FieldNeQuickParameters.java

  1. /* Copyright 2002-2024 CS GROUP
  2.  * Licensed to CS GROUP (CS) under one or more
  3.  * contributor license agreements.  See the NOTICE file distributed with
  4.  * this work for additional information regarding copyright ownership.
  5.  * CS licenses this file to You under the Apache License, Version 2.0
  6.  * (the "License"); you may not use this file except in compliance with
  7.  * the License.  You may obtain a copy of the License at
  8.  *
  9.  *   http://www.apache.org/licenses/LICENSE-2.0
  10.  *
  11.  * Unless required by applicable law or agreed to in writing, software
  12.  * distributed under the License is distributed on an "AS IS" BASIS,
  13.  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  14.  * See the License for the specific language governing permissions and
  15.  * limitations under the License.
  16.  */
  17. package org.orekit.models.earth.ionosphere;

  19. import org.hipparchus.Field;
  20. import org.hipparchus.CalculusFieldElement;
  21. import org.hipparchus.util.FastMath;
  22. import org.hipparchus.util.FieldSinCos;
  23. import org.hipparchus.util.MathArrays;
  24. import org.hipparchus.util.SinCos;
  25. import org.orekit.time.DateComponents;
  26. import org.orekit.time.DateTimeComponents;
  27. import org.orekit.time.TimeComponents;

  29. /**
  30.  * This class perfoms the computation of the parameters used by the NeQuick model.
  31.  *
  32.  * @author Bryan Cazabonne
  33.  *
  34.  * @see "European Union (2016). European GNSS (Galileo) Open Service-Ionospheric Correction
  35.  *       Algorithm for Galileo Single Frequency Users. 1.2."
  36.  *
  37.  * @since 10.1
  38.  */
  39. class FieldNeQuickParameters <T extends CalculusFieldElement<T>> {

  41.     /** Solar zenith angle at day night transition, degrees. */
  42.     private static final double X0 = 86.23292796211615;

  44.     /** F2 layer maximum density. */
  45.     private final T nmF2;

  47.     /** F2 layer maximum density height [km]. */
  48.     private final T hmF2;

  50.     /** F1 layer maximum density height [km]. */
  51.     private final T hmF1;

  53.     /** E layer maximum density height [km]. */
  54.     private final T hmE;

  56.     /** F2 layer bottom thickness parameter [km]. */
  57.     private final T b2Bot;

  59.     /** F1 layer top thickness parameter [km]. */
  60.     private final T b1Top;

  62.     /** F1 layer bottom thickness parameter [km]. */
  63.     private final T b1Bot;

  65.     /** E layer top thickness parameter [km]. */
  66.     private final T beTop;

  68.     /** E layer bottom thickness parameter [km]. */
  69.     private final T beBot;

  71.     /** topside thickness parameter [km]. */
  72.     private final T h0;

  74.     /** Layer amplitudes. */
  75.     private final T[] amplitudes;

  77.     /**
  78.      * Build a new instance.
  79.      * @param field field of the elements
  80.      * @param dateTime current date time components
  81.      * @param f2 F2 coefficients used by the F2 layer
  82.      * @param fm3 Fm3 coefficients used by the F2 layer
  83.      * @param latitude latitude of a point along the integration path, in radians
  84.      * @param longitude longitude of a point along the integration path, in radians
  85.      * @param alpha effective ionisation level coefficients
  86.      * @param modipGrip modip grid
  87.      */
  88.     FieldNeQuickParameters(final Field<T> field, final DateTimeComponents dateTime, final double[][][] f2,
  89.                            final double[][][] fm3, final T latitude, final T longitude,
  90.                            final double[] alpha, final double[][] modipGrip) {

  92.         // Zero
  93.         final T zero = field.getZero();

  95.         // MODIP in degrees
  96.         final T modip = computeMODIP(latitude, longitude, modipGrip);
  97.         // Effective ionisation level Az
  98.         final T az = computeAz(modip, alpha);
  99.         // Effective sunspot number (Eq. 19)
  100.         final T azr = FastMath.sqrt(az.subtract(63.7).multiply(1123.6).add(167273.0)).subtract(408.99);
  101.         // Date and Time components
  102.         final DateComponents date = dateTime.getDate();
  103.         final TimeComponents time = dateTime.getTime();
  104.         // Hours
  105.         final double hours  = time.getSecondsInUTCDay() / 3600.0;
  106.         // Effective solar zenith angle in radians
  107.         final T xeff = computeEffectiveSolarAngle(date.getMonth(), hours, latitude, longitude);

