362 lines
13 KiB
JavaScript
362 lines
13 KiB
JavaScript
/* 2012-03-26
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Copyright 2012 Christopher Weiss (cmweiss@gmail.com)
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Suggestions for improvements are appreciated.
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Adapted from the geomagc software and World Magnetic Model of the NOAA
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Satellite and Information Service, National Geophysical Data Center
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http://www.ngdc.noaa.gov/geomag/WMM/DoDWMM.shtml
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geoMagFactory() requires a world magnetic model (WMM) object. The helper
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function cof2Obj(), available in cof2Obj.js, takes the text of WMM.COF and
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returns an object suitable for geoMagFactory(). A syncronous XMLHttpRequest
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to fetch the WMM.COF is recommended in a web environment. The helper
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function syncXHR(), available in syncXHR.js, takes the url of the WMM.COF
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file and returns the WMM.COF file as text.
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Usage:
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geoMagFactory(wmm) returns a function which can compute the Earth's
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magnetic field.
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The returned function requires two arguments, latitude and longitude (in
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decimal degrees), and, optionally, altitude in feet (default is 0), and
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a date object (default is the current system time).
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let cof = syncXHR('http://host/path/WMM.COF'),
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wmm = cof2Obj(cof),
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geoMag = geoMagFactory(wmm),
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latitude = 40.0, // decimal degrees (north is positive)
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longitude = -80.0, // decimal degrees (east is positive)
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altitude = 0, // feet (optional, default is 0)
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time = new Date(2012, 4, 20), // (optional, default is the current
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// system time)
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myGeoMag = geoMag(latitude, longitude, altitude, time),
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magneticletiation = myGeoMag.dec, // Geomagnetic declination
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// (letiation) in decimal degrees
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// -- east is positive
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magneticDip = myGeoMag.dip, // Geomagnetic dip in decimal degrees
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// (down is positive)
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magneticFieldIntensity = myGeoMag.ti, // Total intensity of the
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// geomagnetic field in
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// nanoteslas
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magneticBH = myGeoMag.bh, // Horizontal intensity of the geomagnetic
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// field in nT
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magneticBX = myGeoMag.bx, // North component of the geomagnetic field
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// in nT
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magneticBY = myGeoMag.by, // East component of the geomagnetic field
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// in nT
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magneticBZ = myGeoMag.bz, // Vertical component of the geomagnetic
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// field (down is positive)
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lat = myGeoMag.lat, // input latitude
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lon = myGeoMag.lon; // input longitude
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*/
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/*jslint plusplus: true */
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function geoMagFactory(wmm) {
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'use strict';
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function rad2deg(rad) {
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return rad * (180 / Math.PI);
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}
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function deg2rad(deg) {
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return deg * (Math.PI / 180);
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}
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let i, model, epoch = wmm.epoch,
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z = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
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maxord = 12,
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tc = [z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(),
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z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(),
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z.slice()],
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sp = z.slice(),
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cp = z.slice(),
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pp = z.slice(),
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p = [z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(),
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z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(),
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z.slice()],
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dp = [z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(),
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z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(),
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z.slice()],
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a = 6378.137,
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b = 6356.7523142,
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re = 6371.2,
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a2 = a * a,
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b2 = b * b,
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c2 = a2 - b2,
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a4 = a2 * a2,
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b4 = b2 * b2,
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c4 = a4 - b4,
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c = [z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(),
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z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(),
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z.slice()],
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cd = [z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(),
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z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(),
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z.slice()],
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n, m,
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snorm = [z.slice(), z.slice(), z.slice(), z.slice(), z.slice(),
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z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(),
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z.slice(), z.slice()],
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j,
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k = [z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(),
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z.slice(), z.slice(), z.slice(), z.slice(), z.slice(), z.slice(),
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z.slice()],
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flnmj,
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fn = [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13],
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fm = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12],
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D2;
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tc[0][0] = 0;
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sp[0] = 0.0;
