/*
  This file is part of CDO. CDO is a collection of Operators to
  manipulate and analyse Climate model Data.

  Copyright (C) 2003-2018 Uwe Schulzweida, <uwe.schulzweida AT mpimet.mpg.de>
  See COPYING file for copying and redistribution conditions.

  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; version 2 of the License.

  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.
*/

/*
   This module contains the following operators:

      Rhopot      rhopot          potential density
*/


#include <cdi.h>
#include "cdo.h"
#include "cdo_int.h"
#include "pstream.h"
#include "grid.h"


/*
!>
!! transformation from potential to in situ temperature
!! according to Bryden, 1973, "New polynomials for thermal expansion,
!! adiabatic temperature gradient and potential temperature of sea
!! water". Deep Sea Research and Oceanographic Abstracts. 20, 401-408
!! (GILL P.602), which gives the inverse transformation for an
!! approximate value, all terms linear in t are taken after that one
!! newton step.  for the check value 8.4678516 the accuracy is 0.2
!! mikrokelvin.
!!
*/

/* compute density from insitu temperature */
static
double potrho_1(double t, double sal, double p)
{
  double r_a0 = 999.842594, r_a1 = 6.793952e-2, r_a2 = -9.095290e-3,
         r_a3 = 1.001685e-4, r_a4 = -1.120083e-6, r_a5 = 6.536332e-9,
         r_b0 = 8.24493e-1, r_b1 = -4.0899e-3, r_b2 = 7.6438e-5,
         r_b3 = -8.2467e-7, r_b4 = 5.3875e-9,
         r_c0 = -5.72466e-3, r_c1 = 1.0227e-4, r_c2 = -1.6546e-6,
         r_d0 = 4.8314e-4,
         r_e0 = 19652.21, r_e1 = 148.4206, r_e2 = -2.327105,
         r_e3 = 1.360477e-2, r_e4 = -5.155288e-5,
         r_f0 = 54.6746, r_f1 = -0.603459, r_f2 = 1.09987e-2,
         r_f3 = -6.1670e-5,
         r_g0 = 7.944e-2, r_g1 = 1.6483e-2, r_g2 = -5.3009e-4,
         r_h0 = 3.239908, r_h1 = 1.43713e-3, r_h2 = 1.16092e-4,
         r_h3 = -5.77905e-7,
         r_ai0 = 2.2838e-3, r_ai1 = -1.0981e-5, r_ai2 = -1.6078e-6,
         r_aj0 = 1.91075e-4,
         r_ak0 = 8.50935e-5, r_ak1 = -6.12293e-6, r_ak2 = 5.2787e-8,
         r_am0 = -9.9348e-7, r_am1 = 2.0816e-8, r_am2 = 9.1697e-10;

  double s = MAX(sal, 0.0);
  double s3h = sqrt(s*s*s);

  double rho = (r_a0 + t * (r_a1 + t * (r_a2 + t * (r_a3 + t * (r_a4 + t * r_a5))))
            + s * (r_b0 + t * (r_b1 + t * (r_b2 + t * (r_b3 + t * r_b4))))    
            + r_d0 * s*s                 
            + s3h * (r_c0 + t * (r_c1 + r_c2 * t)))                           
           / (1.                                                            
             - p / (p * (r_h0 + t * (r_h1 + t * (r_h2 + t * r_h3))            
                         + s * (r_ai0 + t * (r_ai1 + r_ai2 * t))              
                         + r_aj0 * s3h                                        
                         + (r_ak0 + t * (r_ak1 + t * r_ak2)                   
                         + s * (r_am0 + t * (r_am1 + t * r_am2))) * p)        
                    + r_e0 + t * (r_e1 + t * (r_e2 + t * (r_e3 + t * r_e4)))  
                    + s * (r_f0 + t * (r_f1 + t * (r_f2 + t * r_f3)))         
                    + s3h * (r_g0 + t * (r_g1 + r_g2 * t))));

  return rho;
}

/*
#define N 4
int main (int argc, char *argv[])
{
  int i;
  {
    double p    = 0;
    double t[N] = {22, 25, 28, 31};
    double s[N] = {35, 35, 35, 35};
    double x[N] = {24.219, 23.343, 22.397, 21.384};
    double r[N];
  
    potrho_1d(t, s, p, r, N);

    for ( i = 0; i < N; ++i )
      printf("%d %5g %3g %8g %8g %8g %10.3f\n", i, p, s[i], t[i], x[i], r[i], r[i]-x[i]);
  }

