m s-1)
+ windspdCanopyBottom, & ! intent(out): windspeed at the height of the bottom of the canopy (m s-1)
+ leafResistance, & ! intent(out): mean leaf boundary layer resistance per unit leaf area (s m-1)
+ groundResistance, & ! intent(out): below canopy aerodynamic resistance (s m-1)
+ canopyResistance, & ! intent(out): above canopy aerodynamic resistance (s m-1)
+ ! output: derivatives in scalar resistances
+ dGroundResistance_dTGround, & ! intent(out): derivative in ground resistance w.r.t. ground temperature (s m-1 K-1)
+ dGroundResistance_dTCanopy, & ! intent(out): derivative in ground resistance w.r.t. canopy temperature (s m-1 K-1)
+ dGroundResistance_dTCanair, & ! intent(out): derivative in ground resistance w.r.t. canopy air temperature (s m-1 K-1)
+ dCanopyResistance_dTCanopy, & ! intent(out): derivative in canopy resistance w.r.t. canopy temperature (s m-1 K-1)
+ dCanopyResistance_dTCanair, & ! intent(out): derivative in canopy resistance w.r.t. canopy air temperature (s m-1 K-1)
+ ! output: error control
+ err,message ) ! intent(out): error control
+ ! -----------------------------------------------------------------------------------------------------------------------------------------
+ ! compute aerodynamic resistances
+ ! Refs: Choudhury and Monteith (4-layer model for heat budget of homogenous surfaces; QJRMS, 1988)
+ ! Niu and Yang (Canopy effects on snow processes; JGR, 2004)
+ ! Mahat et al. (Below-canopy turbulence in a snowmelt model, WRR, 2012)
+ implicit none
+ ! input: model control
+ logical(lgt),intent(in) :: computeVegFlux ! logical flag to compute vegetation fluxes (.false. if veg buried by snow)
+ logical(lgt),intent(in) :: derivDesired ! logical flag to indicate if analytical derivatives are desired
+ integer(i4b),intent(in) :: ixVegTraits ! choice of parameterization for vegetation roughness length and displacement height
+ integer(i4b),intent(in) :: ixWindProfile ! choice of canopy wind profile
+ integer(i4b),intent(in) :: ixStability ! choice of stability function
+ ! input: above-canopy forcing data
+ real(rkind),intent(in) :: mHeight ! measurement height (m)
+ real(rkind),intent(in) :: airtemp ! air temperature at some height above the surface (K)
+ real(rkind),intent(in) :: windspd ! wind speed at some height above the surface (m s-1)
+ ! input: temperature (canopy, ground, canopy air space)
+ real(rkind),intent(in) :: canairTemp ! temperature of the canopy air space (K)
+ real(rkind),intent(in) :: groundTemp ! ground temperature (K)
+ ! input: diagnostic variables
+ real(rkind),intent(in) :: exposedVAI ! exposed vegetation area index -- leaf plus stem (m2 m-2)
+ real(rkind),intent(in) :: snowDepth ! snow depth (m)
+ ! input: parameters
+ real(rkind),intent(in) :: z0Ground ! roughness length of the ground (below canopy or non-vegetated surface [snow]) (m)
+ real(rkind),intent(in) :: z0CanopyParam ! roughness length of the canopy (m)
+ real(rkind),intent(in) :: zpdFraction ! zero plane displacement / canopy height (-)
+ real(rkind),intent(in) :: critRichNumber ! critical value for the bulk Richardson number where turbulence ceases (-)
+ real(rkind),intent(in) :: Louis79_bparam ! parameter in Louis (1979) stability function
+ real(rkind),intent(in) :: Mahrt87_eScale ! exponential scaling factor in the Mahrt (1987) stability function
+ real(rkind),intent(in) :: windReductionParam ! canopy wind reduction parameter (-)
+ real(rkind),intent(in) :: leafExchangeCoeff ! turbulent exchange coeff between canopy surface and canopy air ( m s-(1/2) )
+ real(rkind),intent(in) :: leafDimension ! characteristic leaf dimension (m)
+ real(rkind),intent(in) :: heightCanopyTop ! height at the top of the vegetation canopy (m)
+ real(rkind),intent(in) :: heightCanopyBottom ! height at the bottom of the vegetation canopy (m)
+ ! output: stability corrections
+ real(rkind),intent(out) :: RiBulkCanopy ! bulk Richardson number for the canopy (-)
+ real(rkind),intent(out) :: RiBulkGround ! bulk Richardson number for the ground surface (-)
+ real(rkind),intent(out) :: canopyStabilityCorrection ! stability correction for the canopy (-)
+ real(rkind),intent(out) :: groundStabilityCorrection ! stability correction for the ground surface (-)
+ ! output: scalar resistances
+ real(rkind),intent(out) :: z0Canopy ! roughness length of the vegetation canopy (m)
+ real(rkind),intent(out) :: windReductionFactor ! canopy wind reduction factor (-)
+ real(rkind),intent(out) :: zeroPlaneDisplacement ! zero plane displacement (m)
+ real(rkind),intent(out) :: eddyDiffusCanopyTop ! eddy diffusivity for heat at the top of the canopy (m2 s-1)
+ real(rkind),intent(out) :: frictionVelocity ! friction velocity (m s-1)
+ real(rkind),intent(out) :: windspdCanopyTop ! windspeed at the top of the canopy (m s-1)
+ real(rkind),intent(out) :: windspdCanopyBottom ! windspeed at the height of the bottom of the canopy (m s-1)
+ real(rkind),intent(out) :: leafResistance ! mean leaf boundary layer resistance per unit leaf area (s m-1)
+ real(rkind),intent(out) :: groundResistance ! below canopy aerodynamic resistance (s m-1)
+ real(rkind),intent(out) :: canopyResistance ! above canopy aerodynamic resistance (s m-1)
+ ! output: derivatives in scalar resistances
+ real(rkind),intent(out) :: dGroundResistance_dTGround ! derivative in ground resistance w.r.t. ground temperature (s m-1 K-1)
+ real(rkind),intent(out) :: dGroundResistance_dTCanopy ! derivative in ground resistance w.r.t. canopy temperature (s m-1 K-1)
+ real(rkind),intent(out) :: dGroundResistance_dTCanair ! derivative in ground resistance w.r.t. canopy air temperature (s m-1 K-1)
+ real(rkind),intent(out) :: dCanopyResistance_dTCanopy ! derivative in canopy resistance w.r.t. canopy temperature (s m-1 K-1)
+ real(rkind),intent(out) :: dCanopyResistance_dTCanair ! derivative in canopy resistance w.r.t. canopy air temperature (s m-1 K-1)
+ ! output: error control
+ integer(i4b),intent(out) :: err ! error code
+ character(*),intent(out) :: message ! error message
+ ! -----------------------------------------------------------------------------------------------------------------------------------------
+ ! local variables: general
+ character(LEN=256) :: cmessage ! error message of downwind routine
+ ! local variables: vegetation roughness and dispalcement height
+ real(rkind),parameter :: oneThird=1._rkind/3._rkind ! 1/3
+ real(rkind),parameter :: twoThirds=2._rkind/3._rkind ! 2/3
+ real(rkind),parameter :: C_r = 0.3 ! roughness element drag coefficient (-) from Raupach (BLM, 1994)
+ real(rkind),parameter :: C_s = 0.003_rkind ! substrate surface drag coefficient (-) from Raupach (BLM, 1994)
+ real(rkind),parameter :: approxDragCoef_max = 0.3_rkind ! maximum value of the approximate drag coefficient (-) from Raupach (BLM, 1994)
+ real(rkind),parameter :: psi_h = 0.193_rkind ! roughness sub-layer influence function (-) from Raupach (BLM, 1994)
+ real(rkind),parameter :: c_d1 = 7.5_rkind ! scaling parameter used to define displacement height (-) from Raupach (BLM, 1994)
+ real(rkind),parameter :: cd_CM = 0.2_rkind ! mean drag coefficient for individual leaves (-) from Choudhury and Monteith (QJRMS, 1988)
+ real(rkind) :: funcLAI ! temporary variable to calculate zero plane displacement for the canopy
+ real(rkind) :: fracCanopyHeight ! zero plane displacement expressed as a fraction of canopy height
+ real(rkind) :: approxDragCoef ! approximate drag coefficient used in the computation of canopy roughness length (-)
+ ! local variables: resistance
+ real(rkind) :: canopyExNeut ! surface-atmosphere exchange coefficient under neutral conditions (-)
+ real(rkind) :: groundExNeut ! surface-atmosphere exchange coefficient under neutral conditions (-)
+ real(rkind) :: sfc2AtmExchangeCoeff_canopy ! surface-atmosphere exchange coefficient after stability corrections (-)
+ real(rkind) :: groundResistanceNeutral ! ground resistance under neutral conditions (s m-1)
+ real(rkind) :: windConvFactor_fv ! factor to convert friction velocity to wind speed at top of canopy (-)
+ real(rkind) :: windConvFactor ! factor to convert wind speed at top of canopy to wind speed at a given height in the canopy (-)
+ real(rkind) :: referenceHeight ! z0Canopy+zeroPlaneDisplacement (m)
+ real(rkind) :: windspdRefHeight ! windspeed at the reference height (m/s)
+ real(rkind) :: heightAboveGround ! height above the snow surface (m)
+ real(rkind) :: heightCanopyTopAboveSnow ! height at the top of the vegetation canopy relative to snowpack (m)
+ real(rkind) :: heightCanopyBottomAboveSnow ! height at the bottom of the vegetation canopy relative to snowpack (m)
+ real(rkind),parameter :: xTolerance=0.1_rkind ! tolerance to handle the transition from exponential to log-below canopy
+ ! local variables: derivatives
+ real(rkind) :: dFV_dT ! derivative in friction velocity w.r.t. canopy air temperature
+ real(rkind) :: dED_dT ! derivative in eddy diffusivity at the top of the canopy w.r.t. canopy air temperature
+ real(rkind) :: dGR_dT ! derivative in neutral ground resistance w.r.t. canopy air temperature
+ real(rkind) :: tmp1,tmp2 ! temporary variables used in calculation of ground resistance
+ real(rkind) :: dCanopyStabilityCorrection_dRich ! derivative in stability correction w.r.t. Richardson number for the canopy (-)
+ real(rkind) :: dGroundStabilityCorrection_dRich ! derivative in stability correction w.r.t. Richardson number for the ground surface (-)
+ real(rkind) :: dCanopyStabilityCorrection_dAirTemp ! (not used) derivative in stability correction w.r.t. air temperature (K-1)
+ real(rkind) :: dGroundStabilityCorrection_dAirTemp ! (not used) derivative in stability correction w.r.t. air temperature (K-1)
+ real(rkind) :: dCanopyStabilityCorrection_dCasTemp ! derivative in canopy stability correction w.r.t. canopy air space temperature (K-1)
+ real(rkind) :: dGroundStabilityCorrection_dCasTemp ! derivative in ground stability correction w.r.t. canopy air space temperature (K-1)
+ real(rkind) :: dGroundStabilityCorrection_dSfcTemp ! derivative in ground stability correction w.r.t. surface temperature (K-1)
+ real(rkind) :: singleLeafConductance ! leaf boundary layer conductance (m s-1)
+ real(rkind) :: canopyLeafConductance ! leaf boundary layer conductance -- scaled up to the canopy (m s-1)
+ real(rkind) :: leaf2CanopyScaleFactor ! factor to scale from the leaf to the canopy [m s-(1/2)]
+ ! -----------------------------------------------------------------------------------------------------------------------------------------
+ ! initialize error control
+ err=0; message='aeroResist/'
+
+ ! check that measurement height is above the top of the canopy
+ if(mHeight < heightCanopyTop)then
+ err=20; message=trim(message)//'measurement height is below the top of the canopy'; return
+ end if
+
+ ! -----------------------------------------------------------------------------------------------------------------------------------------
+ ! * compute vegetation poperties (could be done at the same time as phenology.. does not have to be in the flux routine!)
+ if(computeVegFlux) then ! (if vegetation is exposed)
+
+ ! ***** identify zero plane displacement, roughness length, and surface temperature for the canopy (m)
+ ! First, calculate new coordinate system above snow - use these to scale wind profiles and resistances
+ ! NOTE: the new coordinate system makes zeroPlaneDisplacement and z0Canopy consistent
+ heightCanopyTopAboveSnow = heightCanopyTop - snowDepth
+ heightCanopyBottomAboveSnow = max(heightCanopyBottom - snowDepth, 0.0_rkind)
+ select case(ixVegTraits)
+
+ ! Raupach (BLM 1994) "Simplified expressions..."
+ case(Raupach_BLM1994)
! (compute zero-plane displacement)
funcLAI = sqrt(c_d1*exposedVAI)
fracCanopyHeight = -(1._rkind - exp(-funcLAI))/funcLAI + 1._rkind
@@ -2214,1151 +2121,1110 @@ module vegNrgFlux_module
! (coupute roughness length of the veg canopy)
approxDragCoef = min( sqrt(C_s + C_r*exposedVAI/2._rkind), approxDragCoef_max)
z0Canopy = (1._rkind - fracCanopyHeight) * exp(-vkc*approxDragCoef - psi_h) * (heightCanopyTopAboveSnow-heightCanopyBottomAboveSnow)
-
- ! Choudhury and Monteith (QJRMS 1988) "A four layer model for the heat budget..."
- case(CM_QJRMS1988)
+
+ ! Choudhury and Monteith (QJRMS 1988) "A four layer model for the heat budget..."
+ case(CM_QJRMS1988)
funcLAI = cd_CM*exposedVAI
zeroPlaneDisplacement = 1.1_rkind*heightCanopyTopAboveSnow*log(1._rkind + funcLAI**0.25_rkind)
if(funcLAI < 0.2_rkind)then
- z0Canopy = z0Ground + 0.3_rkind*heightCanopyTopAboveSnow*funcLAI**0.5_rkind
+ z0Canopy = z0Ground + 0.3_rkind*heightCanopyTopAboveSnow*funcLAI**0.5_rkind
else
- z0Canopy = 0.3_rkind*heightCanopyTopAboveSnow*(1._rkind - zeroPlaneDisplacement/heightCanopyTopAboveSnow)
+ z0Canopy = 0.3_rkind*heightCanopyTopAboveSnow*(1._rkind - zeroPlaneDisplacement/heightCanopyTopAboveSnow)
end if
-
- ! constant parameters dependent on the vegetation type
- case(vegTypeTable)
+
+ ! constant parameters dependent on the vegetation type
+ case(vegTypeTable)
zeroPlaneDisplacement = zpdFraction*heightCanopyTopAboveSnow ! zero-plane displacement (m)
z0Canopy = z0CanopyParam ! roughness length of the veg canopy (m)
-
- ! check
- case default
+
+ ! check
+ case default
err=10; message=trim(message)//"unknown parameterization for vegetation roughness length and displacement height"; return
-
- end select ! vegetation traits (z0, zpd)
-
- ! check zero plane displacement
- if(zeroPlaneDisplacement < heightCanopyBottomAboveSnow)then
- write(*,'(a,1x,10(f12.5,1x))') 'heightCanopyTop, snowDepth, heightCanopyTopAboveSnow, heightCanopyBottomAboveSnow, exposedVAI = ', &
- heightCanopyTop, snowDepth, heightCanopyTopAboveSnow, heightCanopyBottomAboveSnow, exposedVAI
- message=trim(message)//'zero plane displacement is below the canopy bottom'
- err=20; return
- endif
-
- ! check measurement height
- if(mHeight < zeroPlaneDisplacement)then; err=20; message=trim(message)//'measurement height is below the displacement height'; return; end if
- if(mHeight < z0Canopy)then; err=20; message=trim(message)//'measurement height is below the roughness length'; return; end if
-
- ! -----------------------------------------------------------------------------------------------------------------------------------------
- ! -----------------------------------------------------------------------------------------------------------------------------------------
- ! * compute resistance for the case where the canopy is exposed
- ! compute the stability correction for resistance from canopy air space to air above the canopy (-)
- call aStability(&
- ! input
- derivDesired, & ! input: logical flag to compute analytical derivatives
- ixStability, & ! input: choice of stability function
- ! input: forcing data, diagnostic and state variables
- mHeight, & ! input: measurement height (m)
- airTemp, & ! input: air temperature above the canopy (K)
- canairTemp, & ! input: temperature of the canopy air space (K)
- windspd, & ! input: wind speed above the canopy (m s-1)
- ! input: stability parameters
- critRichNumber, & ! input: critical value for the bulk Richardson number where turbulence ceases (-)
- Louis79_bparam, & ! input: parameter in Louis (1979) stability function
- Mahrt87_eScale, & ! input: exponential scaling factor in the Mahrt (1987) stability function
- ! output
- RiBulkCanopy, & ! output: bulk Richardson number (-)
- canopyStabilityCorrection, & ! output: stability correction for turbulent heat fluxes (-)
- dCanopyStabilityCorrection_dRich, & ! output: derivative in stability correction w.r.t. Richardson number for the canopy (-)
- dCanopyStabilityCorrection_dAirTemp, & ! output: (not used) derivative in stability correction w.r.t. air temperature (K-1)
- dCanopyStabilityCorrection_dCasTemp, & ! output: derivative in stability correction w.r.t. canopy air space temperature (K-1)
- err, cmessage ) ! output: error control
- if(err/=0)then; message=trim(message)//trim(cmessage); return; end if
-
- ! compute turbulent exchange coefficient (-)
- canopyExNeut = (vkc**2._rkind) / ( log((mHeight - zeroPlaneDisplacement)/z0Canopy))**2._rkind ! coefficient under conditions of neutral stability
- sfc2AtmExchangeCoeff_canopy = canopyExNeut*canopyStabilityCorrection ! after stability corrections
-
- ! compute the friction velocity (m s-1)
- frictionVelocity = windspd * sqrt(sfc2AtmExchangeCoeff_canopy)
-
- ! compute the above-canopy resistance (s m-1)
- canopyResistance = 1._rkind/(sfc2AtmExchangeCoeff_canopy*windspd)
- if(canopyResistance < 0._rkind)then; err=20; message=trim(message)//'canopy resistance < 0'; return; end if
-
- ! compute windspeed at the top of the canopy above snow depth (m s-1)
- ! NOTE: stability corrections cancel out
- windConvFactor_fv = log((heightCanopyTopAboveSnow - zeroPlaneDisplacement)/z0Canopy) / log((mHeight - snowDepth - zeroPlaneDisplacement)/z0Canopy)
- windspdCanopyTop = windspd*windConvFactor_fv
-
- ! compute the windspeed reduction
- ! Refs: Norman et al. (Ag. Forest Met., 1995) -- citing Goudriaan (1977 manuscript "crop micrometeorology: a simulation study", Wageningen).
