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f.c
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/*******************************************************************************
*-----------------------------------------------------------------------------*
* File : f.c (PIHM v.2.0) *
* Function : Model Kernel: Building ODE system for each physical process *
*-----------------------------------------------------------------------------*
* *
*-----------------------------------------------------------------------------*
* Developer of PIHM v.2.0: Mukesh Kumar ([email protected]) *
* Developer of PIHM v.1.0: Yizhong Qu ([email protected]) *
*-----------------------------------------------------------------------------*
* *
*-----------------------------------------------------------------------------*
* NOTE: f.c has gone a massive revamp (essentially rewritten) since PIHM v.1.0*
* *
*...........MODFICATIONS/ADDITIONS incorporated in f.c (PIHM v.2.0)...........*
* a) Surface Flow: *
* --> Correction of diffusion wave approximation (calculation of dh/ds) *
* i. Calculation of dh/ds performed using planar slope connecting*
* neighboring centroids *
* ii.Reflection of elements at boundaries and rivers for dh/ds *
* calculation
* --> Correction of kinematic wave approximation (dh/ds calculation based*
* on elevation only instead of head *
* --> Correction of gradient for cases with steep change in topography *
* b) Subsurface Flow: *
* --> Addition of macropore phenomena *
* --> Addition of rectangular cell beneath a river element *
* --> Implementation of two layered subsurface model(sat/unsat) based on *
* Richard's eqn *
* --> Incorporation of Vertical and Horizontal Anisotropy *
* --> Use of geologic data *
* c) River Flow: *
* --> Correction of kinematic and diff. wave approximation of SV eqn *
* --> Incorporation of flexible river shapes *
* --> Separate incorporation of leakage and lateral flow *
* --> Correction of bank overland flow for extreme cases *
* --> Addition of aquifer cells below river elements *
* c) Surface/Subsurface Coupling: *
* --> Implementation of First order coupling through (in/ex)filtration *
* based on head continuity *
* d) Evaporation: *
* --> Incorporation of ET from ground/subsurface/vegetation *
* --> Incorporation of landcover properties for calculation of each ET *
* component *
* e) Computational: *
* --> Use of temporary state variables in calculation. Note: Never change*
* core state variables *
* f) Miscellaneous (other advantages realtive to PIHM1.0): No maximum *
* constraint on gw level. Accordingly, no numerical constraints on subsur- *
* face flux terms.Faster Implementation. Led to first large scale model *
* application.
*-----------------------------------------------------------------------------*
* *
*-----------------------------------------------------------------------------*
* For questions or comments, please contact *
* --> Mukesh Kumar ([email protected]) *
* --> Prof. Chris Duffy ([email protected]) *
* This code is free for research purpose only. *
* Please provide relevant references if you use this code in your research work*
*-----------------------------------------------------------------------------*
* *
* REFERENCES: *
* PIHM2.0: *
* a) Kumar, M., 2008, "Development and Implementation of a Multiscale, *
* Multiprocess Hydrologic Model". PhD Thesis, Penn State University *
* b) Kumar, M, G.Bhatt & C.Duffy, "Coupling of Data and Processes in *
* a Mesoscale Watershed", Advances in Water Resources (submitted) *
* PIHM1.0: *
* a) Qu, Y., 2005, "An Integrated hydrologic model for multiproces *
* simulation using semi-discrete finite volume approach".PhD Thesis, PSU *
* b) Qu, Y. & C. Duffy, 2007, "A semidiscrete finite volume formulation *
* for multiprocess watershed simulation". Water Resources Research *
*******************************************************************************/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#include "nvector_serial.h"
#include "sundialstypes.h"
#include "pihm.h"
#define multF 2
#define MINpsi -70
#define EPS 0.05
#define THRESH 0.0
#define UNIT_C 1440 /* Note 60*24 for calculation of yDot in m/min units while forcing is in m/day. */
#define GRAV 9.8*60*60 /* Note the dependence on physical units */
realtype Interpolation(TSD *Data, realtype t);
realtype returnVal(realtype rArea, realtype rPerem, realtype eqWid,realtype ap_Bool)
{
if(ap_Bool==1)
{
return rArea;
}
else if(ap_Bool==2)
{
return rPerem;
}
else
{
return eqWid;
}
}
realtype CS_AreaOrPerem(int rivOrder, realtype rivDepth, realtype rivCoeff, realtype a_pBool)
{
realtype rivArea, rivPerem, eq_Wid;
switch(rivOrder)
{
case 1:
rivArea = rivDepth*rivCoeff;
rivPerem= 2.0*rivDepth+rivCoeff;
eq_Wid=rivCoeff;
return returnVal(rivArea, rivPerem, eq_Wid, a_pBool);
case 2:
rivArea = pow(rivDepth,2)/rivCoeff;
rivPerem = 2.0*rivDepth*pow(1+pow(rivCoeff,2),0.5)/rivCoeff;
eq_Wid=2.0*pow(rivDepth+EPS,1/(rivOrder-1))/pow(rivCoeff,1/(rivOrder-1));
return returnVal(rivArea, rivPerem, eq_Wid, a_pBool);
case 3:
rivArea = 4*pow(rivDepth,1.5)/(3*pow(rivCoeff,0.5));
rivPerem =(pow(rivDepth*(1+4*rivCoeff*rivDepth)/rivCoeff,0.5))+(log(2*pow(rivCoeff*rivDepth,0.5)+pow(1+4*rivCoeff*rivDepth,0.5))/(2*rivCoeff));