  109.         // Coefficients for F2 layer parameters
  110.         // Compute the array of interpolated coefficients for foF2 (Eq. 44)
  111.         final T[][] af2 = MathArrays.buildArray(field, 76, 13);
  112.         for (int j = 0; j < 76; j++) {
  113.             for (int k = 0; k < 13; k++ ) {
  114.                 af2[j][k] = azr.multiply(0.01).negate().add(1.0).multiply(f2[0][j][k]).add(azr.multiply(0.01).multiply(f2[1][j][k]));
  115.             }
  116.         }

  118.         // Compute the array of interpolated coefficients for M(3000)F2 (Eq. 46)
  119.         final T[][] am3 = MathArrays.buildArray(field, 49, 9);
  120.         for (int j = 0; j < 49; j++) {
  121.             for (int k = 0; k < 9; k++ ) {
  122.                 am3[j][k] = azr.multiply(0.01).negate().add(1.0).multiply(fm3[0][j][k]).add(azr.multiply(0.01).multiply(fm3[1][j][k]));
  123.             }
  124.         }

  126.         // E layer maximum density height in km (Eq. 78)
  127.         this.hmE = field.getZero().newInstance(120.0);
  128.         // E layer critical frequency in MHz
  129.         final T foE = computefoE(date.getMonth(), az, xeff, latitude);
  130.         // E layer maximum density in 10^11 m-3 (Eq. 36)
  131.         final T nmE = foE.multiply(foE).multiply(0.124);

  133.         // Time argument (Eq. 49)
  134.         final double t = FastMath.toRadians(15 * hours) - FastMath.PI;
  135.         // Compute Fourier time series for foF2 and M(3000)F2
  136.         final T[] cf2 = computeCF2(field, af2, t);
  137.         final T[] cm3 = computeCm3(field, am3, t);
  138.         // F2 layer critical frequency in MHz
  139.         final T foF2 = computefoF2(field, modip, cf2, latitude, longitude);
  140.         // Maximum Usable Frequency factor
  141.         final T mF2  = computeMF2(field, modip, cm3, latitude, longitude);
  142.         // F2 layer maximum density in 10^11 m-3
  143.         this.nmF2 = foF2.multiply(foF2).multiply(0.124);
  144.         // F2 layer maximum density height in km
  145.         this.hmF2 = computehmF2(field, foE, foF2, mF2);

  147.         // F1 layer critical frequency in MHz
  148.         final T foF1 = computefoF1(field, foE, foF2);
  149.         // F1 layer maximum density in 10^11 m-3
  150.         final T nmF1;
  151.         if (foF1.getReal() <= 0.0 && foE.getReal() > 2.0) {
  152.             final T foEpopf = foE.add(0.5);
  153.             nmF1 = foEpopf.multiply(foEpopf).multiply(0.124);
  154.         } else {
  155.             nmF1 = foF1.multiply(foF1).multiply(0.124);
  156.         }
  157.         // F1 layer maximum density height in km
  158.         this.hmF1 = hmF2.add(hmE).multiply(0.5);

  160.         // Thickness parameters (Eq. 85 to 89)
  161.         final T a = clipExp(FastMath.log(foF2.multiply(foF2)).multiply(0.857).add(FastMath.log(mF2).multiply(2.02)).add(-3.467)).multiply(0.01);
  162.         this.b2Bot = nmF2.divide(a).multiply(0.385);
  163.         this.b1Top = hmF2.subtract(hmF1).multiply(0.3);
  164.         this.b1Bot = hmF1.subtract(hmE).multiply(0.5);
  165.         this.beTop = FastMath.max(b1Bot, zero.newInstance(7.0));
  166.         this.beBot = zero.newInstance(5.0);

  168.         // Layer amplitude coefficients
  169.         this.amplitudes = computeLayerAmplitudes(field, nmE, nmF1, foF1);

  171.         // Topside thickness parameter
  172.         this.h0 = computeH0(field, date.getMonth(), azr);
  173.     }

  175.     /**
  176.      * Get the F2 layer maximum density.
  177.      * @return nmF2
  178.      */
  179.     public T getNmF2() {
  180.         return nmF2;
  181.     }

  183.     /**
  184.      * Get the F2 layer maximum density height.
  185.      * @return hmF2 in km
  186.      */
  187.     public T getHmF2() {
  188.         return hmF2;
  189.     }

  191.     /**
  192.      * Get the F1 layer maximum density height.
  193.      * @return hmF1 in km
  194.      */
  195.     public T getHmF1() {
  196.         return hmF1;
  197.     }

