coremag.cxx

// coremag.cxx -- compute local magnetic variation given position,
//                altitude, and date
//
// This is an implementation of the NIMA (formerly DMA) WMM2000
//
//    http://www.nima.mil/GandG/ngdc-wmm2000.html
//
// Copyright (C) 2000  Edward A Williams <Ed_Williams@compuserve.com>
//
// Adapted from Excel 3.0 version 3/27/94 EAW
// Recoded in C++ by Starry Chan
// WMM95 added and rearranged in ANSI-C EAW 7/9/95
// Put shell around program and made Borland & GCC compatible EAW 11/22/95
// IGRF95 added 2/96 EAW
// WMM2000 IGR2000 added 2/00 EAW
// Released under GPL 3/26/00 EAW
// Adaptions and modifications for the SimGear project  3/27/2000 CLO
//
// Removed all pow() calls and made static roots[][] arrays to
// save many sqrt() calls on subsequent invocations
// left old code as SGMagVarOrig() for testing purposes
// 3/28/2000  Norman Vine -- nhv@yahoo.com
//
// Put in some bullet-proofing to handle magnetic and geographic poles.
// 3/28/2000 EAW
//
// Updated coefficient arrays to use the current WMM2005 model,
// (valid between 2005.0 and 2010.0)
// Also removed unused variables and corrected earth radii constants
// to the values for WGS84 and WMM2005.
// Reference:
//     McLean, S., S. Macmillan, S. Maus, V. Lesur, A.
//     Thomson, and D. Dater, December 2004, The
//     US/UK World Magnetic Model for 2005-2010,
//     NOAA Technical Report NESDIS/NGDC-1.
//
// 25/10/2006  Wim Van Hoydonck -- wim.van.hoydonck@gmail.com
//

//  The routine uses a spherical harmonic expansion of the magnetic
// potential up to twelfth order, together with its time variation, as
// described in Chapter 4 of "Geomagnetism, Vol 1, Ed. J.A.Jacobs,
// Academic Press (London 1987)". The program first converts geodetic
// coordinates (lat/long on elliptic earth and altitude) to spherical
// geocentric (spherical lat/long and radius) coordinates. Using this,
// the spherical (B_r, B_theta, B_phi) magnetic field components are
// computed from the model. These are finally referred to surface (X, Y,
// Z) coordinates.
//
//   Fields are accurate to better than 200nT, variation and dip to
// better than 0.5 degrees, with the exception of the declination near
// the magnetic poles (where it is ill-defined) where the error may reach
// 4 degrees or more.
//
//   Variation is undefined at both the geographic and  
// magnetic poles, even though the field itself is well-behaved. To
// avoid the routine blowing up, latitude entries corresponding to
// the geographic poles are slightly offset. At the magnetic poles,
// the routine returns zero variation.


//
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Library General Public
// License as published by the Free Software Foundation; either
// version 2 of the License, or (at your option) any later version.
//
// This library 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
// Library 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., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
//
// $Id: coremag_8cxx_source.html,v 1.3 2010/02/23 22:10:12 curt Exp $


#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#include <simgear/constants.h>
#include <simgear/sg_inlines.h>

#include "coremag.hxx"

static const double a = 6378.137;       /* semi-major axis (equatorial radius) of WGS84 ellipsoid */
static const double b = 6356.7523142;   /* semi-minor axis referenced to the WGS84 ellipsoid */
static const double r_0 = 6371.2;       /* standard Earth magnetic reference radius  */

static double gnm_wmm2005[13][13] =
{
    {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {-29556.8, -1671.7, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {-2340.6, 3046.9, 1657.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {1335.4, -2305.1, 1246.7, 674.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {919.8, 798.1, 211.3, -379.4, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {-227.4, 354.6, 208.7, -136.5, -168.3, -14.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {73.2, 69.7, 76.7, -151.2, -14.9, 14.6, -86.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {80.1, -74.5, -1.4, 38.5, 12.4, 9.5, 5.7, 1.8, 0.0, 0.0, 0.0, 0.0, 0.0},
    {24.9, 7.7, -11.6, -6.9, -18.2, 10.0, 9.2, -11.6, -5.2, 0.0, 0.0, 0.0, 0.0},
    {5.6, 9.9, 3.5, -7.0, 5.1, -10.8, -1.3, 8.8, -6.7, -9.1, 0.0, 0.0, 0.0},
    {-2.3, -6.3, 1.6, -2.6, 0.0, 3.1, 0.4, 2.1, 3.9, -0.1, -2.3, 0.0, 0.0},
    {2.8, -1.6, -1.7, 1.7, -0.1, 0.1, -0.7, 0.7, 1.8, 0.0, 1.1, 4.1, 0.0},
    {-2.4, -0.4, 0.2, 0.8, -0.3, 1.1, -0.5, 0.4, -0.3, -0.3, -0.1, -0.3, -0.1},
};

