OceanLoading.java
/* Copyright 2002-2024 CS GROUP
* Licensed to CS GROUP (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.displacement;
import java.util.HashMap;
import java.util.Map;
import java.util.function.Function;
import org.hipparchus.analysis.UnivariateFunction;
import org.hipparchus.analysis.interpolation.SplineInterpolator;
import org.hipparchus.analysis.polynomials.PolynomialSplineFunction;
import org.hipparchus.geometry.euclidean.threed.Vector3D;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.SinCos;
import org.orekit.bodies.GeodeticPoint;
import org.orekit.bodies.OneAxisEllipsoid;
import org.orekit.data.BodiesElements;
import org.orekit.frames.Frame;
/**
* Modeling of displacement of reference points due to ocean loading.
* <p>
* This class implements the same model as IERS HARDIP.F program. For a
* given site, this model uses a set of amplitudes and phases for the 11
* main tides (M₂, S₂, N₂, K₂, K₁, O₁, P₁, Q₁, Mf, Mm, and Ssa) in BLQ
* format as provided by the <a
* href="http://holt.oso.chalmers.se/loading/">Bos-Scherneck web site</a>
* at Onsala Space Observatory. From these elements, additional admittances
* are derived using spline interpolation based on tides frequencies for
* a total of 342 tides, including the 11 main tides.
* </p>
* <p>
* This implementation is a complete rewrite of the original HARDISP.F program
* developed by Duncan Agnew and copyright 2008 IERS Conventions center. This
* derived work is not endorsed by the IERS conventions center. What remains
* from the original program is the model (spline interpolation and coefficients).
* The code by itself is completely different, using the underlying mathematical
* library for spline interpolation and the existing Orekit features for nutation
* arguments, time and time scales handling, tides modeling...
* </p>
* <p>
* Instances of this class are guaranteed to be immutable
* </p>
* <p>
* The original HARDISP.F program is distributed with the following notice:
* </p>
* <pre>
* Copyright (C) 2008
* IERS Conventions Center
*
* ==================================
* IERS Conventions Software License
* ==================================
*
* NOTICE TO USER:
*
* BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING TERMS AND CONDITIONS
* WHICH APPLY TO ITS USE.
*
* 1. The Software is provided by the IERS Conventions Center ("the
* Center").
*
* 2. Permission is granted to anyone to use the Software for any
* purpose, including commercial applications, free of charge,
* subject to the conditions and restrictions listed below.
*
* 3. You (the user) may adapt the Software and its algorithms for your
* own purposes and you may distribute the resulting "derived work"
* to others, provided that the derived work complies with the
* following requirements:
*
* a) Your work shall be clearly identified so that it cannot be
* mistaken for IERS Conventions software and that it has been
* neither distributed by nor endorsed by the Center.
*
* b) Your work (including source code) must contain descriptions of
* how the derived work is based upon and/or differs from the
* original Software.
*
* c) The name(s) of all modified routine(s) that you distribute
* shall be changed.
*
* d) The origin of the IERS Conventions components of your derived
* work must not be misrepresented; you must not claim that you
* wrote the original Software.
*
* e) The source code must be included for all routine(s) that you
* distribute. This notice must be reproduced intact in any
* source distribution.
*
* 4. In any published work produced by the user and which includes
* results achieved by using the Software, you shall acknowledge
* that the Software was used in obtaining those results.
*
* 5. The Software is provided to the user "as is" and the Center makes
* no warranty as to its use or performance. The Center does not
* and cannot warrant the performance or results which the user may
* obtain by using the Software. The Center makes no warranties,
* express or implied, as to non-infringement of third party rights,
* merchantability, or fitness for any particular purpose. In no
* event will the Center be liable to the user for any consequential,
* incidental, or special damages, including any lost profits or lost
* savings, even if a Center representative has been advised of such
* damages, or for any claim by any third party.