- windReductionFactor = windReductionParam * exposedVAI**twoThirds * (heightCanopyTopAboveSnow - heightCanopyBottomAboveSnow)**oneThird / leafDimension**oneThird
-
- ! compute windspeed at the height z0Canopy+zeroPlaneDisplacement (m s-1)
- referenceHeight = z0Canopy+zeroPlaneDisplacement
- windConvFactor = exp(-windReductionFactor*(1._rkind - (referenceHeight/heightCanopyTopAboveSnow)))
- windspdRefHeight = windspdCanopyTop*windConvFactor
-
- ! compute windspeed at the bottom of the canopy relative to the snow depth (m s-1)
- windConvFactor = exp(-windReductionFactor*(1._rkind - (heightCanopyBottomAboveSnow/heightCanopyTopAboveSnow)))
- windspdCanopyBottom = windspdCanopyTop*windConvFactor
-
- ! compute the leaf boundary layer resistance (s m-1)
- singleLeafConductance = leafExchangeCoeff*sqrt(windspdCanopyTop/leafDimension)
- leaf2CanopyScaleFactor = (2._rkind/windReductionFactor) * (1._rkind - exp(-windReductionFactor/2._rkind)) ! factor to scale from the leaf to the canopy
- canopyLeafConductance = singleLeafConductance*leaf2CanopyScaleFactor
- leafResistance = 1._rkind/(canopyLeafConductance)
- if(leafResistance < 0._rkind)then; err=20; message=trim(message)//'leaf resistance < 0'; return; end if
-
- ! compute eddy diffusivity for heat at the top of the canopy (m2 s-1)
- ! Note: use of friction velocity here includes stability adjustments
- ! Note: max used to avoid dividing by zero
- eddyDiffusCanopyTop = max(vkc*FrictionVelocity*(heightCanopyTopAboveSnow - zeroPlaneDisplacement), mpe)
-
- ! compute the resistance between the surface and canopy air UNDER NEUTRAL CONDITIONS (s m-1)
-
- ! case 1: assume exponential profile extends from the snow depth plus surface roughness length to the displacement height plus vegetation roughness
- if(ixWindProfile==exponential .or. heightCanopyBottomAboveSnow<z0Ground+xTolerance)then
-
- ! compute the neutral ground resistance
- tmp1 = exp(-windReductionFactor* z0Ground/heightCanopyTopAboveSnow)
- tmp2 = exp(-windReductionFactor*(z0Canopy+zeroPlaneDisplacement)/heightCanopyTopAboveSnow)
- groundResistanceNeutral = ( heightCanopyTopAboveSnow*exp(windReductionFactor) / (windReductionFactor*eddyDiffusCanopyTop) ) * (tmp1 - tmp2) ! s m-1
-
- ! case 2: logarithmic profile from snow depth plus roughness height to bottom of the canopy
- ! NOTE: heightCanopyBottomAboveSnow>z0Ground+xTolerance
- else
-
- ! compute the neutral ground resistance
- ! (first, component between heightCanopyBottomAboveSnow and z0Canopy+zeroPlaneDisplacement)
- tmp1 = exp(-windReductionFactor* heightCanopyBottomAboveSnow/heightCanopyTopAboveSnow)
- tmp2 = exp(-windReductionFactor*(z0Canopy+zeroPlaneDisplacement)/heightCanopyTopAboveSnow)
- groundResistanceNeutral = ( heightCanopyTopAboveSnow*exp(windReductionFactor) / (windReductionFactor*eddyDiffusCanopyTop) ) * (tmp1 - tmp2)
- ! (add log-below-canopy component)
- groundResistanceNeutral = groundResistanceNeutral + (1._rkind/(max(0.1_rkind,windspdCanopyBottom)*vkc**2._rkind))*(log(heightCanopyBottomAboveSnow/z0Ground))**2._rkind
-
- endif ! switch between exponential profile and log-below-canopy
-
- ! compute the stability correction for resistance from the ground to the canopy air space (-)
- ! NOTE: here we are interested in the windspeed at height z0Canopy+zeroPlaneDisplacement
- call aStability(&
- ! input
- derivDesired, & ! input: logical flag to compute analytical derivatives
- ixStability, & ! input: choice of stability function
- ! input: forcing data, diagnostic and state variables
- referenceHeight, & ! input: height of the canopy air space temperature/wind (m)
- canairTemp, & ! input: temperature of the canopy air space (K)
- groundTemp, & ! input: temperature of the ground surface (K)
- max(0.1_rkind,windspdRefHeight), & ! input: wind speed at height z0Canopy+zeroPlaneDisplacement (m s-1)
- ! input: stability parameters
- critRichNumber, & ! input: critical value for the bulk Richardson number where turbulence ceases (-)
- Louis79_bparam, & ! input: parameter in Louis (1979) stability function
- Mahrt87_eScale, & ! input: exponential scaling factor in the Mahrt (1987) stability function
- ! output
- RiBulkGround, & ! output: bulk Richardson number (-)
- groundStabilityCorrection, & ! output: stability correction for turbulent heat fluxes (-)
- dGroundStabilityCorrection_dRich, & ! output: derivative in stability correction w.r.t. Richardson number for the canopy (-)
- dGroundStabilityCorrection_dCasTemp, & ! output: derivative in stability correction w.r.t. canopy air space temperature (K-1)
- dGroundStabilityCorrection_dSfcTemp, & ! output: derivative in stability correction w.r.t. surface temperature (K-1)
- err, cmessage ) ! output: error control
- if(err/=0)then; message=trim(message)//trim(cmessage); return; end if
-
- ! compute the ground resistance
- groundResistance = groundResistanceNeutral / groundStabilityCorrection
- if(groundResistance < 0._rkind)then; err=20; message=trim(message)//'ground resistance < 0 [vegetation is present]'; return; end if
-
- ! -----------------------------------------------------------------------------------------------------------------------------------------
- ! -----------------------------------------------------------------------------------------------------------------------------------------
- ! * compute resistance for the case without a canopy (bare ground, or canopy completely buried with snow)
- else
-
- ! no canopy, so set huge resistances (not used)
- canopyResistance = 1.e12_rkind ! not used: huge resistance, so conductance is essentially zero
- leafResistance = 1.e12_rkind ! not used: huge resistance, so conductance is essentially zero
-
- ! check that measurement height above the ground surface is above the roughness length
- if(mHeight < snowDepth+z0Ground)then; err=20; message=trim(message)//'measurement height < snow depth + roughness length'; return; end if
-
- ! compute the resistance between the surface and canopy air UNDER NEUTRAL CONDITIONS (s m-1)
- groundExNeut = (vkc**2._rkind) / ( log((mHeight - snowDepth)/z0Ground)**2._rkind) ! turbulent transfer coefficient under conditions of neutral stability (-)
- groundResistanceNeutral = 1._rkind / (groundExNeut*windspd)
-
- ! define height above the snow surface
- heightAboveGround = mHeight - snowDepth
-
- ! check that measurement height above the ground surface is above the roughness length
- if(heightAboveGround < z0Ground)then
- print*, 'z0Ground = ', z0Ground
- print*, 'mHeight = ', mHeight
- print*, 'snowDepth = ', snowDepth
- print*, 'heightAboveGround = ', heightAboveGround
- message=trim(message)//'height above ground < roughness length [likely due to snow accumulation]'
- err=20; return
- end if
-
- ! compute ground stability correction
- call aStability(&
- ! input
- derivDesired, & ! input: logical flag to compute analytical derivatives
- ixStability, & ! input: choice of stability function
- ! input: forcing data, diagnostic and state variables
- heightAboveGround, & ! input: measurement height above the ground surface (m)
- airtemp, & ! input: temperature above the ground surface (K)
- groundTemp, & ! input: trial value of surface temperature -- "surface" is either canopy or ground (K)
- windspd, & ! input: wind speed above the ground surface (m s-1)
- ! input: stability parameters
- critRichNumber, & ! input: critical value for the bulk Richardson number where turbulence ceases (-)
- Louis79_bparam, & ! input: parameter in Louis (1979) stability function
- Mahrt87_eScale, & ! input: exponential scaling factor in the Mahrt (1987) stability function
- ! output
- RiBulkGround, & ! output: bulk Richardson number (-)
- groundStabilityCorrection, & ! output: stability correction for turbulent heat fluxes (-)
- dGroundStabilityCorrection_dRich, & ! output: derivative in stability correction w.r.t. Richardson number for the ground surface (-)
- dGroundStabilityCorrection_dAirTemp, & ! output: (not used) derivative in stability correction w.r.t. air temperature (K-1)
- dGroundStabilityCorrection_dSfcTemp, & ! output: derivative in stability correction w.r.t. surface temperature (K-1)
- err, cmessage ) ! output: error control
- if(err/=0)then; message=trim(message)//trim(cmessage); return; end if
-
- ! compute the ground resistance (after stability corrections)
- groundResistance = groundResistanceNeutral/groundStabilityCorrection
- if(groundResistance < 0._rkind)then; err=20; message=trim(message)//'ground resistance < 0 [no vegetation]'; return; end if
-
- ! set all canopy variables to missing (no canopy!)
- z0Canopy = missingValue ! roughness length of the vegetation canopy (m)
- RiBulkCanopy = missingValue ! bulk Richardson number for the canopy (-)
- windReductionFactor = missingValue ! canopy wind reduction factor (-)
- zeroPlaneDisplacement = missingValue ! zero plane displacement (m)
- canopyStabilityCorrection = missingValue ! stability correction for the canopy (-)
- eddyDiffusCanopyTop = missingValue ! eddy diffusivity for heat at the top of the canopy (m2 s-1)
- frictionVelocity = missingValue ! friction velocity (m s-1)
- windspdCanopyTop = missingValue ! windspeed at the top of the canopy (m s-1)
- windspdCanopyBottom = missingValue ! windspeed at the height of the bottom of the canopy (m s-1)
-
- end if ! (if no canopy)
-
- ! -----------------------------------------------------------------------------------------------------------------------------------------
- ! -----------------------------------------------------------------------------------------------------------------------------------------
- ! -----------------------------------------------------------------------------------------------------------------------------------------
- ! -----------------------------------------------------------------------------------------------------------------------------------------
- ! * compute derivatives
- if(derivDesired)then ! if analytical derivatives are desired
-
- ! derivatives for the vegetation canopy
- if(computeVegFlux) then ! (if vegetation is exposed)
-
- ! ***** compute derivatives w.r.t. canopy temperature
- ! NOTE: derivatives are zero because using canopy air space temperature
- dCanopyResistance_dTCanopy = 0._rkind ! derivative in canopy resistance w.r.t. canopy temperature (s m-1 K-1)
- dGroundResistance_dTCanopy = 0._rkind ! derivative in ground resistance w.r.t. canopy temperature (s m-1 K-1)
-
- ! ***** compute derivatives w.r.t. ground temperature (s m-1 K-1)
- dGroundResistance_dTGround = -(groundResistanceNeutral*dGroundStabilityCorrection_dSfcTemp)/(groundStabilityCorrection**2._rkind)
-
- ! ***** compute derivatives w.r.t. temperature of the canopy air space (s m-1 K-1)
- ! derivative in canopy resistance w.r.t. canopy air temperature (s m-1 K-1)
- dCanopyResistance_dTCanair = -dCanopyStabilityCorrection_dCasTemp/(windspd*canopyExNeut*canopyStabilityCorrection**2._rkind)
- ! derivative in ground resistance w.r.t. canopy air temperature (s m-1 K-1)
- ! (compute derivative in NEUTRAL ground resistance w.r.t. canopy air temperature (s m-1 K-1))
- dFV_dT = windspd*canopyExNeut*dCanopyStabilityCorrection_dCasTemp/(sqrt(sfc2AtmExchangeCoeff_canopy)*2._rkind) ! d(frictionVelocity)/d(canopy air temperature)
- dED_dT = dFV_dT*vkc*(heightCanopyTopAboveSnow - zeroPlaneDisplacement) ! d(eddyDiffusCanopyTop)d(canopy air temperature)
- dGR_dT = -dED_dT*(tmp1 - tmp2)*heightCanopyTopAboveSnow*exp(windReductionFactor) / (windReductionFactor*eddyDiffusCanopyTop**2._rkind) ! d(groundResistanceNeutral)/d(canopy air temperature)
- ! (stitch everything together -- product rule)
- dGroundResistance_dTCanair = dGR_dT/groundStabilityCorrection - groundResistanceNeutral*dGroundStabilityCorrection_dCasTemp/(groundStabilityCorrection**2._rkind)
-
+
+ end select ! vegetation traits (z0, zpd)
+
+ ! check zero plane displacement
+ if(zeroPlaneDisplacement < heightCanopyBottomAboveSnow)then
+ write(*,'(a,1x,10(f12.5,1x))') 'heightCanopyTop, snowDepth, heightCanopyTopAboveSnow, heightCanopyBottomAboveSnow, exposedVAI = ', &
+ heightCanopyTop, snowDepth, heightCanopyTopAboveSnow, heightCanopyBottomAboveSnow, exposedVAI
+ message=trim(message)//'zero plane displacement is below the canopy bottom'
+ err=20; return
+ endif
+
+ ! check measurement height
+ if(mHeight < zeroPlaneDisplacement)then; err=20; message=trim(message)//'measurement height is below the displacement height'; return; end if
+ if(mHeight < z0Canopy)then; err=20; message=trim(message)//'measurement height is below the roughness length'; return; end if
+
+ ! -----------------------------------------------------------------------------------------------------------------------------------------
+ ! -----------------------------------------------------------------------------------------------------------------------------------------
+ ! * compute resistance for the case where the canopy is exposed
+ ! compute the stability correction for resistance from canopy air space to air above the canopy (-)
+ call aStability(&
+ ! input
+ derivDesired, & ! input: logical flag to compute analytical derivatives
+ ixStability, & ! input: choice of stability function
+ ! input: forcing data, diagnostic and state variables
+ mHeight, & ! input: measurement height (m)
+ airTemp, & ! input: air temperature above the canopy (K)
+ canairTemp, & ! input: temperature of the canopy air space (K)
+ windspd, & ! input: wind speed above the canopy (m s-1)
+ ! input: stability parameters
+ critRichNumber, & ! input: critical value for the bulk Richardson number where turbulence ceases (-)
+ Louis79_bparam, & ! input: parameter in Louis (1979) stability function
+ Mahrt87_eScale, & ! input: exponential scaling factor in the Mahrt (1987) stability function
+ ! output
+ RiBulkCanopy, & ! output: bulk Richardson number (-)
+ canopyStabilityCorrection, & ! output: stability correction for turbulent heat fluxes (-)
+ dCanopyStabilityCorrection_dRich, & ! output: derivative in stability correction w.r.t. Richardson number for the canopy (-)
+ dCanopyStabilityCorrection_dAirTemp, & ! output: (not used) derivative in stability correction w.r.t. air temperature (K-1)
+ dCanopyStabilityCorrection_dCasTemp, & ! output: derivative in stability correction w.r.t. canopy air space temperature (K-1)
+ err, cmessage ) ! output: error control
+ if(err/=0)then; message=trim(message)//trim(cmessage); return; end if
+
+ ! compute turbulent exchange coefficient (-)
+ canopyExNeut = (vkc**2._rkind) / ( log((mHeight - zeroPlaneDisplacement)/z0Canopy))**2._rkind ! coefficient under conditions of neutral stability
+ sfc2AtmExchangeCoeff_canopy = canopyExNeut*canopyStabilityCorrection ! after stability corrections
+
+ ! compute the friction velocity (m s-1)
+ frictionVelocity = windspd * sqrt(sfc2AtmExchangeCoeff_canopy)
+
+ ! compute the above-canopy resistance (s m-1)
+ canopyResistance = 1._rkind/(sfc2AtmExchangeCoeff_canopy*windspd)
+ if(canopyResistance < 0._rkind)then; err=20; message=trim(message)//'canopy resistance < 0'; return; end if
+
+ ! compute windspeed at the top of the canopy above snow depth (m s-1)
+ ! NOTE: stability corrections cancel out
+ windConvFactor_fv = log((heightCanopyTopAboveSnow - zeroPlaneDisplacement)/z0Canopy) / log((mHeight - snowDepth - zeroPlaneDisplacement)/z0Canopy)
+ windspdCanopyTop = windspd*windConvFactor_fv
+
+ ! compute the windspeed reduction
+ ! Refs: Norman et al. (Ag. Forest Met., 1995) -- citing Goudriaan (1977 manuscript "crop micrometeorology: a simulation study", Wageningen).
+ windReductionFactor = windReductionParam * exposedVAI**twoThirds * (heightCanopyTopAboveSnow - heightCanopyBottomAboveSnow)**oneThird / leafDimension**oneThird
+
+ ! compute windspeed at the height z0Canopy+zeroPlaneDisplacement (m s-1)
+ referenceHeight = z0Canopy+zeroPlaneDisplacement
+ windConvFactor = exp(-windReductionFactor*(1._rkind - (referenceHeight/heightCanopyTopAboveSnow)))
+ windspdRefHeight = windspdCanopyTop*windConvFactor
+
+ ! compute windspeed at the bottom of the canopy relative to the snow depth (m s-1)
+ windConvFactor = exp(-windReductionFactor*(1._rkind - (heightCanopyBottomAboveSnow/heightCanopyTopAboveSnow)))
+ windspdCanopyBottom = windspdCanopyTop*windConvFactor
+
+ ! compute the leaf boundary layer resistance (s m-1)
+ singleLeafConductance = leafExchangeCoeff*sqrt(windspdCanopyTop/leafDimension)
+ leaf2CanopyScaleFactor = (2._rkind/windReductionFactor) * (1._rkind - exp(-windReductionFactor/2._rkind)) ! factor to scale from the leaf to the canopy
+ canopyLeafConductance = singleLeafConductance*leaf2CanopyScaleFactor
+ leafResistance = 1._rkind/(canopyLeafConductance)
+ if(leafResistance < 0._rkind)then; err=20; message=trim(message)//'leaf resistance < 0'; return; end if
+
+ ! compute eddy diffusivity for heat at the top of the canopy (m2 s-1)
+ ! Note: use of friction velocity here includes stability adjustments
+ ! Note: max used to avoid dividing by zero
+ eddyDiffusCanopyTop = max(vkc*FrictionVelocity*(heightCanopyTopAboveSnow - zeroPlaneDisplacement), mpe)
+
+ ! compute the resistance between the surface and canopy air UNDER NEUTRAL CONDITIONS (s m-1)
+
+ ! case 1: assume exponential profile extends from the snow depth plus surface roughness length to the displacement height plus vegetation roughness
+ if(ixWindProfile==exponential .or. heightCanopyBottomAboveSnow<z0Ground+xTolerance)then
+
+ ! compute the neutral ground resistance
+ tmp1 = exp(-windReductionFactor* z0Ground/heightCanopyTopAboveSnow)
+ tmp2 = exp(-windReductionFactor*(z0Canopy+zeroPlaneDisplacement)/heightCanopyTopAboveSnow)
+ groundResistanceNeutral = ( heightCanopyTopAboveSnow*exp(windReductionFactor) / (windReductionFactor*eddyDiffusCanopyTop) ) * (tmp1 - tmp2) ! s m-1
+
+ ! case 2: logarithmic profile from snow depth plus roughness height to bottom of the canopy
+ ! NOTE: heightCanopyBottomAboveSnow>z0Ground+xTolerance
+ else
+
+ ! compute the neutral ground resistance
+ ! (first, component between heightCanopyBottomAboveSnow and z0Canopy+zeroPlaneDisplacement)
+ tmp1 = exp(-windReductionFactor* heightCanopyBottomAboveSnow/heightCanopyTopAboveSnow)
+ tmp2 = exp(-windReductionFactor*(z0Canopy+zeroPlaneDisplacement)/heightCanopyTopAboveSnow)
+ groundResistanceNeutral = ( heightCanopyTopAboveSnow*exp(windReductionFactor) / (windReductionFactor*eddyDiffusCanopyTop) ) * (tmp1 - tmp2)
+ ! (add log-below-canopy component)
+ groundResistanceNeutral = groundResistanceNeutral + (1._rkind/(max(0.1_rkind,windspdCanopyBottom)*vkc**2._rkind))*(log(heightCanopyBottomAboveSnow/z0Ground))**2._rkind
+
+ endif ! switch between exponential profile and log-below-canopy
+
+ ! compute the stability correction for resistance from the ground to the canopy air space (-)
+ ! NOTE: here we are interested in the windspeed at height z0Canopy+zeroPlaneDisplacement
+ call aStability(&
+ ! input
+ derivDesired, & ! input: logical flag to compute analytical derivatives
+ ixStability, & ! input: choice of stability function
+ ! input: forcing data, diagnostic and state variables
+ referenceHeight, & ! input: height of the canopy air space temperature/wind (m)
+ canairTemp, & ! input: temperature of the canopy air space (K)
+ groundTemp, & ! input: temperature of the ground surface (K)
+ max(0.1_rkind,windspdRefHeight), & ! input: wind speed at height z0Canopy+zeroPlaneDisplacement (m s-1)
+ ! input: stability parameters
+ critRichNumber, & ! input: critical value for the bulk Richardson number where turbulence ceases (-)
+ Louis79_bparam, & ! input: parameter in Louis (1979) stability function
+ Mahrt87_eScale, & ! input: exponential scaling factor in the Mahrt (1987) stability function
+ ! output
+ RiBulkGround, & ! output: bulk Richardson number (-)
+ groundStabilityCorrection, & ! output: stability correction for turbulent heat fluxes (-)
+ dGroundStabilityCorrection_dRich, & ! output: derivative in stability correction w.r.t. Richardson number for the canopy (-)
+ dGroundStabilityCorrection_dCasTemp, & ! output: derivative in stability correction w.r.t. canopy air space temperature (K-1)
+ dGroundStabilityCorrection_dSfcTemp, & ! output: derivative in stability correction w.r.t. surface temperature (K-1)
+ err, cmessage ) ! output: error control
+ if(err/=0)then; message=trim(message)//trim(cmessage); return; end if
+
+ ! compute the ground resistance
+ groundResistance = groundResistanceNeutral / groundStabilityCorrection
+ if(groundResistance < 0._rkind)then; err=20; message=trim(message)//'ground resistance < 0 [vegetation is present]'; return; end if
+
+ ! -----------------------------------------------------------------------------------------------------------------------------------------
+ ! -----------------------------------------------------------------------------------------------------------------------------------------
+ ! * compute resistance for the case without a canopy (bare ground, or canopy completely buried with snow)
+ else
+
+ ! no canopy, so set huge resistances (not used)
+ canopyResistance = 1.e12_rkind ! not used: huge resistance, so conductance is essentially zero
+ leafResistance = 1.e12_rkind ! not used: huge resistance, so conductance is essentially zero
+
+ ! check that measurement height above the ground surface is above the roughness length
+ if(mHeight < snowDepth+z0Ground)then; err=20; message=trim(message)//'measurement height < snow depth + roughness length'; return; end if
+
+ ! compute the resistance between the surface and canopy air UNDER NEUTRAL CONDITIONS (s m-1)
+ groundExNeut = (vkc**2._rkind) / ( log((mHeight - snowDepth)/z0Ground)**2._rkind) ! turbulent transfer coefficient under conditions of neutral stability (-)
+ groundResistanceNeutral = 1._rkind / (groundExNeut*windspd)
+
+ ! define height above the snow surface
+ heightAboveGround = mHeight - snowDepth
+
+ ! check that measurement height above the ground surface is above the roughness length
+ if(heightAboveGround < z0Ground)then
+ print*, 'z0Ground = ', z0Ground
+ print*, 'mHeight = ', mHeight
+ print*, 'snowDepth = ', snowDepth
+ print*, 'heightAboveGround = ', heightAboveGround
+ message=trim(message)//'height above ground < roughness length [likely due to snow accumulation]'
+ err=20; return
+ end if
+
+ ! compute ground stability correction
+ call aStability(&
+ ! input
+ derivDesired, & ! input: logical flag to compute analytical derivatives
+ ixStability, & ! input: choice of stability function
+ ! input: forcing data, diagnostic and state variables
+ heightAboveGround, & ! input: measurement height above the ground surface (m)
+ airtemp, & ! input: temperature above the ground surface (K)
+ groundTemp, & ! input: trial value of surface temperature -- "surface" is either canopy or ground (K)
+ windspd, & ! input: wind speed above the ground surface (m s-1)
+ ! input: stability parameters
+ critRichNumber, & ! input: critical value for the bulk Richardson number where turbulence ceases (-)
+ Louis79_bparam, & ! input: parameter in Louis (1979) stability function
+ Mahrt87_eScale, & ! input: exponential scaling factor in the Mahrt (1987) stability function
+ ! output
+ RiBulkGround, & ! output: bulk Richardson number (-)
+ groundStabilityCorrection, & ! output: stability correction for turbulent heat fluxes (-)
+ dGroundStabilityCorrection_dRich, & ! output: derivative in stability correction w.r.t. Richardson number for the ground surface (-)
+ dGroundStabilityCorrection_dAirTemp, & ! output: (not used) derivative in stability correction w.r.t. air temperature (K-1)
+ dGroundStabilityCorrection_dSfcTemp, & ! output: derivative in stability correction w.r.t. surface temperature (K-1)
+ err, cmessage ) ! output: error control
+ if(err/=0)then; message=trim(message)//trim(cmessage); return; end if
+
+ ! compute the ground resistance (after stability corrections)
+ groundResistance = groundResistanceNeutral/groundStabilityCorrection
+ if(groundResistance < 0._rkind)then; err=20; message=trim(message)//'ground resistance < 0 [no vegetation]'; return; end if
+
+ ! set all canopy variables to missing (no canopy!)
