m_optproperties.cc

Go to the documentation of this file.

/* Copyright (C) 2002-2012
   Sreerekha T.R. <rekha@uni-bremen.de>
   Claudia Emde <claudia.emde@dlr.de>
   Cory Davies <cory@met.ed.ac.uk>
  
   This program is free software; you can redistribute it and/or
   modify it under the terms of the GNU General Public License as
   published by the Free Software Foundation; either version 2 of the
   License, or (at your option) any later version.
  
   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.
  
   You should have received a copy of the GNU General Public License
   along with this program; if not, write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
   USA. */
 
/*===========================================================================
  === External declarations
  ===========================================================================*/
 
#include <cfloat>
#include <cmath>
#include "array.h"
#include "arts.h"
#include "auto_md.h"
#include "check_input.h"
#include "exceptions.h"
#include "interpolation.h"
#include "logic.h"
#include "math_funcs.h"
#include "matpackIII.h"
#include "matpackVII.h"
#include "messages.h"
#include "montecarlo.h"
#include "optproperties.h"
#include "sorting.h"
#include "xml_io.h"
 
extern const Numeric PI;
extern const Numeric DEG2RAD;
extern const Numeric RAD2DEG;
 
#define PART_TYPE scat_data[i_ss][i_se].ptype
#define F_DATAGRID scat_data[i_ss][i_se].f_grid
#define T_DATAGRID scat_data[i_ss][i_se].T_grid
#define ZA_DATAGRID scat_data[i_ss][i_se].za_grid
#define AA_DATAGRID scat_data[i_ss][i_se].aa_grid
#define PHA_MAT_DATA scat_data[i_ss][i_se].pha_mat_data
#define EXT_MAT_DATA scat_data[i_ss][i_se].ext_mat_data
#define ABS_VEC_DATA scat_data[i_ss][i_se].abs_vec_data
 
// If particle number density is below this value,
// no transformations will be performed
#define PND_LIMIT 1e-12
 
/* Workspace method: Doxygen documentation will be auto-generated */
void pha_mat_sptFromData(  // Output:
    Tensor5& pha_mat_spt,
    // Input:
    const ArrayOfArrayOfSingleScatteringData& scat_data,
    const Vector& za_grid,
    const Vector& aa_grid,
    const Index& za_index,  // propagation directions
    const Index& aa_index,
    const Index& f_index,
    const Vector& f_grid,
    const Numeric& rtp_temperature,
    const Tensor4& pnd_field,
    const Index& scat_p_index,
    const Index& scat_lat_index,
    const Index& scat_lon_index,
    const Verbosity& verbosity) {
  const Index stokes_dim = pha_mat_spt.ncols();
  if (stokes_dim > 4 || stokes_dim < 1) {
    throw runtime_error(
        "The dimension of the stokes vector \n"
        "must be 1,2,3 or 4");
  }
 
  // Determine total number of scattering elements
  const Index N_se_total = TotalNumberOfElements(scat_data);
  if (N_se_total != pnd_field.nbooks()) {
    ostringstream os;
    os << "Total number of scattering elements in scat_data "
       << "inconsistent with size of pnd_field.";
    throw runtime_error(os.str());
  }
  // as pha_mat_spt is typically initiallized from pnd_field, this theoretically
  // checks the same as the runtime_error above. Still, we keep it to be on the
  // save side.
  assert(pha_mat_spt.nshelves() == N_se_total);
 
  // Check that we don't have scat_data_mono here. Only checking the first
  // scat element, assuming the other elements have been processed in the same
  // manner. That's save against having mono data, but not against having
  // individual elements produced with only a single frequency. This, however,
  // has been checked by scat_data_raw reading routines (ScatSpecies/Element*Add/Read).
  // Unsafe, however, remain when ReadXML is used directly or if scat_data(_raw) is
  // (partly) produced from scat_data_singleTmatrix.
  if (scat_data[0][0].f_grid.nelem() < 2) {
    ostringstream os;
    os << "Scattering data seems to be *scat_data_mono* (1 freq point only),\n"
       << "but frequency interpolable data (*scat_data* with >=2 freq points) "
       << "is expected here.";
    throw runtime_error(os.str());
  }
 
  const Index N_ss = scat_data.nelem();
 
  // Phase matrix in laboratory coordinate system. Dimensions:
  // [frequency, za_inc, aa_inc, stokes_dim, stokes_dim]
  Tensor5 pha_mat_data_int;
 
  Index i_se_flat = 0;
  // Loop over scattering species
  for (Index i_ss = 0; i_ss < N_ss; i_ss++) {
    const Index N_se = scat_data[i_ss].nelem();
 
    // Loop over the included scattering elements
    for (Index i_se = 0; i_se < N_se; i_se++) {
      // If the particle number density at a specific point in the
      // atmosphere for the i_se scattering element is zero, we don't need
      // to do the transfromation!
      if (pnd_field(i_se_flat, scat_p_index, scat_lat_index, scat_lon_index) >
          PND_LIMIT) {
        // First we have to transform the data from the coordinate system
        // used in the database (depending on the kind of ptype) to the
        // laboratory coordinate system.
 
        // Frequency and temperature interpolation:
 
        // Container for data at one frequency and one temperature.
        pha_mat_data_int.resize(PHA_MAT_DATA.nshelves(),
                                PHA_MAT_DATA.nbooks(),
                                PHA_MAT_DATA.npages(),
                                PHA_MAT_DATA.nrows(),
                                PHA_MAT_DATA.ncols());
 
        // Gridpositions:
        GridPos freq_gp;
        gridpos(freq_gp, F_DATAGRID, f_grid[f_index]);
        GridPos t_gp;
        Vector itw;
 
        Index ti = -1;
 
        if (PHA_MAT_DATA.nvitrines() == 1)  // just 1 T_grid element
        {
          ti = 0;
        } else if (rtp_temperature < 0.)  // coding for 'not interpolate, but
                                          // pick one temperature'
        {
          if (rtp_temperature > -10.)  // lowest T-point
          {
            ti = 0;
          } else if (rtp_temperature > -20.)  // highest T-point
          {
            ti = T_DATAGRID.nelem() - 1;
          } else  // median T-point
          {
            ti = T_DATAGRID.nelem() / 2;
          }
        }
 
        if (ti < 0)  // temperature interpolation
        {
          ostringstream os;
          os << "In pha_mat_sptFromData.\n"
             << "The temperature grid of the scattering data does not\n"
             << "cover the atmospheric temperature at cloud location.\n"
             << "The data should include the value T = " << rtp_temperature
             << " K.";
          chk_interpolation_grids(os.str(), T_DATAGRID, rtp_temperature);
 
          gridpos(t_gp, T_DATAGRID, rtp_temperature);
 
          // Interpolation weights:
          itw.resize(4);
          interpweights(itw, freq_gp, t_gp);
 
          for (Index i_za_sca = 0; i_za_sca < PHA_MAT_DATA.nshelves();
               i_za_sca++)
            for (Index i_aa_sca = 0; i_aa_sca < PHA_MAT_DATA.nbooks();
                 i_aa_sca++)
              for (Index i_za_inc = 0; i_za_inc < PHA_MAT_DATA.npages();
                   i_za_inc++)
                for (Index i_aa_inc = 0; i_aa_inc < PHA_MAT_DATA.nrows();
                     i_aa_inc++)
                  for (Index i = 0; i < PHA_MAT_DATA.ncols(); i++)
                    // Interpolation of phase matrix:
                    pha_mat_data_int(
                        i_za_sca, i_aa_sca, i_za_inc, i_aa_inc, i) =
                        interp(itw,
                               PHA_MAT_DATA(joker,
                                            joker,
                                            i_za_sca,
                                            i_aa_sca,
                                            i_za_inc,
                                            i_aa_inc,
                                            i),
                               freq_gp,
                               t_gp);
        } else {
          // Interpolation weights:
          itw.resize(2);
          interpweights(itw, freq_gp);
          for (Index i_za_sca = 0; i_za_sca < PHA_MAT_DATA.nshelves();
               i_za_sca++)
            for (Index i_aa_sca = 0; i_aa_sca < PHA_MAT_DATA.nbooks();
                 i_aa_sca++)
              for (Index i_za_inc = 0; i_za_inc < PHA_MAT_DATA.npages();
                   i_za_inc++)
                for (Index i_aa_inc = 0; i_aa_inc < PHA_MAT_DATA.nrows();
                     i_aa_inc++)
                  for (Index i = 0; i < PHA_MAT_DATA.ncols(); i++)
                    // Interpolation of phase matrix:
                    pha_mat_data_int(
                        i_za_sca, i_aa_sca, i_za_inc, i_aa_inc, i) =
                        interp(itw,
                               PHA_MAT_DATA(joker,
                                            ti,
                                            i_za_sca,
                                            i_aa_sca,
                                            i_za_inc,
                                            i_aa_inc,
                                            i),
                               freq_gp);
        }
 
        // Do the transformation into the laboratory coordinate system.
        for (Index za_inc_idx = 0; za_inc_idx < za_grid.nelem();
             za_inc_idx++) {
          for (Index aa_inc_idx = 0; aa_inc_idx < aa_grid.nelem();
               aa_inc_idx++) {
            pha_matTransform(
                pha_mat_spt(i_se_flat, za_inc_idx, aa_inc_idx, joker, joker),
                pha_mat_data_int,
                ZA_DATAGRID,
                AA_DATAGRID,
                PART_TYPE,
                za_index,
                aa_index,
                za_inc_idx,
                aa_inc_idx,
                za_grid,
                aa_grid,
                verbosity);
          }
        }
      }
      i_se_flat++;
    }
  }
}
 
/* Workspace method: Doxygen documentation will be auto-generated */
void pha_mat_sptFromDataDOITOpt(  // Output:
    Tensor5& pha_mat_spt,
    // Input:
    const ArrayOfTensor7& pha_mat_sptDOITOpt,
    const ArrayOfArrayOfSingleScatteringData& scat_data_mono,
    const Index& doit_za_grid_size,
    const Vector& aa_grid,
    const Index& za_index,  // propagation directions
    const Index& aa_index,
    const Numeric& rtp_temperature,
    const Tensor4& pnd_field,
    const Index& scat_p_index,
    const Index& scat_lat_index,
    const Index& scat_lon_index,
    const Verbosity&) {
  const Index N_se_total = TotalNumberOfElements(scat_data_mono);
 
  if (N_se_total != pnd_field.nbooks()) {
    ostringstream os;
    os << "Total number of scattering elements in scat_data_mono "
       << "inconsistent with size of pnd_field.";
    throw runtime_error(os.str());
  }
  // as pha_mat_spt is typically initiallized from pnd_field, this theoretically
  // checks the same as the runtime_error above. Still, we keep it to be on the
  // save side.
  assert(pha_mat_spt.nshelves() == N_se_total);
 
  // atmosphere_dim = 3
  if (pnd_field.ncols() > 1) {
    assert(pha_mat_sptDOITOpt.nelem() == N_se_total);
    // Assuming that if the size is o.k. for one scattering element, it will
    // also be o.k. for the other scattering elements.
    assert(pha_mat_sptDOITOpt[0].nlibraries() ==
           scat_data_mono[0][0].T_grid.nelem());
    assert(pha_mat_sptDOITOpt[0].nvitrines() == doit_za_grid_size);
    assert(pha_mat_sptDOITOpt[0].nshelves() == aa_grid.nelem());
    assert(pha_mat_sptDOITOpt[0].nbooks() == doit_za_grid_size);
    assert(pha_mat_sptDOITOpt[0].npages() == aa_grid.nelem());
  }
 
  // atmosphere_dim = 1, only zenith angle required for scattered directions.
  else if (pnd_field.ncols() == 1) {
    //assert(is_size(scat_theta, doit_za_grid_size, 1,
    //                doit_za_grid_size, aa_grid.nelem()));
 
    assert(pha_mat_sptDOITOpt.nelem() == TotalNumberOfElements(scat_data_mono));
    // Assuming that if the size is o.k. for one scattering element, it will
    // also be o.k. for the other scattering elements.
    assert(pha_mat_sptDOITOpt[0].nlibraries() ==
           scat_data_mono[0][0].T_grid.nelem());
    assert(pha_mat_sptDOITOpt[0].nvitrines() == doit_za_grid_size);
    assert(pha_mat_sptDOITOpt[0].nshelves() == 1);
    assert(pha_mat_sptDOITOpt[0].nbooks() == doit_za_grid_size);
    assert(pha_mat_sptDOITOpt[0].npages() == aa_grid.nelem());
  }
 
  assert(doit_za_grid_size > 0);
 
  // Check that we do indeed have scat_data_mono here. Only checking the first
  // scat element, assuming the other elements have been processed in the same
  // manner. That's save against having scat_data here if that originated from
  // scat_data_raw reading routines (ScatSpecies/Element*Add/Read), it's not safe
  // against data read by ReadXML directly or if scat_data(_raw) has been (partly)
  // produced from scat_data_singleTmatrix. That would be too costly here,
  // though.
  // Also, we can't check here whether data is at the correct frequency since we
  // don't know f_grid and f_index here (we could pass it in, though).
  if (scat_data_mono[0][0].f_grid.nelem() > 1) {
    ostringstream os;
    os << "Scattering data seems to be *scat_data* (several freq points),\n"
       << "but *scat_data_mono* (1 freq point only) is expected here.";
    throw runtime_error(os.str());
  }
 
  // Create equidistant zenith angle grid
  Vector za_grid;
  nlinspace(za_grid, 0, 180, doit_za_grid_size);
 
  const Index N_ss = scat_data_mono.nelem();
  const Index stokes_dim = pha_mat_spt.ncols();
 
  if (stokes_dim > 4 || stokes_dim < 1) {
    throw runtime_error(
        "The dimension of the stokes vector \n"
        "must be 1,2,3 or 4");
  }
 
  GridPos T_gp;
  Vector itw(2);
 
  // Initialisation
  pha_mat_spt = 0.;
 
  Index i_se_flat = 0;
 
  // Do the transformation into the laboratory coordinate system.
  for (Index i_ss = 0; i_ss < N_ss; i_ss++) {
    const Index N_se = scat_data_mono[i_ss].nelem();
 
    for (Index i_se = 0; i_se < N_se; i_se++) {
      // If the particle number density at a specific point in the
      // atmosphere for the i_se scattering element is zero, we don't need
      // to do the transformation!
      if (pnd_field(i_se_flat, scat_p_index, scat_lat_index, scat_lon_index) >
          PND_LIMIT)  //TRS
      {
        Index nT = scat_data_mono[i_ss][i_se].pha_mat_data.nvitrines();
        Index ti = -1;
 
        if (nT == 1)  // just 1 T_grid element
        {
          ti = 0;
        } else if (rtp_temperature < 0.)  // coding for 'not interpolate, but
                                          // pick one temperature'
        {
          if (rtp_temperature > -10.)  // lowest T-point
          {
            ti = 0;
          } else if (rtp_temperature > -20.)  // highest T-point
          {
            ti = nT - 1;
          } else  // median T-point
          {
            ti = nT / 2;
          }
        } else {
          ostringstream os;
          os << "In pha_mat_sptFromDataDOITOpt.\n"
             << "The temperature grid of the scattering data does not\n"
             << "cover the atmospheric temperature at cloud location.\n"
             << "The data should include the value T = " << rtp_temperature
             << " K.";
          chk_interpolation_grids(
              os.str(), scat_data_mono[i_ss][i_se].T_grid, rtp_temperature);
 
