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WorldMagneticModel.js
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WorldMagneticModel.js
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/* DOD World Magnetic Model 2010-2015
See bottom of file for info from original Fortran source code
Reminder - this is just a model! See the USGS and BGS sites for predicted accuracy.
Usage is
var wmm = new WorldMagneticModel();
then
var dec = wmm.declination(0.0, 59.0, -2.0, 2008.5);
parameters are
altitude in kilometres
decimal degree latitude, -ve for south
decimal degree longitude, -ve for west
date as year + fraction of year
return is declination angle in decimal degrees,
+ve for Magnetic North East of True North
(-999 for < 2010.0 and >= 2015.0)
The method knownAnswerTest yields a maximum declination error of 0.12% on the USGS test data set.
This is assumed to be down to the use of double rather than single precision floating point arithmetic.
The maximum error is at 0 latitude, 120W longitude. The value produced by this code at this point is 9.191 degrees.
This is the same answer as produced by the BGS calculator at http://www.geomag.bgs.ac.uk/gifs/wmm_calc.html
*/
function WorldMagneticModel (){
/* 2010 - 2015 coefficients from WMM.COF */
this.coff = [
" 1, 0, -29556.8, 0.0, 8.0, 0.0",
" 1, 1, -1671.7, 5079.8, 10.6, -20.9",
" 2, 0, -2340.6, 0.0, -15.1, 0.0",
" 2, 1, 3046.9, -2594.7, -7.8, -23.2",
" 2, 2, 1657.0, -516.7, -0.8, -14.6",
" 3, 0, 1335.4, 0.0, 0.4, 0.0",
" 3, 1, -2305.1, -199.9, -2.6, 5.0",
" 3, 2, 1246.7, 269.3, -1.2, -7.0",
" 3, 3, 674.0, -524.2, -6.5, -0.6",
" 4, 0, 919.8, 0.0, -2.5, 0.0",
" 4, 1, 798.1, 281.5, 2.8, 2.2",
" 4, 2, 211.3, -226.0, -7.0, 1.6",
" 4, 3, -379.4, 145.8, 6.2, 5.8",
" 4, 4, 100.0, -304.7, -3.8, 0.1",
" 5, 0, -227.4, 0.0, -2.8, 0.0",
" 5, 1, 354.6, 42.4, 0.7, 0.0",
" 5, 2, 208.7, 179.8, -3.2, 1.7",
" 5, 3, -136.5, -123.0, -1.1, 2.1",
" 5, 4, -168.3, -19.5, 0.1, 4.8",
" 5, 5, -14.1, 103.6, -0.8, -1.1",
" 6, 0, 73.2, 0.0, -0.7, 0.0",
" 6, 1, 69.7, -20.3, 0.4, -0.6",
" 6, 2, 76.7, 54.7, -0.3, -1.9",
" 6, 3, -151.2, 63.6, 2.3, -0.4",
" 6, 4, -14.9, -63.4, -2.1, -0.5",
" 6, 5, 14.6, -0.1, -0.6, -0.3",
" 6, 6, -86.3, 50.4, 1.4, 0.7",
" 7, 0, 80.1, 0.0, 0.2, 0.0",
" 7, 1, -74.5, -61.5, -0.1, 0.6",
" 7, 2, -1.4, -22.4, -0.3, 0.4",
" 7, 3, 38.5, 7.2, 1.1, 0.2",
" 7, 4, 12.4, 25.4, 0.6, 0.3",
" 7, 5, 9.5, 11.0, 0.5, -0.8",
" 7, 6, 5.7, -26.4, -0.4, -0.2",
" 7, 7, 1.8, -5.1, 0.6, 0.1",
" 8, 0, 24.9, 0.0, 0.1, 0.0",
" 8, 1, 7.7, 11.2, 0.3, -0.2",
" 8, 2, -11.6, -21.0, -0.4, 0.1",
" 8, 3, -6.9, 9.6, 0.3, 0.3",
" 8, 4, -18.2, -19.8, -0.3, 0.4",
" 8, 5, 10.0, 16.1, 0.2, 0.1",
" 8, 6, 9.2, 7.7, 0.4, -0.2",
" 8, 7, -11.6, -12.9, -0.7, 0.4",
" 8, 8, -5.2, -0.2, 0.4, 0.4",
