soil_models.hh

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/* 
 * File:   hydro_functions.hh
 * Author: jb
 *
 * Created on May 17, 2010, 1:52 PM
 */
 
#ifndef _HYDRO_FUNCTIONS_HH
#define _HYDRO_FUNCTIONS_HH
 
 
#include "badiff.h"  // for B::d, B::deriv, B::diff, B::getBTypeNameHV, B::o...
#include "fadbad.h"  // for B
namespace internal { class Irmay; }
namespace internal { class VanGenuchten; }
 
 
// todo: 
// objekt por SoilModel - jedna sada primarnich i pomocnych parametru
// konzistentni hydrologicke funkce
//
// potreboval bych mit vice modelu, z orezavanim i bez nej,
// orezavani zpusobuje velke residuum v miste nespojitosti derivace saturace
 
// problem - jak pouzit funktory, FADBAD, aproximace a 
// inverzi (inverze tlak v zav. na vlhkosti)
//
// podrobnejsi vyzkum ohledne hydrologickych funkci
// vodivost vyplyva s kapilarnich modelu (jak presne?)
// co vlhkost?
 
/**
 * One of possibly more classes specifying dependence of the relative conductivity and the relative water content on the
 * pressure head. These functions (@p conductivity and @p water_content, respectively) are templates to allow evaluation of
 * the derivatives through fadbad lib.
 */
 
struct SoilData {
    double  n;              // power parameter
    double  alpha;           // pressure head scaling
    double  Qr;             // residual water content
    double  Qs;             // saturated water content
    double  cut_fraction;   // in (0,1), fraction of relative Q where to cut and rescale the retention curve
    double  Ks;             // saturated conductivity
//    double  Kk;             // conductivity at the cut point
};
 
 
/**
 * Pure virtual interface, of all models.
 */
class SoilModelBase {
public:
    enum SoilModelType {
        van_genuchten=0,
        irmay=1
    };
 
    typedef fadbad::B<double> DiffDouble;
 
    virtual void reset(SoilData soil)=0;
 
    virtual double conductivity( const double &phead) const =0;
    virtual auto conductivity_diff(const DiffDouble &p_head)->DiffDouble const =0;
 
    virtual double water_content( const double &phead) const =0;
    virtual auto water_content_diff(const DiffDouble &p_head)->DiffDouble const =0;
 
    virtual ~SoilModelBase() {};
};
 
 
template <class Model>
class SoilModelImplBase : public SoilModelBase {
public:
    // We assume that Model have method templates:
    // template <class T>  T conductivity_(const T &h) const;
    // template <class T>  T water_content_(const T &h) const;
 
 
 
    typedef SoilModelBase::DiffDouble DiffDouble;
 
    SoilModelImplBase(double cut_fraction = 0.999);
 
    void reset(SoilData data) override;
 
    double conductivity( const double &p_head) const override;
    auto conductivity_diff(const DiffDouble &p_head)->DiffDouble const override;
 
    double water_content( const double &p_head) const override;
    auto water_content_diff(const DiffDouble &p_head)->DiffDouble const override;
 
    ~SoilModelImplBase() {}
 
private:
    Model model_;
    double cut_fraction_;
};
 
 
 
// ************************************** Internal model definitions
namespace internal {
 
class VanGenuchten {
public:
    VanGenuchten();
 
    void reset_(SoilData soil);
 
    template <class T>
    T conductivity_(const T &h) const;
 
    template <class T>
    T water_content_(const T &h) const;
 
protected:
 
    template <class T> T Q_rel(const T &h) const;
    template <class T> T Q_rel_inv(const T &q) const;
 
    // input parameters
    SoilData  soil_param_;
 
    // constant conductivity parameters
    double Bpar;
    double Ppar;
    double K_lower_limit;
 
    // aux values
    double m;
    double Qs_nc;       // saturated value of continuation of cut water content function
 
 
    double FFQr, FFQs;
    double Hs;
 
};
 
 
 
class Irmay : public VanGenuchten {
public:
    Irmay();
 
    template <class T>
    T conductivity_(const T &h) const;
};
 
} // close namespace internal
 
 
typedef SoilModelImplBase<internal::VanGenuchten> SoilModel_VanGenuchten;
typedef SoilModelImplBase<internal::Irmay> SoilModel_Irmay;
 
