/**
******************************************************************************
*
* @file worldmagmodel.cpp
* @author The OpenPilot Team, http://www.openpilot.org Copyright (C) 2010.
* @brief Utilities to find the location of openpilot GCS files:
* - Plugins Share directory path
*
* @brief Source file for the World Magnetic Model
* This is a port of code available from the US NOAA.
*
* The hard coded coefficients should be valid until 2015.
*
* Updated coeffs from ..
* http://www.ngdc.noaa.gov/geomag/WMM/wmm_ddownload.shtml
*
* NASA C source code ..
* http://www.ngdc.noaa.gov/geomag/WMM/wmm_wdownload.shtml
*
* Major changes include:
* - No geoid model (altitude must be geodetic WGS-84)
* - Floating point calculation (not double precision)
* - Hard coded coefficients for model
* - Elimination of user interface
* - Elimination of dynamic memory allocation
*
* @see The GNU Public License (GPL) Version 3
*
*****************************************************************************/
/*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program; if not, write to the Free Software Foundation, Inc.,
* 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
#include "worldmagmodel.h"
#include <stdint.h>
#include <QDebug>
#include <math.h>
#include <qmath.h>
#define RAD2DEG(rad) ((rad) * (180.0 / M_PI))
#define DEG2RAD(deg) ((deg) * (M_PI / 180.0))
// updated coeffs available from http://www.ngdc.noaa.gov/geomag/WMM/wmm_ddownload.shtml
const double CoeffFile[91][6] = {
{0, 0, 0, 0, 0, 0},
{1, 0, -29496.6, 0.0, 11.6, 0.0},
{1, 1, -1586.3, 4944.4, 16.5, -25.9},
{2, 0, -2396.6, 0.0, -12.1, 0.0},
{2, 1, 3026.1, -2707.7, -4.4, -22.5},
{2, 2, 1668.6, -576.1, 1.9, -11.8},
{3, 0, 1340.1, 0.0, 0.4, 0.0},
{3, 1, -2326.2, -160.2, -4.1, 7.3},
{3, 2, 1231.9, 251.9, -2.9, -3.9},
{3, 3, 634.0, -536.6, -7.7, -2.6},
{4, 0, 912.6, 0.0, -1.8, 0.0},
{4, 1, 808.9, 286.4, 2.3, 1.1},
{4, 2, 166.7, -211.2, -8.7, 2.7},
{4, 3, -357.1, 164.3, 4.6, 3.9},
{4, 4, 89.4, -309.1, -2.1, -0.8},
{5, 0, -230.9, 0.0, -1.0, 0.0},
{5, 1, 357.2, 44.6, 0.6, 0.4},
{5, 2, 200.3, 188.9, -1.8, 1.8},
{5, 3, -141.1, -118.2, -1.0, 1.2},
{5, 4, -163.0, 0.0, 0.9, 4.0},
{5, 5, -7.8, 100.9, 1.0, -0.6},
{6, 0, 72.8, 0.0, -0.2, 0.0},
{6, 1, 68.6, -20.8, -0.2, -0.2},
{6, 2, 76.0, 44.1, -0.1, -2.1},
{6, 3, -141.4, 61.5, 2.0, -0.4},
{6, 4, -22.8, -66.3, -1.7, -0.6},
{6, 5, 13.2, 3.1, -0.3, 0.5},
{6, 6, -77.9, 55.0, 1.7, 0.9},
{7, 0, 80.5, 0.0, 0.1, 0.0},
{7, 1, -75.1, -57.9, -0.1, 0.7},
{7, 2, -4.7, -21.1, -0.6, 0.3},
{7, 3, 45.3, 6.5, 1.3, -0.1},
{7, 4, 13.9, 24.9, 0.4, -0.1},
{7, 5, 10.4, 7.0, 0.3, -0.8},
{7, 6, 1.7, -27.7, -0.7, -0.3},
{7, 7, 4.9, -3.3, 0.6, 0.3},
{8, 0, 24.4, 0.0, -0.1, 0.0},
{8, 1, 8.1, 11.0, 0.1, -0.1},
{8, 2, -14.5, -20.0, -0.6, 0.2},
{8, 3, -5.6, 11.9, 0.2, 0.4},
{8, 4, -19.3, -17.4, -0.2, 0.4},
{8, 5, 11.5, 16.7, 0.3, 0.1},
{8, 6, 10.9, 7.0, 0.3, -0.1},
{8, 7, -14.1, -10.8, -0.6, 0.4},
{8, 8, -3.7, 1.7, 0.2, 0.3},
{9, 0, 5.4, 0.0, 0.0, 0.0},
{9, 1, 9.4, -20.5, -0.1, 0.0},
{9, 2, 3.4, 11.5, 0.0, -0.2},
{9, 3, -5.2, 12.8, 0.3, 0.0},
{9, 4, 3.1, -7.2, -0.4, -0.1},
{9, 5, -12.4, -7.4, -0.3, 0.1},
{9, 6, -0.7, 8.0, 0.1, 0.0},
{9, 7, 8.4, 2.1, -0.1, -0.2},
{9, 8, -8.5, -6.1, -0.4, 0.3},
{9, 9, -10.1, 7.0, -0.2, 0.2},
{10, 0, -2.0, 0.0, 0.0, 0.0},
{10, 1, -6.3, 2.8, 0.0, 0.1},
{10, 2, 0.9, -0.1, -0.1, -0.1},
{10, 3, -1.1, 4.7, 0.2, 0.0},
{10, 4, -0.2, 4.4, 0.0, -0.1},
{10, 5, 2.5, -7.2, -0.1, -0.1},
{10, 6, -0.3, -1.0, -0.2, 0.0},
{10, 7, 2.2, -3.9, 0.0, -0.1},
{10, 8, 3.1, -2.0, -0.1, -0.2},