*
* Correspondence concerning IERS Conventions software should be
* addressed as follows:
*
* Gerard Petit
* Internet email: gpetit[at]bipm.org
* Postal address: IERS Conventions Center
* Time, frequency and gravimetry section, BIPM
* Pavillon de Breteuil
* 92312 Sevres FRANCE
*
* or
*
* Brian Luzum
* Internet email: brian.luzum[at]usno.navy.mil
* Postal address: IERS Conventions Center
* Earth Orientation Department
* 3450 Massachusetts Ave, NW
* Washington, DC 20392
* </pre>
* @see org.orekit.estimation.measurements.GroundStation
* @since 9.1
* @author Luc Maisonobe
*/
public class OceanLoading implements StationDisplacement {
// CHECKSTYLE: stop Indentation check
/** Amplitudes of all tides used. */
private static final double[] CARTWRIGHT_EDDEN_AMPLITUDE = {
0.632208, 0.294107, 0.121046, 0.079915, 0.023818, -0.023589, 0.022994,
0.019333, -0.017871, 0.017192, 0.016018, 0.004671, -0.004662, -0.004519,
0.004470, 0.004467, 0.002589, -0.002455, -0.002172, 0.001972, 0.001947,
0.001914, -0.001898, 0.001802, 0.001304, 0.001170, 0.001130, 0.001061,
-0.001022, -0.001017, 0.001014, 0.000901, -0.000857, 0.000855, 0.000855,
0.000772, 0.000741, 0.000741, -0.000721, 0.000698, 0.000658, 0.000654,
-0.000653, 0.000633, 0.000626, -0.000598, 0.000590, 0.000544, 0.000479,
-0.000464, 0.000413, -0.000390, 0.000373, 0.000366, 0.000366, -0.000360,
-0.000355, 0.000354, 0.000329, 0.000328, 0.000319, 0.000302, 0.000279,
-0.000274, -0.000272, 0.000248, -0.000225, 0.000224, -0.000223, -0.000216,
0.000211, 0.000209, 0.000194, 0.000185, -0.000174, -0.000171, 0.000159,
0.000131, 0.000127, 0.000120, 0.000118, 0.000117, 0.000108, 0.000107,
0.000105, -0.000102, 0.000102, 0.000099, -0.000096, 0.000095, -0.000089,
-0.000085, -0.000084, -0.000081, -0.000077, -0.000072, -0.000067, 0.000066,
0.000064, 0.000063, 0.000063, 0.000063, 0.000062, 0.000062, -0.000060,
0.000056, 0.000053, 0.000051, 0.000050, 0.368645, -0.262232, -0.121995,
-0.050208, 0.050031, -0.049470, 0.020620, 0.020613, 0.011279, -0.009530,
-0.009469, -0.008012, 0.007414, -0.007300, 0.007227, -0.007131, -0.006644,
0.005249, 0.004137, 0.004087, 0.003944, 0.003943, 0.003420, 0.003418,
0.002885, 0.002884, 0.002160, -0.001936, 0.001934, -0.001798, 0.001690,
0.001689, 0.001516, 0.001514, -0.001511, 0.001383, 0.001372, 0.001371,
-0.001253, -0.001075, 0.001020, 0.000901, 0.000865, -0.000794, 0.000788,
0.000782, -0.000747, -0.000745, 0.000670, -0.000603, -0.000597, 0.000542,
0.000542, -0.000541, -0.000469, -0.000440, 0.000438, 0.000422, 0.000410,
-0.000374, -0.000365, 0.000345, 0.000335, -0.000321, -0.000319, 0.000307,
0.000291, 0.000290, -0.000289, 0.000286, 0.000275, 0.000271, 0.000263,
-0.000245, 0.000225, 0.000225, 0.000221, -0.000202, -0.000200, -0.000199,
0.000192, 0.000183, 0.000183, 0.000183, -0.000170, 0.000169, 0.000168,
0.000162, 0.000149, -0.000147, -0.000141, 0.000138, 0.000136, 0.000136,
