/* 2012-03-26 Copyright 2012 Christopher Weiss (cmweiss@gmail.com) Suggestions for improvements are appreciated. Adapted from the geomagc software and World Magnetic Model of the NOAA Satellite and Information Service, National Geophysical Data Center http://www.ngdc.noaa.gov/geomag/WMM/DoDWMM.shtml geoMagFactory() requires a world magnetic model (WMM) object. The helper function cof2Obj(), available in cof2Obj.js, takes the text of WMM.COF and returns an object suitable for geoMagFactory(). A syncronous XMLHttpRequest to fetch the WMM.COF is recommended in a web environment. The helper function syncXHR(), available in syncXHR.js, takes the url of the WMM.COF file and returns the WMM.COF file as text. Usage: geoMagFactory(wmm) returns a function which can compute the Earth's magnetic field. The returned function requires two arguments, latitude and longitude (in decimal degrees), and, optionally, altitude in feet (default is 0), and a date object (default is the current system time). let cof = syncXHR('http://host/path/WMM.COF'), wmm = cof2Obj(cof), geoMag = geoMagFactory(wmm), latitude = 40.0, // decimal degrees (north is positive) longitude = -80.0, // decimal degrees (east is positive) altitude = 0, // feet (optional, default is 0) time = new Date(2012, 4, 20), // (optional, default is the current // system time) myGeoMag = geoMag(latitude, longitude, altitude, time), magneticletiation = myGeoMag.dec, // Geomagnetic declination // (letiation) in decimal degrees // -- east is positive magneticDip = myGeoMag.dip, // Geomagnetic dip in decimal degrees // (down is positive) magneticFieldIntensity = myGeoMag.ti, // Total intensity of the // geomagnetic field in // nanoteslas magneticBH = myGeoMag.bh, // Horizontal intensity of the geomagnetic // field in nT magneticBX = myGeoMag.bx, // North component of the geomagnetic field // in nT magneticBY = myGeoMag.by, // East component of the geomagnetic field // in nT magneticBZ = myGeoMag.bz, // Vertical component of the geomagnetic // field (down is positive) lat = myGeoMag.lat, // input latitude lon = myGeoMag.lon; // input longitude */ /*jslint plusplus: true */ function geoMagFactory(wmm) { 'use strict'; function rad2deg(rad) { return rad * (180 / Math.PI); } function deg2rad(deg) { return deg * (Math.PI / 180); } let i, model, epoch = wmm.epoch, z = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], maxord = 12, tc = [z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice()], sp = z.slice(), cp = z.slice(), pp = z.slice(), p = [z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice()], dp = [z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice()], a = 6378.137, b = 6356.7523142, re = 6371.2, a2 = a * a, b2 = b * b, c2 = a2 - b2, a4 = a2 * a2, b4 = b2 * b2, c4 = a4 - b4, c = [z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice()], cd = [z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice()], n, m, snorm = [z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice()], j, k = [z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice()], flnmj, fn = [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], fm = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], D2; tc[0][0] = 0; sp[0] = 0.0; cp[0] = 1.0; pp[0] = 1.0; p[0][0] = 1; model = wmm.wmm; for (i in model) { if (model.hasOwnProperty(i)) { if (model[i].m <= model[i].n) { c[model[i].m][model[i].n] = model[i].gnm; cd[model[i].m][model[i].n] = model[i].dgnm; if (model[i].m !== 0) { c[model[i].n][model[i].m - 1] = model[i].hnm; cd[model[i].n][model[i].m - 1] = model[i].dhnm; } } } } wmm = null; model = null; /* CONVERT SCHMIDT NORMALIZED GAUSS COEFFICIENTS TO UNNORMALIZED */ snorm[0][0] = 1; for (n = 1; n <= maxord; n++) { snorm[0][n] = snorm[0][n - 1] * (2 * n - 1) / n; j = 2; for (m = 0, D2 = (n - m + 1); D2 > 0; D2--, m++) { k[m][n] = (((n - 1) * (n - 1)) - (m * m)) / ((2 * n - 1) * (2 * n - 3)); if (m > 0) { flnmj = ((n - m + 1) * j) / (n + m); snorm[m][n] = snorm[m - 1][n] * Math.sqrt(flnmj); j = 1; c[n][m - 1] = snorm[m][n] * c[n][m - 1]; cd[n][m - 1] = snorm[m][n] * cd[n][m - 1]; } c[m][n] = snorm[m][n] * c[m][n]; cd[m][n] = snorm[m][n] * cd[m][n]; } } k[1][1] = 0.0; return function (glat, glon, h, date) { function decimalDate(date) { date = date || new Date(); let year = date.getUTCFullYear(), daysInYear = 365 + (((year % 400 === 0) || (year % 4 === 0 && (year % 100 > 0))) ? 1 : 0), msInYear = daysInYear * 24 * 60 * 60 * 1000; return date.getUTCFullYear() + (date.valueOf() - Date.UTC(year, 0)) / msInYear; } let alt = (h / 3280.8399) || 0, // convert h (in feet) to kilometers or set default of 0 time = decimalDate(date), dt = time - epoch, rlat = deg2rad(glat), rlon = deg2rad(glon), srlon = Math.sin(rlon), srlat = Math.sin(rlat), crlon = Math.cos(rlon), crlat = Math.cos(rlat), srlat2 = srlat * srlat, crlat2 = crlat * crlat, q, q1, q2, ct, st, r2, r, d, ca, sa, aor, ar, br = 0.0, bt = 0.0, bp = 0.0, bpp = 0.0, par, temp1, temp2, parp, D4, bx, by, bz, bh, ti, dec, dip, gv; sp[1] = srlon; cp[1] = crlon; /* CONVERT FROM GEODETIC COORDS. TO SPHERICAL COORDS. */ q = Math.sqrt(a2 - c2 * srlat2); q1 = alt * q; q2 = ((q1 + a2) / (q1 + b2)) * ((q1 + a2) / (q1 + b2)); ct = srlat / Math.sqrt(q2 * crlat2 + srlat2); st = Math.sqrt(1.0 - (ct * ct)); r2 = (alt * alt) + 2.0 * q1 + (a4 - c4 * srlat2) / (q * q); r = Math.sqrt(r2); d = Math.sqrt(a2 * crlat2 + b2 * srlat2); ca = (alt + d) / r; sa = c2 * crlat * srlat / (r * d); for (m = 2; m <= maxord; m++) { sp[m] = sp[1] * cp[m - 1] + cp[1] * sp[m - 1]; cp[m] = cp[1] * cp[m - 1] - sp[1] * sp[m - 1]; } aor = re / r; ar = aor * aor; for (n = 1; n <= maxord; n++) { ar = ar * aor; for (m = 0, D4 = (n + m + 1); D4 > 0; D4--, m++) { /* COMPUTE UNNORMALIZED ASSOCIATED LEGENDRE POLYNOMIALS AND DERIVATIVES VIA RECURSION RELATIONS */ if (n === m) { p[m][n] = st * p[m - 1][n - 1]; dp[m][n] = st * dp[m - 1][n - 1] + ct * p[m - 1][n - 1]; } else if (n === 1 && m === 0) { p[m][n] = ct * p[m][n - 1]; dp[m][n] = ct * dp[m][n - 1] - st * p[m][n - 1]; } else if (n > 1 && n !== m) { if (m > n - 2) { p[m][n - 2] = 0; } if (m > n - 2) { dp[m][n - 2] = 0.0; } p[m][n] = ct * p[m][n - 1] - k[m][n] * p[m][n - 2]; dp[m][n] = ct * dp[m][n - 1] - st * p[m][n - 1] - k[m][n] * dp[m][n - 2]; } /* TIME ADJUST THE GAUSS COEFFICIENTS */ tc[m][n] = c[m][n] + dt * cd[m][n]; if (m !== 0) { tc[n][m - 1] = c[n][m - 1] + dt * cd[n][m - 1]; } /* ACCUMULATE TERMS OF THE SPHERICAL HARMONIC EXPANSIONS */ par = ar * p[m][n]; if (m === 0) { temp1 = tc[m][n] * cp[m]; temp2 = tc[m][n] * sp[m]; } else { temp1 = tc[m][n] * cp[m] + tc[n][m - 1] * sp[m]; temp2 = tc[m][n] * sp[m] - tc[n][m - 1] * cp[m]; } bt = bt - ar * temp1 * dp[m][n]; bp += (fm[m] * temp2 * par); br += (fn[n] * temp1 * par); /* SPECIAL CASE: NORTH/SOUTH GEOGRAPHIC POLES */ if (st === 0.0 && m === 1) { if (n === 1) { pp[n] = pp[n - 1]; } else { pp[n] = ct * pp[n - 1] - k[m][n] * pp[n - 2]; } parp = ar * pp[n]; bpp += (fm[m] * temp2 * parp); } } } bp = (st === 0.0 ? bpp : bp / st); /* ROTATE MAGNETIC VECTOR COMPONENTS FROM SPHERICAL TO GEODETIC COORDINATES */ bx = -bt * ca - br * sa; by = bp; bz = bt * sa - br * ca; /* COMPUTE DECLINATION (DEC), INCLINATION (DIP) AND TOTAL INTENSITY (TI) */ bh = Math.sqrt((bx * bx) + (by * by)); ti = Math.sqrt((bh * bh) + (bz * bz)); dec = rad2deg(Math.atan2(by, bx)); dip = rad2deg(Math.atan2(bz, bh)); /* COMPUTE MAGNETIC GRID letIATION IF THE CURRENT GEODETIC POSITION IS IN THE ARCTIC OR ANTARCTIC (I.E. GLAT > +55 DEGREES OR GLAT < -55 DEGREES) OTHERWISE, SET MAGNETIC GRID letIATION TO -999.0 */ if (Math.abs(glat) >= 55.0) { if (glat > 0.0 && glon >= 0.0) { gv = dec - glon; } else if (glat > 0.0 && glon < 0.0) { gv = dec + Math.abs(glon); } else if (glat < 0.0 && glon >= 0.0) { gv = dec + glon; } else if (glat < 0.0 && glon < 0.0) { gv = dec - Math.abs(glon); } if (gv > 180.0) { gv -= 360.0; } else if (gv < -180.0) { gv += 360.0; } } return {dec: dec, dip: dip, ti: ti, bh: bh, bx: bx, by: by, bz: bz, lat: glat, lon: glon, gv: gv, epoch: epoch}; }; } /* cof2Obj.js Converts the WMM.COF text to a JSON object usable by geoMagFactory(). */ function cof2Obj() { let cof=" 2020.0 WMM-2020 12/10/2019|1 