+ z0Canopy = missingValue ! roughness length of the vegetation canopy (m)
+ RiBulkCanopy = missingValue ! bulk Richardson number for the canopy (-)
+ windReductionFactor = missingValue ! canopy wind reduction factor (-)
+ zeroPlaneDisplacement = missingValue ! zero plane displacement (m)
+ canopyStabilityCorrection = missingValue ! stability correction for the canopy (-)
+ eddyDiffusCanopyTop = missingValue ! eddy diffusivity for heat at the top of the canopy (m2 s-1)
+ frictionVelocity = missingValue ! friction velocity (m s-1)
+ windspdCanopyTop = missingValue ! windspeed at the top of the canopy (m s-1)
+ windspdCanopyBottom = missingValue ! windspeed at the height of the bottom of the canopy (m s-1)
+
+ end if ! (if no canopy)
+
+ ! -----------------------------------------------------------------------------------------------------------------------------------------
+ ! -----------------------------------------------------------------------------------------------------------------------------------------
+ ! -----------------------------------------------------------------------------------------------------------------------------------------
+ ! -----------------------------------------------------------------------------------------------------------------------------------------
+ ! * compute derivatives
+ if(derivDesired)then ! if analytical derivatives are desired
+
+ ! derivatives for the vegetation canopy
+ if(computeVegFlux) then ! (if vegetation is exposed)
+
+ ! ***** compute derivatives w.r.t. canopy temperature
+ ! NOTE: derivatives are zero because using canopy air space temperature
+ dCanopyResistance_dTCanopy = 0._rkind ! derivative in canopy resistance w.r.t. canopy temperature (s m-1 K-1)
+ dGroundResistance_dTCanopy = 0._rkind ! derivative in ground resistance w.r.t. canopy temperature (s m-1 K-1)
+
+ ! ***** compute derivatives w.r.t. ground temperature (s m-1 K-1)
+ dGroundResistance_dTGround = -(groundResistanceNeutral*dGroundStabilityCorrection_dSfcTemp)/(groundStabilityCorrection**2._rkind)
+
+ ! ***** compute derivatives w.r.t. temperature of the canopy air space (s m-1 K-1)
+ ! derivative in canopy resistance w.r.t. canopy air temperature (s m-1 K-1)
+ dCanopyResistance_dTCanair = -dCanopyStabilityCorrection_dCasTemp/(windspd*canopyExNeut*canopyStabilityCorrection**2._rkind)
+ ! derivative in ground resistance w.r.t. canopy air temperature (s m-1 K-1)
+ ! (compute derivative in NEUTRAL ground resistance w.r.t. canopy air temperature (s m-1 K-1))
+ dFV_dT = windspd*canopyExNeut*dCanopyStabilityCorrection_dCasTemp/(sqrt(sfc2AtmExchangeCoeff_canopy)*2._rkind) ! d(frictionVelocity)/d(canopy air temperature)
+ dED_dT = dFV_dT*vkc*(heightCanopyTopAboveSnow - zeroPlaneDisplacement) ! d(eddyDiffusCanopyTop)d(canopy air temperature)
+ dGR_dT = -dED_dT*(tmp1 - tmp2)*heightCanopyTopAboveSnow*exp(windReductionFactor) / (windReductionFactor*eddyDiffusCanopyTop**2._rkind) ! d(groundResistanceNeutral)/d(canopy air temperature)
+ ! (stitch everything together -- product rule)
+ dGroundResistance_dTCanair = dGR_dT/groundStabilityCorrection - groundResistanceNeutral*dGroundStabilityCorrection_dCasTemp/(groundStabilityCorrection**2._rkind)
+
! ***** compute resistances for non-vegetated surfaces (e.g., snow)
- else
-
- ! set canopy derivatives to zero (non-vegetated, remember)
- dCanopyResistance_dTCanopy = 0._rkind
- dGroundResistance_dTCanopy = 0._rkind
-
- ! compute derivatives for ground resistance
- dGroundResistance_dTGround = -dGroundStabilityCorrection_dSfcTemp/(windspd*groundExNeut*groundStabilityCorrection**2._rkind)
-
- end if ! (switch between vegetated and non-vegetated surfaces)
-
- ! * analytical derivatives not desired
- else
- dGroundResistance_dTGround = missingValue
- dGroundResistance_dTCanopy = missingValue
- dCanopyResistance_dTCanopy = missingValue
- end if
-
- ! test
- !print*, 'dGroundResistance_dTGround = ', dGroundResistance_dTGround
- !print*, 'dGroundResistance_dTCanopy = ', dGroundResistance_dTCanopy
- !print*, 'dCanopyResistance_dTCanopy = ', dCanopyResistance_dTCanopy
- !pause 'in aeroResist'
-
- end subroutine aeroResist
-
-
- ! *******************************************************************************************************
- ! private subroutine soilResist: compute soil moisture factor controlling stomatal resistance
- ! *******************************************************************************************************
- subroutine soilResist(&
- ! input (model decisions)
- ixSoilResist, & ! intent(in): choice of function for the soil moisture control on stomatal resistance
- ixGroundwater, & ! intent(in): choice of groundwater representation
- ! input (state variables)
- mLayerMatricHead, & ! intent(in): matric head in each layer (m)
- mLayerVolFracLiq, & ! intent(in): volumetric fraction of liquid water in each layer
- scalarAquiferStorage, & ! intent(in): aquifer storage (m)
- ! input (diagnostic variables)
- mLayerRootDensity, & ! intent(in): root density in each layer (-)
- scalarAquiferRootFrac, & ! intent(in): fraction of roots below the lowest unsaturated layer (-)
- ! input (parameters)
- plantWiltPsi, & ! intent(in): matric head at wilting point (m)
- soilStressParam, & ! intent(in): parameter in the exponential soil stress function (-)
- critSoilWilting, & ! intent(in): critical vol. liq. water content when plants are wilting (-)
- critSoilTranspire, & ! intent(in): critical vol. liq. water content when transpiration is limited (-)
- critAquiferTranspire, & ! intent(in): critical aquifer storage value when transpiration is limited (m)
- ! output
- wAvgTranspireLimitFac, & ! intent(out): weighted average of the transpiration limiting factor (-)
- mLayerTranspireLimitFac, & ! intent(out): transpiration limiting factor in each layer (-)
- aquiferTranspireLimitFac, & ! intent(out): transpiration limiting factor for the aquifer (-)
- err,message) ! intent(out): error control
- ! -----------------------------------------------------------------------------------------------------------------------------------------
- USE mDecisions_module, only: NoahType,CLM_Type,SiB_Type ! options for the choice of function for the soil moisture control on stomatal resistance
- USE mDecisions_module, only: bigBucket ! named variable that defines the "bigBucket" groundwater parameterization
- implicit none
- ! input (model decisions)
- integer(i4b),intent(in) :: ixSoilResist ! choice of function for the soil moisture control on stomatal resistance
- integer(i4b),intent(in) :: ixGroundwater ! choice of groundwater representation
- ! input (variables)
- real(rkind),intent(in) :: mLayerMatricHead(:) ! matric head in each layer (m)
- real(rkind),intent(in) :: mLayerVolFracLiq(:) ! volumetric fraction of liquid water in each layer (-)
- real(rkind),intent(in) :: scalarAquiferStorage ! aquifer storage (m)
- ! input (diagnostic variables)
- real(rkind),intent(in) :: mLayerRootDensity(:) ! root density in each layer (-)
- real(rkind),intent(in) :: scalarAquiferRootFrac ! fraction of roots below the lowest unsaturated layer (-)
- ! input (parameters)
- real(rkind),intent(in) :: plantWiltPsi ! matric head at wilting point (m)
- real(rkind),intent(in) :: soilStressParam ! parameter in the exponential soil stress function (-)
- real(rkind),intent(in) :: critSoilWilting ! critical vol. liq. water content when plants are wilting (-)
- real(rkind),intent(in) :: critSoilTranspire ! critical vol. liq. water content when transpiration is limited (-)
- real(rkind),intent(in) :: critAquiferTranspire ! critical aquifer storage value when transpiration is limited (m)
- ! output
- real(rkind),intent(out) :: wAvgTranspireLimitFac ! intent(out): weighted average of the transpiration limiting factor (-)
- real(rkind),intent(out) :: mLayerTranspireLimitFac(:) ! intent(out): transpiration limiting factor in each layer (-)
- real(rkind),intent(out) :: aquiferTranspireLimitFac ! intent(out): transpiration limiting factor for the aquifer (-)
- integer(i4b),intent(out) :: err ! error code
- character(*),intent(out) :: message ! error message
- ! local variables
- real(rkind) :: gx ! stress function for the soil layers
- real(rkind),parameter :: verySmall=epsilon(gx) ! a very small number
- integer(i4b) :: iLayer ! index of soil layer
- ! initialize error control
- err=0; message='soilResist/'
-
- ! ** compute the factor limiting transpiration for each soil layer (-)
- wAvgTranspireLimitFac = 0._rkind ! (initialize the weighted average)
- do iLayer=1,size(mLayerMatricHead)
- ! compute the soil stress function
- select case(ixSoilResist)
- case(NoahType) ! thresholded linear function of volumetric liquid water content
+ else
+
+ ! set canopy derivatives to zero (non-vegetated, remember)
+ dCanopyResistance_dTCanopy = 0._rkind
+ dGroundResistance_dTCanopy = 0._rkind
+
+ ! compute derivatives for ground resistance
+ dGroundResistance_dTGround = -dGroundStabilityCorrection_dSfcTemp/(windspd*groundExNeut*groundStabilityCorrection**2._rkind)
+
+ end if ! (switch between vegetated and non-vegetated surfaces)
+
+ ! * analytical derivatives not desired
+ else
+ dGroundResistance_dTGround = missingValue
+ dGroundResistance_dTCanopy = missingValue
+ dCanopyResistance_dTCanopy = missingValue
+ end if
+
+end subroutine aeroResist
+
+
+! *******************************************************************************************************
+! private subroutine soilResist: compute soil moisture factor controlling stomatal resistance
+! *******************************************************************************************************
+subroutine soilResist(&
+ ! input (model decisions)
+ ixSoilResist, & ! intent(in): choice of function for the soil moisture control on stomatal resistance
+ ixGroundwater, & ! intent(in): choice of groundwater representation
+ ! input (state variables)
+ mLayerMatricHead, & ! intent(in): matric head in each layer (m)
+ mLayerVolFracLiq, & ! intent(in): volumetric fraction of liquid water in each layer
+ scalarAquiferStorage, & ! intent(in): aquifer storage (m)
+ ! input (diagnostic variables)
+ mLayerRootDensity, & ! intent(in): root density in each layer (-)
+ scalarAquiferRootFrac, & ! intent(in): fraction of roots below the lowest unsaturated layer (-)
+ ! input (parameters)
+ plantWiltPsi, & ! intent(in): matric head at wilting point (m)
+ soilStressParam, & ! intent(in): parameter in the exponential soil stress function (-)
+ critSoilWilting, & ! intent(in): critical vol. liq. water content when plants are wilting (-)
+ critSoilTranspire, & ! intent(in): critical vol. liq. water content when transpiration is limited (-)
+ critAquiferTranspire, & ! intent(in): critical aquifer storage value when transpiration is limited (m)
+ ! output
+ wAvgTranspireLimitFac, & ! intent(out): weighted average of the transpiration limiting factor (-)
+ mLayerTranspireLimitFac, & ! intent(out): transpiration limiting factor in each layer (-)
+ aquiferTranspireLimitFac, & ! intent(out): transpiration limiting factor for the aquifer (-)
+ err,message) ! intent(out): error control
+ ! -----------------------------------------------------------------------------------------------------------------------------------------
+ USE mDecisions_module, only: NoahType,CLM_Type,SiB_Type ! options for the choice of function for the soil moisture control on stomatal resistance
+ USE mDecisions_module, only: bigBucket ! named variable that defines the "bigBucket" groundwater parameterization
+ implicit none
+ ! input (model decisions)
+ integer(i4b),intent(in) :: ixSoilResist ! choice of function for the soil moisture control on stomatal resistance
+ integer(i4b),intent(in) :: ixGroundwater ! choice of groundwater representation
+ ! input (variables)
+ real(rkind),intent(in) :: mLayerMatricHead(:) ! matric head in each layer (m)
+ real(rkind),intent(in) :: mLayerVolFracLiq(:) ! volumetric fraction of liquid water in each layer (-)
+ real(rkind),intent(in) :: scalarAquiferStorage ! aquifer storage (m)
+ ! input (diagnostic variables)
+ real(rkind),intent(in) :: mLayerRootDensity(:) ! root density in each layer (-)
+ real(rkind),intent(in) :: scalarAquiferRootFrac ! fraction of roots below the lowest unsaturated layer (-)
+ ! input (parameters)
+ real(rkind),intent(in) :: plantWiltPsi ! matric head at wilting point (m)
+ real(rkind),intent(in) :: soilStressParam ! parameter in the exponential soil stress function (-)
+ real(rkind),intent(in) :: critSoilWilting ! critical vol. liq. water content when plants are wilting (-)
+ real(rkind),intent(in) :: critSoilTranspire ! critical vol. liq. water content when transpiration is limited (-)
+ real(rkind),intent(in) :: critAquiferTranspire ! critical aquifer storage value when transpiration is limited (m)
+ ! output
+ real(rkind),intent(out) :: wAvgTranspireLimitFac ! intent(out): weighted average of the transpiration limiting factor (-)
+ real(rkind),intent(out) :: mLayerTranspireLimitFac(:) ! intent(out): transpiration limiting factor in each layer (-)
+ real(rkind),intent(out) :: aquiferTranspireLimitFac ! intent(out): transpiration limiting factor for the aquifer (-)
+ integer(i4b),intent(out) :: err ! error code
+ character(*),intent(out) :: message ! error message
+ ! local variables
+ real(rkind) :: gx ! stress function for the soil layers
+ real(rkind),parameter :: verySmall=epsilon(gx) ! a very small number
+ integer(i4b) :: iLayer ! index of soil layer
+ ! initialize error control
+ err=0; message='soilResist/'
+
+ ! ** compute the factor limiting transpiration for each soil layer (-)
+ wAvgTranspireLimitFac = 0._rkind ! (initialize the weighted average)
+ do iLayer=1,size(mLayerMatricHead)
+ ! compute the soil stress function
+ select case(ixSoilResist)
+ case(NoahType) ! thresholded linear function of volumetric liquid water content
gx = (mLayerVolFracLiq(iLayer) - critSoilWilting) / (critSoilTranspire - critSoilWilting)
- case(CLM_Type) ! thresholded linear function of matric head
+ case(CLM_Type) ! thresholded linear function of matric head
if(mLayerMatricHead(iLayer) > plantWiltPsi)then
- gx = 1._rkind - mLayerMatricHead(iLayer)/plantWiltPsi
+ gx = 1._rkind - mLayerMatricHead(iLayer)/plantWiltPsi
else
- gx = 0._rkind
+ gx = 0._rkind
end if
- case(SiB_Type) ! exponential of the log of matric head
+ case(SiB_Type) ! exponential of the log of matric head
if(mLayerMatricHead(iLayer) < 0._rkind)then ! (unsaturated)
- gx = 1._rkind - exp( -soilStressParam * ( log(plantWiltPsi/mLayerMatricHead(iLayer)) ) )
+ gx = 1._rkind - exp( -soilStressParam * ( log(plantWiltPsi/mLayerMatricHead(iLayer)) ) )
else ! (saturated)
- gx = 1._rkind
+ gx = 1._rkind
end if
- case default ! check identified the option
+ case default ! check identified the option
err=20; message=trim(message)//'cannot identify option for soil resistance'; return
- end select
- ! save the factor for the given layer (ensure between zero and one)
- mLayerTranspireLimitFac(iLayer) = min( max(verySmall,gx), 1._rkind)
- ! compute the weighted average (weighted by root density)
- wAvgTranspireLimitFac = wAvgTranspireLimitFac + mLayerTranspireLimitFac(iLayer)*mLayerRootDensity(iLayer)
- end do ! (looping through soil layers)
-
- ! ** compute the factor limiting evaporation in the aquifer
- if(scalarAquiferRootFrac > verySmall)then
- ! check that aquifer root fraction is allowed
- if(ixGroundwater /= bigBucket)then
- message=trim(message)//'aquifer evaporation only allowed for the big groundwater bucket -- increase the soil depth to account for roots'
- err=20; return
- end if
- ! compute the factor limiting evaporation for the aquifer
- aquiferTranspireLimitFac = min(scalarAquiferStorage/critAquiferTranspire, 1._rkind)
- else ! (if there are roots in the aquifer)
- aquiferTranspireLimitFac = 0._rkind
- end if
-
- ! compute the weighted average (weighted by root density)
- wAvgTranspireLimitFac = wAvgTranspireLimitFac + aquiferTranspireLimitFac*scalarAquiferRootFrac
-
- end subroutine soilResist
-
-
- ! ********************************************************************************
- ! private subroutine turbFluxes: compute turbulent heat fluxes
- ! ********************************************************************************
- subroutine turbFluxes(&
- ! input: model control
- computeVegFlux, & ! intent(in): logical flag to compute vegetation fluxes (.false. if veg buried by snow)
- ixDerivMethod, & ! intent(in): choice of method used to compute derivative (analytical or numerical)
- ! input: above-canopy forcing data
- airtemp, & ! intent(in): air temperature at some height above the surface (K)
- airpres, & ! intent(in): air pressure of the air above the vegetation canopy (Pa)
- VPair, & ! intent(in): vapor pressure of the air above the vegetation canopy (Pa)
- ! input: latent heat of sublimation/vaporization
- latHeatSubVapCanopy, & ! intent(in): latent heat of sublimation/vaporization for the vegetation canopy (J kg-1)
- latHeatSubVapGround, & ! intent(in): latent heat of sublimation/vaporization for the ground surface (J kg-1)
- ! input: canopy and ground temperature
- canairTemp, & ! intent(in): temperature of the canopy air space (K)
- canopyTemp, & ! intent(in): canopy temperature (K)
- groundTemp, & ! intent(in): ground temperature (K)
- satVP_CanopyTemp, & ! intent(in): saturation vapor pressure at the temperature of the veg canopy (Pa)
- satVP_GroundTemp, & ! intent(in): saturation vapor pressure at the temperature of the ground (Pa)
- dSVPCanopy_dCanopyTemp, & ! intent(in): derivative in canopy saturation vapor pressure w.r.t. canopy temperature (Pa K-1)
- dSVPGround_dGroundTemp, & ! intent(in): derivative in ground saturation vapor pressure w.r.t. ground temperature (Pa K-1)
- ! input: diagnostic variables
- exposedVAI, & ! intent(in): exposed vegetation area index -- leaf plus stem (m2 m-2)
- canopyWetFraction, & ! intent(in): fraction of canopy that is wet [0-1]
- dCanopyWetFraction_dWat, & ! intent(in): derivative in the canopy wetted fraction w.r.t. total water content (kg-1 m-2)
- dCanopyWetFraction_dT, & ! intent(in): derivative in wetted fraction w.r.t. canopy temperature (K-1)
- canopySunlitLAI, & ! intent(in): sunlit leaf area (-)
- canopyShadedLAI, & ! intent(in): shaded leaf area (-)
- soilRelHumidity, & ! intent(in): relative humidity in the soil pores [0-1]
- soilResistance, & ! intent(in): resistance from the soil (s m-1)
- leafResistance, & ! intent(in): mean leaf boundary layer resistance per unit leaf area (s m-1)
- groundResistance, & ! intent(in): below canopy aerodynamic resistance (s m-1)
- canopyResistance, & ! intent(in): above canopy aerodynamic resistance (s m-1)
- stomResistSunlit, & ! intent(in): stomatal resistance for sunlit leaves (s m-1)
- stomResistShaded, & ! intent(in): stomatal resistance for shaded leaves (s m-1)
- ! input: derivatives in scalar resistances
- dGroundResistance_dTGround, & ! intent(in): derivative in ground resistance w.r.t. ground temperature (s m-1 K-1)
- dGroundResistance_dTCanopy, & ! intent(in): derivative in ground resistance w.r.t. canopy temperature (s m-1 K-1)
- dGroundResistance_dTCanair, & ! intent(in): derivative in ground resistance w.r.t. canopy air temperature (s m-1 K-1)
- dCanopyResistance_dTCanopy, & ! intent(in): derivative in canopy resistance w.r.t. canopy temperature (s m-1 K-1)
- dCanopyResistance_dTCanair, & ! intent(in): derivative in canopy resistance w.r.t. canopy air temperature (s m-1 K-1)
- ! output: conductances (used to check derivative calculations)
- leafConductance, & ! intent(out): leaf conductance (m s-1)
- canopyConductance, & ! intent(out): canopy conductance (m s-1)
- groundConductanceSH, & ! intent(out): ground conductance for sensible heat (m s-1)
- groundConductanceLH, & ! intent(out): ground conductance for latent heat -- includes soil resistance (m s-1)
- evapConductance, & ! intent(out): conductance for evaporation (m s-1)
- transConductance, & ! intent(out): conductance for transpiration (m s-1)
- totalConductanceSH, & ! intent(out): total conductance for sensible heat (m s-1)
- totalConductanceLH, & ! intent(out): total conductance for latent heat (m s-1)
- ! output: canopy air space variables
- VP_CanopyAir, & ! intent(out): vapor pressure of the canopy air space (Pa)
- ! output: fluxes from the vegetation canopy
- senHeatCanopy, & ! intent(out): sensible heat flux from the canopy to the canopy air space (W m-2)
- latHeatCanopyEvap, & ! intent(out): latent heat flux associated with evaporation from the canopy to the canopy air space (W m-2)
- latHeatCanopyTrans, & ! intent(out): latent heat flux associated with transpiration from the canopy to the canopy air space (W m-2)
- ! output: fluxes from non-vegetated surfaces (ground surface below vegetation, bare ground, or snow covered vegetation)
- senHeatGround, & ! intent(out): sensible heat flux from ground surface below vegetation, bare ground, or snow covered vegetation (W m-2)
- latHeatGround, & ! intent(out): latent heat flux from ground surface below vegetation, bare ground, or snow covered vegetation (W m-2)
- ! output: total heat fluxes to the atmosphere
- senHeatTotal, & ! intent(out): total sensible heat flux to the atmosphere (W m-2)
- latHeatTotal, & ! intent(out): total latent heat flux to the atmosphere (W m-2)
- ! output: net fluxes
- turbFluxCanair, & ! intent(out): net turbulent heat fluxes at the canopy air space (W m-2)
- turbFluxCanopy, & ! intent(out): net turbulent heat fluxes at the canopy (W m-2)
- turbFluxGround, & ! intent(out): net turbulent heat fluxes at the ground surface (W m-2)
- ! output: flux derivatives
- dTurbFluxCanair_dTCanair, & ! intent(out): derivative in net canopy air space fluxes w.r.t. canopy air temperature (W m-2 K-1)
- dTurbFluxCanair_dTCanopy, & ! intent(out): derivative in net canopy air space fluxes w.r.t. canopy temperature (W m-2 K-1)
- dTurbFluxCanair_dTGround, & ! intent(out): derivative in net canopy air space fluxes w.r.t. ground temperature (W m-2 K-1)
- dTurbFluxCanopy_dTCanair, & ! intent(out): derivative in net canopy turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
- dTurbFluxCanopy_dTCanopy, & ! intent(out): derivative in net canopy turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
- dTurbFluxCanopy_dTGround, & ! intent(out): derivative in net canopy turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
- dTurbFluxGround_dTCanair, & ! intent(out): derivative in net ground turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