static double hnm_wmm2005[13][13]=
{
    {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 5079.8, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, -2594.7, -516.7, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, -199.9, 269.3, -524.2, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 281.5, -226.0, 145.8, -304.7, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 42.4, 179.8, -123.0, -19.5, 103.6, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, -20.3, 54.7, 63.6, -63.4, -0.1, 50.4, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, -61.5, -22.4, 7.2, 25.4, 11.0, -26.4, -5.1, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 11.2, -21.0, 9.6, -19.8, 16.1, 7.7, -12.9, -0.2, 0.0, 0.0, 0.0, 0.0},
    {0.0, -20.1, 12.9, 12.6, -6.7, -8.1, 8.0, 2.9, -7.9, 6.0, 0.0, 0.0, 0.0},
    {0.0, 2.4, 0.2, 4.4, 4.8, -6.5, -1.1, -3.4, -0.8, -2.3, -7.9, 0.0, 0.0},
    {0.0, 0.3, 1.2, -0.8, -2.5, 0.9, -0.6, -2.7, -0.9, -1.3, -2.0, -1.2, 0.0},
    {0.0, -0.4, 0.3, 2.4, -2.6, 0.6, 0.3, 0.0, 0.0, 0.3, -0.9, -0.4, 0.8},
};

static double gtnm_wmm2005[13][13]=
{
    {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {8.0, 10.6, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {-15.1, -7.8, -0.8, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.4, -2.6, -1.2, -6.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {-2.5, 2.8, -7.0, 6.2, -3.8, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {-2.8, 0.7, -3.2, -1.1, 0.1, -0.8, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {-0.7, 0.4, -0.3, 2.3, -2.1, -0.6, 1.4, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.2, -0.1, -0.3, 1.1, 0.6, 0.5, -0.4, 0.6, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.1, 0.3, -0.4, 0.3, -0.3, 0.2, 0.4, -0.7, 0.4, 0.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
};

static double htnm_wmm2005[13][13]=
{
    {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, -20.9, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, -23.2, -14.6, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 5.0, -7.0, -0.6, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 2.2, 1.6, 5.8, 0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 1.7, 2.1, 4.8, -1.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, -0.6, -1.9, -0.4, -0.5, -0.3, 0.7, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 0.6, 0.4, 0.2, 0.3, -0.8, -0.2, 0.1, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, -0.2, 0.1, 0.3, 0.4, 0.1, -0.2, 0.4, 0.4, 0.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
};

static const int nmax = 12;

static double P[13][13];
static double DP[13][13];
static double gnm[13][13];
static double hnm[13][13];
static double sm[13];
static double cm[13];

static double root[13];
static double roots[13][13][2];

/* Convert date to Julian day    1950-2049 */
unsigned long int yymmdd_to_julian_days( int yy, int mm, int dd )
{
    unsigned long jd;
 
    yy = (yy < 50) ? (2000 + yy) : (1900 + yy);
    jd = dd - 32075L + 1461L * (yy + 4800L + (mm - 14) / 12 ) / 4;
    jd = jd + 367L * (mm - 2 - (mm - 14) / 12*12) / 12;
    jd = jd - 3 * ((yy + 4900L + (mm - 14) / 12) / 100) / 4;

    /* printf("julian date = %d\n", jd ); */
    return jd;
} 


/*
 * return variation (in radians) given geodetic latitude (radians),
 * longitude(radians), height (km) and (Julian) date
 * N and E lat and long are positive, S and W negative
*/

double calc_magvar( double lat, double lon, double h, long dat, double* field )
{
    /* output field B_r,B_th,B_phi,B_x,B_y,B_z */
    int n,m;
    /* reference date for current model is 1 januari 2005 */
    long date0_wmm2005 = yymmdd_to_julian_days(5,1,1);

    double yearfrac,sr,r,theta,c,s,psi,fn,fn_0,B_r,B_theta,B_phi,X,Y,Z;
    double sinpsi, cospsi, inv_s;

    static int been_here = 0;

    double sinlat = sin(lat);
    double coslat = cos(lat);

    /* convert to geocentric coords: */
    // sr = sqrt(pow(a*coslat,2.0)+pow(b*sinlat,2.0));
    sr = sqrt(a*a*coslat*coslat + b*b*sinlat*sinlat);
    /* sr is effective radius */
    theta = atan2(coslat * (h*sr + a*a),
                  sinlat * (h*sr + b*b));
    /* theta is geocentric co-latitude */

    r = h*h + 2.0*h * sr +
        (a*a*a*a - ( a*a*a*a - b*b*b*b ) * sinlat*sinlat ) / 
        (a*a - (a*a - b*b) * sinlat*sinlat );

    r = sqrt(r);