  199.     /**
  200.      * Get the E layer maximum density height.
  201.      * @return hmE in km
  202.      */
  203.     public T getHmE() {
  204.         return hmE;
  205.     }

  207.     /**
  208.      * Get the F2 layer thickness parameter (bottom).
  209.      * @return B2Bot in km
  210.      */
  211.     public T getB2Bot() {
  212.         return b2Bot;
  213.     }

  215.     /**
  216.      * Get the F1 layer thickness parameter (top).
  217.      * @return B1Top in km
  218.      */
  219.     public T getB1Top() {
  220.         return b1Top;
  221.     }

  223.     /**
  224.      * Get the F1 layer thickness parameter (bottom).
  225.      * @return B1Bot in km
  226.      */
  227.     public T getB1Bot() {
  228.         return b1Bot;
  229.     }

  231.     /**
  232.      * Get the E layer thickness parameter (bottom).
  233.      * @return BeBot in km
  234.      */
  235.     public T getBEBot() {
  236.         return beBot;
  237.     }

  239.     /**
  240.      * Get the E layer thickness parameter (top).
  241.      * @return BeTop in km
  242.      */
  243.     public T getBETop() {
  244.         return beTop;
  245.     }

  247.     /**
  248.      * Get the F2, F1 and E layer amplitudes.
  249.      * <p>
  250.      * The resulting element is an array having the following form:
  251.      * <ul>
  252.      * <li>double[0] = A1 → F2 layer amplitude
  253.      * <li>double[1] = A2 → F1 layer amplitude
  254.      * <li>double[2] = A3 → E  layer amplitude
  255.      * </ul>
  256.      * @return layer amplitudes
  257.      */
  258.     public T[] getLayerAmplitudes() {
  259.         return amplitudes.clone();
  260.     }

  262.     /**
  263.      * Get the topside thickness parameter H0.
  264.      * @return H0 in km
  265.      */
  266.     public T getH0() {
  267.         return h0;
  268.     }

  270.     /**
  271.      * Computes the value of the modified dip latitude (MODIP) for the
  272.      * given latitude and longitude.
  273.      *
  274.      * @param lat receiver latitude, radians
  275.      * @param lon receiver longitude, radians
  276.      * @param stModip modip grid
  277.      * @return the MODIP in degrees
  278.      */
  279.     private T computeMODIP(final T lat, final T lon, final double[][] stModip) {

  281.         // Zero
  282.         final T zero = lat.getField().getZero();

  284.         // For the MODIP computation, the latitude and longitude have to be converted in degrees
  285.         final T latitude  = FastMath.toDegrees(lat);
  286.         final T longitude = FastMath.toDegrees(lon);

  288.         // Extreme cases
  289.         if (latitude.getReal() == 90.0 || latitude.getReal() == -90.0) {
  290.             return latitude;
  291.         }

  293.         // Auxiliary parameter l (Eq. 6 to 8)
  294.         final int lF = (int) ((longitude.getReal() + 180) * 0.1);
  295.         int l = lF - 2;
  296.         if (l < -2) {
  297.             l += 36;
  298.         } else if (l > 33) {
  299.             l -= 36;
  300.         }

  302.         // Auxiliary parameter a (Eq. 9 to 11)
  303.         final T a  = latitude.add(90).multiply(0.2).add(1.0);
  304.         final T aF = FastMath.floor(a);
  305.         // Eq. 10
  306.         final T x = a.subtract(aF);
  307.         // Eq. 11
  308.         final int i = (int) aF.getReal() - 2;

  310.         // zi coefficients (Eq. 12 and 13)
  311.         final T z1 = interpolate(zero.add(stModip[i + 1][l + 2]), zero.add(stModip[i + 2][l + 2]),
  312.                                       zero.add(stModip[i + 3][l + 2]), zero.add(stModip[i + 4][l + 2]), x);
  313.         final T z2 = interpolate(zero.add(stModip[i + 1][l + 3]), zero.add(stModip[i + 2][l + 3]),
  314.                                       zero.add(stModip[i + 3][l + 3]), zero.add(stModip[i + 4][l + 3]), x);
  315.         final T z3 = interpolate(zero.add(stModip[i + 1][l + 4]), zero.add(stModip[i + 2][l + 4]),
  316.                                       zero.add(stModip[i + 3][l + 4]), zero.add(stModip[i + 4][l + 4]), x);
  317.         final T z4 = interpolate(zero.add(stModip[i + 1][l + 5]), zero.add(stModip[i + 2][l + 5]),
  318.                                       zero.add(stModip[i + 3][l + 5]), zero.add(stModip[i + 4][l + 5]), x);