          // Gridpositions:
          gridpos(T_gp, scat_data_mono[i_ss][i_se].T_grid, rtp_temperature);
          // Interpolation weights:
          interpweights(itw, T_gp);
        }
 
        for (Index za_inc_idx = 0; za_inc_idx < doit_za_grid_size;
             za_inc_idx++) {
          for (Index aa_inc_idx = 0; aa_inc_idx < aa_grid.nelem();
               aa_inc_idx++) {
            if (ti < 0)  // Temperature interpolation
            {
              for (Index i = 0; i < stokes_dim; i++) {
                for (Index j = 0; j < stokes_dim; j++) {
                  pha_mat_spt(i_se_flat, za_inc_idx, aa_inc_idx, i, j) =
                      interp(itw,
                             pha_mat_sptDOITOpt[i_se_flat](joker,
                                                           za_index,
                                                           aa_index,
                                                           za_inc_idx,
                                                           aa_inc_idx,
                                                           i,
                                                           j),
                             T_gp);
                }
              }
            } else {
              pha_mat_spt(i_se_flat, za_inc_idx, aa_inc_idx, joker, joker) =
                  pha_mat_sptDOITOpt[i_se_flat](ti,
                                                za_index,
                                                aa_index,
                                                za_inc_idx,
                                                aa_inc_idx,
                                                joker,
                                                joker);
            }
          }
        }
      }  // TRS
 
      i_se_flat++;
    }
  }
}
 
/* Workspace method: Doxygen documentation will be auto-generated */
void opt_prop_sptFromData(  // Output and Input:
    ArrayOfPropagationMatrix& ext_mat_spt,
    ArrayOfStokesVector& abs_vec_spt,
    // Input:
    const ArrayOfArrayOfSingleScatteringData& scat_data,
    const Vector& za_grid,
    const Vector& aa_grid,
    const Index& za_index,  // propagation directions
    const Index& aa_index,
    const Index& f_index,
    const Vector& f_grid,
    const Numeric& rtp_temperature,
    const Tensor4& pnd_field,
    const Index& scat_p_index,
    const Index& scat_lat_index,
    const Index& scat_lon_index,
    const Verbosity& verbosity) {
  const Index N_ss = scat_data.nelem();
  const Numeric za_sca = za_grid[za_index];
  const Numeric aa_sca = aa_grid[aa_index];
 
  DEBUG_ONLY(const Index N_se_total = TotalNumberOfElements(scat_data);
             if (N_ss) {
               assert(ext_mat_spt[0].NumberOfFrequencies() == N_se_total);
               assert(abs_vec_spt[0].NumberOfFrequencies() == N_se_total);
             });
 
  // Check that we don't have scat_data_mono here. Only checking the first
  // scat element, assuming the other elements have been processed in the same
  // manner. That's save against having mono data, but not against having
  // individual elements produced with only a single frequency. This, however,
  // has been checked by scat_data_raw reading routines (ScatSpecies/Element*Add/Read).
  // Unsafe, however, remain when ReadXML is used directly or if scat_data(_raw) is
  // (partly) produced from scat_data_singleTmatrix.
  if (scat_data[0][0].f_grid.nelem() < 2) {
    ostringstream os;
    os << "Scattering data seems to be *scat_data_mono* (1 freq point only),\n"
       << "but frequency interpolable data (*scat_data* with >=2 freq points) "
       << "is expected here.";
    throw runtime_error(os.str());
  }
 
  // Phase matrix in laboratory coordinate system. Dimensions:
  // [frequency, za_inc, aa_inc, stokes_dim, stokes_dim]
  Tensor3 ext_mat_data_int;
  Tensor3 abs_vec_data_int;
 
  // Initialisation
  ext_mat_spt = 0.;
  abs_vec_spt = 0.;
 
  Index i_se_flat = 0;
  // Loop over the included scattering species
  for (Index i_ss = 0; i_ss < N_ss; i_ss++) {
    const Index N_se = scat_data[i_ss].nelem();
 
    // Loop over the included scattering elements
    for (Index i_se = 0; i_se < N_se; i_se++) {
      // If the particle number density at a specific point in the
      // atmosphere for the i_se scattering element is zero, we don't need
      // to do the transformation
 
      if (pnd_field(i_se_flat, scat_p_index, scat_lat_index, scat_lon_index) >
          PND_LIMIT) {
        // First we have to transform the data from the coordinate system
        // used in the database (depending on the kind of ptype) to the
        // laboratory coordinate system.
 
        // Frequency interpolation:
 
        // The data is interpolated on one frequency.
        //
        // Resize the variables for the interpolated data:
        //
        ext_mat_data_int.resize(
            EXT_MAT_DATA.npages(), EXT_MAT_DATA.nrows(), EXT_MAT_DATA.ncols());
        //
        abs_vec_data_int.resize(
            ABS_VEC_DATA.npages(), ABS_VEC_DATA.nrows(), ABS_VEC_DATA.ncols());
 
        // Gridpositions:
        GridPos freq_gp;
        gridpos(freq_gp, F_DATAGRID, f_grid[f_index]);
        GridPos t_gp;
        Vector itw;
 
        if (T_DATAGRID.nelem() > 1) {
          ostringstream os;
          os << "In opt_prop_sptFromData.\n"
             << "The temperature grid of the scattering data does not\n"
             << "cover the atmospheric temperature at cloud location.\n"
             << "The data should include the value T = " << rtp_temperature
             << " K.";
          chk_interpolation_grids(os.str(), T_DATAGRID, rtp_temperature);
 
          gridpos(t_gp, T_DATAGRID, rtp_temperature);
 
          // Interpolation weights:
          itw.resize(4);
          interpweights(itw, freq_gp, t_gp);
 
          for (Index i_za_sca = 0; i_za_sca < EXT_MAT_DATA.npages();
               i_za_sca++) {
            for (Index i_aa_sca = 0; i_aa_sca < EXT_MAT_DATA.nrows();
                 i_aa_sca++) {
              //
              // Interpolation of extinction matrix:
              //
              for (Index i = 0; i < EXT_MAT_DATA.ncols(); i++) {
                ext_mat_data_int(i_za_sca, i_aa_sca, i) =
                    interp(itw,
                           EXT_MAT_DATA(joker, joker, i_za_sca, i_aa_sca, i),
                           freq_gp,
                           t_gp);
              }
            }
          }
 
          for (Index i_za_sca = 0; i_za_sca < ABS_VEC_DATA.npages();
               i_za_sca++) {
            for (Index i_aa_sca = 0; i_aa_sca < ABS_VEC_DATA.nrows();
                 i_aa_sca++) {
              //
              // Interpolation of absorption vector:
              //
              for (Index i = 0; i < ABS_VEC_DATA.ncols(); i++) {
                abs_vec_data_int(i_za_sca, i_aa_sca, i) =
                    interp(itw,
                           ABS_VEC_DATA(joker, joker, i_za_sca, i_aa_sca, i),
                           freq_gp,
                           t_gp);
              }
            }
          }
        } else {
          // Interpolation weights:
          itw.resize(2);
          interpweights(itw, freq_gp);
 
          for (Index i_za_sca = 0; i_za_sca < EXT_MAT_DATA.npages();
               i_za_sca++) {
            for (Index i_aa_sca = 0; i_aa_sca < EXT_MAT_DATA.nrows();
                 i_aa_sca++) {
              //
              // Interpolation of extinction matrix:
              //
              for (Index i = 0; i < EXT_MAT_DATA.ncols(); i++) {
                ext_mat_data_int(i_za_sca, i_aa_sca, i) =
                    interp(itw,
                           EXT_MAT_DATA(joker, 0, i_za_sca, i_aa_sca, i),
                           freq_gp);
              }
            }
          }
 
          for (Index i_za_sca = 0; i_za_sca < ABS_VEC_DATA.npages();
               i_za_sca++) {
            for (Index i_aa_sca = 0; i_aa_sca < ABS_VEC_DATA.nrows();
                 i_aa_sca++) {
              //
              // Interpolation of absorption vector:
              //
              for (Index i = 0; i < ABS_VEC_DATA.ncols(); i++) {
                abs_vec_data_int(i_za_sca, i_aa_sca, i) =
                    interp(itw,
                           ABS_VEC_DATA(joker, 0, i_za_sca, i_aa_sca, i),
                           freq_gp);
              }
            }
          }
        }
 
        //
        // Do the transformation into the laboratory coordinate system.
        //
        // Extinction matrix:
        //
        ext_matTransform(ext_mat_spt[i_se_flat],
                         ext_mat_data_int,
                         ZA_DATAGRID,
                         AA_DATAGRID,
                         PART_TYPE,
                         za_sca,
                         aa_sca,
                         verbosity);
        //
        // Absorption vector:
        //
        abs_vecTransform(abs_vec_spt[i_se_flat],
                         abs_vec_data_int,
                         ZA_DATAGRID,
                         AA_DATAGRID,
                         PART_TYPE,
                         za_sca,
                         aa_sca,
                         verbosity);
      }
 
      i_se_flat++;
    }
  }
}
 
/* Workspace method: Doxygen documentation will be auto-generated */
void opt_prop_sptFromScat_data(  // Output and Input:
    ArrayOfPropagationMatrix& ext_mat_spt,
    ArrayOfStokesVector& abs_vec_spt,
    // Input:
    const ArrayOfArrayOfSingleScatteringData& scat_data,
    const Index& scat_data_checked,
    const Vector& za_grid,
    const Vector& aa_grid,
    const Index& za_index,  // propagation directions
    const Index& aa_index,
    const Index& f_index,
    const Numeric& rtp_temperature,
    const Tensor4& pnd_field,
    const Index& scat_p_index,
    const Index& scat_lat_index,
    const Index& scat_lon_index,
    const Verbosity& verbosity) {
  if (scat_data_checked != 1)
    throw runtime_error(
        "The scattering data must be flagged to have "
        "passed a consistency check (scat_data_checked=1).");
 
  const Index N_ss = scat_data.nelem();
  const Index stokes_dim = ext_mat_spt[0].StokesDimensions();
  const Numeric za_sca = za_grid[za_index];
  const Numeric aa_sca = aa_grid[aa_index];
 
  if (stokes_dim > 4 || stokes_dim < 1) {
    throw runtime_error(
        "The dimension of the stokes vector \n"
        "must be 1,2,3 or 4");
  }
 
  DEBUG_ONLY(const Index N_se_total = TotalNumberOfElements(scat_data);)
  assert(ext_mat_spt.nelem() == N_se_total);
  assert(abs_vec_spt.nelem() == N_se_total);
 
  // Phase matrix in laboratory coordinate system. Dimensions:
  // [frequency, za_inc, aa_inc, stokes_dim, stokes_dim]
  Tensor3 ext_mat_data_int;
  Tensor3 abs_vec_data_int;
 
  // Initialisation
  for (auto& pm : ext_mat_spt) pm.SetZero();
  for (auto& sv : abs_vec_spt) sv.SetZero();
 
  Index this_f_index;
 
  Index i_se_flat = 0;
  // Loop over the included scattering species
  for (Index i_ss = 0; i_ss < N_ss; i_ss++) {
    const Index N_se = scat_data[i_ss].nelem();
 
    // Loop over the included scattering elements
    for (Index i_se = 0; i_se < N_se; i_se++) {
      // If the particle number density at a specific point in the
      // atmosphere for the i_se scattering element is zero, we don't need
      // to do the transformation
 
      if (pnd_field(i_se_flat, scat_p_index, scat_lat_index, scat_lon_index) >
          PND_LIMIT) {
        // First we have to transform the data from the coordinate system
        // used in the database (depending on the kind of ptype) to the
        // laboratory coordinate system.
 
        // Resize the variables for the interpolated data (1freq, 1T):
        ext_mat_data_int.resize(
            EXT_MAT_DATA.npages(), EXT_MAT_DATA.nrows(), EXT_MAT_DATA.ncols());
        abs_vec_data_int.resize(
            ABS_VEC_DATA.npages(), ABS_VEC_DATA.nrows(), ABS_VEC_DATA.ncols());
 
        // Gridpositions and interpolation weights;
        GridPos t_gp;
        Vector itw;
        if (EXT_MAT_DATA.nbooks() > 1 || ABS_VEC_DATA.nbooks() > 1) {
          ostringstream os;
          os << "In opt_prop_sptFromScat_data.\n"
             << "The temperature grid of the scattering data does not\n"
             << "cover the atmospheric temperature at cloud location.\n"
             << "The data should include the value T = " << rtp_temperature
             << " K.";
          chk_interpolation_grids(os.str(), T_DATAGRID, rtp_temperature);
 
          gridpos(t_gp, T_DATAGRID, rtp_temperature);
 
          // Interpolation weights:
          itw.resize(2);
          interpweights(itw, t_gp);
        }
 
        // Frequency extraction and temperature interpolation
 
        if (EXT_MAT_DATA.nshelves() == 1)
          this_f_index = 0;
        else
          this_f_index = f_index;
 
        if (EXT_MAT_DATA.nbooks() > 1) {
          // Interpolation of extinction matrix:
          for (Index i_za_sca = 0; i_za_sca < EXT_MAT_DATA.npages();
               i_za_sca++) {
            for (Index i_aa_sca = 0; i_aa_sca < EXT_MAT_DATA.nrows();
                 i_aa_sca++) {
              for (Index i = 0; i < EXT_MAT_DATA.ncols(); i++) {
                ext_mat_data_int(i_za_sca, i_aa_sca, i) = interp(
                    itw,
                    EXT_MAT_DATA(this_f_index, joker, i_za_sca, i_aa_sca, i),
                    t_gp);
              }
            }
          }
        } else {
          ext_mat_data_int = EXT_MAT_DATA(this_f_index, 0, joker, joker, joker);
          /*
                  for (Index i_za_sca = 0; i_za_sca < EXT_MAT_DATA.npages();
                       i_za_sca++)
                  {
                      for(Index i_aa_sca = 0; i_aa_sca < EXT_MAT_DATA.nrows();
                          i_aa_sca++)
                      {
                          for (Index i = 0; i < EXT_MAT_DATA.ncols(); i++)
                          {
                              ext_mat_data_int(i_za_sca, i_aa_sca, i) =
                                EXT_MAT_DATA(this_f_index, 0,
                                                 i_za_sca, i_aa_sca, i);
                          }
                      }
                  } */
        }
 
        if (ABS_VEC_DATA.nshelves() == 1)
          this_f_index = 0;
        else
          this_f_index = f_index;
 
        if (ABS_VEC_DATA.nbooks() > 1) {
          // Interpolation of absorption vector:
          for (Index i_za_sca = 0; i_za_sca < ABS_VEC_DATA.npages();
               i_za_sca++) {
            for (Index i_aa_sca = 0; i_aa_sca < ABS_VEC_DATA.nrows();
                 i_aa_sca++) {
              for (Index i = 0; i < ABS_VEC_DATA.ncols(); i++) {
                abs_vec_data_int(i_za_sca, i_aa_sca, i) = interp(
                    itw,
                    ABS_VEC_DATA(this_f_index, joker, i_za_sca, i_aa_sca, i),
                    t_gp);
              }
            }
          }
        } else {
          abs_vec_data_int = ABS_VEC_DATA(this_f_index, 0, joker, joker, joker);
          /*
                  for (Index i_za_sca = 0; i_za_sca < ABS_VEC_DATA.npages();
                       i_za_sca++)
                  {
                      for(Index i_aa_sca = 0; i_aa_sca < ABS_VEC_DATA.nrows();
                          i_aa_sca++)
                      {
                          for (Index i = 0; i < ABS_VEC_DATA.ncols(); i++)
                          {
                              abs_vec_data_int(i_za_sca, i_aa_sca, i) =
                                ABS_VEC_DATA(this_f_index, 0,
                                                 i_za_sca, i_aa_sca, i);
                          }
                      }
                  } */
        }
 
        //
        // Do the transformation into the laboratory coordinate system.
        //
        // Extinction matrix:
        ext_matTransform(ext_mat_spt[i_se_flat],
                         ext_mat_data_int,
                         ZA_DATAGRID,
                         AA_DATAGRID,
                         PART_TYPE,
                         za_sca,
                         aa_sca,
                         verbosity);
        // Absorption vector:
        abs_vecTransform(abs_vec_spt[i_se_flat],
                         abs_vec_data_int,
                         ZA_DATAGRID,
                         AA_DATAGRID,
                         PART_TYPE,
                         za_sca,
                         aa_sca,
                         verbosity);
      }
      i_se_flat++;
    }
  }
}
 
/* Workspace method: Doxygen documentation will be auto-generated */
void opt_prop_bulkCalc(  // Output and Input:
    PropagationMatrix& ext_mat,
    StokesVector& abs_vec,
    // Input:
    const ArrayOfPropagationMatrix& ext_mat_spt,
    const ArrayOfStokesVector& abs_vec_spt,
    const Tensor4& pnd_field,
    const Index& scat_p_index,
    const Index& scat_lat_index,
    const Index& scat_lon_index,
    const Verbosity&) {
  Index N_se = abs_vec_spt.nelem();
  //assert( ext_mat_spt.npages()==N_se )
  if (ext_mat_spt.nelem() not_eq N_se) {
    ostringstream os;
    os << "Number of scattering elements in *abs_vec_spt* and *ext_mat_spt*\n"
       << "does not agree.";
    throw runtime_error(os.str());
  }
 
  Index stokes_dim = abs_vec_spt[0].StokesDimensions();
  //assert( ext_mat_spt.ncols()==stokes_dim && ext_mat_spt.nrows()==stokes_dim )
  if (ext_mat_spt[0].StokesDimensions() not_eq stokes_dim) {
    ostringstream os;
    os << "*stokes_dim* of *abs_vec_spt* and *ext_mat_spt* does not agree.";
    throw runtime_error(os.str());
  }
  if (stokes_dim > 4 || stokes_dim < 1) {
    ostringstream os;
    os << "The dimension of stokes vector can only be 1, 2, 3, or 4.";
    throw runtime_error(os.str());
  }
 
  ext_mat = PropagationMatrix(1, stokes_dim);
  ext_mat.SetZero();  // Initialize to zero!
  abs_vec = StokesVector(1, stokes_dim);
  abs_vec.SetZero();  // Initialize to zero!
 
