1 // magvar.cxx -- compute local magnetic variation given position,
4 // This is an implimentation of the NIMA WMM 2000
6 // http://www.nima.mil/GandG/ngdc-wmm2000.html
8 // Copyright (C) 2000 Edward A Williams <Ed_Williams@compuserve.com>
10 // Adapted from Excel 3.0 version 3/27/94 EAW
11 // Recoded in C++ by Starry Chan
12 // WMM95 added and rearranged in ANSI-C EAW 7/9/95
13 // Put shell around program and made Borland & GCC compatible EAW 11/22/95
14 // IGRF95 added 2/96 EAW
15 // WMM2000 IGR2000 added 2/00 EAW
16 // Released under GPL 3/26/00 EAW
17 // Adaptions and modifications for the SimGear project 3/27/2000 CLO
19 // This program is free software; you can redistribute it and/or
20 // modify it under the terms of the GNU General Public License as
21 // published by the Free Software Foundation; either version 2 of the
22 // License, or (at your option) any later version.
24 // This program is distributed in the hope that it will be useful, but
25 // WITHOUT ANY WARRANTY; without even the implied warranty of
26 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
27 // General Public License for more details.
29 // You should have received a copy of the GNU General Public License
30 // along with this program; if not, write to the Free Software
31 // Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
43 #define max(a,b) (((a) > (b)) ? (a) : (b))
45 static const double pi = 3.14159265358979;
46 static const double a = 6378.16; /* major radius (km) IAU66 ellipsoid */
47 static const double f = 1.0 / 298.25; /* inverse flattening IAU66 ellipsoid */
48 static const double b = 6378.16 * (1.0 -1.0 / 298.25 );
49 /* minor radius b=a*(1-f) */
50 static const double r_0 = 6371.2; /* "mean radius" for spherical harmonic expansion */
52 static double gnm_wmm2000[13][13] =
54 {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},
55 {-29616.0, -1722.7, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
56 {-2266.7, 3070.2, 1677.6, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
57 {1322.4, -2291.5, 1255.9, 724.8, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
58 {932.1, 786.3, 250.6, -401.5, 106.2, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
59 {-211.9, 351.6, 220.8, -134.5, -168.8, -13.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
60 {73.8, 68.2, 74.1, -163.5, -3.8, 17.1, -85.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
61 {77.4, -73.9, 2.2, 35.7, 7.3, 5.2, 8.4, -1.5, 0.0, 0.0, 0.0, 0.0, 0.0},
62 {23.3, 7.3, -8.5, -6.6, -16.9, 8.6, 4.9, -7.8, -7.6, 0.0, 0.0, 0.0, 0.0},
63 {5.7, 8.5, 2.0, -9.8, 7.6, -7.0, -2.0, 9.2, -2.2, -6.6, 0.0, 0.0, 0.0},
64 {-2.2, -5.7, 1.6, -3.7, -0.6, 4.1, 2.2, 2.2, 4.6, 2.3, 0.1, 0.0, 0.0},
65 {3.3, -1.1, -2.4, 2.6, -1.3, -1.7, -0.6, 0.4, 0.7, -0.3, 2.3, 4.2, 0.0},
66 {-1.5, -0.2, -0.3, 0.5, 0.2, 0.9, -1.4, 0.6, -0.6, -1.0, -0.3, 0.3, 0.4},
69 static double hnm_wmm2000[13][13]=
71 {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},
72 {0.0, 5194.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
73 {0.0, -2484.8, -467.9, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
74 {0.0, -224.7, 293.0, -486.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
75 {0.0, 273.3, -227.9, 120.9, -302.7, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
76 {0.0, 42.0, 173.8, -135.0, -38.6, 105.2, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
77 {0.0, -17.4, 61.2, 63.2, -62.9, 0.2, 43.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
78 {0.0, -62.3, -24.5, 8.9, 23.4, 15.0, -27.6, -7.8, 0.0, 0.0, 0.0, 0.0, 0.0},
79 {0.0, 12.4, -20.8, 8.4, -21.2, 15.5, 9.1, -15.5, -5.4, 0.0, 0.0, 0.0, 0.0},
80 {0.0, -20.4, 13.9, 12.0, -6.2, -8.6, 9.4, 5.0, -8.4, 3.2, 0.0, 0.0, 0.0},
81 {0.0, 0.9, -0.7, 3.9, 4.8, -5.3, -1.0, -2.4, 1.3, -2.3, -6.4, 0.0, 0.0},
82 {0.0, -1.5, 0.7, -1.1, -2.3, 1.3, -0.6, -2.8, -1.6, -0.1, -1.9, 1.4, 0.0},
83 {0.0, -1.0, 0.7, 2.2, -2.5, -0.2, 0.0, -0.2, 0.0, 0.2, -0.9, -0.2, 1.0},
86 static double gtnm_wmm2000[13][13]=
88 {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},
89 {14.7, 11.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
90 {-13.6, -0.7, -1.8, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
91 {0.3, -4.3, 0.9, -8.4, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
92 {-1.6, 0.9, -7.6, 2.2, -3.2, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
93 {-0.9, -0.2, -2.5, -2.7, -0.9, 1.7, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
94 {1.2, 0.2, 1.7, 1.6, -0.1, -0.3, 0.8, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
95 {-0.4, -0.8, -0.2, 1.1, 0.4, 0.0, -0.2, -0.2, 0.0, 0.0, 0.0, 0.0, 0.0},
96 {-0.3, 0.6, -0.8, 0.3, -0.2, 0.5, 0.0, -0.6, 0.1, 0.0, 0.0, 0.0, 0.0},