  320.         // Auxiliary parameter b (Eq. 14 and 15)
  321.         final T b  = longitude.add(180).multiply(0.1);
  322.         final T bF = FastMath.floor(b);
  323.         final T y  = b.subtract(bF);

  325.         // MODIP (Ref Eq. 16)
  326.         final T modip = interpolate(z1, z2, z3, z4, y);

  328.         return modip;
  329.     }

  331.     /**
  332.      * This method computes the effective ionisation level Az.
  333.      * <p>
  334.      * This parameter is used for the computation of the Total Electron Content (TEC).
  335.      * </p>
  336.      * @param modip modified dip latitude (MODIP) in degrees
  337.      * @param alpha effective ionisation level coefficients
  338.      * @return the ionisation level Az
  339.      */
  340.     private T computeAz(final T modip, final double[] alpha) {
  341.         // Field
  342.         final Field<T> field = modip.getField();
  343.         // Zero
  344.         final T zero = field.getZero();
  345.         // Particular condition (Eq. 17)
  346.         if (alpha[0] == 0.0 && alpha[1] == 0.0 && alpha[2] == 0.0) {
  347.             return zero.newInstance(63.7);
  348.         }
  349.         // Az = a0 + modip * a1 + modip^2 * a2 (Eq. 18)
  350.         T az = modip.multiply(alpha[2]).add(alpha[1]).multiply(modip).add(alpha[0]);
  351.         // If Az < 0 -> Az = 0
  352.         az = FastMath.max(zero, az);
  353.         // If Az > 400 -> Az = 400
  354.         az = FastMath.min(zero.newInstance(400.0), az);
  355.         return az;
  356.     }

  358.     /**
  359.      * This method computes the effective solar zenith angle.
  360.      * <p>
  361.      * The effective solar zenith angle is compute as a function of the
  362.      * solar zenith angle and the solar zenith angle at day night transition.
  363.      * </p>
  364.      * @param month current month of the year
  365.      * @param hours universal time (hours)
  366.      * @param latitude in radians
  367.      * @param longitude in radians
  368.      * @return the effective solar zenith angle, radians
  369.      */
  370.     private T computeEffectiveSolarAngle(final int month,
  371.                                          final double hours,
  372.                                          final T latitude,
  373.                                          final T longitude) {
  374.         // Zero
  375.         final T zero = latitude.getField().getZero();
  376.         // Local time (Eq.4)
  377.         final T lt = longitude.divide(FastMath.toRadians(15.0)).add(hours);
  378.         // Day of year at the middle of the month (Eq. 20)
  379.         final double dy = 30.5 * month - 15.0;
  380.         // Time (Eq. 21)
  381.         final double t = dy + (18 - hours) / 24;
  382.         // Arguments am and al (Eq. 22 and 23)
  383.         final double am = FastMath.toRadians(0.9856 * t - 3.289);
  384.         final double al = am + FastMath.toRadians(1.916 * FastMath.sin(am) + 0.020 * FastMath.sin(2.0 * am) + 282.634);
  385.         // Sine and cosine of solar declination (Eq. 24 and 25)
  386.         final double sDec = 0.39782 * FastMath.sin(al);
  387.         final double cDec = FastMath.sqrt(1. - sDec * sDec);
  388.         // Solar zenith angle, deg (Eq. 26 and 27)
  389.         final FieldSinCos<T> scLat   = FastMath.sinCos(latitude);
  390.         final T coef    = lt.negate().add(12.0).multiply(FastMath.PI / 12);
  391.         final T cZenith = scLat.sin().multiply(sDec).add(scLat.cos().multiply(cDec).multiply(FastMath.cos(coef)));
  392.         final T angle   = FastMath.atan2(FastMath.sqrt(cZenith.multiply(cZenith).negate().add(1.0)), cZenith);
  393.         final T x       = FastMath.toDegrees(angle);
  394.         // Effective solar zenith angle (Eq. 28)
  395.         final T xeff = join(clipExp(x.multiply(0.2).negate().add(20.0)).multiply(0.24).negate().add(90.0), x,
  396.                 zero.newInstance(12.0), x.subtract(X0));
  397.         return FastMath.toRadians(xeff);
  398.     }

