Anisotropic2.cpp

#include <cmath>
#include "Anisotropic2.h"
#include "AtmosModel.h"
#include "Constants.h"
#include "Pvl.h"
#include "PvlGroup.h"
#include "IException.h"
#include "IString.h"

using std::min;
using std::max;

namespace Isis {
  Anisotropic2::Anisotropic2(Pvl &pvl, PhotoModel &pmodel) : AtmosModel(pvl, pmodel) {
  }

  
  void Anisotropic2::AtmosModelAlgorithm(double phase, double incidence, double emission) {
    double xx;
    double munot, mu;
    double emunot, emu;
    double munotp, mup;
    double gmunot, gmu;
    double hpsq1;
    double f1munot, f2munot, f3munot;
    double f1mmunot, f2mmunot, f3mmunot;
    double maxval;
    double f1mu, f2mu, f3mu;
    double f1mmu, f2mmu, f3mmu;
    double sum;
    double prod;
    double cosazss;
    double xystuff;
    double xmunot_0, ymunot_0;
    double xmu_0, ymu_0;
    double cxx, cyy;
    double xmunot_1, ymunot_1;
    double xmu_1, ymu_1;

    if(p_atmosBha == 0.0) {
      p_atmosBha = 1.0e-6;
    }

    if(p_atmosTau == 0.0) {
      p_pstd = 0.0;
      p_trans = 1.0;
      p_trans0 = 1.0;
      p_sbar = 0.0;
      p_transs = 1.0;
      return;
    }

    if(p_atmosWha == 1.0) {
      QString msg = "Anisotropic conservative case not implemented yet - WHA parameter cannot be set to 1.0.";
      msg += "This will cause negative planetary curvature to occur.";
      throw IException(IException::User, msg, _FILEINFO_);
    }

    if(TauOrWhaChanged()) {
      // preparation includes exponential integrals e sub 2 through 5
      p_wha2 = 0.5 * p_atmosWha;
      p_wham = 1.0 - p_atmosWha;
      p_e1   = AtmosModel::En(1, p_atmosTau);
      p_e1_2 = AtmosModel::En(1, 2.0 * p_atmosTau);
      p_e2   = AtmosModel::En(2, p_atmosTau);
      p_e3   = AtmosModel::En(3, p_atmosTau);
      p_e4   = AtmosModel::En(4, p_atmosTau);
      p_e5   = AtmosModel::En(5, p_atmosTau);

      // chandra's gmn functions require fm and fn at mu=-1
      xx = -p_atmosTau;
      if(xx < -69.0) {
        p_em = 0.0;
      }
      else if(xx > 69.0) {
        p_em = 1.0e30;
      }
      else {
        p_em = exp(xx);
      }

      p_f1m = log(2.0) - p_em * p_e1 + p_e1_2;
      p_f2m = -1.0 * (p_f1m + p_em * p_e2 - 1.0);
      p_f3m = -1.0 * (p_f2m + p_em * p_e3 - 0.5);
      p_f4m = -1.0 * (p_f3m + p_em * p_e4 - (1.0 / 3.0));
      p_g12 = (p_atmosTau * p_e1 * p_e2 + p_f1m + p_f2m) * 0.5;
      p_g13 = (p_atmosTau * p_e1 * p_e3 + p_f1m + p_f3m) * (1.0 / 3.0);
      p_g14 = (p_atmosTau * p_e1 * p_e4 + p_f1m + p_f4m) * 0.25;
      p_g32 = (p_atmosTau * p_e3 * p_e2 + p_f3m + p_f2m) * 0.25;
      p_g33 = (p_atmosTau * p_e3 * p_e3 + p_f3m + p_f3m) * 0.2;
      p_g34 = (p_atmosTau * p_e3 * p_e4 + p_f3m * p_f4m) * (1.0 / 6.0);