{10, 9, -1.0, -2.0, -0.2, 0.0},
{10, 10, -2.8, -8.3, -0.2, -0.1},
{11, 0, 3.0, 0.0, 0.0, 0.0},
{11, 1, -1.5, 0.2, 0.0, 0.0},
{11, 2, -2.1, 1.7, 0.0, 0.1},
{11, 3, 1.7, -0.6, 0.1, 0.0},
{11, 4, -0.5, -1.8, 0.0, 0.1},
{11, 5, 0.5, 0.9, 0.0, 0.0},
{11, 6, -0.8, -0.4, 0.0, 0.1},
{11, 7, 0.4, -2.5, 0.0, 0.0},
{11, 8, 1.8, -1.3, 0.0, -0.1},
{11, 9, 0.1, -2.1, 0.0, -0.1},
{11, 10, 0.7, -1.9, -0.1, 0.0},
{11, 11, 3.8, -1.8, 0.0, -0.1},
{12, 0, -2.2, 0.0, 0.0, 0.0},
{12, 1, -0.2, -0.9, 0.0, 0.0},
{12, 2, 0.3, 0.3, 0.1, 0.0},
{12, 3, 1.0, 2.1, 0.1, 0.0},
{12, 4, -0.6, -2.5, -0.1, 0.0},
{12, 5, 0.9, 0.5, 0.0, 0.0},
{12, 6, -0.1, 0.6, 0.0, 0.1},
{12, 7, 0.5, 0.0, 0.0, 0.0},
{12, 8, -0.4, 0.1, 0.0, 0.0},
{12, 9, -0.4, 0.3, 0.0, 0.0},
{12, 10, 0.2, -0.9, 0.0, 0.0},
{12, 11, -0.8, -0.2, -0.1, 0.0},
{12, 12, 0.0, 0.9, 0.1, 0.0}
};
namespace Utils {
WorldMagModel::WorldMagModel()
{
Initialize();
}
int WorldMagModel::GetMagVector(double LLA[3], int Month, int Day, int Year, double Be[3])
{
double Lat = LLA[0];
double Lon = LLA[1];
double AltEllipsoid = LLA[2];
// ***********
// range check supplied params
if (Lat < -90) return -1; // error
if (Lat > 90) return -2; // error
if (Lon < -180) return -3; // error
if (Lon > 180) return -4; // error
// ***********
WMMtype_CoordSpherical CoordSpherical;
WMMtype_CoordGeodetic CoordGeodetic;
WMMtype_GeoMagneticElements GeoMagneticElements;
Initialize();
CoordGeodetic.lambda = Lon;
CoordGeodetic.phi = Lat;
CoordGeodetic.HeightAboveEllipsoid = AltEllipsoid;
// Convert from geodeitic to Spherical Equations: 17-18, WMM Technical report
GeodeticToSpherical(&CoordGeodetic, &CoordSpherical);
if (DateToYear(Month, Day, Year) < 0)
return -5; // error
// Compute the geoMagnetic field elements and their time change
if (Geomag(&CoordSpherical, &CoordGeodetic, &GeoMagneticElements) < 0)
return -6; // error
// set the returned values
Be[0] = GeoMagneticElements.X * 1e-2;
Be[1] = GeoMagneticElements.Y * 1e-2;
Be[2] = GeoMagneticElements.Z * 1e-2;
// ***********
return 0; // OK
}
void WorldMagModel::Initialize()
{ // Sets default values for WMM subroutines.
// UPDATES : Ellip and MagneticModel
// Sets WGS-84 parameters
Ellip.a = 6378.137; // semi-major axis of the ellipsoid in km
Ellip.b = 6356.7523142; // semi-minor axis of the ellipsoid in km
Ellip.fla = 1 / 298.257223563; // flattening
Ellip.eps = sqrt(1 - (Ellip.b * Ellip.b) / (Ellip.a * Ellip.a)); // first eccentricity
Ellip.epssq = (Ellip.eps * Ellip.eps); // first eccentricity squared
Ellip.re = 6371.2; // Earth's radius in km
// Sets Magnetic Model parameters
MagneticModel.nMax = WMM_MAX_MODEL_DEGREES;
MagneticModel.nMaxSecVar = WMM_MAX_SECULAR_VARIATION_MODEL_DEGREES;
MagneticModel.SecularVariationUsed = 0;
// Really, Really needs to be read from a file - out of date in 2015 at latest
MagneticModel.EditionDate = 5.7863328170559505e-307;
MagneticModel.epoch = 2010.0;
sprintf(MagneticModel.ModelName, "WMM-2010");
}
int WorldMagModel::Geomag(WMMtype_CoordSpherical *CoordSpherical, WMMtype_CoordGeodetic *CoordGeodetic, WMMtype_GeoMagneticElements *GeoMagneticElements)
/*
The main subroutine that calls a sequence of WMM sub-functions to calculate the magnetic field elements for a single point.
The function expects the model coefficients and point coordinates as input and returns the magnetic field elements and
their rate of change. Though, this subroutine can be called successively to calculate a time series, profile or grid
of magnetic field, these are better achieved by the subroutine WMM_Grid.