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cp[0] = 1.0;
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pp[0] = 1.0;
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p[0][0] = 1;
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model = wmm.wmm;
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for (i in model) {
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if (model.hasOwnProperty(i)) {
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if (model[i].m <= model[i].n) {
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c[model[i].m][model[i].n] = model[i].gnm;
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cd[model[i].m][model[i].n] = model[i].dgnm;
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if (model[i].m !== 0) {
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c[model[i].n][model[i].m - 1] = model[i].hnm;
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cd[model[i].n][model[i].m - 1] = model[i].dhnm;
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}
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}
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}
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}
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wmm = null;
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model = null;
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/* CONVERT SCHMIDT NORMALIZED GAUSS COEFFICIENTS TO UNNORMALIZED */
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snorm[0][0] = 1;
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for (n = 1; n <= maxord; n++) {
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snorm[0][n] = snorm[0][n - 1] * (2 * n - 1) / n;
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j = 2;
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for (m = 0, D2 = (n - m + 1); D2 > 0; D2--, m++) {
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k[m][n] = (((n - 1) * (n - 1)) - (m * m)) /
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((2 * n - 1) * (2 * n - 3));
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if (m > 0) {
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flnmj = ((n - m + 1) * j) / (n + m);
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snorm[m][n] = snorm[m - 1][n] * Math.sqrt(flnmj);
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j = 1;
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c[n][m - 1] = snorm[m][n] * c[n][m - 1];
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cd[n][m - 1] = snorm[m][n] * cd[n][m - 1];
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}
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c[m][n] = snorm[m][n] * c[m][n];
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cd[m][n] = snorm[m][n] * cd[m][n];
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}
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}
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k[1][1] = 0.0;
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return function (glat, glon, h, date) {
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function decimalDate(date) {
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date = date || new Date();
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let year = date.getUTCFullYear(),
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daysInYear = 365 +
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(((year % 400 === 0) || (year % 4 === 0 && (year % 100 > 0))) ? 1 : 0),
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msInYear = daysInYear * 24 * 60 * 60 * 1000;
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return date.getUTCFullYear() + (date.valueOf() - Date.UTC(year, 0)) / msInYear;
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}
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let alt = (h / 3280.8399) || 0, // convert h (in feet) to kilometers or set default of 0
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time = decimalDate(date),
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dt = time - epoch,
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rlat = deg2rad(glat),
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rlon = deg2rad(glon),
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srlon = Math.sin(rlon),
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srlat = Math.sin(rlat),
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crlon = Math.cos(rlon),
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crlat = Math.cos(rlat),
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srlat2 = srlat * srlat,
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crlat2 = crlat * crlat,
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q,
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q1,
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q2,
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ct,
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st,
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r2,
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r,
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d,
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ca,
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sa,
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aor,
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ar,
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br = 0.0,
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bt = 0.0,
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bp = 0.0,
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bpp = 0.0,
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par,
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temp1,
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temp2,
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parp,
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D4,
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bx,
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by,
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bz,
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bh,
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ti,
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dec,
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dip,
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gv;
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sp[1] = srlon;
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cp[1] = crlon;
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/* CONVERT FROM GEODETIC COORDS. TO SPHERICAL COORDS. */
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q = Math.sqrt(a2 - c2 * srlat2);
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q1 = alt * q;
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q2 = ((q1 + a2) / (q1 + b2)) * ((q1 + a2) / (q1 + b2));
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ct = srlat / Math.sqrt(q2 * crlat2 + srlat2);
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st = Math.sqrt(1.0 - (ct * ct));
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r2 = (alt * alt) + 2.0 * q1 + (a4 - c4 * srlat2) / (q * q);
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r = Math.sqrt(r2);
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d = Math.sqrt(a2 * crlat2 + b2 * srlat2);
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ca = (alt + d) / r;
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sa = c2 * crlat * srlat / (r * d);
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for (m = 2; m <= maxord; m++) {
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sp[m] = sp[1] * cp[m - 1] + cp[1] * sp[m - 1];
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cp[m] = cp[1] * cp[m - 1] - sp[1] * sp[m - 1];
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}
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aor = re / r;
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ar = aor * aor;
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for (n = 1; n <= maxord; n++) {
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ar = ar * aor;
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for (m = 0, D4 = (n + m + 1); D4 > 0; D4--, m++) {
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/*
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COMPUTE UNNORMALIZED ASSOCIATED LEGENDRE POLYNOMIALS
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AND DERIVATIVES VIA RECURSION RELATIONS
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*/
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if (n === m) {
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p[m][n] = st * p[m - 1][n - 1];
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dp[m][n] = st * dp[m - 1][n - 1] + ct *
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p[m - 1][n - 1];
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} else if (n === 1 && m === 0) {
