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Friction.cpp
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Friction.cpp
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/*!\file Friction.c
* \brief: implementation of the Friction object
*/
/*Headers:*/
/*{{{*/
#ifdef HAVE_CONFIG_H
#include <config.h>
#else
#error "Cannot compile with HAVE_CONFIG_H symbol! run configure first!"
#endif
#include "../classes.h"
#include "shared/shared.h"
#include "../../modules/InputUpdateFromConstantx/InputUpdateFromConstantx.h"
/*}}}*/
/*Constructors/destructors*/
Friction::Friction(){/*{{{*/
this->element=NULL;
this->law = 0;
this->linearize = 0;
this->apply_dim = 1.;
this->domaintype = -1;
this->vx_input=NULL;
this->vy_input=NULL;
this->vz_input=NULL;
this->alpha2_list=NULL;
this->alpha2_complement_list=NULL;
}
/*}}}*/
Friction::Friction(Element* element_in){/*{{{*/
/* Determine the dimension according to the domain type automatically.
* There are exceptions, e.g. HO, which needs the user to specify the dimension used in Friciton.*/
/*Intermediaries*/
int linearization_type;
this->element=element_in;
this->linearize = 0;
/* Load necessary parameters */
element_in->FindParam(&this->law,FrictionLawEnum);
element_in->FindParam(&this->domaintype,DomainTypeEnum);
/* Load VxBase and VyBase for this special case */
switch(this->domaintype){
case Domain2DhorizontalEnum:
this->apply_dim = 2.;
this->vx_input = element_in->GetInput(VxBaseEnum); _assert_(this->vx_input);
this->vy_input = element_in->GetInput(VyBaseEnum); _assert_(this->vy_input);
this->vz_input = NULL;
break;
case Domain2DverticalEnum:
this->apply_dim = 2.;
this->vx_input = element_in->GetInput(VxEnum); _assert_(this->vx_input);
this->vy_input = element_in->GetInput(VyEnum); _assert_(this->vy_input);
this->vz_input = NULL;
break;
case Domain3DEnum:
this->apply_dim = 3.;
this->vx_input = element_in->GetInput(VxEnum); _assert_(this->vx_input);
this->vy_input = element_in->GetInput(VyEnum); _assert_(this->vy_input);
this->vz_input = element_in->GetInput(VzEnum); _assert_(this->vz_input);
break;
default: _error_("mesh "<<EnumToStringx(domaintype)<<" not supported yet");
}
if(this->law==1 || this->law==2){
element_in->FindParam(&linearization_type,FrictionLinearizeEnum);
if(linearization_type==0){
/*Don't do anything*/
}
else if(linearization_type==1){
int numvertices = this->element->GetNumberOfVertices();
this->alpha2_list = xNew<IssmDouble>(numvertices);
this->alpha2_complement_list = xNew<IssmDouble>(numvertices);
Gauss* gauss=this->element->NewGauss();
for(int iv=0;iv<numvertices;iv++){
gauss->GaussVertex(iv);
this->GetAlpha2(&this->alpha2_list[iv], gauss);
this->GetAlphaComplement(&this->alpha2_complement_list[iv], gauss);
}
this->linearize = linearization_type; /*Change back, we are now all set!*/
delete gauss;
}
else if(linearization_type==2){
this->alpha2_list = xNew<IssmDouble>(1);
this->alpha2_complement_list = xNew<IssmDouble>(1);
Gauss* gauss=element->NewGauss(1); gauss->GaussPoint(0);
this->GetAlpha2(&this->alpha2_list[0], gauss);
this->GetAlphaComplement(&this->alpha2_complement_list[0], gauss);
this->linearize = linearization_type; /*Change back, we are now all set!*/
delete gauss;
}
else{
_error_("not supported yet");
}
}
}
/*}}}*/
Friction::Friction(Element* element_in,int dim) : Friction(element_in) {/*{{{*/
this->apply_dim = reCast<IssmPDouble>(dim);
}
/*}}}*/
Friction::Friction(Element* element_in,IssmPDouble dim) : Friction(element_in) {/*{{{*/
this->apply_dim = dim;