- dTurbFluxGround_dTCanopy, & ! intent(out): derivative in net ground turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
- dTurbFluxGround_dTGround, & ! intent(out): derivative in net ground turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
- ! output: liquid flux derivatives (canopy evap)
- dLatHeatCanopyEvap_dCanWat, & ! intent(out): derivative in latent heat of canopy evaporation w.r.t. canopy total water content (J kg-1 s-1)
- dLatHeatCanopyEvap_dTCanair, & ! intent(out): derivative in latent heat of canopy evaporation w.r.t. canopy air temperature (W m-2 K-1)
- dLatHeatCanopyEvap_dTCanopy, & ! intent(out): derivative in latent heat of canopy evaporation w.r.t. canopy temperature (W m-2 K-1)
- dLatHeatCanopyEvap_dTGround, & ! intent(out): derivative in latent heat of canopy evaporation w.r.t. ground temperature (W m-2 K-1)
- ! output: liquid flux derivatives (ground evap)
- dLatHeatGroundEvap_dCanWat, & ! intent(out): derivative in latent heat of ground evaporation w.r.t. canopy total water content (J kg-1 s-1)
- dLatHeatGroundEvap_dTCanair, & ! intent(out): derivative in latent heat of ground evaporation w.r.t. canopy air temperature
- dLatHeatGroundEvap_dTCanopy, & ! intent(out): derivative in latent heat of ground evaporation w.r.t. canopy temperature
- dLatHeatGroundEvap_dTGround, & ! intent(out): derivative in latent heat of ground evaporation w.r.t. ground temperature
- ! output: latent heat flux derivatives (canopy trans)
- dLatHeatCanopyTrans_dCanWat, & ! intent(out): derivative in the latent heat of canopy transpiration w.r.t. canopy total water (J kg-1 s-1)
- dLatHeatCanopyTrans_dTCanair, & ! intent(out): derivative in the latent heat of canopy transpiration w.r.t. canopy air temperature
- dLatHeatCanopyTrans_dTCanopy, & ! intent(out): derivative in the latent heat of canopy transpiration w.r.t. canopy temperature
- dLatHeatCanopyTrans_dTGround, & ! intent(out): derivative in the latent heat of canopy transpiration w.r.t. ground temperature
- ! output: cross derivatives
- dTurbFluxCanair_dCanWat, & ! intent(out): derivative in net canopy air space fluxes w.r.t. canopy total water content (J kg-1 s-1)
- dTurbFluxCanopy_dCanWat, & ! intent(out): derivative in net canopy turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
- dTurbFluxGround_dCanWat, & ! intent(out): derivative in net ground turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
- ! output: error control
- err,message ) ! intent(out): error control
- ! -----------------------------------------------------------------------------------------------------------------------------------------
- implicit none
- ! input: model control
- logical(lgt),intent(in) :: computeVegFlux ! logical flag to compute vegetation fluxes (.false. if veg buried by snow)
- integer(i4b),intent(in) :: ixDerivMethod ! choice of method used to compute derivative (analytical or numerical)
- ! input: above-canopy forcing data
- real(rkind),intent(in) :: airtemp ! air temperature at some height above the surface (K)
- real(rkind),intent(in) :: airpres ! air pressure of the air above the vegetation canopy (Pa)
- real(rkind),intent(in) :: VPair ! vapor pressure of the air above the vegetation canopy (Pa)
- ! input: latent heat of sublimation/vaporization
- real(rkind),intent(in) :: latHeatSubVapCanopy ! latent heat of sublimation/vaporization for the vegetation canopy (J kg-1)
- real(rkind),intent(in) :: latHeatSubVapGround ! latent heat of sublimation/vaporization for the ground surface (J kg-1)
- ! input: canopy and ground temperature
- real(rkind),intent(in) :: canairTemp ! temperature of the canopy air space (K)
- real(rkind),intent(in) :: canopyTemp ! canopy temperature (K)
- real(rkind),intent(in) :: groundTemp ! ground temperature (K)
- real(rkind),intent(in) :: satVP_CanopyTemp ! saturation vapor pressure at the temperature of the veg canopy (Pa)
- real(rkind),intent(in) :: satVP_GroundTemp ! saturation vapor pressure at the temperature of the ground (Pa)
- real(rkind),intent(in) :: dSVPCanopy_dCanopyTemp ! derivative in canopy saturation vapor pressure w.r.t. canopy temperature (Pa K-1)
- real(rkind),intent(in) :: dSVPGround_dGroundTemp ! derivative in ground saturation vapor pressure w.r.t. ground temperature (Pa K-1)
- ! input: diagnostic variables
- real(rkind),intent(in) :: exposedVAI ! exposed vegetation area index -- leaf plus stem (m2 m-2)
- real(rkind),intent(in) :: canopyWetFraction ! fraction of canopy that is wet [0-1]
- real(rkind),intent(in) :: dCanopyWetFraction_dWat ! derivative in the canopy wetted fraction w.r.t. liquid water content (kg-1 m-2)
- real(rkind),intent(in) :: dCanopyWetFraction_dT ! derivative in the canopy wetted fraction w.r.t. canopy temperature (K-1)
- real(rkind),intent(in) :: canopySunlitLAI ! sunlit leaf area (-)
- real(rkind),intent(in) :: canopyShadedLAI ! shaded leaf area (-)
- real(rkind),intent(in) :: soilRelHumidity ! relative humidity in the soil pores [0-1]
- real(rkind),intent(in) :: soilResistance ! resistance from the soil (s m-1)
- real(rkind),intent(in) :: leafResistance ! mean leaf boundary layer resistance per unit leaf area (s m-1)
- real(rkind),intent(in) :: groundResistance ! below canopy aerodynamic resistance (s m-1)
- real(rkind),intent(in) :: canopyResistance ! above canopy aerodynamic resistance (s m-1)
- real(rkind),intent(in) :: stomResistSunlit ! stomatal resistance for sunlit leaves (s m-1)
- real(rkind),intent(in) :: stomResistShaded ! stomatal resistance for shaded leaves (s m-1)
- ! input: derivatives in scalar resistances
- real(rkind),intent(in) :: dGroundResistance_dTGround ! derivative in ground resistance w.r.t. ground temperature (s m-1 K-1)
- real(rkind),intent(in) :: dGroundResistance_dTCanopy ! derivative in ground resistance w.r.t. canopy temperature (s m-1 K-1)
- real(rkind),intent(in) :: dGroundResistance_dTCanair ! derivative in ground resistance w.r.t. canopy air temperature (s m-1 K-1)
- real(rkind),intent(in) :: dCanopyResistance_dTCanopy ! derivative in canopy resistance w.r.t. canopy temperature (s m-1 K-1)
- real(rkind),intent(in) :: dCanopyResistance_dTCanair ! derivative in canopy resistance w.r.t. canopy air temperature (s m-1 K-1)
- ! ---------------------------------------------------------------------------------------------------------------------------------------------------------------
- ! output: conductances -- used to test derivatives
- real(rkind),intent(out) :: leafConductance ! leaf conductance (m s-1)
- real(rkind),intent(out) :: canopyConductance ! canopy conductance (m s-1)
- real(rkind),intent(out) :: groundConductanceSH ! ground conductance for sensible heat (m s-1)
- real(rkind),intent(out) :: groundConductanceLH ! ground conductance for latent heat -- includes soil resistance (m s-1)
- real(rkind),intent(out) :: evapConductance ! conductance for evaporation (m s-1)
- real(rkind),intent(out) :: transConductance ! conductance for transpiration (m s-1)
- real(rkind),intent(out) :: totalConductanceSH ! total conductance for sensible heat (m s-1)
- real(rkind),intent(out) :: totalConductanceLH ! total conductance for latent heat (m s-1)
- ! output: canopy air space variables
- real(rkind),intent(out) :: VP_CanopyAir ! vapor pressure of the canopy air space (Pa)
- ! output: fluxes from the vegetation canopy
- real(rkind),intent(out) :: senHeatCanopy ! sensible heat flux from the canopy to the canopy air space (W m-2)
- real(rkind),intent(out) :: latHeatCanopyEvap ! latent heat flux associated with evaporation from the canopy to the canopy air space (W m-2)
- real(rkind),intent(out) :: latHeatCanopyTrans ! latent heat flux associated with transpiration from the canopy to the canopy air space (W m-2)
- ! output: fluxes from non-vegetated surfaces (ground surface below vegetation, bare ground, or snow covered vegetation)
- real(rkind),intent(out) :: senHeatGround ! sensible heat flux from ground surface below vegetation, bare ground, or snow covered vegetation (W m-2)
- real(rkind),intent(out) :: latHeatGround ! latent heat flux from ground surface below vegetation, bare ground, or snow covered vegetation (W m-2)
- ! output: total heat fluxes to the atmosphere
- real(rkind),intent(out) :: senHeatTotal ! total sensible heat flux to the atmosphere (W m-2)
- real(rkind),intent(out) :: latHeatTotal ! total latent heat flux to the atmosphere (W m-2)
- ! output: net fluxes
- real(rkind),intent(out) :: turbFluxCanair ! net turbulent heat fluxes at the canopy air space (W m-2)
- real(rkind),intent(out) :: turbFluxCanopy ! net turbulent heat fluxes at the canopy (W m-2)
- real(rkind),intent(out) :: turbFluxGround ! net turbulent heat fluxes at the ground surface (W m-2)
- ! output: energy flux derivatives
- real(rkind),intent(out) :: dTurbFluxCanair_dTCanair ! derivative in net canopy air space fluxes w.r.t. canopy air temperature (W m-2 K-1)
- real(rkind),intent(out) :: dTurbFluxCanair_dTCanopy ! derivative in net canopy air space fluxes w.r.t. canopy temperature (W m-2 K-1)
- real(rkind),intent(out) :: dTurbFluxCanair_dTGround ! derivative in net canopy air space fluxes w.r.t. ground temperature (W m-2 K-1)
- real(rkind),intent(out) :: dTurbFluxCanopy_dTCanair ! derivative in net canopy turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
- real(rkind),intent(out) :: dTurbFluxCanopy_dTCanopy ! derivative in net canopy turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
- real(rkind),intent(out) :: dTurbFluxCanopy_dTGround ! derivative in net canopy turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
- real(rkind),intent(out) :: dTurbFluxGround_dTCanair ! derivative in net ground turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
- real(rkind),intent(out) :: dTurbFluxGround_dTCanopy ! derivative in net ground turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
- real(rkind),intent(out) :: dTurbFluxGround_dTGround ! derivative in net ground turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
- ! output: liquid flux derivatives (canopy evap)
- real(rkind),intent(out) :: dLatHeatCanopyEvap_dCanWat ! derivative in latent heat of canopy evaporation w.r.t. canopy total water content (W kg-1)
- real(rkind),intent(out) :: dLatHeatCanopyEvap_dTCanair ! derivative in latent heat of canopy evaporation w.r.t. canopy air temperature (W m-2 K-1)
- real(rkind),intent(out) :: dLatHeatCanopyEvap_dTCanopy ! derivative in latent heat of canopy evaporation w.r.t. canopy temperature (W m-2 K-1)
- real(rkind),intent(out) :: dLatHeatCanopyEvap_dTGround ! derivative in latent heat of canopy evaporation w.r.t. ground temperature (W m-2 K-1)
- ! output: liquid flux derivatives (ground evap)
- real(rkind),intent(out) :: dLatHeatGroundEvap_dCanWat ! derivative in latent heat of ground evaporation w.r.t. canopy total water content (J kg-1 s-1)
- real(rkind),intent(out) :: dLatHeatGroundEvap_dTCanair ! derivative in latent heat of ground evaporation w.r.t. canopy air temperature (W m-2 K-1)
- real(rkind),intent(out) :: dLatHeatGroundEvap_dTCanopy ! derivative in latent heat of ground evaporation w.r.t. canopy temperature (W m-2 K-1)
- real(rkind),intent(out) :: dLatHeatGroundEvap_dTGround ! derivative in latent heat of ground evaporation w.r.t. ground temperature (W m-2 K-1)
- ! output: latent heat flux derivatives (canopy trans)
- real(rkind) :: dLatHeatCanopyTrans_dCanWat ! derivative in the latent heat of canopy transpiration w.r.t. canopy total water (J kg-1 s-1)
- real(rkind) :: dLatHeatCanopyTrans_dTCanair ! derivative in the latent heat of canopy transpiration w.r.t. canopy air temperature
- real(rkind) :: dLatHeatCanopyTrans_dTCanopy ! derivative in the latent heat of canopy transpiration w.r.t. canopy temperature
- real(rkind) :: dLatHeatCanopyTrans_dTGround ! derivative in the latent heat of canopy transpiration flux w.r.t. ground temperature
- ! output: cross derivatives
- real(rkind),intent(out) :: dTurbFluxCanair_dCanWat ! derivative in net canopy air space fluxes w.r.t. canopy total water content (J kg-1 s-1)
- real(rkind),intent(out) :: dTurbFluxCanopy_dCanWat ! derivative in net canopy turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
- real(rkind),intent(out) :: dTurbFluxGround_dCanWat ! derivative in net ground turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
- ! output: error control
- integer(i4b),intent(out) :: err ! error code
- character(*),intent(out) :: message ! error message
- ! -----------------------------------------------------------------------------------------------------------------------------------------
- ! local variables -- general
- real(rkind) :: fpart1,fpart2 ! different parts of a function
- real(rkind) :: dPart0,dpart1,dpart2 ! derivatives for different parts of a function
- ! local variables -- "constants"
- real(rkind) :: volHeatCapacityAir ! volumetric heat capacity of air (J m-3)
- real(rkind) :: latentHeatConstant ! latent heat constant (kg m-3 K-1)
- ! local variables -- derivatives for energy conductances
- real(rkind) :: dEvapCond_dCanopyTemp ! derivative in evap conductance w.r.t. canopy temperature
- real(rkind) :: dTransCond_dCanopyTemp ! derivative in trans conductance w.r.t. canopy temperature
- real(rkind) :: dCanopyCond_dCanairTemp ! derivative in canopy conductance w.r.t. canopy air temperature
- real(rkind) :: dCanopyCond_dCanopyTemp ! derivative in canopy conductance w.r.t. canopy temperature
- real(rkind) :: dGroundCondSH_dCanairTemp ! derivative in ground conductance of sensible heat w.r.t. canopy air temperature
- real(rkind) :: dGroundCondSH_dCanopyTemp ! derivative in ground conductance of sensible heat w.r.t. canopy temperature
- real(rkind) :: dGroundCondSH_dGroundTemp ! derivative in ground conductance of sensible heat w.r.t. ground temperature
- ! local variables -- derivatives for mass conductances
- real(rkind) :: dGroundCondLH_dCanairTemp ! derivative in ground conductance w.r.t. canopy air temperature
- real(rkind) :: dGroundCondLH_dCanopyTemp ! derivative in ground conductance w.r.t. canopy temperature
- real(rkind) :: dGroundCondLH_dGroundTemp ! derivative in ground conductance w.r.t. ground temperature
- ! local variables -- derivatives for the canopy air space variables
- real(rkind) :: fPart_VP ! part of the function for vapor pressure of the canopy air space
- real(rkind) :: leafConductanceTr ! leaf conductance for transpiration (m s-1)
- real(rkind) :: dVPCanopyAir_dTCanair ! derivative in the vapor pressure of the canopy air space w.r.t. temperature of the canopy air space
- real(rkind) :: dVPCanopyAir_dTCanopy ! derivative in the vapor pressure of the canopy air space w.r.t. temperature of the canopy
- real(rkind) :: dVPCanopyAir_dTGround ! derivative in the vapor pressure of the canopy air space w.r.t. temperature of the ground
- real(rkind) :: dVPCanopyAir_dWetFrac ! derivative of vapor pressure in the canopy air space w.r.t. wetted fraction of the canopy
- real(rkind) :: dVPCanopyAir_dCanWat ! derivative of vapor pressure in the canopy air space w.r.t. canopy total water content
- ! local variables -- sensible heat flux derivatives
- real(rkind) :: dSenHeatTotal_dTCanair ! derivative in the total sensible heat flux w.r.t. canopy air temperature
- real(rkind) :: dSenHeatTotal_dTCanopy ! derivative in the total sensible heat flux w.r.t. canopy air temperature
- real(rkind) :: dSenHeatTotal_dTGround ! derivative in the total sensible heat flux w.r.t. ground temperature
- real(rkind) :: dSenHeatCanopy_dTCanair ! derivative in the canopy sensible heat flux w.r.t. canopy air temperature
- real(rkind) :: dSenHeatCanopy_dTCanopy ! derivative in the canopy sensible heat flux w.r.t. canopy temperature
- real(rkind) :: dSenHeatCanopy_dTGround ! derivative in the canopy sensible heat flux w.r.t. ground temperature
- real(rkind) :: dSenHeatGround_dTCanair ! derivative in the ground sensible heat flux w.r.t. canopy air temperature
- real(rkind) :: dSenHeatGround_dTCanopy ! derivative in the ground sensible heat flux w.r.t. canopy temperature
- real(rkind) :: dSenHeatGround_dTGround ! derivative in the ground sensible heat flux w.r.t. ground temperature
- ! local variables -- wetted fraction derivatives
- real(rkind) :: dLatHeatCanopyEvap_dWetFrac ! derivative in the latent heat of canopy evaporation w.r.t. canopy wet fraction (W m-2)
- real(rkind) :: dLatHeatCanopyTrans_dWetFrac ! derivative in the latent heat of canopy transpiration w.r.t. canopy wet fraction (W m-2)
- ! -----------------------------------------------------------------------------------------------------------------------------------------
- ! initialize error control
- err=0; message='turbFluxes/'
-
- ! compute constants
- volHeatCapacityAir = iden_air*cp_air ! volumetric heat capacity of air (J m-3)
- latentHeatConstant = iden_air*w_ratio/airpres ! latent heat constant for (kg m-3 Pa-1)
-
- ! *****
- ! * compute conductances, and derivatives...
- ! ******************************************
-
- ! compute conductances for sensible heat (m s-1)
- if(computeVegFlux)then
- leafConductance = exposedVAI/leafResistance
- leafConductanceTr = canopySunlitLAI/(leafResistance+stomResistSunlit) + canopyShadedLAI/(leafResistance+stomResistShaded)
- canopyConductance = 1._rkind/canopyResistance
- else
- leafConductance = 0._rkind
- canopyConductance = 0._rkind
- end if
- groundConductanceSH = 1._rkind/groundResistance
-
- ! compute total conductance for sensible heat
- totalConductanceSH = leafConductance + groundConductanceSH + canopyConductance
-
- ! compute conductances for latent heat (m s-1)
- if(computeVegFlux)then
- evapConductance = canopyWetFraction*leafConductance
- transConductance = (1._rkind - canopyWetFraction) * leafConductanceTr
- !write(*,'(a,10(f14.8,1x))') 'canopySunlitLAI, canopyShadedLAI, stomResistSunlit, stomResistShaded, leafResistance, canopyWetFraction = ', &
- ! canopySunlitLAI, canopyShadedLAI, stomResistSunlit, stomResistShaded, leafResistance, canopyWetFraction
- else
- evapConductance = 0._rkind
- transConductance = 0._rkind
- end if
- groundConductanceLH = 1._rkind/(groundResistance + soilResistance) ! NOTE: soilResistance accounts for fractional snow, and =0 when snow cover is 100%
- totalConductanceLH = evapConductance + transConductance + groundConductanceLH + canopyConductance
-
- ! check sensible heat conductance
- if(totalConductanceSH < -tinyVal .or. groundConductanceSH < -tinyVal .or. canopyConductance < -tinyVal)then
- message=trim(message)//'negative conductance for sensible heat'
- err=20; return
- endif
-
- ! check latent heat conductance
- if(totalConductanceLH < tinyVal .or. groundConductanceLH < -tinyVal)then
- message=trim(message)//'negative conductance for latent heat'
+ end select
+ ! save the factor for the given layer (ensure between zero and one)
+ mLayerTranspireLimitFac(iLayer) = min( max(verySmall,gx), 1._rkind)
+ ! compute the weighted average (weighted by root density)
+ wAvgTranspireLimitFac = wAvgTranspireLimitFac + mLayerTranspireLimitFac(iLayer)*mLayerRootDensity(iLayer)
+ end do ! (looping through soil layers)
+
+ ! ** compute the factor limiting evaporation in the aquifer
+ if(scalarAquiferRootFrac > verySmall)then
+ ! check that aquifer root fraction is allowed
+ if(ixGroundwater /= bigBucket)then
+ message=trim(message)//'aquifer evaporation only allowed for the big groundwater bucket -- increase the soil depth to account for roots'
err=20; return
- endif
-
- ! * compute derivatives
- ! NOTE: it may be more efficient to compute these derivatives when computing resistances
- if(ixDerivMethod == analytical)then
-
- ! compute derivatives in individual conductances for sensible heat w.r.t. canopy temperature (m s-1 K-1)
- if(computeVegFlux)then
- dEvapCond_dCanopyTemp = dCanopyWetFraction_dT*leafConductance ! derivative in evap conductance w.r.t. canopy temperature
- dTransCond_dCanopyTemp = -dCanopyWetFraction_dT*leafConductanceTr ! derivative in trans conductance w.r.t. canopy temperature
- dCanopyCond_dCanairTemp = -dCanopyResistance_dTCanair/canopyResistance**2._rkind ! derivative in canopy conductance w.r.t. canopy air emperature
- dCanopyCond_dCanopyTemp = -dCanopyResistance_dTCanopy/canopyResistance**2._rkind ! derivative in canopy conductance w.r.t. canopy temperature
- dGroundCondSH_dCanairTemp = -dGroundResistance_dTCanair/groundResistance**2._rkind ! derivative in ground conductance w.r.t. canopy air temperature
- dGroundCondSH_dCanopyTemp = -dGroundResistance_dTCanopy/groundResistance**2._rkind ! derivative in ground conductance w.r.t. canopy temperature
- dGroundCondSH_dGroundTemp = -dGroundResistance_dTGround/groundResistance**2._rkind ! derivative in ground conductance w.r.t. ground temperature
- else
- dEvapCond_dCanopyTemp = 0._rkind ! derivative in evap conductance w.r.t. canopy temperature
- dTransCond_dCanopyTemp = 0._rkind ! derivative in trans conductance w.r.t. canopy temperature
- dCanopyCond_dCanairTemp = 0._rkind ! derivative in canopy conductance w.r.t. canopy air emperature
- dCanopyCond_dCanopyTemp = 0._rkind ! derivative in canopy conductance w.r.t. canopy temperature
- dGroundCondSH_dCanairTemp = 0._rkind ! derivative in ground conductance w.r.t. canopy air temperature
- dGroundCondSH_dCanopyTemp = 0._rkind ! derivative in ground conductance w.r.t. canopy temperature
- dGroundCondSH_dGroundTemp = -dGroundResistance_dTGround/groundResistance**2._rkind ! derivative in ground conductance w.r.t. ground temperature
- end if
-
- ! compute derivatives in individual conductances for latent heat w.r.t. canopy temperature (m s-1 K-1)
- if(computeVegFlux)then
- dGroundCondLH_dCanairTemp = -dGroundResistance_dTCanair/(groundResistance+soilResistance)**2._rkind ! derivative in ground conductance w.r.t. canopy air temperature
- dGroundCondLH_dCanopyTemp = -dGroundResistance_dTCanopy/(groundResistance+soilResistance)**2._rkind ! derivative in ground conductance w.r.t. canopy temperature
- dGroundCondLH_dGroundTemp = -dGroundResistance_dTGround/(groundResistance+soilResistance)**2._rkind ! derivative in ground conductance w.r.t. ground temperature
- else
- dGroundCondLH_dCanairTemp = 0._rkind ! derivative in ground conductance w.r.t. canopy air temperature
- dGroundCondLH_dCanopyTemp = 0._rkind ! derivative in ground conductance w.r.t. canopy temperature
- dGroundCondLH_dGroundTemp = -dGroundResistance_dTGround/(groundResistance+soilResistance)**2._rkind ! derivative in ground conductance w.r.t. ground temperature
- end if
-
- end if ! (if computing analytical derivatives)
-
- ! *****
- ! * compute sensible and latent heat fluxes, and derivatives...