97 {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},
98 {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},
99 {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},
100 {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},
103 static double htnm_wmm2000[13][13]=
105 {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},
106 {0.0, -20.4, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
107 {0.0, -21.5, -9.6, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
108 {0.0, 6.4, -1.3, -13.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
109 {0.0, 2.3, 0.7, 3.7, -0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
110 {0.0, 0.0, 2.1, 2.3, 3.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
111 {0.0, -0.3, -1.7, -0.9, -1.0, -0.1, 1.9, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
112 {0.0, 1.4, 0.2, 0.7, 0.4, -0.3, -0.8, -0.1, 0.0, 0.0, 0.0, 0.0, 0.0},
113 {0.0, -0.5, 0.1, -0.2, 0.0, 0.1, -0.1, 0.3, 0.2, 0.0, 0.0, 0.0, 0.0},
114 {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},
115 {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},
116 {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},
117 {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},
120 static const int nmax = 12;
122 static double P[13][13];
123 static double DP[13][13];
124 static double gnm[13][13];
125 static double hnm[13][13];
126 static double sm[13];
127 static double cm[13];
130 /* Convert date to Julian day 1950-2049 */
131 unsigned long int yymmdd_to_julian_days( int yy, int mm, int dd )
135 yy = (yy < 50) ? (2000 + yy) : (1900 + yy);
136 jd = dd - 32075L + 1461L * (yy + 4800L + (mm - 14) / 12 ) / 4;
137 jd = jd + 367L * (mm - 2 - (mm - 14) / 12*12) / 12;
138 jd = jd - 3 * ((yy + 4900L + (mm - 14) / 12) / 100) / 4;
140 /* printf("julian date = %d\n", jd ); */
145 /* Convert degrees to radians */
146 double deg_to_rad( double deg )
152 /* Convert radians to degrees */
153 double rad_to_deg( double rad )
159 /* return variation (in degrees) given geodetic latitude (radians), longitude
160 (radians) ,height (km) and (Julian) date
161 N and E lat and long are positive, S and W negative
164 double SGMagVar( double lat, double lon, double h, long dat, double* field )
166 /* output field B_r,B_th,B_phi,B_x,B_y,B_z */
168 /* reference dates */
169 long date0_wmm2000 = yymmdd_to_julian_days(0,1,1);
171 double yearfrac,sr,r,theta,c,s,psi,fn,B_r,B_theta,B_phi,X,Y,Z;
173 /* convert to geocentric coords: */
174 sr = sqrt(pow(a*cos(lat),2.0)+pow(b*sin(lat),2.0));
175 /* sr is effective radius */
176 theta = atan2(cos(lat) * (h * sr + a * a),
177 sin(lat) * (h * sr + b * b));
178 /* theta is geocentric co-latitude */
180 r = h * h + 2.0*h * sr +
181 (pow(a,4.0) - (pow(a,4.0) - pow(b,4.0)) * pow(sin(lat),2.0)) /
182 (a * a - (a * a - b * b) * pow(sin(lat),2.0));
186 /* r is geocentric radial distance */
191 for ( n = 0; n <= nmax; n++ ) {
192 for ( m = 0; m <= n; m++ ) {
198 /* diagonal elements */
206 for ( n = 2; n <= nmax; n++ ) {
207 P[n][n] = P[n-1][n-1] * s * sqrt((2.0*n-1) / (2.0*n));
208 DP[n][n] = (DP[n-1][n-1] * s + P[n-1][n-1] * c) *
209 sqrt((2.0*n-1) / (2.0*n));
213 for ( m = 0; m <= nmax; m++ ) {
214 for ( n = max(m + 1, 2); n <= nmax; n++ ) {
215 P[n][m] = (P[n-1][m] * c * (2.0*n-1) - P[n-2][m] *
216 sqrt(1.0*(n-1)*(n-1) - m * m)) /
217 sqrt(1.0* n * n - m * m);
218 DP[n][m] = ((DP[n-1][m] * c - P[n-1][m] * s) *
219 (2.0*n-1) - DP[n-2][m] *
220 sqrt(1.0*(n-1) * (n-1) - m * m)) /
221 sqrt(1.0* n * n - m * m);
225 /* compute gnm, hnm at dat */
227 yearfrac = (dat - date0_wmm2000) / 365.25;
228 for ( n = 1; n <= nmax; n++ ) {
229 for ( m = 0; m <= nmax; m++ ) {
230 gnm[n][m] = gnm_wmm2000[n][m] + yearfrac * gtnm_wmm2000[n][m];
231 hnm[n][m] = hnm_wmm2000[n][m] + yearfrac * htnm_wmm2000[n][m];
235 /* compute sm (sin(m lon) and cm (cos(m lon)) */
236 for ( m = 0; m <= nmax; m++ ) {
237 sm[m] = sin(m * lon);
238 cm[m] = cos(m * lon);
241 /* compute B fields */
246 for ( n = 1; n <= nmax; n++ ) {
250 for ( m = 0; m <= n; m++ ) {
251 c1_n=c1_n + (gnm[n][m] * cm[m] + hnm[n][m] * sm[m]) * P[n][m];
252 c2_n=c2_n + (gnm[n][m] * cm[m] + hnm[n][m] * sm[m]) * DP[n][m];
253 c3_n=c3_n + m * (gnm[n][m] * sm[m] - hnm[n][m] * cm[m]) * P[n][m];
256 B_r = B_r + (n + 1) * c1_n * fn;
257 B_theta = B_theta - c2_n * fn;
258 B_phi = B_phi + c3_n * fn / s;
261 /* Find geodetic field components: */
262 psi = theta - (pi / 2.0 - lat);
263 X = -B_theta * cos(psi) - B_r * sin(psi);
265 Z = B_theta * sin(psi) - B_r * cos(psi);
272 field[5]=Z; /* output fields */
274 /* find variation, leave in radians! */
275 return atan2(Y, X); /* E is positive */