1 // coremag.cxx -- compute local magnetic variation given position,
4 // This is an implementation of the NIMA (formerly DMA) WMM2000
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 // Removed all pow() calls and made static roots[][] arrays to
20 // save many sqrt() calls on subsequent invocations
21 // left old code as SGMagVarOrig() for testing purposes
22 // 3/28/2000 Norman Vine -- nhv@yahoo.com
24 // Put in some bullet-proofing to handle magnetic and geographic poles.
27 // Updated coefficient arrays to use the current wmm2005 model,
28 // (valid between 2005.0 and 2010.0)
29 // Also removed unused variables and corrected earth radii constants
30 // to the values for WGS84 and WMM2005.
32 // McLean, S., S. Macmillan, S. Maus, V. Lesur, A.
33 // Thomson, and D. Dater, December 2004, The
34 // US/UK World Magnetic Model for 2005-2010,
35 // NOAA Technical Report NESDIS/NGDC-1.
37 // 25/10/2006 Wim Van Hoydonck -- wim.van.hoydonck@gmail.com
40 // Updated coefficient arrays to use the current WMM2015 model,
41 // (valid between 2015.0 and 2020.0)
42 // Also removed unused variables and corrected earth radii constants
43 // to the values for WGS84 and WMM2015.
45 // A. Chulliat , S. Macmillan, P. Alken, C. Beggan, M.
46 // Nair, B. Hamilton, A. Woods, V. Ridley,
47 // S Maus, and A Thomson, December 2014, The
48 // US/UK World Magnetic Model for 2015-2020,
49 // NOAA Technical Report WMM2015_Report.pdf
51 // 18/06/2015 Jean-Paul Anceaux -- j.p.r.anceaux@gmail.com
54 // The routine uses a spherical harmonic expansion of the magnetic
55 // potential up to twelfth order, together with its time variation, as
56 // described in Chapter 4 of "Geomagnetism, Vol 1, Ed. J.A.Jacobs,
57 // Academic Press (London 1987)". The program first converts geodetic
58 // coordinates (lat/long on elliptic earth and altitude) to spherical
59 // geocentric (spherical lat/long and radius) coordinates. Using this,
60 // the spherical (B_r, B_theta, B_phi) magnetic field components are
61 // computed from the model. These are finally referred to surface (X, Y,
64 // Fields are accurate to better than 200nT, variation and dip to
65 // better than 0.5 degrees, with the exception of the declination near
66 // the magnetic poles (where it is ill-defined) where the error may reach
69 // Variation is undefined at both the geographic and
70 // magnetic poles, even though the field itself is well-behaved. To
71 // avoid the routine blowing up, latitude entries corresponding to
72 // the geographic poles are slightly offset. At the magnetic poles,
73 // the routine returns zero variation.
77 // This library is free software; you can redistribute it and/or
78 // modify it under the terms of the GNU Library General Public
79 // License as published by the Free Software Foundation; either
80 // version 2 of the License, or (at your option) any later version.
82 // This library is distributed in the hope that it will be useful,
83 // but WITHOUT ANY WARRANTY; without even the implied warranty of
84 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
85 // Library General Public License for more details.