  PropagationMatrix ext_mat_part(1, stokes_dim);
  ext_mat_part.SetZero();
  StokesVector abs_vec_part(1, stokes_dim);
  abs_vec_part.SetZero();
 
  // this is the loop over the different scattering elements
  for (Index l = 0; l < N_se; l++) {
    abs_vec_part.MultiplyAndAdd(
        pnd_field(l, scat_p_index, scat_lat_index, scat_lon_index),
        abs_vec_spt[l]);
    ext_mat_part.MultiplyAndAdd(
        pnd_field(l, scat_p_index, scat_lat_index, scat_lon_index),
        ext_mat_spt[l]);
  }
 
  //Add absorption due single scattering element.
  abs_vec += abs_vec_part;
  //Add extinction matrix due single scattering element to *ext_mat*.
  ext_mat += ext_mat_part;
}
 
/* Workspace method: Doxygen documentation will be auto-generated */
void ext_matAddGas(PropagationMatrix& ext_mat,
                   const ArrayOfPropagationMatrix& propmat_clearsky,
                   const Verbosity&) {
  // Number of Stokes parameters:
  const Index stokes_dim = ext_mat.StokesDimensions();
 
  // The second dimension of ext_mat must also match the number of
  // Stokes parameters:
  if (stokes_dim != propmat_clearsky[0].StokesDimensions())
    throw runtime_error(
        "Col dimension of propmat_clearsky "
        "inconsistent with col dimension in ext_mat.");
 
  // Number of frequencies:
  const Index f_dim = ext_mat.NumberOfFrequencies();
 
  // This must be consistent with the second dimension of
  // propmat_clearsky. Check this:
  if (f_dim != propmat_clearsky[0].NumberOfFrequencies())
    throw runtime_error(
        "Frequency dimension of ext_mat and propmat_clearsky\n"
        "are inconsistent in ext_matAddGas.");
 
  for (auto& pm : propmat_clearsky) ext_mat += pm;
}
 
/* Workspace method: Doxygen documentation will be auto-generated */
void abs_vecAddGas(StokesVector& abs_vec,
                   const ArrayOfPropagationMatrix& propmat_clearsky,
                   const Verbosity&) {
  // Number of frequencies:
  const Index f_dim = abs_vec.NumberOfFrequencies();
  const Index stokes_dim = abs_vec.StokesDimensions();
 
  // This must be consistent with the second dimension of
  // propmat_clearsky. Check this:
  if (f_dim != propmat_clearsky[0].NumberOfFrequencies())
    throw runtime_error(
        "Frequency dimension of abs_vec and propmat_clearsky\n"
        "are inconsistent in abs_vecAddGas.");
  if (stokes_dim != propmat_clearsky[0].StokesDimensions())
    throw runtime_error(
        "Stokes dimension of abs_vec and propmat_clearsky\n"
        "are inconsistent in abs_vecAddGas.");
 
  // Loop all frequencies. Of course this includes the special case
  // that there is only one frequency.
  for (auto& pm : propmat_clearsky)
    abs_vec += pm;  // Defined to only add to the
 
  // We don't have to do anything about higher elements of abs_vec,
  // since scalar gas absorption only influences the first element.
}
 
/* Workspace method: Doxygen documentation will be auto-generated */
/*
void ext_matAddGasZeeman( Tensor3&      ext_mat,
                          const Tensor3&  ext_mat_zee,
                          const Verbosity&)
{
  // Number of Stokes parameters:
  const Index stokes_dim = ext_mat.ncols();
 
  // The second dimension of ext_mat must also match the number of
  // Stokes parameters:
  if ( stokes_dim != ext_mat.nrows() )
    throw runtime_error("Row dimension of ext_mat inconsistent with "
                        "column dimension."); 
 
  for ( Index i=0; i<stokes_dim; ++i )
    {
      for ( Index j=0; j<stokes_dim; ++j )
        {
          // Add the zeeman extinction to extinction matrix.
          ext_mat(joker,i,j) += ext_mat_zee(joker, i, j);
        }
      
    }
}
*/
 
/* Workspace method: Doxygen documentation will be auto-generated */
/*
void abs_vecAddGasZeeman( Matrix&      abs_vec,
                          const Matrix& abs_vec_zee,
                          const Verbosity&)
{
  // Number of Stokes parameters:
  const Index stokes_dim = abs_vec_zee.ncols();
  // that there is only one frequency.
  for ( Index j=0; j<stokes_dim; ++j )
    {
      abs_vec(joker,j) += abs_vec_zee(joker,j);
    }
}
*/
 
/* Workspace method: Doxygen documentation will be auto-generated */
void pha_matCalc(Tensor4& pha_mat,
                 const Tensor5& pha_mat_spt,
                 const Tensor4& pnd_field,
                 const Index& atmosphere_dim,
                 const Index& scat_p_index,
                 const Index& scat_lat_index,
                 const Index& scat_lon_index,
                 const Verbosity&) {
  Index N_se = pha_mat_spt.nshelves();
  Index Nza = pha_mat_spt.nbooks();
  Index Naa = pha_mat_spt.npages();
  Index stokes_dim = pha_mat_spt.nrows();
 
  pha_mat.resize(Nza, Naa, stokes_dim, stokes_dim);
 
  // Initialisation
  pha_mat = 0.0;
 
  Index ilat = 0;
  Index ilon = 0;
  if (atmosphere_dim > 1) ilat = scat_lat_index;
  if (atmosphere_dim > 2) ilon = scat_lon_index;
 
  if (atmosphere_dim == 1) {
    // For 1d atmospheres, we additinally integrate the phase matrix over the
    // azimuth, because there is no azimuth dependency of the incoming
    // field.
 
    Numeric grid_step_size_azimuth = 360. / (Numeric)(Naa - 1) * DEG2RAD;
 
    // this is a loop over the different scattering elements
    for (Index pt_index = 0; pt_index < N_se; ++pt_index)
      // these are loops over zenith angle and azimuth angle
      for (Index za_index = 0; za_index < Nza; ++za_index)
        for (Index aa_index = 0; aa_index < Naa - 1; ++aa_index)
          // now the last two loops over the stokes dimension.
          for (Index stokes_index_1 = 0; stokes_index_1 < stokes_dim;
               ++stokes_index_1)
            for (Index stokes_index_2 = 0; stokes_index_2 < stokes_dim;
                 ++stokes_index_2)
              //summation of the product of pnd_field and
              //pha_mat_spt.
              pha_mat(za_index, 0, stokes_index_1, stokes_index_2) +=
                  ((pha_mat_spt(pt_index,
                                za_index,
                                aa_index,
                                stokes_index_1,
                                stokes_index_2) +
                    pha_mat_spt(pt_index,
                                za_index,
                                aa_index + 1,
                                stokes_index_1,
                                stokes_index_2)) /
                   2 * grid_step_size_azimuth *
                   pnd_field(pt_index, scat_p_index, ilat, ilon));
  } else {
    // this is a loop over the different scattering elements
    for (Index pt_index = 0; pt_index < N_se; ++pt_index)
      // these are loops over zenith angle and azimuth angle
      for (Index za_index = 0; za_index < Nza; ++za_index)
        for (Index aa_index = 0; aa_index < Naa; ++aa_index)
          // now the last two loops over the stokes dimension.
          for (Index stokes_index_1 = 0; stokes_index_1 < stokes_dim;
               ++stokes_index_1)
            for (Index stokes_index_2 = 0; stokes_index_2 < stokes_dim;
                 ++stokes_index_2)
              //summation of the product of pnd_field and
              //pha_mat_spt.
              pha_mat(za_index, aa_index, stokes_index_1, stokes_index_2) +=
                  (pha_mat_spt(pt_index,
                               za_index,
                               aa_index,
                               stokes_index_1,
                               stokes_index_2) *
                   pnd_field(pt_index, scat_p_index, ilat, ilon));
  }
}
 
/* Workspace method: Doxygen documentation will be auto-generated */
void scat_dataCheck(  //Input:
    const ArrayOfArrayOfSingleScatteringData& scat_data,
    const String& check_type,
    const Numeric& threshold,
    const Verbosity& verbosity) {
  CREATE_OUT0;
  CREATE_OUT1;
  CREATE_OUT2;
  //CREATE_OUT3;
 
  // FIXME:
  // so far, this works for both scat_data and scat_data_raw. Needs to be
  // adapted, though, once we have WSM that can create Z/K/a with different
  // f/T dimensions than scat_data_single.f/T_grid.
 
  const Index N_ss = scat_data.nelem();
 
  // 1) any negative values in Z11, K11, or a1? K11>=a1?
  // 2) scat_data containing any NaN?
  // 3) sca_mat norm sufficiently good (int(Z11)~=K11-a1?)
 
  // Loop over the included scattering species
  out2 << " checking for negative values in Z11, K11, and a1, and for K11<a1\n";
  for (Index i_ss = 0; i_ss < N_ss; i_ss++) {
    const Index N_se = scat_data[i_ss].nelem();
 
    // Loop over the included scattering elements
    for (Index i_se = 0; i_se < N_se; i_se++) {
      for (Index f = 0; f < F_DATAGRID.nelem(); f++) {
        for (Index zai = 0; zai < ABS_VEC_DATA.npages(); zai++)
          for (Index aai = 0; aai < ABS_VEC_DATA.nrows(); aai++) {
            for (Index t = 0; t < T_DATAGRID.nelem(); t++) {
              if (EXT_MAT_DATA(f, t, zai, aai, 0) < 0 ||
                  ABS_VEC_DATA(f, t, zai, aai, 0) < 0) {
                ostringstream os;
                os << "Scatt. species #" << i_ss << " element #" << i_se
                   << " contains negative K11 or a1 at f#" << f << ", T#" << t
                   << ", za#" << zai << ", aa#" << aai << "\n";
                throw runtime_error(os.str());
              }
              if (EXT_MAT_DATA(f, t, zai, aai, 0) <
                  ABS_VEC_DATA(f, t, zai, aai, 0)) {
                ostringstream os;
                os << "Scatt. species #" << i_ss << " element #" << i_se
                   << " has K11<a1 at f#" << f << ", T#" << t << ", za#" << zai
                   << ", aa#" << aai << "\n";
                throw runtime_error(os.str());
              }
            }
            // Since allowing pha_mat to have a single T entry only (while
            // T_grid, ext_mat, abs_vec have more), we need a separate T loop
            // for pha_mat
            Index nTpha = PHA_MAT_DATA.nvitrines();
            for (Index t = 0; t < nTpha; t++) {
              for (Index zas = 0; zas < PHA_MAT_DATA.nshelves(); zas++)
                for (Index aas = 0; aas < PHA_MAT_DATA.nbooks(); aas++)
                  if (PHA_MAT_DATA(f, t, zas, aas, zai, aai, 0) < 0) {
                    ostringstream os;
                    os << "Scatt. species #" << i_ss << " element #" << i_se
                       << " contains negative Z11 at f#" << f << ", T#" << t
                       << " (of " << nTpha << "), za_sca#" << zas << ", aa_sca#"
                       << aas << ", za_inc#" << zai << ", aa_inc#" << aai
                       << "\n";
                    throw runtime_error(os.str());
                  }
            }
          }
      }
    }
  }
 
  // Loop over the included scattering species
  out2 << " checking for NaN anywhere in Z, K, and a\n";
  for (Index i_ss = 0; i_ss < N_ss; i_ss++) {
    const Index N_se = scat_data[i_ss].nelem();
 
    // Loop over the included scattering elements
    for (Index i_se = 0; i_se < N_se; i_se++) {
      for (Index f = 0; f < F_DATAGRID.nelem(); f++) {
        for (Index zai = 0; zai < ABS_VEC_DATA.npages(); zai++)
          for (Index aai = 0; aai < ABS_VEC_DATA.nrows(); aai++) {
            for (Index t = 0; t < T_DATAGRID.nelem(); t++) {
              for (Index st = 0; st < ABS_VEC_DATA.ncols(); st++)
                if (std::isnan(ABS_VEC_DATA(f, t, zai, aai, st))) {
                  ostringstream os;
                  os << "Scatt. species #" << i_ss << " element #" << i_se
                     << " contains NaN in abs_vec at f#" << f << ", T#" << t
                     << ", za#" << zai << ", aa#" << aai << ", stokes #" << st
                     << "\n";
                  throw runtime_error(os.str());
                }
              for (Index st = 0; st < EXT_MAT_DATA.ncols(); st++)
                if (std::isnan(EXT_MAT_DATA(f, t, zai, aai, st))) {
                  ostringstream os;
                  os << "Scatt. species #" << i_ss << " element #" << i_se
                     << " contains NaN in ext_mat at f#" << f << ", T#" << t
                     << ", za#" << zai << ", aa#" << aai << ", stokes #" << st
                     << "\n";
                  throw runtime_error(os.str());
                }
            }
            Index nTpha = PHA_MAT_DATA.nvitrines();
            for (Index t = 0; t < nTpha; t++) {
              for (Index zas = 0; zas < PHA_MAT_DATA.nshelves(); zas++)
                for (Index aas = 0; aas < PHA_MAT_DATA.nbooks(); aas++)
                  for (Index st = 0; st < PHA_MAT_DATA.ncols(); st++)
                    if (std::isnan(
                            PHA_MAT_DATA(f, t, zas, aas, zai, aai, st))) {
                      ostringstream os;
                      os << "Scatt. species #" << i_ss << " element #" << i_se
                         << " contains NaN in pha_mat at f#" << f << ", T#" << t
                         << " (of " << nTpha << "), za_sca#" << zas
                         << ", aa_sca#" << aas << ", za_inc#" << zai
                         << ", aa_inc#" << aai << ", stokes #"
                         << "\n";
                      throw runtime_error(os.str());
                    }
            }
          }
      }
    }
  }
 
  if (check_type.toupper() == "ALL") {
    // Loop over the included scattering species
    out2 << " checking normalization of scattering matrix\n";
    for (Index i_ss = 0; i_ss < N_ss; i_ss++) {
      const Index N_se = scat_data[i_ss].nelem();
 
      // Loop over the included scattering elements
      for (Index i_se = 0; i_se < N_se; i_se++)
        if (T_DATAGRID.nelem() == PHA_MAT_DATA.nvitrines()) switch (PART_TYPE) {
            case PTYPE_TOTAL_RND: {
              for (Index f = 0; f < F_DATAGRID.nelem(); f++) {
                for (Index t = 0; t < T_DATAGRID.nelem(); t++) {
                  Numeric Csca = AngIntegrate_trapezoid(
                      PHA_MAT_DATA(f, t, joker, 0, 0, 0, 0), ZA_DATAGRID);
                  Numeric Cext_data = EXT_MAT_DATA(f, t, 0, 0, 0);
                  //Numeric Cabs = Cext_data - Csca;
                  Numeric Cabs_data = ABS_VEC_DATA(f, t, 0, 0, 0);
                  Numeric Csca_data = Cext_data - Cabs_data;
 