" 9, 0, 5.6, 0.0, 0.0, 0.0",
" 9, 1, 9.9, -20.1, 0.0, 0.0",
" 9, 2, 3.5, 12.9, 0.0, 0.0",
" 9, 3, -7.0, 12.6, 0.0, 0.0",
" 9, 4, 5.1, -6.7, 0.0, 0.0",
" 9, 5, -10.8, -8.1, 0.0, 0.0",
" 9, 6, -1.3, 8.0, 0.0, 0.0",
" 9, 7, 8.8, 2.9, 0.0, 0.0",
" 9, 8, -6.7, -7.9, 0.0, 0.0",
" 9, 9, -9.1, 6.0, 0.0, 0.0",
" 10, 0, -2.3, 0.0, 0.0, 0.0",
" 10, 1, -6.3, 2.4, 0.0, 0.0",
" 10, 2, 1.6, 0.2, 0.0, 0.0",
" 10, 3, -2.6, 4.4, 0.0, 0.0",
" 10, 4, 0.0, 4.8, 0.0, 0.0",
" 10, 5, 3.1, -6.5, 0.0, 0.0",
" 10, 6, 0.4, -1.1, 0.0, 0.0",
" 10, 7, 2.1, -3.4, 0.0, 0.0",
" 10, 8, 3.9, -0.8, 0.0, 0.0",
" 10, 9, -0.1, -2.3, 0.0, 0.0",
" 10, 10, -2.3, -7.9, 0.0, 0.0",
" 11, 0, 2.8, 0.0, 0.0, 0.0",
" 11, 1, -1.6, 0.3, 0.0, 0.0",
" 11, 2, -1.7, 1.2, 0.0, 0.0",
" 11, 3, 1.7, -0.8, 0.0, 0.0",
" 11, 4, -0.1, -2.5, 0.0, 0.0",
" 11, 5, 0.1, 0.9, 0.0, 0.0",
" 11, 6, -0.7, -0.6, 0.0, 0.0",
" 11, 7, 0.7, -2.7, 0.0, 0.0",
" 11, 8, 1.8, -0.9, 0.0, 0.0",
" 11, 9, 0.0, -1.3, 0.0, 0.0",
" 11, 10, 1.1, -2.0, 0.0, 0.0",
" 11, 11, 4.1, -1.2, 0.0, 0.0",
" 12, 0, -2.4, 0.0, 0.0, 0.0",
" 12, 1, -0.4, -0.4, 0.0, 0.0",
" 12, 2, 0.2, 0.3, 0.0, 0.0",
" 12, 3, 0.8, 2.4, 0.0, 0.0",
" 12, 4, -0.3, -2.6, 0.0, 0.0",
" 12, 5, 1.1, 0.6, 0.0, 0.0",
" 12, 6, -0.5, 0.3, 0.0, 0.0",
" 12, 7, 0.4, 0.0, 0.0, 0.0",
" 12, 8, -0.3, 0.0, 0.0, 0.0",
" 12, 9, -0.3, 0.3, 0.0, 0.0",
" 12, 10, -0.1, -0.9, 0.0, 0.0",
" 12, 11, -0.3, -0.4, 0.0, 0.0",
" 12, 12, -0.1, 0.8, 0.0, 0.0"
];
/* static variables */
/* some 13x13 2D arrays */
this.c = new Array(13);
this.cd = new Array(13);
this.tc = new Array(13);
this.dp = new Array(13);
this.k = new Array(13);
for(var i=0; i< 13; i++)
{
this.c[i] = new Array(13);
this.cd[i] = new Array(13);
this.tc[i] = new Array(13);
this.dp[i] = new Array(13);
this.k[i] = new Array(13);
}
/* some 1D arrays */
this.snorm = new Array(169);
this.sp = new Array(13);
this.cp = new Array(13);
this.fn = new Array(13);
this.fm = new Array(13);
this.pp = new Array(13);
/* locals */
var maxdeg = 12;
var maxord;
var i,j,D1,D2,n,m;
var a,b,a2,b2,c2,a4,b4,c4,re;
var gnm,hnm,dgnm,dhnm,flnmj;
var c_str;
var c_flds;
/* INITIALIZE CONSTANTS */
maxord = maxdeg;
this.sp[0] = 0.0;
this.cp[0] = this.snorm[0] = this.pp[0] = 1.0;
this.dp[0][0] = 0.0;
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;
/* READ WORLD MAGNETIC MODEL SPHERICAL HARMONIC COEFFICIENTS */
this.c[0][0] = 0.0;
this.cd[0][0] = 0.0;
for(i=0; i<this.coff.length; i++)
{
c_str = this.coff[i];
c_flds = c_str.split(",");
n = parseInt(c_flds[0]);
m = parseInt(c_flds[1]);
gnm = parseFloat(c_flds[2]);
hnm = parseFloat(c_flds[3]);
dgnm = parseFloat(c_flds[4]);
dhnm = parseFloat(c_flds[5]);
if (m <= n)
{
this.c[m][n] = gnm;
this.cd[m][n] = dgnm;
if (m != 0)
{
this.c[n][m-1] = hnm;
this.cd[n][m-1] = dhnm;