87 // You should have received a copy of the GNU General Public License
88 // along with this program; if not, write to the Free Software
89 // Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
98 #include <simgear/constants.h>
99 #include <simgear/sg_inlines.h>
101 #include "coremag.hxx"
103 static const double a = 6378.137; /* semi-major axis (equatorial radius) of WGS84 ellipsoid */
104 static const double b = 6356.7523142; /* semi-minor axis referenced to the WGS84 ellipsoid */
105 static const double r_0 = 6371.2; /* standard Earth magnetic reference radius */
107 static double gnm_wmm2015[13][13] =
109 {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},
110 {-29438.5, -1501.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
111 {-2445.3, 3012.5, 1676.6, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
112 {1351.1, -2352.3, 1225.6, 581.9, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
113 {907.2, 813.7, 120.3, -335.0, 70.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
114 {-232.6, 360.1, 192.4, -141.0, -157.4, 4.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
115 {69.5, 67.4, 72.8, -129.8, -29.0, 13.2, -70.9, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
116 {81.6, -76.1, -6.8, 51.9, 15.0, 9.3, -2.8, 6.7, 0.0, 0.0, 0.0, 0.0, 0.0},
117 {24.0, 8.6, -16.9, -3.2, -20.6, 13.3, 11.7, -16.0, -2.0, 0.0, 0.0, 0.0, 0.0},
118 {5.4, 8.8, 3.1, -3.1, 0.6, -13.3, -0.1, 8.7, -9.1, -10.5, 0.0, 0.0, 0.0},
119 {-1.9, -6.5, 0.2, 0.6, -0.6, 1.7, -0.7, 2.1, 2.3, -1.8, -3.6, 0.0, 0.0},
120 {3.1, -1.5, -2.3, 2.1, -0.9, 0.6, -0.7, 0.2, 1.7, -0.2, 0.4, 3.5, 0.0},
121 {-2.0, -0.3, 0.4, 1.3, -0.9, 0.9, 0.1, 0.5, -0.4, -0.4, 0.2, -0.9, 0.0},
124 static double hnm_wmm2015[13][13]=
126 {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},
127 {0.0, 4796.2, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
128 {0.0, -2845.6, -642.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
129 {0.0, -115.3, 245.0, -538.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
130 {0.0, 283.4, -188.6, 180.9, -329.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
131 {0.0, 47.4, 196.9, -119.4, 16.1, 100.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
132 {0.0, -20.7, 33.2, 58.8, -66.5, 7.3, 62.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
133 {0.0, -54.1, -19.4, 5.6, 24.4, 3.3, -27.5, -2.3, 0.0, 0.0, 0.0, 0.0, 0.0},
134 {0.0, 10.2, -18.1, 13.2, -14.6, 16.2, 5.7, -9.1, 2.2, 0.0, 0.0, 0.0, 0.0},
135 {0.0, -21.6, 10.8, 11.7, -6.8, -6.9, 7.8, 1.0, -3.9, 8.5, 0.0, 0.0, 0.0},
136 {0.0, 3.3, -0.3, 4.6, 4.4, -7.9, -0.6, -4.1, -2.8, -1.1, -8.7, 0.0, 0.0},
137 {0.0, -0.1, 2.1, -0.7, -1.1, 0.7, -0.2, -2.1, -1.5, -2.5, -2.0, -2.3, 0.0},
138 {0.0, -1.0, 0.5, 1.8, -2.2, 0.3, 0.7, -0.1, 0.3, 0.2, -0.9, -0.2, 0.7},
141 static double gtnm_wmm2015[13][13]=
143 {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},
144 {10.7, 17.9, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
