MendesPavlisModel.java
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package org.orekit.models.earth.troposphere;
import java.util.Collections;
import java.util.List;
import org.hipparchus.Field;
import org.hipparchus.CalculusFieldElement;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathArrays;
import org.orekit.bodies.FieldGeodeticPoint;
import org.orekit.bodies.GeodeticPoint;
import org.orekit.time.AbsoluteDate;
import org.orekit.time.FieldAbsoluteDate;
import org.orekit.utils.ParameterDriver;
/** The Mendes - Pavlis tropospheric delay model for optical techniques.
* It is valid for a wide range of wavelengths from 0.355µm to 1.064µm (Mendes and Pavlis, 2003)
*
* @see "Mendes, V. B., & Pavlis, E. C. (2004). High‐accuracy zenith delay prediction at
* optical wavelengths. Geophysical Research Letters, 31(14)."
*
* @see "Petit, G. and Luzum, B. (eds.), IERS Conventions (2010),
* IERS Technical Note No. 36, BKG (2010)"
*
* @author Bryan Cazabonne
*/
public class MendesPavlisModel implements DiscreteTroposphericModel, MappingFunction {
/** Coefficients for the dispertion equation for the hydrostatic component [µm<sup>-2</sup>]. */
private static final double[] K_COEFFICIENTS = {
238.0185, 19990.975, 57.362, 579.55174
};
/** Coefficients for the dispertion equation for the non-hydrostatic component. */
private static final double[] W_COEFFICIENTS = {
295.235, 2.6422, -0.032380, 0.004028
};
/** Coefficients for the mapping function. */
private static final double[][] A_COEFFICIENTS = {
{12100.8e-7, 1729.5e-9, 319.1e-7, -1847.8e-11},
{30496.5e-7, 234.4e-8, -103.5e-6, -185.6e-10},
{6877.7e-5, 197.2e-7, -345.8e-5, 106.0e-9}
};
/** Carbon dioxyde content (IAG recommendations). */
private static final double C02 = 0.99995995;
/** Laser wavelength [µm]. */
private double lambda;
/** The atmospheric pressure [hPa]. */
private double P0;
/** The temperature at the station [K]. */
private double T0;
/** Water vapor pressure at the laser site [hPa]. */
private double e0;
/** Create a new Mendes-Pavlis model for the troposphere.
* This initialisation will compute the water vapor pressure
* thanks to the values of the pressure, the temperature and the humidity
* @param t0 the temperature at the station, K
* @param p0 the atmospheric pressure at the station, hPa
* @param rh the humidity at the station, percent (50% → 0.5)
* @param lambda laser wavelength, µm
* */
public MendesPavlisModel(final double t0, final double p0,
final double rh, final double lambda) {
this.P0 = p0;
this.T0 = t0;
this.e0 = getWaterVapor(rh);
this.lambda = lambda;
}
/** Create a new Mendes-Pavlis model using a standard atmosphere model.
*
* <ul>
* <li>temperature: 18 degree Celsius
* <li>pressure: 1013.25 hPa
* <li>humidity: 50%
* </ul>
*
* @param lambda laser wavelength, µm
*
* @return a Mendes-Pavlis model with standard environmental values
*/
public static MendesPavlisModel getStandardModel(final double lambda) {
return new MendesPavlisModel(273.15 + 18, 1013.25, 0.5, lambda);
}
/** {@inheritDoc} */
@Override
public double pathDelay(final double elevation, final GeodeticPoint point,
final double[] parameters, final AbsoluteDate date) {
// Zenith delay
final double[] zenithDelay = computeZenithDelay(point, parameters, date);
// Mapping function
final double[] mappingFunction = mappingFactors(elevation, point, date);
// Tropospheric path delay
return zenithDelay[0] * mappingFunction[0] + zenithDelay[1] * mappingFunction[1];
}
/** {@inheritDoc} */
@Override
public <T extends CalculusFieldElement<T>> T pathDelay(final T elevation, final FieldGeodeticPoint<T> point,
final T[] parameters, final FieldAbsoluteDate<T> date) {
// Zenith delay
final T[] delays = computeZenithDelay(point, parameters, date);
// Mapping function
final T[] mappingFunction = mappingFactors(elevation, point, date);
// Tropospheric path delay
return delays[0].multiply(mappingFunction[0]).add(delays[1].multiply(mappingFunction[1]));
}
/** This method allows the computation of the zenith hydrostatic and
* zenith wet delay. The resulting element is an array having the following form:
* <ul>
* <li>double[0] = D<sub>hz</sub> → zenith hydrostatic delay
* <li>double[1] = D<sub>wz</sub> → zenith wet delay
* </ul>
* @param point station location
* @param parameters tropospheric model parameters
* @param date current date
* @return a two components array containing the zenith hydrostatic and wet delays.
