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canopy.cpp
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canopy.cpp
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//copied from Canopy.f90
//6.6.13
#include "uebpgdecls.h"
//*******************************************************************************************************************
//* CANOPY RADIATION TRANSMISSION PROCESSES
//*******************************************************************************************************************
//
// Copyright (C) 2012 David Tarboton, Utah State University, [email protected]. http://www.engineering.usu.edu/dtarb
//
// This file is part of UEB.
//
// UEB is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// UEB is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// A copy of the GNU General Public License is included in the file gpl.txt.
// This is also available at: http://www.gnu.org/licenses/.
//
// if you wish to use or incorporate this program (or parts of it) into
// other software that does not meet the GNU General Public License
// conditions contact the author to request permission.
// David G. Tarboton
// Utah State University
// 8200 Old Main Hill
// Logan, UT 84322-8200
// USA
// http://www.engineering.usu.edu/dtarb/
// email: [email protected]
//
//********** PARTITION OF INCOMING SOLAR RADIATION INTO DIRECT AND DIFFUSE BEFORE IT HITS THE CANOPY *************
// Partition the incoming solar radiation into direct and diffuse components
void PSOLRAD( float Qsi, float atff, float *param, float cf,
float &Taufb, float &Taufd, float &Qsib, float &Qsid) // Output variables:
{
float Taufc, as,bs,Lambda;
as = param[27]; // Fraction of extraterrestaial radiation on cloudy day,Shuttleworth (1993)
bs = param[28]; // (as+bs):Fraction of extraterrestaial radiation on clear day, Shuttleworth (1993)
Lambda = param[29]; // Ratio of diffuse atm radiation to direct for cler sky,from Dingman (1993)
Taufc = findMax (atff, as+bs); // Mac atmosphereci transmittance for clear sky
if (cf == 0)
{
Taufb = Lambda*Taufc; // Direct solar radiation atm.transmittance
Taufd = (1.0 - Lambda)*Taufc; // Diffuse solar radiation atm.transmittance
}
else if (cf == 1)
{
Taufb = 0.0;
Taufd = atff;
}
else
{
Taufb = Lambda*(1.0 - cf)*(as+bs);
Taufd = atff- Taufb;
}
// Direct canopy solar radiation incident at the canopy
Qsib = Taufb*Qsi/(Taufb+Taufd);
// Diffuse canopy solar radiation incident at the canopy
Qsid = Taufd*Qsi/(Taufb+Taufd);
return;
}
//*********** TRANSMISSION OF DIRECT AND DIFFUSE SOLAR RADIATION THROUGH THE CANOPY ***************
// Estimates the direct and diffuse solar radiation fractions transmitted through the canopy
void TRANSRADCAN (float COSZEN, float *sitev, float *param,
float &Betab, float &Betad, float &Taub, float &Taud) // Output variables: Transmission and Reflection fractions
{
float EXPI, kk, Taubh,Taudh, Beta,Rho;
float Cc = sitev[4], // Leaf Area Index
Hcan = sitev[5], // Canopy height
LAI = sitev[6], // Leaf Area Index
alpha = param[23], //
