geomag_calc.cc

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/* Copyright (C) 2003-2012 Nikolay Koulev <nkoulev@uni-bremen.de>
  
   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. */

#include <iostream>
#include <cmath>
#include "arts.h"
#include "matpackI.h"
#include "xml_io.h"
#include "legendre.h"


extern const Numeric PI;
extern const Numeric DEG2RAD;
extern const Numeric EARTH_RADIUS;

void magfield_nk(// Output
                 Numeric& B_r, // radial component of the geomagnetic field in [nT].
                 Numeric& B_th, // latitudinal component of the geomagnetic field in [nT].
                 Numeric& B_ph, // longitudinal component of the geomagnetic field in [nT].
                 
                 // Input
                 const Numeric r, // radial distance to the point in [km]
                 const Numeric theta, // geocentric colatitude of the point in [deg]
                 const Numeric phi, // longitude of the point in [deg].
                 // All coordinates - geocentric!
                 
                 const Index Ny, // number of elapsed years after an epoch year, J - [0,4]
                 const Verbosity& verbosity
                )
  
{
  
  Numeric Phi = phi * DEG2RAD; // Longitude angle in radian.
  Numeric Theta = PI/2 - theta * DEG2RAD; // Colatitude angle in radian.
    
  // Initializing values of the magnetic field components.
  B_r = 0;
  B_th = 0;
  B_ph = 0;

  Matrix M;
  
  xml_read_from_file ("geomag_coefficients.xml", M, verbosity);
  
  // M(i,0) and M(i,1) - the vectors with the values of the first and second coefficients 
  // of the IGRF model.
  // M(i,2) and M(i,3) - the vectors with the values of the anual rate of change of the 
  // first and second coefficient of of the IGRF model. 
  
  
  // Loop over the degree number l of the Legendre polynomes.
  for (Index l = 1; l <= 10; l++)
    {
      // Loop over the order number m of the Legendre polynomes.
      for (Index m = 0; m <= l; m++)
        {

          // Relating the row index in M to the coresponding 
          // degree number l and order number m.
          Index   j = l * (l + 1) / 2 + m - 1; 

          // Calculating the associated Schmidt quasi-normalized Legendre 
          // polynomial for a degree number l and order number m.
          Numeric P_lm = 
            g_legendre_poly_norm_schmidt (l, m, cos(Theta));

          // Calculating the derivative of the associated Schmidt quasi-normalized 
          // Legendre polynomial for a degree number l and order number m.
          Numeric dP_lm = 
            g_legendre_poly_norm_schmidt_deriv3 (l, m, cos(Theta));


          // Calculating the radial (upward) component of the magnetic field.
          B_r += pow((Numeric)(l + 2), EARTH_RADIUS / r) * (Numeric)(l + 1) * 
            ((M(j,0) + (Numeric)Ny * M(j,2)) * cos((Numeric)m * Phi) 
             + (M(j,1) + (Numeric)Ny * M(j,3)) * sin((Numeric)m * Phi)) 
            * P_lm;

          // Calculating the latitudinal (southward) component of the magnetic field. 
          B_th += pow(l + 2, EARTH_RADIUS / r) * 
            ((M(j,0) + (Numeric)Ny * M(j,2)) * cos((Numeric)m * Phi) 
             + (M(j,1) + (Numeric)Ny * M(j,3)) * sin((Numeric)m * Phi)) *
            dP_lm * sin(Theta);



          // Calculating the longitudinal (eastward) component of the magnetic field.
          B_ph += pow(l + 2, EARTH_RADIUS / r) * (Numeric)m *
            ((M(j,0) + (Numeric)Ny * M(j,2)) * sin((Numeric)m * Phi) 
             - (M(j,1) + (Numeric)Ny * M(j,3)) * cos((Numeric)m * Phi)) *
            P_lm / sin(Theta);


        }
    }
  
}