0.000127, 0.000127, -0.000126, -0.000121, -0.000121, 0.000117, -0.000116,
-0.000114, -0.000114, -0.000114, 0.000114, 0.000113, 0.000109, 0.000108,
0.000106, -0.000106, -0.000106, 0.000105, 0.000104, -0.000103, -0.000100,
-0.000100, -0.000100, 0.000099, -0.000098, 0.000093, 0.000093, 0.000090,
-0.000088, 0.000083, -0.000083, -0.000082, -0.000081, -0.000079, -0.000077,
-0.000075, -0.000075, -0.000075, 0.000071, 0.000071, -0.000071, 0.000068,
0.000068, 0.000065, 0.000065, 0.000064, 0.000064, 0.000064, -0.000064,
-0.000060, 0.000056, 0.000056, 0.000053, 0.000053, 0.000053, -0.000053,
0.000053, 0.000053, 0.000052, 0.000050, -0.066607, -0.035184, -0.030988,
0.027929, -0.027616, -0.012753, -0.006728, -0.005837, -0.005286, -0.004921,
-0.002884, -0.002583, -0.002422, 0.002310, 0.002283, -0.002037, 0.001883,
-0.001811, -0.001687, -0.001004, -0.000925, -0.000844, 0.000766, 0.000766,
-0.000700, -0.000495, -0.000492, 0.000491, 0.000483, 0.000437, -0.000416,
-0.000384, 0.000374, -0.000312, -0.000288, -0.000273, 0.000259, 0.000245,
-0.000232, 0.000229, -0.000216, 0.000206, -0.000204, -0.000202, 0.000200,
0.000195, -0.000190, 0.000187, 0.000180, -0.000179, 0.000170, 0.000153,
-0.000137, -0.000119, -0.000119, -0.000112, -0.000110, -0.000110, 0.000107,
-0.000095, -0.000095, -0.000091, -0.000090, -0.000081, -0.000079, -0.000079,
0.000077, -0.000073, 0.000069, -0.000067, -0.000066, 0.000065, 0.000064,
-0.000062, 0.000060, 0.000059, -0.000056, 0.000055, -0.000051
};
// CHECKSTYLE: resume Indentation check
// CHECKSTYLE: stop NoWhitespaceAfter check
/** Doodson arguments for all tides used. */
private static final int[][] DOODSON_ARGUMENTS = {
{ 2, 0, 0, 0, 0, 0 }, { 2, 2, -2, 0, 0, 0 }, { 2, -1, 0, 1, 0, 0 },
{ 2, 2, 0, 0, 0, 0 }, { 2, 2, 0, 0, 1, 0 }, { 2, 0, 0, 0, -1, 0 },
{ 2, -1, 2, -1, 0, 0 }, { 2, -2, 2, 0, 0, 0 }, { 2, 1, 0, -1, 0, 0 },
{ 2, 2, -3, 0, 0, 1 }, { 2, -2, 0, 2, 0, 0 }, { 2, -3, 2, 1, 0, 0 },
{ 2, 1, -2, 1, 0, 0 }, { 2, -1, 0, 1, -1, 0 }, { 2, 3, 0, -1, 0, 0 },
{ 2, 1, 0, 1, 0, 0 }, { 2, 2, 0, 0, 2, 0 }, { 2, 2, -1, 0, 0, -1 },
{ 2, 0, -1, 0, 0, 1 }, { 2, 1, 0, 1, 1, 0 }, { 2, 3, 0, -1, 1, 0 },
{ 2, 0, 1, 0, 0, -1 }, { 2, 0, -2, 2, 0, 0 }, { 2, -3, 0, 3, 0, 0 },
{ 2, -2, 3, 0, 0, -1 }, { 2, 4, 0, 0, 0, 0 }, { 2, -1, 1, 1, 0, -1 },
{ 2, -1, 3, -1, 0, -1 }, { 2, 2, 0, 0, -1, 0 }, { 2, -1, -1, 1, 0, 1 },
{ 2, 4, 0, 0, 1, 0 }, { 2, -3, 4, -1, 0, 0 }, { 2, -1, 2, -1, -1, 0 },
{ 2, 3, -2, 1, 0, 0 }, { 2, 1, 2, -1, 0, 0 }, { 2, -4, 2, 2, 0, 0 },
{ 2, 4, -2, 0, 0, 0 }, { 2, 0, 2, 0, 0, 0 }, { 2, -2, 2, 0, -1, 0 },
{ 2, 2, -4, 0, 0, 2 }, { 2, 2, -2, 0, -1, 0 }, { 2, 1, 0, -1, -1, 0 },
{ 2, -1, 1, 0, 0, 0 }, { 2, 2, -1, 0, 0, 1 }, { 2, 2, 1, 0, 0, -1 },
{ 2, -2, 0, 2, -1, 0 }, { 2, -2, 4, -2, 0, 0 }, { 2, 2, 2, 0, 0, 0 },
{ 2, -4, 4, 0, 0, 0 }, { 2, -1, 0, -1, -2, 0 }, { 2, 1, 2, -1, 1, 0 },