      // chandra's g'mn functions require g'11 and f at mu=+1
      xx = p_atmosTau;
      if(xx < -69.0) {
        p_e = 0.0;
      }
      else if(xx > 69.0) {
        p_e = 1.0e30;
      }
      else {
        p_e = exp(xx);
      }

      p_f1 = Eulgam() + log(p_atmosTau) + p_e * p_e1;
      p_f2 = p_f1 + p_e * p_e2 - 1.0;
      p_f3 = p_f2 + p_e * p_e3 - 0.5;
      p_f4 = p_f3 + p_e * p_e4 - (1.0 / 3.0);
      p_g11p = AtmosModel::G11Prime(p_atmosTau);
      p_g12p = (p_atmosTau * (p_e1 - p_g11p) + p_em * (p_f1 + p_f2)) * 0.25;
      p_g13p = (p_atmosTau * (0.5 * p_e1 - p_g12p) + p_em * (p_f1 + p_f3)) * 0.2;
      p_g14p = (p_atmosTau * ((1.0 / 3.0) * p_e1 - p_g13p) + p_em * (p_f1 + p_f4)) * (1.0 / 6.0);
      p_g32p = (p_atmosTau * (p_e1 - p_g13p) + p_em * (p_f3 + p_f2)) * (1.0 / 6.0);
      p_g33p = (p_atmosTau * (0.5 * p_e1 - p_g32p) + p_em * (p_f3 + p_f3)) * 0.142857;
      p_g34p = (p_atmosTau * ((1.0 / 3.0) * p_e1 - p_g33p) + p_em * (p_f3 + p_f4)) * 0.125;

      // first, get the required quantities for the axisymmetric m=0 part
      // zeroth moments of (uncorrected) x and y times characteristic fn
      p_x0_0 = p_wha2 * (1.0 + (1.0 / 3.0) * p_atmosBha * p_wham + p_wha2 * (p_g12 + p_atmosBha *
                         p_wham * (p_g14 + p_g32) + pow(p_atmosBha, 2.0) * pow(p_wham, 2.0) * p_g34));
      p_y0_0 = p_wha2 * (p_e2 + p_atmosBha * p_wham * p_e4 + p_wha2 * (p_g12p
                         + p_atmosBha * p_wham * (p_g14p + p_g32p) +
                         pow(p_atmosBha, 2.0) * pow(p_wham, 2.0) * p_g34p));

      // higher-order correction term for x and y
      p_delta_0 = (1.0 - (p_x0_0 + p_y0_0) - (1.0 - p_atmosWha * (1.0 + (1.0 / 3.0) * p_atmosBha *
                                              p_wham)) / (1.0 - (p_x0_0 - p_y0_0))) / (p_atmosWha * (0.5 - p_e3 + p_atmosBha * p_wham * (0.25 - p_e5)));

      //  moments of (corrected) x and y
      p_alpha0_0 = 1.0 + p_wha2 * (p_g12 + p_atmosBha * p_wham * p_g32) + p_delta_0 * (0.5 - p_e3);
      p_alpha1_0 = 0.5 + p_wha2 * (p_g13 + p_atmosBha * p_wham * p_g33) + p_delta_0 * ((1.0 / 3.0) - p_e4);
      p_beta0_0 = p_e2 + p_wha2 * (p_g12p + p_atmosBha * p_wham * p_g32p) + p_delta_0 * (0.5 - p_e3);
      p_beta1_0 = p_e3 + p_wha2 * (p_g13p + p_atmosBha * p_wham * p_g33p) + p_delta_0 * ((1.0 / 3.0) - p_e4);

      // gamma will be a weighted sum of m=0 x and y functions
      // but unlike before, call the weights q1 and p1, and we also
      // need additional weights q0 and p0
      p_fac = 2.0 - p_atmosWha * p_alpha0_0;
      p_den = pow(p_fac, 2.0) - pow((p_atmosWha * p_beta0_0), 2.0);
      p_q0 = p_atmosBha * p_atmosWha * p_wham * (p_fac * p_alpha1_0 - p_atmosWha * p_beta0_0 * p_beta1_0) / p_den;
      p_p0 = p_atmosBha * p_atmosWha * p_wham * (-p_fac * p_beta1_0 - p_atmosWha * p_beta0_0 * p_alpha1_0) / p_den;
      p_q02p02 = p_q0 * p_q0 - p_p0 * p_p0;
      p_q1 = (2.0 * p_wham * p_fac) / p_den;
      p_p1 = (2.0 * p_wham * p_atmosWha * p_beta0_0) / p_den;
      p_q12p12 = p_q1 * p_q1 - p_p1 * p_p1;

      // sbar is total diffuse illumination and comes from moments
      p_sbar = 1.0 - 2.0 * (p_q1 * p_alpha1_0 + p_p1 * p_beta1_0);