G = param[25]; //
// For open area where no vegetaion canopy is present
if (LAI == 0 )
{
Taub = 1.0;
Taud = 1.0;
Betab = 0.0;
Betad = 0.0;
}
else
{
// Transmission without scattering
LAI = Cc*LAI; // Effective leaf area index
Rho = LAI/Hcan; // leaf density per unit height of the canopy
// Multiple scattering light penetration
kk = sqrt(1 - alpha); // k-prime in the paper
EXPI = EXPINT(kk*G*LAI); // Exponential integral function
// Deep Canopy Solution
// Avoid divide by 0 error when COSZEN is 0
if(COSZEN <= 0)
Taubh=0.0;
else
Taubh = exp(-1*kk*G*Rho*Hcan/COSZEN); // Transmission function for deep canopy : Direct
Taudh = (1 - kk*G*Rho*Hcan) * exp(-1*kk*G*Rho*Hcan) + pow((kk*G*Rho*Hcan),2)*EXPI; // Transmission function for deep canopy : Diffuse
Beta = (1-kk)/(1+kk); // BetaPrime : reflection coefficient for infinitely deep canopy
// Finite Canopy Solution
Taub = Taubh*(1 - pow(Beta,2)) / (1 - pow(Beta,2)*pow(Taubh,2)); // Direct fraction of radiation transmitted down through the canopy
Taud = Taudh*(1-pow(Beta,2))/(1-pow(Beta,2)*pow(Taudh,2)); // Diffuse fraction of radiation transmitted down through the canopy
Betab = Beta*(1-pow(Taubh,2)) /(1-pow(Beta,2)*pow(Taubh,2)); // Direct fraction of radiation scattered up from the canopy
Betad = Beta*(1-pow(Taudh,2)) /(1-pow(Beta,2)*pow(Taudh,2)); // Diffuse fraction of radiation scattered up from the canopy
}
return;
}
//****************** NET CANOPY & SUB CANOPY SOLAR RADIATION *********************************
// Computes the net canopy and sub-canopy solar radiation
// considering the multiple scatterings of radiation by the canopy and multile reflections
// between the canopy and the snow surface
void NETSOLRAD(float Ta,float A,float Betab,float Betad,float Wc,float Taub,float Taud,
float Qsib,float Qsid,float *param, float Fs,float &Qsns,float &Qsnc) // Output: Qsns,Qsnc (Net subcanopy, canopy solar radiation)
{
float f1b, f2b, f3b, f1d, f2d, f3d;
// Net radiation at snow surface below canopy
f1b = (1-A)*Taub/(1-Betad*(1-Taud)*A) ;
f1d = (1-A)*Taud/(1-Betad*(1-Taud)*A);
Qsns = f1b*Qsib + f1d*Qsid;
if (Taub == 1) // (For LAI=0, Qsnc gives the numerical errors, so)
Qsnc = 0.0;
else
{
// Net canopy solar radiation
f3b = ((1-A)*Betab + A*Taub*Taud)/(1-Betad*(1-Taud)*A);
f3d = ((1-A)*Betad + A*Taud*Taud)/(1-Betad*(1-Taud)*A);
f2b = 1- f1b-f3b;
f2d = 1- f1d-f3d;
Qsnc = f2b*Qsib + f2d*Qsid;
}
return;
}
//****************** NET CANOPY & SUB CANOPY LONGWAVE RADIATION ******************************
// Computes the net canopy and beneath canopy longwave radiation
void NETLONGRAD(float RH,float Ta,float Tss,float Tc,float Tk,float Fs,float EmC,float EmS,float SBC,float cf,float *sitev,float Qli,float *param,
float &Qlis, float &Qlns,float &Qlnc ) // Output: Qsns,Qsnc
{
float EXPI, kk, Beta, Betad, Tak, Tssk, EmCS, Tck, Qle, Qlcd, Qlcu, Rho, Taudh, Taud;
float Cc = sitev[4], // Leaf Area Index
Hcan = sitev[5], // Canopy height
LAI = sitev[6], // Leaf Area Index
alphaL= param[24],
G = param[25];
// ea = SVPW(TA)*RH // Air vapor pressure