                  /*
                    out3 << "  Coefficients in database: "
                         << "Cext: " << Cext_data << " Cabs: " << Cabs_data
                         << " Csca: " << Csca_data << "\n"
                         << "  Calculated coefficients: "
                         << "Cabs calc: " << Cabs
                         << " Csca calc: " << Csca << "\n"
                         << "  Deviations "
                         << "Cabs: " << 1e2*Cabs/Cabs_data-1e2
                         << "% Csca: " << 1e2*Csca/Csca_data-1e2
                         << "% Alb: " << (Csca-Csca_data)/Cext_data << "\n";
                    */
 
                  //if (abs(Csca/Csca_data-1.)*Csca_data/Cext_data > threshold)
                  // below equivalent to the above
                  // (it's actually the (absolute) albedo deviation!)
                  if (abs(Csca - Csca_data) / Cext_data > threshold) {
                    ostringstream os;
                    os << "  Deviations in scat_data too large:\n"
                       << "  scat dev [%] " << 1e2 * Csca / Csca_data - 1e2
                       << " at nominal (actual) albedo of "
                       << Csca_data / Cext_data << " (" << Csca / Cext_data
                       << ").\n"
                       << "  Check entry for scattering element " << i_se
                       << " of scattering species " << i_ss << " at " << f
                       << ".frequency and " << t << ".temperature!\n";
                    throw runtime_error(os.str());
                  }
                }
              }
              break;
            }
 
            case PTYPE_AZIMUTH_RND: {
              for (Index f = 0; f < F_DATAGRID.nelem(); f++) {
                for (Index t = 0; t < T_DATAGRID.nelem(); t++) {
                  for (Index iza = 0; iza < ABS_VEC_DATA.npages(); iza++) {
                    Numeric Csca =
                        2 * AngIntegrate_trapezoid(
                                PHA_MAT_DATA(f, t, joker, joker, iza, 0, 0),
                                ZA_DATAGRID,
                                AA_DATAGRID);
                    Numeric Cext_data = EXT_MAT_DATA(f, t, iza, 0, 0);
                    //Numeric Cabs = Cext_data - Csca;
                    Numeric Cabs_data = ABS_VEC_DATA(f, t, iza, 0, 0);
                    Numeric Csca_data = Cext_data - Cabs_data;
 
                    /*
                      out3 << "  Coefficients in database: "
                           << "Cext: " << Cext_data << " Cabs: " << Cabs_data
                           << " Csca: " << Csca_data << "\n"
                           << "  Calculated coefficients: "
                           << "Cabs calc: " << Cabs
                           << " Csca calc: " << Csca << "\n"
                           << "  Deviations "
                           << "Cabs: " << 1e2*Cabs/Cabs_data-1e2
                           << "% Csca: " << 1e2*Csca/Csca_data-1e2
                           << "% Alb: " << (Csca-Csca_data)/Cext_data << "\n";
                      */
 
                    //if (abs(Csca/Csca_data-1.)*Csca_data/Cext_data > threshold)
                    // below equivalent to the above
                    // (it's actually the (absolute) albedo deviation!)
                    if (abs(Csca - Csca_data) / Cext_data > threshold) {
                      ostringstream os;
                      os << "  Deviations in scat_data too large:\n"
                         << "  scat dev [%] " << 1e2 * Csca / Csca_data - 1e2
                         << " at nominal (actual) albedo of "
                         << Csca_data / Cext_data << " (" << Csca / Cext_data
                         << ").\n"
                         << "  Check entry for scattering element " << i_se
                         << " of scattering species " << i_ss << " at " << f
                         << ". frequency, " << t << ". temperature, and " << iza
                         << ". incident polar angle!\n";
                      throw runtime_error(os.str());
                    }
                  }
                }
              }
              break;
            }
 
            default: {
              out0
                  << "  WARNING:\n"
                  << "  scat_data consistency check not implemented (yet?!) for\n"
                  << "  ptype " << PART_TYPE << "!\n";
            }
          }
        else
          out2 << "  WARNING:\n"
               << "  scat_data norm check can not be performed for pha_mat-only"
               << " T-reduced scattering elements\n"
               << "  as found in scatt element #" << i_se
               << " of scatt species #" << i_ss << "!\n";
    }
  } else if (check_type.toupper() == "SANE") {
    out1 << "  WARNING:\n"
         << "  Normalization check on pha_mat switched off.\n"
         << "  Scattering solution might be wrong.\n";
  } else {
    ostringstream os;
    os << "Invalid value for argument *check_type*: '" << check_type << "'.\n";
    os << "Valid values are 'all' or 'none'.";
    throw runtime_error(os.str());
  }
}
 
/* Workspace method: Doxygen documentation will be auto-generated */
void DoitScatteringDataPrepare(
    Workspace& ws,  //Output:
    ArrayOfTensor7& pha_mat_sptDOITOpt,
    ArrayOfArrayOfSingleScatteringData& scat_data_mono,
    Tensor7& pha_mat_doit,
    //Output and Input:
    Vector& aa_grid,
    //Input:
    const Index& doit_za_grid_size,
    const ArrayOfArrayOfSingleScatteringData& scat_data,
    const Index& scat_data_checked,
    const Index& f_index,
    const Index& atmosphere_dim,
    const Index& stokes_dim,
    const Tensor3& t_field,
    const ArrayOfIndex& cloudbox_limits,
    const Tensor4& pnd_field,
    const Agenda& pha_mat_spt_agenda,
    const Verbosity& verbosity) {
  if (scat_data_checked != 1)
    throw runtime_error(
        "The scattering data must be flagged to have "
        "passed a consistency check (scat_data_checked=1).");
 
  // Number of azimuth angles.
  const Index Naa = aa_grid.nelem();
  Vector grid_stepsize(2);
  grid_stepsize[0] = 180. / (Numeric)(doit_za_grid_size - 1);
  //grid_stepsize[1] = 360./(Numeric)(Naa - 1);
 
  // Initialize variable *pha_mat_spt*
  Tensor5 pha_mat_spt_local(pnd_field.nbooks(),
                            doit_za_grid_size,
                            aa_grid.nelem(),
                            stokes_dim,
                            stokes_dim,
                            0.);
  Tensor4 pha_mat_local(doit_za_grid_size, Naa, stokes_dim, stokes_dim, 0.);
  Tensor6 pha_mat_local_out(cloudbox_limits[1] - cloudbox_limits[0] + 1,
                            doit_za_grid_size,
                            doit_za_grid_size,
                            Naa,
                            stokes_dim,
                            stokes_dim,
                            0.);
 
  // Interpolate all the data in frequency
  scat_data_monoExtract(scat_data_mono, scat_data, f_index, verbosity);
 
  // For 1D calculation the scat_aa dimension is not required:
  Index N_aa_sca;
  if (atmosphere_dim == 1)
    N_aa_sca = 1;
  else
    N_aa_sca = aa_grid.nelem();
 
  Vector za_grid;
  nlinspace(za_grid, 0, 180, doit_za_grid_size);
 
  assert(scat_data.nelem() == scat_data_mono.nelem());
 
  const Index N_ss = scat_data.nelem();
  // FIXME: We need this still as a workspace variable because pha_mat_spt_agenda
  // contains a WS method that requires it as input
  pha_mat_sptDOITOpt.resize(TotalNumberOfElements(scat_data));
 
  Index i_se_flat = 0;
  for (Index i_ss = 0; i_ss < N_ss; i_ss++) {
    const Index N_se = scat_data[i_ss].nelem();
 
    for (Index i_se = 0; i_se < N_se; i_se++) {
      Index N_T = scat_data_mono[i_ss][i_se].T_grid.nelem();
      pha_mat_sptDOITOpt[i_se_flat].resize(N_T,
                                           doit_za_grid_size,
                                           N_aa_sca,
                                           doit_za_grid_size,
                                           aa_grid.nelem(),
                                           stokes_dim,
                                           stokes_dim);
 
      //    Initialize:
      pha_mat_sptDOITOpt[i_se_flat] = 0.;
 
      // Calculate all scattering angles for all combinations of incoming
      // and scattered directions and interpolation.
      for (Index t_idx = 0; t_idx < N_T; t_idx++) {
        // These are the scattered directions as called in *scat_field_calc*
        for (Index za_sca_idx = 0; za_sca_idx < doit_za_grid_size;
             za_sca_idx++) {
          for (Index aa_sca_idx = 0; aa_sca_idx < N_aa_sca; aa_sca_idx++) {
            // Integration is performed over all incoming directions
            for (Index za_inc_idx = 0; za_inc_idx < doit_za_grid_size;
                 za_inc_idx++) {
              for (Index aa_inc_idx = 0; aa_inc_idx < aa_grid.nelem();
                   aa_inc_idx++) {
                pha_matTransform(
                    pha_mat_sptDOITOpt[i_se_flat](t_idx,
                                                  za_sca_idx,
                                                  aa_sca_idx,
                                                  za_inc_idx,
                                                  aa_inc_idx,
                                                  joker,
                                                  joker),
                    scat_data_mono[i_ss][i_se].pha_mat_data(
                        0, t_idx, joker, joker, joker, joker, joker),
                    scat_data_mono[i_ss][i_se].za_grid,
                    scat_data_mono[i_ss][i_se].aa_grid,
                    scat_data_mono[i_ss][i_se].ptype,
                    za_sca_idx,
                    aa_sca_idx,
                    za_inc_idx,
                    aa_inc_idx,
                    za_grid,
                    aa_grid,
                    verbosity);
              }
            }
          }
        }
      }
 
      i_se_flat++;
    }
  }
  // Interpolate phase matrix to current grid
  pha_mat_doit.resize(cloudbox_limits[1] - cloudbox_limits[0] + 1,
                      doit_za_grid_size,
                      N_aa_sca,
                      doit_za_grid_size,
                      Naa,
                      stokes_dim,
                      stokes_dim);
  pha_mat_doit = 0;
 
  if (atmosphere_dim == 1) {
    Index aa_index_local = 0;
 
    // Get pha_mat at the grid positions
    // Since atmosphere_dim = 1, there is no loop over lat and lon grids
    for (Index p_index = 0; p_index <= cloudbox_limits[1] - cloudbox_limits[0];
         p_index++) {
      Numeric rtp_temperature_local =
          t_field(p_index + cloudbox_limits[0], 0, 0);
      //There is only loop over zenith angle grid ; no azimuth angle grid.
      for (Index za_index_local = 0;
           za_index_local < doit_za_grid_size;
           za_index_local++) {
        // Dummy index
        Index index_zero = 0;
 
        // Calculate the phase matrix of individual scattering elements
        pha_mat_spt_agendaExecute(ws,
                                  pha_mat_spt_local,
                                  za_index_local,
                                  index_zero,
                                  index_zero,
                                  p_index,
                                  aa_index_local,
                                  rtp_temperature_local,
                                  pha_mat_spt_agenda);
 
        // Sum over all scattering elements
        pha_matCalc(pha_mat_local,
                    pha_mat_spt_local,
                    pnd_field,
                    atmosphere_dim,
                    p_index,
                    0,
                    0,
                    verbosity);
        pha_mat_doit(
            p_index, za_index_local, 0, joker, joker, joker, joker) =
            pha_mat_local;
      }
    }
 
    // Set incoming azimuth grid scattering to zero, because there is no
    // no azimuth dependcy for 1d atmospheres
    aa_grid.resize(1);
    aa_grid = 0;
  }
}
 
/* Workspace method: Doxygen documentation will be auto-generated */
void scat_dataCalc(ArrayOfArrayOfSingleScatteringData& scat_data,
                   const ArrayOfArrayOfSingleScatteringData& scat_data_raw,
                   const Vector& f_grid,
                   const Index& interp_order,
                   const Verbosity&)
// FIXME: when we allow K, a, Z to be on different f and T grids, their use in
// the scatt solvers needs to be reviewed again and adaptedto this!
{
  //Extrapolation factor:
  //const Numeric extpolfac = 0.5;
 
  Index nf = f_grid.nelem();
 
  // Check, whether single scattering data contains the right frequencies:
  // The check was changed to allow extrapolation at the boundaries of the
  // frequency grid.
  const String which_interpolation = "scat_data_raw.f_grid to f_grid";
  for (Index i_ss = 0; i_ss < scat_data_raw.nelem(); i_ss++) {
    for (Index i_se = 0; i_se < scat_data_raw[i_ss].nelem(); i_se++) {
      // Check for the special case that ssd.f_grid f_grid have only one
      // element. If identical, that's  fine. If not, throw error.
      if (scat_data_raw[i_ss][i_se].f_grid.nelem() == 1 && nf == 1)
        if (!is_same_within_epsilon(scat_data_raw[i_ss][i_se].f_grid[0],
                                    f_grid[0],
                                    2 * DBL_EPSILON)) {
          ostringstream os;
          os << "There is a problem with the grids for the following "
             << "interpolation:\n"
             << which_interpolation << "\n"
             << "If original grid has only 1 element, the new grid must also have\n"
             << "only a single element and hold the same value as the original grid.";
          throw runtime_error(os.str());
        }
 
      // check with extrapolation
      chk_interpolation_grids(which_interpolation,
                              scat_data_raw[i_ss][i_se].f_grid,
                              f_grid,
                              interp_order);
    }
  }
 
  //Initialise scat_data
  scat_data.resize(scat_data_raw.nelem());
 
  // Loop over the included scattering species
  for (Index i_ss = 0; i_ss < scat_data_raw.nelem(); i_ss++) {
    const Index N_se = scat_data_raw[i_ss].nelem();
 
    //Initialise scat_data
    scat_data[i_ss].resize(N_se);
 
    // Loop over the included scattering elements
    for (Index i_se = 0; i_se < N_se; i_se++) {
      //Stuff that doesn't need interpolating
      PART_TYPE = scat_data_raw[i_ss][i_se].ptype;
      F_DATAGRID = f_grid;
      T_DATAGRID = scat_data_raw[i_ss][i_se].T_grid;
      ZA_DATAGRID = scat_data_raw[i_ss][i_se].za_grid;
      AA_DATAGRID = scat_data_raw[i_ss][i_se].aa_grid;
 
      //Sizing SSD data containers
      PHA_MAT_DATA.resize(nf,
                          scat_data_raw[i_ss][i_se].pha_mat_data.nvitrines(),
                          scat_data_raw[i_ss][i_se].pha_mat_data.nshelves(),
                          scat_data_raw[i_ss][i_se].pha_mat_data.nbooks(),
                          scat_data_raw[i_ss][i_se].pha_mat_data.npages(),
                          scat_data_raw[i_ss][i_se].pha_mat_data.nrows(),
                          scat_data_raw[i_ss][i_se].pha_mat_data.ncols());
      EXT_MAT_DATA.resize(nf,
                          scat_data_raw[i_ss][i_se].ext_mat_data.nbooks(),
                          scat_data_raw[i_ss][i_se].ext_mat_data.npages(),
                          scat_data_raw[i_ss][i_se].ext_mat_data.nrows(),
                          scat_data_raw[i_ss][i_se].ext_mat_data.ncols());
      ABS_VEC_DATA.resize(nf,
                          scat_data_raw[i_ss][i_se].abs_vec_data.nbooks(),
                          scat_data_raw[i_ss][i_se].abs_vec_data.npages(),
                          scat_data_raw[i_ss][i_se].abs_vec_data.nrows(),
                          scat_data_raw[i_ss][i_se].abs_vec_data.ncols());
 
      const bool single_se_fgrid =
          (scat_data_raw[i_ss][i_se].f_grid.nelem() == 1);
      if (!single_se_fgrid) {
        // Gridpositions:
        ArrayOfGridPosPoly freq_gp(nf);
        ;
        gridpos_poly(
            freq_gp, scat_data_raw[i_ss][i_se].f_grid, f_grid, interp_order);
 
        // Interpolation weights:
        Matrix itw(nf, interp_order + 1);
        interpweights(itw, freq_gp);
 