INPUT: Ellip
CoordSpherical
CoordGeodetic
TimedMagneticModel
OUTPUT : GeoMagneticElements
*/
{
WMMtype_MagneticResults MagneticResultsSph;
WMMtype_MagneticResults MagneticResultsGeo;
WMMtype_MagneticResults MagneticResultsSphVar;
WMMtype_MagneticResults MagneticResultsGeoVar;
WMMtype_LegendreFunction LegendreFunction;
WMMtype_SphericalHarmonicVariables SphVariables;
// Compute Spherical Harmonic variables
ComputeSphericalHarmonicVariables(CoordSpherical, MagneticModel.nMax, &SphVariables);
// Compute ALF
if (AssociatedLegendreFunction(CoordSpherical, MagneticModel.nMax, &LegendreFunction) < 0)
return -1; // error
// Accumulate the spherical harmonic coefficients
Summation(&LegendreFunction, &SphVariables, CoordSpherical, &MagneticResultsSph);
// Sum the Secular Variation Coefficients
SecVarSummation(&LegendreFunction, &SphVariables, CoordSpherical, &MagneticResultsSphVar);
// Map the computed Magnetic fields to Geodeitic coordinates
RotateMagneticVector(CoordSpherical, CoordGeodetic, &MagneticResultsSph, &MagneticResultsGeo);
// Map the secular variation field components to Geodetic coordinates
RotateMagneticVector(CoordSpherical, CoordGeodetic, &MagneticResultsSphVar, &MagneticResultsGeoVar);
// Calculate the Geomagnetic elements, Equation 18 , WMM Technical report
CalculateGeoMagneticElements(&MagneticResultsGeo, GeoMagneticElements);
// Calculate the secular variation of each of the Geomagnetic elements
CalculateSecularVariation(&MagneticResultsGeoVar, GeoMagneticElements);
return 0; // OK
}
void WorldMagModel::ComputeSphericalHarmonicVariables(WMMtype_CoordSpherical *CoordSpherical, int nMax, WMMtype_SphericalHarmonicVariables *SphVariables)
{
/* Computes Spherical variables
Variables computed are (a/r)^(n+2), cos_m(lamda) and sin_m(lambda) for spherical harmonic
summations. (Equations 10-12 in the WMM Technical Report)
INPUT Ellip data structure with the following elements
float a; semi-major axis of the ellipsoid
float b; semi-minor axis of the ellipsoid
float fla; flattening
float epssq; first eccentricity squared
float eps; first eccentricity
float re; mean radius of ellipsoid
CoordSpherical A data structure with the following elements
float lambda; ( longitude)
float phig; ( geocentric latitude )
float r; ( distance from the center of the ellipsoid)
nMax integer ( Maxumum degree of spherical harmonic secular model)\
OUTPUT SphVariables Pointer to the data structure with the following elements
float RelativeRadiusPower[WMM_MAX_MODEL_DEGREES+1]; [earth_reference_radius_km sph. radius ]^n
float cos_mlambda[WMM_MAX_MODEL_DEGREES+1]; cp(m) - cosine of (mspherical coord. longitude)
float sin_mlambda[WMM_MAX_MODEL_DEGREES+1]; sp(m) - sine of (mspherical coord. longitude)
*/
double cos_lambda = cos(DEG2RAD(CoordSpherical->lambda));
double sin_lambda = sin(DEG2RAD(CoordSpherical->lambda));
/* for n = 0 ... model_order, compute (Radius of Earth / Spherica radius r)^(n+2)
for n 1..nMax-1 (this is much faster than calling pow MAX_N+1 times). */
SphVariables->RelativeRadiusPower[0] = (Ellip.re / CoordSpherical->r) * (Ellip.re / CoordSpherical->r);
for (int n = 1; n <= nMax; n++)
SphVariables->RelativeRadiusPower[n] = SphVariables->RelativeRadiusPower[n - 1] * (Ellip.re / CoordSpherical->r);
/*
Compute cos(m*lambda), sin(m*lambda) for m = 0 ... nMax
cos(a + b) = cos(a)*cos(b) - sin(a)*sin(b)
sin(a + b) = cos(a)*sin(b) + sin(a)*cos(b)
*/
SphVariables->cos_mlambda[0] = 1.0;
SphVariables->sin_mlambda[0] = 0.0;
SphVariables->cos_mlambda[1] = cos_lambda;
SphVariables->sin_mlambda[1] = sin_lambda;
for (int m = 2; m <= nMax; m++)
{
SphVariables->cos_mlambda[m] = SphVariables->cos_mlambda[m - 1] * cos_lambda - SphVariables->sin_mlambda[m - 1] * sin_lambda;
SphVariables->sin_mlambda[m] = SphVariables->cos_mlambda[m - 1] * sin_lambda + SphVariables->sin_mlambda[m - 1] * cos_lambda;
}
}
int WorldMagModel::AssociatedLegendreFunction(WMMtype_CoordSpherical *CoordSpherical, int nMax, WMMtype_LegendreFunction *LegendreFunction)
{
/* Computes all of the Schmidt-semi normalized associated Legendre
functions up to degree nMax. If nMax <= 16, function WMM_PcupLow is used.
Otherwise WMM_PcupHigh is called.
INPUT CoordSpherical A data structure with the following elements
float lambda; ( longitude)
float phig; ( geocentric latitude )
float r; ( distance from the center of the ellipsoid)
nMax integer ( Maxumum degree of spherical harmonic secular model)
LegendreFunction Pointer to data structure with the following elements
float *Pcup; ( pointer to store Legendre Function )
float *dPcup; ( pointer to store Derivative of Lagendre function )
OUTPUT LegendreFunction Calculated Legendre variables in the data structure
*/
double sin_phi = sin(DEG2RAD(CoordSpherical->phig)); // sin (geocentric latitude)
if (nMax <= 16 || (1 - fabs(sin_phi)) < 1.0e-10) /* If nMax is less tha 16 or at the poles */
PcupLow(LegendreFunction->Pcup, LegendreFunction->dPcup, sin_phi, nMax);
else
{
if (PcupHigh(LegendreFunction->Pcup, LegendreFunction->dPcup, sin_phi, nMax) < 0)
return -1; // error
}
return 0; // OK
}
void WorldMagModel::Summation( WMMtype_LegendreFunction *LegendreFunction,
WMMtype_SphericalHarmonicVariables *SphVariables,
WMMtype_CoordSpherical *CoordSpherical,
WMMtype_MagneticResults *MagneticResults)
{
/* Computes Geomagnetic Field Elements X, Y and Z in Spherical coordinate system using spherical harmonic summation.