  {
    double p    = 300;
    double t[N] = {-2.140, -0.186, 1.771, 3.728};
    double s[N] = {35, 35, 35, 35};
    double x[N] = {42.191, 41.941, 41.649, 41.319};
    double r[N];
  
    potrho_1d(t, s, p, r, N);

    for ( i = 0; i < N; ++i )
      printf("%d %5g %3g %8g %8g %8g %10.3f\n", i, p, s[i], t[i], x[i], r[i], r[i]-x[i]);
  }

  return 0;
}
*/

static
void calc_rhopot(long gridsize, long nlevel, double *pressure, field_type to, field_type sao, field_type rho)
{
  /* pressure units: hPa     */
  /* to units:       Celsius */
  /* sao units:      psu     */

  for ( long levelID = 0; levelID < nlevel; ++levelID )
    {
      long offset = gridsize*levelID;
      double *toptr = to.ptr + offset;
      double *saoptr = sao.ptr + offset;
      double *rhoptr = rho.ptr + offset;

      for ( long i = 0; i < gridsize; ++i )
	{
	  if ( DBL_IS_EQUAL(toptr[i], to.missval) ||
	       DBL_IS_EQUAL(saoptr[i], sao.missval) )
	    {
	      rhoptr[i] = rho.missval;
	    }
	  else
	    {
	      rhoptr[i] = potrho_1(toptr[i], saoptr[i], pressure[levelID]); 
	    }
	}
    }
}


void *Rhopot(void *argument)
{
  int nrecs;
  int varID, levelID;
  int zaxisID;
  int offset;
  size_t nmiss;
  int toID = -1, saoID = -1, thoID = -1;
  char varname[CDI_MAX_NAME], stdname[CDI_MAX_NAME];
  double pin = -1;
  double *single;
  field_type to, sao, rho;

  cdoInitialize(argument);

  if ( operatorArgc() == 1 ) pin = parameter2double(operatorArgv()[0]);
  
  int streamID1 = pstreamOpenRead(cdoStreamName(0));

  int vlistID1 = pstreamInqVlist(streamID1);

  int nvars = vlistNvars(vlistID1);

  for ( varID = 0; varID < nvars; varID++ )
    {
      int code = vlistInqVarCode(vlistID1, varID);
      if ( code <= 0 )
	{
	  vlistInqVarName(vlistID1, varID, varname);
	  vlistInqVarStdname(vlistID1,varID, stdname);
	  strtolower(varname);

	  if      ( strcmp(varname, "to")    == 0 ) code = 20;
	  else if ( strcmp(varname, "sao")   == 0 ) code =  5;
	  else if ( strcmp(varname, "tho")   == 0 ) code =  2;

	  else if ( strcmp(varname, "s")     == 0 ) code = 5;
	  else if ( strcmp(varname, "t")     == 0 ) code = 2;

	  else if ( strcmp(stdname, "sea_water_salinity")              == 0 ) code = 5;
	  else if ( strcmp(stdname, "sea_water_potential_temperature") == 0 ) code = 2;
	}

      if      ( code == 20 ) toID  = varID;
      else if ( code ==  5 ) saoID = varID;
      else if ( code ==  2 ) thoID = varID;
    }

  if ( saoID == -1 ) cdoAbort("Sea water salinity not found!");
  if ( toID  == -1 && thoID != -1 )
    {   
      cdoPrint("Use the CDO operator 'adisit' to convert potential temperature to In-situ temperature.");
      cdoPrint("Here is an example:");
      cdoPrint("   cdo rhopot -adisit %s %s", cdoStreamName(0)->args, cdoStreamName(1)->args);
    }
  if ( toID  == -1 ) cdoAbort("In-situ temperature not found!");

  int gridID = vlistGrid(vlistID1, 0);
  int gridsize = vlist_check_gridsize(vlistID1);

  zaxisID = vlistInqVarZaxis(vlistID1, saoID);
  int nlevel1 = zaxisInqSize(zaxisID);
  zaxisID = vlistInqVarZaxis(vlistID1, toID);
  int nlevel2 = zaxisInqSize(zaxisID);