145 {-8.6, -3.3, 2.4, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
146 {3.1, -6.2, -0.4, -10.4, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
147 {-0.4, 0.8, -9.2, 4.0, -4.2, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
148 {-0.2, 0.1, -1.4, 0.0, 1.3, 3.8, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
149 {-0.5, -0.2, -0.6, 2.4, -1.1, 0.3, 1.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
150 {0.2, -0.2, -0.4, 1.3, 0.2, -0.4, -0.9, 0.3, 0.0, 0.0, 0.0, 0.0, 0.0},
151 {0.0, 0.1, -0.5, 0.5, -0.2, 0.4, 0.2, -0.4, 0.3, 0.0, 0.0, 0.0, 0.0},
152 {0.0, -0.1, -0.1, 0.4, -0.5, -0.2, 0.1, 0.0, -0.2, -0.1, 0.0, 0.0, 0.0},
153 {0.0, 0.0, -0.1, 0.3, -0.1, -0.1, -0.1, 0.0, -0.2, -0.1, -0.2, 0.0, 0.0},
154 {0.0, 0.0, -0.1, 0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.1, -0.1, 0.0},
155 {0.1, 0.0, 0.0, 0.1, -0.1, 0.0, 0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
158 static double htnm_wmm2015[13][13]=
160 {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},
161 {0.0, -26.8, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
162 {0.0, -27.1, -13.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
163 {0.0, 8.4, -0.4, 2.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
164 {0.0, -0.6, 5.3, 3.0, -5.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
165 {0.0, 0.4, 1.6, -1.1, 3.3, 0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
166 {0.0, 0.0, -2.2, -0.7, 0.1, 1.0, 1.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
167 {0.0, 0.7, 0.5, -0.2, -0.1, -0.7, 0.1, 0.1, 0.0, 0.0, 0.0, 0.0, 0.0},
168 {0.0, -0.3, 0.3, 0.3, 0.6, -0.1, -0.2, 0.3, 0.0, 0.0, 0.0, 0.0, 0.0},
169 {0.0, -0.2, -0.1, -0.2, 0.1, 0.1, 0.0, -0.2, 0.4, 0.3, 0.0, 0.0, 0.0},
170 {0.0, 0.1, -0.1, 0.0, 0.0, -0.2, 0.1, -0.1, -0.2, 0.1, -0.1, 0.0, 0.0},
171 {0.0, 0.0, 0.1, 0.0, 0.1, 0.0, 0.0, 0.1, 0.0, -0.1, 0.0, -0.1, 0.0},
172 {0.0, 0.0, 0.0, -0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
175 static const int nmax = 12;
177 static double P[13][13];
178 static double DP[13][13];
179 static double gnm[13][13];
180 static double hnm[13][13];
181 static double sm[13];
182 static double cm[13];
184 static double root[13];
185 static double roots[13][13][2];
187 /* Convert date to Julian day 1950-2049 */
188 unsigned long int yymmdd_to_julian_days( int yy, int mm, int dd )
192 yy = (yy < 50) ? (2000 + yy) : (1900 + yy);
193 jd = dd - 32075L + 1461L * (yy + 4800L + (mm - 14) / 12 ) / 4;
194 jd = jd + 367L * (mm - 2 - (mm - 14) / 12*12) / 12;
195 jd = jd - 3 * ((yy + 4900L + (mm - 14) / 12) / 100) / 4;
197 /* printf("julian date = %d\n", jd ); */
203 * return variation (in radians) given geodetic latitude (radians),
204 * longitude(radians), height (km) and (Julian) date
205 * N and E lat and long are positive, S and W negative
208 double calc_magvar( double lat, double lon, double h, long dat, double* field )
