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Geomagnetism.swift
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Geomagnetism.swift
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/* License Statement from the NOAA
The WMM source code is in the public domain and not licensed or
under copyright. The information and software may be used freely
by the public. As required by 17 U.S.C. 403, third parties producing
copyrighted works consisting predominantly of the material produced
by U.S. government agencies must provide notice with such work(s)
identifying the U.S. Government material incorporated and stating
that such material is not subject to copyright protection.*/
import Foundation
// Add vars to convert to degrees/radians
extension FloatingPoint {
/** Convert to degrees from radians*/
var toDegrees:Self { return self * 180 / .pi }
/** Convert to radians from degrees*/
var toRadians:Self { return self * .pi / 180 }
}
/** Class to calculate magnetic declination, magnetic field strength,
inclination etc. for any point on the earth.
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
© Deep Pradhan, 2017*/
class Geomagnetism {
/** Initializes the instance without calculations*/
init() {
// Initialize constants
maxord = Geomagnetism.MAX_DEG
sp[0] = 0
cp[0] = 1
snorm[0] = 1
pp[0] = 1
dp[0][0] = 0
c[0][0] = 0
cd[0][0] = 0
epoch = Double(Geomagnetism.WMM_COF[0].trimmingCharacters(in: .whitespaces).split(separator: " ")[0])!
var tokens:[String.SubSequence], n:Int, m:Int, gnm:Double, hnm:Double, dgnm:Double, dhnm:Double
for i in (1...Geomagnetism.WMM_COF.count - 1) {
tokens = Geomagnetism.WMM_COF[i].trimmingCharacters(in: .whitespaces).split(separator: " ")
n = Int(tokens[0])!
m = Int(tokens[1])!
gnm = Double(tokens[2])!
hnm = Double(tokens[3])!
dgnm = Double(tokens[4])!
dhnm = Double(tokens[5])!
if m <= n {
c[m][n] = gnm
cd[m][n] = dgnm
if m != 0 {
c[n][m - 1] = hnm
cd[n][m - 1] = dhnm
}
}
}
// Convert schmidt normalized gauss coefficients to unnormalized
snorm[0] = 1
var flnmj:Double, j:Int
for n in (1...maxord) {
snorm[n] = snorm[n - 1] * Double(2 * n - 1) / Double(n)
j = 2
var m:Int = 0, d1:Int = 1, d2:Int = (n - m + d1) / d1
while d2 > 0 {
k[m][n] = Double(((n - 1) * (n - 1)) - (m * m)) / Double((2 * n - 1) * (2 * n - 3))
if m > 0 {
flnmj = Double((n - m + 1) * j) / Double(n + m)
snorm[n + m * 13] = snorm[n + (m - 1) * 13] * sqrt(flnmj)
j = 1
c[n][m - 1] = snorm[n + m * 13] * c[n][m - 1]
cd[n][m - 1] = snorm[n + m * 13] * cd[n][m - 1]
}
c[m][n] = snorm[n + m * 13] * c[m][n]
cd[m][n] = snorm[n + m * 13] * cd[m][n]
d2 -= 1
m += d1
}
fn[n] = Double(n + 1)
fm[n] = Double(n)
}
k[1][1] = 0
fm[0] = 0
otime = -1000
oalt = -1000
olat = -1000
olon = -1000
}
/** Initialise the instance and calculate for given location and date
- parameters:
- longitude: Longitude in decimal degrees
- latitude: Latitude in decimal degrees
- altitude: Altitude in metres (with respect to WGS-1984 ellipsoid)
- date: Date of the calculation*/
convenience init(longitude:Double, latitude:Double, altitude:Double? = 0, date:Date? = Date.init()) {
self.init()
calculate(longitude: longitude, latitude: latitude, altitude: altitude!, date: date!)
}
/** Calculate for given location and date
- parameters:
- longitude: Longitude in decimal degrees
- latitude: Latitude in decimal degrees
- altitude: Altitude in metres (with respect to WGS-1984 ellipsoid)
- date: Date of the calculation*/
func calculate(longitude:Double, latitude:Double, altitude:Double? = 0, date:Date? = Date.init()) {
let rlon:Double = longitude.toRadians,
rlat:Double = latitude.toRadians,
altitudeKm:Double = altitude!.isNaN ? 0 : altitude! / 1000,
calendar:Calendar = Calendar.init(identifier: .gregorian),
year:Int = calendar.component(.year, from: date!),
yearLength:Int = calendar.range(of: .day, in: .year, for: date!)!.count,
yearFraction:Double = Double(year)
+ Double(calendar.ordinality(of: .day, in: .year, for: date!)!)