- ! *************************************************************
-
- ! * compute sensible and latent heat fluxes from the canopy to the canopy air space (W m-2)
- if(computeVegFlux)then
-
- ! compute the vapor pressure in the canopy air space (Pa)
- fPart_VP = canopyConductance*VPair + (evapConductance + transConductance)*satVP_CanopyTemp + groundConductanceLH*satVP_GroundTemp*soilRelHumidity
- VP_CanopyAir = fPart_VP/totalConductanceLH
- !write(*,'(a,10(f20.10,1x))') 'canopyConductance, evapConductance, transConductance, groundConductanceLH, soilRelHumidity = ', &
- ! canopyConductance, evapConductance, transConductance, groundConductanceLH, soilRelHumidity
-
- ! compute sensible heat flux from the canopy air space to the atmosphere
- ! NOTE: canairTemp is a state variable
- senHeatTotal = -volHeatCapacityAir*canopyConductance*(canairTemp - airtemp)
- !print*, 'canairTemp, airtemp, senHeatTotal = ', canairTemp, airtemp, senHeatTotal
-
- ! compute fluxes
- senHeatCanopy = -volHeatCapacityAir*leafConductance*(canopyTemp - canairTemp) ! (positive downwards)
- latHeatCanopyEvap = -latHeatSubVapCanopy*latentHeatConstant*evapConductance*(satVP_CanopyTemp - VP_CanopyAir) ! (positive downwards)
- latHeatCanopyTrans = -LH_vap*latentHeatConstant*transConductance*(satVP_CanopyTemp - VP_CanopyAir) ! (positive downwards)
- !write(*,'(a,10(f25.15,1x))') 'latHeatCanopyEvap, VP_CanopyAir = ', latHeatCanopyEvap, VP_CanopyAir
- !write(*,'(a,10(f25.15,1x))') 'latHeatCanopyTrans, VP_CanopyAir = ', latHeatCanopyTrans, VP_CanopyAir
- !write(*,'(a,10(f25.15,1x))') 'transConductance = ', transConductance
-
- ! check that energy for canopy evaporation does not exhaust the available water
- ! NOTE: do this here, rather than enforcing solution constraints, because energy and mass solutions may be uncoupled
- !if(latHeatSubVapCanopy > LH_vap+verySmall)then ! (sublimation)
- ! maxFlux = -canopyIce*LH_sub/dt ! W m-2
- !else ! (evaporation)
- ! maxFlux = -canopyLiquid*LH_vap/dt ! W m-2
- !end if
- ! NOTE: fluxes are positive downwards
- !if(latHeatCanopyEvap < maxFlux) latHeatCanopyEvap = maxFlux
- !write(*,'(a,10(f20.10,1x))') 'maxFlux, latHeatCanopyEvap = ', maxFlux, latHeatCanopyEvap
-
- ! * no vegetation, so fluxes are zero
- else
- senHeatCanopy = 0._rkind
- latHeatCanopyEvap = 0._rkind
- latHeatCanopyTrans = 0._rkind
- end if
-
- ! compute sensible and latent heat fluxes from the ground to the canopy air space (W m-2)
- if(computeVegFlux)then
- senHeatGround = -volHeatCapacityAir*groundConductanceSH*(groundTemp - canairTemp) ! (positive downwards)
- latHeatGround = -latHeatSubVapGround*latentHeatConstant*groundConductanceLH*(satVP_GroundTemp*soilRelHumidity - VP_CanopyAir) ! (positive downwards)
- else
- senHeatGround = -volHeatCapacityAir*groundConductanceSH*(groundTemp - airtemp) ! (positive downwards)
- latHeatGround = -latHeatSubVapGround*latentHeatConstant*groundConductanceLH*(satVP_GroundTemp*soilRelHumidity - VPair) ! (positive downwards)
- senHeatTotal = senHeatGround
- end if
- !write(*,'(a,10(f25.15,1x))') 'latHeatGround = ', latHeatGround
-
- ! compute latent heat flux from the canopy air space to the atmosphere
- ! NOTE: VP_CanopyAir is a diagnostic variable
- latHeatTotal = latHeatCanopyEvap + latHeatCanopyTrans + latHeatGround
-
- ! * compute derivatives
- if(ixDerivMethod == analytical)then
-
- ! differentiate CANOPY fluxes
- if(computeVegFlux)then
-
- ! compute derivatives of vapor pressure in the canopy air space w.r.t. all state variables
- ! (derivative of vapor pressure in the canopy air space w.r.t. temperature of the canopy air space)
- dPart1 = dCanopyCond_dCanairTemp*VPair + dGroundCondLH_dCanairTemp*satVP_GroundTemp*soilRelHumidity
- dPart2 = -(dCanopyCond_dCanairTemp + dGroundCondLH_dCanairTemp)/(totalConductanceLH**2._rkind)
- dVPCanopyAir_dTCanair = dPart1/totalConductanceLH + fPart_VP*dPart2
- ! (derivative of vapor pressure in the canopy air space w.r.t. temperature of the canopy)
- dPart0 = (evapConductance + transConductance)*dSVPCanopy_dCanopyTemp + (dEvapCond_dCanopyTemp + dTransCond_dCanopyTemp)*satVP_CanopyTemp
- dPart1 = dCanopyCond_dCanopyTemp*VPair + dPart0 + dGroundCondLH_dCanopyTemp*satVP_GroundTemp*soilRelHumidity
- dPart2 = -(dCanopyCond_dCanopyTemp + dEvapCond_dCanopyTemp + dTransCond_dCanopyTemp + dGroundCondLH_dCanopyTemp)/(totalConductanceLH**2._rkind)
- dVPCanopyAir_dTCanopy = dPart1/totalConductanceLH + fPart_VP*dPart2
- ! (derivative of vapor pressure in the canopy air space w.r.t. temperature of the ground)
- dPart1 = dGroundCondLH_dGroundTemp*satVP_GroundTemp*soilRelHumidity + groundConductanceLH*dSVPGround_dGroundTemp*soilRelHumidity
- dPart2 = -dGroundCondLH_dGroundTemp/(totalConductanceLH**2._rkind)
- dVPCanopyAir_dTGround = dPart1/totalConductanceLH + fPart_VP*dPart2
- ! (derivative of vapor pressure in the canopy air space w.r.t. wetted fraction of the canopy)
- dPart1 = (leafConductance - leafConductanceTr)*satVP_CanopyTemp
- dPart2 = -(leafConductance - leafConductanceTr)/(totalConductanceLH**2._rkind)
- dVPCanopyAir_dWetFrac = dPart1/totalConductanceLH + fPart_VP*dPart2
- dVPCanopyAir_dCanWat = dVPCanopyAir_dWetFrac*dCanopyWetFraction_dWat
- !write(*,'(a,5(f20.8,1x))') 'dVPCanopyAir_dTCanair, dVPCanopyAir_dTCanopy, dVPCanopyAir_dTGround, dVPCanopyAir_dWetFrac, dVPCanopyAir_dCanWat = ', &
- ! dVPCanopyAir_dTCanair, dVPCanopyAir_dTCanopy, dVPCanopyAir_dTGround, dVPCanopyAir_dWetFrac, dVPCanopyAir_dCanWat
-
- ! sensible heat from the canopy to the atmosphere
- dSenHeatTotal_dTCanair = -volHeatCapacityAir*canopyConductance - volHeatCapacityAir*dCanopyCond_dCanairTemp*(canairTemp - airtemp)
- dSenHeatTotal_dTCanopy = -volHeatCapacityAir*dCanopyCond_dCanopyTemp*(canairTemp - airtemp)
- dSenHeatTotal_dTGround = 0._rkind
- !write(*,'(a,3(f20.8,1x))') 'dSenHeatTotal_dTCanair, dSenHeatTotal_dTCanopy, dSenHeatTotal_dTGround = ', &
- ! dSenHeatTotal_dTCanair, dSenHeatTotal_dTCanopy, dSenHeatTotal_dTGround
-
- ! sensible heat from the canopy to the canopy air space
- dSenHeatCanopy_dTCanair = volHeatCapacityAir*leafConductance
- dSenHeatCanopy_dTCanopy = -volHeatCapacityAir*leafConductance
- dSenHeatCanopy_dTGround = 0._rkind
- !write(*,'(a,3(f20.8,1x))') 'dSenHeatCanopy_dTCanair, dSenHeatCanopy_dTCanopy, dSenHeatCanopy_dTGround = ', &
- ! dSenHeatCanopy_dTCanair, dSenHeatCanopy_dTCanopy, dSenHeatCanopy_dTGround
-
- ! sensible heat from the ground to the canopy air space
- dSenHeatGround_dTCanair = -volHeatCapacityAir*dGroundCondSH_dCanairTemp*(groundTemp - canairTemp) + volHeatCapacityAir*groundConductanceSH
- dSenHeatGround_dTCanopy = -volHeatCapacityAir*dGroundCondSH_dCanopyTemp*(groundTemp - canairTemp)
- dSenHeatGround_dTGround = -volHeatCapacityAir*dGroundCondSH_dGroundTemp*(groundTemp - canairTemp) - volHeatCapacityAir*groundConductanceSH
- !write(*,'(a,3(f20.8,1x))') 'dSenHeatGround_dTCanair, dSenHeatGround_dTCanopy, dSenHeatGround_dTGround = ', &
- ! dSenHeatGround_dTCanair, dSenHeatGround_dTCanopy, dSenHeatGround_dTGround
-
- ! latent heat associated with canopy evaporation
- ! (initial calculations)
- fPart1 = -latHeatSubVapCanopy*latentHeatConstant*evapConductance
- dPart1 = -latHeatSubVapCanopy*latentHeatConstant*dEvapCond_dCanopyTemp
- fPart2 = satVP_CanopyTemp - VP_CanopyAir
- dPart2 = dSVPCanopy_dCanopyTemp - dVPCanopyAir_dTCanopy
- ! (derivatives)
- dLatHeatCanopyEvap_dTCanair = fPart1*(-dVPCanopyAir_dTCanair)
- dLatHeatCanopyEvap_dTCanopy = fPart1*dpart2 + fPart2*dPart1
- dLatHeatCanopyEvap_dTGround = fPart1*(-dVPCanopyAir_dTGround)
- !write(*,'(a,3(f20.8,1x))') 'dLatHeatCanopyEvap_dTCanair, dLatHeatCanopyEvap_dTCanopy, dLatHeatCanopyEvap_dTGround = ', &
- ! dLatHeatCanopyEvap_dTCanair, dLatHeatCanopyEvap_dTCanopy, dLatHeatCanopyEvap_dTGround
-
- ! latent heat associated with canopy transpiration
- ! (initial calculations)
- fPart1 = -LH_vap*latentHeatConstant*transConductance
- dPart1 = -LH_vap*latentHeatConstant*dTransCond_dCanopyTemp
- ! (derivatives)
- dLatHeatCanopyTrans_dTCanair = fPart1*(-dVPCanopyAir_dTCanair)
- dLatHeatCanopyTrans_dTCanopy = fPart1*dPart2 + fPart2*dPart1
- dLatHeatCanopyTrans_dTGround = fPart1*(-dVPCanopyAir_dTGround)
- !write(*,'(a,3(f20.8,1x))') 'dLatHeatCanopyTrans_dTCanair, dLatHeatCanopyTrans_dTCanopy, dLatHeatCanopyTrans_dTGround = ', &
- ! dLatHeatCanopyTrans_dTCanair, dLatHeatCanopyTrans_dTCanopy, dLatHeatCanopyTrans_dTGround
-
- ! latent heat flux from the ground
- fPart1 = -latHeatSubVapGround*latentHeatConstant*groundConductanceLH ! function of the first part
- fPart2 = (satVP_GroundTemp*soilRelHumidity - VP_CanopyAir) ! function of the second part
- dLatHeatGroundEvap_dTCanair = -latHeatSubVapGround*latentHeatConstant*dGroundCondLH_dCanairTemp*fPart2 - dVPCanopyAir_dTCanair*fPart1
- dLatHeatGroundEvap_dTCanopy = -latHeatSubVapGround*latentHeatConstant*dGroundCondLH_dCanopyTemp*fPart2 - dVPCanopyAir_dTCanopy*fPart1
- dLatHeatGroundEvap_dTGround = -latHeatSubVapGround*latentHeatConstant*dGroundCondLH_dGroundTemp*fPart2 + (dSVPGround_dGroundTemp*soilRelHumidity - dVPCanopyAir_dTGround)*fPart1
- !write(*,'(a,3(f20.8,1x))') 'dLatHeatGroundEvap_dTCanair, dLatHeatGroundEvap_dTCanopy, dLatHeatGroundEvap_dTGround = ', &
- ! dLatHeatGroundEvap_dTCanair, dLatHeatGroundEvap_dTCanopy, dLatHeatGroundEvap_dTGround
-
- ! latent heat associated with canopy evaporation w.r.t. wetted fraction of the canopy
- dPart1 = -latHeatSubVapCanopy*latentHeatConstant*leafConductance
- fPart1 = dPart1*canopyWetFraction
- dLatHeatCanopyEvap_dWetFrac = dPart1*(satVP_CanopyTemp - VP_CanopyAir) + fPart1*(-dVPCanopyAir_dWetFrac)
-
- ! latent heat associated with canopy transpiration w.r.t. wetted fraction of the canopy
- dPart1 = LH_vap*latentHeatConstant*leafConductanceTr ! NOTE: positive, since (1 - wetFrac)
- fPart1 = -dPart1*(1._rkind - canopyWetFraction)
- dLatHeatCanopyTrans_dWetFrac = dPart1*(satVP_CanopyTemp - VP_CanopyAir) + fPart1*(-dVPCanopyAir_dWetFrac)
- !print*, 'dLatHeatCanopyTrans_dWetFrac = ', dLatHeatCanopyTrans_dWetFrac
-
- ! latent heat associated with canopy transpiration w.r.t. canopy total water
- dLatHeatCanopyTrans_dCanWat = dLatHeatCanopyTrans_dWetFrac*dCanopyWetFraction_dWat ! (J s-1 kg-1)
- !print*, 'dLatHeatCanopyTrans_dCanWat = ', dLatHeatCanopyTrans_dCanWat
-
- else ! canopy is undefined
-
- ! set derivatives for canopy fluxes to zero (no canopy, so fluxes are undefined)
- dSenHeatTotal_dTCanair = 0._rkind
- dSenHeatTotal_dTCanopy = 0._rkind
- dSenHeatTotal_dTGround = 0._rkind
- dSenHeatCanopy_dTCanair = 0._rkind
- dSenHeatCanopy_dTCanopy = 0._rkind
- dSenHeatCanopy_dTGround = 0._rkind
- dLatHeatCanopyEvap_dTCanair = 0._rkind
- dLatHeatCanopyEvap_dTCanopy = 0._rkind
- dLatHeatCanopyEvap_dTGround = 0._rkind
- dLatHeatCanopyTrans_dTCanair = 0._rkind
- dLatHeatCanopyTrans_dTCanopy = 0._rkind
- dLatHeatCanopyTrans_dTGround = 0._rkind
-
- ! set derivatives for wetted area and canopy transpiration to zero (no canopy, so fluxes are undefined)
- dLatHeatCanopyEvap_dWetFrac = 0._rkind
- dLatHeatCanopyEvap_dCanWat = 0._rkind
- dLatHeatCanopyTrans_dCanWat = 0._rkind
- dVPCanopyAir_dCanWat = 0._rkind
-
- ! set derivatives for ground fluxes w.r.t canopy temperature to zero (no canopy, so fluxes are undefined)
- dSenHeatGround_dTCanair = 0._rkind
- dSenHeatGround_dTCanopy = 0._rkind
- dLatHeatGroundEvap_dTCanair = 0._rkind
- dLatHeatGroundEvap_dTCanopy = 0._rkind
-
- ! compute derivatives for the ground fluxes w.r.t. ground temperature
- dSenHeatGround_dTGround = (-volHeatCapacityAir*dGroundCondSH_dGroundTemp)*(groundTemp - airtemp) + & ! d(ground sensible heat flux)/d(ground temp)
- (-volHeatCapacityAir*groundConductanceSH)
- dLatHeatGroundEvap_dTGround = (-latHeatSubVapGround*latentHeatConstant*dGroundCondLH_dGroundTemp)*(satVP_GroundTemp*soilRelHumidity - VPair) + & ! d(ground latent heat flux)/d(ground temp)
- (-latHeatSubVapGround*latentHeatConstant*groundConductanceLH)*dSVPGround_dGroundTemp*soilRelHumidity
-
- !print*, 'dGroundCondLH_dGroundTemp = ', dGroundCondLH_dGroundTemp
-
- end if ! (if canopy is defined)
-
- end if ! (if computing analytical derivatives)
-
-
- ! *****
- ! * compute net turbulent fluxes, and derivatives...