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p[m][n] = ct * p[m][n - 1];
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dp[m][n] = ct * dp[m][n - 1] - st * p[m][n - 1];
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} else if (n > 1 && n !== m) {
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if (m > n - 2) { p[m][n - 2] = 0; }
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if (m > n - 2) { dp[m][n - 2] = 0.0; }
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p[m][n] = ct * p[m][n - 1] - k[m][n] * p[m][n - 2];
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dp[m][n] = ct * dp[m][n - 1] - st * p[m][n - 1] -
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k[m][n] * dp[m][n - 2];
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}
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/*
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TIME ADJUST THE GAUSS COEFFICIENTS
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*/
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tc[m][n] = c[m][n] + dt * cd[m][n];
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if (m !== 0) {
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tc[n][m - 1] = c[n][m - 1] + dt * cd[n][m - 1];
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}
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/*
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ACCUMULATE TERMS OF THE SPHERICAL HARMONIC EXPANSIONS
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*/
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par = ar * p[m][n];
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if (m === 0) {
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temp1 = tc[m][n] * cp[m];
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temp2 = tc[m][n] * sp[m];
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} else {
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temp1 = tc[m][n] * cp[m] + tc[n][m - 1] * sp[m];
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temp2 = tc[m][n] * sp[m] - tc[n][m - 1] * cp[m];
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}
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bt = bt - ar * temp1 * dp[m][n];
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bp += (fm[m] * temp2 * par);
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br += (fn[n] * temp1 * par);
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/*
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SPECIAL CASE: NORTH/SOUTH GEOGRAPHIC POLES
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*/
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if (st === 0.0 && m === 1) {
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if (n === 1) {
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pp[n] = pp[n - 1];
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} else {
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pp[n] = ct * pp[n - 1] - k[m][n] * pp[n - 2];
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}
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parp = ar * pp[n];
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bpp += (fm[m] * temp2 * parp);
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}
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}
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}
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bp = (st === 0.0 ? bpp : bp / st);
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/*
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ROTATE MAGNETIC VECTOR COMPONENTS FROM SPHERICAL TO
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GEODETIC COORDINATES
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*/
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bx = -bt * ca - br * sa;
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by = bp;
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bz = bt * sa - br * ca;
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/*
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COMPUTE DECLINATION (DEC), INCLINATION (DIP) AND
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TOTAL INTENSITY (TI)
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*/
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bh = Math.sqrt((bx * bx) + (by * by));
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ti = Math.sqrt((bh * bh) + (bz * bz));
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dec = rad2deg(Math.atan2(by, bx));
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dip = rad2deg(Math.atan2(bz, bh));
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/*
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COMPUTE MAGNETIC GRID letIATION IF THE CURRENT
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GEODETIC POSITION IS IN THE ARCTIC OR ANTARCTIC
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(I.E. GLAT > +55 DEGREES OR GLAT < -55 DEGREES)
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OTHERWISE, SET MAGNETIC GRID letIATION TO -999.0
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*/
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if (Math.abs(glat) >= 55.0) {
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if (glat > 0.0 && glon >= 0.0) {
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gv = dec - glon;
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} else if (glat > 0.0 && glon < 0.0) {
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gv = dec + Math.abs(glon);
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} else if (glat < 0.0 && glon >= 0.0) {
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gv = dec + glon;
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} else if (glat < 0.0 && glon < 0.0) {
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gv = dec - Math.abs(glon);
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}
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if (gv > 180.0) {
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gv -= 360.0;
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} else if (gv < -180.0) { gv += 360.0; }
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}
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return {dec: dec, dip: dip, ti: ti, bh: bh, bx: bx, by: by, bz: bz, lat: glat, lon: glon, gv: gv, epoch: epoch};
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};
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}
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/*
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cof2Obj.js
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Converts the WMM.COF text to a JSON object usable by geoMagFactory().
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*/
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function cof2Obj() {
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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"
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'use strict';
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let modelLines = cof.split('|'),
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wmm = [],
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i, vals, epoch, model, modelDate;
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for (i in modelLines) {
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if (modelLines.hasOwnProperty(i)) {
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vals = modelLines[i].replace(/^\s+|\s+$/g, "").split(/\s+/);
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if (vals.length === 3) {
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epoch = parseFloat(vals[0]);
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model = vals[1];
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modelDate = vals[2];
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} else if (vals.length === 6) {
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wmm.push({
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n: parseInt(vals[0], 10),
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m: parseInt(vals[1], 10),
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gnm: parseFloat(vals[2]),
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hnm: parseFloat(vals[3]),
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dgnm: parseFloat(vals[4]),
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dhnm: parseFloat(vals[5])
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});
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}
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}
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}
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return {epoch: epoch, model: model, modelDate: modelDate, wmm: wmm};
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}
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