}
}
}
/* CONVERT SCHMIDT NORMALIZED GAUSS COEFFICIENTS TO UNNORMALIZED */
this.snorm[0] = 1.0;
for (n=1; n<=maxord; n++)
{
this.snorm[n] = this.snorm[n-1]*(2*n-1)/n;
j = 2;
for (m=0,D1=1,D2=(n-m+D1)/D1; D2>0; D2--,m+=D1)
{
this.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);
this.snorm[n+m*13] = this.snorm[n+(m-1)*13]*Math.sqrt(flnmj);
j = 1;
this.c[n][m-1] = this.snorm[n+m*13]*this.c[n][m-1];
this.cd[n][m-1] = this.snorm[n+m*13]*this.cd[n][m-1];
}
this.c[m][n] = this.snorm[n+m*13]*this.c[m][n];
this.cd[m][n] = this.snorm[n+m*13]*this.cd[m][n];
}
this.fn[n] = (n+1);
this.fm[n] = n;
}
this.k[1][1] = 0.0;
this.fm[0] = 0.0; // !!! WMM C and Fortran both have a bug in that fm[0] is not initialised
}
WorldMagneticModel.prototype.declination = function(altitudeKm, latitudeDegrees, longitudeDegrees, yearFloat){
/* locals */
var a = 6378.137;
var b = 6356.7523142;
var re = 6371.2;
var a2 = a*a;
var b2 = b*b;
var c2 = a2-b2;
var a4 = a2*a2;
var b4 = b2*b2;
var c4 = a4 - b4;
var D3, D4;
var dip, ti, gv, dec;
var n,m;
var pi, dt, rlon, rlat, srlon, srlat, crlon, crlat,srlat2,
crlat2, q, q1, q2, ct, d,aor,ar, br, r2, bpp, par,
temp1,parp,temp2,bx,by,bz,bh,dtr,bp,bt, st,ca,sa;
var maxord = 12;
var alt = altitudeKm;
var glon = longitudeDegrees;
var glat = latitudeDegrees;
/*************************************************************************/
dt = yearFloat - 2005.0;
// if more then 6 years has passed since last epoch update then return invalid
if ((dt < 5.0) || (dt > 10.0))
return -999;
pi = 3.14159265359;
dtr = pi/180.0;
rlon = glon*dtr;
rlat = glat*dtr;
srlon = Math.sin(rlon);
srlat = Math.sin(rlat);
crlon = Math.cos(rlon);
crlat = Math.cos(rlat);
srlat2 = srlat*srlat;
crlat2 = crlat*crlat;
this.sp[1] = srlon;
this.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++)
{
this.sp[m] = this.sp[1]*this.cp[m-1]+this.cp[1]*this.sp[m-1];
this.cp[m] = this.cp[1]*this.cp[m-1]-this.sp[1]*this.sp[m-1];
}
aor = re/r;
ar = aor*aor;
br = bt = bp = bpp = 0.0;
for (n=1; n<=maxord; n++)
{
ar = ar*aor;
for (m=0,D3=1,D4=(n+m+D3)/D3; D4>0; D4--,m+=D3)
{
/*
COMPUTE UNNORMALIZED ASSOCIATED LEGENDRE POLYNOMIALS
AND DERIVATIVES VIA RECURSION RELATIONS
*/
if (n == m)
{
this.snorm[n+m*13] = st*this.snorm[n-1+(m-1)*13];
this.dp[m][n] = st*this.dp[m-1][n-1]+ct*this.snorm[n-1+(m-1)*13];
}
else if (n == 1 && m == 0)
{
this.snorm[n+m*13] = ct*this.snorm[n-1+m*13];
this.dp[m][n] = ct*this.dp[m][n-1]-st*this.snorm[n-1+m*13];
}
else if (n > 1 && n != m)
{
if (m > n-2) this.snorm[n-2+m*13] = 0.0;
if (m > n-2) this.dp[m][n-2] = 0.0;
this.snorm[n+m*13] = ct*this.snorm[n-1+m*13]-this.k[m][n]*this.snorm[n-2+m*13];
this.dp[m][n] = ct*this.dp[m][n-1] - st*this.snorm[n-1+m*13]-this.k[m][n]*this.dp[m][n-2];
}
/*
TIME ADJUST THE GAUSS COEFFICIENTS