 
 
 
 
 
 
 
 
 
/*
 
//FK-------------------------------------------------------------
template <class T>
class FK    //FK - hydraulic conductivity function
{
private:
// function parameters
static const double Bpar;   // = 0.5;
static const double PPar;   // = 2;
 
HydrologyParams par;
 
// auxiliary parameters
double Qa,Qm,Qk,m,Hr,Hk,Hs,C1Qee,C2Qee,Qeer,Qees,Qeek;
public:
    FK(const HydrologyParams &par);
    T operator()(const T&  h);
};
 
template <class T> const double FK<T>::Bpar =0.5;
template <class T> const double FK<T>::PPar =2;
 
template <class T>
FK<T> :: FK(const HydrologyParams &par)
: par(par)
{
 
    m = 1-1/par.n;
 
        Qa=par.Qr;
        Qm=par.Qs / par.cut_fraction;
        //Qk=0.99 * par.Qs;
        Qk=par.Qs;
        C1Qee = 1/(Qm - Qa);
        C2Qee = -Qa/(Qm - Qa);
//    if (par.cut_fraction >0.9999) {
//        Hr=-1000;
//        Hk=Hs=0;
//        return;
//    }
                                                        // fraction =1
        Qees = C1Qee * par.Qs + C2Qee;                  // 1
        Qeek = min(C1Qee * Qk + C2Qee, Qees);           // 1
        Qeer = min(C1Qee * par.Qr + C2Qee, Qeek);       // 0
 
        Hr = -1/par.alfa*pow(pow(Qeer,-1/m)-1,1/par.n); //
        Hs = -1/par.alfa*pow(pow(Qees,-1/m)-1,1/par.n);
        Hk = -1/par.alfa*pow(pow(Qeek,-1/m)-1,1/par.n);
 
        cout << "K: Hr, Hs, Hk:" << Hr << " " << Hs << " " << Hk << endl;
}
 
template <class T>
T FK<T> :: operator()(const T& h)
{
    T Kr,FFQr,FFQ,FFQk,Qee,Qe,Qek,C1Qe,C2Qe,Q;
 
    if (h < Hr) return par.Ks*(1E-200);      // numericaly zero Kr
    else 
      if (h < Hk) {
            Q = Qa + (Qm - Qa)*pow((1 + pow(-par.alfa*h,par.n)),-m);
            Qee = C1Qee*Q + C2Qee;
            FFQr = pow(1 - pow(Qeer,1/m),m);
            FFQ = pow(1 - pow(Qee,1/m),m);
            FFQk = pow(1 - pow(Qeek,1/m),m);
            C1Qe = 1/(par.Qs - par.Qr);
            C2Qe = -par.Qr/(par.Qs - par.Qr);
            Qe = C1Qe*Q + C2Qe;
            Qek = C1Qe*Qk + C2Qe;
            Kr = pow(Qe/Qek,Bpar)*pow((FFQr - FFQ)/(FFQr - FFQk),PPar) * par.Kk/par.Ks;
            return ( max<T>(par.Ks*Kr,par.Ks*(1E-10)) );
    }
    else if(h <= Hs)
    {
         Kr = (1-par.Kk/par.Ks)/(Hs-Hk)*(h-Hs) + 1;
         return ( par.Ks*Kr );
    }
    else return par.Ks;
}
 
 
//FQ--------------------------------------------------------------
template <class T>
class FQ    //FQ - water saturation function
{
HydrologyParams par;
// auxiliary parameters
double  m, Qeer,Qees,Hr,Hs, Qa, Qm;
public:
    FQ(const HydrologyParams &par);
    T operator()(const T&  h);
};
 
template <class T>
FQ<T>::FQ(const HydrologyParams &par)
: par(par)
{
    m = 1 - 1 / par.n;
 
//    if (par.cut_fraction >0.9999) {
//        Hr=-1000;
//        Hs=0;
//        return;
//    }
    Qm=par.Qs / par.cut_fraction;
    Qa=par.Qr;
 