  400.     /**
  401.      * This method computes the E layer critical frequency at a given location.
  402.      * @param month current month
  403.      * @param az ffective ionisation level
  404.      * @param xeff effective solar zenith angle in radians
  405.      * @param latitude latitude in radians
  406.      * @return the E layer critical frequency at a given location in MHz
  407.      */
  408.     private T computefoE(final int month, final T az,
  409.                          final T xeff, final T latitude) {
  410.         // The latitude has to be converted in degrees
  411.         final T lat = FastMath.toDegrees(latitude);
  412.         // Square root of the effective ionisation level
  413.         final T sqAz = FastMath.sqrt(az);
  414.         // seas parameter (Eq. 30 to 32)
  415.         final int seas;
  416.         if (month == 1 || month == 2 || month == 11 || month == 12) {
  417.             seas = -1;
  418.         } else if (month == 3 || month == 4 || month == 9 || month == 10) {
  419.             seas = 0;
  420.         } else {
  421.             seas = 1;
  422.         }
  423.         // Latitudinal dependence (Eq. 33 and 34)
  424.         final T ee = clipExp(lat.multiply(0.3));
  425.         final T seasp = ee.subtract(1.0).divide(ee.add(1.0)).multiply(seas);
  426.         // Critical frequency (Eq. 35)
  427.         final T coef = seasp.multiply(0.019).negate().add(1.112);
  428.         final T foE = FastMath.sqrt(coef .multiply(coef).multiply(sqAz).multiply(FastMath.cos(xeff).pow(0.6)).add(0.49));
  429.         return foE;
  430.     }

  432.     /**
  433.      * Computes the F2 layer height of maximum electron density.
  434.      * @param field field of the elements
  435.      * @param foE E layer layer critical frequency in MHz
  436.      * @param foF2 F2 layer layer critical frequency in MHz
  437.      * @param mF2 maximum usable frequency factor
  438.      * @return hmF2 in km
  439.      */
  440.     private T computehmF2(final Field<T> field, final T foE, final T foF2, final T mF2) {
  441.         // Zero
  442.         final T zero = field.getZero();
  443.         // Ratio
  444.         final T fo = foF2.divide(foE);
  445.         final T ratio = join(fo, zero.newInstance(1.75), zero.newInstance(20.0), fo.subtract(1.75));

  447.         // deltaM parameter
  448.         T deltaM = zero.subtract(0.012);
  449.         if (foE.getReal() >= 1e-30) {
  450.             deltaM = deltaM.add(ratio.subtract(1.215).divide(0.253).reciprocal());
  451.         }

  453.         // hmF2 Eq. 80
  454.         final T mF2Sq = mF2.square();
  455.         final T temp  = FastMath.sqrt(mF2Sq.multiply(0.0196).add(1.0).divide(mF2Sq.multiply(1.2967).subtract(1.0)));
  456.         final T height  = mF2.multiply(1490.0).multiply(temp).divide(mF2.add(deltaM)).subtract(176.0);
  457.         return height;
  458.     }

  460.     /**
  461.      * Computes cf2 coefficients.
  462.      * @param field field of the elements
  463.      * @param af2 interpolated coefficients for foF2
  464.      * @param t time argument
  465.      * @return the cf2 coefficients array
  466.      */
  467.     private T[] computeCF2(final Field<T> field, final T[][] af2, final double t) {
  468.         // Eq. 50
  469.         final T[] cf2 = MathArrays.buildArray(field, 76);
  470.         for (int i = 0; i < cf2.length; i++) {
  471.             T sum = field.getZero();
  472.             for (int k = 0; k < 6; k++) {
  473.                 final SinCos sc = FastMath.sinCos((k + 1) * t);
  474.                 sum = sum.add(af2[i][2 * k + 1].multiply(sc.sin()).add(af2[i][2 * (k + 1)].multiply(sc.cos())));
  475.             }
  476.             cf2[i] = af2[i][0].add(sum);
  477.         }
  478.         return cf2;
  479.     }

  481.     /**
  482.      * Computes Cm3 coefficients.
  483.      * @param field field of the elements
  484.      * @param am3 interpolated coefficients for foF2
  485.      * @param t time argument
  486.      * @return the Cm3 coefficients array
  487.      */
  488.     private T[] computeCm3(final Field<T> field, final T[][] am3, final double t) {
  489.         // Eq. 51
  490.         final T[] cm3 = MathArrays.buildArray(field, 49);
  491.         for (int i = 0; i < cm3.length; i++) {
  492.             T sum = field.getZero();
  493.             for (int k = 0; k < 4; k++) {
  494.                 final SinCos sc = FastMath.sinCos((k + 1) * t);
  495.                 sum = sum.add(am3[i][2 * k + 1].multiply(sc.sin()).add(am3[i][2 * (k + 1)].multiply(sc.cos())));
  496.             }
  497.             cm3[i] = am3[i][0].add(sum);
  498.         }
  499.         return cm3;
  500.     }

