GlobalPressureTemperatureModel.java
/* Copyright 2002-2019 CS Systèmes d'Information
* Licensed to CS Systèmes d'Information (CS) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* CS licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.orekit.models.earth;
import org.hipparchus.util.CombinatoricsUtils;
import org.hipparchus.util.FastMath;
import org.orekit.forces.gravity.potential.GravityFieldFactory;
import org.orekit.frames.Frame;
import org.orekit.time.AbsoluteDate;
import org.orekit.time.DateTimeComponents;
import org.orekit.time.TimeScalesFactory;
/** The Global Pressure and Temperature model.
* This model is an empirical model that provides the temperature and the pressure depending
* the latitude and the longitude of the station.
* <p>
* The Global Pressure and Temperature model is based on spherical harmonics up
* to degree and order of 9. The residual values of this model can reach 20 hPa
* for pressure and 10 ° C for temperature. They are significant for higher latitudes and
* small near the equator (Böhm, 2007)
* </p>
*
* @see J. Böhm, R. Heinkelmann, and H. Schuh (2007),
* Short Note: A global model of pressure and temperature for geodetic applications. J Geod,
* doi:10.1007/s00190-007-0135-3.
*
* @author Bryan Cazabonne
*
*/
public class GlobalPressureTemperatureModel implements WeatherModel {
/** Temperature gradient (°C/m). */
private static final double TEMPERATURE_GRADIENT = -6.5e-3;
/** Geodetic latitude, in radians. */
private final double latitude;
/** Geodetic longitude, in radians. */
private final double longitude;
/** Temperature site, in kelvins. */
private double temperature;
/** Pressure site, in hPa. */
private double pressure;
/** Body frame related to body shape. */
private final Frame bodyFrame;
/** Build a new instance.
* <p>
* At the initialization the values of the pressure and the temperature are set to NaN.
* The user has to call {@link #weatherParameters(double, AbsoluteDate)} method before using
* the values of the pressure and the temperature.
* </p>
* @param latitude geodetic latitude, in radians
* @param longitude geodetic longitude, in radians
* @param bodyFrame the frame to attach to the ellipsoid. The origin is at
* the center of mass, the z axis is the minor axis.
*/
public GlobalPressureTemperatureModel(final double latitude, final double longitude, final Frame bodyFrame) {
this.bodyFrame = bodyFrame;
this.latitude = latitude;
this.longitude = longitude;
this.temperature = Double.NaN;
this.pressure = Double.NaN;
}
/** Get the atmospheric temperature of the station depending its position.
* @return the temperature in kelvins
*/
public double getTemperature() {
return temperature;
}
/** Get the atmospheric pressure of the station depending its position.
* @return the pressure in hPa
*/
public double getPressure() {
return pressure;
}
@Override
public void weatherParameters(final double height, final AbsoluteDate date) {
// Day of year computation
final DateTimeComponents dtc = date.getComponents(TimeScalesFactory.getUTC());