}
/*}}}*/
Friction::~Friction(){/*{{{*/
if(this->linearize){
xDelete<IssmDouble>(this->alpha2_list);
xDelete<IssmDouble>(this->alpha2_complement_list);
}
}
/*}}}*/
/*methods: */
void Friction::Echo(void){/*{{{*/
_printf_("Friction:\n");
_printf_(" Domain type: " << this->domaintype<< "\n");
}
/*}}}*/
void Friction::GetAlphaComplement(IssmDouble* palpha_complement, Gauss* gauss){/*{{{*/
if(this->linearize==0){
switch(this->law){
case 1:
GetAlphaViscousComplement(palpha_complement,gauss);
break;
case 2:
GetAlphaWeertmanComplement(palpha_complement, gauss);
break;
case 3:
GetAlphaHydroComplement(palpha_complement,gauss);
break;
case 4:
GetAlphaTempComplement(palpha_complement,gauss);
break;
case 11:
GetAlphaSchoofComplement(palpha_complement,gauss);
break;
case 13:
GetAlphaCoulomb2Complement(palpha_complement,gauss);
break;
case 14:
GetAlphaRegCoulombComplement(palpha_complement,gauss);
break;
default:
_error_("not supported");
}
}
else if(this->linearize==1){
this->element->ValueP1OnGauss(palpha_complement, this->alpha2_complement_list, gauss);
}
else if(this->linearize==2){
*palpha_complement = this->alpha2_complement_list[0];
}
else{
_error_("not supported yet");
}
/*Checks*/
_assert_(!xIsNan<IssmDouble>(*palpha_complement));
_assert_(!xIsInf<IssmDouble>(*palpha_complement));
}/*}}}*/
void Friction::GetAlphaHydroComplement(IssmDouble* palpha_complement, Gauss* gauss){/*{{{*/
/*diverse: */
IssmDouble q_exp;
IssmDouble C_param;
IssmDouble As;
IssmDouble n;
IssmDouble alpha;
IssmDouble Chi,Gamma;
IssmDouble alpha_complement;
/*Recover parameters: */
element->GetInputValue(&q_exp,gauss,FrictionQEnum);
element->GetInputValue(&C_param,gauss,FrictionCEnum);
element->GetInputValue(&As,gauss,FrictionAsEnum);
element->GetInputValue(&n,gauss,MaterialsRheologyNEnum);
/*Get effective pressure and velocity magnitude*/
IssmDouble Neff = EffectivePressure(gauss);
IssmDouble vmag = VelMag(gauss);
if (q_exp==1){
alpha=1;
}
else{
alpha=(pow(q_exp-1,q_exp-1))/pow(q_exp,q_exp);
}
Chi = vmag/(pow(C_param,n)*pow(Neff,n)*As);
Gamma = (Chi/(1.+alpha*pow(Chi,q_exp)));
/*Check to prevent dividing by zero if vmag==0*/
if(vmag==0.) alpha_complement=0.;
else if(Neff==0.) alpha_complement=0.;
else alpha_complement=-(C_param*Neff/(n*vmag)) *
pow(Gamma,((1.-n)/n)) *
(Gamma/As - (alpha*q_exp*pow(Chi,q_exp-1.)* Gamma * Gamma/As));
/*Assign output pointers:*/
*palpha_complement=alpha_complement;
}
/*}}}*/
void Friction::GetAlphaTempComplement(IssmDouble* palpha_complement, Gauss* gauss){/*{{{*/
/*Here, we want to parameterize the friction as a function of temperature
*
* alpha2 = alpha2_viscous * 1/f(T)
*
* where f(T) = exp((T-Tpmp)/gamma)
*/
/*Intermediaries: */
IssmDouble f,T,pressure,Tpmp,gamma;
IssmDouble alpha_complement;
/*Get viscous part*/
this->GetAlphaViscousComplement(&alpha_complement,gauss);
/*Get pressure melting point (Tpmp) for local pressure and get current temperature*/
element->GetInputValue(&T,gauss,TemperatureEnum);
element->GetInputValue(&pressure,gauss,PressureEnum);
Tpmp = element->TMeltingPoint(pressure);
/*Compute scaling parameter*/
element->parameters->FindParam(&gamma,FrictionGammaEnum);
alpha_complement = alpha_complement/ (exp((T-Tpmp)/gamma)+1e-3);
/*Assign output pointers:*/
*palpha_complement=alpha_complement;
}/*}}}*/
void Friction::GetAlphaViscousComplement(IssmDouble* palpha_complement, Gauss* gauss){/*{{{*/
/* FrictionGetAlpha2 computes alpha2= drag^2 * Neff ^r * vel ^(s-1), with Neff=rho_ice*g*thickness+rho_ice*g*base, r=q/p and s=1/p.