Tak = Ta + Tk;
Tssk = Tss +Tk;
EmCS = EmC*(1-Fs)+EmS*Fs;
Tck = Tc+Tk;
Qle = EmS*SBC*pow(Tssk,4);
if (LAI == 0) // For Open area where no vegetation caonpy is present
{
Qlcd = 0.0;
Qlcu = 0.0;
Qlns = Qli*EmS -Qle; // To avoid numerical errors
Qlnc = 0.0;
}
else
{
// Transmission without scattering
LAI = Cc*LAI;
Rho = LAI/Hcan;
// Downward scattered
kk = sqrt(1-alphaL);
// Upward scattered
Beta = (1-kk)/(1+kk);
EXPI = EXPINT(kk*G*LAI);
// Deep canopy solution
Taudh = (1-kk*G*Rho*Hcan)*exp(-kk*G*Rho*Hcan)+ pow((kk*G*Rho*Hcan),2)*EXPI; // Transmission function for deep canopy : Diffuse
// Finite canopy solution
Taud = (Taudh-pow(Beta,2)*Taudh) /(1-pow(Beta,2)*pow(Taudh,2)); // Transmission function for finite canopy depth
Betad = (Beta-Taudh*Beta*Taudh) /(1-pow(Beta,2)*pow(Taudh,2)); // Scatterd up from top of the canopy at 0 depth
// Canopy emitted longwave radiation
Qlcd = (1-Taud)*EmC*SBC*pow(Tck,4);
Qlcu = (1-Taud)*EmCS*SBC*pow(Tck,4);
// Net sub canopy longwave radiation
Qlns = Taud*Qli*EmS + EmS*Qlcd-Qle + (1.0-Taud)*(1.0 - 1.0)*Qle; //*****#$%^^%#_ Term on the right 1-1=0? 6.6.13
// Net canopy longwave radiation
Qlnc = (((1-Taud)*1)+((1-EmS)*Taud*1)) * Qli + (1-Taud)*Qle*1 // Putting 1 for Emc
+ (1-Taud)*(1-EmS)*1*Qlcu - Qlcu - Qlcd;
if(snowdgtvariteflag2 == 1)
{
cout<<"Outputs from NetLongRad"<<endl;
cout<<setprecision(15)<<Taud<<" "<< Taudh<<" "<<Betad<<" "<<Qlcd<<" "<<Qlcu<<" ";
cout<<setprecision(15)<<Qli<<" "<<Qle<<" "<<Qlns<<" "<<Qlnc<<endl;
}
}
return;
}
//********************************************************************************************************************
//* TURBULENT TRANSFER PROCESSES
//********************************************************************************************************************
//**************** BULK AERODYNAMIC AND CANOPY BOUNDARY LAYER RESISTANCES *******************
// Calculates resistances for the above and beneath canopy turbulent heat fluxes
void AeroRes(float P, float Wc, float V, float Ta, float Tss, float Tc, float Fs, float *param, float *sitev, float Tk,
float &d, float &Z0c, float &Vz, float &Rc, float &Ra, float &Rbc, float &Rl, float &RKINc, float &RKINa, float &RKINbc, float &RKINl) // Output variables
{
float Zm, Kh, Lbmean, Rs, Ri , ndecay, Dc, Rastar, Rbcstar, Rcstar;
float Vstar, Vh, Vc;
float z = param[4], // Nominal meas. height for air temp. and humidity [2m],
zo = param[5], // Surface aerodynamic roughness [m],
Rimax = param[30], // Maximum value of Richardsion number for stability corretion
fstab = param[18], // Stability correction control parameter 0 = no corrections, 1 = full corrections
Wcoeff= param[31], //
Cc = sitev[4], // Canopy Cover
Hcan = sitev[5], // Canopy height
LAI = sitev[6]; // Leaf Area Index
Zm = Hcan + z; // observed wind speed above the canopy
LAI = Cc*LAI;
if(V <= 0)
{
Ra = 0.0;
Rc = 0.0;
Rs = 0.0;
Rbc = 0.0;
Rl = 0.0;
RKINc = 0.0;
RKINa = 0.0;
RKINbc = 0.0;
RKINl = 0.0;
Vz = V;
// if no wind, all resistances are zero; giving fluxes zero
}
else
{
if(LAI == 0) // For open area