- ! **************************************************
-
- ! compute net fluxes
- turbFluxCanair = senHeatTotal - senHeatCanopy - senHeatGround ! net turbulent flux at the canopy air space (W m-2)
- turbFluxCanopy = senHeatCanopy + latHeatCanopyEvap + latHeatCanopyTrans ! net turbulent flux at the canopy (W m-2)
- turbFluxGround = senHeatGround + latHeatGround ! net turbulent flux at the ground surface (W m-2)
- !write(*,'(a,1x,3(f20.10,1x))') 'senHeatCanopy, latHeatCanopyEvap, latHeatCanopyTrans = ', senHeatCanopy, latHeatCanopyEvap, latHeatCanopyTrans
-
- ! * compute derivatives
- if(ixDerivMethod == analytical)then
- ! (energy derivatives)
- dTurbFluxCanair_dTCanair = dSenHeatTotal_dTCanair - dSenHeatCanopy_dTCanair - dSenHeatGround_dTCanair ! derivative in net canopy air space fluxes w.r.t. canopy air temperature (W m-2 K-1)
- dTurbFluxCanair_dTCanopy = dSenHeatTotal_dTCanopy - dSenHeatCanopy_dTCanopy - dSenHeatGround_dTCanopy ! derivative in net canopy air space fluxes w.r.t. canopy temperature (W m-2 K-1)
- dTurbFluxCanair_dTGround = dSenHeatTotal_dTGround - dSenHeatCanopy_dTGround - dSenHeatGround_dTGround ! derivative in net canopy air space fluxes w.r.t. ground temperature (W m-2 K-1)
- dTurbFluxCanopy_dTCanair = dSenHeatCanopy_dTCanair + dLatHeatCanopyEvap_dTCanair + dLatHeatCanopyTrans_dTCanair ! derivative in net canopy turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
- dTurbFluxCanopy_dTCanopy = dSenHeatCanopy_dTCanopy + dLatHeatCanopyEvap_dTCanopy + dLatHeatCanopyTrans_dTCanopy ! derivative in net canopy turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
- dTurbFluxCanopy_dTGround = dSenHeatCanopy_dTGround + dLatHeatCanopyEvap_dTGround + dLatHeatCanopyTrans_dTGround ! derivative in net canopy turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
- dTurbFluxGround_dTCanair = dSenHeatGround_dTCanair + dLatHeatGroundEvap_dTCanair ! derivative in net ground turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
- dTurbFluxGround_dTCanopy = dSenHeatGround_dTCanopy + dLatHeatGroundEvap_dTCanopy ! derivative in net ground turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
- dTurbFluxGround_dTGround = dSenHeatGround_dTGround + dLatHeatGroundEvap_dTGround ! derivative in net ground turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
- ! (liquid water derivatives)
- dLatHeatCanopyEvap_dCanWat = dLatHeatCanopyEvap_dWetFrac*dCanopyWetFraction_dWat ! derivative in latent heat of canopy evaporation w.r.t. canopy total water (W kg-1)
- dLatHeatGroundEvap_dCanWat = latHeatSubVapGround*latentHeatConstant*groundConductanceLH*dVPCanopyAir_dCanWat ! derivative in latent heat of ground evaporation w.r.t. canopy total water (J kg-1 s-1)
- ! (cross deriavtives)
- dTurbFluxCanair_dCanWat = 0._rkind ! derivative in net canopy air space fluxes w.r.t. canopy total water content (J kg-1 s-1)
- dTurbFluxCanopy_dCanWat = dLatHeatCanopyEvap_dCanWat + dLatHeatCanopyTrans_dCanWat ! derivative in net canopy turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
- dTurbFluxGround_dCanWat = dLatHeatGroundEvap_dCanWat ! derivative in net ground turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
- else ! (just make sure we return something)
- ! (energy derivatives)
- dTurbFluxCanair_dTCanair = 0._rkind
- dTurbFluxCanair_dTCanopy = 0._rkind
- dTurbFluxCanair_dTGround = 0._rkind
- dTurbFluxCanopy_dTCanair = 0._rkind
- dTurbFluxCanopy_dTCanopy = 0._rkind
- dTurbFluxCanopy_dTGround = 0._rkind
- dTurbFluxGround_dTCanair = 0._rkind
- dTurbFluxGround_dTCanopy = 0._rkind
- dTurbFluxGround_dTGround = 0._rkind
- ! (liquid water derivatives)
+ end if
+ ! compute the factor limiting evaporation for the aquifer
+ aquiferTranspireLimitFac = min(scalarAquiferStorage/critAquiferTranspire, 1._rkind)
+ else ! (if there are roots in the aquifer)
+ aquiferTranspireLimitFac = 0._rkind
+ end if
+
+ ! compute the weighted average (weighted by root density)
+ wAvgTranspireLimitFac = wAvgTranspireLimitFac + aquiferTranspireLimitFac*scalarAquiferRootFrac
+
+end subroutine soilResist
+
+
+! ********************************************************************************
+! private subroutine turbFluxes: compute turbulent heat fluxes
+! ********************************************************************************
+subroutine turbFluxes(&
+ ! input: model control
+ computeVegFlux, & ! intent(in): logical flag to compute vegetation fluxes (.false. if veg buried by snow)
+ ixDerivMethod, & ! intent(in): choice of method used to compute derivative (analytical or numerical)
+ ! input: above-canopy forcing data
+ airtemp, & ! intent(in): air temperature at some height above the surface (K)
+ airpres, & ! intent(in): air pressure of the air above the vegetation canopy (Pa)
+ VPair, & ! intent(in): vapor pressure of the air above the vegetation canopy (Pa)
+ ! input: latent heat of sublimation/vaporization
+ latHeatSubVapCanopy, & ! intent(in): latent heat of sublimation/vaporization for the vegetation canopy (J kg-1)
+ latHeatSubVapGround, & ! intent(in): latent heat of sublimation/vaporization for the ground surface (J kg-1)
+ ! input: canopy and ground temperature
+ canairTemp, & ! intent(in): temperature of the canopy air space (K)
+ canopyTemp, & ! intent(in): canopy temperature (K)
+ groundTemp, & ! intent(in): ground temperature (K)
+ satVP_CanopyTemp, & ! intent(in): saturation vapor pressure at the temperature of the veg canopy (Pa)
+ satVP_GroundTemp, & ! intent(in): saturation vapor pressure at the temperature of the ground (Pa)
+ dSVPCanopy_dCanopyTemp, & ! intent(in): derivative in canopy saturation vapor pressure w.r.t. canopy temperature (Pa K-1)
+ dSVPGround_dGroundTemp, & ! intent(in): derivative in ground saturation vapor pressure w.r.t. ground temperature (Pa K-1)
+ ! input: diagnostic variables
+ exposedVAI, & ! intent(in): exposed vegetation area index -- leaf plus stem (m2 m-2)
+ canopyWetFraction, & ! intent(in): fraction of canopy that is wet [0-1]
+ dCanopyWetFraction_dWat, & ! intent(in): derivative in the canopy wetted fraction w.r.t. total water content (kg-1 m-2)
+ dCanopyWetFraction_dT, & ! intent(in): derivative in wetted fraction w.r.t. canopy temperature (K-1)
+ canopySunlitLAI, & ! intent(in): sunlit leaf area (-)
+ canopyShadedLAI, & ! intent(in): shaded leaf area (-)
+ soilRelHumidity, & ! intent(in): relative humidity in the soil pores [0-1]
+ soilResistance, & ! intent(in): resistance from the soil (s m-1)
+ leafResistance, & ! intent(in): mean leaf boundary layer resistance per unit leaf area (s m-1)
+ groundResistance, & ! intent(in): below canopy aerodynamic resistance (s m-1)
+ canopyResistance, & ! intent(in): above canopy aerodynamic resistance (s m-1)
+ stomResistSunlit, & ! intent(in): stomatal resistance for sunlit leaves (s m-1)
+ stomResistShaded, & ! intent(in): stomatal resistance for shaded leaves (s m-1)
+ ! input: derivatives in scalar resistances
+ dGroundResistance_dTGround, & ! intent(in): derivative in ground resistance w.r.t. ground temperature (s m-1 K-1)
+ dGroundResistance_dTCanopy, & ! intent(in): derivative in ground resistance w.r.t. canopy temperature (s m-1 K-1)
+ dGroundResistance_dTCanair, & ! intent(in): derivative in ground resistance w.r.t. canopy air temperature (s m-1 K-1)
+ dCanopyResistance_dTCanopy, & ! intent(in): derivative in canopy resistance w.r.t. canopy temperature (s m-1 K-1)
+ dCanopyResistance_dTCanair, & ! intent(in): derivative in canopy resistance w.r.t. canopy air temperature (s m-1 K-1)
+ ! output: conductances (used to check derivative calculations)
+ leafConductance, & ! intent(out): leaf conductance (m s-1)
+ canopyConductance, & ! intent(out): canopy conductance (m s-1)
+ groundConductanceSH, & ! intent(out): ground conductance for sensible heat (m s-1)
+ groundConductanceLH, & ! intent(out): ground conductance for latent heat -- includes soil resistance (m s-1)
+ evapConductance, & ! intent(out): conductance for evaporation (m s-1)
+ transConductance, & ! intent(out): conductance for transpiration (m s-1)
+ totalConductanceSH, & ! intent(out): total conductance for sensible heat (m s-1)
+ totalConductanceLH, & ! intent(out): total conductance for latent heat (m s-1)
+ ! output: canopy air space variables
+ VP_CanopyAir, & ! intent(out): vapor pressure of the canopy air space (Pa)
+ ! output: fluxes from the vegetation canopy
+ senHeatCanopy, & ! intent(out): sensible heat flux from the canopy to the canopy air space (W m-2)
+ latHeatCanopyEvap, & ! intent(out): latent heat flux associated with evaporation from the canopy to the canopy air space (W m-2)
+ latHeatCanopyTrans, & ! intent(out): latent heat flux associated with transpiration from the canopy to the canopy air space (W m-2)
+ ! output: fluxes from non-vegetated surfaces (ground surface below vegetation, bare ground, or snow covered vegetation)
+ senHeatGround, & ! intent(out): sensible heat flux from ground surface below vegetation, bare ground, or snow covered vegetation (W m-2)
+ latHeatGround, & ! intent(out): latent heat flux from ground surface below vegetation, bare ground, or snow covered vegetation (W m-2)
+ ! output: total heat fluxes to the atmosphere
+ senHeatTotal, & ! intent(out): total sensible heat flux to the atmosphere (W m-2)
+ latHeatTotal, & ! intent(out): total latent heat flux to the atmosphere (W m-2)
+ ! output: net fluxes
+ turbFluxCanair, & ! intent(out): net turbulent heat fluxes at the canopy air space (W m-2)
+ turbFluxCanopy, & ! intent(out): net turbulent heat fluxes at the canopy (W m-2)
+ turbFluxGround, & ! intent(out): net turbulent heat fluxes at the ground surface (W m-2)
+ ! output: flux derivatives
+ dTurbFluxCanair_dTCanair, & ! intent(out): derivative in net canopy air space fluxes w.r.t. canopy air temperature (W m-2 K-1)
+ dTurbFluxCanair_dTCanopy, & ! intent(out): derivative in net canopy air space fluxes w.r.t. canopy temperature (W m-2 K-1)
+ dTurbFluxCanair_dTGround, & ! intent(out): derivative in net canopy air space fluxes w.r.t. ground temperature (W m-2 K-1)
+ dTurbFluxCanopy_dTCanair, & ! intent(out): derivative in net canopy turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
+ dTurbFluxCanopy_dTCanopy, & ! intent(out): derivative in net canopy turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
+ dTurbFluxCanopy_dTGround, & ! intent(out): derivative in net canopy turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
+ dTurbFluxGround_dTCanair, & ! intent(out): derivative in net ground turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
+ dTurbFluxGround_dTCanopy, & ! intent(out): derivative in net ground turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
+ dTurbFluxGround_dTGround, & ! intent(out): derivative in net ground turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
+ ! output: liquid flux derivatives (canopy evap)
+ dLatHeatCanopyEvap_dCanWat, & ! intent(out): derivative in latent heat of canopy evaporation w.r.t. canopy total water content (J kg-1 s-1)
+ dLatHeatCanopyEvap_dTCanair, & ! intent(out): derivative in latent heat of canopy evaporation w.r.t. canopy air temperature (W m-2 K-1)
+ dLatHeatCanopyEvap_dTCanopy, & ! intent(out): derivative in latent heat of canopy evaporation w.r.t. canopy temperature (W m-2 K-1)
+ dLatHeatCanopyEvap_dTGround, & ! intent(out): derivative in latent heat of canopy evaporation w.r.t. ground temperature (W m-2 K-1)
+ ! output: liquid flux derivatives (ground evap)
+ dLatHeatGroundEvap_dCanWat, & ! intent(out): derivative in latent heat of ground evaporation w.r.t. canopy total water content (J kg-1 s-1)
+ dLatHeatGroundEvap_dTCanair, & ! intent(out): derivative in latent heat of ground evaporation w.r.t. canopy air temperature
+ dLatHeatGroundEvap_dTCanopy, & ! intent(out): derivative in latent heat of ground evaporation w.r.t. canopy temperature
+ dLatHeatGroundEvap_dTGround, & ! intent(out): derivative in latent heat of ground evaporation w.r.t. ground temperature
+ ! output: latent heat flux derivatives (canopy trans)
+ dLatHeatCanopyTrans_dCanWat, & ! intent(out): derivative in the latent heat of canopy transpiration w.r.t. canopy total water (J kg-1 s-1)
+ dLatHeatCanopyTrans_dTCanair, & ! intent(out): derivative in the latent heat of canopy transpiration w.r.t. canopy air temperature
+ dLatHeatCanopyTrans_dTCanopy, & ! intent(out): derivative in the latent heat of canopy transpiration w.r.t. canopy temperature
+ dLatHeatCanopyTrans_dTGround, & ! intent(out): derivative in the latent heat of canopy transpiration w.r.t. ground temperature
+ ! output: cross derivatives
+ dTurbFluxCanair_dCanWat, & ! intent(out): derivative in net canopy air space fluxes w.r.t. canopy total water content (J kg-1 s-1)
+ dTurbFluxCanopy_dCanWat, & ! intent(out): derivative in net canopy turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
+ dTurbFluxGround_dCanWat, & ! intent(out): derivative in net ground turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
+ ! output: error control
+ err,message ) ! intent(out): error control
+ ! -----------------------------------------------------------------------------------------------------------------------------------------
+ implicit none
+ ! input: model control
+ logical(lgt),intent(in) :: computeVegFlux ! logical flag to compute vegetation fluxes (.false. if veg buried by snow)
+ integer(i4b),intent(in) :: ixDerivMethod ! choice of method used to compute derivative (analytical or numerical)
+ ! input: above-canopy forcing data
+ real(rkind),intent(in) :: airtemp ! air temperature at some height above the surface (K)
+ real(rkind),intent(in) :: airpres ! air pressure of the air above the vegetation canopy (Pa)
+ real(rkind),intent(in) :: VPair ! vapor pressure of the air above the vegetation canopy (Pa)
+ ! input: latent heat of sublimation/vaporization
+ real(rkind),intent(in) :: latHeatSubVapCanopy ! latent heat of sublimation/vaporization for the vegetation canopy (J kg-1)
+ real(rkind),intent(in) :: latHeatSubVapGround ! latent heat of sublimation/vaporization for the ground surface (J kg-1)
+ ! input: canopy and ground temperature
+ real(rkind),intent(in) :: canairTemp ! temperature of the canopy air space (K)
+ real(rkind),intent(in) :: canopyTemp ! canopy temperature (K)
+ real(rkind),intent(in) :: groundTemp ! ground temperature (K)
+ real(rkind),intent(in) :: satVP_CanopyTemp ! saturation vapor pressure at the temperature of the veg canopy (Pa)
+ real(rkind),intent(in) :: satVP_GroundTemp ! saturation vapor pressure at the temperature of the ground (Pa)
+ real(rkind),intent(in) :: dSVPCanopy_dCanopyTemp ! derivative in canopy saturation vapor pressure w.r.t. canopy temperature (Pa K-1)
+ real(rkind),intent(in) :: dSVPGround_dGroundTemp ! derivative in ground saturation vapor pressure w.r.t. ground temperature (Pa K-1)
+ ! input: diagnostic variables
+ real(rkind),intent(in) :: exposedVAI ! exposed vegetation area index -- leaf plus stem (m2 m-2)
+ real(rkind),intent(in) :: canopyWetFraction ! fraction of canopy that is wet [0-1]
+ real(rkind),intent(in) :: dCanopyWetFraction_dWat ! derivative in the canopy wetted fraction w.r.t. liquid water content (kg-1 m-2)
+ real(rkind),intent(in) :: dCanopyWetFraction_dT ! derivative in the canopy wetted fraction w.r.t. canopy temperature (K-1)
+ real(rkind),intent(in) :: canopySunlitLAI ! sunlit leaf area (-)
+ real(rkind),intent(in) :: canopyShadedLAI ! shaded leaf area (-)
+ real(rkind),intent(in) :: soilRelHumidity ! relative humidity in the soil pores [0-1]
+ real(rkind),intent(in) :: soilResistance ! resistance from the soil (s m-1)
+ real(rkind),intent(in) :: leafResistance ! mean leaf boundary layer resistance per unit leaf area (s m-1)
+ real(rkind),intent(in) :: groundResistance ! below canopy aerodynamic resistance (s m-1)
+ real(rkind),intent(in) :: canopyResistance ! above canopy aerodynamic resistance (s m-1)
+ real(rkind),intent(in) :: stomResistSunlit ! stomatal resistance for sunlit leaves (s m-1)
+ real(rkind),intent(in) :: stomResistShaded ! stomatal resistance for shaded leaves (s m-1)
+ ! input: derivatives in scalar resistances
+ real(rkind),intent(in) :: dGroundResistance_dTGround ! derivative in ground resistance w.r.t. ground temperature (s m-1 K-1)
+ real(rkind),intent(in) :: dGroundResistance_dTCanopy ! derivative in ground resistance w.r.t. canopy temperature (s m-1 K-1)
+ real(rkind),intent(in) :: dGroundResistance_dTCanair ! derivative in ground resistance w.r.t. canopy air temperature (s m-1 K-1)
+ real(rkind),intent(in) :: dCanopyResistance_dTCanopy ! derivative in canopy resistance w.r.t. canopy temperature (s m-1 K-1)
+ real(rkind),intent(in) :: dCanopyResistance_dTCanair ! derivative in canopy resistance w.r.t. canopy air temperature (s m-1 K-1)
+ ! ---------------------------------------------------------------------------------------------------------------------------------------------------------------
+ ! output: conductances -- used to test derivatives
+ real(rkind),intent(out) :: leafConductance ! leaf conductance (m s-1)
+ real(rkind),intent(out) :: canopyConductance ! canopy conductance (m s-1)
+ real(rkind),intent(out) :: groundConductanceSH ! ground conductance for sensible heat (m s-1)
+ real(rkind),intent(out) :: groundConductanceLH ! ground conductance for latent heat -- includes soil resistance (m s-1)
+ real(rkind),intent(out) :: evapConductance ! conductance for evaporation (m s-1)
+ real(rkind),intent(out) :: transConductance ! conductance for transpiration (m s-1)
+ real(rkind),intent(out) :: totalConductanceSH ! total conductance for sensible heat (m s-1)
+ real(rkind),intent(out) :: totalConductanceLH ! total conductance for latent heat (m s-1)
+ ! output: canopy air space variables
+ real(rkind),intent(out) :: VP_CanopyAir ! vapor pressure of the canopy air space (Pa)
+ ! output: fluxes from the vegetation canopy
+ real(rkind),intent(out) :: senHeatCanopy ! sensible heat flux from the canopy to the canopy air space (W m-2)
+ real(rkind),intent(out) :: latHeatCanopyEvap ! latent heat flux associated with evaporation from the canopy to the canopy air space (W m-2)
+ real(rkind),intent(out) :: latHeatCanopyTrans ! latent heat flux associated with transpiration from the canopy to the canopy air space (W m-2)
+ ! output: fluxes from non-vegetated surfaces (ground surface below vegetation, bare ground, or snow covered vegetation)
+ real(rkind),intent(out) :: senHeatGround ! sensible heat flux from ground surface below vegetation, bare ground, or snow covered vegetation (W m-2)
+ real(rkind),intent(out) :: latHeatGround ! latent heat flux from ground surface below vegetation, bare ground, or snow covered vegetation (W m-2)
+ ! output: total heat fluxes to the atmosphere
+ real(rkind),intent(out) :: senHeatTotal ! total sensible heat flux to the atmosphere (W m-2)
+ real(rkind),intent(out) :: latHeatTotal ! total latent heat flux to the atmosphere (W m-2)
+ ! output: net fluxes
+ real(rkind),intent(out) :: turbFluxCanair ! net turbulent heat fluxes at the canopy air space (W m-2)
+ real(rkind),intent(out) :: turbFluxCanopy ! net turbulent heat fluxes at the canopy (W m-2)
+ real(rkind),intent(out) :: turbFluxGround ! net turbulent heat fluxes at the ground surface (W m-2)
+ ! output: energy flux derivatives
+ real(rkind),intent(out) :: dTurbFluxCanair_dTCanair ! derivative in net canopy air space fluxes w.r.t. canopy air temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dTurbFluxCanair_dTCanopy ! derivative in net canopy air space fluxes w.r.t. canopy temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dTurbFluxCanair_dTGround ! derivative in net canopy air space fluxes w.r.t. ground temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dTurbFluxCanopy_dTCanair ! derivative in net canopy turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dTurbFluxCanopy_dTCanopy ! derivative in net canopy turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dTurbFluxCanopy_dTGround ! derivative in net canopy turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dTurbFluxGround_dTCanair ! derivative in net ground turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dTurbFluxGround_dTCanopy ! derivative in net ground turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dTurbFluxGround_dTGround ! derivative in net ground turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
+ ! output: liquid flux derivatives (canopy evap)
+ real(rkind),intent(out) :: dLatHeatCanopyEvap_dCanWat ! derivative in latent heat of canopy evaporation w.r.t. canopy total water content (W kg-1)
+ real(rkind),intent(out) :: dLatHeatCanopyEvap_dTCanair ! derivative in latent heat of canopy evaporation w.r.t. canopy air temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dLatHeatCanopyEvap_dTCanopy ! derivative in latent heat of canopy evaporation w.r.t. canopy temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dLatHeatCanopyEvap_dTGround ! derivative in latent heat of canopy evaporation w.r.t. ground temperature (W m-2 K-1)
+ ! output: liquid flux derivatives (ground evap)
+ real(rkind),intent(out) :: dLatHeatGroundEvap_dCanWat ! derivative in latent heat of ground evaporation w.r.t. canopy total water content (J kg-1 s-1)
+ real(rkind),intent(out) :: dLatHeatGroundEvap_dTCanair ! derivative in latent heat of ground evaporation w.r.t. canopy air temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dLatHeatGroundEvap_dTCanopy ! derivative in latent heat of ground evaporation w.r.t. canopy temperature (W m-2 K-1)
+ real(rkind),intent(out) :: dLatHeatGroundEvap_dTGround ! derivative in latent heat of ground evaporation w.r.t. ground temperature (W m-2 K-1)
+ ! output: latent heat flux derivatives (canopy trans)
+ real(rkind) :: dLatHeatCanopyTrans_dCanWat ! derivative in the latent heat of canopy transpiration w.r.t. canopy total water (J kg-1 s-1)
+ real(rkind) :: dLatHeatCanopyTrans_dTCanair ! derivative in the latent heat of canopy transpiration w.r.t. canopy air temperature
+ real(rkind) :: dLatHeatCanopyTrans_dTCanopy ! derivative in the latent heat of canopy transpiration w.r.t. canopy temperature
+ real(rkind) :: dLatHeatCanopyTrans_dTGround ! derivative in the latent heat of canopy transpiration flux w.r.t. ground temperature
+ ! output: cross derivatives
+ real(rkind),intent(out) :: dTurbFluxCanair_dCanWat ! derivative in net canopy air space fluxes w.r.t. canopy total water content (J kg-1 s-1)
+ real(rkind),intent(out) :: dTurbFluxCanopy_dCanWat ! derivative in net canopy turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
+ real(rkind),intent(out) :: dTurbFluxGround_dCanWat ! derivative in net ground turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
+ ! output: error control
+ integer(i4b),intent(out) :: err ! error code
+ character(*),intent(out) :: message ! error message
+ ! -----------------------------------------------------------------------------------------------------------------------------------------
+ ! local variables -- general
+ real(rkind) :: fpart1,fpart2 ! different parts of a function
+ real(rkind) :: dPart0,dpart1,dpart2 ! derivatives for different parts of a function
+ ! local variables -- "constants"
+ real(rkind) :: volHeatCapacityAir ! volumetric heat capacity of air (J m-3)
+ real(rkind) :: latentHeatConstant ! latent heat constant (kg m-3 K-1)
+ ! local variables -- derivatives for energy conductances
+ real(rkind) :: dEvapCond_dCanopyTemp ! derivative in evap conductance w.r.t. canopy temperature
+ real(rkind) :: dTransCond_dCanopyTemp ! derivative in trans conductance w.r.t. canopy temperature
+ real(rkind) :: dCanopyCond_dCanairTemp ! derivative in canopy conductance w.r.t. canopy air temperature
+ real(rkind) :: dCanopyCond_dCanopyTemp ! derivative in canopy conductance w.r.t. canopy temperature
+ real(rkind) :: dGroundCondSH_dCanairTemp ! derivative in ground conductance of sensible heat w.r.t. canopy air temperature
+ real(rkind) :: dGroundCondSH_dCanopyTemp ! derivative in ground conductance of sensible heat w.r.t. canopy temperature
+ real(rkind) :: dGroundCondSH_dGroundTemp ! derivative in ground conductance of sensible heat w.r.t. ground temperature
+ ! local variables -- derivatives for mass conductances
+ real(rkind) :: dGroundCondLH_dCanairTemp ! derivative in ground conductance w.r.t. canopy air temperature
+ real(rkind) :: dGroundCondLH_dCanopyTemp ! derivative in ground conductance w.r.t. canopy temperature
+ real(rkind) :: dGroundCondLH_dGroundTemp ! derivative in ground conductance w.r.t. ground temperature
+ ! local variables -- derivatives for the canopy air space variables
+ real(rkind) :: fPart_VP ! part of the function for vapor pressure of the canopy air space
+ real(rkind) :: leafConductanceTr ! leaf conductance for transpiration (m s-1)
+ real(rkind) :: dVPCanopyAir_dTCanair ! derivative in the vapor pressure of the canopy air space w.r.t. temperature of the canopy air space
+ real(rkind) :: dVPCanopyAir_dTCanopy ! derivative in the vapor pressure of the canopy air space w.r.t. temperature of the canopy
+ real(rkind) :: dVPCanopyAir_dTGround ! derivative in the vapor pressure of the canopy air space w.r.t. temperature of the ground
+ real(rkind) :: dVPCanopyAir_dWetFrac ! derivative of vapor pressure in the canopy air space w.r.t. wetted fraction of the canopy
+ real(rkind) :: dVPCanopyAir_dCanWat ! derivative of vapor pressure in the canopy air space w.r.t. canopy total water content
+ ! local variables -- sensible heat flux derivatives
+ real(rkind) :: dSenHeatTotal_dTCanair ! derivative in the total sensible heat flux w.r.t. canopy air temperature
+ real(rkind) :: dSenHeatTotal_dTCanopy ! derivative in the total sensible heat flux w.r.t. canopy air temperature
+ real(rkind) :: dSenHeatTotal_dTGround ! derivative in the total sensible heat flux w.r.t. ground temperature
+ real(rkind) :: dSenHeatCanopy_dTCanair ! derivative in the canopy sensible heat flux w.r.t. canopy air temperature
+ real(rkind) :: dSenHeatCanopy_dTCanopy ! derivative in the canopy sensible heat flux w.r.t. canopy temperature
+ real(rkind) :: dSenHeatCanopy_dTGround ! derivative in the canopy sensible heat flux w.r.t. ground temperature
+ real(rkind) :: dSenHeatGround_dTCanair ! derivative in the ground sensible heat flux w.r.t. canopy air temperature
+ real(rkind) :: dSenHeatGround_dTCanopy ! derivative in the ground sensible heat flux w.r.t. canopy temperature
+ real(rkind) :: dSenHeatGround_dTGround ! derivative in the ground sensible heat flux w.r.t. ground temperature
+ ! local variables -- wetted fraction derivatives
+ real(rkind) :: dLatHeatCanopyEvap_dWetFrac ! derivative in the latent heat of canopy evaporation w.r.t. canopy wet fraction (W m-2)
+ real(rkind) :: dLatHeatCanopyTrans_dWetFrac ! derivative in the latent heat of canopy transpiration w.r.t. canopy wet fraction (W m-2)
+ ! -----------------------------------------------------------------------------------------------------------------------------------------
+ ! initialize error control
+ err=0; message='turbFluxes/'
+
+ ! compute constants
+ volHeatCapacityAir = iden_air*cp_air ! volumetric heat capacity of air (J m-3)
+ latentHeatConstant = iden_air*w_ratio/airpres ! latent heat constant for (kg m-3 Pa-1)
+
+ ! *****
+ ! * compute conductances, and derivatives...