* FrictionGetAlphaComplement is used in control methods on drag, and it computes:
* alpha_complement= Neff ^r * vel ^(s-1)*/
/*diverse: */
IssmDouble r,s;
IssmDouble drag_p,drag_q;
IssmDouble drag_coefficient;
IssmDouble alpha_complement;
/*Recover parameters: */
element->GetInputValue(&drag_p,gauss,FrictionPEnum);
element->GetInputValue(&drag_q,gauss,FrictionQEnum);
element->GetInputValue(&drag_coefficient, gauss,FrictionCoefficientEnum);
/*compute r and q coefficients: */
r=drag_q/drag_p;
s=1./drag_p;
/*Get effective pressure*/
IssmDouble Neff = EffectivePressure(gauss);
IssmDouble vmag = VelMag(gauss);
if(s==1.){
/*This is to make AD happy and avoid 0^0*/
alpha_complement=pow(Neff,r);
}
else{
/*Check to prevent dividing by zero if vmag==0*/
if(vmag==0. && (s-1.)<0.) alpha_complement=0.;
else alpha_complement=pow(Neff,r)*pow(vmag,(s-1.));
}
/*Assign output pointers:*/
*palpha_complement=alpha_complement;
}
/*}}}*/
void Friction::GetAlphaSchoofComplement(IssmDouble* palpha_complement, Gauss* gauss){/*{{{*/
/* Compute the complement of Schoof's law for inversion
* d alpha2
* -------- = |u_b|^(m-1) *(1+ (C/(Cmax N))^(1/m)|u_b|)^(-m-1)
* dC
*/
/*diverse: */
IssmDouble m,Cmax;
IssmDouble C, coeff;
IssmDouble alpha_complement;
/*Recover parameters: */
element->GetInputValue(&m,gauss,FrictionMEnum);
element->GetInputValue(&Cmax,gauss,FrictionCmaxEnum);
element->GetInputValue(&coeff, gauss,FrictionCEnum);
C = coeff*coeff;
/*Get effective pressure*/
IssmDouble Neff = EffectivePressure(gauss);
IssmDouble vmag = VelMag(gauss);
/*Check to prevent dividing by zero if vmag==0*/
if((vmag==0.) || (Neff == 0.)) {
alpha_complement=0.;
}
else {
alpha_complement= pow(vmag, m-1.)*pow((1 + pow(C/(Cmax*Neff),1./m)*vmag), -m-1.);
}
/*Assign output pointers:*/
*palpha_complement=alpha_complement;
}/*}}}*/
void Friction::GetAlphaWeertmanComplement(IssmDouble* palpha_complement, Gauss* gauss){/*{{{*/
/* Compute the complement of Weertman's law for inversion
* alpha2 = C^2 * vel^(1/m-1)
* alpha_complement = vel^(1/m-1)
*/
/*diverse: */
IssmDouble m;
IssmDouble alpha_complement;
/*Recover parameters: */
element->GetInputValue(&m,gauss,FrictionMEnum);
/*Get effective pressure*/
IssmDouble vmag = VelMag(gauss);
/*Check to prevent dividing by zero if vmag==0*/
if(vmag==0. && (1./m-1.)<0.) alpha_complement=0.;
else alpha_complement= pow(vmag, 1.0/m-1.);
/*Assign output pointers:*/
*palpha_complement=alpha_complement;
}/*}}}*/
void Friction::GetAlphaRegCoulombComplement(IssmDouble* palpha_complement, Gauss* gauss){/*{{{*/
/* Compute the complement of regularised Coulombs law for inversion
* d alpha2
* -------- = |u_b|^(1/m-1) * (|u_b|/u_0 + 1)^(-1/m)
* dC
*/
/*diverse: */
IssmDouble m, u0;
IssmDouble alpha_complement;
/*Recover parameters: */
element->GetInputValue(&m,gauss,FrictionMEnum);
element->parameters->FindParam(&u0,FrictionU0Enum);
/*Get velocity magnitude*/
IssmDouble ub = VelMag(gauss);
/*Check to prevent dividing by zero if vmag==0*/
if(ub==0.) {
alpha_complement=0.;
}
else {
/*Compute friction complement*/
alpha_complement= (pow(ub,1./m-1.)) / pow(ub/u0 + 1.,1./m);
}
/*Assign output pointers:*/
*palpha_complement=alpha_complement;
}/*}}}*/
void Friction::GetAlphaCoulomb2Complement(IssmDouble* palpha_complement, Gauss* gauss){/*{{{*/
/* Compute the complement of Cornford's friction law for inversion
* d alpha2
* ------ = (C*N*v^m)/(C^(2/m)*v + (N/2)^(1/m))^m - (C^(2/m - 1)*C^2*N*v*v^m)/(C^(2/m)*v + (N/2)^(1/m))^(m + 1)
* dC
*/
/*diverse: */
IssmDouble m, C;
IssmDouble alpha_complement;
/*Recover parameters: */
element->GetInputValue(&C,gauss,FrictionCEnum);
element->GetInputValue(&m,gauss,FrictionMEnum);