      // we're not done yet!  still have to calculate the m=1 portion
      // zeroth moments of (uncorrected) x and y times characteristic fn
      p_x0_1 = 0.5 * p_wha2 * p_atmosBha * (1.0 - (1.0 / 3.0) + 0.5 * p_wha2 * p_atmosBha *
                                            (p_g12 - (p_g14 + p_g32) + p_g34));
      p_y0_1 = 0.5 * p_wha2 * p_atmosBha * (p_e2 - p_e4 + 0.5 * p_wha2 * p_atmosBha *
                                            (p_g12p - (p_g14p + p_g32p) + p_g34p));

      // higher-order correction term for x and y
      p_delta_1 = (1.0 - (p_x0_1 + p_y0_1) - (1.0 - (1.0 / 3.0) * p_atmosWha * p_atmosBha) /
                   (1.0 - (p_x0_1 - p_y0_1))) / (p_wha2 * p_atmosBha *
                       ((0.5 - 0.25) - (p_e3 - p_e5)));

      // moments of (corrected) x and y are not needed for m=1, so we're done
      SetOldTau(p_atmosTau);
      SetOldWha(p_atmosWha);
    }

    // correct the path lengths for planetary curvature
    hpsq1 = pow((1.0 + p_atmosHnorm), 2.0) - 1.0;

    if(incidence == 90.0) {
      munot = 0.0;
    }
    else {
      munot = cos((PI / 180.0) * incidence);
    }

    maxval = max(1.0e-30, hpsq1 + munot * munot);
    munotp = p_atmosHnorm / (sqrt(maxval) - munot);
    munotp = max(munotp, p_atmosTau / 69.0);

    if(emission == 90.0) {
      mu = 0.0;
    }
    else {
      mu = cos((PI / 180.0) * emission);
    }

    maxval = max(1.0e-30, hpsq1 + mu * mu);
    mup = p_atmosHnorm / (sqrt(maxval) - mu);
    mup = max(mup, p_atmosTau / 69.0);

    // build the x and y functions of mu0 and mu
    maxval = max(1.0e-30, munotp);
    xx = -p_atmosTau / maxval;
    if(xx < -69.0) {
      emunot = 0.0;
    }
    else if(xx > 69.0) {
      emunot = 1.0e30;
    }
    else {
      emunot = exp(-p_atmosTau / munotp);
    }

    maxval = max(1.0e-30, mup);
    xx = -p_atmosTau / maxval;
    if(xx < -69.0) {
      emu = 0.0;
    }
    else if(xx > 69.0) {
      emu = 1.0e30;
    }
    else {
      emu = exp(-p_atmosTau / mup);
    }

    // in the second approximation the x and y include the f1, f3 functions
    xx = munotp;
    if(fabs(xx - 1.0) < 1.0e-10) {
      f1munot = p_f1;
      f1mmunot = xx * (log(1.0 + 1.0 / xx) - p_e1 * emunot +
                       AtmosModel::En(1, p_atmosTau * (1.0 + 1.0 / xx)));
    }
    else if(xx > 0.0) {
      f1munot = xx * (log(xx / (1.0 - xx)) + p_e1 / emunot +
                      AtmosModel::Ei(p_atmosTau * (1.0 / xx - 1.0)));
      f1mmunot = xx * (log(1.0 + 1.0 / xx) - p_e1 * emunot +
                       AtmosModel::En(1, p_atmosTau * (1.0 + 1.0 / xx)));
    }
    else {
      QString msg = "Negative length of planetary curvature encountered";
      throw IException(IException::Unknown, msg, _FILEINFO_);
    }

    f2munot = munotp * (f1munot + p_e2 / emunot - 1);
    f2mmunot = -munotp * (f1mmunot + p_e2 * emunot - 1);
    f3munot = munotp * (f2munot + p_e3 / emunot - 0.5);
    f3mmunot = -munotp * (f2mmunot + p_e3 * emunot - 0.5);
    xx = mup;

    if(fabs(xx - 1.0) < 1.0e-10) {
      f1mu = p_f1;
      f1mmu = xx * (log(1.0 + 1.0 / xx) - p_e1 * emu + AtmosModel::En(1, p_atmosTau * (1.0 + 1.0 / xx)));
    }
    else if(xx > 0.0) {
      f1mu = xx * (log(xx / (1.0 - xx)) + p_e1 / emu + AtmosModel::Ei(p_atmosTau * (1.0 / xx - 1.0)));
      f1mmu = xx * (log(1.0 + 1.0 / xx) - p_e1 * emu + AtmosModel::En(1, p_atmosTau * (1.0 + 1.0 / xx)));
    }
    else {
      QString msg = "Negative length of planetary curvature encountered";
      throw IException(IException::Unknown, msg, _FILEINFO_);
    }