  502.     /**
  503.      * This method computes the F2 layer critical frequency.
  504.      * @param field field of the elements
  505.      * @param modip modified DIP latitude, in degrees
  506.      * @param cf2 Fourier time series for foF2
  507.      * @param latitude latitude in radians
  508.      * @param longitude longitude in radians
  509.      * @return the F2 layer critical frequency, MHz
  510.      */
  511.     private T computefoF2(final Field<T> field, final T modip, final T[] cf2,
  512.                           final T latitude, final T longitude) {

  514.         // One
  515.         final T one = field.getOne();

  517.         // Legendre grades (Eq. 63)
  518.         final int[] q = new int[] {
  519.             12, 12, 9, 5, 2, 1, 1, 1, 1
  520.         };

  522.         // Array for geographic terms
  523.         final T[] g = MathArrays.buildArray(field, cf2.length);
  524.         g[0] = one;

  526.         // MODIP coefficients Eq. 57
  527.         final T sinMODIP = FastMath.sin(FastMath.toRadians(modip));
  528.         final T[] m = MathArrays.buildArray(field, 12);
  529.         m[0] = one;
  530.         for (int i = 1; i < q[0]; i++) {
  531.             m[i] = sinMODIP.multiply(m[i - 1]);
  532.             g[i] = m[i];
  533.         }

  535.         // Latitude coefficients (Eq. 58)
  536.         final T cosLat = FastMath.cos(latitude);
  537.         final T[] p = MathArrays.buildArray(field, 8);
  538.         p[0] = cosLat;
  539.         for (int n = 2; n < 9; n++) {
  540.             p[n - 1] = cosLat.multiply(p[n - 2]);
  541.         }

  543.         // latitude and longitude terms
  544.         int index = 12;
  545.         for (int i = 1; i < q.length; i++) {
  546.             final FieldSinCos<T> sc = FastMath.sinCos(longitude.multiply(i));
  547.             for (int j = 0; j < q[i]; j++) {
  548.                 g[index++] = m[j].multiply(p[i - 1]).multiply(sc.cos());
  549.                 g[index++] = m[j].multiply(p[i - 1]).multiply(sc.sin());
  550.             }
  551.         }

  553.         // Compute foF2 by linear combination
  554.         final T frequency = one.linearCombination(g, cf2);
  555.         return frequency;
  556.     }

  558.     /**
  559.      * This method computes the Maximum Usable Frequency factor.
  560.      * @param field field of the elements
  561.      * @param modip modified DIP latitude, in degrees
  562.      * @param cm3 Fourier time series for M(3000)F2
  563.      * @param latitude latitude in radians
  564.      * @param longitude longitude in radians
  565.      * @return the Maximum Usable Frequency factor
  566.      */
  567.     private T computeMF2(final Field<T> field, final T modip, final T[] cm3,
  568.                          final T latitude, final T longitude) {

  570.         // One
  571.         final T one = field.getOne();
  572.         // Legendre grades (Eq. 71)
  573.         final int[] r = new int[] {
  574.             7, 8, 6, 3, 2, 1, 1
  575.         };

  577.         // Array for geographic terms
  578.         final T[] g = MathArrays.buildArray(field, cm3.length);
  579.         g[0] = one;

  581.         // MODIP coefficients Eq. 57
  582.         final T sinMODIP = FastMath.sin(FastMath.toRadians(modip));
  583.         final T[] m = MathArrays.buildArray(field, 12);
  584.         m[0] = one;
  585.         for (int i = 1; i < 12; i++) {
  586.             m[i] = sinMODIP.multiply(m[i - 1]);
  587.             if (i < 7) {
  588.                 g[i] = m[i];
  589.             }
  590.         }

  592.         // Latitude coefficients (Eq. 58)
  593.         final T cosLat = FastMath.cos(latitude);
  594.         final T[] p = MathArrays.buildArray(field, 8);
  595.         p[0] = cosLat;
  596.         for (int n = 2; n < 9; n++) {
  597.             p[n - 1] = cosLat.multiply(p[n - 2]);
  598.         }

  600.         // latitude and longitude terms
  601.         int index = 7;
  602.         for (int i = 1; i < r.length; i++) {
  603.             final FieldSinCos<T> sc = FastMath.sinCos(longitude.multiply(i));
  604.             for (int j = 0; j < r[i]; j++) {
  605.                 g[index++] = m[j].multiply(p[i - 1]).multiply(sc.cos());
  606.                 g[index++] = m[j].multiply(p[i - 1]).multiply(sc.sin());
  607.             }
  608.         }