+ ! ******************************************
+
+ ! compute conductances for sensible heat (m s-1)
+ if(computeVegFlux)then
+ leafConductance = exposedVAI/leafResistance
+ leafConductanceTr = canopySunlitLAI/(leafResistance+stomResistSunlit) + canopyShadedLAI/(leafResistance+stomResistShaded)
+ canopyConductance = 1._rkind/canopyResistance
+ else
+ leafConductance = 0._rkind
+ canopyConductance = 0._rkind
+ end if
+ groundConductanceSH = 1._rkind/groundResistance
+
+ ! compute total conductance for sensible heat
+ totalConductanceSH = leafConductance + groundConductanceSH + canopyConductance
+
+ ! compute conductances for latent heat (m s-1)
+ if(computeVegFlux)then
+ evapConductance = canopyWetFraction*leafConductance
+ transConductance = (1._rkind - canopyWetFraction) * leafConductanceTr
+ !write(*,'(a,10(f14.8,1x))') 'canopySunlitLAI, canopyShadedLAI, stomResistSunlit, stomResistShaded, leafResistance, canopyWetFraction = ', &
+ ! canopySunlitLAI, canopyShadedLAI, stomResistSunlit, stomResistShaded, leafResistance, canopyWetFraction
+ else
+ evapConductance = 0._rkind
+ transConductance = 0._rkind
+ end if
+ groundConductanceLH = 1._rkind/(groundResistance + soilResistance) ! NOTE: soilResistance accounts for fractional snow, and =0 when snow cover is 100%
+ totalConductanceLH = evapConductance + transConductance + groundConductanceLH + canopyConductance
+
+ ! check sensible heat conductance
+ if(totalConductanceSH < -tinyVal .or. groundConductanceSH < -tinyVal .or. canopyConductance < -tinyVal)then
+ message=trim(message)//'negative conductance for sensible heat'
+ err=20; return
+ endif
+
+ ! check latent heat conductance
+ if(totalConductanceLH < tinyVal .or. groundConductanceLH < -tinyVal)then
+ message=trim(message)//'negative conductance for latent heat'
+ err=20; return
+ endif
+
+ ! * compute derivatives
+ ! NOTE: it may be more efficient to compute these derivatives when computing resistances
+ if(ixDerivMethod == analytical)then
+
+ ! compute derivatives in individual conductances for sensible heat w.r.t. canopy temperature (m s-1 K-1)
+ if(computeVegFlux)then
+ dEvapCond_dCanopyTemp = dCanopyWetFraction_dT*leafConductance ! derivative in evap conductance w.r.t. canopy temperature
+ dTransCond_dCanopyTemp = -dCanopyWetFraction_dT*leafConductanceTr ! derivative in trans conductance w.r.t. canopy temperature
+ dCanopyCond_dCanairTemp = -dCanopyResistance_dTCanair/canopyResistance**2._rkind ! derivative in canopy conductance w.r.t. canopy air emperature
+ dCanopyCond_dCanopyTemp = -dCanopyResistance_dTCanopy/canopyResistance**2._rkind ! derivative in canopy conductance w.r.t. canopy temperature
+ dGroundCondSH_dCanairTemp = -dGroundResistance_dTCanair/groundResistance**2._rkind ! derivative in ground conductance w.r.t. canopy air temperature
+ dGroundCondSH_dCanopyTemp = -dGroundResistance_dTCanopy/groundResistance**2._rkind ! derivative in ground conductance w.r.t. canopy temperature
+ dGroundCondSH_dGroundTemp = -dGroundResistance_dTGround/groundResistance**2._rkind ! derivative in ground conductance w.r.t. ground temperature
+ else
+ dEvapCond_dCanopyTemp = 0._rkind ! derivative in evap conductance w.r.t. canopy temperature
+ dTransCond_dCanopyTemp = 0._rkind ! derivative in trans conductance w.r.t. canopy temperature
+ dCanopyCond_dCanairTemp = 0._rkind ! derivative in canopy conductance w.r.t. canopy air emperature
+ dCanopyCond_dCanopyTemp = 0._rkind ! derivative in canopy conductance w.r.t. canopy temperature
+ dGroundCondSH_dCanairTemp = 0._rkind ! derivative in ground conductance w.r.t. canopy air temperature
+ dGroundCondSH_dCanopyTemp = 0._rkind ! derivative in ground conductance w.r.t. canopy temperature
+ dGroundCondSH_dGroundTemp = -dGroundResistance_dTGround/groundResistance**2._rkind ! derivative in ground conductance w.r.t. ground temperature
+ end if
+
+ ! compute derivatives in individual conductances for latent heat w.r.t. canopy temperature (m s-1 K-1)
+ if(computeVegFlux)then
+ dGroundCondLH_dCanairTemp = -dGroundResistance_dTCanair/(groundResistance+soilResistance)**2._rkind ! derivative in ground conductance w.r.t. canopy air temperature
+ dGroundCondLH_dCanopyTemp = -dGroundResistance_dTCanopy/(groundResistance+soilResistance)**2._rkind ! derivative in ground conductance w.r.t. canopy temperature
+ dGroundCondLH_dGroundTemp = -dGroundResistance_dTGround/(groundResistance+soilResistance)**2._rkind ! derivative in ground conductance w.r.t. ground temperature
+ else
+ dGroundCondLH_dCanairTemp = 0._rkind ! derivative in ground conductance w.r.t. canopy air temperature
+ dGroundCondLH_dCanopyTemp = 0._rkind ! derivative in ground conductance w.r.t. canopy temperature
+ dGroundCondLH_dGroundTemp = -dGroundResistance_dTGround/(groundResistance+soilResistance)**2._rkind ! derivative in ground conductance w.r.t. ground temperature
+ end if
+
+ end if ! (if computing analytical derivatives)
+
+ ! *****
+ ! * compute sensible and latent heat fluxes, and derivatives...
+ ! *************************************************************
+
+ ! * compute sensible and latent heat fluxes from the canopy to the canopy air space (W m-2)
+ if(computeVegFlux)then
+
+ ! compute the vapor pressure in the canopy air space (Pa)
+ fPart_VP = canopyConductance*VPair + (evapConductance + transConductance)*satVP_CanopyTemp + groundConductanceLH*satVP_GroundTemp*soilRelHumidity
+ VP_CanopyAir = fPart_VP/totalConductanceLH
+
+ ! compute sensible heat flux from the canopy air space to the atmosphere
+ ! NOTE: canairTemp is a state variable
+ senHeatTotal = -volHeatCapacityAir*canopyConductance*(canairTemp - airtemp)
+
+ ! compute fluxes
+ senHeatCanopy = -volHeatCapacityAir*leafConductance*(canopyTemp - canairTemp) ! (positive downwards)
+ latHeatCanopyEvap = -latHeatSubVapCanopy*latentHeatConstant*evapConductance*(satVP_CanopyTemp - VP_CanopyAir) ! (positive downwards)
+ latHeatCanopyTrans = -LH_vap*latentHeatConstant*transConductance*(satVP_CanopyTemp - VP_CanopyAir) ! (positive downwards)
+
+
+ ! * no vegetation, so fluxes are zero
+ else
+ senHeatCanopy = 0._rkind
+ latHeatCanopyEvap = 0._rkind
+ latHeatCanopyTrans = 0._rkind
+ end if
+
+ ! compute sensible and latent heat fluxes from the ground to the canopy air space (W m-2)
+ if(computeVegFlux)then
+ senHeatGround = -volHeatCapacityAir*groundConductanceSH*(groundTemp - canairTemp) ! (positive downwards)
+ latHeatGround = -latHeatSubVapGround*latentHeatConstant*groundConductanceLH*(satVP_GroundTemp*soilRelHumidity - VP_CanopyAir) ! (positive downwards)
+ else
+ senHeatGround = -volHeatCapacityAir*groundConductanceSH*(groundTemp - airtemp) ! (positive downwards)
+ latHeatGround = -latHeatSubVapGround*latentHeatConstant*groundConductanceLH*(satVP_GroundTemp*soilRelHumidity - VPair) ! (positive downwards)
+ senHeatTotal = senHeatGround
+ end if
+
+
+ ! compute latent heat flux from the canopy air space to the atmosphere
+ ! NOTE: VP_CanopyAir is a diagnostic variable
+ latHeatTotal = latHeatCanopyEvap + latHeatCanopyTrans + latHeatGround
+
+ ! * compute derivatives
+ if(ixDerivMethod == analytical)then
+
+ ! differentiate CANOPY fluxes
+ if(computeVegFlux)then
+
+ ! compute derivatives of vapor pressure in the canopy air space w.r.t. all state variables
+ ! (derivative of vapor pressure in the canopy air space w.r.t. temperature of the canopy air space)
+ dPart1 = dCanopyCond_dCanairTemp*VPair + dGroundCondLH_dCanairTemp*satVP_GroundTemp*soilRelHumidity
+ dPart2 = -(dCanopyCond_dCanairTemp + dGroundCondLH_dCanairTemp)/(totalConductanceLH**2._rkind)
+ dVPCanopyAir_dTCanair = dPart1/totalConductanceLH + fPart_VP*dPart2
+ ! (derivative of vapor pressure in the canopy air space w.r.t. temperature of the canopy)
+ dPart0 = (evapConductance + transConductance)*dSVPCanopy_dCanopyTemp + (dEvapCond_dCanopyTemp + dTransCond_dCanopyTemp)*satVP_CanopyTemp
+ dPart1 = dCanopyCond_dCanopyTemp*VPair + dPart0 + dGroundCondLH_dCanopyTemp*satVP_GroundTemp*soilRelHumidity
+ dPart2 = -(dCanopyCond_dCanopyTemp + dEvapCond_dCanopyTemp + dTransCond_dCanopyTemp + dGroundCondLH_dCanopyTemp)/(totalConductanceLH**2._rkind)
+ dVPCanopyAir_dTCanopy = dPart1/totalConductanceLH + fPart_VP*dPart2
+ ! (derivative of vapor pressure in the canopy air space w.r.t. temperature of the ground)
+ dPart1 = dGroundCondLH_dGroundTemp*satVP_GroundTemp*soilRelHumidity + groundConductanceLH*dSVPGround_dGroundTemp*soilRelHumidity
+ dPart2 = -dGroundCondLH_dGroundTemp/(totalConductanceLH**2._rkind)
+ dVPCanopyAir_dTGround = dPart1/totalConductanceLH + fPart_VP*dPart2
+ ! (derivative of vapor pressure in the canopy air space w.r.t. wetted fraction of the canopy)
+ dPart1 = (leafConductance - leafConductanceTr)*satVP_CanopyTemp
+ dPart2 = -(leafConductance - leafConductanceTr)/(totalConductanceLH**2._rkind)
+ dVPCanopyAir_dWetFrac = dPart1/totalConductanceLH + fPart_VP*dPart2
+ dVPCanopyAir_dCanWat = dVPCanopyAir_dWetFrac*dCanopyWetFraction_dWat
+
+ ! sensible heat from the canopy to the atmosphere
+ dSenHeatTotal_dTCanair = -volHeatCapacityAir*canopyConductance - volHeatCapacityAir*dCanopyCond_dCanairTemp*(canairTemp - airtemp)
+ dSenHeatTotal_dTCanopy = -volHeatCapacityAir*dCanopyCond_dCanopyTemp*(canairTemp - airtemp)
+ dSenHeatTotal_dTGround = 0._rkind
+
+ ! sensible heat from the canopy to the canopy air space
+ dSenHeatCanopy_dTCanair = volHeatCapacityAir*leafConductance
+ dSenHeatCanopy_dTCanopy = -volHeatCapacityAir*leafConductance
+ dSenHeatCanopy_dTGround = 0._rkind
+
+ ! sensible heat from the ground to the canopy air space
+ dSenHeatGround_dTCanair = -volHeatCapacityAir*dGroundCondSH_dCanairTemp*(groundTemp - canairTemp) + volHeatCapacityAir*groundConductanceSH
+ dSenHeatGround_dTCanopy = -volHeatCapacityAir*dGroundCondSH_dCanopyTemp*(groundTemp - canairTemp)
+ dSenHeatGround_dTGround = -volHeatCapacityAir*dGroundCondSH_dGroundTemp*(groundTemp - canairTemp) - volHeatCapacityAir*groundConductanceSH
+
+ ! latent heat associated with canopy evaporation
+ ! (initial calculations)
+ fPart1 = -latHeatSubVapCanopy*latentHeatConstant*evapConductance
+ dPart1 = -latHeatSubVapCanopy*latentHeatConstant*dEvapCond_dCanopyTemp
+ fPart2 = satVP_CanopyTemp - VP_CanopyAir
+ dPart2 = dSVPCanopy_dCanopyTemp - dVPCanopyAir_dTCanopy
+ ! (derivatives)
+ dLatHeatCanopyEvap_dTCanair = fPart1*(-dVPCanopyAir_dTCanair)
+ dLatHeatCanopyEvap_dTCanopy = fPart1*dpart2 + fPart2*dPart1
+ dLatHeatCanopyEvap_dTGround = fPart1*(-dVPCanopyAir_dTGround)
+
+ ! latent heat associated with canopy transpiration
+ ! (initial calculations)
+ fPart1 = -LH_vap*latentHeatConstant*transConductance
+ dPart1 = -LH_vap*latentHeatConstant*dTransCond_dCanopyTemp
+ ! (derivatives)
+ dLatHeatCanopyTrans_dTCanair = fPart1*(-dVPCanopyAir_dTCanair)
+ dLatHeatCanopyTrans_dTCanopy = fPart1*dPart2 + fPart2*dPart1
+ dLatHeatCanopyTrans_dTGround = fPart1*(-dVPCanopyAir_dTGround)
+
+ ! latent heat flux from the ground
+ fPart1 = -latHeatSubVapGround*latentHeatConstant*groundConductanceLH ! function of the first part
+ fPart2 = (satVP_GroundTemp*soilRelHumidity - VP_CanopyAir) ! function of the second part
+ dLatHeatGroundEvap_dTCanair = -latHeatSubVapGround*latentHeatConstant*dGroundCondLH_dCanairTemp*fPart2 - dVPCanopyAir_dTCanair*fPart1
+ dLatHeatGroundEvap_dTCanopy = -latHeatSubVapGround*latentHeatConstant*dGroundCondLH_dCanopyTemp*fPart2 - dVPCanopyAir_dTCanopy*fPart1
+ dLatHeatGroundEvap_dTGround = -latHeatSubVapGround*latentHeatConstant*dGroundCondLH_dGroundTemp*fPart2 + (dSVPGround_dGroundTemp*soilRelHumidity - dVPCanopyAir_dTGround)*fPart1
+
+ ! latent heat associated with canopy evaporation w.r.t. wetted fraction of the canopy
+ dPart1 = -latHeatSubVapCanopy*latentHeatConstant*leafConductance
+ fPart1 = dPart1*canopyWetFraction
+ dLatHeatCanopyEvap_dWetFrac = dPart1*(satVP_CanopyTemp - VP_CanopyAir) + fPart1*(-dVPCanopyAir_dWetFrac)
+
+ ! latent heat associated with canopy transpiration w.r.t. wetted fraction of the canopy
+ dPart1 = LH_vap*latentHeatConstant*leafConductanceTr ! NOTE: positive, since (1 - wetFrac)
+ fPart1 = -dPart1*(1._rkind - canopyWetFraction)
+ dLatHeatCanopyTrans_dWetFrac = dPart1*(satVP_CanopyTemp - VP_CanopyAir) + fPart1*(-dVPCanopyAir_dWetFrac)
+
+ ! latent heat associated with canopy transpiration w.r.t. canopy total water
+ dLatHeatCanopyTrans_dCanWat = dLatHeatCanopyTrans_dWetFrac*dCanopyWetFraction_dWat ! (J s-1 kg-1)
+
+
+ else ! canopy is undefined
+
+ ! set derivatives for canopy fluxes to zero (no canopy, so fluxes are undefined)
+ dSenHeatTotal_dTCanair = 0._rkind
+ dSenHeatTotal_dTCanopy = 0._rkind
+ dSenHeatTotal_dTGround = 0._rkind
+ dSenHeatCanopy_dTCanair = 0._rkind
+ dSenHeatCanopy_dTCanopy = 0._rkind
+ dSenHeatCanopy_dTGround = 0._rkind
+ dLatHeatCanopyEvap_dTCanair = 0._rkind
+ dLatHeatCanopyEvap_dTCanopy = 0._rkind
+ dLatHeatCanopyEvap_dTGround = 0._rkind
+ dLatHeatCanopyTrans_dTCanair = 0._rkind
+ dLatHeatCanopyTrans_dTCanopy = 0._rkind
+ dLatHeatCanopyTrans_dTGround = 0._rkind
+
+ ! set derivatives for wetted area and canopy transpiration to zero (no canopy, so fluxes are undefined)
+ dLatHeatCanopyEvap_dWetFrac = 0._rkind
dLatHeatCanopyEvap_dCanWat = 0._rkind
- dLatHeatGroundEvap_dCanWat = 0._rkind
- ! (cross deriavtives)
- dTurbFluxCanair_dCanWat = 0._rkind
- dTurbFluxCanopy_dCanWat = 0._rkind
- dTurbFluxGround_dCanWat = 0._rkind
- end if
-
- end subroutine turbFluxes
-
-
- ! *******************************************************************************************************
- ! private subroutine aStability: compute stability corrections for turbulent heat fluxes (-)
- ! *******************************************************************************************************
- subroutine aStability(&
- ! input: control
- computeDerivative, & ! input: logical flag to compute analytical derivatives
- ixStability, & ! input: choice of stability function
- ! input: forcing data, diagnostic and state variables
- mHeight, & ! input: measurement height (m)
- airTemp, & ! input: air temperature (K)
- sfcTemp, & ! input: surface temperature (K)
- windspd, & ! input: wind speed (m s-1)
- ! input: stability parameters
- critRichNumber, & ! input: critical value for the bulk Richardson number where turbulence ceases (-)
- Louis79_bparam, & ! input: parameter in Louis (1979) stability function
- Mahrt87_eScale, & ! input: exponential scaling factor in the Mahrt (1987) stability function
- ! output
- RiBulk, & ! output: bulk Richardson number (-)
- stabilityCorrection, & ! output: stability correction for turbulent heat fluxes (-)
- dStabilityCorrection_dRich, & ! output: derivative in stability correction w.r.t. Richardson number (-)
- dStabilityCorrection_dAirTemp, & ! output: derivative in stability correction w.r.t. temperature (K-1)
- dStabilityCorrection_dSfcTemp, & ! output: derivative in stability correction w.r.t. temperature (K-1)
- err, message ) ! output: error control
- implicit none
- ! input: control
- logical(lgt),intent(in) :: computeDerivative ! flag to compute the derivative
- integer(i4b),intent(in) :: ixStability ! choice of stability function
- ! input: forcing data, diagnostic and state variables
- real(rkind),intent(in) :: mHeight ! measurement height (m)
- real(rkind),intent(in) :: airtemp ! air temperature (K)
- real(rkind),intent(in) :: sfcTemp ! surface temperature (K)
- real(rkind),intent(in) :: windspd ! wind speed (m s-1)
- ! input: stability parameters
- real(rkind),intent(in) :: critRichNumber ! critical value for the bulk Richardson number where turbulence ceases (-)
- real(rkind),intent(in) :: Louis79_bparam ! parameter in Louis (1979) stability function
- real(rkind),intent(in) :: Mahrt87_eScale ! exponential scaling factor in the Mahrt (1987) stability function
- ! output
- real(rkind),intent(out) :: RiBulk ! bulk Richardson number (-)
- real(rkind),intent(out) :: stabilityCorrection ! stability correction for turbulent heat fluxes (-)
- real(rkind),intent(out) :: dStabilityCorrection_dRich ! derivative in stability correction w.r.t. Richardson number (-)
- real(rkind),intent(out) :: dStabilityCorrection_dAirTemp ! derivative in stability correction w.r.t. air temperature (K-1)
- real(rkind),intent(out) :: dStabilityCorrection_dSfcTemp ! derivative in stability correction w.r.t. surface temperature (K-1)
- integer(i4b),intent(out) :: err ! error code
- character(*),intent(out) :: message ! error message
- ! local
- real(rkind), parameter :: verySmall=1.e-10_rkind ! a very small number (avoid stability of zero)
- real(rkind) :: dRiBulk_dAirTemp ! derivative in the bulk Richardson number w.r.t. air temperature (K-1)
- real(rkind) :: dRiBulk_dSfcTemp ! derivative in the bulk Richardson number w.r.t. surface temperature (K-1)
- real(rkind) :: bPrime ! scaled "b" parameter for stability calculations in Louis (1979)
- ! -----------------------------------------------------------------------------------------------------------------------------------------
- ! initialize error control
- err=0; message='aStability/'
-
- ! compute the bulk Richardson number (-)
- call bulkRichardson(&
- ! input
- airTemp, & ! input: air temperature (K)
- sfcTemp, & ! input: surface temperature (K)
- windspd, & ! input: wind speed (m s-1)
- mHeight, & ! input: measurement height (m)
- computeDerivative, & ! input: flag to compute the derivative
- ! output
- RiBulk, & ! output: bulk Richardson number (-)
- dRiBulk_dAirTemp, & ! output: derivative in the bulk Richardson number w.r.t. air temperature (K-1)
- dRiBulk_dSfcTemp, & ! output: derivative in the bulk Richardson number w.r.t. surface temperature (K-1)
- err,message) ! output: error control
-
- ! set derivative to one if not computing it
- if(.not.computeDerivative)then
- dStabilityCorrection_dRich = 1._rkind
- dStabilityCorrection_dAirTemp = 1._rkind
- dStabilityCorrection_dSfcTemp = 1._rkind
- end if
-
- ! ***** process unstable cases
- if(RiBulk<0._rkind)then
+ dLatHeatCanopyTrans_dCanWat = 0._rkind
+ dVPCanopyAir_dCanWat = 0._rkind
+
+ ! set derivatives for ground fluxes w.r.t canopy temperature to zero (no canopy, so fluxes are undefined)
+ dSenHeatGround_dTCanair = 0._rkind
+ dSenHeatGround_dTCanopy = 0._rkind
+ dLatHeatGroundEvap_dTCanair = 0._rkind
+ dLatHeatGroundEvap_dTCanopy = 0._rkind
+
+ ! compute derivatives for the ground fluxes w.r.t. ground temperature
+ dSenHeatGround_dTGround = (-volHeatCapacityAir*dGroundCondSH_dGroundTemp)*(groundTemp - airtemp) + & ! d(ground sensible heat flux)/d(ground temp)
+ (-volHeatCapacityAir*groundConductanceSH)
+ dLatHeatGroundEvap_dTGround = (-latHeatSubVapGround*latentHeatConstant*dGroundCondLH_dGroundTemp)*(satVP_GroundTemp*soilRelHumidity - VPair) + & ! d(ground latent heat flux)/d(ground temp)
+ (-latHeatSubVapGround*latentHeatConstant*groundConductanceLH)*dSVPGround_dGroundTemp*soilRelHumidity
+
+ end if ! (if canopy is defined)
+
+ end if ! (if computing analytical derivatives)
+
+
+ ! *****
+ ! * compute net turbulent fluxes, and derivatives...