The vector Magnetic field is given by -grad V, where V is Geomagnetic scalar potential
The gradient in spherical coordinates is given by:
dV ^ 1 dV ^ 1 dV ^
grad V = -- r + - -- t + -------- -- p
dr r dt r sin(t) dp
INPUT : LegendreFunction
MagneticModel
SphVariables
CoordSpherical
OUTPUT : MagneticResults
Manoj Nair, June, 2009 Manoj.C.Nair@Noaa.Gov
*/
MagneticResults->Bz = 0.0;
MagneticResults->By = 0.0;
MagneticResults->Bx = 0.0;
for (int n = 1; n <= MagneticModel.nMax; n++)
{
for (int m = 0; m <= n; m++)
{
int index = (n * (n + 1) / 2 + m);
/* nMax (n+2) n m m m
Bz = -SUM (a/r) (n+1) SUM [g cos(m p) + h sin(m p)] P (sin(phi))
n=1 m=0 n n n */
/* Equation 12 in the WMM Technical report. Derivative with respect to radius.*/
MagneticResults->Bz -=
SphVariables->RelativeRadiusPower[n] *
(get_main_field_coeff_g(index) *
SphVariables->cos_mlambda[m] + get_main_field_coeff_h(index) * SphVariables->sin_mlambda[m])
* (double)(n + 1) * LegendreFunction->Pcup[index];
/* 1 nMax (n+2) n m m m
By = SUM (a/r) (m) SUM [g cos(m p) + h sin(m p)] dP (sin(phi))
n=1 m=0 n n n */
/* Equation 11 in the WMM Technical report. Derivative with respect to longitude, divided by radius. */
MagneticResults->By +=
SphVariables->RelativeRadiusPower[n] *
(get_main_field_coeff_g(index) *
SphVariables->sin_mlambda[m] - get_main_field_coeff_h(index) * SphVariables->cos_mlambda[m])
* (double)(m) * LegendreFunction->Pcup[index];
/* nMax (n+2) n m m m
Bx = - SUM (a/r) SUM [g cos(m p) + h sin(m p)] dP (sin(phi))
n=1 m=0 n n n */
/* Equation 10 in the WMM Technical report. Derivative with respect to latitude, divided by radius. */
MagneticResults->Bx -=
SphVariables->RelativeRadiusPower[n] *
(get_main_field_coeff_g(index) *
SphVariables->cos_mlambda[m] + get_main_field_coeff_h(index) * SphVariables->sin_mlambda[m])
* LegendreFunction->dPcup[index];
}
}
double cos_phi = cos(DEG2RAD(CoordSpherical->phig));
if (fabs(cos_phi) > 1.0e-10)
{
MagneticResults->By = MagneticResults->By / cos_phi;
}
else
{
/* Special calculation for component - By - at Geographic poles.
* If the user wants to avoid using this function, please make sure that
* the latitude is not exactly +/-90. An option is to make use the function
* WMM_CheckGeographicPoles.
*/
SummationSpecial(SphVariables, CoordSpherical, MagneticResults);
}
}
void WorldMagModel::SecVarSummation( WMMtype_LegendreFunction *LegendreFunction,
WMMtype_SphericalHarmonicVariables *SphVariables,
WMMtype_CoordSpherical *CoordSpherical,
WMMtype_MagneticResults *MagneticResults)
{
/*This Function sums the secular variation coefficients to get the secular variation of the Magnetic vector.
INPUT : LegendreFunction
MagneticModel
SphVariables
CoordSpherical
OUTPUT : MagneticResults
*/
MagneticModel.SecularVariationUsed = true;
MagneticResults->Bz = 0.0;
MagneticResults->By = 0.0;
MagneticResults->Bx = 0.0;
for (int n = 1; n <= MagneticModel.nMaxSecVar; n++)
{
for (int m = 0; m <= n; m++)
{
int index = (n * (n + 1) / 2 + m);
/* nMax (n+2) n m m m
Bz = -SUM (a/r) (n+1) SUM [g cos(m p) + h sin(m p)] P (sin(phi))
n=1 m=0 n n n */
/* Derivative with respect to radius.*/
MagneticResults->Bz -=
SphVariables->RelativeRadiusPower[n] *
(get_secular_var_coeff_g(index) *
SphVariables->cos_mlambda[m] + get_secular_var_coeff_h(index) * SphVariables->sin_mlambda[m])
* (double)(n + 1) * LegendreFunction->Pcup[index];
/* 1 nMax (n+2) n m m m
By = SUM (a/r) (m) SUM [g cos(m p) + h sin(m p)] dP (sin(phi))
n=1 m=0 n n n */
/* Derivative with respect to longitude, divided by radius. */
MagneticResults->By +=
SphVariables->RelativeRadiusPower[n] *
(get_secular_var_coeff_g(index) *
SphVariables->sin_mlambda[m] - get_secular_var_coeff_h(index) * SphVariables->cos_mlambda[m])
* (double)(m) * LegendreFunction->Pcup[index];
/* nMax (n+2) n m m m
Bx = - SUM (a/r) SUM [g cos(m p) + h sin(m p)] dP (sin(phi))
n=1 m=0 n n n */
/* Derivative with respect to latitude, divided by radius. */
MagneticResults->Bx -=
SphVariables->RelativeRadiusPower[n] *
(get_secular_var_coeff_g(index) *
SphVariables->cos_mlambda[m] + get_secular_var_coeff_h(index) * SphVariables->sin_mlambda[m])
* LegendreFunction->dPcup[index];
}
}
double cos_phi = cos(DEG2RAD(CoordSpherical->phig));
if (fabs(cos_phi) > 1.0e-10)
{
MagneticResults->By = MagneticResults->By / cos_phi;
}
else
{ /* Special calculation for component By at Geographic poles */
SecVarSummationSpecial(SphVariables, CoordSpherical, MagneticResults);
}
}
void WorldMagModel::RotateMagneticVector( WMMtype_CoordSpherical *CoordSpherical,
WMMtype_CoordGeodetic *CoordGeodetic,
WMMtype_MagneticResults *MagneticResultsSph,
WMMtype_MagneticResults *MagneticResultsGeo)
{
/* Rotate the Magnetic Vectors to Geodetic Coordinates
Manoj Nair, June, 2009 Manoj.C.Nair@Noaa.Gov
Equation 16, WMM Technical report
INPUT : CoordSpherical : Data structure WMMtype_CoordSpherical with the following elements