final int dofyear = dtc.getDate().getDayOfYear();
// Reference day: 28 January 1980 (Niell, 1996)
final int t0 = 28;
final double coef = ((dofyear + 1 - t0) / 365.25) * 2 * FastMath.PI;
final double cosCoef = FastMath.cos(coef);
// Compute Legendre Polynomials Pnm(sin(phi))
final int degree = 9;
final int order = 9;
final LegendrePolynomials p = new LegendrePolynomials(degree, order);
// Geoid for height computation
final Geoid geoid = new Geoid(GravityFieldFactory.getNormalizedProvider(degree, order),
ReferenceEllipsoid.getWgs84(bodyFrame));
// Corrected height
final double correctedheight = FastMath.max(0.0, height - geoid.getUndulation(latitude, longitude, date));
// Eq. 4 (Ref)
double meanT0 = 0.0;
double amplitudeT0 = 0.0;
double meanP0 = 0.0;
double amplitudeP0 = 0.0;
final ABCoefficients abCoef = new ABCoefficients();
int j = 0;
for (int n = 0; n <= 9; n++) {
for (int m = 0; m <= n; m++) {
final double pCosmLambda = p.getPnm(n, m) * FastMath.cos(m * longitude);
final double pSinmLambda = p.getPnm(n, m) * FastMath.sin(m * longitude);
meanT0 = meanT0 +
(abCoef.getAnmTemperatureMean(j) * pCosmLambda + abCoef.getBnmTemperatureMean(j) * pSinmLambda);
amplitudeT0 = amplitudeT0 +
(abCoef.getAnmTemperatureAmpl(j) * pCosmLambda + abCoef.getBnmTemperatureAmpl(j) * pSinmLambda);
meanP0 = meanP0 +
(abCoef.getAnmPressureMean(j) * pCosmLambda + abCoef.getBnmPressureMean(j) * pSinmLambda);
amplitudeP0 = amplitudeP0 +
(abCoef.getAnmPressureAmpl(j) * pCosmLambda + abCoef.getBnmPressureAmpl(j) * pSinmLambda);
j = j + 1;
}
}
// Eq. 3 (Ref)
final double temp0 = meanT0 + amplitudeT0 * cosCoef;
final double pres0 = meanP0 + amplitudeP0 * cosCoef;
// Compute pressure and temperature Eq. 1 and 2 (Ref)
final double degrees = temp0 + TEMPERATURE_GRADIENT * correctedheight;
this.temperature = degrees + 273.15;
this.pressure = pres0 * FastMath.pow(1.0 - correctedheight * 0.0000226, 5.225);
}
/** Computes the P<sub>nm</sub>(sin(Φ)) coefficients of Eq. 4 (Ref).
* The computation of the Legendre polynomials is performed following:
* Heiskanen and Moritz, Physical Geodesy, 1967, eq. 1-62
*/
private class LegendrePolynomials {
/** Array for the Legendre polynomials. */
private double[][] pCoef;
/** Create Legendre polynomials for the given degree and order.
* @param degree degree of the spherical harmonics
* @param order order of the spherical harmonics
*/
LegendrePolynomials(final int degree, final int order) {
this.pCoef = new double[degree + 1][order + 1];
final double t = FastMath.sin(latitude);
final double t2 = t * t;
for (int n = 0; n <= degree; n++) {
// m shall be <= n (Heiskanen and Moritz, 1967, pp 21)
for (int m = 0; m <= FastMath.min(n, order); m++) {
// r = int((n - m) / 2)
final int r = (int) (n - m) / 2;
double sum = 0.;
for (int k = 0; k <= r; k++) {
final double term = FastMath.pow(-1.0, k) * CombinatoricsUtils.factorialDouble(2 * n - 2 * k) /
(CombinatoricsUtils.factorialDouble(k) * CombinatoricsUtils.factorialDouble(n - k) *
CombinatoricsUtils.factorialDouble(n - m - 2 * k)) *