        //Phase matrix data
        for (Index t_index = 0;
             t_index < scat_data_raw[i_ss][i_se].pha_mat_data.nvitrines();
             t_index++) {
          for (Index i_za_sca = 0;
               i_za_sca < scat_data_raw[i_ss][i_se].pha_mat_data.nshelves();
               i_za_sca++) {
            for (Index i_aa_sca = 0;
                 i_aa_sca < scat_data_raw[i_ss][i_se].pha_mat_data.nbooks();
                 i_aa_sca++) {
              for (Index i_za_inc = 0;
                   i_za_inc < scat_data_raw[i_ss][i_se].pha_mat_data.npages();
                   i_za_inc++) {
                for (Index i_aa_inc = 0;
                     i_aa_inc < scat_data_raw[i_ss][i_se].pha_mat_data.nrows();
                     i_aa_inc++) {
                  for (Index i = 0;
                       i < scat_data_raw[i_ss][i_se].pha_mat_data.ncols();
                       i++) {
                    interp(scat_data[i_ss][i_se].pha_mat_data(joker,
                                                              t_index,
                                                              i_za_sca,
                                                              i_aa_sca,
                                                              i_za_inc,
                                                              i_aa_inc,
                                                              i),
                           itw,
                           scat_data_raw[i_ss][i_se].pha_mat_data(joker,
                                                                  t_index,
                                                                  i_za_sca,
                                                                  i_aa_sca,
                                                                  i_za_inc,
                                                                  i_aa_inc,
                                                                  i),
                           freq_gp);
                  }
                }
              }
            }
          }
        }
 
        //Extinction matrix data
        for (Index t_index = 0;
             t_index < scat_data_raw[i_ss][i_se].ext_mat_data.nbooks();
             t_index++) {
          for (Index i_za_sca = 0;
               i_za_sca < scat_data_raw[i_ss][i_se].ext_mat_data.npages();
               i_za_sca++) {
            for (Index i_aa_sca = 0;
                 i_aa_sca < scat_data_raw[i_ss][i_se].ext_mat_data.nrows();
                 i_aa_sca++) {
              for (Index i = 0;
                   i < scat_data_raw[i_ss][i_se].ext_mat_data.ncols();
                   i++) {
                interp(scat_data[i_ss][i_se].ext_mat_data(
                           joker, t_index, i_za_sca, i_aa_sca, i),
                       itw,
                       scat_data_raw[i_ss][i_se].ext_mat_data(
                           joker, t_index, i_za_sca, i_aa_sca, i),
                       freq_gp);
              }
            }
          }
        }
 
        //Absorption vector data
        for (Index t_index = 0;
             t_index < scat_data_raw[i_ss][i_se].abs_vec_data.nbooks();
             t_index++) {
          for (Index i_za_sca = 0;
               i_za_sca < scat_data_raw[i_ss][i_se].abs_vec_data.npages();
               i_za_sca++) {
            for (Index i_aa_sca = 0;
                 i_aa_sca < scat_data_raw[i_ss][i_se].abs_vec_data.nrows();
                 i_aa_sca++) {
              for (Index i = 0;
                   i < scat_data_raw[i_ss][i_se].abs_vec_data.ncols();
                   i++) {
                interp(scat_data[i_ss][i_se].abs_vec_data(
                           joker, t_index, i_za_sca, i_aa_sca, i),
                       itw,
                       scat_data_raw[i_ss][i_se].abs_vec_data(
                           joker, t_index, i_za_sca, i_aa_sca, i),
                       freq_gp);
              }
            }
          }
        }
      } else {
        assert(nf == 1);
        // we do only have one f_grid value in old and new data (and they have
        // been confirmed to be the same), hence only need to copy over/reassign
        // the data.
        scat_data[i_ss][i_se].pha_mat_data =
            scat_data_raw[i_ss][i_se].pha_mat_data;
        scat_data[i_ss][i_se].ext_mat_data =
            scat_data_raw[i_ss][i_se].ext_mat_data;
        scat_data[i_ss][i_se].abs_vec_data =
            scat_data_raw[i_ss][i_se].abs_vec_data;
      }
    }
  }
}
 
/* Workspace method: Doxygen documentation will be auto-generated */
void scat_dataReduceT(ArrayOfArrayOfSingleScatteringData& scat_data,
                      const Index& i_ss,
                      const Numeric& T,
                      const Index& interp_order,
                      const Index& phamat_only,
                      const Numeric& threshold,
                      const Verbosity&) {
  // We are directly acting on the scat_data entries, modifying them
  // individually. That is, we don't need to resize these arrays. Only the
  // pha_mat and probably ext_mat and abs_vec Tensors (in the latter case also
  // T_grid!).
 
  // Check that species i_ss exists at all in scat_data
  const Index nss = scat_data.nelem();
  if (nss <= i_ss) {
    ostringstream os;
    os << "Can not T-reduce scattering species #" << i_ss << ".\n"
       << "*scat_data* contains only " << nss << " scattering species.";
    throw runtime_error(os.str());
  }
 
  // Loop over the included scattering elements
  for (Index i_se = 0; i_se < scat_data[i_ss].nelem(); i_se++) {
    // At very first check validity of the scatt elements ptype (so far we only
    // handle PTYPE_TOTAL_RND and PTYPE_AZIMUTH_RND).
    if (PART_TYPE != PTYPE_TOTAL_RND and PART_TYPE != PTYPE_AZIMUTH_RND) {
      ostringstream os;
      os << "Only ptypes " << PTYPE_TOTAL_RND << " and " << PTYPE_AZIMUTH_RND
         << " can be handled.\n"
         << "Scattering element #" << i_se << " has ptype " << PART_TYPE << ".";
      throw runtime_error(os.str());
    }
 
    // If ssd.T_grid already has only a single point, we do nothing.
    // This is not necessarily expected behaviour. BUT, it is in line with
    // previous use (that if nT==1, then assume ssd constant in T).
    Index nT = T_DATAGRID.nelem();
    if (nT > 1) {
      // Check, that we not have data that has already been T-reduced (in
      // pha_mat only. complete ssd T-reduce should have been sorted away
      // already above).
      if (PHA_MAT_DATA.nvitrines() != nT) {
        ostringstream os;
        os << "Single scattering data of scat element #" << i_se
           << " of scat species #" << i_ss << "\n"
           << "seems to have undergone some temperature grid manipulation in\n"
           << "*pha_mat_data* already. That can not be done twice!";
        throw runtime_error(os.str());
      }
 
      // Check that ext_mat and abs_vec have the same temp dimensions as T_grid.
      // This should always be true, if not it's a bug not a user mistake, hence
      // use assert.
      assert(EXT_MAT_DATA.nbooks() == nT and ABS_VEC_DATA.nbooks() == nT);
 
      // Check that T_grid is consistent with requested interpolation order
      ostringstream ost;
      ost << "Scattering data temperature interpolation for\n"
          << "scat element #" << i_se << " of scat species #" << i_ss << ".";
      chk_interpolation_grids(ost.str(), T_DATAGRID, T, interp_order);
 
      // Gridpositions:
      GridPosPoly gp_T;
      gridpos_poly(gp_T, T_DATAGRID, T, interp_order);
      Vector itw(interp_order + 1);
      interpweights(itw, gp_T);
 
      //Sizing of temporary SSD data containers
      Tensor7 phamat_tmp(PHA_MAT_DATA.nlibraries(),
                         1,
                         PHA_MAT_DATA.nshelves(),
                         PHA_MAT_DATA.nbooks(),
                         PHA_MAT_DATA.npages(),
                         PHA_MAT_DATA.nrows(),
                         PHA_MAT_DATA.ncols(),
                         0.);
      Tensor5 extmat_tmp(EXT_MAT_DATA.nshelves(),
                         1,
                         EXT_MAT_DATA.npages(),
                         EXT_MAT_DATA.nrows(),
                         EXT_MAT_DATA.ncols(),
                         0.);
      Tensor5 absvec_tmp(ABS_VEC_DATA.nshelves(),
                         1,
                         ABS_VEC_DATA.npages(),
                         ABS_VEC_DATA.nrows(),
                         ABS_VEC_DATA.ncols(),
                         0.);
 
      // a1) temp interpol of pha mat
      //We have to apply the interpolation separately for each of the pha_mat
      //entries, i.e. loop over all remaining size dimensions
      //We don't apply any transformation here, but interpolate the actual
      //stored ssd (i.e. not the 4x4matrices, but the 7-16 elements separately).
      for (Index i_f = 0; i_f < PHA_MAT_DATA.nlibraries(); i_f++)
        for (Index i_za1 = 0; i_za1 < PHA_MAT_DATA.nshelves(); i_za1++)
          for (Index i_aa1 = 0; i_aa1 < PHA_MAT_DATA.nbooks(); i_aa1++)
            for (Index i_za2 = 0; i_za2 < PHA_MAT_DATA.npages(); i_za2++)
              for (Index i_aa2 = 0; i_aa2 < PHA_MAT_DATA.nrows(); i_aa2++)
                for (Index i_st = 0; i_st < PHA_MAT_DATA.ncols(); i_st++)
                  phamat_tmp(i_f, 0, i_za1, i_aa1, i_za2, i_aa2, i_st) =
                      interp(itw,
                             PHA_MAT_DATA(
                                 i_f, joker, i_za1, i_aa1, i_za2, i_aa2, i_st),
                             gp_T);
 
      // a2) temp interpol of ext and abs.
      //We do that regardless of whether they should be reduced or not, because
      //we need them also for norm checking / renorming.
      for (Index i_f = 0; i_f < EXT_MAT_DATA.nshelves(); i_f++)
        for (Index i_za = 0; i_za < EXT_MAT_DATA.npages(); i_za++)
          for (Index i_aa = 0; i_aa < EXT_MAT_DATA.nrows(); i_aa++) {
            for (Index i_st = 0; i_st < EXT_MAT_DATA.ncols(); i_st++)
              extmat_tmp(i_f, 0, i_za, i_aa, i_st) =
                  interp(itw, EXT_MAT_DATA(i_f, joker, i_za, i_aa, i_st), gp_T);
            for (Index i_st = 0; i_st < ABS_VEC_DATA.ncols(); i_st++)
              absvec_tmp(i_f, 0, i_za, i_aa, i_st) =
                  interp(itw, ABS_VEC_DATA(i_f, joker, i_za, i_aa, i_st), gp_T);
          }
 
      // Norm & other consistency checks.
      // All done separately for PTYPE_TOTAL_RND and PTYPE_AZIMUTH_RND (the
      // latter needs to loop over scat_za_inc).
      //
      // b) calculate norm of T-reduced pha mat
      // c) check pha mat norm vs. sca xs from ext-abs at T_interpol
      // d) Ensure that T-reduced data is consistent/representative of all data.
      //    and throw error/disallow reduction if sca xs varying too much.
      // d1) in case of pha_mat only reduction, the scat xs (pha_mat norm) needs
      // to be consistent with the sca xs from over the ext/abs T_grid. This is
      // essentially an energy conservation issue. That is, we should be as
      // strict here as with pha_mat norm deviations in general (however, should
      // we allow the norm at T_grid to deviate by a threshold from the
      // T_interpol norm (that should be a little looser) or from the ext-abs
      // derived expected norm?).
      // d2) in case of all-ssp reduction, the data should still be
      // representative. b)&c) ensure data consistency in itself, making this
      // rather an error on the SSP as such. Hence, we might be a little more
      // loose here.
      // d) the resulting check for d1) and d2) is the same (ext-abs sca xs at
      // T_interpol vs ext-abs sca xs at T_grid), but we use different
      // thresholds.
      //
      // FIXME?
      // Regarding b)&c) should we also calc norm of original-T pha mats? To get
      // a measure how strong they already deviate from expected norm (As we can
      // not be more exact here than what is already in the original data...).
      // On the other hand, a certain accuracy should be guaranteed from
      // scat_dataCheck already.
      // Hence, for now we skip that (but maybe added later when proves
      // necessary).
      //
      // FIXME?
      // Regarding d1), we could alternatively make sure here that norm at
      // T_interpol is good. And later on ignore any deviations between norm and
      // ext-abs sca xs and instead blindly renorm to expected norm (would that
      // be ok? correct norm here, doesn't imply correct norm at whatever scat
      // angle grids the user is applying. for that, we could in place also calc
      // the original-data norm. but that might be expensive (as we can't do
      // that from ext-abs sca xs, because we don't know to which T that refers.
      // that would go away if we'd actually store pha_mat normed to 1 or 4Pi.
      // but that's prob not going to happen. is it? Another option would be to
      // introduce an additional T_grid, eg T_grid_phamat.). which we actually
      // want to avoid :-/
 
      Numeric this_threshold;
      String errmsg;
      if (phamat_only) {
        this_threshold = threshold;
        errmsg =
            "T-reduced *pha_mat_data* norm (=sca xs) deviates too "
            "much from non-reduced *ext_mat_data* and *abs_vec_data*:";
      } else {
        this_threshold = 2 * threshold;
        errmsg =
            "T-reduced *scat_data* deviates too much from original "
            "*scat_data*:";
      }
 
      // The norm-check code is copied and slightly adapted from scat_dataCheck.
      // Might be better to make a functon out of this and use in both places
      // for consistency.
      //
      // FIXME: no checks on higher Stokes elements are done. Should there?
      // Which?
      switch (PART_TYPE) {
        case PTYPE_TOTAL_RND: {
          for (Index f = 0; f < F_DATAGRID.nelem(); f++) {
            // b) calculate norm of T-reduced pha mat
            Numeric Csca = AngIntegrate_trapezoid(
                phamat_tmp(f, 0, joker, 0, 0, 0, 0), ZA_DATAGRID);
            Numeric Cext_data = extmat_tmp(f, 0, 0, 0, 0);
            //Numeric Cabs = Cext_data - Csca;
            Numeric Cabs_data = absvec_tmp(f, 0, 0, 0, 0);
            Numeric Csca_data = Cext_data - Cabs_data;
 
            /*
            cout << "  Coefficients in data: "
                 << "Cext: " << Cext_data << " Cabs: " << Cabs_data
                 << " Csca: " << Csca_data << "\n"
                 << "  Calculated coefficients: "
                 << "Cabs calc: " << Cabs
                 << " Csca calc: " << Csca << "\n"
                 << "  Deviations "
                 << "Cabs: " << 1e2*Cabs/Cabs_data-1e2
                 << "% Csca: " << 1e2*Csca/Csca_data-1e2
                 << "% Alb: " << (Csca-Csca_data)/Cext_data << "\n";
            */
 
            // c) check pha mat norm vs. sca xs from ext-abs at T_interpol (as
            // albedo dev check)
            if (abs(Csca - Csca_data) / Cext_data > threshold) {
              ostringstream os;
              os << "  Deviations in T-reduced scat_data too large:\n"
                 << "  scat dev [%] " << 1e2 * Csca / Csca_data - 1e2
                 << " at nominal (actual) albedo of " << Csca_data / Cext_data
                 << " (" << Csca / Cext_data << ").\n"
                 << "  Problem occurs for scattering element #" << i_se
                 << " at " << f << ".frequency!\n";
              throw runtime_error(os.str());
            }
            Numeric norm_dev = (Csca - Csca) / Cext_data;
 