{
Vz = V;
Rbc = (1.0/(pow(K_vc,2)*Vz)*pow((log(z/zo)),2.0) )*1/Hs_f; // sub layer snow resistance; Hs_f: to convert resistance second to hour
Ri = Gra_v*(Ta-Tss)*z /(pow(Vz,2.0)*(0.5*(Ta+Tss)+273.15));
if (Ri > Rimax)
Ri= Rimax;
if (Ri > 0)
Rbcstar = Rbc/pow((1-5*Ri),2); // Bulk
else
Rbcstar = Rbc/(pow((1-5*Ri),0.75));
RKINbc = 1.0/Rbcstar; // Bulk conductance
}
else
{
WINDTRANab(V, Zm, param, sitev, Vstar, Vh, d, Z0c, Vz, Vc); // Output wind speed within canopy at height 2 m
// Aerodynamic Resistances for Canopy
ndecay = Wcoeff*LAI; //(Wcoeff=0.5 for TWDEF, 0.6 for Niwot) // wind speed decay coefficient inside canopy
Kh = pow(K_vc,2.0)*V*(Hcan-d)/(log((Zm-d)/Z0c));
// Above canopy aerodynamic resistance
Ra = (1.0* 1.0/(pow(K_vc,2.0)*V)*log((Zm-d)/(Z0c))*log((Zm-d) /(Hcan-d))
+ Hcan/(Kh*ndecay) * (exp(ndecay-ndecay*(d+Z0c)/Hcan)-1.0) )*1/Hs_f; // Increased ten times (Calder 1990, Lundberg and Halldin 1994)
// Below canopy aerodynamic resistance
Rc =(Hcan*exp(ndecay)/(Kh*ndecay)*(exp(-ndecay*z/Hcan)-exp(-ndecay*(d+Z0c)/Hcan))) *1/Hs_f;
Rs = (1.0/(pow(K_vc,2)*Vz)*pow((log(z/zo)),2.0))*1/Hs_f;
Rc = Rc+ Rs; // Total below canopy resistance
// Bulk aerodynamic resistance (used when there is no snow in the canopy)
Rbc = Rc+Ra; // Total aerodynamic resistance from ground to above canopy used when there is no snow on canopy
// Boundary layer resistance of canopy(Rl)
Dc = .04; // Deckinson et.al (1986);Bonan(1991): Characterstics dimension (m) of leaves (average width) // put in parameters later
Lbmean = 0.02/ndecay *sqrt(Vc/Dc)* (1-exp(-ndecay/2));
Rl = 1/(LAI*Lbmean)*1/Hs_f;
// Leaf boundary layer conductance: reciprocal of resistance
RKINl = 1.0/Rl;
// Correction for Ra, Rc and Rac for stable and unstable condition
Ri = Gra_v*(Ta-Tss)*z /(pow(Vz,2.0)*(0.5*(Ta+Tss)+273.15)); // wind speed unit should not be changed.
if (Ri > Rimax)
Ri= Rimax;
if (Ri > 0)
{
Rastar = Ra; ///((1-5*Ri)**2) // Above canopy
Rcstar = Rc /(pow((1-5*Ri),2)); // Below canpy
Rbcstar = Rbc; // /((1-5*Ri)**2) // Bulk
} // Rlstar = Rl/((1-5*Ri)**2) // leaf boundary layer
else
{
Rastar = Ra; ///(1-5*Ri)**0.75
Rcstar = Rc /pow((1-5*Ri),0.75);
Rbcstar = Rbc; // /(1-5*Ri)**0.75
} // Rlstar = Rl/(1-5*Ri)**0.75
// Turbulent (heat and vapor) transfer coefficient (Conductance) //
RKINa = 1.0/Rastar; // Above canopy
RKINc = 1.0/Rcstar; // Below canpy
RKINbc = 1.0/Rbcstar; // Bulk
// RKINl = 1.0/Rlstar // leaf boundary layer
}
if(snowdgtvariteflag2 == 1)
{
cout<<"In aeroRes"<<endl;
cout<<std::setprecision(15)<<ndecay<<" "<<Kh<<" "<<Ra<<" "<<Rc<<" "<<Rs<<" "<<Rbc<<" "<<Lbmean<<" "<< Rl<<" "<< RKINc<<" "<< RKINa<<" "<< RKINbc<<" "<< RKINl<<endl;
}
}
return;
}
//********************* WIND PROFILES ****************************************************************
// Calculates wind at the 2 m above the surface and at the sink using the input of measured wind at 2 m above the canopy
void WINDTRANab(float V, float Zm, float *param, float *sitev,float &Vstar,float &Vh,float &d,float &Z0c,float &Vz,float &Vc) // Out put wind speed within canopy at height 2 m
