Anisotropic1.cpp

#include <cmath>
#include "Anisotropic1.h"
#include "AtmosModel.h"
#include "IException.h"
#include "IString.h"

using std::max;

namespace Isis {
  Anisotropic1::Anisotropic1(Pvl &pvl, PhotoModel &pmodel) : AtmosModel(pvl, pmodel) {

    // Set default values
    p_atmosAlpha0_0 = 0.0;
    p_atmosAlpha1_0 = 0.0;
    p_atmosBeta0_0 = 0.0;
    p_atmosBeta1_0 = 0.0;
    p_atmosDelta_0 = 0.0;
    p_atmosDelta_1 = 0.0;
    p_atmosDen = 0.0;
    p_atmosE2 = 0.0;
    p_atmosE3 = 0.0;
    p_atmosE4 = 0.0;
    p_atmosE5 = 0.0;
    p_atmosFac = 0.0;
    p_atmosP0 = 0.0;
    p_atmosP1 = 0.0;
    p_atmosQ0 = 0.0;
    p_atmosQ02p02 = 0.0;
    p_atmosQ1 = 0.0;
    p_atmosQ12p12 = 0.0;
    p_atmosWha2 = 0.0;
    p_atmosWham = 0.0;
    p_atmosX0_0 = 0.0;
    p_atmosX0_1 = 0.0;
    p_atmosY0_0 = 0.0;
    p_atmosY0_1 = 0.0;

  }

  void Anisotropic1::AtmosModelAlgorithm(double phase, double incidence, double emission) {
    double hpsq1;
    double munot, munotp;
    double maxval;
    double mu, mup;
    double xx;
    double emunot, emu;
    double gmunot, gmu;
    double sum, prod;
    double cosazss;
    double xmunot_0, ymunot_0;
    double xmu_0, ymu_0;
    double xmunot_1, ymunot_1;
    double xmu_1, ymu_1;
    double cxx, cyy;
    double xystuff;

    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_atmosWha2 = 0.5 * p_atmosWha;
      p_atmosWham = 1.0 - p_atmosWha;
      p_atmosE2 = AtmosModel::En(2, p_atmosTau);
      p_atmosE3 = AtmosModel::En(3, p_atmosTau);
      p_atmosE4 = AtmosModel::En(4, p_atmosTau);
      p_atmosE5 = AtmosModel::En(5, p_atmosTau);
      // first, get the required quantities for the axisymmetric m=0 part
      // zeroth moments of (uncorrected) x and y times characteristic fn
      p_atmosX0_0 = p_atmosWha2 * (1.0 + (1.0 / 3.0) * p_atmosBha *
                                   p_atmosWham);
      p_atmosY0_0 = p_atmosWha2 * (p_atmosE2 + p_atmosBha * p_atmosWham *
                                   p_atmosE4);
      // higher-order correction term for x and y
      p_atmosDelta_0 = (1.0 - (p_atmosX0_0 + p_atmosY0_0) - (1.0 - p_atmosWha *
                        (1.0 + (1.0 / 3.0) * p_atmosBha * p_atmosWham)) / (1.0 -
                            (p_atmosX0_0 - p_atmosY0_0))) / (p_atmosWha * (0.5 - p_atmosE3 +
                                p_atmosBha * p_atmosWham * (0.25 - p_atmosE5)));

      // moments of (corrected) x and y
      p_atmosAlpha0_0 = 1.0 + p_atmosDelta_0 * (0.5 - p_atmosE3);
      p_atmosAlpha1_0 = 0.5 + p_atmosDelta_0 * ((1.0 / 3.0) - p_atmosE4);
      p_atmosBeta0_0 = p_atmosE2 + p_atmosDelta_0 * (0.5 - p_atmosE3);
      p_atmosBeta1_0 = p_atmosE3 + p_atmosDelta_0 * ((1.0 / 3.0) - p_atmosE4);
      // 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_atmosFac = 2.0 - p_atmosWha * p_atmosAlpha0_0;
      p_atmosDen = pow(p_atmosFac, 2.0) - pow(p_atmosWha * p_atmosBeta0_0, 2.0);
      p_atmosQ0 = p_atmosBha * p_atmosWha * p_atmosWham * (p_atmosFac *
                  p_atmosAlpha1_0 - p_atmosWha * p_atmosBeta0_0 * p_atmosBeta1_0) /
                  p_atmosDen;
      p_atmosP0 = p_atmosBha * p_atmosWha * p_atmosWham * (-p_atmosFac *
                  p_atmosBeta1_0 - p_atmosWha * p_atmosBeta0_0 * p_atmosAlpha1_0) /
                  p_atmosDen;
      p_atmosQ02p02 = p_atmosQ0 * p_atmosQ0 - p_atmosP0 * p_atmosP0;
      p_atmosQ1 = (2.0 * p_atmosWham * p_atmosFac) / p_atmosDen;
      p_atmosP1 = (2.0 * p_atmosWham * p_atmosWha * p_atmosBeta0_0) /
                  p_atmosDen;
      p_atmosQ12p12 = p_atmosQ1 * p_atmosQ1 - p_atmosP1 * p_atmosP1;
      // sbar is total diffuse illumination and comes from moments
      p_sbar = 1.0 - 2.0 * (p_atmosQ1 * p_atmosAlpha1_0 + p_atmosP1 *
                            p_atmosBeta1_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_atmosX0_1 = 0.5 * p_atmosWha2 * p_atmosBha * (1.0 - (1.0 / 3.0));
      p_atmosY0_1 = 0.5 * p_atmosWha2 * p_atmosBha * (p_atmosE2 - p_atmosE4);
      // higher-order correction term for x and y
      p_atmosDelta_1 = (1.0 - (p_atmosX0_1 + p_atmosY0_1) - (1.0 -
                        (1.0 / 3.0) * p_atmosWha * p_atmosBha) / (1.0 - (p_atmosX0_1 -
                            p_atmosY0_1))) / (p_atmosWha2 * p_atmosBha * ((0.5 - 0.25) -
                                              (p_atmosE3 - p_atmosE5)));
      // 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);
    }

    // first for m=0
    xmunot_0 = 1.0 + p_atmosDelta_0 * munotp * (1.0 - emunot);
    ymunot_0 = emunot + p_atmosDelta_0 * munotp * (1.0 - emunot);
    xmu_0 = 1.0 + p_atmosDelta_0 * mup * (1.0 - emu);
    ymu_0 = emu + p_atmosDelta_0 * mup * (1.0 - emu);

    // then for m=1
    xmunot_1 = 1.0 + p_atmosDelta_1 * munotp * (1.0 - emunot);
    ymunot_1 = emunot + p_atmosDelta_1 * munotp * (1.0 - emunot);
    xmu_1 = 1.0 + p_atmosDelta_1 * mup * (1.0 - emu);
    ymu_1 = emu + p_atmosDelta_1 * mup * (1.0 - emu);

    // gamma1 functions come from x and y with m=0
    gmunot = p_atmosP1 * xmunot_0 + p_atmosQ1 * ymunot_0;
    gmu = p_atmosP1 * xmu_0 + p_atmosQ1 * 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_atmosQ0 * sum + (p_atmosQ02p02 - p_atmosBha *
                                   p_atmosQ12p12) * prod;
    cyy = 1.0 + p_atmosQ0 * sum + (p_atmosQ02p02 - p_atmosBha *
                                   p_atmosQ12p12) * 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_atmosP0 * 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 *Anisotropic1Plugin(Isis::Pvl &pvl, Isis::PhotoModel &pmodel) {
  return new Isis::Anisotropic1(pvl, pmodel);
}