    f2mu = mup * (f1mu + p_e2 / emu - 1);
    f2mmu = -mup * (f1mmu + p_e2 * emu - 1);
    f3mu = mup * (f2mu + p_e3 / emu - 0.5);
    f3mmu = -mup * (f2mmu + p_e3 * emu - 0.5);

    // first for m=0
    xmunot_0 = 1.0 + p_wha2 * (f1mmunot + p_atmosBha * p_wham * f3mmunot) + p_delta_0 * munotp * (1.0 - emunot);
    ymunot_0 = emunot * (1.0 + p_wha2 * (f1munot + p_atmosBha * p_wham * f3munot)) +
               p_delta_0 * munotp * (1.0 - emunot);
    xmu_0 = 1.0 + p_wha2 * (f1mmu + p_atmosBha * p_wham * f3mmu) + p_delta_0 * mup * (1.0 - emu);
    ymu_0 = emu * (1.0 + p_wha2 * (f1mu + p_atmosBha * p_wham * f3mu)) + p_delta_0 * mup * (1.0 - emu);

    // then for m=1
    xmunot_1 = 1.0 + 0.5 * p_wha2 * p_atmosBha * (f1mmunot - f3mmunot) + p_delta_1 * munotp * (1.0 - emunot);
    ymunot_1 = emunot * (1.0 + 0.5 * p_wha2 * p_atmosBha *
                         (f1munot - f3munot)) + p_delta_1 * munotp * (1.0 - emunot);
    xmu_1 = 1.0 + 0.5 * p_wha2 * p_atmosBha * (f1mmu - f3mmu) + p_delta_1 * mup * (1.0 - emu);
    ymu_1 = emu * (1.0 + 0.5 * p_wha2 * p_atmosBha * (f1mu - f3mu)) + p_delta_1 * mup * (1.0 - emu);

    // gamma1 functions come from x and y with m=0
    gmunot = p_p1 * xmunot_0 + p_q1 * ymunot_0;
    gmu = p_p1 * xmu_0 + p_q1 * ymu_0;

    // purely atmos term uses x and y of both orders and is complex
    sum = munot + mu;
    prod = munot * mu;
    cxx = 1.0 - p_q0 * sum + (p_q02p02 - p_atmosBha * p_q12p12) * prod;
    cyy = 1.0 + p_q0 * sum + (p_q02p02 - p_atmosBha * p_q12p12) * prod;

    if(phase == 90.0) {
      cosazss = 0.0 - munot * mu;
    }
    else {
      cosazss = cos((PI / 180.0) * phase) - munot * mu;
    }

    xystuff = cxx * xmunot_0 * xmu_0 - cyy * ymunot_0 *
              ymu_0 - p_p0 * sum * (xmu_0 * ymunot_0 + ymu_0 * xmunot_0) + cosazss * p_atmosBha * (xmu_1 *
                  xmunot_1 - ymu_1 * ymunot_1);
    p_pstd = 0.25 * p_atmosWha * munotp / (munotp + mup) * xystuff;

    // xmitted surface term uses gammas from m=0
    p_trans = gmunot * gmu;

    // finally, never-scattered term is given by pure attenuation
    p_trans0 = emunot * emu;

    // Calculate the transmission of light that must be subtracted from a
    // shadow. This includes direct flux and the scattered flux in the
    // upsun half of the sky downwelling onto the surface, and the usual
    // transmission upward. NOTE: We need to derive the analytic expression
    // for the light from half the sky in the Legendre scattering model. Until
    // we do so, we are setting the shadow transmission to the purely
    // unscattered part (same as trans0). This will give a result but is
    // not fully consistent with how the other scattering models are
    // implemented.
    p_transs = p_trans0;
  }
}


extern "C" Isis::AtmosModel *Anisotropic2Plugin(Isis::Pvl &pvl,
    Isis::PhotoModel &pmodel) {

  return new Isis::Anisotropic2(pvl, pmodel);
}