*/
public double[] computeZenithDelay(final GeodeticPoint point, final double[] parameters, final AbsoluteDate date) {
final double fsite = getSiteFunctionValue(point);
// Array for zenith delay
final double[] delay = new double[2];
// Dispertion Equation for the Hydrostatic component
final double sigma = 1 / lambda;
final double sigma2 = sigma * sigma;
final double coef1 = K_COEFFICIENTS[0] + sigma2;
final double coef2 = K_COEFFICIENTS[0] - sigma2;
final double coef3 = K_COEFFICIENTS[2] + sigma2;
final double coef4 = K_COEFFICIENTS[2] - sigma2;
final double frac1 = coef1 / (coef2 * coef2);
final double frac2 = coef3 / (coef4 * coef4);
final double fLambdaH = 0.01 * (K_COEFFICIENTS[1] * frac1 + K_COEFFICIENTS[3] * frac2) * C02;
// Zenith delay for the hydrostatic component
delay[0] = 0.002416579 * (fLambdaH / fsite) * P0;
// Dispertion Equation for the Non-Hydrostatic component
final double sigma4 = sigma2 * sigma2;
final double sigma6 = sigma4 * sigma2;
final double w1s2 = 3 * W_COEFFICIENTS[1] * sigma2;
final double w2s4 = 5 * W_COEFFICIENTS[2] * sigma4;
final double w3s6 = 7 * W_COEFFICIENTS[3] * sigma6;
final double fLambdaNH = 0.003101 * (W_COEFFICIENTS[0] + w1s2 + w2s4 + w3s6);
// Zenith delay for the non-hydrostatic component
delay[1] = 0.0001 * (5.316 * fLambdaNH - 3.759 * fLambdaH) * (e0 / fsite);
return delay;
}
/** This method allows the computation of the zenith hydrostatic and
* zenith wet delay. The resulting element is an array having the following form:
* <ul>
* <li>T[0] = D<sub>hz</sub> → zenith hydrostatic delay
* <li>T[1] = D<sub>wz</sub> → zenith wet delay
* </ul>
* @param <T> type of the elements
* @param point station location
* @param parameters tropospheric model parameters
* @param date current date
* @return a two components array containing the zenith hydrostatic and wet delays.