+ ! **************************************************
+
+ ! compute net fluxes
+ turbFluxCanair = senHeatTotal - senHeatCanopy - senHeatGround ! net turbulent flux at the canopy air space (W m-2)
+ turbFluxCanopy = senHeatCanopy + latHeatCanopyEvap + latHeatCanopyTrans ! net turbulent flux at the canopy (W m-2)
+ turbFluxGround = senHeatGround + latHeatGround ! net turbulent flux at the ground surface (W m-2)
+
+ ! * compute derivatives
+ if(ixDerivMethod == analytical)then
+ ! (energy derivatives)
+ dTurbFluxCanair_dTCanair = dSenHeatTotal_dTCanair - dSenHeatCanopy_dTCanair - dSenHeatGround_dTCanair ! derivative in net canopy air space fluxes w.r.t. canopy air temperature (W m-2 K-1)
+ dTurbFluxCanair_dTCanopy = dSenHeatTotal_dTCanopy - dSenHeatCanopy_dTCanopy - dSenHeatGround_dTCanopy ! derivative in net canopy air space fluxes w.r.t. canopy temperature (W m-2 K-1)
+ dTurbFluxCanair_dTGround = dSenHeatTotal_dTGround - dSenHeatCanopy_dTGround - dSenHeatGround_dTGround ! derivative in net canopy air space fluxes w.r.t. ground temperature (W m-2 K-1)
+ dTurbFluxCanopy_dTCanair = dSenHeatCanopy_dTCanair + dLatHeatCanopyEvap_dTCanair + dLatHeatCanopyTrans_dTCanair ! derivative in net canopy turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
+ dTurbFluxCanopy_dTCanopy = dSenHeatCanopy_dTCanopy + dLatHeatCanopyEvap_dTCanopy + dLatHeatCanopyTrans_dTCanopy ! derivative in net canopy turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
+ dTurbFluxCanopy_dTGround = dSenHeatCanopy_dTGround + dLatHeatCanopyEvap_dTGround + dLatHeatCanopyTrans_dTGround ! derivative in net canopy turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
+ dTurbFluxGround_dTCanair = dSenHeatGround_dTCanair + dLatHeatGroundEvap_dTCanair ! derivative in net ground turbulent fluxes w.r.t. canopy air temperature (W m-2 K-1)
+ dTurbFluxGround_dTCanopy = dSenHeatGround_dTCanopy + dLatHeatGroundEvap_dTCanopy ! derivative in net ground turbulent fluxes w.r.t. canopy temperature (W m-2 K-1)
+ dTurbFluxGround_dTGround = dSenHeatGround_dTGround + dLatHeatGroundEvap_dTGround ! derivative in net ground turbulent fluxes w.r.t. ground temperature (W m-2 K-1)
+ ! (liquid water derivatives)
+ dLatHeatCanopyEvap_dCanWat = dLatHeatCanopyEvap_dWetFrac*dCanopyWetFraction_dWat ! derivative in latent heat of canopy evaporation w.r.t. canopy total water (W kg-1)
+ dLatHeatGroundEvap_dCanWat = latHeatSubVapGround*latentHeatConstant*groundConductanceLH*dVPCanopyAir_dCanWat ! derivative in latent heat of ground evaporation w.r.t. canopy total water (J kg-1 s-1)
+ ! (cross deriavtives)
+ dTurbFluxCanair_dCanWat = 0._rkind ! derivative in net canopy air space fluxes w.r.t. canopy total water content (J kg-1 s-1)
+ dTurbFluxCanopy_dCanWat = dLatHeatCanopyEvap_dCanWat + dLatHeatCanopyTrans_dCanWat ! derivative in net canopy turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
+ dTurbFluxGround_dCanWat = dLatHeatGroundEvap_dCanWat ! derivative in net ground turbulent fluxes w.r.t. canopy total water content (J kg-1 s-1)
+ else ! (just make sure we return something)
+ ! (energy derivatives)
+ dTurbFluxCanair_dTCanair = 0._rkind
+ dTurbFluxCanair_dTCanopy = 0._rkind
+ dTurbFluxCanair_dTGround = 0._rkind
+ dTurbFluxCanopy_dTCanair = 0._rkind
+ dTurbFluxCanopy_dTCanopy = 0._rkind
+ dTurbFluxCanopy_dTGround = 0._rkind
+ dTurbFluxGround_dTCanair = 0._rkind
+ dTurbFluxGround_dTCanopy = 0._rkind
+ dTurbFluxGround_dTGround = 0._rkind
+ ! (liquid water derivatives)
+ dLatHeatCanopyEvap_dCanWat = 0._rkind
+ dLatHeatGroundEvap_dCanWat = 0._rkind
+ ! (cross deriavtives)
+ dTurbFluxCanair_dCanWat = 0._rkind
+ dTurbFluxCanopy_dCanWat = 0._rkind
+ dTurbFluxGround_dCanWat = 0._rkind
+ end if
+
+end subroutine turbFluxes
+
+
+! *******************************************************************************************************
+! private subroutine aStability: compute stability corrections for turbulent heat fluxes (-)
+! *******************************************************************************************************
+subroutine aStability(&
+ ! input: control
+ computeDerivative, & ! input: logical flag to compute analytical derivatives
+ ixStability, & ! input: choice of stability function
+ ! input: forcing data, diagnostic and state variables
+ mHeight, & ! input: measurement height (m)
+ airTemp, & ! input: air temperature (K)
+ sfcTemp, & ! input: surface temperature (K)
+ windspd, & ! input: wind speed (m s-1)
+ ! input: stability parameters
+ critRichNumber, & ! input: critical value for the bulk Richardson number where turbulence ceases (-)
+ Louis79_bparam, & ! input: parameter in Louis (1979) stability function
+ Mahrt87_eScale, & ! input: exponential scaling factor in the Mahrt (1987) stability function
+ ! output
+ RiBulk, & ! output: bulk Richardson number (-)
+ stabilityCorrection, & ! output: stability correction for turbulent heat fluxes (-)
+ dStabilityCorrection_dRich, & ! output: derivative in stability correction w.r.t. Richardson number (-)
+ dStabilityCorrection_dAirTemp, & ! output: derivative in stability correction w.r.t. temperature (K-1)
+ dStabilityCorrection_dSfcTemp, & ! output: derivative in stability correction w.r.t. temperature (K-1)
+ err, message ) ! output: error control
+ implicit none
+ ! input: control
+ logical(lgt),intent(in) :: computeDerivative ! flag to compute the derivative
+ integer(i4b),intent(in) :: ixStability ! choice of stability function
+ ! input: forcing data, diagnostic and state variables
+ real(rkind),intent(in) :: mHeight ! measurement height (m)
+ real(rkind),intent(in) :: airtemp ! air temperature (K)
+ real(rkind),intent(in) :: sfcTemp ! surface temperature (K)
+ real(rkind),intent(in) :: windspd ! wind speed (m s-1)
+ ! input: stability parameters
+ real(rkind),intent(in) :: critRichNumber ! critical value for the bulk Richardson number where turbulence ceases (-)
+ real(rkind),intent(in) :: Louis79_bparam ! parameter in Louis (1979) stability function
+ real(rkind),intent(in) :: Mahrt87_eScale ! exponential scaling factor in the Mahrt (1987) stability function
+ ! output
+ real(rkind),intent(out) :: RiBulk ! bulk Richardson number (-)
+ real(rkind),intent(out) :: stabilityCorrection ! stability correction for turbulent heat fluxes (-)
+ real(rkind),intent(out) :: dStabilityCorrection_dRich ! derivative in stability correction w.r.t. Richardson number (-)
+ real(rkind),intent(out) :: dStabilityCorrection_dAirTemp ! derivative in stability correction w.r.t. air temperature (K-1)
+ real(rkind),intent(out) :: dStabilityCorrection_dSfcTemp ! derivative in stability correction w.r.t. surface temperature (K-1)
+ integer(i4b),intent(out) :: err ! error code
+ character(*),intent(out) :: message ! error message
+ ! local
+ real(rkind), parameter :: verySmall=1.e-10_rkind ! a very small number (avoid stability of zero)
+ real(rkind) :: dRiBulk_dAirTemp ! derivative in the bulk Richardson number w.r.t. air temperature (K-1)
+ real(rkind) :: dRiBulk_dSfcTemp ! derivative in the bulk Richardson number w.r.t. surface temperature (K-1)
+ real(rkind) :: bPrime ! scaled "b" parameter for stability calculations in Louis (1979)
+ ! -----------------------------------------------------------------------------------------------------------------------------------------
+ ! initialize error control
+ err=0; message='aStability/'
+
+ ! compute the bulk Richardson number (-)
+ call bulkRichardson(&
+ ! input
+ airTemp, & ! input: air temperature (K)
+ sfcTemp, & ! input: surface temperature (K)
+ windspd, & ! input: wind speed (m s-1)
+ mHeight, & ! input: measurement height (m)
+ computeDerivative, & ! input: flag to compute the derivative
+ ! output
+ RiBulk, & ! output: bulk Richardson number (-)
+ dRiBulk_dAirTemp, & ! output: derivative in the bulk Richardson number w.r.t. air temperature (K-1)
+ dRiBulk_dSfcTemp, & ! output: derivative in the bulk Richardson number w.r.t. surface temperature (K-1)
+ err,message) ! output: error control
+
+ ! set derivative to one if not computing it
+ if(.not.computeDerivative)then
+ dStabilityCorrection_dRich = 1._rkind
+ dStabilityCorrection_dAirTemp = 1._rkind
+ dStabilityCorrection_dSfcTemp = 1._rkind
+ end if
+
+ ! ***** process unstable cases
+ if(RiBulk<0._rkind)then
+ ! compute surface-atmosphere exchange coefficient (-)
+ stabilityCorrection = (1._rkind - 16._rkind*RiBulk)**0.5_rkind
+ ! compute derivative in surface-atmosphere exchange coefficient w.r.t. temperature (K-1)
+ if(computeDerivative)then
+ dStabilityCorrection_dRich = (-16._rkind) * 0.5_rkind*(1._rkind - 16._rkind*RiBulk)**(-0.5_rkind)
+ dStabilityCorrection_dAirTemp = dRiBulk_dAirTemp * dStabilityCorrection_dRich
+ dStabilityCorrection_dSfcTemp = dRiBulk_dSfcTemp * dStabilityCorrection_dRich
+ end if
+ return
+ end if
+
+ ! ***** process stable cases
+ select case(ixStability)
+
+ ! ("standard" stability correction, a la Anderson 1976)
+ case(standard)
! compute surface-atmosphere exchange coefficient (-)
- stabilityCorrection = (1._rkind - 16._rkind*RiBulk)**0.5_rkind
+ if(RiBulk < critRichNumber) stabilityCorrection = (1._rkind - 5._rkind*RiBulk)**2._rkind
+ if(RiBulk >= critRichNumber) stabilityCorrection = verySmall
! compute derivative in surface-atmosphere exchange coefficient w.r.t. temperature (K-1)
if(computeDerivative)then
- dStabilityCorrection_dRich = (-16._rkind) * 0.5_rkind*(1._rkind - 16._rkind*RiBulk)**(-0.5_rkind)
- dStabilityCorrection_dAirTemp = dRiBulk_dAirTemp * dStabilityCorrection_dRich
- dStabilityCorrection_dSfcTemp = dRiBulk_dSfcTemp * dStabilityCorrection_dRich
- end if
- return
- end if
-
- ! ***** process stable cases
- select case(ixStability)
-
- ! ("standard" stability correction, a la Anderson 1976)
- case(standard)
- ! compute surface-atmosphere exchange coefficient (-)
- if(RiBulk < critRichNumber) stabilityCorrection = (1._rkind - 5._rkind*RiBulk)**2._rkind
- if(RiBulk >= critRichNumber) stabilityCorrection = verySmall
- ! compute derivative in surface-atmosphere exchange coefficient w.r.t. temperature (K-1)
- if(computeDerivative)then
if(RiBulk < critRichNumber) dStabilityCorrection_dRich = (-5._rkind) * 2._rkind*(1._rkind - 5._rkind*RiBulk)
if(RiBulk >= critRichNumber) dStabilityCorrection_dRich = verySmall
- end if
-
+ end if
+
! (Louis 1979)
case(louisInversePower)
- ! scale the "b" parameter for stable conditions
- bprime = Louis79_bparam/2._rkind
- ! compute surface-atmosphere exchange coefficient (-)
- stabilityCorrection = 1._rkind / ( (1._rkind + bprime*RiBulk)**2._rkind )
- if(stabilityCorrection < epsilon(stabilityCorrection)) stabilityCorrection = epsilon(stabilityCorrection)
- ! compute derivative in surface-atmosphere exchange coefficient w.r.t. temperature (K-1)
- if(computeDerivative)then
+ ! scale the "b" parameter for stable conditions
+ bprime = Louis79_bparam/2._rkind
+ ! compute surface-atmosphere exchange coefficient (-)
+ stabilityCorrection = 1._rkind / ( (1._rkind + bprime*RiBulk)**2._rkind )
+ if(stabilityCorrection < epsilon(stabilityCorrection)) stabilityCorrection = epsilon(stabilityCorrection)
+ ! compute derivative in surface-atmosphere exchange coefficient w.r.t. temperature (K-1)
+ if(computeDerivative)then
dStabilityCorrection_dRich = bprime * (-2._rkind)*(1._rkind + bprime*RiBulk)**(-3._rkind)
- end if
-
- ! (Mahrt 1987)
- case(mahrtExponential)
- ! compute surface-atmosphere exchange coefficient (-)
- stabilityCorrection = exp(-Mahrt87_eScale * RiBulk)
- if(stabilityCorrection < epsilon(stabilityCorrection)) stabilityCorrection = epsilon(stabilityCorrection)
- ! compute derivative in surface-atmosphere exchange coefficient w.r.t. temperature (K-1)
- if(computeDerivative)then
+ end if
+
+ ! (Mahrt 1987)
+ case(mahrtExponential)
+ ! compute surface-atmosphere exchange coefficient (-)
+ stabilityCorrection = exp(-Mahrt87_eScale * RiBulk)
+ if(stabilityCorrection < epsilon(stabilityCorrection)) stabilityCorrection = epsilon(stabilityCorrection)
+ ! compute derivative in surface-atmosphere exchange coefficient w.r.t. temperature (K-1)
+ if(computeDerivative)then
dStabilityCorrection_dRich = (-Mahrt87_eScale) * exp(-Mahrt87_eScale * RiBulk)
- end if
-
- ! (return error if the stability correction method is not found)
- case default
- err=10; message=trim(message)//"optionNotFound[stability correction]"; return
-
- end select
-
- ! get the stability correction with respect to air temperature and surface temperature
- ! NOTE: air temperature is used for canopy air temperature, which is a model state variable
- if(computeDerivative)then
- dStabilityCorrection_dAirTemp = dRiBulk_dAirTemp * dStabilityCorrection_dRich
- dStabilityCorrection_dSfcTemp = dRiBulk_dSfcTemp * dStabilityCorrection_dRich
- end if
-
- end subroutine aStability
-
-
- ! *******************************************************************************************************
- ! private subroutine bulkRichardson: compute bulk Richardson number
- ! *******************************************************************************************************
- subroutine bulkRichardson(&
- ! input
- airTemp, & ! input: air temperature (K)
- sfcTemp, & ! input: surface temperature (K)
- windspd, & ! input: wind speed (m s-1)
- mHeight, & ! input: measurement height (m)
- computeDerivative, & ! input: flag to compute the derivative
- ! output
- RiBulk, & ! output: bulk Richardson number (-)
- dRiBulk_dAirTemp, & ! output: derivative in the bulk Richardson number w.r.t. air temperature (K-1)
- dRiBulk_dSfcTemp, & ! output: derivative in the bulk Richardson number w.r.t. surface temperature (K-1)
- err,message) ! output: error control
- implicit none
- ! input
- real(rkind),intent(in) :: airtemp ! air temperature (K)
- real(rkind),intent(in) :: sfcTemp ! surface temperature (K)
- real(rkind),intent(in) :: windspd ! wind speed (m s-1)
- real(rkind),intent(in) :: mHeight ! measurement height (m)
- logical(lgt),intent(in) :: computeDerivative ! flag to compute the derivative
- ! output
- real(rkind),intent(inout) :: RiBulk ! bulk Richardson number (-)
- real(rkind),intent(out) :: dRiBulk_dAirTemp ! derivative in the bulk Richardson number w.r.t. air temperature (K-1)
- real(rkind),intent(out) :: dRiBulk_dSfcTemp ! derivative in the bulk Richardson number w.r.t. surface temperature (K-1)
- integer(i4b),intent(out) :: err ! error code
- character(*),intent(out) :: message ! error message
- ! local variables
- real(rkind) :: T_grad ! gradient in temperature between the atmosphere and surface (K)
- real(rkind) :: T_mean ! mean of the atmosphere and surface temperature (K)
- real(rkind) :: RiMult ! dimensionless scaling factor (-)
- ! initialize error control
- err=0; message='bulkRichardson/'
- ! compute local variables
- T_grad = airtemp - sfcTemp
- T_mean = 0.5_rkind*(airtemp + sfcTemp)
- RiMult = (gravity*mHeight)/(windspd*windspd)
- ! compute the Richardson number
- RiBulk = (T_grad/T_mean) * RiMult
- ! compute the derivative in the Richardson number
- if(computeDerivative)then
- dRiBulk_dAirTemp = RiMult/T_mean - RiMult*T_grad/(0.5_rkind*((airtemp + sfcTemp)**2._rkind))
- dRiBulk_dSfcTemp = -RiMult/T_mean - RiMult*T_grad/(0.5_rkind*((airtemp + sfcTemp)**2._rkind))
- else
- dRiBulk_dAirTemp = 1._rkind
- dRiBulk_dSfcTemp = 1._rkind
- end if
- end subroutine bulkRichardson
-
-
- end module vegNrgFlux_module
-
\ No newline at end of file
+ end if
+
+ ! (return error if the stability correction method is not found)
+ case default
+ err=10; message=trim(message)//"optionNotFound[stability correction]"; return
+
+ end select
+
+ ! get the stability correction with respect to air temperature and surface temperature
+ ! NOTE: air temperature is used for canopy air temperature, which is a model state variable
+ if(computeDerivative)then
+ dStabilityCorrection_dAirTemp = dRiBulk_dAirTemp * dStabilityCorrection_dRich
+ dStabilityCorrection_dSfcTemp = dRiBulk_dSfcTemp * dStabilityCorrection_dRich
+ end if
+
+end subroutine aStability
+
+
+! *******************************************************************************************************
+! private subroutine bulkRichardson: compute bulk Richardson number
+! *******************************************************************************************************
+subroutine bulkRichardson(&
+ ! input
+ airTemp, & ! input: air temperature (K)
+ sfcTemp, & ! input: surface temperature (K)
+ windspd, & ! input: wind speed (m s-1)
+ mHeight, & ! input: measurement height (m)
+ computeDerivative, & ! input: flag to compute the derivative
+ ! output
+ RiBulk, & ! output: bulk Richardson number (-)
+ dRiBulk_dAirTemp, & ! output: derivative in the bulk Richardson number w.r.t. air temperature (K-1)
+ dRiBulk_dSfcTemp, & ! output: derivative in the bulk Richardson number w.r.t. surface temperature (K-1)
+ err,message) ! output: error control
+implicit none
+! input
+real(rkind),intent(in) :: airtemp ! air temperature (K)
+real(rkind),intent(in) :: sfcTemp ! surface temperature (K)
+real(rkind),intent(in) :: windspd ! wind speed (m s-1)
+real(rkind),intent(in) :: mHeight ! measurement height (m)
+logical(lgt),intent(in) :: computeDerivative ! flag to compute the derivative
+! output
+real(rkind),intent(inout) :: RiBulk ! bulk Richardson number (-)
+real(rkind),intent(out) :: dRiBulk_dAirTemp ! derivative in the bulk Richardson number w.r.t. air temperature (K-1)
+real(rkind),intent(out) :: dRiBulk_dSfcTemp ! derivative in the bulk Richardson number w.r.t. surface temperature (K-1)
+integer(i4b),intent(out) :: err ! error code
+character(*),intent(out) :: message ! error message
+! local variables
+real(rkind) :: T_grad ! gradient in temperature between the atmosphere and surface (K)
+real(rkind) :: T_mean ! mean of the atmosphere and surface temperature (K)
+real(rkind) :: RiMult ! dimensionless scaling factor (-)
+ ! initialize error control
+ err=0; message='bulkRichardson/'
+ ! compute local variables
+ T_grad = airtemp - sfcTemp
+ T_mean = 0.5_rkind*(airtemp + sfcTemp)
+ RiMult = (gravity*mHeight)/(windspd*windspd)
+ ! compute the Richardson number
+ RiBulk = (T_grad/T_mean) * RiMult
+ ! compute the derivative in the Richardson number
+ if(computeDerivative)then
+ dRiBulk_dAirTemp = RiMult/T_mean - RiMult*T_grad/(0.5_rkind*((airtemp + sfcTemp)**2._rkind))
+ dRiBulk_dSfcTemp = -RiMult/T_mean - RiMult*T_grad/(0.5_rkind*((airtemp + sfcTemp)**2._rkind))
+ else
+ dRiBulk_dAirTemp = 1._rkind
+ dRiBulk_dSfcTemp = 1._rkind
+ end if
+end subroutine bulkRichardson
+
+
+end module vegNrgFlux_module