0 -29404.5 0.0 6.7 0.0|1 1 -1450.7 4652.9 7.7 -25.1|2 0 -2500.0 0.0 -11.5 0.0|2 1 2982.0 -2991.6 -7.1 -30.2|2 2 1676.8 -734.8 -2.2 -23.9|3 0 1363.9 0.0 2.8 0.0|3 1 -2381.0 -82.2 -6.2 5.7|3 2 1236.2 241.8 3.4 -1.0|3 3 525.7 -542.9 -12.2 1.1|4 0 903.1 0.0 -1.1 0.0|4 1 809.4 282.0 -1.6 0.2|4 2 86.2 -158.4 -6.0 6.9|4 3 -309.4 199.8 5.4 3.7|4 4 47.9 -350.1 -5.5 -5.6|5 0 -234.4 0.0 -0.3 0.0|5 1 363.1 47.7 0.6 0.1|5 2 187.8 208.4 -0.7 2.5|5 3 -140.7 -121.3 0.1 -0.9|5 4 -151.2 32.2 1.2 3.0|5 5 13.7 99.1 1.0 0.5|6 0 65.9 0.0 -0.6 0.0|6 1 65.6 -19.1 -0.4 0.1|6 2 73.0 25.0 0.5 -1.8|6 3 -121.5 52.7 1.4 -1.4|6 4 -36.2 -64.4 -1.4 0.9|6 5 13.5 9.0 -0.0 0.1|6 6 -64.7 68.1 0.8 1.0|7 0 80.6 0.0 -0.1 0.0|7 1 -76.8 -51.4 -0.3 0.5|7 2 -8.3 -16.8 -0.1 0.6|7 3 56.5 2.3 0.7 -0.7|7 4 15.8 23.5 0.2 -0.2|7 5 6.4 -2.2 -0.5 -1.2|7 6 -7.2 -27.2 -0.8 0.2|7 7 9.8 -1.9 1.0 0.3|8 0 23.6 0.0 -0.1 0.0|8 1 9.8 8.4 0.1 -0.3|8 2 -17.5 -15.3 -0.1 0.7|8 3 -0.4 12.8 0.5 -0.2|8 4 -21.1 -11.8 -0.1 0.5|8 5 15.3 14.9 0.4 -0.3|8 6 13.7 3.6 0.5 -0.5|8 7 -16.5 -6.9 0.0 0.4|8 8 -0.3 2.8 0.4 0.1|9 0 5.0 0.0 -0.1 0.0|9 1 8.2 -23.3 -0.2 -0.3|9 2 2.9 11.1 -0.0 0.2|9 3 -1.4 9.8 0.4 -0.4|9 4 -1.1 -5.1 -0.3 0.4|9 5 -13.3 -6.2 -0.0 0.1|9 6 1.1 7.8 0.3 -0.0|9 7 8.9 0.4 -0.0 -0.2|9 8 -9.3 -1.5 -0.0 0.5|9 9 -11.9 9.7 -0.4 0.2|10 0 -1.9 0.0 0.0 0.0|10 1 -6.2 3.4 -0.0 -0.0|10 2 -0.1 -0.2 -0.0 0.1|10 3 1.7 3.5 0.2 -0.3|10 4 -0.9 4.8 -0.1 0.1|10 5 0.6 -8.6 -0.2 -0.2|10 6 -0.9 -0.1 -0.0 0.1|10 7 1.9 -4.2 -0.1 -0.0|10 8 1.4 -3.4 -0.2 -0.1|10 9 -2.4 -0.1 -0.1 0.2|10 10 -3.9 -8.8 -0.0 -0.0|11 0 3.0 0.0 -0.0 0.0|11 1 -1.4 -0.0 -0.1 -0.0|11 2 -2.5 2.6 -0.0 0.1|11 3 2.4 -0.5 0.0 0.0|11 4 -0.9 -0.4 -0.0 0.2|11 5 0.3 0.6 -0.1 -0.0|11 6 -0.7 -0.2 0.0 0.0|11 7 -0.1 -1.7 -0.0 0.1|11 8 1.4 -1.6 -0.1 -0.0|11 9 -0.6 -3.0 -0.1 -0.1|11 10 0.2 -2.0 -0.1 0.0|11 11 3.1 -2.6 -0.1 -0.0|12 0 -2.0 0.0 0.0 0.0|12 1 -0.1 -1.2 -0.0 -0.0|12 2 0.5 0.5 -0.0 0.0|12 3 1.3 1.3 0.0 -0.1|12 4 -1.2 -1.8 -0.0 0.1|12 5 0.7 0.1 -0.0 -0.0|12 6 0.3 0.7 0.0 0.0|12 7 0.5 -0.1 -0.0 -0.0|12 8 -0.2 0.6 0.0 0.1|12 9 -0.5 0.2 -0.0 -0.0|12 10 0.1 -0.9 -0.0 -0.0|12 11 -1.1 -0.0 -0.0 0.0|12 12 -0.3 0.5 -0.1 -0.1" 'use strict'; let modelLines = cof.split('|'), wmm = [], i, vals, epoch, model, modelDate; for (i in modelLines) { if (modelLines.hasOwnProperty(i)) { vals = modelLines[i].replace(/^\s+|\s+$/g, "").split(/\s+/); if (vals.length === 3) { epoch = parseFloat(vals[0]); model = vals[1]; modelDate = vals[2]; } else if (vals.length === 6) { wmm.push({ n: parseInt(vals[0], 10), m: parseInt(vals[1], 10), gnm: parseFloat(vals[2]), hnm: parseFloat(vals[3]), dgnm: parseFloat(vals[4]), dhnm: parseFloat(vals[5]) }); } } } return {epoch: epoch, model: model, modelDate: modelDate, wmm: wmm}; }