  610.         // Compute m3000 by linear combination
  611.         final T m3000 = one.linearCombination(g, cm3);
  612.         return m3000;
  613.     }

  615.     /**
  616.      * This method computes the F1 layer critical frequency.
  617.      * <p>
  618.      * This computation performs the algorithm exposed in Annex F
  619.      * of the reference document.
  620.      * </p>
  621.      * @param field field of the elements
  622.      * @param foE the E layer critical frequency, MHz
  623.      * @return the F1 layer critical frequency, MHz
  624.      * @param foF2 the F2 layer critical frequency, MHz
  625.      */
  626.     private T computefoF1(final Field<T> field, final T foE, final T foF2) {
  627.         final T zero = field.getZero();
  628.         final T temp  = join(foE.multiply(1.4), zero, zero.newInstance(1000.0), foE.subtract(2.0));
  629.         final T temp2 = join(zero, temp, zero.newInstance(1000.0), foE.subtract(temp));
  630.         final T value = join(temp2, temp2.multiply(0.85), zero.newInstance(60.0), foF2.multiply(0.85).subtract(temp2));
  631.         if (value.getReal() < 1.0E-6) {
  632.             return zero;
  633.         } else {
  634.             return value;
  635.         }
  636.     }

  638.     /**
  639.      * This method allows the computation of the F2, F1 and E layer amplitudes.
  640.      * <p>
  641.      * The resulting element is an array having the following form:
  642.      * <ul>
  643.      * <li>double[0] = A1 → F2 layer amplitude
  644.      * <li>double[1] = A2 → F1 layer amplitude
  645.      * <li>double[2] = A3 → E  layer amplitude
  646.      * </ul>
  647.      * </p>
  648.      * @param field field of the elements
  649.      * @param nmE E layer maximum density in 10^11 m-3
  650.      * @param nmF1 F1 layer maximum density in 10^11 m-3
  651.      * @param foF1 F1 layer critical frequency in MHz
  652.      * @return a three components array containing the layer amplitudes
  653.      */
  654.     private T[] computeLayerAmplitudes(final Field<T> field, final T nmE, final T nmF1, final T foF1) {
  655.         // Zero
  656.         final T zero = field.getZero();

  658.         // Initialize array
  659.         final T[] amplitude = MathArrays.buildArray(field, 3);

  661.         // F2 layer amplitude (Eq. 90)
  662.         final T a1 = nmF2.multiply(4.0);
  663.         amplitude[0] = a1;

  665.         // F1 and E layer amplitudes (Eq. 91 to 98)
  666.         if (foF1.getReal() < 0.5) {
  667.             amplitude[1] = zero;
  668.             amplitude[2] = nmE.subtract(epst(a1, hmF2, b2Bot, hmE)).multiply(4.0);
  669.         } else {
  670.             T a2a = zero;
  671.             T a3a = nmE.multiply(4.0);
  672.             for (int i = 0; i < 5; i++) {
  673.                 a2a = nmF1.subtract(epst(a1, hmF2, b2Bot, hmF1)).subtract(epst(a3a, hmE, beTop, hmF1)).multiply(4.0);
  674.                 a2a = join(a2a, nmF1.multiply(0.8), field.getOne(), a2a.subtract(nmF1.multiply(0.8)));
  675.                 a3a = nmE.subtract(epst(a2a, hmF1, b1Bot, hmE)).subtract(epst(a1, hmF2, b2Bot, hmE)).multiply(4.0);
  676.             }
  677.             amplitude[1] = a2a;
  678.             amplitude[2] = join(a3a, zero.newInstance(0.05), zero.newInstance(60.0), a3a.subtract(0.005));
  679.         }

  681.         return amplitude;
  682.     }

  684.     /**
  685.      * This method computes the topside thickness parameter H0.
  686.      *
  687.      * @param field field of the elements
  688.      * @param month current month
  689.      * @param azr effective sunspot number
  690.      * @return H0 in km
  691.      */
  692.     private T computeH0(final Field<T> field, final int month, final T azr) {

  694.         // One
  695.         final T one = field.getOne();

  697.         // Auxiliary parameter ka (Eq. 99 and 100)
  698.         final T ka;
  699.         if (month > 3 && month < 10) {
  700.             // month = 4,5,6,7,8,9
  701.             ka = azr.multiply(0.014).add(hmF2.multiply(0.008)).negate().add(6.705);
  702.         } else {
  703.             // month = 1,2,3,10,11,12
  704.             final T ratio = hmF2.divide(b2Bot);
  705.             ka = ratio.multiply(ratio).multiply(0.097).add(nmF2.multiply(0.153)).add(-7.77);
  706.         }