/*Get effective pressure and velocity magnitude*/
IssmDouble N = EffectivePressure(gauss);
IssmDouble v = VelMag(gauss);
/*Compute alpha*/
if(v<1e-10){
alpha_complement = 0.;
}
else{
alpha_complement= pow(0.5*N,1./m+1)* pow(v,m-1.) * pow(v*pow(C,1./m) +pow(0.5*N,1./m) ,-m-1.);
}
/*Assign output pointers:*/
*palpha_complement=alpha_complement/2.;
}/*}}}*/
void Friction::GetAlpha2(IssmDouble* palpha2, Gauss* gauss){/*{{{*/
if(this->linearize==0){
switch(this->law){
case 1:
GetAlpha2Viscous(palpha2,gauss);
break;
case 2:
GetAlpha2Weertman(palpha2,gauss);
break;
case 3:
GetAlpha2Hydro(palpha2,gauss);
break;
case 4:
GetAlpha2Temp(palpha2,gauss);
break;
case 5:
GetAlpha2WaterLayer(palpha2,gauss);
break;
case 6:
GetAlpha2WeertmanTemp(palpha2,gauss);
break;
case 7:
GetAlpha2Coulomb(palpha2,gauss);
break;
case 8:
GetAlpha2Shakti(palpha2,gauss);
break;
case 9:
GetAlpha2Josh(palpha2,gauss);
break;
case 10:
GetAlpha2PISM(palpha2,gauss);
break;
case 11:
GetAlpha2Schoof(palpha2,gauss);
break;
case 12:
GetAlpha2Tsai(palpha2,gauss);
break;
case 13:
GetAlpha2Coulomb2(palpha2,gauss);
break;
case 14:
GetAlpha2RegCoulomb(palpha2,gauss);
break;
case 15:
GetAlpha2RegCoulomb2(palpha2,gauss);
break;
default:
_error_("Friction law "<< this->law <<" not supported");
}
}
else if(this->linearize==1){
this->element->ValueP1OnGauss(palpha2, this->alpha2_list, gauss);
}
else if(this->linearize==2){
*palpha2 = this->alpha2_list[0];
}
else{
_error_("not supported yet");
}
/*Checks*/
_assert_(!xIsNan<IssmDouble>(*palpha2));
_assert_(!xIsInf<IssmDouble>(*palpha2));
_assert_(*palpha2>=0);
}/*}}}*/
void Friction::GetAlpha2Coulomb(IssmDouble* palpha2, Gauss* gauss){/*{{{*/
/*This routine calculates the basal friction coefficient
alpha2= drag^2 * Neff ^r * | vel | ^(s-1), with Neff=rho_ice*g*thickness+rho_ice*g*base, r=q/p and s=1/p
alpha2= min(drag^2 * Neff ^r * | vel | ^(s-1), drag_coulomb^2 * Neff*/
/*diverse: */
IssmDouble r,s;
IssmDouble drag_p, drag_q;
IssmDouble drag_coefficient,drag_coefficient_coulomb;
IssmDouble alpha2,alpha2_coulomb;
/*Recover parameters: */
element->GetInputValue(&drag_p,gauss,FrictionPEnum);
element->GetInputValue(&drag_q,gauss,FrictionQEnum);
element->GetInputValue(&drag_coefficient, gauss,FrictionCoefficientEnum);
element->GetInputValue(&drag_coefficient_coulomb, gauss,FrictionCoefficientcoulombEnum);
IssmDouble rho_water = element->FindParam(MaterialsRhoSeawaterEnum);
IssmDouble rho_ice = element->FindParam(MaterialsRhoIceEnum);
IssmDouble gravity = element->FindParam(ConstantsGEnum);
//compute r and q coefficients: */
r=drag_q/drag_p;
s=1./drag_p;
/*Get effective pressure*/
bool ispwHydro,ispwStochastic;
IssmDouble Neff;
element->parameters->FindParam(&ispwStochastic,StochasticForcingIsWaterPressureEnum);
element->parameters->FindParam(&ispwHydro,HydrologyIsWaterPressureArmaEnum);
if(ispwStochastic || ispwHydro){
/*Retrieve pre-computed water pressure and compute ice pressure*/
IssmDouble p_ice,p_water,Neff_limit;
element->GetInputValue(&p_water,gauss,FrictionWaterPressureEnum);
element->parameters->FindParam(&Neff_limit,FrictionEffectivePressureLimitEnum);
p_ice = IcePressure(gauss);
Neff = max(Neff_limit*p_ice, p_ice - p_water);
}
else{
/*Compute effective pressure directly*/
Neff = EffectivePressure(gauss);
}
/*Get velocity magnitude*/
IssmDouble vmag = VelMag(gauss);
if(s==1.){
/*This is to make AD happy and avoid 0^0*/
alpha2=drag_coefficient*drag_coefficient*pow(Neff,r);
}
else{
/*Check to prevent dividing by zero if vmag==0*/
if(vmag==0. && (s-1.)<0.) alpha2=0.;
else alpha2=drag_coefficient*drag_coefficient*pow(Neff,r)*pow(vmag,(s-1.));
}