210 /* output field B_r,B_th,B_phi,B_x,B_y,B_z */
212 /* reference date for current model is 1 januari 2015 */
213 long date0_wmm2015 = yymmdd_to_julian_days(15,1,1);
215 double yearfrac,sr,r,theta,c,s,psi,fn,fn_0,B_r,B_theta,B_phi,X,Y,Z;
216 double sinpsi, cospsi, inv_s;
218 static int been_here = 0;
220 double sinlat = sin(lat);
221 double coslat = cos(lat);
223 /* convert to geocentric coords: */
224 // sr = sqrt(pow(a*coslat,2.0)+pow(b*sinlat,2.0));
225 sr = sqrt(a*a*coslat*coslat + b*b*sinlat*sinlat);
226 /* sr is effective radius */
227 theta = atan2(coslat * (h*sr + a*a),
228 sinlat * (h*sr + b*b));
229 /* theta is geocentric co-latitude */
231 r = h*h + 2.0*h * sr +
232 (a*a*a*a - ( a*a*a*a - b*b*b*b ) * sinlat*sinlat ) /
233 (a*a - (a*a - b*b) * sinlat*sinlat );
237 /* r is geocentric radial distance */
240 /* protect against zero divide at geographic poles */
241 inv_s = 1.0 / (s + (s == 0.)*1.0e-8);
243 /* zero out arrays */
244 for ( n = 0; n <= nmax; n++ ) {
245 for ( m = 0; m <= n; m++ ) {
251 /* diagonal elements */
259 // these values will not change for subsequent function calls
261 for ( n = 2; n <= nmax; n++ ) {
262 root[n] = sqrt((2.0*n-1) / (2.0*n));
265 for ( m = 0; m <= nmax; m++ ) {
267 for ( n = SG_MAX2(m + 1, 2); n <= nmax; n++ ) {
268 roots[m][n][0] = sqrt((n-1)*(n-1) - mm);
269 roots[m][n][1] = 1.0 / sqrt( n*n - mm);
275 for ( n=2; n <= nmax; n++ ) {
276 // double root = sqrt((2.0*n-1) / (2.0*n));
277 P[n][n] = P[n-1][n-1] * s * root[n];
278 DP[n][n] = (DP[n-1][n-1] * s + P[n-1][n-1] * c) *
283 for ( m = 0; m <= nmax; m++ ) {
285 for ( n = SG_MAX2(m + 1, 2); n <= nmax; n++ ) {
286 // double root1 = sqrt((n-1)*(n-1) - mm);
287 // double root2 = 1.0 / sqrt( n*n - mm);
288 P[n][m] = (P[n-1][m] * c * (2.0*n-1) -
289 P[n-2][m] * roots[m][n][0]) *
292 DP[n][m] = ((DP[n-1][m] * c - P[n-1][m] * s) *
293 (2.0*n-1) - DP[n-2][m] * roots[m][n][0]) *
298 /* compute Gauss coefficients gnm and hnm of degree n and order m for the desired time
299 achieved by adjusting the coefficients at time t0 for linear secular variation */
301 yearfrac = (dat - date0_wmm2015) / 365.25;
302 for ( n = 1; n <= nmax; n++ ) {
303 for ( m = 0; m <= nmax; m++ ) {
304 gnm[n][m] = gnm_wmm2015[n][m] + yearfrac * gtnm_wmm2015[n][m];
305 hnm[n][m] = hnm_wmm2015[n][m] + yearfrac * htnm_wmm2015[n][m];
309 /* compute sm (sin(m lon) and cm (cos(m lon)) */
310 for ( m = 0; m <= nmax; m++ ) {
311 sm[m] = sin(m * lon);
312 cm[m] = cos(m * lon);
315 /* compute B fields */
322 for ( n = 1; n <= nmax; n++ ) {
326 for ( m = 0; m <= n; m++ ) {
327 double tmp = (gnm[n][m] * cm[m] + hnm[n][m] * sm[m]);
328 c1_n=c1_n + tmp * P[n][m];
329 c2_n=c2_n + tmp * DP[n][m];
330 c3_n=c3_n + m * (gnm[n][m] * sm[m] - hnm[n][m] * cm[m]) * P[n][m];
332 // fn=pow(r_0/r,n+2.0);
334 B_r = B_r + (n + 1) * c1_n * fn;
335 B_theta = B_theta - c2_n * fn;
336 B_phi = B_phi + c3_n * fn * inv_s;