*/
this.tc[m][n] = this.c[m][n]+dt*this.cd[m][n];
if (m != 0) this.tc[n][m-1] = this.c[n][m-1]+dt*this.cd[n][m-1];
/*
ACCUMULATE TERMS OF THE SPHERICAL HARMONIC EXPANSIONS
*/
par = ar*this.snorm[n+m*13];
if (m == 0)
{
temp1 = this.tc[m][n]*this.cp[m];
temp2 = this.tc[m][n]*this.sp[m];
}
else
{
temp1 = this.tc[m][n]*this.cp[m]+this.tc[n][m-1]*this.sp[m];
temp2 = this.tc[m][n]*this.sp[m]-this.tc[n][m-1]*this.cp[m];
}
bt = bt-ar*temp1*this.dp[m][n];
bp += (this.fm[m]*temp2*par);
br += (this.fn[n]*temp1*par);
/*
SPECIAL CASE: NORTH/SOUTH GEOGRAPHIC POLES
*/
if (st == 0.0 && m == 1)
{
if (n == 1) this.pp[n] = this.pp[n-1];
else this.pp[n] = this.ct*this.pp[n-1]-this.k[m][n]*this.pp[n-2];
parp = ar*this.pp[n];
bpp += (this.fm[m]*temp2*parp);
}
}
}
if (st == 0.0)
bp = bpp;
else
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 = Math.atan2(by,bx)/dtr;
dip = Math.atan2(bz,bh)/dtr;
/*
COMPUTE MAGNETIC GRID VARIATION IF THE CURRENT
GEODETIC POSITION IS IN THE ARCTIC OR ANTARCTIC
(I.E. GLAT > +55 DEGREES OR GLAT < -55 DEGREES)
OTHERWISE, SET MAGNETIC GRID VARIATION TO -999.0
*/
gv = -999.0;
if (Math.abs(glat) >= 55.0)
{
if (glat > 0.0 && glon >= 0.0) gv = dec-glon;
if (glat > 0.0 && glon < 0.0) gv = dec+Math.abs(glon);
if (glat < 0.0 && glon >= 0.0) gv = dec+glon;
if (glat < 0.0 && glon < 0.0) gv = dec-Math.abs(glon);
if (gv > +180.0) gv -= 360.0;
if (gv < -180.0) gv += 360.0;
}
return dec;
}
WorldMagneticModel.prototype.knownAnswerTest = function(){
/* http://www.ngdc.noaa.gov/geomag/WMM/data/2006TestValues_WMM2005.pdf */
/* Lat Lon Dec */
/* Lon 240 = 120W, Lon 300 = 60W */
var kat = [
"80.00 ,0.00 ,-7.55 ",
"80.00 ,60.00 ,35.53 ",
"80.00 ,120.00 ,0.85 ",
"80.00 ,180.00 ,9.32 ",
"80.00 ,240.00 ,36.35 ",
"80.00 ,300.00 ,-55.92 ",
"40.00 ,0.00 ,-1.13 ",
"40.00 ,60.00 ,4.98 ",
"40.00 ,120.00 ,-7.27 ",
"40.00 ,180.00 ,5.85 ",
"40.00 ,240.00 ,14.93 ",
"40.00 ,300.00 ,-17.98 ",
"0.00 ,0.00 ,-6.60 ",
"0.00 ,60.00 ,-4.20 ",
"0.00 ,120.00 ,1.12 ",
"0.00 ,180.00 ,9.63 ",
"0.00 ,240.00 ,9.18 ",
"0.00 ,300.00 ,-14.48 ",
"-40.00 ,0.00 ,-23.47 ",
"-40.00 ,60.00 ,-45.20 ",
"-40.00 ,120.00 ,-3.42 ",
"-40.00 ,180.00 ,21.73 ",
"-40.00 ,240.00 ,22.43 ",
"-40.00 ,300.00 ,-2.45 ",
"-80.00 ,0.00 ,-21.65 ",
"-80.00 ,60.00 ,-74.13 ",
"-80.00 ,120.00 ,-140.50 ",
"-80.00 ,180.00 ,131.73 ",
"-80.00 ,240.00 ,70.50 ",
"-80.00 ,300.00 ,23.95 "
];
var maxErr = 0.0;
for(var i=0; i<kat.length; i++){
var c_str = kat[i];
var c_flds = c_str.split(",");
var lat = parseFloat(c_flds[0]);
var lon = parseFloat(c_flds[1]);
var exp = parseFloat(c_flds[2]);
var maxExp;
var dec = this.declination(0,lat,lon,2006.0);
if(Math.abs(dec-exp) > maxErr){
maxErr = Math.abs(dec-exp);
maxExp = exp;
}
}
return maxErr * 100 / maxExp;//max % error
}