{
float Z = param[4], // Nominal meas. height for air temp. and humidity [2m],
Wcoeff= param[31], //
Cc = sitev[4], // Canopy Cover
Hcan = sitev[5], // Canopy height
LAI = sitev[6], // Leaf Area Index
Ycage = sitev[8]; // Parameters for wind speed transformation
LAI = Cc*LAI;
// Roughness length (z0c) and zero plane displacement(d) for canopy [Periera, 1982]
if(V <= 0)
{
Vz= 0.0;
Vc= 0.0;
}
else
{
d = Hcan*(0.05 + (pow(LAI,0.20))/2 + (Ycage-1)/20);
if (LAI < 1)
Z0c= 0.1*Hcan;
else
Z0c = Hcan*(0.23 - (pow(LAI,0.25))/10 - (Ycage-1)/67);
Vstar = K_vc*V/log((Zm-d)/Z0c); //Friction velocity
// Wind speed at height,Z from the ground/snow surface below canopy (Exponential profile from canopy height to below canopy)
Vh = 1.0/K_vc*Vstar*log((Hcan-d)/Z0c); //Wind speed at the height of canopy (Logarithmic profile above canopy to canopy)
Vz = 1.0* Vh*exp(-Wcoeff*LAI*(1-Z/Hcan));
Vc = 1.0* Vh*exp(-Wcoeff*LAI*(1-(d+Z0c)/Hcan)); //To estimate canopy boundary layer conductance
// Vc = 1.0* Vh*exp(-Wcoeff*LAI*(1-6./Hcan)**Beta)
}
return;
}
//************************ TURBULENT FLUXES (ABOVE AND BELOW THE CANOPY *******************************
// Calculates the turbulent heat fluxes (sensible and latent heat fluxes) and condensation/sublimation.
void TURBFLUX (float Ws, float Wc, float A, float Tk,float Tc,float Ta,float Tss, float RH, float V,float Ea,float P,float *param,float *sitev,
float &d, float &Z0c, float &Vz, float &Rkinc, float &Rkinbc, float &Tac, float &Fs, float &Ess, float &Esc, // Output variables
float &QHc, float &QEc, float &Ec, float &QHs, float &QEs, float &Es, float &QH, float &QE, float &E )
{
float RHOA, Eac, Tak, Tck;
float Rc, Ra, Rbc, Rl, Rkina, Rkinl, Eak, Tack, RHOAc;
float radFracdenom;
float z = param[4], // Nominal meas. height for air temp. and humidity [2m],
zo = param[5], // Surface aerodynamic roughness [m],
fstab = param[18], // Stability correction control parameter 0 = no corrections, 1 = full corrections
Apr = sitev[1], // Atmospheric Pressure [Pa],
Cc = sitev[4], // Canopy Coverage
LAI = sitev[6]; // Leaf Area Index
Tak = Ta + Tk;
Tck = Tc + Tk;
RHOA = Apr/(Ra_g*Tak); // RHOA in kg/m3, APr: Atm Press
Ea = svpw(Ta) * RH; // Actual vapor pressure sorrounding canopy
if(snowdgtvariteflag2 == 1)
{
cout<<std::setprecision(15)<<Ea<<endl;
}
// Wind less coefficient:
float EHoA = 0.0, // for sensibleheat flux
EHoC = 0.0,
EHoS = 0.0,
EEoA = 0.0, // for latent heat flux
EEoC = 0.0,
EEoS = 0.0;
AeroRes (P, Wc,V, Ta, Tss, Tc, Fs, param, sitev,Tk,
d, Z0c, Vz, Rc, Ra, Rbc, Rl, Rkinc, Rkina, Rkinbc, Rkinl); // Output variables
if(snowdgtvariteflag2 == 1)
{
cout<<"Outputs from aeroRes"<<endl;
cout<<std::setprecision(15)<<d<<" "<< Z0c<<" "<< Vz<<" "<< Rc<<" "<< Ra<<" "<< Rbc<<" "<< Rl<<" "<< Rkinc<<" "<< Rkina<<" "<< Rkinbc<<" "<< Rkinl<<endl;
}
if(snowdgtvariteflag2 == 1)
cout<<"LAI: "<<LAI<<endl;
if (V <= 0)
{
QHc = 0.0;
QEc = 0.0;
Ec = 0.0;
QHs = 0.0;
QEs = 0.0;
Es = 0.0;
Tac = Ta; // Though We don't need Tac when V=0.