if(vmag==0.){
alpha2_coulomb=0.;
}
else{
//alpha2_coulomb=drag_coefficient_coulomb*drag_coefficient_coulomb*rho_ice*gravity*max(0.,thickness-floatation_thickness)/vmag;
alpha2_coulomb=drag_coefficient_coulomb*drag_coefficient_coulomb*Neff/vmag;
}
if(alpha2_coulomb<alpha2) alpha2=alpha2_coulomb;
/*Assign output pointers:*/
*palpha2=alpha2;
}/*}}}*/
void Friction::GetAlpha2Hydro(IssmDouble* palpha2, Gauss* gauss){/*{{{*/
/*This routine calculates the basal friction coefficient
Based on Gagliardini 2007, needs a good effective pressure computation
Not tested so far so use at your own risks
alpha2= NeffC[Chi/(1+alpha*Chi^q)]^(1/n)*|vel|^(-1) with
Chi=|vel|/(C^n*Neff^n*As)
alpha=(q-1)^(q-1)/q^q */
/*diverse: */
IssmDouble q_exp;
IssmDouble C_param;
IssmDouble As;
IssmDouble n;
IssmDouble alpha;
IssmDouble Chi,Gamma;
IssmDouble alpha2;
/*Recover parameters: */
element->GetInputValue(&q_exp,gauss,FrictionQEnum);
element->GetInputValue(&C_param,gauss,FrictionCEnum);
element->GetInputValue(&As,gauss,FrictionAsEnum);
element->GetInputValue(&n,gauss,MaterialsRheologyNEnum);
/*Get effective pressure*/
IssmDouble Neff = EffectivePressure(gauss);
IssmDouble vmag = VelMag(gauss);
//compute alpha and Chi coefficients: */
if (q_exp==1){
alpha=1;
}
else{
alpha=(pow(q_exp-1,q_exp-1))/pow(q_exp,q_exp);
}
Chi=vmag/(pow(C_param,n)*pow(Neff,n)*As);
Gamma=(Chi/(1. + alpha * pow(Chi,q_exp)));
/*Check to prevent dividing by zero if vmag==0*/
if(vmag==0.) alpha2=0.;
else if (Neff==0) alpha2=0.0;
else alpha2=Neff * C_param * pow(Gamma,1./n) * pow(vmag,-1);
/*Assign output pointers:*/
*palpha2=alpha2;
}/*}}}*/
void Friction::GetAlpha2Shakti(IssmDouble* palpha2, Gauss* gauss){/*{{{*/
/* FrictionGetAlpha2 computes alpha2= drag^2 * Neff, with Neff=rho_ice*g*thickness+rho_ice*g*(head-base)*/
/*diverse: */
IssmDouble pressure_ice,pressure_water;
IssmDouble Neff;
IssmDouble drag_coefficient;
IssmDouble base,thickness,head,sealevel;
IssmDouble alpha2;
/*Recover parameters: */
element->GetInputValue(&thickness, gauss,ThicknessEnum);
element->GetInputValue(&base, gauss,BaseEnum);
element->GetInputValue(&head, gauss,HydrologyHeadEnum);
element->GetInputValue(&sealevel, gauss,SealevelEnum);
element->GetInputValue(&drag_coefficient, gauss,FrictionCoefficientEnum);
IssmDouble rho_water = element->FindParam(MaterialsRhoFreshwaterEnum);
IssmDouble rho_ice = element->FindParam(MaterialsRhoIceEnum);
IssmDouble gravity = element->FindParam(ConstantsGEnum);
//From base and thickness, compute effective pressure when drag is viscous:
pressure_ice = rho_ice*gravity*thickness;
pressure_water = rho_water*gravity*(head-base+sealevel);
Neff=pressure_ice-pressure_water;
if(Neff<0.) Neff=0.;
alpha2=drag_coefficient*drag_coefficient*Neff;
/*Assign output pointers:*/
*palpha2=alpha2;
}
/*}}}*/
void Friction::GetAlpha2Temp(IssmDouble* palpha2, Gauss* gauss){/*{{{*/
/*Here, we want to parameterize the friction as a function of temperature
*
* alpha2 = alpha2_viscous * 1/f(T)
*
* where f(T) = exp((T-Tpmp)/gamma)
*/
/*Intermediaries: */
IssmDouble f,T,pressure,Tpmp,gamma;
IssmDouble alpha2;
/*Get viscous part*/
this->GetAlpha2Viscous(&alpha2,gauss);
/*Get pressure melting point (Tpmp) for local pressure and get current temperature*/
element->GetInputValue(&T,gauss,TemperatureEnum);
element->GetInputValue(&pressure,gauss,PressureEnum);
Tpmp = element->TMeltingPoint(pressure);
/*Compute scaling parameter*/
element->parameters->FindParam(&gamma,FrictionGammaEnum);
alpha2 = alpha2 / (exp((T-Tpmp)/gamma)+1e-3);
/*Assign output pointers:*/
*palpha2=alpha2;
}/*}}}*/
void Friction::GetAlpha2Josh(IssmDouble* palpha2, Gauss* gauss){/*{{{*/