{ 2, -1, -2, 3, 0, 0 }, { 2, 3, -2, 1, 1, 0 }, { 2, 4, 0, -2, 0, 0 },
{ 2, 0, 0, 2, 0, 0 }, { 2, 0, 2, -2, 0, 0 }, { 2, 0, 2, 0, 1, 0 },
{ 2, -3, 3, 1, 0, -1 }, { 2, 0, 0, 0, -2, 0 }, { 2, 4, 0, 0, 2, 0 },
{ 2, 4, -2, 0, 1, 0 }, { 2, 0, 0, 0, 0, 2 }, { 2, 1, 0, 1, 2, 0 },
{ 2, 0, -2, 0, -2, 0 }, { 2, -2, 1, 0, 0, 1 }, { 2, -2, 1, 2, 0, -1 },
{ 2, -1, 1, -1, 0, 1 }, { 2, 5, 0, -1, 0, 0 }, { 2, 1, -3, 1, 0, 1 },
{ 2, -2, -1, 2, 0, 1 }, { 2, 3, 0, -1, 2, 0 }, { 2, 1, -2, 1, -1, 0 },
{ 2, 5, 0, -1, 1, 0 }, { 2, -4, 0, 4, 0, 0 }, { 2, -3, 2, 1, -1, 0 },
{ 2, -2, 1, 1, 0, 0 }, { 2, 4, 0, -2, 1, 0 }, { 2, 0, 0, 2, 1, 0 },
{ 2, -5, 4, 1, 0, 0 }, { 2, 0, 2, 0, 2, 0 }, { 2, -1, 2, 1, 0, 0 },
{ 2, 5, -2, -1, 0, 0 }, { 2, 1, -1, 0, 0, 0 }, { 2, 2, -2, 0, 0, 2 },
{ 2, -5, 2, 3, 0, 0 }, { 2, -1, -2, 1, -2, 0 }, { 2, -3, 5, -1, 0, -1 },
{ 2, -1, 0, 0, 0, 1 }, { 2, -2, 0, 0, -2, 0 }, { 2, 0, -1, 1, 0, 0 },
{ 2, -3, 1, 1, 0, 1 }, { 2, 3, 0, -1, -1, 0 }, { 2, 1, 0, 1, -1, 0 },
{ 2, -1, 2, 1, 1, 0 }, { 2, 0, -3, 2, 0, 1 }, { 2, 1, -1, -1, 0, 1 },
{ 2, -3, 0, 3, -1, 0 }, { 2, 0, -2, 2, -1, 0 }, { 2, -4, 3, 2, 0, -1 },
{ 2, -1, 0, 1, -2, 0 }, { 2, 5, 0, -1, 2, 0 }, { 2, -4, 5, 0, 0, -1 },
{ 2, -2, 4, 0, 0, -2 }, { 2, -1, 0, 1, 0, 2 }, { 2, -2, -2, 4, 0, 0 },
{ 2, 3, -2, -1, -1, 0 }, { 2, -2, 5, -2, 0, -1 }, { 2, 0, -1, 0, -1, 1 },
{ 2, 5, -2, -1, 1, 0 }, { 1, 1, 0, 0, 0, 0 }, { 1, -1, 0, 0, 0, 0 },
{ 1, 1, -2, 0, 0, 0 }, { 1, -2, 0, 1, 0, 0 }, { 1, 1, 0, 0, 1, 0 },
{ 1, -1, 0, 0, -1, 0 }, { 1, 2, 0, -1, 0, 0 }, { 1, 0, 0, 1, 0, 0 },
{ 1, 3, 0, 0, 0, 0 }, { 1, -2, 2, -1, 0, 0 }, { 1, -2, 0, 1, -1, 0 },
{ 1, -3, 2, 0, 0, 0 }, { 1, 0, 0, -1, 0, 0 }, { 1, 1, 0, 0, -1, 0 },
{ 1, 3, 0, 0, 1, 0 }, { 1, 1, -3, 0, 0, 1 }, { 1, -3, 0, 2, 0, 0 },
{ 1, 1, 2, 0, 0, 0 }, { 1, 0, 0, 1, 1, 0 }, { 1, 2, 0, -1, 1, 0 },
{ 1, 0, 2, -1, 0, 0 }, { 1, 2, -2, 1, 0, 0 }, { 1, 3, -2, 0, 0, 0 },
{ 1, -1, 2, 0, 0, 0 }, { 1, 1, 1, 0, 0, -1 }, { 1, 1, -1, 0, 0, 1 },
{ 1, 4, 0, -1, 0, 0 }, { 1, -4, 2, 1, 0, 0 }, { 1, 0, -2, 1, 0, 0 },
{ 1, -2, 2, -1, -1, 0 }, { 1, 3, 0, -2, 0, 0 }, { 1, -1, 0, 2, 0, 0 },
{ 1, -1, 0, 0, -2, 0 }, { 1, 3, 0, 0, 2, 0 }, { 1, -3, 2, 0, -1, 0 },
{ 1, 4, 0, -1, 1, 0 }, { 1, 0, 0, -1, -1, 0 }, { 1, 1, -2, 0, -1, 0 },
{ 1, -3, 0, 2, -1, 0 }, { 1, 1, 0, 0, 2, 0 }, { 1, 1, -1, 0, 0, -1 },
{ 1, -1, -1, 0, 0, 1 }, { 1, 0, 2, -1, 1, 0 }, { 1, -1, 1, 0, 0, -1 },
{ 1, -1, -2, 2, 0, 0 }, { 1, 2, -2, 1, 1, 0 }, { 1, -4, 0, 3, 0, 0 },
{ 1, -1, 2, 0, 1, 0 }, { 1, 3, -2, 0, 1, 0 }, { 1, 2, 0, -1, -1, 0 },
{ 1, 0, 0, 1, -1, 0 }, { 1, -2, 2, 1, 0, 0 }, { 1, 4, -2, -1, 0, 0 },
{ 1, -3, 3, 0, 0, -1 }, { 1, -2, 1, 1, 0, -1 }, { 1, -2, 3, -1, 0, -1 },
{ 1, 0, -2, 1, -1, 0 }, { 1, -2, -1, 1, 0, 1 }, { 1, 4, -2, 1, 0, 0 },
{ 1, -4, 4, -1, 0, 0 }, { 1, -4, 2, 1, -1, 0 }, { 1, 5, -2, 0, 0, 0 },
{ 1, 3, 0, -2, 1, 0 }, { 1, -5, 2, 2, 0, 0 }, { 1, 2, 0, 1, 0, 0 },