eq_Wid=2.0*pow(rivDepth+EPS,1/(rivOrder-1))/pow(rivCoeff,1/(rivOrder-1));
return returnVal(rivArea, rivPerem, eq_Wid, a_pBool);
case 4:
rivArea = 3*pow(rivDepth,4.0/3.0)/(2*pow(rivCoeff,1.0/3.0));
rivPerem = 2*((pow(rivDepth*(1+9*pow(rivCoeff,2.0/3.0)*rivDepth),0.5)/3)+(log(3*pow(rivCoeff,1.0/3.0)*pow(rivDepth,0.5)+pow(1+9*pow(rivCoeff,2.0/3.0)*rivDepth,0.5))/(9*pow(rivCoeff,1.0/3.0))));
eq_Wid=2.0*pow(rivDepth+EPS,1/(rivOrder-1))/pow(rivCoeff,1/(rivOrder-1));
return returnVal(rivArea, rivPerem, eq_Wid, a_pBool);
default:
printf("\n Relevant Values entered are wrong");
printf("\n Depth: %lf\tCoeff: %lf\tOrder: %d\t");
return 0;
}
}
OverlandFlow(realtype **flux, int loci, int locj, realtype avg_y, realtype grad_y, realtype avg_sf, realtype crossA, realtype avg_rough)
{
flux[loci][locj] = crossA*pow(avg_y, 2.0/3.0)*grad_y/(sqrt(fabs(avg_sf))*avg_rough);
// flux[loci][locj] = (grad_y>0?1:-1)*crossA*pow(avg_y, 2.0/3.0)*sqrt(fabs(grad_y))/(avg_rough);
}
OLFeleToriv(realtype eleYtot,realtype EleZ,realtype cwr,realtype rivZmax,realtype rivYtot,realtype **fluxriv,int loci,int locj,realtype length)
{
realtype threshEle;
if(rivZmax < EleZ)
{
threshEle = EleZ;
}
else
{
threshEle = rivZmax;
}
if (rivYtot > eleYtot)
{
if (eleYtot > threshEle)
{
fluxriv[loci][locj] = cwr*2.0*sqrt(2*GRAV*UNIT_C*UNIT_C)*length*sqrt(rivYtot-eleYtot)*(rivYtot-threshEle)/3.0;
}
else
{
if(threshEle<rivYtot)
{
fluxriv[loci][locj] = cwr*2.0*sqrt(2*GRAV*UNIT_C*UNIT_C)*length*sqrt(rivYtot-threshEle)*(rivYtot-threshEle)/3.0;
}
else
{
fluxriv[loci][locj]=0.0;
}
}
}
else
{
if (rivYtot > threshEle)
{
fluxriv[loci][locj] = -cwr*2.0*sqrt(2*GRAV*UNIT_C*UNIT_C)*length*sqrt(eleYtot - rivYtot)*(eleYtot - threshEle)/3.0;
}
else
{
if(threshEle<eleYtot)
{
fluxriv[loci][locj] = -cwr*2.0*sqrt(2*GRAV*UNIT_C*UNIT_C)*length*sqrt(eleYtot - threshEle)*(eleYtot - threshEle)/3.0;
}
else
{
fluxriv[loci][locj]=0.0;
}
}
}
}
/*
realtype avgY(realtype zi,realtype zinabr,realtype yi,realtype yinabr)
{
if(zinabr>zi)
{
if(zinabr>zi+yi)
{
return yinabr/2;
}
else
{
return (yi+zi-zinabr+yinabr)/2;
}
}
else
{
if(zi>zinabr+yinabr)
{
return yi/2;
}
else
{
return (yi+yinabr+zinabr-zi)/2;
}
}
}
*/
/* Note: above formulation doesnt' satisfies upwind/downwind scheme.*/
realtype avgY(realtype diff, realtype yi, realtype yinabr)
{
if(diff>0)
{
if(yi>1*EPS/100)
{
// return 0.5*(yi+yinabr);
// return ((yinabr>yi)?0:1.0*yi); /* Note the if-else TRUE case can be possible only for Kinematic case */
return 1.0*yi;
}
else
{
return 0;
}
}
else
{
if(yinabr>1*EPS/100)
{
// return 0.5*(yi+yinabr);
// return ((yi>yinabr)?0:1.0*yinabr); /* Note the if-else TRUE case can be possible only for Kinematic case */
return 1.0*yinabr;
}
else
{
return 0;
}
}
}
realtype effKV(realtype ksatFunc,realtype gradY,realtype macKV,realtype KV,realtype areaF)
{
if(ksatFunc>=0.98)
{
return (macKV*areaF+KV*(1-areaF)*ksatFunc);
}
else
{
if(fabs(gradY)*ksatFunc*KV<=1*KV*ksatFunc)
{
return KV*ksatFunc;
}
else
{
if(fabs(gradY)*ksatFunc*KV<(macKV*areaF+KV*(1-areaF)*ksatFunc))
{
return (macKV*areaF*ksatFunc+KV*(1-areaF)*ksatFunc);
}
else
{
return (macKV*areaF+KV*(1-areaF)*ksatFunc);
}
}
}
}
realtype effKH(int mp,realtype tmpY, realtype aqDepth, realtype MacD, realtype MacKsatH, realtype areaF, realtype ksatH)
{
if(mp==1)
{
if(tmpY>aqDepth-MacD)
{
if(tmpY>aqDepth)
{
return (MacKsatH*MacD*areaF+ksatH*(aqDepth-MacD*areaF))/aqDepth;
}
else
{
return (MacKsatH*(tmpY-(aqDepth-MacD))*areaF+ksatH*(aqDepth-MacD+(tmpY-(aqDepth-MacD))*(1-areaF)))/tmpY;
}
}
else
{
return ksatH;
}
}
else
{
return ksatH;
}
}
void f(realtype t, N_Vector CV_Y, N_Vector CV_Ydot, void *DS)
{
int i, j,inabr;
realtype Delta, Gamma;
realtype Rn, T, Vel, RH, VP,P,LAI,zero_dh,cnpy_h,rl,r_a,r_s,alpha_r,f_r,eta_s,beta_s,Rmax;
realtype Avg_Y_Surf, Dif_Y_Surf,Grad_Y_Surf, Avg_Sf,Distance;
realtype Cwr,TotalY_Riv, TotalY_Riv_down,CrossA,CrossAdown,AvgCrossA,Perem, Perem_down,Avg_Rough,Avg_Perem,Avg_Y_Riv,Dif_Y_Riv,Grad_Y_Riv,Wid,Wid_down,Avg_Wid;
realtype Avg_Y_Sub, Dif_Y_Sub,Avg_Ksat, Grad_Y_Sub,nabrAqDepth,AquiferDepth, Deficit,elemSatn,satKfunc,effK,effKnabr,TotalY_Ele,TotalY_Ele_down;
realtype *Y, *DY;
Model_Data MD;
Y = NV_DATA_S(CV_Y);
DY = NV_DATA_S(CV_Ydot);
MD = (Model_Data) DS;
/* Initialization of temporary state variables */
for(i=0; i<3*MD->NumEle+2*MD->NumRiv; i++)
{
MD->DummyY[i]=(Y[i]>=0)?Y[i]:0;
DY[i]=0;
if(i<MD->NumRiv)
{
MD->FluxRiv[i][0]=0;
MD->FluxRiv[i][10]=0;
}
if((MD->SurfMode==2)&&(i<MD->NumEle))
{
for(j=0;j<3;j++)
{
MD->Ele[i].surfH[j]=(MD->Ele[i].nabr[j]>0)?((MD->Ele[i].BC[j]>-4)?(MD->Ele[MD->Ele[i].nabr[j]-1].zmax+MD->DummyY[MD->Ele[i].nabr[j]-1]):((MD->DummyY[-(MD->Ele[i].BC[j]/4)-1+3*MD->NumEle]>MD->Riv[-(MD->Ele[i].BC[j]/4)-1].depth)?MD->Riv[-(MD->Ele[i].BC[j]/4)-1].zmin+MD->DummyY[-(MD->Ele[i].BC[j]/4)-1+3*MD->NumEle]:MD->Riv[-(MD->Ele[i].BC[j]/4)-1].zmax)):((MD->Ele[i].BC[j]!=1)?(MD->Ele[i].zmax+MD->DummyY[i]):Interpolation(&MD->TSD_EleBC[(MD->Ele[i].BC[j])-1], t));
}
MD->Ele[i].dhBYdx=-1*(MD->Ele[i].surfY[2]*(MD->Ele[i].surfH[1]-MD->Ele[i].surfH[0])+MD->Ele[i].surfY[1]*(MD->Ele[i].surfH[0]-MD->Ele[i].surfH[2])+MD->Ele[i].surfY[0]*(MD->Ele[i].surfH[2]-MD->Ele[i].surfH[1]))/(MD->Ele[i].surfX[2]*(MD->Ele[i].surfY[1]-MD->Ele[i].surfY[0])+MD->Ele[i].surfX[1]*(MD->Ele[i].surfY[0]-MD->Ele[i].surfY[2])+MD->Ele[i].surfX[0]*(MD->Ele[i].surfY[2]-MD->Ele[i].surfY[1]));