*/
public <T extends CalculusFieldElement<T>> T[] computeZenithDelay(final FieldGeodeticPoint<T> point, final T[] parameters,
final FieldAbsoluteDate<T> date) {
final Field<T> field = date.getField();
final T zero = field.getZero();
final T fsite = getSiteFunctionValue(point);
// Array for zenith delay
final T[] delay = MathArrays.buildArray(field, 2);
// Dispertion Equation for the Hydrostatic component
final T sigma = zero.add(1 / lambda);
final T sigma2 = sigma.multiply(sigma);
final T coef1 = sigma2.add(K_COEFFICIENTS[0]);
final T coef2 = sigma2.negate().add(K_COEFFICIENTS[0]);
final T coef3 = sigma2.add(K_COEFFICIENTS[2]);
final T coef4 = sigma2.negate().add(K_COEFFICIENTS[2]);
final T frac1 = coef1.divide(coef2.multiply(coef2));
final T frac2 = coef3.divide(coef4.multiply(coef4));
final T fLambdaH = frac1.multiply(K_COEFFICIENTS[1]).add(frac2.multiply(K_COEFFICIENTS[3])).multiply(0.01 * C02);
// Zenith delay for the hydrostatic component
delay[0] = fLambdaH.divide(fsite).multiply(P0).multiply(0.002416579);
// Dispertion Equation for the Non-Hydrostatic component
final T sigma4 = sigma2.multiply(sigma2);
final T sigma6 = sigma4.multiply(sigma2);
final T w1s2 = sigma2.multiply(3 * W_COEFFICIENTS[1]);
final T w2s4 = sigma4.multiply(5 * W_COEFFICIENTS[2]);
final T w3s6 = sigma6.multiply(7 * W_COEFFICIENTS[3]);
final T fLambdaNH = w1s2.add(w2s4).add(w3s6).add(W_COEFFICIENTS[0]).multiply(0.003101);
// Zenith delay for the non-hydrostatic component
delay[1] = fLambdaNH.multiply(5.316).subtract(fLambdaH.multiply(3.759)).multiply(fsite.divide(e0).reciprocal()).multiply(0.0001);
return delay;
}
/** With the Mendes Pavlis tropospheric model, the mapping
* function is not split into hydrostatic and wet component.
* <p>
* Therefore, the two components of the resulting array are equals.
* <ul>
* <li>double[0] = m(e) → total mapping function
* <li>double[1] = m(e) → total mapping function
* </ul>
* <p>
* The total delay will thus be computed as:<br>
* δ = D<sub>hz</sub> * m(e) + D<sub>wz</sub> * m(e)<br>
* δ = (D<sub>hz</sub> + D<sub>wz</sub>) * m(e) = δ<sub>z</sub> * m(e)
*/
@Override
public double[] mappingFactors(final double elevation, final GeodeticPoint point,
final AbsoluteDate date) {
final double sinE = FastMath.sin(elevation);
final double T2degree = T0 - 273.15;
// Mapping function coefficients
final double a1 = computeMFCoeffient(A_COEFFICIENTS[0][0], A_COEFFICIENTS[0][1],
A_COEFFICIENTS[0][2], A_COEFFICIENTS[0][3],
T2degree, point);
final double a2 = computeMFCoeffient(A_COEFFICIENTS[1][0], A_COEFFICIENTS[1][1],
A_COEFFICIENTS[1][2], A_COEFFICIENTS[1][3],
T2degree, point);
final double a3 = computeMFCoeffient(A_COEFFICIENTS[2][0], A_COEFFICIENTS[2][1],
A_COEFFICIENTS[2][2], A_COEFFICIENTS[2][3],
T2degree, point);
// Numerator
final double numMP = 1 + a1 / (1 + a2 / (1 + a3));
// Denominator
final double denMP = sinE + a1 / (sinE + a2 / (sinE + a3));
final double factor = numMP / denMP;
return new double[] {
factor,
factor
};
}
/** With the Mendes Pavlis tropospheric model, the mapping
* function is not split into hydrostatic and wet component.
* <p>
* Therefore, the two components of the resulting array are equals.