float lambda; ( longitude)
float phig; ( geocentric latitude )
float r; ( distance from the center of the ellipsoid)
CoordGeodetic : Data structure WMMtype_CoordGeodetic with the following elements
float lambda; (longitude)
float phi; ( geodetic latitude)
float HeightAboveEllipsoid; (height above the ellipsoid (HaE) )
float HeightAboveGeoid;(height above the Geoid )
MagneticResultsSph : Data structure WMMtype_MagneticResults with the following elements
float Bx; North
float By; East
float Bz; Down
OUTPUT: MagneticResultsGeo Pointer to the data structure WMMtype_MagneticResults, with the following elements
float Bx; North
float By; East
float Bz; Down
*/
/* Difference between the spherical and Geodetic latitudes */
double Psi = DEG2RAD(CoordSpherical->phig - CoordGeodetic->phi);
/* Rotate spherical field components to the Geodeitic system */
MagneticResultsGeo->Bz = MagneticResultsSph->Bx * sin(Psi) + MagneticResultsSph->Bz * cos(Psi);
MagneticResultsGeo->Bx = MagneticResultsSph->Bx * cos(Psi) - MagneticResultsSph->Bz * sin(Psi);
MagneticResultsGeo->By = MagneticResultsSph->By;
}
void WorldMagModel::CalculateGeoMagneticElements(WMMtype_MagneticResults *MagneticResultsGeo, WMMtype_GeoMagneticElements *GeoMagneticElements)
{
/* Calculate all the Geomagnetic elements from X,Y and Z components
INPUT MagneticResultsGeo Pointer to data structure with the following elements
float Bx; ( North )
float By; ( East )
float Bz; ( Down )
OUTPUT GeoMagneticElements Pointer to data structure with the following elements
float Decl; (Angle between the magnetic field vector and true north, positive east)
float Incl; Angle between the magnetic field vector and the horizontal plane, positive down
float F; Magnetic Field Strength
float H; Horizontal Magnetic Field Strength
float X; Northern component of the magnetic field vector
float Y; Eastern component of the magnetic field vector
float Z; Downward component of the magnetic field vector
*/
GeoMagneticElements->X = MagneticResultsGeo->Bx;
GeoMagneticElements->Y = MagneticResultsGeo->By;
GeoMagneticElements->Z = MagneticResultsGeo->Bz;
GeoMagneticElements->H = sqrt(MagneticResultsGeo->Bx * MagneticResultsGeo->Bx + MagneticResultsGeo->By * MagneticResultsGeo->By);
GeoMagneticElements->F = sqrt(GeoMagneticElements->H * GeoMagneticElements->H + MagneticResultsGeo->Bz * MagneticResultsGeo->Bz);
GeoMagneticElements->Decl = RAD2DEG(atan2(GeoMagneticElements->Y, GeoMagneticElements->X));
GeoMagneticElements->Incl = RAD2DEG(atan2(GeoMagneticElements->Z, GeoMagneticElements->H));
}
void WorldMagModel::CalculateSecularVariation(WMMtype_MagneticResults *MagneticVariation, WMMtype_GeoMagneticElements *MagneticElements)
{
/* This takes the Magnetic Variation in x, y, and z and uses it to calculate the secular variation of each of the Geomagnetic elements.
INPUT MagneticVariation Data structure with the following elements
float Bx; ( North )
float By; ( East )
float Bz; ( Down )
OUTPUT MagneticElements Pointer to the data structure with the following elements updated
float Decldot; Yearly Rate of change in declination
float Incldot; Yearly Rate of change in inclination
float Fdot; Yearly rate of change in Magnetic field strength
float Hdot; Yearly rate of change in horizontal field strength
float Xdot; Yearly rate of change in the northern component
float Ydot; Yearly rate of change in the eastern component
float Zdot; Yearly rate of change in the downward component
float GVdot;Yearly rate of chnage in grid variation
*/
MagneticElements->Xdot = MagneticVariation->Bx;
MagneticElements->Ydot = MagneticVariation->By;
MagneticElements->Zdot = MagneticVariation->Bz;
MagneticElements->Hdot = (MagneticElements->X * MagneticElements->Xdot + MagneticElements->Y * MagneticElements->Ydot) / MagneticElements->H; //See equation 19 in the WMM technical report
MagneticElements->Fdot =
(MagneticElements->X * MagneticElements->Xdot +
MagneticElements->Y * MagneticElements->Ydot + MagneticElements->Z * MagneticElements->Zdot) / MagneticElements->F;
MagneticElements->Decldot =
180.0 / M_PI * (MagneticElements->X * MagneticElements->Ydot -
MagneticElements->Y * MagneticElements->Xdot) / (MagneticElements->H * MagneticElements->H);
MagneticElements->Incldot =
180.0 / M_PI * (MagneticElements->H * MagneticElements->Zdot -
MagneticElements->Z * MagneticElements->Hdot) / (MagneticElements->F * MagneticElements->F);
MagneticElements->GVdot = MagneticElements->Decldot;
}
int WorldMagModel::PcupHigh(double *Pcup, double *dPcup, double x, int nMax)
{
/* This function evaluates all of the Schmidt-semi normalized associated Legendre
functions up to degree nMax. The functions are initially scaled by
10^280 sin^m in order to minimize the effects of underflow at large m
near the poles (see Holmes and Featherstone 2002, J. Geodesy, 76, 279-299).