{ 1, 1, 3, 0, 0, -1 }, { 1, -2, 0, 1, -2, 0 }, { 1, 4, 0, -1, 2, 0 },
{ 1, 1, -4, 0, 0, 2 }, { 1, 5, 0, -2, 0, 0 }, { 1, -1, 0, 2, 1, 0 },
{ 1, -2, 1, 0, 0, 0 }, { 1, 4, -2, 1, 1, 0 }, { 1, -3, 4, -2, 0, 0 },
{ 1, -1, 3, 0, 0, -1 }, { 1, 3, -3, 0, 0, 1 }, { 1, 5, -2, 0, 1, 0 },
{ 1, 1, 2, 0, 1, 0 }, { 1, 2, 0, 1, 1, 0 }, { 1, -5, 4, 0, 0, 0 },
{ 1, -2, 0, -1, -2, 0 }, { 1, 5, 0, -2, 1, 0 }, { 1, 1, 2, -2, 0, 0 },
{ 1, 1, -2, 2, 0, 0 }, { 1, -2, 2, 1, 1, 0 }, { 1, 0, 3, -1, 0, -1 },
{ 1, 2, -3, 1, 0, 1 }, { 1, -2, -2, 3, 0, 0 }, { 1, -1, 2, -2, 0, 0 },
{ 1, -4, 3, 1, 0, -1 }, { 1, -4, 0, 3, -1, 0 }, { 1, -1, -2, 2, -1, 0 },
{ 1, -2, 0, 3, 0, 0 }, { 1, 4, 0, -3, 0, 0 }, { 1, 0, 1, 1, 0, -1 },
{ 1, 2, -1, -1, 0, 1 }, { 1, 2, -2, 1, -1, 0 }, { 1, 0, 0, -1, -2, 0 },
{ 1, 2, 0, 1, 2, 0 }, { 1, 2, -2, -1, -1, 0 }, { 1, 0, 0, 1, 2, 0 },
{ 1, 0, 1, 0, 0, 0 }, { 1, 2, -1, 0, 0, 0 }, { 1, 0, 2, -1, -1, 0 },
{ 1, -1, -2, 0, -2, 0 }, { 1, -3, 1, 0, 0, 1 }, { 1, 3, -2, 0, -1, 0 },
{ 1, -1, -1, 0, -1, 1 }, { 1, 4, -2, -1, 1, 0 }, { 1, 2, 1, -1, 0, -1 },
{ 1, 0, -1, 1, 0, 1 }, { 1, -2, 4, -1, 0, 0 }, { 1, 4, -4, 1, 0, 0 },
{ 1, -3, 1, 2, 0, -1 }, { 1, -3, 3, 0, -1, -1 }, { 1, 1, 2, 0, 2, 0 },
{ 1, 1, -2, 0, -2, 0 }, { 1, 3, 0, 0, 3, 0 }, { 1, -1, 2, 0, -1, 0 },
{ 1, -2, 1, -1, 0, 1 }, { 1, 0, -3, 1, 0, 1 }, { 1, -3, -1, 2, 0, 1 },
{ 1, 2, 0, -1, 2, 0 }, { 1, 6, -2, -1, 0, 0 }, { 1, 2, 2, -1, 0, 0 },
{ 1, -1, 1, 0, -1, -1 }, { 1, -2, 3, -1, -1, -1 }, { 1, -1, 0, 0, 0, 2 },
{ 1, -5, 0, 4, 0, 0 }, { 1, 1, 0, 0, 0, -2 }, { 1, -2, 1, 1, -1, -1 },
{ 1, 1, -1, 0, 1, 1 }, { 1, 1, 2, 0, 0, -2 }, { 1, -3, 1, 1, 0, 0 },
{ 1, -4, 4, -1, -1, 0 }, { 1, 1, 0, -2, -1, 0 }, { 1, -2, -1, 1, -1, 1 },
{ 1, -3, 2, 2, 0, 0 }, { 1, 5, -2, -2, 0, 0 }, { 1, 3, -4, 2, 0, 0 },
{ 1, 1, -2, 0, 0, 2 }, { 1, -1, 4, -2, 0, 0 }, { 1, 2, 2, -1, 1, 0 },
{ 1, -5, 2, 2, -1, 0 }, { 1, 1, -3, 0, -1, 1 }, { 1, 1, 1, 0, 1, -1 },
{ 1, 6, -2, -1, 1, 0 }, { 1, -2, 2, -1, -2, 0 }, { 1, 4, -2, 1, 2, 0 },
{ 1, -6, 4, 1, 0, 0 }, { 1, 5, -4, 0, 0, 0 }, { 1, -3, 4, 0, 0, 0 },
{ 1, 1, 2, -2, 1, 0 }, { 1, -2, 1, 0, -1, 0 }, { 0, 2, 0, 0, 0, 0 },
{ 0, 1, 0, -1, 0, 0 }, { 0, 0, 2, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0 },
{ 0, 2, 0, 0, 1, 0 }, { 0, 3, 0, -1, 0, 0 }, { 0, 1, -2, 1, 0, 0 },
{ 0, 2, -2, 0, 0, 0 }, { 0, 3, 0, -1, 1, 0 }, { 0, 0, 1, 0, 0, -1 },
{ 0, 2, 0, -2, 0, 0 }, { 0, 2, 0, 0, 2, 0 }, { 0, 3, -2, 1, 0, 0 },
{ 0, 1, 0, -1, -1, 0 }, { 0, 1, 0, -1, 1, 0 }, { 0, 4, -2, 0, 0, 0 },
{ 0, 1, 0, 1, 0, 0 }, { 0, 0, 3, 0, 0, -1 }, { 0, 4, 0, -2, 0, 0 },
{ 0, 3, -2, 1, 1, 0 }, { 0, 3, -2, -1, 0, 0 }, { 0, 4, -2, 0, 1, 0 },
{ 0, 0, 2, 0, 1, 0 }, { 0, 1, 0, 1, 1, 0 }, { 0, 4, 0, -2, 1, 0 },
{ 0, 3, 0, -1, 2, 0 }, { 0, 5, -2, -1, 0, 0 }, { 0, 1, 2, -1, 0, 0 },
{ 0, 1, -2, 1, -1, 0 }, { 0, 1, -2, 1, 1, 0 }, { 0, 2, -2, 0, -1, 0 },