MD->Ele[i].dhBYdy=-1*(MD->Ele[i].surfX[2]*(MD->Ele[i].surfH[1]-MD->Ele[i].surfH[0])+MD->Ele[i].surfX[1]*(MD->Ele[i].surfH[0]-MD->Ele[i].surfH[2])+MD->Ele[i].surfX[0]*(MD->Ele[i].surfH[2]-MD->Ele[i].surfH[1]))/(MD->Ele[i].surfY[2]*(MD->Ele[i].surfX[1]-MD->Ele[i].surfX[0])+MD->Ele[i].surfY[1]*(MD->Ele[i].surfX[0]-MD->Ele[i].surfX[2])+MD->Ele[i].surfY[0]*(MD->Ele[i].surfX[2]-MD->Ele[i].surfX[1]));
}
}
/* Lateral Flux Calculation between Triangular elements Follows */
for(i=0; i<MD->NumEle; i++)
{
AquiferDepth=(MD->Ele[i].zmax-MD->Ele[i].zmin);
for(j=0; j<3; j++)
{
if(MD->Ele[i].nabr[j] > 0)
{
/***************************************************************************/
/* Subsurface Lateral Flux Calculation between Triangular elements Follows */
/***************************************************************************/
Dif_Y_Sub = (MD->DummyY[i+2*MD->NumEle] + MD->Ele[i].zmin) - (MD->DummyY[MD->Ele[i].nabr[j]-1 + 2*MD->NumEle] + MD->Ele[MD->Ele[i].nabr[j]-1].zmin);
// Avg_Y_Sub=avgY(MD->Ele[i].zmin,MD->Ele[MD->Ele[i].nabr[j]-1].zmin,MD->DummyY[i+2*MD->NumEle],MD->DummyY[MD->Ele[i].nabr[j]-1 + 2*MD->NumEle]);
Avg_Y_Sub=avgY(Dif_Y_Sub,MD->DummyY[i+2*MD->NumEle],MD->DummyY[MD->Ele[i].nabr[j]-1 + 2*MD->NumEle]);
Distance = sqrt(pow((MD->Ele[i].x - MD->Ele[MD->Ele[i].nabr[j] - 1].x), 2) + pow((MD->Ele[i].y - MD->Ele[MD->Ele[i].nabr[j] - 1].y), 2));
Grad_Y_Sub = Dif_Y_Sub/Distance;
/* take care of macropore effect */
effK=effKH(MD->Ele[i].Macropore,MD->DummyY[i+2*MD->NumEle],AquiferDepth,MD->Ele[i].macD,MD->Ele[i].macKsatH,MD->Ele[i].vAreaF,MD->Ele[i].KsatH);
inabr=MD->Ele[i].nabr[j]-1;
nabrAqDepth=(MD->Ele[inabr].zmax-MD->Ele[inabr].zmin);
effKnabr=effKH(MD->Ele[inabr].Macropore,MD->DummyY[inabr+2*MD->NumEle],nabrAqDepth,MD->Ele[inabr].macD,MD->Ele[inabr].macKsatH,MD->Ele[inabr].vAreaF,MD->Ele[inabr].KsatH);
/* It should be weighted average. However, there is an ambiguity about distance used */
Avg_Ksat=0.5*(effK+effKnabr);
/* groundwater flow modeled by Darcy's law */
MD->FluxSub[i][j] = Avg_Ksat*Grad_Y_Sub*Avg_Y_Sub*MD->Ele[i].edge[j];
/***************************************************************************/
/* Surface Lateral Flux Calculation between Triangular elements Follows */
/***************************************************************************/
Dif_Y_Surf = (MD->SurfMode==1)?(MD->Ele[i].zmax-MD->Ele[MD->Ele[i].nabr[j] - 1].zmax):(MD->DummyY[i] + MD->Ele[i].zmax) - (MD->DummyY[MD->Ele[i].nabr[j] - 1] + MD->Ele[MD->Ele[i].nabr[j] - 1].zmax);
// Avg_Y_Surf=avgY(MD->Ele[i].zmax,MD->Ele[MD->Ele[i].nabr[j] - 1].zmax,MD->DummyY[i],MD->DummyY[MD->Ele[i].nabr[j]-1]);
Avg_Y_Surf=avgY(Dif_Y_Surf,MD->DummyY[i],MD->DummyY[MD->Ele[i].nabr[j]-1]);
Grad_Y_Surf = Dif_Y_Surf/Distance;
Avg_Sf=sqrt(pow(MD->Ele[i].dhBYdx,2)+pow(MD->Ele[i].dhBYdy,2));
Avg_Sf=(MD->SurfMode==1)?(Grad_Y_Surf>0?Grad_Y_Surf:EPS/pow(10.0,6)):(Avg_Sf>EPS/pow(10.0,6))?Avg_Sf:EPS/pow(10.0,6);
/* Weighting needed */
Avg_Rough = 0.5*(MD->Ele[i].Rough + MD->Ele[MD->Ele[i].nabr[j] - 1].Rough);
CrossA = Avg_Y_Surf*MD->Ele[i].edge[j];
OverlandFlow(MD->FluxSurf,i,j, Avg_Y_Surf,Grad_Y_Surf,Avg_Sf,CrossA,Avg_Rough);
}
/************************************************/
/* Boundary condition Flux Calculations Follows */
/************************************************/
else
{
/* No flow (natural) boundary condition is default */
if(MD->Ele[i].BC[j] == 0)
{
MD->FluxSurf[i][j] = 0;
MD->FluxSub[i][j] = 0;
}
else if(MD->Ele[i].BC[j] == 1) /* Note: ideally different boundary conditions need to be incorporated for surf and subsurf respectively */
/* Note: the formulation assumes only dirichlet TS right now */
{
MD->FluxSurf[i][j] = 0; /* Note the assumption here is no flow for surface*/
Dif_Y_Sub = (MD->DummyY[i+2*MD->NumEle] + MD->Ele[i].zmin) - Interpolation(&MD->TSD_EleBC[(MD->Ele[i].BC[j])-1], t);
Avg_Y_Sub = avgY(Dif_Y_Sub,MD->DummyY[i+2*MD->NumEle],(Interpolation(&MD->TSD_EleBC[(MD->Ele[i].BC[j])-1], t) - MD->Ele[i].zmin));
// Avg_Y_Sub = (MD->DummyY[i+2*MD->NumEle] + (Interpolation(&MD->TSD_EleBC[(MD->Ele[i].BC[j])-1], t) - MD->Ele[i].zmin))/2;
/* Minimum Distance from circumcenter to the edge of the triangle on which BDD. condition is defined*/
Distance = sqrt(pow(MD->Ele[i].edge[0]*MD->Ele[i].edge[1]*MD->Ele[i].edge[2]/(4*MD->Ele[i].area), 2) - pow(MD->Ele[i].edge[j]/2, 2));
effK=effKH(MD->Ele[i].Macropore,MD->DummyY[i+2*MD->NumEle],AquiferDepth,MD->Ele[i].macD,MD->Ele[i].macKsatH,MD->Ele[i].vAreaF,MD->Ele[i].KsatH);
Avg_Ksat = effK;
Grad_Y_Sub = Dif_Y_Sub/Distance;
MD->FluxSub[i][j] = Avg_Ksat*Grad_Y_Sub*Avg_Y_Sub*MD->Ele[i].edge[j];
}
else /* Neumann BC (Note: MD->Ele[i].BC[j] value have to be = 2+(index of neumann boundary TS)*/
{
MD->FluxSurf[i][j] = Interpolation(&MD->TSD_EleBC[(MD->Ele[i].BC[j])-1], t);
MD->FluxSub[i][j] = Interpolation(&MD->TSD_EleBC[(-MD->Ele[i].BC[j])-1], t);
}
}
}
/**************************************************************************************************/
/* Evaporation Module: [2] is ET from OVLF/SUBF, [1] is Transpiration, [0] is ET loss from canopy */
/**************************************************************************************************/
/* Physical Unit Dependent. Change this */