/* If .range(of: in: for:) returns an invalid value (observed on iOS < 11)
use a leap year test based value for year length*/
/ Double(yearLength >= 365 ? yearLength : (year % 4 == 0 && (year % 25 != 0 || (year % 400 == 0 && year % 4000 != 0)) ? 366 : 365)),
dt:Double = yearFraction - epoch,
srlon:Double = sin(rlon),
srlat:Double = sin(rlat),
crlon:Double = cos(rlon),
crlat:Double = cos(rlat),
srlat2:Double = srlat * srlat,
crlat2:Double = crlat * crlat,
a2:Double = Geomagnetism.WGS84_A * Geomagnetism.WGS84_A,
b2:Double = Geomagnetism.WGS84_B * Geomagnetism.WGS84_B,
c2:Double = a2 - b2,
a4:Double = a2 * a2,
b4:Double = b2 * b2,
c4:Double = a4 - b4
sp[1] = srlon
cp[1] = crlon
// Convert from geodetic coords. to spherical coords.
if altitudeKm != oalt || latitude != olat {
let q:Double = sqrt(a2 - c2 * srlat2),
q1:Double = altitudeKm * q,
q2:Double = ((q1 + a2) / (q1 + b2)) * ((q1 + a2) / (q1 + b2)),
r2:Double = ((altitudeKm * altitudeKm) + 2 * q1 + (a4 - c4 * srlat2) / (q * q))
ct = srlat / sqrt(q2 * crlat2 + srlat2)
st = sqrt(1 - (ct * ct))
r = sqrt(r2)
d = sqrt(a2 * crlat2 + b2 * srlat2)
ca = (altitudeKm + d) / r
sa = c2 * crlat * srlat / (r * d)
}
if longitude != olon {
for m in (2...maxord) {
sp[m] = sp[1] * cp[m - 1] + cp[1] * sp[m - 1]
cp[m] = cp[1] * cp[m - 1] - sp[1] * sp[m - 1]
}
}
let aor:Double = Geomagnetism.IAU66_RADIUS / r
var ar:Double = aor * aor,
br:Double = 0, bt:Double = 0, bp:Double = 0, bpp:Double = 0,
par:Double, parp:Double, temp1:Double, temp2:Double
for n in (1...maxord) {
ar = ar * aor
var m:Int = 0, d3:Int = 1, d4:Int = (n + m + d3) / d3
while d4 > 0 {
// Compute unnormalized associated legendre polynomials and derivatives via recursion relations
if altitudeKm != oalt || latitude != olat {
if n == m {
snorm[n + m * 13] = st * snorm[n - 1 + (m - 1) * 13]
dp[m][n] = st * dp[m - 1][n - 1] + ct * snorm[n - 1 + (m - 1) * 13]
}
if n == 1 && m == 0 {
snorm[n + m * 13] = ct * snorm[n - 1 + m * 13]
dp[m][n] = ct * dp[m][n - 1] - st * snorm[n - 1 + m * 13]
}
if n > 1 && n != m {
if m > n - 2 {
snorm[n - 2 + m * 13] = 0
}
if m > n - 2 {
dp[m][n - 2] = 0
}
snorm[n + m * 13] = ct * snorm[n - 1 + m * 13] - k[m][n] * snorm[n - 2 + m * 13]
dp[m][n] = ct * dp[m][n - 1] - st * snorm[n - 1 + m * 13] - k[m][n] * dp[m][n - 2]
}
}
// Time adjust the gauss coefficients
if yearFraction != otime {
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 * snorm[ n + m * 13]
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 && 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)
}
d4 -= 1
m += d3
}
}
if st == 0 {
bp = bpp
} else {
bp /= st
}
// Rotate magnetic vector components from spherical to geodetic coordinates
// northIntensity must be the east-west field component
// eastIntensity must be the north-south field component
// verticalIntensity must be the vertical field component.
northIntensity = -bt * ca - br * sa
eastIntensity = bp
verticalIntensity = bt * sa - br * ca
// Compute declination (dec), inclination (dip) and total intensity (ti)
horizontalIntensity = sqrt((northIntensity * northIntensity) + (eastIntensity * eastIntensity))
intensity = sqrt((horizontalIntensity * horizontalIntensity) + (verticalIntensity * verticalIntensity))
// Calculate the declination.
declination = atan2(eastIntensity, northIntensity).toDegrees
inclination = atan2(verticalIntensity, horizontalIntensity).toDegrees
otime = yearFraction
oalt = altitudeKm
olat = latitude
olon = longitude
}
/** The input string array which contains each line of input for the wmm.cof input file.