{ 0, 2, -3, 0, 0, 1 }, { 0, 2, -2, 0, 1, 0 }, { 0, 0, 2, -2, 0, 0 },
{ 0, 1, -3, 1, 0, 1 }, { 0, 0, 0, 0, 2, 0 }, { 0, 0, 1, 0, 0, 1 },
{ 0, 1, 2, -1, 1, 0 }, { 0, 3, 0, -3, 0, 0 }, { 0, 2, 1, 0, 0, -1 },
{ 0, 1, -1, -1, 0, 1 }, { 0, 1, 0, 1, 2, 0 }, { 0, 5, -2, -1, 1, 0 },
{ 0, 2, -1, 0, 0, 1 }, { 0, 2, 2, -2, 0, 0 }, { 0, 1, -1, 0, 0, 0 },
{ 0, 5, 0, -3, 0, 0 }, { 0, 2, 0, -2, 1, 0 }, { 0, 1, 1, -1, 0, -1 },
{ 0, 3, -4, 1, 0, 0 }, { 0, 0, 2, 0, 2, 0 }, { 0, 2, 0, -2, -1, 0 },
{ 0, 4, -3, 0, 0, 1 }, { 0, 3, -1, -1, 0, 1 }, { 0, 0, 2, 0, 0, -2 },
{ 0, 3, -3, 1, 0, 1 }, { 0, 2, -4, 2, 0, 0 }, { 0, 4, -2, -2, 0, 0 },
{ 0, 3, 1, -1, 0, -1 }, { 0, 5, -4, 1, 0, 0 }, { 0, 3, -2, -1, -1, 0 },
{ 0, 3, -2, 1, 2, 0 }, { 0, 4, -4, 0, 0, 0 }, { 0, 6, -2, -2, 0, 0 },
{ 0, 5, 0, -3, 1, 0 }, { 0, 4, -2, 0, 2, 0 }, { 0, 2, 2, -2, 1, 0 },
{ 0, 0, 4, 0, 0, -2 }, { 0, 3, -1, 0, 0, 0 }, { 0, 3, -3, -1, 0, 1 },
{ 0, 4, 0, -2, 2, 0 }, { 0, 1, -2, -1, -1, 0 }, { 0, 2, -1, 0, 0, -1 },
{ 0, 4, -4, 2, 0, 0 }, { 0, 2, 1, 0, 1, -1 }, { 0, 3, -2, -1, 1, 0 },
{ 0, 4, -3, 0, 1, 1 }, { 0, 2, 0, 0, 3, 0 }, { 0, 6, -4, 0, 0, 0 }
};
// CHECKSTYLE: resume NoWhitespaceAfter check
/** Cartwright-Edden amplitudes for all tides. */
private static final Map<Tide, Double> CARTWRIGHT_EDDEN_AMPLITUDE_MAP;
static {
CARTWRIGHT_EDDEN_AMPLITUDE_MAP = new HashMap<>(CARTWRIGHT_EDDEN_AMPLITUDE.length);
for (int i = 0; i < CARTWRIGHT_EDDEN_AMPLITUDE.length; ++i) {
CARTWRIGHT_EDDEN_AMPLITUDE_MAP.put(new Tide(DOODSON_ARGUMENTS[i][0], DOODSON_ARGUMENTS[i][1], DOODSON_ARGUMENTS[i][2],
DOODSON_ARGUMENTS[i][3], DOODSON_ARGUMENTS[i][4], DOODSON_ARGUMENTS[i][5]),
CARTWRIGHT_EDDEN_AMPLITUDE[i]);
}
}
/** Earth shape. */
private final OneAxisEllipsoid earth;
/** Data for main tides, for which we have ocean loading coefficients. */
private final MainTideData[][] mainTides;
/** Simple constructor.
* @param earth Earth shape
* @param coefficients coefficients for the considered site
* @see OceanLoadingCoefficientsBLQFactory
*/
public OceanLoading(final OneAxisEllipsoid earth, final OceanLoadingCoefficients coefficients) {
this.earth = earth;
// set up complex admittances, scaled to Cartwright-Edden amplitudes
// and grouped by species (0: long period, 1: diurnal, 2: semi-diurnal)
mainTides = new MainTideData[coefficients.getNbSpecies()][];
for (int i = 0; i < mainTides.length; ++i) {
mainTides[i] = new MainTideData[coefficients.getNbTides(i)];
for (int j = 0; j < mainTides[i].length; ++j) {
final double amplitude = CARTWRIGHT_EDDEN_AMPLITUDE_MAP.get(coefficients.getTide(i, j));
mainTides[i][j] = new MainTideData(coefficients, i, j, FastMath.abs(amplitude));
}
}
}
/** {@inheritDoc} */
@Override
public Vector3D displacement(final BodiesElements elements, final Frame earthFrame,
final Vector3D referencePoint) {
// allocate arrays for each species splines