Rn = Interpolation(&MD->TSD_Rn[MD->Ele[i].Rn-1], t);
// G = Interpolation(&MD->TSD_G[MD->Ele[i].G-1], t);
T = Interpolation(&MD->TSD_Temp[MD->Ele[i].temp-1], t);
Vel = Interpolation(&MD->TSD_WindVel[MD->Ele[i].WindVel-1], t);
RH = Interpolation(&MD->TSD_Humidity[MD->Ele[i].humidity-1], t);
VP = Interpolation(&MD->TSD_Pressure[MD->Ele[i].pressure-1], t);
P = 101.325*pow(10,3)*pow((293-0.0065*MD->Ele[i].zmax)/293,5.26);
Delta = 2503*pow(10,3)*exp(17.27*T/(T+237.3))/(pow(237.3 + T, 2));
Gamma = P*1.0035*0.92/(0.622*2441);
LAI = Interpolation(&MD->TSD_LAI[MD->Ele[i].LC-1], t);
/* zero_dh=Interpolation(&MD->TSD_DH[MD->Ele[i].LC-1], t);
cnpy_h = zero_dh/(1.1*(0.0000001+log(1+pow(0.007*LAI,0.25))));
if(LAI<2.85)
{
rl= 0.0002 + 0.3*cnpy_h*pow(0.07*LAI,0.5);
}
else
{
rl= 0.3*cnpy_h*(1-(zero_dh/cnpy_h));
} */
rl=Interpolation(&MD->TSD_RL[MD->Ele[i].LC-1], t);
r_a = log(MD->Ele[i].windH/rl)*log(10*MD->Ele[i].windH/rl)/(Vel*0.16);
MD->EleET[i][2] = MD->pcCal.Et2*(1-MD->Ele[i].VegFrac)*(Rn*(1-MD->Ele[i].Albedo)*Delta+(1.2*1003.5*((VP/RH)-VP)/r_a))/(1000.0*2441000.0*(Delta+Gamma));
if((MD->Ele[i].zmax-MD->Ele[i].zmin)-MD->DummyY[i+2*MD->NumEle]<MD->Ele[i].RzD)
{
elemSatn=1.0;
}
else
{
elemSatn = ((MD->DummyY[i+MD->NumEle]/(AquiferDepth-MD->DummyY[i+2*MD->NumEle]))>1)?1:((MD->DummyY[i+MD->NumEle]/(AquiferDepth-MD->DummyY[i+2*MD->NumEle]))<0)?0:0.5*(1-cos(3.14*(MD->DummyY[i+MD->NumEle]/(AquiferDepth-MD->DummyY[i+2*MD->NumEle]))));
}
if(LAI>0.0)
{
Rmax = 5000.0/(60*UNIT_C); /* Unit day_per_m */
f_r= 1.1*Rn*(1-exp(-LAI))/(MD->Ele[i].Rs_ref*LAI);
alpha_r= (1+f_r)/(1+(MD->Ele[i].Rmin/Rmax));
eta_s= 1- 0.0016*(pow((24.85-T),2));
beta_s= (elemSatn>EPS/1000.0)?elemSatn:EPS/1000.0;
r_s=((MD->Ele[i].Rmin*alpha_r/(beta_s*LAI*pow(eta_s,4)))> Rmax)?Rmax:(MD->Ele[i].Rmin*alpha_r/(beta_s*LAI*pow(eta_s,4)));
MD->EleET[i][1] = MD->pcCal.Et1*(LAI/MD->Ele[i].LAImax)*MD->Ele[i].VegFrac*(1-pow(((MD->EleIS[i]+MD->EleSnowCanopy[i]<0)?0:(MD->EleIS[i]+MD->EleSnowCanopy[i]))/(MD->EleISmax[i]+MD->EleISsnowmax[i]),2.0/3))*(Rn*(1-MD->Ele[i].Albedo)*Delta+(1.2*1003.5*((VP/RH)-VP)/r_a))/(1000*2441000.0*(Delta+Gamma*(1+r_s/r_a)));
}
else
{
MD->EleET[i][1] =0.0;
}
/* Note: Assumption is OVL flow depth less than EPS/100 is immobile water */
if(MD->DummyY[i+2*MD->NumEle]>AquiferDepth-MD->Ele[i].infD)
{
/* Assumption: infD<macD */
Grad_Y_Sub=(MD->DummyY[i]+MD->Ele[i].zmax-(MD->DummyY[i+2*MD->NumEle]+MD->Ele[i].zmin))/MD->Ele[i].infD;
Grad_Y_Sub=((MD->DummyY[i]<EPS/100)&&(Grad_Y_Sub>0))?0:Grad_Y_Sub;
elemSatn=1.0;
satKfunc=pow(elemSatn,0.5)*pow(-1+pow(1-pow(elemSatn,MD->Ele[i].Beta/(MD->Ele[i].Beta-1)),(MD->Ele[i].Beta-1)/MD->Ele[i].Beta),2);
effK=(MD->Ele[i].Macropore==1)?effKV(satKfunc,Grad_Y_Sub,MD->Ele[i].macKsatV,MD->Ele[i].infKsatV,MD->Ele[i].hAreaF):MD->Ele[i].infKsatV;
MD->EleViR[i] = effK*Grad_Y_Sub;
MD->Recharge[i] = MD->EleViR[i];
DY[i+MD->NumEle] = DY[i+MD->NumEle]+MD->EleViR[i]-MD->Recharge[i];
DY[i+2*MD->NumEle]=DY[i+2*MD->NumEle]+MD->Recharge[i]-((MD->DummyY[i]<EPS/100)?MD->EleET[i][2]:0);
}
else
{
Deficit=AquiferDepth-MD->DummyY[i+2*MD->NumEle];
elemSatn=((MD->DummyY[i+MD->NumEle]/Deficit)>1)?1:((MD->DummyY[i+MD->NumEle]<=0)?EPS/1000.0:MD->DummyY[i+MD->NumEle]/Deficit);
/* Note: for psi calculation using van genuchten relation, cutting the psi-sat tail at small saturation can be performed for computational advantage. If you dont' want to perform this, comment the statement that follows */
elemSatn=(elemSatn<multF*EPS)?multF*EPS:elemSatn;
Avg_Y_Sub=(-(pow(pow(1/elemSatn,MD->Ele[i].Beta/(MD->Ele[i].Beta-1))-1,1/MD->Ele[i].Beta)/MD->Ele[i].Alpha)<MINpsi)?MINpsi:-(pow(pow(1/elemSatn,MD->Ele[i].Beta/(MD->Ele[i].Beta-1))-1,1/MD->Ele[i].Beta)/MD->Ele[i].Alpha);
TotalY_Ele=Avg_Y_Sub+MD->Ele[i].zmin+AquiferDepth-MD->Ele[i].infD;
Grad_Y_Sub=(MD->DummyY[i]+MD->Ele[i].zmax-TotalY_Ele)/MD->Ele[i].infD;
Grad_Y_Sub=((MD->DummyY[i]<EPS/100)&&(Grad_Y_Sub>0))?0:Grad_Y_Sub;
satKfunc=pow(elemSatn,0.5)*pow(-1+pow(1-pow(elemSatn,MD->Ele[i].Beta/(MD->Ele[i].Beta-1)),(MD->Ele[i].Beta-1)/MD->Ele[i].Beta),2);
effK=(MD->Ele[i].Macropore==1)?effKV(satKfunc,Grad_Y_Sub,MD->Ele[i].macKsatV,MD->Ele[i].infKsatV,MD->Ele[i].hAreaF):MD->Ele[i].infKsatV;
// MD->EleViR[i] = 0.5*(effK+MD->Ele[i].infKsatV)*Grad_Y_Sub;
MD->EleViR[i] = 0.5*(effK)*Grad_Y_Sub;
/* Harmonic mean formulation. Note that if unsaturated zone has low saturation, satKfunc becomes very small. Use arithmetic mean instead*/
// MD->Recharge[i] = (elemSatn==0.0)?0:(Deficit<=0)?0:(MD->Ele[i].KsatV*satKfunc*(MD->Ele[i].Alpha*Deficit-2*pow(-1+pow(elemSatn,MD->Ele[i].Beta/(-MD->Ele[i].Beta+1)),1/MD->Ele[i].Beta))/(MD->Ele[i].Alpha*((Deficit+MD->DummyY[i+2*MD->NumEle]*satKfunc))));
/* Arithmetic Mean Formulation */
effK=(MD->Ele[i].Macropore==1)?((MD->DummyY[i+2*MD->NumEle]>AquiferDepth-MD->Ele[i].macD)?effK:MD->Ele[i].KsatV*satKfunc):MD->Ele[i].KsatV*satKfunc;
MD->Recharge[i] = (elemSatn==0.0)?0:(Deficit<=0)?0:(MD->Ele[i].KsatV*MD->DummyY[i+2*MD->NumEle]+effK*Deficit)*(MD->Ele[i].Alpha*Deficit-2*pow(-1+pow(elemSatn,MD->Ele[i].Beta/(-MD->Ele[i].Beta+1)),1/MD->Ele[i].Beta))/(MD->Ele[i].Alpha*pow(Deficit+MD->DummyY[i+2*MD->NumEle],2));
MD->EleET[i][2]=(MD->DummyY[i]<EPS/100)?elemSatn*MD->EleET[i][2]:MD->EleET[i][2];
DY[i+MD->NumEle] = DY[i+MD->NumEle]+MD->EleViR[i]-MD->Recharge[i]-((MD->DummyY[i]<EPS/100)?MD->EleET[i][2]:0);