            // d) Ensure that T-reduced data is consistent/representative of all data.
            // below use theoretical (ext-abs derived) sca xs as reference.
            Csca = Csca_data;
            for (Index t = 0; t < T_DATAGRID.nelem(); t++) {
              Cext_data = EXT_MAT_DATA(f, t, 0, 0, 0);
              Csca_data = Cext_data - ABS_VEC_DATA(f, t, 0, 0, 0);
              Numeric xs_dev = (Csca - Csca_data) / Cext_data;
              if (abs(norm_dev + (Csca - Csca_data) / Cext_data) >
                  this_threshold)
                cout << "Accumulated deviation (abs(" << norm_dev << "+"
                     << xs_dev << ")=" << abs(norm_dev + xs_dev)
                     << " exceeding threshold (" << this_threshold << ").\n";
              if (abs(Csca - Csca_data) / Cext_data > this_threshold) {
                ostringstream os;
                os << "  " << errmsg << "\n"
                   << "  scat dev [%] " << 1e2 * Csca / Csca_data - 1e2
                   << " at nominal (actual) albedo of " << Csca_data / Cext_data
                   << " (" << Csca / Cext_data << ").\n"
                   << "  Problem occurs for scattering element #" << i_se
                   << " at " << f << ".frequency and " << t
                   << ".temperature!\n";
                throw runtime_error(os.str());
              }
            }
          }
          break;
        }
 
        case PTYPE_AZIMUTH_RND: {
          for (Index f = 0; f < F_DATAGRID.nelem(); f++) {
            for (Index iza = 0; iza < ABS_VEC_DATA.npages(); iza++) {
              // b) calculate norm of T-reduced pha mat
              Numeric Csca = 2 * AngIntegrate_trapezoid(
                                     phamat_tmp(f, 0, joker, joker, iza, 0, 0),
                                     ZA_DATAGRID,
                                     AA_DATAGRID);
              Numeric Cext_data = extmat_tmp(f, 0, iza, 0, 0);
              //Numeric Cabs = Cext_data - Csca;
              Numeric Cabs_data = absvec_tmp(f, 0, iza, 0, 0);
              Numeric Csca_data = Cext_data - Cabs_data;
 
              /*
              cout << "  Coefficients in data: "
                   << "Cext: " << Cext_data << " Cabs: " << Cabs_data
                   << " Csca: " << Csca_data << "\n"
                   << "  Calculated coefficients: "
                   << "Cabs calc: " << Cabs
                   << " Csca calc: " << Csca << "\n"
                   << "  Deviations "
                   << "Cabs: " << 1e2*Cabs/Cabs_data-1e2
                   << "% Csca: " << 1e2*Csca/Csca_data-1e2
                   << "% Alb: " << (Csca-Csca_data)/Cext_data << "\n";
              */
 
              // c) check pha mat norm vs. sca xs from ext-abs at T_interpol (as
              // albedo dev check)
              if (abs(Csca - Csca_data) / Cext_data > threshold) {
                ostringstream os;
                os << "  Deviations in T-reduced scat_data too large:\n"
                   << "  scat dev [%] " << 1e2 * Csca / Csca_data - 1e2
                   << " at nominal (actual) albedo of " << Csca_data / Cext_data
                   << " (" << Csca / Cext_data << ").\n"
                   << "  Problem occurs for scattering element #" << i_se
                   << " at " << f << ".frequency, and " << iza
                   << ". incident polar angle!\n";
                throw runtime_error(os.str());
              }
 
              // d) Ensure that T-reduced data is consistent/representative of all data.
              // below use theoretical (ext-abs derived) sca xs as reference.
              Csca = Csca_data;
              for (Index t = 0; t < T_DATAGRID.nelem(); t++) {
                Cext_data = EXT_MAT_DATA(f, t, 0, 0, 0);
                Csca_data = Cext_data - ABS_VEC_DATA(f, t, 0, 0, 0);
                if (abs(Csca - Csca_data) / Cext_data > this_threshold) {
                  ostringstream os;
                  os << "  " << errmsg << "\n"
                     << "  scat dev [%] " << 1e2 * Csca / Csca_data - 1e2
                     << " at nominal (actual) albedo of "
                     << Csca_data / Cext_data << " (" << Csca / Cext_data
                     << ").\n"
                     << "  Problem occurs for scattering element #" << i_se
                     << " at " << f << ".frequency and " << t
                     << ".temperature, and " << iza
                     << ". incident polar angle!\n";
                  throw runtime_error(os.str());
                }
              }
            }
          }
          break;
        }
 
        default: {
          // other ptype cases already excluded above. i.e. we shouldn't end up
          // here. If we do, that's a bug.
          assert(0);
        }
      }
 
      PHA_MAT_DATA = phamat_tmp;
      //We don't need to reset the scat element's grids!
      //Except for T_grid in the case that we reduce ALL three ssd variables.
      if (!phamat_only) {
        T_DATAGRID.resize(1);
        T_DATAGRID = T;
        EXT_MAT_DATA = extmat_tmp;
        ABS_VEC_DATA = absvec_tmp;
      }
    }
  }
}
 
/* Workspace method: Doxygen documentation will be auto-generated */
void scat_data_monoCalc(ArrayOfArrayOfSingleScatteringData& scat_data_mono,
                        const ArrayOfArrayOfSingleScatteringData& scat_data,
                        const Vector& f_grid,
                        const Index& f_index,
                        const Verbosity&) {
  //Extrapolation factor:
  //const Numeric extpolfac = 0.5;
 
  // Check, whether single scattering data contains the right frequencies:
  // The check was changed to allow extrapolation at the boundaries of the
  // frequency grid.
  for (Index h = 0; h < scat_data.nelem(); h++) {
    for (Index i = 0; i < scat_data[h].nelem(); i++) {
      // check with extrapolation
      chk_interpolation_grids("scat_data.f_grid to f_grid",
                              scat_data[h][i].f_grid,
                              f_grid[f_index]);
    }
  }
 
  //Initialise scat_data_mono
  scat_data_mono.resize(scat_data.nelem());
 
  // Loop over the included scattering species
  for (Index i_ss = 0; i_ss < scat_data.nelem(); i_ss++) {
    const Index N_se = scat_data[i_ss].nelem();
 
    //Initialise scat_data_mono
    scat_data_mono[i_ss].resize(N_se);
 
    // Loop over the included scattering elements
    for (Index i_se = 0; i_se < N_se; i_se++) {
      // Gridpositions:
      GridPos freq_gp;
      gridpos(freq_gp, F_DATAGRID, f_grid[f_index]);
 
      // Interpolation weights:
      Vector itw(2);
      interpweights(itw, freq_gp);
 
      //Stuff that doesn't need interpolating
      scat_data_mono[i_ss][i_se].ptype = PART_TYPE;
      scat_data_mono[i_ss][i_se].f_grid.resize(1);
      scat_data_mono[i_ss][i_se].f_grid = f_grid[f_index];
      scat_data_mono[i_ss][i_se].T_grid = scat_data[i_ss][i_se].T_grid;
      scat_data_mono[i_ss][i_se].za_grid = ZA_DATAGRID;
      scat_data_mono[i_ss][i_se].aa_grid = AA_DATAGRID;
 
      //Phase matrix data
      scat_data_mono[i_ss][i_se].pha_mat_data.resize(1,
                                                     PHA_MAT_DATA.nvitrines(),
                                                     PHA_MAT_DATA.nshelves(),
                                                     PHA_MAT_DATA.nbooks(),
                                                     PHA_MAT_DATA.npages(),
                                                     PHA_MAT_DATA.nrows(),
                                                     PHA_MAT_DATA.ncols());
 
      for (Index t_index = 0; t_index < PHA_MAT_DATA.nvitrines(); t_index++) {
        for (Index i_za_sca = 0; i_za_sca < PHA_MAT_DATA.nshelves();
             i_za_sca++) {
          for (Index i_aa_sca = 0; i_aa_sca < PHA_MAT_DATA.nbooks();
               i_aa_sca++) {
            for (Index i_za_inc = 0; i_za_inc < PHA_MAT_DATA.npages();
                 i_za_inc++) {
              for (Index i_aa_inc = 0; i_aa_inc < PHA_MAT_DATA.nrows();
                   i_aa_inc++) {
                for (Index i = 0; i < PHA_MAT_DATA.ncols(); i++) {
                  scat_data_mono[i_ss][i_se].pha_mat_data(
                      0, t_index, i_za_sca, i_aa_sca, i_za_inc, i_aa_inc, i) =
                      interp(itw,
                             PHA_MAT_DATA(joker,
                                          t_index,
                                          i_za_sca,
                                          i_aa_sca,
                                          i_za_inc,
                                          i_aa_inc,
                                          i),
                             freq_gp);
                }
              }
            }
          }
        }
        //Extinction matrix data
        scat_data_mono[i_ss][i_se].ext_mat_data.resize(1,
                                                       T_DATAGRID.nelem(),
                                                       EXT_MAT_DATA.npages(),
                                                       EXT_MAT_DATA.nrows(),
                                                       EXT_MAT_DATA.ncols());
        for (Index i_za_sca = 0; i_za_sca < EXT_MAT_DATA.npages(); i_za_sca++) {
          for (Index i_aa_sca = 0; i_aa_sca < EXT_MAT_DATA.nrows();
               i_aa_sca++) {
            //
            // Interpolation of extinction matrix:
            //
            for (Index i = 0; i < EXT_MAT_DATA.ncols(); i++) {
              scat_data_mono[i_ss][i_se].ext_mat_data(
                  0, t_index, i_za_sca, i_aa_sca, i) =
                  interp(itw,
                         EXT_MAT_DATA(joker, t_index, i_za_sca, i_aa_sca, i),
                         freq_gp);
            }
          }
        }
        //Absorption vector data
        scat_data_mono[i_ss][i_se].abs_vec_data.resize(1,
                                                       T_DATAGRID.nelem(),
                                                       ABS_VEC_DATA.npages(),
                                                       ABS_VEC_DATA.nrows(),
                                                       ABS_VEC_DATA.ncols());
        for (Index i_za_sca = 0; i_za_sca < ABS_VEC_DATA.npages(); i_za_sca++) {
          for (Index i_aa_sca = 0; i_aa_sca < ABS_VEC_DATA.nrows();
               i_aa_sca++) {
            //
            // Interpolation of absorption vector:
            //
            for (Index i = 0; i < ABS_VEC_DATA.ncols(); i++) {
              scat_data_mono[i_ss][i_se].abs_vec_data(
                  0, t_index, i_za_sca, i_aa_sca, i) =
                  interp(itw,
                         ABS_VEC_DATA(joker, t_index, i_za_sca, i_aa_sca, i),
                         freq_gp);
            }
          }
        }
      }
    }
  }
}
 
/* Workspace method: Doxygen documentation will be auto-generated */
void scat_data_monoExtract(ArrayOfArrayOfSingleScatteringData& scat_data_mono,
                           const ArrayOfArrayOfSingleScatteringData& scat_data,
                           const Index& f_index,
                           const Verbosity&) {
  //Initialise scat_data_mono
  scat_data_mono.resize(scat_data.nelem());
 
  // Loop over the included scattering species
  for (Index i_ss = 0; i_ss < scat_data.nelem(); i_ss++) {
    const Index N_se = scat_data[i_ss].nelem();
 
    //Initialise scat_data_mono
    scat_data_mono[i_ss].resize(N_se);
 
    // Loop over the included scattering elements
    for (Index i_se = 0; i_se < N_se; i_se++) {
      Index nf = F_DATAGRID.nelem();
      if (nf == 1) {
        scat_data_mono[i_ss][i_se] = scat_data[i_ss][i_se];
      } else {
        //Stuff that doesn't need interpolating
        scat_data_mono[i_ss][i_se].ptype = PART_TYPE;
        scat_data_mono[i_ss][i_se].T_grid = T_DATAGRID;
        scat_data_mono[i_ss][i_se].za_grid = ZA_DATAGRID;
        scat_data_mono[i_ss][i_se].aa_grid = AA_DATAGRID;
 
        scat_data_mono[i_ss][i_se].f_grid.resize(1);
        scat_data_mono[i_ss][i_se].f_grid = F_DATAGRID[f_index];
 
        Index this_f_index;
 
        //Phase matrix data
        /*scat_data_mono[i_ss][i_se].pha_mat_data.resize(1,
                                                 PHA_MAT_DATA.nvitrines(),
                                                 PHA_MAT_DATA.nshelves(),
                                                 PHA_MAT_DATA.nbooks(),
                                                 PHA_MAT_DATA.npages(),
                                                 PHA_MAT_DATA.nrows(),
                                                 PHA_MAT_DATA.ncols());*/
        this_f_index = (PHA_MAT_DATA.nlibraries() == 1) ? 0 : f_index;
        scat_data_mono[i_ss][i_se].pha_mat_data = PHA_MAT_DATA(
            Range(this_f_index, 1), joker, joker, joker, joker, joker, joker);
 
        //Extinction matrix data
        /*scat_data_mono[i_ss][i_se].ext_mat_data.resize(1, T_DATAGRID.nelem(),
                                                     EXT_MAT_DATA.npages(),
                                                     EXT_MAT_DATA.nrows(),
                                                     EXT_MAT_DATA.ncols());*/
        this_f_index = (EXT_MAT_DATA.nshelves() == 1) ? 0 : f_index;
        scat_data_mono[i_ss][i_se].ext_mat_data =
            EXT_MAT_DATA(Range(this_f_index, 1), joker, joker, joker, joker);
 
        //Absorption vector data
        /*scat_data_mono[i_ss][i_se].abs_vec_data.resize(1, T_DATAGRID.nelem(),
                                                     ABS_VEC_DATA.npages(),
                                                     ABS_VEC_DATA.nrows(),
                                                     ABS_VEC_DATA.ncols());*/
        this_f_index = (ABS_VEC_DATA.nshelves() == 1) ? 0 : f_index;
        scat_data_mono[i_ss][i_se].abs_vec_data =
            ABS_VEC_DATA(Range(this_f_index, 1), joker, joker, joker, joker);
      }
    }
  }
}
 
/* Workspace method: Doxygen documentation will be auto-generated */
void opt_prop_sptFromMonoData(  // Output and Input:
    ArrayOfPropagationMatrix& ext_mat_spt,
    ArrayOfStokesVector& abs_vec_spt,
    // Input:
    const ArrayOfArrayOfSingleScatteringData& scat_data_mono,
    const Vector& za_grid,
    const Vector& aa_grid,
    const Index& za_index,  // propagation directions
    const Index& aa_index,
    const Numeric& rtp_temperature,
    const Tensor4& pnd_field,
    const Index& scat_p_index,
    const Index& scat_lat_index,
    const Index& scat_lon_index,
    const Verbosity& verbosity) {
  DEBUG_ONLY(const Index N_se_total = TotalNumberOfElements(scat_data_mono);)
  const Index stokes_dim = ext_mat_spt[0].StokesDimensions();
  const Numeric za_sca = za_grid[za_index];
  const Numeric aa_sca = aa_grid[aa_index];
 
  if (stokes_dim > 4 or stokes_dim < 1) {
    throw runtime_error(
        "The dimension of the stokes vector \n"
        "must be 1,2,3 or 4");
  }
 
  assert(ext_mat_spt.nelem() == N_se_total);
  assert(abs_vec_spt.nelem() == N_se_total);
 
  // Check that we do indeed have scat_data_mono here. Only checking the first
  // scat element, assuming the other elements have been processed in the same
  // manner. That's save against having scat_data here if that originated from
  // scat_data_raw reading routines (ScatSpecies/Element*Add/Read), it's not safe
  // against data read by ReadXML directly or if scat_data(_raw) has been (partly)
  // produced from scat_data_singleTmatrix. That would be too costly here,
  // though.
  // Also, we can't check here whether data is at the correct frequency since we
  // don't know f_grid and f_index here (we could pass it in, though).
  if (scat_data_mono[0][0].f_grid.nelem() > 1) {
    ostringstream os;
    os << "Scattering data seems to be *scat_data* (several freq points),\n"
       << "but *scat_data_mono* (1 freq point only) is expected here.";
    throw runtime_error(os.str());
  }
 
  // Initialisation
  for (auto& pm : ext_mat_spt) pm.SetZero();
  for (auto& av : abs_vec_spt) av.SetZero();
 
  GridPos t_gp;
 
  Vector itw(2);
 
  Index i_se_flat = 0;
  // Loop over the included scattering elements
  for (Index i_ss = 0; i_ss < scat_data_mono.nelem(); i_ss++) {
    // Loop over the included scattering elements
    for (Index i_se = 0; i_se < scat_data_mono[i_ss].nelem(); i_se++) {
      // If the particle number density at a specific point in the
      // atmosphere for the i_se scattering element is zero, we don't need
      // to do the transformation!
      if (pnd_field(i_se_flat, scat_p_index, scat_lat_index, scat_lon_index) >
          PND_LIMIT) {
        // First we have to transform the data from the coordinate system
        // used in the database (depending on the kind of ptype) to the
        // laboratory coordinate system.
 