}
else
{
if (LAI == 0)
{
// Flux estimation from the open areas when no vanopy is present
QHs = (RHOA* C_p * Rkinbc + EHoS) * (Ta-Tss); // 0.0 added for zero wind condition
QEs = (0.622 * Hne_u/(Ra_g* Tak) * Rkinbc + EEoS) * (Ea - Ess);
Es = -QEs/(Rho_w * Hne_u); // Es in m/hr
QHc = 0.0;
QEc = 0.0;
Ec = 0.0;
if(snowdgtvariteflag2 == 1)
cout<<std::setprecision(15)<<"QHs,QEs,Es,QHc,QEc,Ec"<<" "<<QHs<<" "<<QEs<<" "<<Es<<" "<<QHc<<" "<<QEc<<" "<<Ec<<endl;
}
else
{
radFracdenom = 1*Rkina + 1*Rkinl + 1*Rkinc;
//###### 9.21.13 to avoid div by 0 when Rkina + 1*Rkinl + 1*Rkinc evaluate to zero 0.01 added
//TBC_9.21.13
if (radFracdenom == 0)
{
radFracdenom += 0.01;
cout<<"Warning! a zero denominator! the sum of turbulent conductances Rkina + 1*Rkinl + 1*Rkinc evaluates to zero"<<endl;
cout<<"added 0.01 to avoid numerical error; Need checking results"<<endl;
//getchar();
}
Tac = (Tc*Rkinl + Tss*Rkinc + Ta*Rkina) / radFracdenom; //(1*Rkina + 1*Rkinl + 1*Rkinc);
Eac = (Esc*Rkinl + Ess*Rkinc + Ea*Rkina) / radFracdenom; //(1*Rkina + 1*Rkinl + 1*Rkinc);
Tack = Tac + Tk;
//###### 9.22.13 observed Tac values close to -273 which may lead to Tack = 0
//TBC_9.22.13
if (Tack == 0)
{
Tack += 1.0;
cout<<"Error! Surface temp in function Turbflux() Tack = 0"<<endl;
cout<<"added 1 to avoid numerical error; Need checking results"<<endl;
//getchar();
}
RHOAc = Apr/(Ra_g* Tack);
// Flux from canopy
QHc = (RHOAc* C_p *Rkinl + EHoC)*(Tac - Tc);
if(snowdgtvariteflag2 == 1)
cout<<std::setprecision(15)<<"Tc, Tac,Eac,Tack: "<<Tc<<" "<<Tac<<" "<<Eac<<" "<<Tack<<endl;
if ((Wc == 0) && (P == 0))
{
QEc = 0.0; // No latent heat flux when there is no snow in the caanopy
Ec = 0.0;
}
else
{
QEc = (0.622*Hne_u/(Ra_g*Tack)*Rkinl + EEoC)*(Eac-Esc)*Fs;
Ec = -QEc/(Rho_w*Hne_u);
}
// Flux from snow at ground
QHs =(RHOAc*C_p*Rkinc + EHoS)* (Tac-Tss); // EHoS added for zero wind condition [Jordan et al.(1999); Koivusalo (2002); Herrero et al.(2009) ]
QEs =(0.622*Hne_u/(Ra_g*Tack)*Rkinc+ EEoS)*(Eac-Ess);
Es = -QEs/(Rho_w*Hne_u);
if(snowdgtvariteflag2 == 1)