  if ( nlevel1 != nlevel2 ) cdoAbort("temperature and salinity have different number of levels!");
  int nlevel = nlevel1;

  double *pressure = (double*) Malloc(nlevel*sizeof(double));
  cdoZaxisInqLevels(zaxisID, pressure);

  if ( pin >= 0 ) 
    for ( int i = 0; i < nlevel; ++i ) pressure[i] = pin;
  else
    for ( int i = 0; i < nlevel; ++i ) pressure[i] /= 10;

  if ( cdoVerbose )
    {
      cdoPrint("Level Pressure");
      for ( int i = 0; i < nlevel; ++i )
	cdoPrint("%5d  %g", i+1, pressure[i]);
    }

  field_init(&to);
  field_init(&sao);
  field_init(&rho);
  to.ptr = (double*) Malloc(gridsize*nlevel*sizeof(double));
  sao.ptr = (double*) Malloc(gridsize*nlevel*sizeof(double));
  rho.ptr = (double*) Malloc(gridsize*nlevel*sizeof(double));

  to.nmiss = 0;
  sao.nmiss = 0;
  rho.nmiss = 0;
  
  to.missval = vlistInqVarMissval(vlistID1, toID);
  sao.missval = vlistInqVarMissval(vlistID1, saoID);
  rho.missval = to.missval;

  int datatype = CDI_DATATYPE_FLT32;
  if ( vlistInqVarDatatype(vlistID1, toID) == CDI_DATATYPE_FLT64 &&
       vlistInqVarDatatype(vlistID1, saoID) == CDI_DATATYPE_FLT64 )
    datatype = CDI_DATATYPE_FLT64;

  int vlistID2 = vlistCreate();
  varID = vlistDefVar(vlistID2, gridID, zaxisID, TIME_VARYING);
  vlistDefVarParam(vlistID2, varID, cdiEncodeParam(18, 255, 255));
  vlistDefVarName(vlistID2, varID, "rhopoto");
  vlistDefVarLongname(vlistID2, varID, "Sea water potential density");
  vlistDefVarStdname(vlistID2, varID, "sea_water_potential_density");
  vlistDefVarUnits(vlistID2, varID, "kg m-3");
  vlistDefVarMissval(vlistID2, varID, rho.missval);
  vlistDefVarDatatype(vlistID2, varID, datatype);

  int taxisID1 = vlistInqTaxis(vlistID1);
  int taxisID2 = taxisDuplicate(taxisID1);
  vlistDefTaxis(vlistID2, taxisID2);

  int streamID2 = pstreamOpenWrite(cdoStreamName(1), cdoFiletype());
  pstreamDefVlist(streamID2, vlistID2);

  int tsID = 0;
  while ( (nrecs = pstreamInqTimestep(streamID1, tsID)) )
    {
      taxisCopyTimestep(taxisID2, taxisID1);
      pstreamDefTimestep(streamID2, tsID);
	       
      for ( int recID = 0; recID < nrecs; ++recID )
	{
	  pstreamInqRecord(streamID1, &varID, &levelID);

	  offset = gridsize*levelID;

	  if ( varID == toID )
            {
              pstreamReadRecord(streamID1, to.ptr+offset, &nmiss);
              to.nmiss = (size_t) nmiss;
            }
	  if ( varID == saoID )
            {
              pstreamReadRecord(streamID1, sao.ptr+offset, &nmiss);
              sao.nmiss = (size_t) nmiss;
            }
        }

      calc_rhopot(gridsize, nlevel, pressure, to, sao, rho); 

      for ( levelID = 0; levelID < nlevel; ++levelID )
	{
	  offset = gridsize*levelID;
	  single = rho.ptr+offset;

	  nmiss = 0;
	  for ( int i = 0; i < gridsize; ++i )
	    if ( DBL_IS_EQUAL(single[i], rho.missval) ) nmiss++;
 
	  pstreamDefRecord(streamID2, 0, levelID);
	  pstreamWriteRecord(streamID2, single, nmiss);     
	}

      tsID++;
    }

  pstreamClose(streamID2);
  pstreamClose(streamID1);

  vlistDestroy(vlistID2);

  Free(pressure);
  Free(rho.ptr);
  Free(to.ptr);
  Free(sao.ptr);

  cdoFinish();

  return 0;
}