        //
        // Do the transformation into the laboratory coordinate system.
        //
        // Extinction matrix:
        //
        Index ext_npages = scat_data_mono[i_ss][i_se].ext_mat_data.npages();
        Index ext_nrows = scat_data_mono[i_ss][i_se].ext_mat_data.nrows();
        Index ext_ncols = scat_data_mono[i_ss][i_se].ext_mat_data.ncols();
        Index abs_npages = scat_data_mono[i_ss][i_se].abs_vec_data.npages();
        Index abs_nrows = scat_data_mono[i_ss][i_se].abs_vec_data.nrows();
        Index abs_ncols = scat_data_mono[i_ss][i_se].abs_vec_data.ncols();
 
        //Check that scattering data temperature range covers required temperature
        ConstVectorView t_grid = scat_data_mono[i_ss][i_se].T_grid;
 
        if (t_grid.nelem() > 1) {
          ostringstream os;
          os << "In opt_prop_sptFromMonoData.\n"
             << "The temperature grid of the scattering data does not\n"
             << "cover the atmospheric temperature at cloud location.\n"
             << "The data should include the value T = " << rtp_temperature
             << " K.";
          chk_interpolation_grids(os.str(), t_grid, rtp_temperature);
 
          //interpolate over temperature
          Tensor3 ext_mat_data1temp(ext_npages, ext_nrows, ext_ncols);
          gridpos(t_gp, t_grid, rtp_temperature);
          interpweights(itw, t_gp);
          for (Index i_p = 0; i_p < ext_npages; i_p++) {
            for (Index i_r = 0; i_r < ext_nrows; i_r++) {
              for (Index i_c = 0; i_c < ext_ncols; i_c++) {
                ext_mat_data1temp(i_p, i_r, i_c) =
                    interp(itw,
                           scat_data_mono[i_ss][i_se].ext_mat_data(
                               0, joker, i_p, i_r, i_c),
                           t_gp);
              }
            }
          }
          ext_matTransform(ext_mat_spt[i_se_flat],
                           ext_mat_data1temp,
                           scat_data_mono[i_ss][i_se].za_grid,
                           scat_data_mono[i_ss][i_se].aa_grid,
                           scat_data_mono[i_ss][i_se].ptype,
                           za_sca,
                           aa_sca,
                           verbosity);
        } else {
          ext_matTransform(ext_mat_spt[i_se_flat],
                           scat_data_mono[i_ss][i_se].ext_mat_data(
                               0, 0, joker, joker, joker),
                           scat_data_mono[i_ss][i_se].za_grid,
                           scat_data_mono[i_ss][i_se].aa_grid,
                           scat_data_mono[i_ss][i_se].ptype,
                           za_sca,
                           aa_sca,
                           verbosity);
        }
        //
        // Absorption vector:
        //
 
        if (t_grid.nelem() > 1) {
          Tensor3 abs_vec_data1temp(abs_npages, abs_nrows, abs_ncols);
          //interpolate over temperature
          for (Index i_p = 0; i_p < abs_npages; i_p++) {
            for (Index i_r = 0; i_r < abs_nrows; i_r++) {
              for (Index i_c = 0; i_c < abs_ncols; i_c++) {
                abs_vec_data1temp(i_p, i_r, i_c) =
                    interp(itw,
                           scat_data_mono[i_ss][i_se].abs_vec_data(
                               0, joker, i_p, i_r, i_c),
                           t_gp);
              }
            }
          }
          abs_vecTransform(abs_vec_spt[i_se_flat],
                           abs_vec_data1temp,
                           scat_data_mono[i_ss][i_se].za_grid,
                           scat_data_mono[i_ss][i_se].aa_grid,
                           scat_data_mono[i_ss][i_se].ptype,
                           za_sca,
                           aa_sca,
                           verbosity);
        } else {
          abs_vecTransform(abs_vec_spt[i_se_flat],
                           scat_data_mono[i_ss][i_se].abs_vec_data(
                               0, 0, joker, joker, joker),
                           scat_data_mono[i_ss][i_se].za_grid,
                           scat_data_mono[i_ss][i_se].aa_grid,
                           scat_data_mono[i_ss][i_se].ptype,
                           za_sca,
                           aa_sca,
                           verbosity);
        }
      }
 
      i_se_flat++;
    }
  }
}
 
/* Workspace method: Doxygen documentation will be auto-generated */
void pha_mat_sptFromMonoData(  // Output:
    Tensor5& pha_mat_spt,
    // Input:
    const ArrayOfArrayOfSingleScatteringData& scat_data_mono,
    const Index& doit_za_grid_size,
    const Vector& aa_grid,
    const Index& za_index,  // propagation directions
    const Index& aa_index,
    const Numeric& rtp_temperature,
    const Tensor4& pnd_field,
    const Index& scat_p_index,
    const Index& scat_lat_index,
    const Index& scat_lon_index,
    const Verbosity& verbosity) {
  Vector za_grid;
  nlinspace(za_grid, 0, 180, doit_za_grid_size);
 
  const Index N_se_total = TotalNumberOfElements(scat_data_mono);
  if (N_se_total != pnd_field.nbooks()) {
    ostringstream os;
    os << "Total number of scattering elements in *scat_data_mono* "
       << "inconsistent with size of pnd_field.";
    throw runtime_error(os.str());
  }
  // as pha_mat_spt is typically initialized from pnd_field, this theoretically
  // checks the same as the runtime_error above. Still, we keep it to be on the
  // save side.
  assert(pha_mat_spt.nshelves() == N_se_total);
 
  const Index stokes_dim = pha_mat_spt.ncols();
  if (stokes_dim > 4 || stokes_dim < 1) {
    throw runtime_error(
        "The dimension of the stokes vector \n"
        "must be 1,2,3 or 4");
  }
 
  // Check that we do indeed have scat_data_mono here. Only checking the first
  // scat element, assuming the other elements have been processed in the same
  // manner. That's save against having scat_data here if that originated from
  // scat_data_raw reading routines (ScatSpecies/Element*Add/Read), it's not safe
  // against data read by ReadXML directly or if scat_data(_raw) has been (partly)
  // produced from scat_data_singleTmatrix. That would be too costly here,
  // though.
  // Also, we can't check here whether data is at the correct frequency since we
  // don't know f_grid and f_index here (we could pass it in, though).
  if (scat_data_mono[0][0].f_grid.nelem() > 1) {
    ostringstream os;
    os << "Scattering data seems to be *scat_data* (several freq points),\n"
       << "but *scat_data_mono* (1 freq point only) is expected here.";
    throw runtime_error(os.str());
  }
 
  GridPos T_gp = {0, {0, 1}}, Tred_gp;
  Vector itw(2);
 
  // Initialisation
  pha_mat_spt = 0.;
 
  Index i_se_flat = 0;
  for (Index i_ss = 0; i_ss < scat_data_mono.nelem(); i_ss++) {
    for (Index i_se = 0; i_se < scat_data_mono[i_ss].nelem(); i_se++) {
      // If the particle number density at a specific point in the
      // atmosphere for scattering element i_se is zero, we don't need to
      // do the transformation!
      if (pnd_field(i_se_flat, scat_p_index, scat_lat_index, scat_lon_index) >
          PND_LIMIT) {
        // Temporary phase matrix which includes all temperatures.
        Index nT = scat_data_mono[i_ss][i_se].pha_mat_data.nvitrines();
        Tensor3 pha_mat_spt_tmp(nT, pha_mat_spt.nrows(), pha_mat_spt.ncols());
 
        pha_mat_spt_tmp = 0.;
 
        Index ti = -1;
        if (nT == 1)  // just 1 T_grid element
        {
          ti = 0;
        } else if (rtp_temperature < 0.)  // coding for 'not interpolate, but
                                          // pick one temperature'
        {
          if (rtp_temperature > -10.)  // lowest T-point
          {
            ti = 0;
          } else if (rtp_temperature > -20.)  // highest T-point
          {
            ti = nT - 1;
          } else  // median T-point
          {
            ti = nT / 2;
          }
        } else {
          ostringstream os;
          os << "In pha_mat_sptFromMonoData.\n"
             << "The temperature grid of the scattering data does not\n"
             << "cover the atmospheric temperature at cloud location.\n"
             << "The data should include the value T = " << rtp_temperature
             << " K.";
          chk_interpolation_grids(
              os.str(), scat_data_mono[i_ss][i_se].T_grid, rtp_temperature);
 
          // Gridpositions:
          gridpos(T_gp, scat_data_mono[i_ss][i_se].T_grid, rtp_temperature);
          gridpos_copy(Tred_gp, T_gp);
          Tred_gp.idx = 0;
          // Interpolation weights:
          interpweights(itw, Tred_gp);
        }
 
        // Do the transformation into the laboratory coordinate system.
        for (Index za_inc_idx = 0; za_inc_idx < doit_za_grid_size;
             za_inc_idx++) {
          for (Index aa_inc_idx = 0; aa_inc_idx < aa_grid.nelem();
               aa_inc_idx++) {
            if (ti < 0)  // Temperature interpolation
            {
              for (Index t_idx = 0; t_idx < 2; t_idx++) {
                pha_matTransform(
                    pha_mat_spt_tmp(t_idx, joker, joker),
                    scat_data_mono[i_ss][i_se].pha_mat_data(
                        0, t_idx + T_gp.idx, joker, joker, joker, joker, joker),
                    scat_data_mono[i_ss][i_se].za_grid,
                    scat_data_mono[i_ss][i_se].aa_grid,
                    scat_data_mono[i_ss][i_se].ptype,
                    za_index,
                    aa_index,
                    za_inc_idx,
                    aa_inc_idx,
                    za_grid,
                    aa_grid,
                    verbosity);
              }
 
              for (Index i = 0; i < stokes_dim; i++) {
                for (Index j = 0; j < stokes_dim; j++) {
                  pha_mat_spt(i_se_flat, za_inc_idx, aa_inc_idx, i, j) =
                      interp(itw, pha_mat_spt_tmp(joker, i, j), Tred_gp);
                }
              }
            } else  // no temperature interpolation required
            {
              pha_matTransform(
                  pha_mat_spt(i_se_flat, za_inc_idx, aa_inc_idx, joker, joker),
                  scat_data_mono[i_ss][i_se].pha_mat_data(
                      0, ti, joker, joker, joker, joker, joker),
                  scat_data_mono[i_ss][i_se].za_grid,
                  scat_data_mono[i_ss][i_se].aa_grid,
                  scat_data_mono[i_ss][i_se].ptype,
                  za_index,
                  aa_index,
                  za_inc_idx,
                  aa_inc_idx,
                  za_grid,
                  aa_grid,
                  verbosity);
            }
          }
        }
      }
 
      i_se_flat++;
    }
  }
}
 
/* Workspace method: Doxygen documentation will be auto-generated */
void pha_mat_sptFromScat_data(  // Output:
    Tensor5& pha_mat_spt,
    // Input:
    const ArrayOfArrayOfSingleScatteringData& scat_data,
    const Index& scat_data_checked,
    const Vector& za_grid,
    const Vector& aa_grid,
    const Index& za_index,  // propagation directions
    const Index& aa_index,
    const Index& f_index,
    const Numeric& rtp_temperature,
    const Tensor4& pnd_field,
    const Index& scat_p_index,
    const Index& scat_lat_index,
    const Index& scat_lon_index,
    const Verbosity& verbosity) {
  if (scat_data_checked != 1)
    throw runtime_error(
        "The scattering data must be flagged to have "
        "passed a consistency check (scat_data_checked=1).");
 
  const Index stokes_dim = pha_mat_spt.ncols();
  if (stokes_dim > 4 || stokes_dim < 1) {
    throw runtime_error(
        "The dimension of the stokes vector \n"
        "must be 1,2,3 or 4");
  }
 
  // Determine total number of scattering elements
  const Index N_se_total = TotalNumberOfElements(scat_data);
  if (N_se_total != pnd_field.nbooks()) {
    ostringstream os;
    os << "Total number of scattering elements in scat_data "
       << "inconsistent with size of pnd_field.";
    throw runtime_error(os.str());
  }
  // as pha_mat_spt is typically initialized from pnd_field, this theoretically
  // checks the same as the runtime_error above. Still, we keep it to be on the
  // save side.
  assert(pha_mat_spt.nshelves() == N_se_total);
 
  const Index N_ss = scat_data.nelem();
 
  // Phase matrix in laboratory coordinate system. Dimensions:
  // [frequency, za_inc, aa_inc, stokes_dim, stokes_dim]
  Tensor5 pha_mat_data_int;
 
  Index this_f_index;
 
  Index i_se_flat = 0;
  // Loop over scattering species
  for (Index i_ss = 0; i_ss < N_ss; i_ss++) {
    const Index N_se = scat_data[i_ss].nelem();
 
    // Loop over the included scattering elements
    for (Index i_se = 0; i_se < N_se; i_se++) {
      // If the particle number density at a specific point in the
      // atmosphere for the i_se scattering element is zero, we don't need
      // to do the transfromation!
      if (abs(pnd_field(
              i_se_flat, scat_p_index, scat_lat_index, scat_lon_index)) >
          PND_LIMIT) {
        // First we have to transform the data from the coordinate system
        // used in the database (depending on the kind of ptype) to the
        // laboratory coordinate system.
 
        // Resize the variables for the interpolated data (1freq, 1T):
        pha_mat_data_int.resize(PHA_MAT_DATA.nshelves(),
                                PHA_MAT_DATA.nbooks(),
                                PHA_MAT_DATA.npages(),
                                PHA_MAT_DATA.nrows(),
                                PHA_MAT_DATA.ncols());
 
        // Frequency extraction and temperature interpolation
 
        // Gridpositions and interpolation weights;
        GridPos t_gp;
        Vector itw;
        Index this_T_index = -1;
        if (PHA_MAT_DATA.nvitrines() == 1) {
          this_T_index = 0;
        } else if (rtp_temperature < 0.)  // coding for 'not interpolate, but
                                          // pick one temperature'
        {
          if (rtp_temperature > -10.)  // lowest T-point
          {
            this_T_index = 0;
          } else if (rtp_temperature > -20.)  // highest T-point
          {
            this_T_index = PHA_MAT_DATA.nvitrines() - 1;
          } else  // median T-point
          {
            this_T_index = PHA_MAT_DATA.nvitrines() / 2;
          }
        } else {
          ostringstream os;
          os << "In pha_mat_sptFromScat_data.\n"
             << "The temperature grid of the scattering data does not\n"
             << "cover the atmospheric temperature at cloud location.\n"
             << "The data should include the value T = " << rtp_temperature
             << " K.";
          chk_interpolation_grids(os.str(), T_DATAGRID, rtp_temperature);
 
          gridpos(t_gp, T_DATAGRID, rtp_temperature);
 
          // Interpolation weights:
          itw.resize(2);
          interpweights(itw, t_gp);
        }
 
        if (PHA_MAT_DATA.nlibraries() == 1)
          this_f_index = 0;
        else
          this_f_index = f_index;
 
        if (this_T_index < 0) {
          // Interpolation of scattering matrix:
          for (Index i_za_sca = 0; i_za_sca < PHA_MAT_DATA.nshelves();
               i_za_sca++)
            for (Index i_aa_sca = 0; i_aa_sca < PHA_MAT_DATA.nbooks();
                 i_aa_sca++)
              for (Index i_za_inc = 0; i_za_inc < PHA_MAT_DATA.npages();
                   i_za_inc++)
                for (Index i_aa_inc = 0; i_aa_inc < PHA_MAT_DATA.nrows();
                     i_aa_inc++)
                  for (Index i = 0; i < PHA_MAT_DATA.ncols(); i++)
                    pha_mat_data_int(
                        i_za_sca, i_aa_sca, i_za_inc, i_aa_inc, i) =
                        interp(itw,
                               PHA_MAT_DATA(this_f_index,
                                            joker,
                                            i_za_sca,
                                            i_aa_sca,
                                            i_za_inc,
                                            i_aa_inc,
                                            i),
                               t_gp);
        } else {
          pha_mat_data_int = PHA_MAT_DATA(
              this_f_index, this_T_index, joker, joker, joker, joker, joker);
          /*
                  for (Index i_za_sca = 0;
                       i_za_sca < PHA_MAT_DATA.nshelves(); i_za_sca++)
                    for (Index i_aa_sca = 0;
                         i_aa_sca < PHA_MAT_DATA.nbooks(); i_aa_sca++)
                      for (Index i_za_inc = 0;
                           i_za_inc < PHA_MAT_DATA.npages(); i_za_inc++)
                        for (Index i_aa_inc = 0;
                             i_aa_inc < PHA_MAT_DATA.nrows(); i_aa_inc++)
                          for (Index i = 0; i < PHA_MAT_DATA.ncols(); i++)
                            // Interpolation of phase matrix:
                            pha_mat_data_int(i_za_sca, i_aa_sca,
                                             i_za_inc, i_aa_inc, i) =
                                PHA_MAT_DATA(this_f_index, this_T_index,
                                                 i_za_sca, i_aa_sca,
                  */
        }
 