/*Here, we want to parameterize the friction as a function of temperature
*
* alpha2 = alpha2_viscous * 1/f(T)
*
* where f(T) = exp((T-Tpmp)/gamma)
*/
/*Intermediaries: */
IssmDouble T,Tpmp,deltaT,deltaTref,pressure,diff,drag_coefficient;
IssmDouble alpha2,time,gamma,ref,alp_new,alphascaled;
const IssmDouble yts = 365*24*3600.;
/*Get viscous part*/
this->GetAlpha2Viscous(&alpha2,gauss);
/*Get delta Refs*/
element->GetInputValue(&deltaTref,gauss,FrictionPressureAdjustedTemperatureEnum);
element->GetInputValue(&drag_coefficient, gauss,FrictionCoefficientEnum);
/*New*/
/*element->GetInputValue(&deltaTrefsfc,gauss,FrictionSurfaceTemperatureEnum);
* element->GetInputValue(&Tpdd,gauss,TemperaturePDDEnum);
* */
/*Compute delta T*/
element->GetInputValue(&T,gauss,TemperatureEnum);
element->GetInputValue(&pressure,gauss,PressureEnum);
Tpmp = element->TMeltingPoint(pressure);
deltaT = T-Tpmp;
/*Compute gamma*/
element->parameters->FindParam(&time,TimeEnum);
element->parameters->FindParam(&gamma,FrictionGammaEnum);
ref = exp(deltaTref/gamma);
alp_new = ref/exp(deltaT/gamma);
alphascaled = sqrt(alp_new)*drag_coefficient;
if (alphascaled > 300) alp_new = (300/drag_coefficient)*(300/drag_coefficient);
alp_new=alp_new*alpha2;
/*Assign output pointers:*/
*palpha2=alp_new;
}/*}}}*/
void Friction::GetAlpha2Viscous(IssmDouble* palpha2, Gauss* gauss){/*{{{*/
/*This routine calculates the basal friction coefficient
alpha2= drag^2 * Neff ^r * | vel | ^(s-1), with Neff=rho_ice*g*thickness+rho_ice*g*base, r=q/p and s=1/p**/
/*diverse: */
IssmDouble r,s;
IssmDouble drag_p, drag_q;
IssmDouble drag_coefficient;
IssmDouble alpha2;
/*Recover parameters: */
element->GetInputValue(&drag_p,gauss,FrictionPEnum);
element->GetInputValue(&drag_q,gauss,FrictionQEnum);
element->GetInputValue(&drag_coefficient, gauss,FrictionCoefficientEnum);
/*compute r and q coefficients: */
r=drag_q/drag_p;
s=1./drag_p;
/*Get effective pressure and basal velocity*/
IssmDouble vmag = VelMag(gauss);
bool ispwHydro,ispwStochastic;
IssmDouble Neff;
element->parameters->FindParam(&ispwStochastic,StochasticForcingIsWaterPressureEnum);
element->parameters->FindParam(&ispwHydro,HydrologyIsWaterPressureArmaEnum);
if(ispwStochastic || ispwHydro){
/*Retrieve pre-computed water pressure and compute ice pressure*/
IssmDouble p_ice,p_water,Neff_limit;
element->GetInputValue(&p_water,gauss,FrictionWaterPressureEnum);
element->parameters->FindParam(&Neff_limit,FrictionEffectivePressureLimitEnum);
p_ice = IcePressure(gauss);
Neff = max(Neff_limit*p_ice, p_ice - p_water);
}
else{
/*Compute effective pressure directly*/
Neff = EffectivePressure(gauss);
}
/*Check to prevent dividing by zero if vmag==0*/
if(s==1.){
/*This is to make AD happy and avoid 0^0*/
alpha2=drag_coefficient*drag_coefficient*pow(Neff,r);
}
else{
if(vmag==0. && (s-1.)<0.) alpha2=0.;
else alpha2=drag_coefficient*drag_coefficient*pow(Neff,r)*pow(vmag,(s-1.));
}
/*Assign output pointers:*/
*palpha2=alpha2;
}/*}}}*/
void Friction::GetAlpha2WaterLayer(IssmDouble* palpha2, Gauss* gauss){/*{{{*/
/*This routine calculates the basal friction coefficient
alpha2= drag^2 * Neff ^r * | vel | ^(s-1), with Neff=rho_ice*g*thickness+rho_ice*g*base, r=q/p and s=1/p**/
/*diverse: */
IssmDouble r,s;
IssmDouble drag_p, drag_q;
IssmDouble Neff,F;
IssmDouble thickness,base,sealevel;
IssmDouble drag_coefficient,water_layer;
IssmDouble alpha2;
/*Recover parameters: */
element->parameters->FindParam(&F,FrictionFEnum);
element->GetInputValue(&drag_p,gauss,FrictionPEnum);
element->GetInputValue(&drag_q,gauss,FrictionQEnum);
element->GetInputValue(&thickness, gauss,ThicknessEnum);