cout<<std::setprecision(15)<<"QHs,QEs,Es,QHc,QEc,Ec"<<" "<<QHs<<" "<<QEs<<" "<<Es<<" "<<QHc<<" "<<QEc<<" "<<Ec<<endl;
}
// Total flux *** moved back 6.25.13
QH = QHs + QHc;
QE = QEs + QEc;
E = Es + Ec;
}
// Total flux*******moved here 6.6.13=> moved back up 6.25.13
/*QH = QHs + QHc;
QE = QEs + QEc;
E = Es + Ec; */
return;
}
//************************** RATE OF INTERCEPTION AND MAX INTERCEPTION ***********************
// Calculates amount of snow intercepted by the canopy
void INTERCEPT (float Ta, float LAI,float P, float Wc, float dt, float Inmax, float Uc, float Cc,
// Output variables
float &ieff, float &Ur, float &intc)
{
float Intma;
//Uc and Cc directly called instead of the param/sitev arrays 6.6.13
//Uc = param(27) // Unloading rate coefficient (Per hour) (Hedstrom and pomeroy, 1998)
//Cc = sitev(5) // Canopy Coverage
if (LAI == 0)
Cc = 0.0;
// Interception rate (di/dt)
if (P == 0)
{
intc = 0.0;
ieff = 0.0;
}
else
{
Intma = 0.0;
if (Wc < Inmax)
{
intc = Cc*(1.0 - Wc *Cc/(Inmax)) * P;
ieff = Cc*(1.0 - Wc* Cc/(Inmax)); // Interception efficiency (di/dp)
Intma = Inmax - Wc;
if (intc >= Intma)
intc = Intma;
}
else
{
intc = 0.0;
ieff = 0.0;
}
}
// Unloading rate
Ur = Uc * (Wc + (intc*dt)/2); // Melt and Evap. are subtracted
// half of the current interception is also considered for unloading
return;
}
//****************************** ENERGY ADVECTED BY RAIN **********************************
// Calculates the heat advected to the snowpack due to rain
float QPF(float PR, float TA, float TO, float PS, float RHOW, float HF, float CW, float CS)
{
float TRAIN, TSNOW, QPF_v;
if(TA > TO)
{
TRAIN = TA;
TSNOW = TO;
}// TO : Freezing Temp (int.e.0C)
else
{
TRAIN = TO;
TSNOW = TA;
}
QPF_v = PR * RHOW *(HF + CW *(TRAIN-TO)) + PS*RHOW*CS*(TSNOW-TO);
return QPF_v;
}
//****************************** PREHELP () ***************************************************
// Routine to correct energy and mass fluxes when
// numerical overshoots dictate that W was changed in
// the calling routine - either because W went negative
// or due to the liquid fraction being held constant.