DY[i+2*MD->NumEle]=DY[i+2*MD->NumEle]+MD->Recharge[i];
}
DY[i] = DY[i]+MD->EleNetPrep[i] - MD->EleViR[i]-((MD->DummyY[i]<EPS/100)?0:MD->EleET[i][2]);
if(MD->DummyY[i+2*MD->NumEle]>AquiferDepth-MD->Ele[i].RzD)
{
DY[i+2*MD->NumEle]=DY[i+2*MD->NumEle]-MD->EleET[i][1];
}
else
{
DY[i+MD->NumEle] = DY[i+MD->NumEle]-MD->EleET[i][1];
}
}
/* Lateral Flux Calculation between River-River and River-Triangular elements Follows */
for(i=0; i<MD->NumRiv; i++)
{
TotalY_Riv = MD->DummyY[i + 3*MD->NumEle] + MD->Riv[i].zmin;
Perem = CS_AreaOrPerem(MD->Riv_Shape[MD->Riv[i].shape - 1].interpOrd,MD->DummyY[i + 3*MD->NumEle],MD->Riv[i].coeff,2);
if(MD->Riv[i].down > 0)
{
/****************************************************************/
/* Lateral Flux Calculation between River-River element Follows */
/****************************************************************/
TotalY_Riv_down = MD->DummyY[MD->Riv[i].down - 1 + 3*MD->NumEle] + MD->Riv[MD->Riv[i].down - 1].zmin;
Perem_down = CS_AreaOrPerem(MD->Riv_Shape[MD->Riv[MD->Riv[i].down - 1].shape - 1].interpOrd,MD->DummyY[MD->Riv[i].down - 1 + 3*MD->NumEle],MD->Riv[MD->Riv[i].down - 1].coeff,2);
Avg_Perem = (Perem + Perem_down)/2.0;
Avg_Rough = (MD->Riv_Mat[MD->Riv[i].material - 1].Rough + MD->Riv_Mat[MD->Riv[MD->Riv[i].down - 1].material-1].Rough)/2.0;
Distance = 0.5*(MD->Riv[i].Length+MD->Riv[MD->Riv[i].down - 1].Length);
Dif_Y_Riv=(MD->RivMode==1)?(MD->Riv[i].zmin-MD->Riv[MD->Riv[i].down - 1].zmin):(TotalY_Riv - TotalY_Riv_down);
Grad_Y_Riv = Dif_Y_Riv/Distance;
Avg_Sf = (Grad_Y_Riv>0)?Grad_Y_Riv:EPS;
CrossA = CS_AreaOrPerem(MD->Riv_Shape[MD->Riv[i].shape - 1].interpOrd,MD->DummyY[i + 3*MD->NumEle],MD->Riv[i].coeff,1);
CrossAdown = CS_AreaOrPerem(MD->Riv_Shape[MD->Riv[MD->Riv[i].down - 1].shape - 1].interpOrd,MD->DummyY[MD->Riv[i].down - 1 + 3*MD->NumEle],MD->Riv[MD->Riv[i].down - 1].coeff,1);
AvgCrossA=0.5*(CrossA+CrossAdown);
Avg_Y_Riv=(Avg_Perem==0)?0:(AvgCrossA/Avg_Perem);
OverlandFlow(MD->FluxRiv,i,1, Avg_Y_Riv,Grad_Y_Riv,Avg_Sf,CrossA,Avg_Rough);
/* accumulate to get in-flow for down segments: [0] for inflow, [1] for outflow */
MD->FluxRiv[MD->Riv[i].down - 1][0] = MD->FluxRiv[MD->Riv[i].down - 1][0] - MD->FluxRiv[i][1];
/************************************************************************/
/* Lateral Flux Calculation between Element Beneath River (EBR) and EBR */
/************************************************************************/
TotalY_Ele = MD->DummyY[i + 3*MD->NumEle+MD->NumRiv] + MD->Ele[i+MD->NumEle].zmin;
TotalY_Ele_down = MD->DummyY[MD->Riv[i].down - 1 + 3*MD->NumEle+MD->NumRiv] + MD->Ele[MD->Riv[i].down - 1+MD->NumEle].zmin;
Wid = CS_AreaOrPerem(MD->Riv_Shape[MD->Riv[i].shape - 1].interpOrd,MD->Riv[i].depth,MD->Riv[i].coeff,3);
Wid_down = CS_AreaOrPerem(MD->Riv_Shape[MD->Riv[MD->Riv[i].down - 1].shape - 1].interpOrd,MD->Riv[MD->Riv[i].down - 1].depth,MD->Riv[MD->Riv[i].down - 1].coeff,3);
Avg_Wid = (Wid + Wid_down)/2.0;
Distance = 0.5*(MD->Riv[i].Length+MD->Riv[MD->Riv[i].down - 1].Length);
Dif_Y_Sub=TotalY_Ele - TotalY_Ele_down;
// Avg_Y_Sub=avgY(MD->Ele[i+MD->NumEle].zmin,MD->Ele[MD->Riv[i].down - 1+MD->NumEle].zmin,MD->DummyY[i + 3*MD->NumEle+MD->NumRiv],MD->DummyY[MD->Riv[i].down - 1 + 3*MD->NumEle+MD->NumRiv]);
Avg_Y_Sub=avgY(Dif_Y_Sub,MD->DummyY[i + 3*MD->NumEle+MD->NumRiv],MD->DummyY[MD->Riv[i].down - 1 + 3*MD->NumEle+MD->NumRiv]);
Grad_Y_Sub = Dif_Y_Sub/Distance;
/* take care of macropore effect */
AquiferDepth=MD->Ele[i+MD->NumEle].zmax-MD->Ele[i+MD->NumEle].zmin;
// effK=MD->Ele[i+MD->NumEle].KsatH;
effK=0.5*(effKH(MD->Ele[MD->Riv[i].LeftEle-1].Macropore,MD->DummyY[MD->Riv[i].LeftEle-1+2*MD->NumEle],MD->Ele[MD->Riv[i].LeftEle-1].zmax-MD->Ele[MD->Riv[i].LeftEle-1].zmin,MD->Ele[MD->Riv[i].LeftEle-1].macD,MD->Ele[MD->Riv[i].LeftEle-1].macKsatH,MD->Ele[MD->Riv[i].LeftEle-1].vAreaF,MD->Ele[MD->Riv[i].LeftEle-1].KsatH)+effKH(MD->Ele[MD->Riv[i].RightEle-1].Macropore,MD->DummyY[MD->Riv[i].RightEle-1+2*MD->NumEle],MD->Ele[MD->Riv[i].RightEle-1].zmax-MD->Ele[MD->Riv[i].RightEle-1].zmin,MD->Ele[MD->Riv[i].RightEle-1].macD,MD->Ele[MD->Riv[i].RightEle-1].macKsatH,MD->Ele[MD->Riv[i].RightEle-1].vAreaF,MD->Ele[MD->Riv[i].RightEle-1].KsatH));
inabr=MD->Riv[i].down - 1;
nabrAqDepth=(MD->Ele[inabr].zmax-MD->Ele[inabr].zmin);
// effKnabr=MD->Ele[inabr+MD->NumEle].KsatH;
effKnabr=0.5*(effKH(MD->Ele[MD->Riv[inabr].LeftEle-1].Macropore,MD->DummyY[MD->Riv[inabr].LeftEle-1+2*MD->NumEle],MD->Ele[MD->Riv[inabr].LeftEle-1].zmax-MD->Ele[MD->Riv[inabr].LeftEle-1].zmin,MD->Ele[MD->Riv[inabr].LeftEle-1].macD,MD->Ele[MD->Riv[inabr].LeftEle-1].macKsatH,MD->Ele[MD->Riv[inabr].LeftEle-1].vAreaF,MD->Ele[MD->Riv[inabr].LeftEle-1].KsatH)+effKH(MD->Ele[MD->Riv[inabr].RightEle-1].Macropore,MD->DummyY[MD->Riv[inabr].RightEle-1+2*MD->NumEle],MD->Ele[MD->Riv[inabr].RightEle-1].zmax-MD->Ele[MD->Riv[inabr].RightEle-1].zmin,MD->Ele[MD->Riv[inabr].RightEle-1].macD,MD->Ele[MD->Riv[inabr].RightEle-1].macKsatH,MD->Ele[MD->Riv[inabr].RightEle-1].vAreaF,MD->Ele[MD->Riv[inabr].RightEle-1].KsatH));
Avg_Ksat=0.5*(effK+effKnabr);
/* groundwater flow modeled by Darcy's law */
MD->FluxRiv[i][9] = Avg_Ksat*Grad_Y_Sub*Avg_Y_Sub*Avg_Wid;
/* accumulate to get in-flow for down segments: [10] for inflow, [9] for outflow */