final UnivariateFunction[] realZSpline = new UnivariateFunction[mainTides.length];
final UnivariateFunction[] imaginaryZSpline = new UnivariateFunction[mainTides.length];
final UnivariateFunction[] realWSpline = new UnivariateFunction[mainTides.length];
final UnivariateFunction[] imaginaryWSpline = new UnivariateFunction[mainTides.length];
final UnivariateFunction[] realSSpline = new UnivariateFunction[mainTides.length];
final UnivariateFunction[] imaginarySSpline = new UnivariateFunction[mainTides.length];
// prepare splines for each species
for (int i = 0; i < mainTides.length; ++i) {
// compute current rates
final double[] rates = new double[mainTides[i].length];
for (int j = 0; j < rates.length; ++j) {
rates[j] = mainTides[i][j].tide.getRate(elements);
}
// set up splines for the current rates
realZSpline[i] = spline(rates, mainTides[i], d -> d.realZ);
imaginaryZSpline[i] = spline(rates, mainTides[i], d -> d.imaginaryZ);
realWSpline[i] = spline(rates, mainTides[i], d -> d.realW);
imaginaryWSpline[i] = spline(rates, mainTides[i], d -> d.imaginaryW);
realSSpline[i] = spline(rates, mainTides[i], d -> d.realS);
imaginarySSpline[i] = spline(rates, mainTides[i], d -> d.imaginaryS);
}
// evaluate all harmonics using interpolated admittances
double dz = 0;
double dw = 0;
double ds = 0;
for (final Map.Entry<Tide, Double> entry : CARTWRIGHT_EDDEN_AMPLITUDE_MAP.entrySet()) {
final Tide tide = entry.getKey();
final double amplitude = entry.getValue();
final int i = tide.getTauMultiplier();
final double rate = tide.getRate(elements);
// apply splines for the current rate of this tide
final double rZ = realZSpline[i].value(rate);
final double iZ = imaginaryZSpline[i].value(rate);
final double rW = realWSpline[i].value(rate);
final double iW = imaginaryWSpline[i].value(rate);
final double rS = realSSpline[i].value(rate);
final double iS = imaginarySSpline[i].value(rate);
// phase for the current tide, including corrections
final double correction;
if (tide.getTauMultiplier() == 0) {
correction = FastMath.PI;
} else if (tide.getTauMultiplier() == 1) {
correction = 0.5 * FastMath.PI;
} else {
correction = 0.0;
}
final double phase = tide.getPhase(elements) + correction;
dz += amplitude * FastMath.hypot(rZ, iZ) * FastMath.cos(phase + FastMath.atan2(iZ, rZ));
dw += amplitude * FastMath.hypot(rW, iW) * FastMath.cos(phase + FastMath.atan2(iW, rW));
ds += amplitude * FastMath.hypot(rS, iS) * FastMath.cos(phase + FastMath.atan2(iS, rS));
}
// convert to proper frame
final GeodeticPoint gp = earth.transform(referencePoint, earthFrame, elements.getDate());
return new Vector3D(dz, gp.getZenith(),
dw, gp.getWest(),
ds, gp.getSouth());
}
/** Get a spline function for interpolating between main tide data.
* @param rates rates for the tides species
* @param data data for the tides species
* @param selector data selector
* @return spline function for interpolating the selected data