void PREHELP( float W1,float W,float DT,float &FM,float FM1,float fac,float PS,float PRAIN,float &E,float RHOW,float HF,float &Q,float &QM,float &MR, float &QE, float HSF)
{
float QOTHER;
FM = (W1-W)/DT*fac-FM1;
MR = findMax( 0.0 , (PS + PRAIN - FM - E));
E = PS + PRAIN - FM - MR;
// Because melt rate changes the advected energy also changes. Here
// advected and melt energy are separated,
QOTHER = Q + QM - QE;
// then the part due to melt recalculated
QM = MR*RHOW*HF;
// then the part due to evaporation recalculated
QE = -E*RHOW*HSF;
// Energy recombined
Q = QOTHER - QM + QE;
return;
}
//****************** EXPONENTIAL INTEGRAL FUNCTION *****************************************
// Computes the exponential integral function for the given value
float EXPINT (float LAI)
{
float a0,a1,a2,a3,a4,a5,b1,b2,b3,b4, EXPINT_v;
if(LAI == 0 )
EXPINT_v = 1.0;
else if(LAI <= 1)
{
a0= -0.57721566;
a1= 0.99999193;
a2= -0.24991055;
a3= 0.05519968;
a4= -0.00976004;
a5= 0.00107857;
EXPINT_v = a0 + a1*LAI + a2*pow(LAI,2) + a3*pow(LAI,3) + a4*pow(LAI,4) + a5*pow(LAI,5) - log(LAI);
}
else
{
a1= 8.5733287401;
a2= 18.0590169730;
a3= 8.6347637343;
a4= 0.2677737343;
b1= 9.5733223454;
b2= 25.6329561486;
b3= 21.0996530827;
b4= 3.9584969228;
EXPINT_v = (pow(LAI,4) + a1*pow(LAI,3) + a2*pow(LAI,2) + a3*LAI + a4)/
((pow(LAI,4) + b1*pow(LAI,3) + b2*pow(LAI,2) + b3*LAI + b4)*LAI*exp(LAI));
}
return EXPINT_v;
}
// Reference Book:Handbook of mathematical functions with Formulas, Graphs, and Mathematical Tables
// Edited by Milton Abramowitz and Irene A. Stegun, Volume 55, Issue 1972, page no. 231
// Dover Publications, Inc, Mineola, New York.
//*************************** SVP () ***********************************************************
// Calculates the vapour pressure at a specified temperature over water or ice
// depending upon temperature. Temperature is celsius here.
float svp(float T)
{
float SVPv;
if(T >= 0)
SVPv = svpw(T);
else
SVPv = svpi(T);
return SVPv;
}
//*************************** SVPW () **********************************************************
// Calculates the vapour pressure at a specified temperature over water
// using polynomial from Lowe (1977).
float svpw(float T)
{
float SVPWv;
SVPWv = 6.107799961 + T * (0.4436518521 + T * (0.01428945805 +
T * (0.0002650648471 + T * (3.031240936*pow(10,-6) +
T * (2.034080948*pow(10,-8) + T * 6.136820929*pow(10,-11))))));
SVPWv = 100*SVPWv; // convert from mb to Pa
return SVPWv;
}
//*************************** SVPI () *********************************************************
// Calculates the vapour pressure at a specified temperature over ice.
// using polynomial from Lowe (1977).
float svpi(float T)
{
float SVPIv;
SVPIv = 6.109177956 + T * (0.503469897 + T * (0.01886013408 +
T * (0.0004176223716 + T * (5.82472028*pow(10,-6) +
T * (4.838803174*pow(10,-8) + T * 1.838826904*pow(10,-10))))));
SVPIv = SVPIv * 100; // convert from mb to Pa
return SVPIv;
}
//**********************************************************************************************
// Estimates reflection and scattering coefficient
float Tau1(float Rho, float G, float h, float COSZEN, float kk)
{
float Tau1v;
if(h == 0)
Tau1v =1.0; // To avoid computational error when coszen =0
else if (COSZEN == 0)
Tau1v = 0;
else Tau1v = exp(- kk*G*Rho*h/COSZEN);
return Tau1v;
}
//************************************************************************************************
float Tau2(float Rho, float G, float h, float kk, float EXPI)
{
float tau2v = (1-kk*G*Rho*h)*exp(-kk*G*Rho*h) + pow((kk*G*Rho*h), 2)*EXPI; // is the penetration function for deep canopy: diffuse
return tau2v;
}
//************************************************************************************************