element->GetInputValue(&base, gauss,BaseEnum);
element->GetInputValue(&sealevel, gauss,SealevelEnum);
element->GetInputValue(&drag_coefficient, gauss,FrictionCoefficientEnum);
element->GetInputValue(&water_layer, gauss,FrictionWaterLayerEnum);
IssmDouble rho_water = element->FindParam(MaterialsRhoSeawaterEnum);
IssmDouble rho_ice = element->FindParam(MaterialsRhoIceEnum);
IssmDouble gravity = element->FindParam(ConstantsGEnum);
//compute r and q coefficients: */
r=drag_q/drag_p;
s=1./drag_p;
//From base and thickness, compute effective pressure when drag is viscous:
if(base>0) base=0;
if(water_layer==0) Neff=gravity*rho_ice*thickness+gravity*rho_water*(base-sealevel);
else if(water_layer>0) Neff=gravity*rho_ice*thickness*F;
else _error_("negative water layer thickness");
if(Neff<0) Neff=0;
IssmDouble vmag = VelMag(gauss);
if(s==1.){
/*This is to make AD happy and avoid 0^0*/
alpha2=drag_coefficient*drag_coefficient*pow(Neff,r);
}
else{
/*Check to prevent dividing by zero if vmag==0*/
if(vmag==0. && (s-1.)<0.) alpha2=0.;
else alpha2=drag_coefficient*drag_coefficient*pow(Neff,r)*pow(vmag,(s-1.));
}
/*Assign output pointers:*/
*palpha2=alpha2;
}/*}}}*/
void Friction::GetAlpha2Weertman(IssmDouble* palpha2, Gauss* gauss){/*{{{*/
/*This routine calculates the basal friction coefficient alpha2= C^2 |v|^(1/m-1) */
/*diverse: */
IssmDouble C,m;
IssmDouble alpha2;
/*Recover parameters: */
element->GetInputValue(&C,gauss,FrictionCEnum);
element->GetInputValue(&m,gauss,FrictionMEnum);
/*Get velocity magnitude*/
IssmDouble vmag = VelMag(gauss);
/*Check to prevent dividing by zero if vmag==0*/
if(vmag==0. && (1./m-1.)<0.) alpha2=0.;
else alpha2=C*C*pow(vmag,(1./m-1.));
/*Assign output pointers:*/
*palpha2=alpha2;
}/*}}}*/
void Friction::GetAlpha2WeertmanTemp(IssmDouble* palpha2, Gauss* gauss){/*{{{*/
/*Here, we want to parameterize the friction as a function of temperature
*
* alpha2 = alpha2_weertman * 1/f(T)
*
* where f(T) = exp((T-Tpmp)/gamma)
*/
/*Intermediaries: */
IssmDouble f,T,pressure,Tpmp,gamma;
IssmDouble alpha2;
/*Get viscous part*/
this->GetAlpha2Weertman(&alpha2,gauss);
/*Get pressure melting point (Tpmp) for local pressure and get current temperature*/
element->GetInputValue(&T,gauss,TemperatureEnum);
element->GetInputValue(&pressure,gauss,PressureEnum);
Tpmp = element->TMeltingPoint(pressure);
/*Compute scaling parameter*/
element->parameters->FindParam(&gamma,FrictionGammaEnum);
alpha2 = alpha2 / exp((T-Tpmp)/gamma);
/*Assign output pointers:*/
*palpha2=alpha2;
}/*}}}*/
void Friction::GetAlpha2PISM(IssmDouble* palpha2, Gauss* gauss){/*{{{*/
/*Here, we want to parameterize the friction using a pseudoplastic friction law,
* computing the basal shear stress as
*
* alpha2 = tau_c (u_b/(abs(u_b)^(1-q)*u_0^q))
*
* The yield stress tau_c is a function of the effective pressure N
* using a Mohr-Coloumb criterion, so that
* tau_c = tan(phi)*N,
* where phi is the till friction angle, representing sediment strength
*
* The effective pressure is given by Eq. (5) in Aschwanden et al. 2016:
*
* N = delta * P0 * 10^((e_0/Cc)(1-(W/Wmax)))
*
* W is calculated by a non-conserving hydrology model in HydrologyPismAnalysis.cpp
*
* see Aschwanden et al. 2016 and Bueler and Brown, 2009 for more details
*/
/*compute ice overburden pressure P0*/
IssmDouble thickness,base,P0;
element->GetInputValue(&thickness, gauss,ThicknessEnum);
element->GetInputValue(&base, gauss,BaseEnum);
//element->GetInputValue(&sealevel, gauss,SealevelEnum);
IssmDouble rho_ice = element->FindParam(MaterialsRhoIceEnum);
IssmDouble gravity = element->FindParam(ConstantsGEnum);
P0 = gravity*rho_ice*thickness;
/*Compute effective pressure*/