Note that this function performs the same operation as WMM_PcupLow.
However this function also can be used for high degree (large nMax) models.
Calling Parameters:
INPUT
nMax: Maximum spherical harmonic degree to compute.
x: cos(colatitude) or sin(latitude).
OUTPUT
Pcup: A vector of all associated Legendgre polynomials evaluated at
x up to nMax. The lenght must by greater or equal to (nMax+1)*(nMax+2)/2.
dPcup: Derivative of Pcup(x) with respect to latitude
Notes:
Adopted from the FORTRAN code written by Mark Wieczorek September 25, 2005.
Manoj Nair, Nov, 2009 Manoj.C.Nair@Noaa.Gov
Change from the previous version
The prevous version computes the derivatives as
dP(n,m)(x)/dx, where x = sin(latitude) (or cos(colatitude) ).
However, the WMM Geomagnetic routines requires dP(n,m)(x)/dlatitude.
Hence the derivatives are multiplied by sin(latitude).
Removed the options for CS phase and normalizations.
Note: In geomagnetism, the derivatives of ALF are usually found with
respect to the colatitudes. Here the derivatives are found with respect
to the latitude. The difference is a sign reversal for the derivative of
the Associated Legendre Functions.
The derivates can't be computed for latitude = |90| degrees.
*/
double f1[WMM_NUMPCUP];
double f2[WMM_NUMPCUP];
double PreSqr[WMM_NUMPCUP];
int m;
if (fabs(x) == 1.0)
{
// printf("Error in PcupHigh: derivative cannot be calculated at poles\n");
return -2;
}
double scalef = 1.0e-280;
for (int n = 0; n <= 2 * nMax + 1; ++n)
PreSqr[n] = sqrt((double)(n));
int k = 2;
for (int n = 2; n <= nMax; n++)
{
k = k + 1;
f1[k] = (double)(2 * n - 1) / n;
f2[k] = (double)(n - 1) / n;
for (int m = 1; m <= n - 2; m++)
{
k = k + 1;
f1[k] = (double)(2 * n - 1) / PreSqr[n + m] / PreSqr[n - m];
f2[k] = PreSqr[n - m - 1] * PreSqr[n + m - 1] / PreSqr[n + m] / PreSqr[n - m];
}
k = k + 2;
}
/*z = sin (geocentric latitude) */
double z = sqrt((1.0 - x) * (1.0 + x));
double pm2 = 1.0;
Pcup[0] = 1.0;
dPcup[0] = 0.0;
if (nMax == 0)
return -3;
double pm1 = x;
Pcup[1] = pm1;
dPcup[1] = z;
k = 1;
for (int n = 2; n <= nMax; n++)
{
k = k + n;
double plm = f1[k] * x * pm1 - f2[k] * pm2;
Pcup[k] = plm;
dPcup[k] = (double)(n) * (pm1 - x * plm) / z;
pm2 = pm1;
pm1 = plm;
}
double pmm = PreSqr[2] * scalef;
double rescalem = 1.0 / scalef;
int kstart = 0;
for (m = 1; m <= nMax - 1; ++m)
{
rescalem = rescalem * z;
/* Calculate Pcup(m,m) */
kstart = kstart + m + 1;
pmm = pmm * PreSqr[2 * m + 1] / PreSqr[2 * m];
Pcup[kstart] = pmm * rescalem / PreSqr[2 * m + 1];
dPcup[kstart] = -((double)(m) * x * Pcup[kstart] / z);
pm2 = pmm / PreSqr[2 * m + 1];
/* Calculate Pcup(m+1,m) */
k = kstart + m + 1;
pm1 = x * PreSqr[2 * m + 1] * pm2;
Pcup[k] = pm1 * rescalem;
dPcup[k] = ((pm2 * rescalem) * PreSqr[2 * m + 1] - x * (double)(m + 1) * Pcup[k]) / z;
/* Calculate Pcup(n,m) */
for (int n = m + 2; n <= nMax; ++n)
{
k = k + n;
double plm = x * f1[k] * pm1 - f2[k] * pm2;
Pcup[k] = plm * rescalem;
dPcup[k] = (PreSqr[n + m] * PreSqr[n - m] * (pm1 * rescalem) - (double)(n) * x * Pcup[k]) / z;
pm2 = pm1;
pm1 = plm;
}
}
/* Calculate Pcup(nMax,nMax) */
rescalem = rescalem * z;
kstart = kstart + m + 1;
pmm = pmm / PreSqr[2 * nMax];
Pcup[kstart] = pmm * rescalem;
dPcup[kstart] = -(double)(nMax) * x * Pcup[kstart] / z;
// *********
return 0; // OK
}
void WorldMagModel::PcupLow(double *Pcup, double *dPcup, double x, int nMax)
{
/* This function evaluates all of the Schmidt-semi normalized associated Legendre functions up to degree nMax.
Calling Parameters:
INPUT
nMax: Maximum spherical harmonic degree to compute.
x: cos(colatitude) or sin(latitude).
OUTPUT
Pcup: A vector of all associated Legendgre polynomials evaluated at
x up to nMax.
dPcup: Derivative of Pcup(x) with respect to latitude
Notes: Overflow may occur if nMax > 20 , especially for high-latitudes.
Use WMM_PcupHigh for large nMax.
Writted by Manoj Nair, June, 2009 . Manoj.C.Nair@Noaa.Gov.