    /* r is geocentric radial distance */
    c = cos(theta);
    s = sin(theta);
    /* protect against zero divide at geographic poles */
    inv_s =  1.0 / (s + (s == 0.)*1.0e-8); 

    /* zero out arrays */
    for ( n = 0; n <= nmax; n++ ) {
        for ( m = 0; m <= n; m++ ) {
            P[n][m] = 0;
            DP[n][m] = 0;
        }
    }

    /* diagonal elements */
    P[0][0] = 1;
    P[1][1] = s;
    DP[0][0] = 0;
    DP[1][1] = c;
    P[1][0] = c ;
    DP[1][0] = -s;

    // these values will not change for subsequent function calls
    if( !been_here ) {
        for ( n = 2; n <= nmax; n++ ) {
            root[n] = sqrt((2.0*n-1) / (2.0*n));
        }

        for ( m = 0; m <= nmax; m++ ) {
            double mm = m*m;
            for ( n = SG_MAX2(m + 1, 2); n <= nmax; n++ ) {
                roots[m][n][0] = sqrt((n-1)*(n-1) - mm);
                roots[m][n][1] = 1.0 / sqrt( n*n - mm);
            }
        }
        been_here = 1;
    }

    for ( n=2; n <= nmax; n++ ) {
        // double root = sqrt((2.0*n-1) / (2.0*n));
        P[n][n] = P[n-1][n-1] * s * root[n];
        DP[n][n] = (DP[n-1][n-1] * s + P[n-1][n-1] * c) *
            root[n];
    }

    /* lower triangle */
    for ( m = 0; m <= nmax; m++ ) {
        // double mm = m*m;
        for ( n = SG_MAX2(m + 1, 2); n <= nmax; n++ ) {
            // double root1 = sqrt((n-1)*(n-1) - mm);
            // double root2 = 1.0 / sqrt( n*n - mm);
            P[n][m] = (P[n-1][m] * c * (2.0*n-1) -
                       P[n-2][m] * roots[m][n][0]) *
                roots[m][n][1];

            DP[n][m] = ((DP[n-1][m] * c - P[n-1][m] * s) *
                        (2.0*n-1) - DP[n-2][m] * roots[m][n][0]) *
                roots[m][n][1];
        }
    }

    /* compute Gauss coefficients gnm and hnm of degree n and order m for the desired time
       achieved by adjusting the coefficients at time t0 for linear secular variation */
    /* WMM2005 */
    yearfrac = (dat - date0_wmm2005) / 365.25;
    for ( n = 1; n <= nmax; n++ ) {
        for ( m = 0; m <= nmax; m++ ) {
            gnm[n][m] = gnm_wmm2005[n][m] + yearfrac * gtnm_wmm2005[n][m];
            hnm[n][m] = hnm_wmm2005[n][m] + yearfrac * htnm_wmm2005[n][m];
        }
    }

    /* compute sm (sin(m lon) and cm (cos(m lon)) */
    for ( m = 0; m <= nmax; m++ ) {
        sm[m] = sin(m * lon);
        cm[m] = cos(m * lon);
    }

    /* compute B fields */
    B_r = 0.0;
    B_theta = 0.0;
    B_phi = 0.0;
    fn_0 = r_0/r;
    fn = fn_0 * fn_0;

    for ( n = 1; n <= nmax; n++ ) {
        double c1_n=0;
        double c2_n=0;
        double c3_n=0;
        for ( m = 0; m <= n; m++ ) {
            double tmp = (gnm[n][m] * cm[m] + hnm[n][m] * sm[m]); 
            c1_n=c1_n + tmp * P[n][m];
            c2_n=c2_n + tmp * DP[n][m];
            c3_n=c3_n + m * (gnm[n][m] * sm[m] - hnm[n][m] * cm[m]) * P[n][m];
        }
        // fn=pow(r_0/r,n+2.0);
        fn *= fn_0;
        B_r = B_r + (n + 1) * c1_n * fn;
        B_theta = B_theta - c2_n * fn;
        B_phi = B_phi + c3_n * fn * inv_s;
    }

    /* Find geodetic field components: */
    psi = theta - ((M_PI / 2.0) - lat);
    sinpsi = sin(psi);
    cospsi = cos(psi);
    X = -B_theta * cospsi - B_r * sinpsi;
    Y = B_phi;
    Z = B_theta * sinpsi - B_r * cospsi;

    field[0]=B_r;
    field[1]=B_theta;
    field[2]=B_phi;
    field[3]=X;
    field[4]=Y;
    field[5]=Z;   /* output fields */

    /* find variation in radians */
    /* return zero variation at magnetic pole X=Y=0. */
    /* E is positive */
    return (X != 0. || Y != 0.) ? atan2(Y, X) : (double) 0.;  
}