MD->FluxRiv[MD->Riv[i].down - 1][10] = MD->FluxRiv[MD->Riv[i].down - 1][10] - MD->FluxRiv[i][9];
}
else
{
switch(MD->Riv[i].down)
{
case -1:
/* Dirichlet boundary condition */
TotalY_Riv_down = Interpolation(&MD->TSD_Riv[(MD->Riv[i].BC)-1], t) + (MD->Node[MD->Riv[i].ToNode-1].zmax -MD->Riv[i].depth);
Distance = sqrt(pow(MD->Riv[i].x - MD->Node[MD->Riv[i].ToNode-1].x, 2) + pow(MD->Riv[i].y - MD->Node[MD->Riv[i].ToNode-1].y, 2));
Grad_Y_Riv = (TotalY_Riv - TotalY_Riv_down)/Distance;
/* Note: do i need to change else part here for diff wave */
Avg_Sf = (MD->RivMode==1)?Grad_Y_Riv:Grad_Y_Riv;;
Avg_Rough = MD->Riv_Mat[MD->Riv[i].material-1].Rough;
Avg_Y_Riv = avgY(Grad_Y_Riv,MD->DummyY[i + 3*MD->NumEle],Interpolation(&MD->TSD_Riv[(MD->Riv[i].BC)-1], t));
Avg_Perem = Perem;
CrossA = CS_AreaOrPerem(MD->Riv_Shape[MD->Riv[i].shape - 1].interpOrd,MD->DummyY[i + 3*MD->NumEle],MD->Riv[i].coeff,1);
Avg_Y_Riv=(Perem==0)?0:(CrossA/Avg_Perem);
OverlandFlow(MD->FluxRiv,i,1, Avg_Y_Riv,Grad_Y_Riv,Avg_Sf,CrossA,Avg_Rough);
break;
case -2:
/* Neumann boundary condition */
MD->FluxRiv[i][1] = Interpolation(&MD->TSD_Riv[MD->Riv[i].BC-1], t);
break;
case -3:
/* zero-depth-gradient boundary conditions */
Distance = sqrt(pow(MD->Riv[i].x - MD->Node[MD->Riv[i].ToNode-1].x, 2) + pow(MD->Riv[i].y - MD->Node[MD->Riv[i].ToNode-1].y, 2));
Grad_Y_Riv = (MD->Riv[i].zmin - (MD->Node[MD->Riv[i].ToNode-1].zmax -MD->Riv[i].depth))/Distance;
Avg_Rough = MD->Riv_Mat[MD->Riv[i].material-1].Rough;
Avg_Y_Riv = MD->DummyY[i + 3*MD->NumEle];
Avg_Perem = Perem;
CrossA = CS_AreaOrPerem(MD->Riv_Shape[MD->Riv[i].shape - 1].interpOrd,MD->DummyY[i + 3*MD->NumEle],MD->Riv[i].coeff,1);
MD->FluxRiv[i][1] = sqrt(Grad_Y_Riv)*CrossA*((Avg_Perem>0)?pow(CrossA/Avg_Perem,2.0/3.0):0)/Avg_Rough;
break;
case -4:
/* Critical Depth boundary conditions */
CrossA = CS_AreaOrPerem(MD->Riv_Shape[MD->Riv[i].shape - 1].interpOrd,MD->DummyY[i + 3*MD->NumEle],MD->Riv[i].coeff,1);
MD->FluxRiv[i][1] = CrossA*sqrt(GRAV*UNIT_C*UNIT_C*MD->DummyY[i + 3*MD->NumEle]); /* Note the dependence on physical units */
break;
default:
printf("Fatal Error: River Routing Boundary Condition Type Is Wrong!");
exit(1);
}
/* Note: bdd condition for subsurface element can be changed. Assumption: No flow condition */
MD->FluxRiv[i][9]=0;
}
if(MD->Riv[i].LeftEle > 0)
{
/*****************************************************************************/
/* Lateral Surface Flux Calculation between River-Triangular element Follows */
/*****************************************************************************/
OLFeleToriv(MD->DummyY[MD->Riv[i].LeftEle - 1]+MD->Ele[MD->Riv[i].LeftEle - 1].zmax,MD->Ele[MD->Riv[i].LeftEle - 1].zmax,MD->Riv_Mat[MD->Riv[i].material-1].Cwr, MD->Riv[i].zmax,TotalY_Riv,MD->FluxRiv,i,2,MD->Riv[i].Length);
/*********************************************************************************/
/* Lateral Sub-surface Flux Calculation between River-Triangular element Follows */
/*********************************************************************************/
Dif_Y_Sub = (MD->DummyY[i+3*MD->NumEle] + MD->Riv[i].zmin) - (MD->DummyY[MD->Riv[i].LeftEle-1 + 2*MD->NumEle] + MD->Ele[MD->Riv[i].LeftEle-1].zmin);
// Avg_Y_Sub=(MD->DummyY[MD->Riv[i].LeftEle-1 + 2*MD->NumEle]+MD->Ele[MD->Riv[i].LeftEle-1].zmin-MD->Riv[i].zmin)>0?MD->DummyY[MD->Riv[i].LeftEle-1 + 2*MD->NumEle]+MD->Ele[MD->Riv[i].LeftEle-1].zmin-MD->Riv[i].zmin:0;
/* This is head at river edge representation */
// Avg_Y_Sub = ((MD->Riv[i].zmax-(MD->Ele[MD->Riv[i].LeftEle-1].zmax-MD->Ele[MD->Riv[i].LeftEle-1].zmin)+MD->DummyY[MD->Riv[i].LeftEle-1 + 2*MD->NumEle])>MD->Riv[i].zmin)?((MD->Riv[i].zmax-(MD->Ele[MD->Riv[i].LeftEle-1].zmax-MD->Ele[MD->Riv[i].LeftEle-1].zmin)+MD->DummyY[MD->Riv[i].LeftEle-1 + 2*MD->NumEle])-MD->Riv[i].zmin):0;
/* This is head in neighboring cell represention */
Avg_Y_Sub = MD->Ele[MD->Riv[i].LeftEle-1].zmin>MD->Riv[i].zmin?MD->DummyY[MD->Riv[i].LeftEle-1 + 2*MD->NumEle]:((MD->Ele[MD->Riv[i].LeftEle-1].zmin+MD->DummyY[MD->Riv[i].LeftEle-1 + 2*MD->NumEle])>MD->Riv[i].zmin?(MD->Ele[MD->Riv[i].LeftEle-1].zmin+MD->DummyY[MD->Riv[i].LeftEle-1 + 2*MD->NumEle]-MD->Riv[i].zmin):0);
// Avg_Y_Sub=avgY(MD->Riv[i].zmin,MD->Riv[i].zmin,MD->DummyY[i+3*MD->NumEle],Avg_Y_Sub);
Avg_Y_Sub=avgY(Dif_Y_Sub,MD->DummyY[i+3*MD->NumEle],Avg_Y_Sub);
effK=MD->Riv[i].KsatH;
Distance = sqrt(pow((MD->Riv[i].x - MD->Ele[MD->Riv[i].LeftEle - 1].x), 2) + pow((MD->Riv[i].y - MD->Ele[MD->Riv[i].LeftEle - 1].y), 2));
Grad_Y_Sub = Dif_Y_Sub/Distance;
/* take care of macropore effect */
inabr=MD->Riv[i].LeftEle-1;
AquiferDepth=(MD->Ele[inabr].zmax-MD->Ele[inabr].zmin);
effKnabr=effKH(MD->Ele[inabr].Macropore,MD->DummyY[inabr+2*MD->NumEle],AquiferDepth,MD->Ele[inabr].macD,MD->Ele[inabr].macKsatH,MD->Ele[inabr].vAreaF,MD->Ele[inabr].KsatH);
Avg_Ksat=0.5*(effK+effKnabr);
MD->FluxRiv[i][4]=MD->Riv[i].Length*Avg_Ksat*Grad_Y_Sub*Avg_Y_Sub;
/***********************************************************************************/
/* Lateral Flux between rectangular element (beneath river) and triangular element */
/***********************************************************************************/
Dif_Y_Sub = (MD->DummyY[i+3*MD->NumEle+MD->NumRiv] + MD->Ele[i+MD->NumEle].zmin) - (MD->DummyY[MD->Riv[i].LeftEle-1 + 2*MD->NumEle] + MD->Ele[MD->Riv[i].LeftEle-1].zmin);