    Qeer = (par.Qr - Qa)/ (Qm - Qa);
    Qees = (par.Qs - Qa)/ (Qm - Qa);
    Hr = -1 / par.alfa * pow( pow(Qeer,-1/m)-1, 1/par.n);
    Hs = -1 / par.alfa * pow( pow(Qees,-1/m)-1, 1/par.n);
 
    cout << "Q: Hr, Hs:" << Hr << " " << Hs << " " << endl;
}
 
 
template <class T>
T FQ<T>::operator()(const T& h)
{
    T  Qee;
 
    if (h < Hr) return par.Qr;
    else if (h < Hs) {
        Qee = pow( 1 + pow(-par.alfa * h, par.n), -m);
        return Qa + (Qm - Qa) * Qee;
    }
    else return par.Qs;
 
}
 
//FC--------------------------------------------------------------
template <class T>
class FC    //FC - water capacity function FQ derivative
{
HydrologyParams par;
// auxiliary parameters
double  m, C1Qee,C2Qee,Qeer,Qees,Hr,Hs, Qa, Qm;
public:
    FC(const HydrologyParams &par);
    T operator()(const T&  h);
};
 
template <class T>
FC<T>::FC(const HydrologyParams &par)
: par(par)
{
    m = 1 - 1 / par.n;
    Qm=par.Qs / par.cut_fraction;
    Qa=par.Qr;
 
    C1Qee = 1/(Qm - Qa);
    C2Qee = -Qa/(Qm - Qa);
    Qeer = C1Qee * par.Qr + C2Qee;
    Qees = C1Qee * par.Qs + C2Qee;
    Hr = -1 / par.alfa * pow( pow(Qeer,-1/m)-1, 1/par.n);
    Hs = -1 / par.alfa * pow( pow(Qees,-1/m)-1, 1/par.n);
}
 
 
template <class T>
T FC<T>::operator()(const T& h)
{
    T  C1;
 
    if (h <= Hr)
        return 0.0;
    else if ( h < Hs ) {
        C1=pow( 1 + pow( -par.alfa * h, par.n), -m-1);
        return (Qm - Qa) * m * par.n * pow(par.alfa, par.n)*pow(-h, par.n-1)*C1;
    }
    else
        return 0.0;
}
 
 
! ************************************************************************
! FH - inverse water saturation function
! **************************************
real pure function FH_4(h,Matr)
implicit none
integer,INTENT(IN) :: Matr
real, INTENT(IN) :: h
  FH_4=FH_8(DBLE(h),Matr)
end function FH_4
 
double precision pure function FH_8(Qe,Matr)
implicit none
integer, INTENT(IN) :: Matr
double precision,INTENT(IN) :: Qe
double precision :: n,m,Qr,Qs,Qa,Qm,Alfa,Q,Qee
 
  Qr=par(1,Matr)
  Qs=par(2,Matr)
  Qa=par(3,Matr)
  Qm=par(4,Matr)
  Alfa=par(5,Matr)
  n=par(6,Matr)
  m=1-1/n
  Q=Qr+(Qs-Qr)*Qe
  Qee=dmax1((Q-Qa)/(Qm-Qa),1d-3)
  Qee=dmin1(Qee,1-1d-15)
  FH_8=-1/Alfa*(Qee**(-1/m)-1)**(1/n)
end function FH_8
*/
 
// Conductivity for analytical solution
/*
class HydroModel_analytical
{
public:
    HydroModel_analytical(ParameterHandler &prm) {};
 
    /// Maximum point of capacity. (computed numericaly from eq. atan(x)*2x=1 )
    inline double cap_arg_max() const { return -0.765378926665788882857; }
 
    template <class T>
    T FK(const T &h) const
    {
        if (h>=0.0) return ( 2.0 );
        return ( 2.0 / (1+h*h) );
    }
 
    template <class T>
    T FQ(const T &h) const
    {
        static T pi_half =std::atan(1.0)*2;
        if (h>=0.0) return ( 2.0*pi_half*pi_half );
        T a_tan = atan(h);
        return ( 2*pi_half*pi_half - a_tan*a_tan );
    }
private:
    double arg_cap_max;
};
 
 
class HydroModel_linear
{
    HydroModel_linear(ParameterHandler &prm) {};
 
public:
    template <class T>
    T FK(const T &h) const {
        return 1.0;
    }
 
    template <class T>
    T FQ(const T &h) const {
        return h;
    }
};
 
*/
#endif  /* _HYDRO_FUNCTIONS_HH */