FastMath.pow(t, n - m - 2 * k);
sum = sum + term;
}
pCoef[n][m] = FastMath.pow(2, -n) * FastMath.pow(1.0 - t2, 0.5 * m) * sum;
}
}
}
/** Return the coefficient P<sub>nm</sub>.
* @param n index
* @param m index
* @return The coefficient P<sub>nm</sub>
*/
public double getPnm(final int n, final int m) {
return pCoef[n][m];
}
}
private static class ABCoefficients {
/** Mean A<sub>nm</sub> coefficients for the pressure. */
private static final double[] A_PRESSURE_MEAN = {
1.0108e+03,
8.4886e+00,
1.4799e+00,
-1.3897e+01,
3.7516e-03,
-1.4936e-01,
1.2232e+01,
-7.6615e-01,
-6.7699e-02,
8.1002e-03,
-1.5874e+01,
3.6614e-01,
-6.7807e-02,
-3.6309e-03,
5.9966e-04,
4.8163e+00,
-3.7363e-01,
-7.2071e-02,
1.9998e-03,
-6.2385e-04,
-3.7916e-04,
4.7609e+00,
-3.9534e-01,
8.6667e-03,
1.1569e-02,
1.1441e-03,
-1.4193e-04,
-8.5723e-05,
6.5008e-01,
-5.0889e-01,
-1.5754e-02,
-2.8305e-03,
5.7458e-04,
3.2577e-05,
-9.6052e-06,
-2.7974e-06,
1.3530e+00,
-2.7271e-01,
-3.0276e-04,
3.6286e-03,
-2.0398e-04,
1.5846e-05,
-7.7787e-06,
1.1210e-06,
9.9020e-08,
5.5046e-01,
-2.7312e-01,
3.2532e-03,
-2.4277e-03,
1.1596e-04,
2.6421e-07,
-1.3263e-06,
2.7322e-07,
1.4058e-07,
4.9414e-09
};
/** Mean B<sub>nm</sub> coefficients for the pressure. */
private static final double[] B_PRESSURE_MEAN = {
0.0000e+00,
0.0000e+00,
-1.2878e+00,
0.0000e+00,
7.0444e-01,
3.3222e-01,
0.0000e+00,
-2.9636e-01,
7.2248e-03,
7.9655e-03,
0.0000e+00,
1.0854e+00,
1.1145e-02,
-3.6513e-02,
3.1527e-03,
0.0000e+00,
-4.8434e-01,
5.2023e-02,
-1.3091e-02,
1.8515e-03,
1.5422e-04,
0.0000e+00,
6.8298e-01,
2.5261e-03,
-9.9703e-04,
-1.0829e-03,
+1.7688e-04,
-3.1418e-05,
+0.0000e+00,
-3.7018e-01,
4.3234e-02,
7.2559e-03,
3.1516e-04,
2.0024e-05,
-8.0581e-06,
-2.3653e-06,
0.0000e+00,
1.0298e-01,
-1.5086e-02,
5.6186e-03,
3.2613e-05,
4.0567e-05,
-1.3925e-06,
-3.6219e-07,
-2.0176e-08,
0.0000e+00,
-1.8364e-01,
1.8508e-02,
7.5016e-04,
-9.6139e-05,
-3.1995e-06,
1.3868e-07,
-1.9486e-07,
3.0165e-10,
-6.4376e-10
};
/** Amplitude A<sub>nm</sub> coefficients for the pressure. */
private static final double[] A_PRESSURE_AMPLITUDE = {
-1.0444e-01,
1.6618e-01,
-6.3974e-02,
1.0922e+00,
5.7472e-01,
-3.0277e-01,
-3.5087e+00,
7.1264e-03,
-1.4030e-01,
3.7050e-02,
4.0208e-01,
-3.0431e-01,
-1.3292e-01,
4.6746e-03,
-1.5902e-04,
2.8624e+00,
-3.9315e-01,
-6.4371e-02,
1.6444e-02,
-2.3403e-03,
4.2127e-05,
1.9945e+00,
-6.0907e-01,
-3.5386e-02,
-1.0910e-03,
-1.2799e-04,
4.0970e-05,
2.2131e-05,
-5.3292e-01,
-2.9765e-01,
-3.2877e-02,
1.7691e-03,
5.9692e-05,
3.1725e-05,
2.0741e-05,
-3.7622e-07,
2.6372e+00,
-3.1165e-01,
1.6439e-02,
2.1633e-04,
1.7485e-04,
2.1587e-05,
6.1064e-06,
-1.3755e-08,
-7.8748e-08,
-5.9152e-01,
-1.7676e-01,
8.1807e-03,
1.0445e-03,
2.3432e-04,
9.3421e-06,
2.8104e-06,
-1.5788e-07,
-3.0648e-08,
2.6421e-10
};
/** Amplitude B<sub>nm</sub> coefficients for the pressure. */
private static final double[] B_PRESSURE_AMPLITUDE = {
0.0000e+00,
0.0000e+00,
9.3340e-01,
0.0000e+00,
8.2346e-01,
2.2082e-01,
0.0000e+00,
9.6177e-01,
-1.5650e-02,
1.2708e-03,
0.0000e+00,
-3.9913e-01,
2.8020e-02,
2.8334e-02,