// Avg_Y_Sub=((MD->DummyY[MD->Riv[i].LeftEle-1 + 2*MD->NumEle]+MD->Ele[MD->Riv[i].LeftEle-1].zmin-MD->Riv[i].zmin)>0)?MD->Riv[i].zmin-MD->Ele[MD->Riv[i].LeftEle-1].zmin:MD->DummyY[MD->Riv[i].LeftEle-1 + 2*MD->NumEle];
/* This is head at river edge representation */
// Avg_Y_Sub = ((MD->Riv[i].zmax-(MD->Ele[MD->Riv[i].LeftEle-1].zmax-MD->Ele[MD->Riv[i].LeftEle-1].zmin)+MD->DummyY[MD->Riv[i].LeftEle-1 + 2*MD->NumEle])>MD->Riv[i].zmin)?MD->Riv[i].zmin-(MD->Riv[i].zmax-(MD->Ele[MD->Riv[i].LeftEle-1].zmax-MD->Ele[MD->Riv[i].LeftEle-1].zmin)):MD->DummyY[MD->Riv[i].LeftEle-1 + 2*MD->NumEle];
/* This is head in neighboring cell represention */
Avg_Y_Sub = MD->Ele[MD->Riv[i].LeftEle-1].zmin>MD->Riv[i].zmin?0:((MD->Ele[MD->Riv[i].LeftEle-1].zmin+MD->DummyY[MD->Riv[i].LeftEle-1 + 2*MD->NumEle])>MD->Riv[i].zmin?(MD->Riv[i].zmin-MD->Ele[MD->Riv[i].LeftEle-1].zmin):MD->DummyY[MD->Riv[i].LeftEle-1 + 2*MD->NumEle]);
// Avg_Y_Sub=avgY(MD->Ele[i+MD->NumEle].zmin,MD->Ele[MD->Riv[i].LeftEle-1].zmin,MD->DummyY[i+3*MD->NumEle+MD->NumRiv],Avg_Y_Sub);
Avg_Y_Sub=avgY(Dif_Y_Sub,MD->DummyY[i+3*MD->NumEle+MD->NumRiv],Avg_Y_Sub);
AquiferDepth=(MD->Ele[i+MD->NumEle].zmax-MD->Ele[i+MD->NumEle].zmin);
// effK=MD->Ele[i+MD->NumEle].KsatH;
effK=0.5*(effKH(MD->Ele[MD->Riv[i].LeftEle-1].Macropore,MD->DummyY[MD->Riv[i].LeftEle-1+2*MD->NumEle],MD->Ele[MD->Riv[i].LeftEle-1].zmax-MD->Ele[MD->Riv[i].LeftEle-1].zmin,MD->Ele[MD->Riv[i].LeftEle-1].macD,MD->Ele[MD->Riv[i].LeftEle-1].macKsatH,MD->Ele[MD->Riv[i].LeftEle-1].vAreaF,MD->Ele[MD->Riv[i].LeftEle-1].KsatH)+effKH(MD->Ele[MD->Riv[i].RightEle-1].Macropore,MD->DummyY[MD->Riv[i].RightEle-1+2*MD->NumEle],MD->Ele[MD->Riv[i].RightEle-1].zmax-MD->Ele[MD->Riv[i].RightEle-1].zmin,MD->Ele[MD->Riv[i].RightEle-1].macD,MD->Ele[MD->Riv[i].RightEle-1].macKsatH,MD->Ele[MD->Riv[i].RightEle-1].vAreaF,MD->Ele[MD->Riv[i].RightEle-1].KsatH));
inabr=MD->Riv[i].LeftEle-1;
nabrAqDepth=(MD->Ele[inabr].zmax-MD->Ele[inabr].zmin);
effKnabr=effKH(MD->Ele[inabr].Macropore,MD->DummyY[inabr+2*MD->NumEle],nabrAqDepth,MD->Ele[inabr].macD,MD->Ele[inabr].macKsatH,MD->Ele[inabr].vAreaF,MD->Ele[inabr].KsatH);
Avg_Ksat=0.5*(effK+effKnabr);
Grad_Y_Sub = Dif_Y_Sub/Distance; /* take care of macropore effect */
MD->FluxRiv[i][7]=MD->Riv[i].Length*Avg_Ksat*Grad_Y_Sub*Avg_Y_Sub;
/* replace flux term */
for(j=0; j < 3; j++)
{
if(MD->Ele[MD->Riv[i].LeftEle - 1].nabr[j] == MD->Riv[i].RightEle)
{
MD->FluxSurf[MD->Riv[i].LeftEle - 1][j] = -MD->FluxRiv[i][2];
MD->FluxSub[MD->Riv[i].LeftEle - 1][j] = -MD->FluxRiv[i][4];
MD->FluxSub[MD->Riv[i].LeftEle - 1][j] = MD->FluxSub[MD->Riv[i].LeftEle - 1][j] -MD->FluxRiv[i][7];
break;
}
}
}
if (MD->Riv[i].RightEle > 0)
{
/*****************************************************************************/
/* Lateral Surface Flux Calculation between River-Triangular element Follows */
/*****************************************************************************/
OLFeleToriv(MD->DummyY[MD->Riv[i].RightEle - 1]+MD->Ele[MD->Riv[i].RightEle - 1].zmax,MD->Ele[MD->Riv[i].RightEle - 1].zmax,MD->Riv_Mat[MD->Riv[i].material-1].Cwr, MD->Riv[i].zmax,TotalY_Riv,MD->FluxRiv,i,3,MD->Riv[i].Length);
/*********************************************************************************/
/* Lateral Sub-surface Flux Calculation between River-Triangular element Follows */
/*********************************************************************************/
Dif_Y_Sub = (MD->DummyY[i+3*MD->NumEle] + MD->Riv[i].zmin) - (MD->DummyY[MD->Riv[i].RightEle-1 + 2*MD->NumEle] + MD->Ele[MD->Riv[i].RightEle-1].zmin);
// Avg_Y_Sub=(MD->DummyY[MD->Riv[i].RightEle-1 + 2*MD->NumEle]+MD->Ele[MD->Riv[i].RightEle-1].zmin-MD->Riv[i].zmin>0)?MD->DummyY[MD->Riv[i].RightEle-1 + 2*MD->NumEle]+MD->Ele[MD->Riv[i].RightEle-1].zmin-MD->Riv[i].zmin:0;
/* This is head at river edge representation */
// Avg_Y_Sub = ((MD->Riv[i].zmax-(MD->Ele[MD->Riv[i].RightEle-1].zmax-MD->Ele[MD->Riv[i].RightEle-1].zmin)+MD->DummyY[MD->Riv[i].RightEle-1 + 2*MD->NumEle])>MD->Riv[i].zmin)?((MD->Riv[i].zmax-(MD->Ele[MD->Riv[i].RightEle-1].zmax-MD->Ele[MD->Riv[i].RightEle-1].zmin)+MD->DummyY[MD->Riv[i].RightEle-1 + 2*MD->NumEle])-MD->Riv[i].zmin):0;
/* This is head in neighboring cell represention */
Avg_Y_Sub = MD->Ele[MD->Riv[i].RightEle-1].zmin>MD->Riv[i].zmin?MD->DummyY[MD->Riv[i].RightEle-1 + 2*MD->NumEle]:((MD->Ele[MD->Riv[i].RightEle-1].zmin+MD->DummyY[MD->Riv[i].RightEle-1 + 2*MD->NumEle])>MD->Riv[i].zmin?(MD->Ele[MD->Riv[i].RightEle-1].zmin+MD->DummyY[MD->Riv[i].RightEle-1 + 2*MD->NumEle]-MD->Riv[i].zmin):0);
// Avg_Y_Sub=avgY(MD->Riv[i].zmin,MD->Riv[i].zmin,MD->DummyY[i+3*MD->NumEle],Avg_Y_Sub);
Avg_Y_Sub=avgY(Dif_Y_Sub,MD->DummyY[i+3*MD->NumEle],Avg_Y_Sub);
effK=MD->Riv[i].KsatH;
Distance = sqrt(pow((MD->Riv[i].x - MD->Ele[MD->Riv[i].RightEle - 1].x), 2) + pow((MD->Riv[i].y - MD->Ele[MD->Riv[i].RightEle - 1].y), 2));
Grad_Y_Sub = Dif_Y_Sub/Distance;
/* take care of macropore effect */
inabr=MD->Riv[i].RightEle-1;
AquiferDepth=(MD->Ele[inabr].zmax-MD->Ele[inabr].zmin);
effKnabr=effKH(MD->Ele[inabr].Macropore,MD->DummyY[inabr+2*MD->NumEle],AquiferDepth,MD->Ele[inabr].macD,MD->Ele[inabr].macKsatH,MD->Ele[inabr].vAreaF,MD->Ele[inabr].KsatH);
Avg_Ksat=0.5*(effK+effKnabr);