*/
private UnivariateFunction spline(final double[] rates, final MainTideData[] data,
final Function<MainTideData, Double> selector) {
final double[] y = new double[data.length];
for (int i = 0; i < y.length; ++i) {
y[i] = selector.apply(data[i]);
}
final PolynomialSplineFunction psf = new SplineInterpolator().interpolate(rates, y);
// as per HARDISP program EVAL subroutine, if spline evaluation is outside of range,
// the closest value is used. This occurs for example for long period tides.
// The main tides have rates 0.0821°/h, 0.5444°/h and 1.0980°/h. However,
// tide 55565 has rate 0.0022°/h, which is below the min rate and tide 75565 has
// rate 1.1002°/h, which is above max rate
final double[] knots = psf.getKnots();
final double minRate = knots[0];
final double valueAtMinRate = psf.value(minRate);
final double maxRate = knots[knots.length - 1];
final double valueAtMaxRate = psf.value(maxRate);
return t -> (t < minRate) ? valueAtMinRate : (t > maxRate) ? valueAtMaxRate : psf.value(t);
}
/** Container for main tide data. */
private static class MainTideData {
/** Tide for which we have ocean loading coefficients. */
private final Tide tide;
/** Scaled real part of admittance along zenith axis. */
private final double realZ;
/** Scaled imaginary part of admittance along zenith axis. */
private final double imaginaryZ;
/** Scaled real part of admittance along west axis. */
private final double realW;
/** Scaled imaginary part of admittance along west axis. */
private final double imaginaryW;
/** Scaled real part of admittance along south axis. */
private final double realS;
/** Scaled imaginary part of admittance south axis. */
private final double imaginaryS;
/** Simple constructor.
* @param coefficients coefficients for the considered site
* @param i tide species
* @param j tide index in the species
* @param absAmplitude absolute value of the Cartwright-Edden amplitude of the tide
*/
MainTideData(final OceanLoadingCoefficients coefficients, final int i, final int j, final double absAmplitude) {
// Sine and Cosine of difference angles
final SinCos scZenith = FastMath.sinCos(coefficients.getZenithPhase(i, j));
final SinCos scWest = FastMath.sinCos(coefficients.getWestPhase(i, j));
final SinCos scSouth = FastMath.sinCos(coefficients.getSouthPhase(i, j));
// Initialize attributes
tide = coefficients.getTide(i, j);
realZ = coefficients.getZenithAmplitude(i, j) * scZenith.cos() / absAmplitude;
imaginaryZ = coefficients.getZenithAmplitude(i, j) * scZenith.sin() / absAmplitude;
realW = coefficients.getWestAmplitude(i, j) * scWest.cos() / absAmplitude;
imaginaryW = coefficients.getWestAmplitude(i, j) * scWest.sin() / absAmplitude;
realS = coefficients.getSouthAmplitude(i, j) * scSouth.cos() / absAmplitude;
imaginaryS = coefficients.getSouthAmplitude(i, j) * scSouth.sin() / absAmplitude;
}
}
}