8.5980e-04,
0.0000e+00,
3.0545e-01,
-2.1691e-02,
6.4067e-04,
-3.6528e-05,
-1.1166e-04,
0.0000e+00,
-7.6974e-02,
-1.8986e-02,
+5.6896e-03,
-2.4159e-04,
-2.3033e-04,
-9.6783e-06,
0.0000e+00,
-1.0218e-01,
-1.3916e-02,
-4.1025e-03,
-5.1340e-05,
-7.0114e-05,
-3.3152e-07,
1.6901e-06,
0.0000e+00,
-1.2422e-02,
+2.5072e-03,
+1.1205e-03,
-1.3034e-04,
-2.3971e-05,
-2.6622e-06,
5.7852e-07,
4.5847e-08,
0.0000e+00,
4.4777e-02,
-3.0421e-03,
2.6062e-05,
-7.2421e-05,
1.9119e-06,
3.9236e-07,
2.2390e-07,
2.9765e-09,
-4.6452e-09
};
/** Mean A<sub>nm</sub> coefficients for the temperature. */
private static final double[] A_TEMPERATURE_MEAN = {
1.6257e+01,
2.1224e+00,
9.2569e-01,
-2.5974e+01,
1.4510e+00,
9.2468e-02,
-5.3192e-01,
2.1094e-01,
-6.9210e-02,
-3.4060e-02,
-4.6569e+00,
2.6385e-01,
-3.6093e-02,
1.0198e-02,
-1.8783e-03,
7.4983e-01,
1.1741e-01,
3.9940e-02,
5.1348e-03,
5.9111e-03,
8.6133e-06,
6.3057e-01,
1.5203e-01,
3.9702e-02,
4.6334e-03,
2.4406e-04,
1.5189e-04,
1.9581e-07,
5.4414e-01,
3.5722e-01,
5.2763e-02,
4.1147e-03,
-2.7239e-04,
-5.9957e-05,
1.6394e-06,
-7.3045e-07,
-2.9394e+00,
5.5579e-02,
1.8852e-02,
3.4272e-03,
-2.3193e-05,
-2.9349e-05,
3.6397e-07,
2.0490e-06,
-6.4719e-08,
-5.2225e-01,
2.0799e-01,
1.3477e-03,
3.1613e-04,
-2.2285e-04,
-1.8137e-05,
-1.5177e-07,
6.1343e-07,
7.8566e-08,
1.0749e-09
};
/** Mean B<sub>nm</sub> coefficients for the temperature. */
private static final double[] B_TEMPERATURE_MEAN = {
0.0000e+00,
0.0000e+00,
1.0210e+00,
0.0000e+00,
6.0194e-01,
1.2292e-01,
0.0000e+00,
-4.2184e-01,
1.8230e-01,
4.2329e-02,
0.0000e+00,
9.3312e-02,
9.5346e-02,
-1.9724e-03,
5.8776e-03,
0.0000e+00,
-2.0940e-01,
3.4199e-02,
-5.7672e-03,
-2.1590e-03,
5.6815e-04,
0.0000e+00,
2.2858e-01,
1.2283e-02,
-9.3679e-03,
-1.4233e-03,
-1.5962e-04,
4.0160e-05,
0.0000e+00,
3.6353e-02,
-9.4263e-04,
-3.6762e-03,
5.8608e-05,
-2.6391e-05,
3.2095e-06,
-1.1605e-06,
0.0000e+00,
1.6306e-01,
1.3293e-02,
-1.1395e-03,
5.1097e-05,
3.3977e-05,
7.6449e-06,
-1.7602e-07,
-7.6558e-08,
0.0000e+00,
-4.5415e-02,
-1.8027e-02,
3.6561e-04,
-1.1274e-04,
1.3047e-05,
2.0001e-06,
-1.5152e-07,
-2.7807e-08,
7.7491e-09
};
/** Amplitude A<sub>nm</sub> coefficients for the temperature. */
private static final double[] A_TEMPERATURE_AMPLITUDE = {
-1.8654e+00,
-9.0041e+00,
-1.2974e-01,
-3.6053e+00,
2.0284e-02,
2.1872e-01,
-1.3015e+00,
4.0355e-01,
2.2216e-01,
-4.0605e-03,
1.9623e+00,
4.2887e-01,
2.1437e-01,
-1.0061e-02,
-1.1368e-03,
-6.9235e-02,
5.6758e-01,
1.1917e-01,
-7.0765e-03,
3.0017e-04,
3.0601e-04,
1.6559e+00,
2.0722e-01,
6.0013e-02,
1.7023e-04,
-9.2424e-04,
1.1269e-05,
-6.9911e-06,
-2.0886e+00,
-6.7879e-02,
-8.5922e-04,
-1.6087e-03,
-4.5549e-05,
3.3178e-05,
-6.1715e-06,
-1.4446e-06,
-3.7210e-01,
1.5775e-01,
-1.7827e-03,
-4.4396e-04,
2.2844e-04,
-1.1215e-05,
-2.1120e-06,
-9.6421e-07,
-1.4170e-08,
7.8720e-01,
-4.4238e-02,
-1.5120e-03,
-9.4119e-04,
4.0645e-06,
-4.9253e-06,
-1.8656e-06,
-4.0736e-07,
-4.9594e-08,
1.6134e-09
};
/** Amplitude B<sub>nm</sub> coefficients for the temperature. */
private static final double[] B_TEMPERATURE_AMPLITUDE = {