        // Do the transformation into the laboratory coordinate system.
        for (Index za_inc_idx = 0; za_inc_idx < za_grid.nelem();
             za_inc_idx++) {
          for (Index aa_inc_idx = 0; aa_inc_idx < aa_grid.nelem();
               aa_inc_idx++) {
            pha_matTransform(
                pha_mat_spt(i_se_flat, za_inc_idx, aa_inc_idx, joker, joker),
                pha_mat_data_int,
                ZA_DATAGRID,
                AA_DATAGRID,
                PART_TYPE,
                za_index,
                aa_index,
                za_inc_idx,
                aa_inc_idx,
                za_grid,
                aa_grid,
                verbosity);
          }
        }
      }
      i_se_flat++;
    }
  }
}
 
/* Workspace method: Doxygen documentation will be auto-generated */
void ScatSpeciesMerge(  //WS Output:
    Tensor4& pnd_field,
    ArrayOfArrayOfSingleScatteringData& scat_data,
    ArrayOfArrayOfScatteringMetaData& scat_meta,
    ArrayOfString& scat_species,
    Index& cloudbox_checked,
    //WS Input:
    const Index& atmosphere_dim,
    const Index& cloudbox_on,
    const ArrayOfIndex& cloudbox_limits,
    const Tensor3& t_field,
    const Tensor3& z_field,
    const Matrix& z_surface,
    const Verbosity& /*verbosity*/) {
  // FIXME:
  // so far, this works for both scat_data and scat_data_raw. Needs to be
  // adapted, though, once we have WSM that can create Z/K/a with different
  // f/T dimensions than scat_data_single.f/T_grid.
 
  // cloudbox variable state should be ok before entering here
  if (!cloudbox_checked)
    throw std::runtime_error(
        "You must call *cloudbox_checkedCalc* before this method.");
  //however, we modify cloudbox variables. hence force re-checking the new
  //variables by resetting cloudbox_checked to False.
  cloudbox_checked = 0;
 
  if (atmosphere_dim != 1)
    throw std::runtime_error(
        "Merging scattering elements only works with a 1D atmoshere");
 
  // Cloudbox on/off?
  if (!cloudbox_on) {
    /* Must initialise pnd_field anyway; but empty */
    pnd_field.resize(0, 0, 0, 0);
    return;
  }
 
  // ------- setup new pnd_field and scat_data -------------------
  ArrayOfIndex limits(2);
  //pressure
  limits[0] = cloudbox_limits[0];
  limits[1] = cloudbox_limits[1] + 1;
 
  Tensor4 pnd_field_merged(
      limits[1] - limits[0], limits[1] - limits[0], 1, 1, 0.);
 
  ArrayOfArrayOfSingleScatteringData scat_data_merged;
  scat_data_merged.resize(1);
  scat_data_merged[0].resize(pnd_field_merged.nbooks());
  ArrayOfArrayOfScatteringMetaData scat_meta_merged;
  scat_meta_merged.resize(1);
  scat_meta_merged[0].resize(pnd_field_merged.nbooks());
  ArrayOfString scat_species_merged;
  scat_species_merged.resize(1);
  scat_species_merged[0] = "mergedfield-mergedpsd";
  for (Index sp = 0; sp < scat_data_merged[0].nelem(); sp++) {
    SingleScatteringData& this_part = scat_data_merged[0][sp];
    this_part.ptype = scat_data[0][0].ptype;
    this_part.description = "Merged scattering elements";
    this_part.f_grid = scat_data[0][0].f_grid;
    this_part.za_grid = scat_data[0][0].za_grid;
    this_part.aa_grid = scat_data[0][0].aa_grid;
    this_part.pha_mat_data.resize(scat_data[0][0].pha_mat_data.nlibraries(),
                                  1,
                                  scat_data[0][0].pha_mat_data.nshelves(),
                                  scat_data[0][0].pha_mat_data.nbooks(),
                                  scat_data[0][0].pha_mat_data.npages(),
                                  scat_data[0][0].pha_mat_data.nrows(),
                                  scat_data[0][0].pha_mat_data.ncols());
    this_part.ext_mat_data.resize(scat_data[0][0].ext_mat_data.nshelves(),
                                  1,
                                  scat_data[0][0].ext_mat_data.npages(),
                                  scat_data[0][0].ext_mat_data.nrows(),
                                  scat_data[0][0].ext_mat_data.ncols());
    this_part.abs_vec_data.resize(scat_data[0][0].abs_vec_data.nshelves(),
                                  1,
                                  scat_data[0][0].abs_vec_data.npages(),
                                  scat_data[0][0].abs_vec_data.nrows(),
                                  scat_data[0][0].abs_vec_data.ncols());
    this_part.pha_mat_data = 0.;
    this_part.ext_mat_data = 0.;
    this_part.abs_vec_data = 0.;
    this_part.T_grid.resize(1);
    this_part.T_grid[0] = t_field(sp, 0, 0);
 
    ScatteringMetaData& this_meta = scat_meta_merged[0][sp];
    ostringstream os;
    os << "Merged scattering element of cloudbox-level #" << sp;
    this_meta.description = os.str();
    this_meta.source = "ARTS internal";
    this_meta.refr_index = "Unknown";
    this_meta.mass = -1.;
    this_meta.diameter_max = -1.;
    this_meta.diameter_volume_equ = -1.;
    this_meta.diameter_area_equ_aerodynamical = -1.;
  }
 
  // Check that all scattering elements have same ptype and data dimensions
  SingleScatteringData& first_part = scat_data[0][0];
  for (Index i_ss = 0; i_ss < scat_data.nelem(); i_ss++) {
    for (Index i_se = 0; i_se < scat_data[i_ss].nelem(); i_se++) {
      SingleScatteringData& orig_part = scat_data[i_ss][i_se];
 
      if (orig_part.ptype != first_part.ptype)
        throw std::runtime_error(
            "All scattering elements must have the same type");
 
      if (orig_part.f_grid.nelem() != first_part.f_grid.nelem())
        throw std::runtime_error(
            "All scattering elements must have the same f_grid");
 
      if (!is_size(orig_part.pha_mat_data(
                       joker, 0, joker, joker, joker, joker, joker),
                   first_part.pha_mat_data.nlibraries(),
                   first_part.pha_mat_data.nshelves(),
                   first_part.pha_mat_data.nbooks(),
                   first_part.pha_mat_data.npages(),
                   first_part.pha_mat_data.nrows(),
                   first_part.pha_mat_data.ncols()))
        throw std::runtime_error(
            "All scattering elements must have the same pha_mat_data size"
            " (except for temperature).");
 
      if (!is_size(orig_part.ext_mat_data(joker, 0, joker, joker, joker),
                   first_part.ext_mat_data.nshelves(),
                   first_part.ext_mat_data.npages(),
                   first_part.ext_mat_data.nrows(),
                   first_part.ext_mat_data.ncols()))
        throw std::runtime_error(
            "All scattering elements must have the same ext_mat_data size"
            " (except for temperature).");
 
      if (!is_size(orig_part.abs_vec_data(joker, 0, joker, joker, joker),
                   first_part.abs_vec_data.nshelves(),
                   first_part.abs_vec_data.npages(),
                   first_part.abs_vec_data.nrows(),
                   first_part.abs_vec_data.ncols()))
        throw std::runtime_error(
            "All scattering elements must have the same abs_vec_data size"
            " (except for temperature).");
    }
  }
 
  //----- Start pnd_field_merged and scat_data_array_merged calculations -----
 
  GridPos T_gp;
  Vector itw(2);
 
  Index nlevels = pnd_field_merged.nbooks();
  // loop over pressure levels in cloudbox
  for (Index i_lv = 0; i_lv < nlevels - 1; i_lv++) {
    pnd_field_merged(i_lv, i_lv, 0, 0) = 1.;
 
    SingleScatteringData& this_part = scat_data_merged[0][i_lv];
    for (Index i_ss = 0; i_ss < scat_data.nelem(); i_ss++) {
      for (Index i_se = 0; i_se < scat_data[i_ss].nelem(); i_se++) {
        SingleScatteringData& orig_part = scat_data[i_ss][i_se];
        const Index pnd_index = FlattenedIndex(scat_data, i_ss, i_se);
 
        // If the particle number density at a specific point in the
        // atmosphere for the i_se scattering element is zero, we don't
        // need to do the transformation!
        if (pnd_field(pnd_index, i_lv, 0, 0) > PND_LIMIT)  //TRS
        {
          Numeric temperature = this_part.T_grid[0];
          if (orig_part.T_grid.nelem() > 1) {
            ostringstream os;
            os << "The temperature grid of the scattering data "
               << "does not cover the\n"
               << "atmospheric temperature at cloud location. "
               << "The data should\n"
               << "include the value T = " << temperature << " K.\n"
               << "Offending particle is scat_data[" << i_ss << "][" << i_se
               << "]:\n"
               << "Description: " << orig_part.description << "\n";
            chk_interpolation_grids(os.str(), orig_part.T_grid, temperature);
 
            // Gridpositions:
            gridpos(T_gp, orig_part.T_grid, temperature);
            // Interpolation weights:
            interpweights(itw, T_gp);
          }
 
 
          // Loop over frequencies
          for (Index i_f = 0; i_f < orig_part.pha_mat_data.nlibraries();
               i_f++) {
            // Loop over zenith angles
            for (Index i_za = 0; i_za < orig_part.ext_mat_data.npages();
                 i_za++) {
              // Loop over azimuth angles
              for (Index i_aa = 0; i_aa < orig_part.ext_mat_data.nrows();
                   i_aa++) {
                // Weighted sum of ext_mat_data and abs_vec_data
                if (orig_part.T_grid.nelem() == 1) {
                  Vector v = orig_part.ext_mat_data(i_f, 0, i_za, i_aa, joker);
                  v *= pnd_field(pnd_index, i_lv, 0, 0);
                  this_part.ext_mat_data(i_f, 0, i_za, 0, joker) += v;
 
                  v = orig_part.abs_vec_data(i_f, 0, i_za, i_aa, joker);
                  v *= pnd_field(pnd_index, i_lv, 0, 0);
                  this_part.abs_vec_data(i_f, 0, i_za, i_aa, joker) += v;
                } else {
                  for (Index i = 0; i < orig_part.ext_mat_data.ncols(); i++) {
                    // Temperature interpolation
                    this_part.ext_mat_data(i_f, 0, i_za, i_aa, i) +=
                        pnd_field(pnd_index, i_lv, 0, 0) *
                        interp(
                            itw,
                            orig_part.ext_mat_data(i_f, joker, i_za, i_aa, i),
                            T_gp);
                  }
                  for (Index i = 0; i < orig_part.abs_vec_data.ncols(); i++) {
                    // Temperature interpolation
                    this_part.abs_vec_data(i_f, 0, i_za, i_aa, i) +=
                        pnd_field(pnd_index, i_lv, 0, 0) *
                        interp(
                            itw,
                            orig_part.abs_vec_data(i_f, joker, i_za, i_aa, i),
                            T_gp);
                  }
                }
              }
            }
 
 
            // Loop over outgoing zenith angles
            for (Index i_za_out = 0;
                 i_za_out < orig_part.pha_mat_data.nshelves();
                 i_za_out++) {
              // Loop over outgoing azimuth angles
              for (Index i_aa_out = 0;
                   i_aa_out < orig_part.pha_mat_data.nbooks();
                   i_aa_out++) {
                // Loop over incoming zenith angles
                for (Index i_za_inc = 0;
                     i_za_inc < orig_part.pha_mat_data.npages();
                     i_za_inc++) {
                  // Loop over incoming azimuth angles
                  for (Index i_aa_inc = 0;
                       i_aa_inc < orig_part.pha_mat_data.nrows();
                       i_aa_inc++) {
                    // Weighted sum of pha_mat_data
                    if (orig_part.T_grid.nelem() == 1) {
                      Vector v = orig_part.pha_mat_data(i_f,
                                                        0,
                                                        i_za_out,
                                                        i_aa_out,
                                                        i_za_inc,
                                                        i_aa_inc,
                                                        joker);
                      v *= pnd_field(pnd_index, i_lv, 0, 0);
                      this_part.pha_mat_data(i_f,
                                             0,
                                             i_za_out,
                                             i_aa_out,
                                             i_za_inc,
                                             i_aa_inc,
                                             joker) = v;
                    } else {
                      // Temperature interpolation
                      for (Index i = 0; i < orig_part.pha_mat_data.ncols();
                           i++) {
                        this_part.pha_mat_data(i_f,
                                               0,
                                               i_za_out,
                                               i_aa_out,
                                               i_za_inc,
                                               i_aa_inc,
                                               i) +=
                            pnd_field(pnd_index, i_lv, 0, 0) *
                            interp(itw,
                                   orig_part.pha_mat_data(i_f,
                                                          joker,
                                                          i_za_out,
                                                          i_aa_out,
                                                          i_za_inc,
                                                          i_aa_inc,
                                                          i),
                                   T_gp);
                      }
                    }
                  }
                }
              }
            }
          }
        }
      }
    }
  }
 
  // Set new pnd_field at lowest altitude to 0 if the cloudbox doesn't touch
  // the ground.
  // The consistency for the original pnd_field has already been ensured by
  // cloudbox_checkedCalc
  if (z_field(cloudbox_limits[0], 0, 0) > z_surface(0, 0))
    pnd_field_merged(0, 0, 0, 0) = 0.;
 
  pnd_field = pnd_field_merged;
  scat_data = scat_data_merged;
  scat_meta = scat_meta_merged;
  scat_species = scat_species_merged;
}
 
/* Workspace method: Doxygen documentation will be auto-generated */
void ExtractFromMetaSingleScatSpecies(
    //WS Output:
    Vector& meta_param,
    //WS Input:
    const ArrayOfArrayOfScatteringMetaData& scat_meta,
    const String& meta_name,
    const Index& scat_species_index,
    const Verbosity& /*verbosity*/) {
  if (scat_species_index < 0) {
    ostringstream os;
    os << "scat_species_index can't be <0!";
    throw runtime_error(os.str());
  }
 
  const Index nss = scat_meta.nelem();
 
  // check that scat_meta actually has at least scat_species_index elements
  if (!(nss > scat_species_index)) {
    ostringstream os;
    os << "Can not extract data for scattering species #" << scat_species_index
       << "\n"
       << "because scat_meta has only " << nss << " elements.";
    throw runtime_error(os.str());
  }
 
  const Index nse = scat_meta[scat_species_index].nelem();
  meta_param.resize(nse);
 
  for (Index i = 0; i < nse; i++) {
    if (meta_name == "mass")
      meta_param[i] = scat_meta[scat_species_index][i].mass;
    else if (meta_name == "diameter_max")
      meta_param[i] = scat_meta[scat_species_index][i].diameter_max;
    else if (meta_name == "diameter_volume_equ")
      meta_param[i] = scat_meta[scat_species_index][i].diameter_volume_equ;
    else if (meta_name == "diameter_area_equ_aerodynamical")
      meta_param[i] =
          scat_meta[scat_species_index][i].diameter_area_equ_aerodynamical;
    else {
      ostringstream os;
      os << "Meta parameter \"" << meta_name << "\"is unknown.";
      throw runtime_error(os.str());
    }
  }
}