Note: In geomagnetism, the derivatives of ALF are usually found with
respect to the colatitudes. Here the derivatives are found with respect
to the latitude. The difference is a sign reversal for the derivative of
the Associated Legendre Functions.
*/
double schmidtQuasiNorm[WMM_NUMPCUP];
Pcup[0] = 1.0;
dPcup[0] = 0.0;
/*sin (geocentric latitude) - sin_phi */
double z = sqrt((1.0 - x) * (1.0 + x));
/* First, Compute the Gauss-normalized associated Legendre functions */
for (int n = 1; n <= nMax; n++)
{
for (int m = 0; m <= n; m++)
{
int index = (n * (n + 1) / 2 + m);
if (n == m)
{
int index1 = (n - 1) * n / 2 + m - 1;
Pcup[index] = z * Pcup[index1];
dPcup[index] = z * dPcup[index1] + x * Pcup[index1];
}
else
if (n == 1 && m == 0)
{
int index1 = (n - 1) * n / 2 + m;
Pcup[index] = x * Pcup[index1];
dPcup[index] = x * dPcup[index1] - z * Pcup[index1];
}
else
if (n > 1 && n != m)
{
int index1 = (n - 2) * (n - 1) / 2 + m;
int index2 = (n - 1) * n / 2 + m;
if (m > n - 2)
{
Pcup[index] = x * Pcup[index2];
dPcup[index] = x * dPcup[index2] - z * Pcup[index2];
}
else
{
double k = (double)(((n - 1) * (n - 1)) - (m * m)) / (double)((2 * n - 1) * (2 * n - 3));
Pcup[index] = x * Pcup[index2] - k * Pcup[index1];
dPcup[index] = x * dPcup[index2] - z * Pcup[index2] - k * dPcup[index1];
}
}
}
}
/*Compute the ration between the Gauss-normalized associated Legendre
functions and the Schmidt quasi-normalized version. This is equivalent to
sqrt((m==0?1:2)*(n-m)!/(n+m!))*(2n-1)!!/(n-m)! */
schmidtQuasiNorm[0] = 1.0;
for (int n = 1; n <= nMax; n++)
{
int index = (n * (n + 1) / 2);
int index1 = (n - 1) * n / 2;
/* for m = 0 */
schmidtQuasiNorm[index] = schmidtQuasiNorm[index1] * (double)(2 * n - 1) / (double)n;
for (int m = 1; m <= n; m++)
{
index = (n * (n + 1) / 2 + m);
index1 = (n * (n + 1) / 2 + m - 1);
schmidtQuasiNorm[index] = schmidtQuasiNorm[index1] * sqrt((double)((n - m + 1) * (m == 1 ? 2 : 1)) / (double)(n + m));
}
}
/* Converts the Gauss-normalized associated Legendre
functions to the Schmidt quasi-normalized version using pre-computed
relation stored in the variable schmidtQuasiNorm */
for (int n = 1; n <= nMax; n++)
{
for (int m = 0; m <= n; m++)
{
int index = (n * (n + 1) / 2 + m);
Pcup[index] = Pcup[index] * schmidtQuasiNorm[index];
dPcup[index] = -dPcup[index] * schmidtQuasiNorm[index];
/* The sign is changed since the new WMM routines use derivative with respect to latitude insted of co-latitude */
}
}
}
void WorldMagModel::SummationSpecial(WMMtype_SphericalHarmonicVariables *SphVariables, WMMtype_CoordSpherical *CoordSpherical, WMMtype_MagneticResults *MagneticResults)
{
/* Special calculation for the component By at Geographic poles.
Manoj Nair, June, 2009 manoj.c.nair@noaa.gov
INPUT: MagneticModel
SphVariables
CoordSpherical
OUTPUT: MagneticResults
CALLS : none
See Section 1.4, "SINGULARITIES AT THE GEOGRAPHIC POLES", WMM Technical report
*/
double PcupS[WMM_NUMPCUPS];
PcupS[0] = 1;
double schmidtQuasiNorm1 = 1.0;
MagneticResults->By = 0.0;
double sin_phi = sin(DEG2RAD(CoordSpherical->phig));
for (int n = 1; n <= MagneticModel.nMax; n++)
{
/*Compute the ration between the Gauss-normalized associated Legendre
functions and the Schmidt quasi-normalized version. This is equivalent to
sqrt((m==0?1:2)*(n-m)!/(n+m!))*(2n-1)!!/(n-m)! */
int index = (n * (n + 1) / 2 + 1);
double schmidtQuasiNorm2 = schmidtQuasiNorm1 * (double)(2 * n - 1) / (double)n;
double schmidtQuasiNorm3 = schmidtQuasiNorm2 * sqrt((double)(n * 2) / (double)(n + 1));
schmidtQuasiNorm1 = schmidtQuasiNorm2;
if (n == 1)
{
PcupS[n] = PcupS[n - 1];
}
else
{
double k = (double)(((n - 1) * (n - 1)) - 1) / (double)((2 * n - 1) * (2 * n - 3));
PcupS[n] = sin_phi * PcupS[n - 1] - k * PcupS[n - 2];
}
/* 1 nMax (n+2) n m m m
By = SUM (a/r) (m) SUM [g cos(m p) + h sin(m p)] dP (sin(phi))
n=1 m=0 n n n */
/* Equation 11 in the WMM Technical report. Derivative with respect to longitude, divided by radius. */
MagneticResults->By +=
SphVariables->RelativeRadiusPower[n] *
(get_main_field_coeff_g(index) *
SphVariables->sin_mlambda[1] - get_main_field_coeff_h(index) * SphVariables->cos_mlambda[1])
* PcupS[n] * schmidtQuasiNorm3;
}
}
void WorldMagModel::SecVarSummationSpecial(WMMtype_SphericalHarmonicVariables *SphVariables, WMMtype_CoordSpherical *CoordSpherical, WMMtype_MagneticResults *MagneticResults)
{
/*Special calculation for the secular variation summation at the poles.