339 /* Find geodetic field components: */
340 psi = theta - ((M_PI / 2.0) - lat);
343 X = -B_theta * cospsi - B_r * sinpsi;
345 Z = B_theta * sinpsi - B_r * cospsi;
352 field[5]=Z; /* output fields */
354 /* find variation in radians */
355 /* return zero variation at magnetic pole X=Y=0. */
357 return (X != 0. || Y != 0.) ? atan2(Y, X) : (double) 0.;
361 #ifdef TEST_NHV_HACKS
362 double SGMagVarOrig( double lat, double lon, double h, long dat, double* field )
364 /* output field B_r,B_th,B_phi,B_x,B_y,B_z */
366 /* reference dates */
367 long date0_wmm2015 = yymmdd_to_julian_days(5,1,1);
369 double yearfrac,sr,r,theta,c,s,psi,fn,B_r,B_theta,B_phi,X,Y,Z;
371 /* convert to geocentric coords: */
372 sr = sqrt(pow(a*cos(lat),2.0)+pow(b*sin(lat),2.0));
373 /* sr is effective radius */
374 theta = atan2(cos(lat) * (h * sr + a * a),
375 sin(lat) * (h * sr + b * b));
376 /* theta is geocentric co-latitude */
378 r = h * h + 2.0*h * sr +
379 (pow(a,4.0) - (pow(a,4.0) - pow(b,4.0)) * pow(sin(lat),2.0)) /
380 (a * a - (a * a - b * b) * pow(sin(lat),2.0));
384 /* r is geocentric radial distance */
388 /* zero out arrays */
389 for ( n = 0; n <= nmax; n++ ) {
390 for ( m = 0; m <= n; m++ ) {
396 /* diagonal elements */
404 for ( n = 2; n <= nmax; n++ ) {
405 P[n][n] = P[n-1][n-1] * s * sqrt((2.0*n-1) / (2.0*n));
406 DP[n][n] = (DP[n-1][n-1] * s + P[n-1][n-1] * c) *
407 sqrt((2.0*n-1) / (2.0*n));
411 for ( m = 0; m <= nmax; m++ ) {
412 for ( n = SG_MAX2(m + 1, 2); n <= nmax; n++ ) {
413 P[n][m] = (P[n-1][m] * c * (2.0*n-1) - P[n-2][m] *
414 sqrt(1.0*(n-1)*(n-1) - m * m)) /
415 sqrt(1.0* n * n - m * m);
416 DP[n][m] = ((DP[n-1][m] * c - P[n-1][m] * s) *
417 (2.0*n-1) - DP[n-2][m] *
418 sqrt(1.0*(n-1) * (n-1) - m * m)) /
419 sqrt(1.0* n * n - m * m);
423 /* compute gnm, hnm at dat */
425 yearfrac = (dat - date0_wmm2015) / 365.25;
426 for ( n = 1; n <= nmax; n++ ) {
427 for ( m = 0; m <= nmax; m++ ) {
428 gnm[n][m] = gnm_wmm2015[n][m] + yearfrac * gtnm_wmm2015[n][m];
429 hnm[n][m] = hnm_wmm2015[n][m] + yearfrac * htnm_wmm2015[n][m];
433 /* compute sm (sin(m lon) and cm (cos(m lon)) */
434 for ( m = 0; m <= nmax; m++ ) {
435 sm[m] = sin(m * lon);
436 cm[m] = cos(m * lon);
439 /* compute B fields */
444 for ( n = 1; n <= nmax; n++ ) {
448 for ( m = 0; m <= n; m++ ) {
449 c1_n=c1_n + (gnm[n][m] * cm[m] + hnm[n][m] * sm[m]) * P[n][m];
450 c2_n=c2_n + (gnm[n][m] * cm[m] + hnm[n][m] * sm[m]) * DP[n][m];
451 c3_n=c3_n + m * (gnm[n][m] * sm[m] - hnm[n][m] * cm[m]) * P[n][m];
454 B_r = B_r + (n + 1) * c1_n * fn;
455 B_theta = B_theta - c2_n * fn;
456 B_phi = B_phi + c3_n * fn / s;
459 /* Find geodetic field components: */
460 psi = theta - (pi / 2.0 - lat);
461 X = -B_theta * cos(psi) - B_r * sin(psi);
463 Z = B_theta * sin(psi) - B_r * cos(psi);
470 field[5]=Z; /* output fields */
472 /* find variation, leave in radians! */
473 return atan2(Y, X); /* E is positive */
475 #endif // TEST_NHV_HACKS