  708.         // Auxiliary parameter kb (Eq. 101 and 102)
  709.         T kb = join(ka, one.newInstance(2.0), one, ka.subtract(2.0));
  710.         kb = join(one.newInstance(8.0), kb, one, kb.subtract(8.0));

  712.         // Auxiliary parameter Ha (Eq. 103)
  713.         final T hA = kb.multiply(b2Bot);

  715.         // Auxiliary parameters x and v (Eq. 104 and 105)
  716.         final T x = hA.subtract(150.0).multiply(0.01);
  717.         final T v = x.multiply(0.041163).subtract(0.183981).multiply(x).add(1.424472);

  719.         // Topside thickness parameter (Eq. 106)
  720.         final T h = hA.divide(v);
  721.         return h;
  722.     }

  724.     /**
  725.      * A clipped exponential function.
  726.      * <p>
  727.      * This function, describe in section F.2.12.2 of the reference document, is
  728.      * recommanded for the computation of exponential values.
  729.      * </p>
  730.      * @param power power for exponential function
  731.      * @return clipped exponential value
  732.      */
  733.     private T clipExp(final T power) {
  734.         final T zero = power.getField().getZero();
  735.         if (power.getReal() > 80.0) {
  736.             return zero.newInstance(5.5406E34);
  737.         } else if (power.getReal() < -80) {
  738.             return zero.newInstance(1.8049E-35);
  739.         } else {
  740.             return FastMath.exp(power);
  741.         }
  742.     }

  744.     /**
  745.      * This method provides a third order interpolation function
  746.      * as recommended in the reference document (Ref Eq. 128 to Eq. 138)
  747.      *
  748.      * @param z1 z1 coefficient
  749.      * @param z2 z2 coefficient
  750.      * @param z3 z3 coefficient
  751.      * @param z4 z4 coefficient
  752.      * @param x position
  753.      * @return a third order interpolation
  754.      */
  755.     private T interpolate(final T z1, final T z2,
  756.                           final T z3, final T z4,
  757.                           final T x) {

  759.         if (FastMath.abs(2.0 * x.getReal()) < 1e-10) {
  760.             return z2;
  761.         }

  763.         final T delta = x.multiply(2.0).subtract(1.0);
  764.         final T g1 = z3.add(z2);
  765.         final T g2 = z3.subtract(z2);
  766.         final T g3 = z4.add(z1);
  767.         final T g4 = z4.subtract(z1).divide(3.0);
  768.         final T a0 = g1.multiply(9.0).subtract(g3);
  769.         final T a1 = g2.multiply(9.0).subtract(g4);
  770.         final T a2 = g3.subtract(g1);
  771.         final T a3 = g4.subtract(g2);
  772.         final T zx = delta.multiply(a3).add(a2).multiply(delta).add(a1).multiply(delta).add(a0).multiply(0.0625);

  774.         return zx;
  775.     }

  777.     /**
  778.      * Allows smooth joining of functions f1 and f2
  779.      * (i.e. continuous first derivatives) at origin.
  780.      * <p>
  781.      * This function, describe in section F.2.12.1 of the reference document, is
  782.      * recommanded for computational efficiency.
  783.      * </p>
  784.      * @param dF1 first function
  785.      * @param dF2 second function
  786.      * @param dA width of transition region
  787.      * @param dX x value
  788.      * @return the computed value
  789.      */
  790.     private T join(final T dF1, final T dF2,
  791.                    final T dA, final T dX) {
  792.         final T ee = clipExp(dA.multiply(dX));
  793.         return dF1.multiply(ee).add(dF2).divide(ee.add(1.0));
  794.     }

  796.     /**
  797.      * The Epstein function.
  798.      * <p>
  799.      * This function, describe in section 2.5.1 of the reference document, is used
  800.      * as a basis analytical function in NeQuick for the construction of the ionospheric layers.
  801.      * </p>
  802.      * @param x x parameter
  803.      * @param y y parameter
  804.      * @param z z parameter
  805.      * @param w w parameter
  806.      * @return value of the epstein function
  807.      */
  808.     private T epst(final T x, final T y,
  809.                    final T z, final T w) {
  810.         final T ex  = clipExp(w.subtract(y).divide(z));
  811.         final T opex = ex.add(1.0);
  812.         final T epst = x.multiply(ex).divide(opex.multiply(opex));
  813.         return epst;
  814.     }

  816. }
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