* The columns in this file are as follows: n, m, gnm, hnm, dgnm, dhnm*/
private static let WMM_COF:[String] = [
" 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"]
/** Mean radius of IAU-66 ellipsoid, in km*/
private static let IAU66_RADIUS:Double = 6371.2
/** Semi-major axis of WGS-1984 ellipsoid, in km*/
private static let WGS84_A:Double = 6378.137
/** Semi-minor axis of WGS-1984 ellipsoid, in km*/
private static let WGS84_B:Double = 6356.7523142
/** The maximum number of degrees of the spherical harmonic model*/
private static let MAX_DEG:Int = 12
/** Geomagnetic declination (decimal degrees) [opposite of variation, positive Eastward/negative Westward]*/
private(set) var declination:Double = Double.nan
/** Geomagnetic inclination/dip angle (degrees) [positive downward]*/
private(set) var inclination:Double = Double.nan
/** Geomagnetic field intensity/strength (nano Teslas)*/
private(set) var intensity:Double = Double.nan
/** Geomagnetic horizontal field intensity/strength (nano Teslas)*/
private(set) var horizontalIntensity:Double = Double.nan
/** Geomagnetic vertical field intensity/strength (nano Teslas) [positive downward]*/
private(set) var verticalIntensity:Double = Double.nan
/** Geomagnetic North South (northerly component) field intensity/strength (nano Tesla)*/
private(set) var northIntensity:Double = Double.nan
/** Geomagnetic East West (easterly component) field intensity/strength (nano Teslas)*/
private(set) var eastIntensity:Double = Double.nan
/** The maximum order of spherical harmonic model*/
private var maxord:Int
/** The Gauss coefficients of main geomagnetic model (nt)*/
private var c:[[Double]] = Array(repeating: Array(repeating: Double.nan, count: 13), count: 13)
/** The Gauss coefficients of secular geomagnetic model (nt/yr)*/
private var cd:[[Double]] = Array(repeating: Array(repeating: Double.nan, count: 13), count: 13)
/** The time adjusted geomagnetic gauss coefficients (nt)*/
private var tc:[[Double]] = Array(repeating: Array(repeating: Double.nan, count: 13), count: 13)
/** The theta derivative of p(n,m) (unnormalized)*/
private var dp:[[Double]] = Array(repeating: Array(repeating: Double.nan, count: 13), count: 13)
/** The Schmidt normalization factors*/
private var snorm:[Double] = Array(repeating: Double.nan, count: 169)
/** The sine of (m*spherical coordinate longitude)*/
private var sp:[Double] = Array(repeating: Double.nan, count: 13)
/** The cosine of (m*spherical coordinate longitude)*/
private var cp:[Double] = Array(repeating: Double.nan, count: 13)
private var fn:[Double] = Array(repeating: Double.nan, count: 13)
private var fm:[Double] = Array(repeating: Double.nan, count: 13)
/** The associated Legendre polynomials for m = 1 (unnormalized)*/
private var pp:[Double] = Array(repeating: Double.nan, count: 13)
private var k:[[Double]] = Array(repeating: Array(repeating: Double.nan, count: 13), count: 13)
/** The variables otime (old time), oalt (old altitude),
* olat (old latitude), olon (old longitude), are used to
* store the values used from the previous calculation to
* save on calculation time if some inputs don't change*/
private var otime:Double, oalt:Double, olat:Double, olon:Double
/** The date in years, for the start of the valid time of the fit coefficients*/
private var epoch:Double
private var r:Double = Double.nan, d:Double = Double.nan, ca:Double = Double.nan,
sa:Double = Double.nan, ct:Double = Double.nan, st:Double = Double.nan
}