* <ul>
* <li>double[0] = m(e) → total mapping function
* <li>double[1] = m(e) → total mapping function
* </ul>
* <p>
* The total delay will thus be computed as:<br>
* δ = D<sub>hz</sub> * m(e) + D<sub>wz</sub> * m(e)<br>
* δ = (D<sub>hz</sub> + D<sub>wz</sub>) * m(e) = δ<sub>z</sub> * m(e)
*/
@Override
public <T extends CalculusFieldElement<T>> T[] mappingFactors(final T elevation, final FieldGeodeticPoint<T> point,
final FieldAbsoluteDate<T> date) {
final Field<T> field = date.getField();
final T sinE = FastMath.sin(elevation);
final double T2degree = T0 - 273.15;
// Mapping function coefficients
final T a1 = computeMFCoeffient(A_COEFFICIENTS[0][0], A_COEFFICIENTS[0][1],
A_COEFFICIENTS[0][2], A_COEFFICIENTS[0][3],
T2degree, point);
final T a2 = computeMFCoeffient(A_COEFFICIENTS[1][0], A_COEFFICIENTS[1][1],
A_COEFFICIENTS[1][2], A_COEFFICIENTS[1][3],
T2degree, point);
final T a3 = computeMFCoeffient(A_COEFFICIENTS[2][0], A_COEFFICIENTS[2][1],
A_COEFFICIENTS[2][2], A_COEFFICIENTS[2][3],
T2degree, point);
// Numerator
final T numMP = a1.divide(a2.divide(a3.add(1.0)).add(1.0)).add(1.0);
// Denominator
final T denMP = a1.divide(a2.divide(a3.add(sinE)).add(sinE)).add(sinE);
final T factor = numMP.divide(denMP);
final T[] mapping = MathArrays.buildArray(field, 2);
mapping[0] = factor;
mapping[1] = factor;
return mapping;
}
/** {@inheritDoc} */
@Override
public List<ParameterDriver> getParametersDrivers() {
return Collections.emptyList();
}
/** Get the laser frequency parameter f(lambda).
*
* @param point station location
* @return the laser frequency parameter f(lambda).
*/
private double getSiteFunctionValue(final GeodeticPoint point) {
return 1. - 0.00266 * FastMath.cos(2. * point.getLatitude()) - 0.00000028 * point.getAltitude();
}
/** Get the laser frequency parameter f(lambda).
*
* @param <T> type of the elements
* @param point station location
* @return the laser frequency parameter f(lambda).
*/
private <T extends CalculusFieldElement<T>> T getSiteFunctionValue(final FieldGeodeticPoint<T> point) {
return FastMath.cos(point.getLatitude().multiply(2.)).multiply(0.00266).add(point.getAltitude().multiply(0.00000028)).negate().add(1.);
}
/** Compute the coefficients of the Mapping Function.
*
* @param T the temperature at the station site, °C
* @param a0 first coefficient
* @param a1 second coefficient
* @param a2 third coefficient
* @param a3 fourth coefficient
* @param point station location
* @return the value of the coefficient
*/
private double computeMFCoeffient(final double a0, final double a1, final double a2, final double a3,
final double T, final GeodeticPoint point) {
return a0 + a1 * T + a2 * FastMath.cos(point.getLatitude()) + a3 * point.getAltitude();
}
/** Compute the coefficients of the Mapping Function.
*
* @param <T> type of the elements
* @param T the temperature at the station site, °C
* @param a0 first coefficient
* @param a1 second coefficient
* @param a2 third coefficient
* @param a3 fourth coefficient
* @param point station location
* @return the value of the coefficient
*/
private <T extends CalculusFieldElement<T>> T computeMFCoeffient(final double a0, final double a1, final double a2, final double a3,
final double T, final FieldGeodeticPoint<T> point) {
return point.getAltitude().multiply(a3).add(FastMath.cos(point.getLatitude()).multiply(a2)).add(a0 + a1 * T);
}
/** Get the water vapor.
* The water vapor model is the one of Giacomo and Davis as indicated in IERS TN 32, chap. 9.
*
* See: Giacomo, P., Equation for the dertermination of the density of moist air, Metrologia, V. 18, 1982
*
* @param rh relative humidity, in percent (50% → 0.5).
* @return the water vapor, in mbar (1 mbar = 1 hPa).
*/
private double getWaterVapor(final double rh) {
// saturation water vapor, equation (3) of reference paper, in mbar
// with amended 1991 values (see reference paper)
final double es = 0.01 * FastMath.exp((1.2378847 * 1e-5) * T0 * T0 -
(1.9121316 * 1e-2) * T0 +
33.93711047 -
(6.3431645 * 1e3) * 1. / T0);
// enhancement factor, equation (4) of reference paper
final double fw = 1.00062 + (3.14 * 1e-6) * P0 + (5.6 * 1e-7) * FastMath.pow(T0 - 273.15, 2);
final double e = rh * fw * es;
return e;
}
}