IssmDouble N,delta,W,Wmax,e0,Cc;
element->parameters->FindParam(&delta,FrictionDeltaEnum);
element->parameters->FindParam(&e0,FrictionVoidRatioEnum);
element->GetInputValue(&Cc,gauss,FrictionSedimentCompressibilityCoefficientEnum);
element->GetInputValue(&W,gauss,WatercolumnEnum);
element->GetInputValue(&Wmax,gauss,HydrologyWatercolumnMaxEnum);
/*Check that water column height is within 0 and upper bound, correct if needed*/
if(W>Wmax) W=Wmax;
if(W<0) W=0.;
N = delta*P0*pow(10.,(e0/Cc)*(1.-W/Wmax));
/*Get till friction angles, defined by user [deg]*/
IssmDouble phi;
element->GetInputValue(&phi,gauss,FrictionTillFrictionAngleEnum);
/*Convert till friction angle from user-defined deg to rad, which Matlab uses*/
phi = phi*PI/180.;
/*Compute yield stress following a Mohr-Colomb criterion*/
IssmDouble tau_c = N*tan(phi);
/*Compute basal speed*/
IssmDouble ub;
element->GetInputValue(&ub,gauss,VelEnum);
/*now compute alpha^2*/
IssmDouble u0,q;
element->parameters->FindParam(&u0,FrictionThresholdSpeedEnum);
element->parameters->FindParam(&q,FrictionPseudoplasticityExponentEnum);
IssmDouble alpha2 = tau_c/(pow(ub+1.e-10,1.-q)*pow(u0,q));
/*Assign output pointers:*/
*palpha2=alpha2;
}/*}}}*/
void Friction::GetAlpha2Schoof(IssmDouble* palpha2, Gauss* gauss){/*{{{*/
/*This routine calculates the basal friction coefficient
*
* C^2 |u_b|^(m-1)
* alpha2= __________________________
* (1+(C^2/(Cmax Neff))^1/m |u_b| )^m
*
* */
/*diverse: */
IssmDouble C,Cmax,m,alpha2;
/*Recover parameters: */
element->GetInputValue(&Cmax,gauss,FrictionCmaxEnum);
element->GetInputValue(&C,gauss,FrictionCEnum);
element->GetInputValue(&m,gauss,FrictionMEnum);
/*Get effective pressure*/
bool ispwStochastic;
IssmDouble Neff;
element->parameters->FindParam(&ispwStochastic,StochasticForcingIsWaterPressureEnum);
if(ispwStochastic){
/*Retrieve stochastic water pressure and compute ice pressure*/
IssmDouble p_ice,p_water,Neff_limit;
element->GetInputValue(&p_water,gauss,FrictionWaterPressureEnum);
element->parameters->FindParam(&Neff_limit,FrictionEffectivePressureLimitEnum);
p_ice = IcePressure(gauss);
Neff = max(Neff_limit*p_ice, p_ice - p_water);
}
else{
/*Compute effective pressure directly*/
Neff = EffectivePressure(gauss);
}
/*Get velocity magnitude*/
IssmDouble ub = VelMag(gauss);
/*Compute alpha^2*/
if((ub<1e-10) ||(Neff==0.0)){
alpha2 = 0.;
}
else{
alpha2= (C*C*pow(ub,m-1.)) / pow(1.+ pow(C*C/(Cmax*Neff),1./m)*ub,m);
}
/*Assign output pointers:*/
*palpha2=alpha2;
}/*}}}*/
void Friction::GetAlpha2Tsai(IssmDouble* palpha2, Gauss* gauss){/*{{{*/
/*This routine calculates the basal friction coefficient
*
* alpha2= min(C |ub|^m , f N ) / |ub|
*
* */
/*diverse: */
IssmDouble C,f,m,alpha2;
/*Recover parameters: */
element->GetInputValue(&f,gauss,FrictionfEnum);
element->GetInputValue(&C,gauss,FrictionCEnum);
element->GetInputValue(&m,gauss,FrictionMEnum);
/*Get effective pressure and velocity magnitude*/
IssmDouble N = EffectivePressure(gauss);
IssmDouble ub = VelMag(gauss);
/*Compute alpha^2*/
if(ub<1e-10){
alpha2 = 0.;
}
else{
alpha2= C*pow(ub,m);
if(alpha2>f*N) alpha2 = f*N;
alpha2 = alpha2/ub;
}
/*Assign output pointers:*/
*palpha2=alpha2;
}/*}}}*/
void Friction::GetAlpha2Coulomb2(IssmDouble* palpha2, Gauss* gauss){/*{{{*/
/*This routine calculates the basal friction coefficient
*
* C^2 |u_b|^(m-1) * (.5*N)
* alpha2= ___________________________________
* (C^(2/m) |u_b| + (0.5*N)^(1/m) )^m
*
* */
/*diverse: */
IssmDouble C,m,alpha2;
/*Recover parameters: */
element->GetInputValue(&C,gauss,FrictionCEnum);
element->GetInputValue(&m,gauss,FrictionMEnum);
/*Get effective pressure and velocity magnitude*/