MD->FluxRiv[i][5]=MD->Riv[i].Length*Avg_Ksat*Grad_Y_Sub*Avg_Y_Sub;
/***********************************************************************************/
/* Lateral Flux between rectangular element (beneath river) and triangular element */
/***********************************************************************************/
Dif_Y_Sub = (MD->DummyY[i+3*MD->NumEle+MD->NumRiv] + MD->Ele[i+MD->NumEle].zmin) - (MD->DummyY[MD->Riv[i].RightEle-1 + 2*MD->NumEle] + MD->Ele[MD->Riv[i].RightEle-1].zmin);
// Avg_Y_Sub=((MD->DummyY[MD->Riv[i].RightEle-1 + 2*MD->NumEle]+MD->Ele[MD->Riv[i].RightEle-1].zmin-MD->Riv[i].zmin)>0)?MD->Riv[i].zmin-MD->Ele[MD->Riv[i].RightEle-1].zmin:MD->DummyY[MD->Riv[i].RightEle-1 + 2*MD->NumEle];
/* This is head at river edge representation */
// Avg_Y_Sub = ((MD->Riv[i].zmax-(MD->Ele[MD->Riv[i].RightEle-1].zmax-MD->Ele[MD->Riv[i].RightEle-1].zmin)+MD->DummyY[MD->Riv[i].RightEle-1 + 2*MD->NumEle])>MD->Riv[i].zmin)?MD->Riv[i].zmin-(MD->Riv[i].zmax-(MD->Ele[MD->Riv[i].RightEle-1].zmax-MD->Ele[MD->Riv[i].RightEle-1].zmin)):MD->DummyY[MD->Riv[i].RightEle-1 + 2*MD->NumEle];
/* This is head in neighboring cell represention */
Avg_Y_Sub = MD->Ele[MD->Riv[i].RightEle-1].zmin>MD->Riv[i].zmin?0:((MD->Ele[MD->Riv[i].RightEle-1].zmin+MD->DummyY[MD->Riv[i].RightEle-1 + 2*MD->NumEle])>MD->Riv[i].zmin?(MD->Riv[i].zmin-MD->Ele[MD->Riv[i].RightEle-1].zmin):MD->DummyY[MD->Riv[i].RightEle-1 + 2*MD->NumEle]);
// Avg_Y_Sub=avgY(MD->Ele[i+MD->NumEle].zmin,MD->Ele[MD->Riv[i].RightEle-1].zmin,MD->DummyY[i+3*MD->NumEle+MD->NumRiv],Avg_Y_Sub);
Avg_Y_Sub=avgY(Dif_Y_Sub,MD->DummyY[i+3*MD->NumEle+MD->NumRiv],Avg_Y_Sub);
AquiferDepth=(MD->Ele[i+MD->NumEle].zmax-MD->Ele[i+MD->NumEle].zmin);
// effK=MD->Ele[i+MD->NumEle].KsatH;
effK=0.5*(effKH(MD->Ele[MD->Riv[i].LeftEle-1].Macropore,MD->DummyY[MD->Riv[i].LeftEle-1+2*MD->NumEle],MD->Ele[MD->Riv[i].LeftEle-1].zmax-MD->Ele[MD->Riv[i].LeftEle-1].zmin,MD->Ele[MD->Riv[i].LeftEle-1].macD,MD->Ele[MD->Riv[i].LeftEle-1].macKsatH,MD->Ele[MD->Riv[i].LeftEle-1].vAreaF,MD->Ele[MD->Riv[i].LeftEle-1].KsatH)+effKH(MD->Ele[MD->Riv[i].RightEle-1].Macropore,MD->DummyY[MD->Riv[i].RightEle-1+2*MD->NumEle],MD->Ele[MD->Riv[i].RightEle-1].zmax-MD->Ele[MD->Riv[i].RightEle-1].zmin,MD->Ele[MD->Riv[i].RightEle-1].macD,MD->Ele[MD->Riv[i].RightEle-1].macKsatH,MD->Ele[MD->Riv[i].RightEle-1].vAreaF,MD->Ele[MD->Riv[i].RightEle-1].KsatH));
inabr=MD->Riv[i].RightEle-1;
nabrAqDepth=(MD->Ele[inabr].zmax-MD->Ele[inabr].zmin);
effKnabr=effKH(MD->Ele[inabr].Macropore,MD->DummyY[inabr+2*MD->NumEle],nabrAqDepth,MD->Ele[inabr].macD,MD->Ele[inabr].macKsatH,MD->Ele[inabr].vAreaF,MD->Ele[inabr].KsatH);
Avg_Ksat=0.5*(effK+effKnabr);
Grad_Y_Sub = Dif_Y_Sub/Distance; /* take care of macropore effect */
MD->FluxRiv[i][8]=MD->Riv[i].Length*Avg_Ksat*Grad_Y_Sub*Avg_Y_Sub;
/* replace flux item */
for(j=0; j < 3; j++)
{
if(MD->Ele[MD->Riv[i].RightEle - 1].nabr[j] == MD->Riv[i].LeftEle)
{
MD->FluxSurf[MD->Riv[i].RightEle - 1][j] = -MD->FluxRiv[i][3];
MD->FluxSub[MD->Riv[i].RightEle - 1][j] = -MD->FluxRiv[i][5];
MD->FluxSub[MD->Riv[i].RightEle - 1][j] = MD->FluxSub[MD->Riv[i].RightEle - 1][j] -MD->FluxRiv[i][8];
break;
}
}
}
Avg_Wid=CS_AreaOrPerem(MD->Riv_Shape[MD->Riv[i].shape - 1].interpOrd,MD->DummyY[i + 3*MD->NumEle],MD->Riv[i].coeff,3);
Dif_Y_Riv=(MD->Riv[i].zmin-(MD->DummyY[i + 3*MD->NumEle+MD->NumRiv]+MD->Ele[i+MD->NumEle].zmin))>0?MD->DummyY[i + 3*MD->NumEle]:MD->DummyY[i + 3*MD->NumEle]+MD->Riv[i].zmin-(MD->DummyY[i + 3*MD->NumEle+MD->NumRiv]+MD->Ele[i+MD->NumEle].zmin);
Grad_Y_Riv=Dif_Y_Riv/MD->Riv[i].bedThick;
MD->FluxRiv[i][6]=MD->Riv[i].KsatV*Avg_Wid*MD->Riv[i].Length*Grad_Y_Riv;
}
for(i=0; i<MD->NumEle; i++)
{
for(j=0; j<3; j++)
{
DY[i] = DY[i] - MD->FluxSurf[i][j]/MD->Ele[i].area;
DY[i+2*MD->NumEle] = DY[i+2*MD->NumEle] - MD->FluxSub[i][j]/MD->Ele[i].area;
}
DY[i+MD->NumEle] = DY[i+MD->NumEle]/(MD->Ele[i].Porosity*UNIT_C);
DY[i+2*MD->NumEle] = DY[i+2*MD->NumEle]/(MD->Ele[i].Porosity*UNIT_C);
DY[i]=DY[i]/(UNIT_C);
}
for(i=0; i<MD->NumRiv; i++)
{
for(j=0;j<=6;j++)
{
/* Note the limitation due to d(v)/dt=a*dy/dt+y*da/dt for CS other than rectangle */
DY[i+3*MD->NumEle] = DY[i+3*MD->NumEle]-MD->FluxRiv[i][j]/(MD->Riv[i].Length*CS_AreaOrPerem(MD->Riv_Shape[MD->Riv[i].shape - 1].interpOrd,MD->Riv[i].depth,MD->Riv[i].coeff,3));
}
DY[i+3*MD->NumEle] = DY[i+3*MD->NumEle]/(UNIT_C);
DY[i+3*MD->NumEle+MD->NumRiv] = DY[i+3*MD->NumEle+MD->NumRiv] -MD->FluxRiv[i][7] -MD->FluxRiv[i][8]-MD->FluxRiv[i][9] -MD->FluxRiv[i][10]+MD->FluxRiv[i][6];
DY[i+3*MD->NumEle+MD->NumRiv] = DY[i+3*MD->NumEle+MD->NumRiv]/(MD->Ele[i+MD->NumEle].Porosity*MD->Riv[i].Length*CS_AreaOrPerem(MD->Riv_Shape[MD->Riv[i].shape - 1].interpOrd,MD->Riv[i].depth,MD->Riv[i].coeff,3)*UNIT_C);
}
}
realtype Interpolation(TSD *Data, realtype t)
{
int i, success;
realtype result;
i=Data->iCounter;
success = 0;
t=t/(UNIT_C);
while(i<Data->length && t>Data->TS[i][0])
{
i++;
}
if(i==0)
{
/* t is smaller than the 1st node */
result = Data->TS[i][1];
}
else if(i >= Data->length)
{
result = Data->TS[i-1][1];
}
else
{
result = ((Data->TS[i][0]-t)*Data->TS[i-1][1] + (t-Data->TS[i-1][0])*Data->TS[i][1])/(Data->TS[i][0]-Data->TS[i-1][0]);
success = 1;
}
if(success == 0)
{
/*
printf("\nWarning: Extrapolation is used ...\n");
*/
}
return result;
}