INPUT: MagneticModel
SphVariables
CoordSpherical
OUTPUT: MagneticResults
*/
double PcupS[WMM_NUMPCUPS];
PcupS[0] = 1;
double schmidtQuasiNorm1 = 1.0;
MagneticResults->By = 0.0;
double sin_phi = sin(DEG2RAD(CoordSpherical->phig));
for (int n = 1; n <= MagneticModel.nMaxSecVar; n++)
{
int index = (n * (n + 1) / 2 + 1);
double schmidtQuasiNorm2 = schmidtQuasiNorm1 * (double)(2 * n - 1) / (double)n;
double schmidtQuasiNorm3 = schmidtQuasiNorm2 * sqrt((double)(n * 2) / (double)(n + 1));
schmidtQuasiNorm1 = schmidtQuasiNorm2;
if (n == 1)
{
PcupS[n] = PcupS[n - 1];
}
else
{
double k = (double)(((n - 1) * (n - 1)) - 1) / (double)((2 * n - 1) * (2 * n - 3));
PcupS[n] = sin_phi * PcupS[n - 1] - k * PcupS[n - 2];
}
/* 1 nMax (n+2) n m m m
By = SUM (a/r) (m) SUM [g cos(m p) + h sin(m p)] dP (sin(phi))
n=1 m=0 n n n */
/* Derivative with respect to longitude, divided by radius. */
MagneticResults->By +=
SphVariables->RelativeRadiusPower[n] *
(get_secular_var_coeff_g(index) *
SphVariables->sin_mlambda[1] - get_secular_var_coeff_h(index) * SphVariables->cos_mlambda[1])
* PcupS[n] * schmidtQuasiNorm3;
}
}
// brief Comput the MainFieldCoeffH accounting for the date
double WorldMagModel::get_main_field_coeff_g(int index)
{
if (index >= WMM_NUMTERMS)
return 0;
double coeff = CoeffFile[index][2];
int a = MagneticModel.nMaxSecVar;
int b = (a * (a + 1) / 2 + a);
for (int n = 1; n <= MagneticModel.nMax; n++)
{
for (int m = 0; m <= n; m++)
{
int sum_index = (n * (n + 1) / 2 + m);
/* Hacky for now, will solve for which conditions need summing analytically */
if (sum_index != index)
continue;
if (index <= b)
coeff += (decimal_date - MagneticModel.epoch) * get_secular_var_coeff_g(sum_index);
}
}
return coeff;
}
double WorldMagModel::get_main_field_coeff_h(int index)
{
if (index >= WMM_NUMTERMS)
return 0;
double coeff = CoeffFile[index][3];
int a = MagneticModel.nMaxSecVar;
int b = (a * (a + 1) / 2 + a);
for (int n = 1; n <= MagneticModel.nMax; n++)
{
for (int m = 0; m <= n; m++)
{
int sum_index = (n * (n + 1) / 2 + m);
/* Hacky for now, will solve for which conditions need summing analytically */
if (sum_index != index)
continue;
if (index <= b)
coeff += (decimal_date - MagneticModel.epoch) * get_secular_var_coeff_h(sum_index);
}
}
return coeff;
}
double WorldMagModel::get_secular_var_coeff_g(int index)
{
if (index >= WMM_NUMTERMS)
return 0;
return CoeffFile[index][4];
}
double WorldMagModel::get_secular_var_coeff_h(int index)
{
if (index >= WMM_NUMTERMS)
return 0;
return CoeffFile[index][5];
}
int WorldMagModel::DateToYear(int month, int day, int year)
{
// Converts a given calendar date into a decimal year
int temp = 0; // Total number of days
int MonthDays[13] = { 0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 };
int ExtraDay = 0;
if ((year % 4 == 0 && year % 100 != 0) || (year % 400 == 0))
ExtraDay = 1;
MonthDays[2] += ExtraDay;
/******************Validation********************************/
if (month <= 0 || month > 12)
return -1; // error
if (day <= 0 || day > MonthDays[month])
return -2; // error
/****************Calculation of t***************************/
for (int i = 1; i <= month; i++)
temp += MonthDays[i - 1];
temp += day;
decimal_date = year + (temp - 1) / (365.0 + ExtraDay);
return 0; // OK
}
void WorldMagModel::GeodeticToSpherical(WMMtype_CoordGeodetic *CoordGeodetic, WMMtype_CoordSpherical *CoordSpherical)
{
// Converts Geodetic coordinates to Spherical coordinates
// Convert geodetic coordinates, (defined by the WGS-84
// reference ellipsoid), to Earth Centered Earth Fixed Cartesian
// coordinates, and then to spherical coordinates.
double CosLat = cos(DEG2RAD(CoordGeodetic->phi));
double SinLat = sin(DEG2RAD(CoordGeodetic->phi));
// compute the local radius of curvature on the WGS-84 reference ellipsoid
double rc = Ellip.a / sqrt(1.0 - Ellip.epssq * SinLat * SinLat);
// compute ECEF Cartesian coordinates of specified point (for longitude=0)
double xp = (rc + CoordGeodetic->HeightAboveEllipsoid) * CosLat;
double zp = (rc * (1.0 - Ellip.epssq) + CoordGeodetic->HeightAboveEllipsoid) * SinLat;
// compute spherical radius and angle lambda and phi of specified point
CoordSpherical->r = sqrt(xp * xp + zp * zp);
CoordSpherical->phig = RAD2DEG(asin(zp / CoordSpherical->r)); // geocentric latitude
CoordSpherical->lambda = CoordGeodetic->lambda; // longitude
}
}