#ifdef TEST_NHV_HACKS
double SGMagVarOrig( double lat, double lon, double h, long dat, double* field )
{
    /* output field B_r,B_th,B_phi,B_x,B_y,B_z */
    int n,m;
    /* reference dates */
    long date0_wmm2005 = yymmdd_to_julian_days(5,1,1);

    double yearfrac,sr,r,theta,c,s,psi,fn,B_r,B_theta,B_phi,X,Y,Z;

    /* convert to geocentric coords: */
    sr = sqrt(pow(a*cos(lat),2.0)+pow(b*sin(lat),2.0));
    /* sr is effective radius */
    theta = atan2(cos(lat) * (h * sr + a * a),
                  sin(lat) * (h * sr + b * b));
    /* theta is geocentric co-latitude */

    r = h * h + 2.0*h * sr +
        (pow(a,4.0) - (pow(a,4.0) - pow(b,4.0)) * pow(sin(lat),2.0)) / 
        (a * a - (a * a - b * b) * pow(sin(lat),2.0));

    r = sqrt(r);

    /* r is geocentric radial distance */
    c = cos(theta);
    s = sin(theta);

    /* zero out arrays */
    for ( n = 0; n <= nmax; n++ ) {
        for ( m = 0; m <= n; m++ ) {
            P[n][m] = 0;
            DP[n][m] = 0;
        }
    }

    /* diagonal elements */
    P[0][0] = 1;
    P[1][1] = s;
    DP[0][0] = 0;
    DP[1][1] = c;
    P[1][0] = c ;
    DP[1][0] = -s;

    for ( n = 2; n <= nmax; n++ ) {
        P[n][n] = P[n-1][n-1] * s * sqrt((2.0*n-1) / (2.0*n));
        DP[n][n] = (DP[n-1][n-1] * s + P[n-1][n-1] * c) *
            sqrt((2.0*n-1) / (2.0*n));
    }

    /* lower triangle */
    for ( m = 0; m <= nmax; m++ ) {
        for ( n = SG_MAX2(m + 1, 2); n <= nmax; n++ ) {
            P[n][m] = (P[n-1][m] * c * (2.0*n-1) - P[n-2][m] *
                       sqrt(1.0*(n-1)*(n-1) - m * m)) /
                sqrt(1.0* n * n - m * m);
            DP[n][m] = ((DP[n-1][m] * c - P[n-1][m] * s) *
                        (2.0*n-1) - DP[n-2][m] *
                        sqrt(1.0*(n-1) * (n-1) - m * m)) /
                sqrt(1.0* n * n - m * m);
        }
    }

    /* compute gnm, hnm at dat */
    /* WMM2005 */
    yearfrac = (dat - date0_wmm2005) / 365.25;
    for ( n = 1; n <= nmax; n++ ) {
        for ( m = 0; m <= nmax; m++ ) {
            gnm[n][m] = gnm_wmm2005[n][m] + yearfrac * gtnm_wmm2005[n][m];
            hnm[n][m] = hnm_wmm2005[n][m] + yearfrac * htnm_wmm2005[n][m];
        }
    }

    /* compute sm (sin(m lon) and cm (cos(m lon)) */
    for ( m = 0; m <= nmax; m++ ) {
        sm[m] = sin(m * lon);
        cm[m] = cos(m * lon);
    }

    /* compute B fields */
    B_r = 0.0;
    B_theta = 0.0;
    B_phi = 0.0;

    for ( n = 1; n <= nmax; n++ ) {
        double c1_n=0;
        double c2_n=0;
        double c3_n=0;
        for ( m = 0; m <= n; m++ ) {
            c1_n=c1_n + (gnm[n][m] * cm[m] + hnm[n][m] * sm[m]) * P[n][m];
            c2_n=c2_n + (gnm[n][m] * cm[m] + hnm[n][m] * sm[m]) * DP[n][m];
            c3_n=c3_n + m * (gnm[n][m] * sm[m] - hnm[n][m] * cm[m]) * P[n][m];
        }
        fn=pow(r_0/r,n+2.0);
        B_r = B_r + (n + 1) * c1_n * fn;
        B_theta = B_theta - c2_n * fn;
        B_phi = B_phi + c3_n * fn / s;
    }

    /* Find geodetic field components: */
    psi = theta - (pi / 2.0 - lat);
    X = -B_theta * cos(psi) - B_r * sin(psi);
    Y = B_phi;
    Z = B_theta * sin(psi) - B_r * cos(psi);

    field[0]=B_r;
    field[1]=B_theta;
    field[2]=B_phi;
    field[3]=X;
    field[4]=Y;
    field[5]=Z;   /* output fields */

    /* find variation, leave in radians! */
    return atan2(Y, X);  /* E is positive */
}
#endif // TEST_NHV_HACKS

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