0.0000e+00,
0.0000e+00,
-8.9895e-01,
0.0000e+00,
-1.0790e+00,
-1.2699e-01,
0.0000e+00,
-5.9033e-01,
3.4865e-02,
-3.2614e-02,
0.0000e+00,
-2.4310e-02,
1.5607e-02,
-2.9833e-02,
-5.9048e-03,
0.0000e+00,
2.8383e-01,
4.0509e-02,
-1.8834e-02,
-1.2654e-03,
-1.3794e-04,
0.0000e+00,
1.3306e-01,
3.4960e-02,
-3.6799e-03,
-3.5626e-04,
1.4814e-04,
3.7932e-06,
0.0000e+00,
2.0801e-01,
6.5640e-03,
-3.4893e-03,
-2.7395e-04,
7.4296e-05,
-7.9927e-06,
-1.0277e-06,
0.0000e+00,
3.6515e-02,
-7.4319e-03,
-6.2873e-04,
8.2461e-05,
3.1095e-05,
-5.3860e-07,
-1.2055e-07,
-1.1517e-07,
0.0000e+00,
3.1404e-02,
1.5580e-02,
-1.1428e-03,
3.3529e-05,
1.0387e-05,
-1.9378e-06,
-2.7327e-07,
7.5833e-09,
-9.2323e-09
};
/** Build a new instance. */
ABCoefficients() {
}
/** Get the value of the mean A<sub>nm</sub> pressure coefficient for the given index.
* @param index index
* @return the mean A<sub>nm</sub> pressure coefficient for the given index
*/
public double getAnmPressureMean(final int index) {
return A_PRESSURE_MEAN[index];
}
/** Get the value of the mean B<sub>nm</sub> pressure coefficient for the given index.
* @param index index
* @return the mean B<sub>nm</sub> pressure coefficient for the given index
*/
public double getBnmPressureMean(final int index) {
return B_PRESSURE_MEAN[index];
}
/** Get the value of the amplitude A<sub>nm</sub> pressure coefficient for the given index.
* @param index index
* @return the amplitude A<sub>nm</sub> pressure coefficient for the given index.
*/
public double getAnmPressureAmpl(final int index) {
return A_PRESSURE_AMPLITUDE[index];
}
/** Get the value of the amplitude B<sub>nm</sub> pressure coefficient for the given index.
* @param index index
* @return the amplitude B<sub>nm</sub> pressure coefficient for the given index
*/
public double getBnmPressureAmpl(final int index) {
return B_PRESSURE_AMPLITUDE[index];
}
/** Get the value of the mean A<sub>nm</sub> temperature coefficient for the given index.
* @param index index
* @return the mean A<sub>nm</sub> temperature coefficient for the given index
*/
public double getAnmTemperatureMean(final int index) {
return A_TEMPERATURE_MEAN[index];
}
/** Get the value of the mean B<sub>nm</sub> temperature coefficient for the given index.
* @param index index
* @return the mean B<sub>nm</sub> temperature coefficient for the given index
*/
public double getBnmTemperatureMean(final int index) {
return B_TEMPERATURE_MEAN[index];
}
/** Get the value of the amplitude A<sub>nm</sub> temperature coefficient for the given index.
* @param index index
* @return the amplitude A<sub>nm</sub> temperature coefficient for the given index.
*/
public double getAnmTemperatureAmpl(final int index) {
return A_TEMPERATURE_AMPLITUDE[index];
}
/** Get the value of the amplitude B<sub>nm</sub> temperature coefficient for the given index.
* @param index index
* @return the amplitude B<sub>nm</sub> temperature coefficient for the given index
*/
public double getBnmTemperatureAmpl(final int index) {
return B_TEMPERATURE_AMPLITUDE[index];
}
}
}