public CelestialLongitudes(int year, int julianDay, int hours)
{
double doubleHour = hours;
int leapDaysSince1901 = ((year - 1901) / 4); //number of leap days between 1901 and Jan 1 of year
double yearsSince1900 = year - 1900; //number of years since 1900
double additionalDays = julianDay + leapDaysSince1901 - 1; // julian Day + leap days.
this.LongitudeOfMoonsNode = 259.1560564 - 19.328185764 * yearsSince1900 - .0529539336 * additionalDays - .0022064139 * doubleHour;
this.LongitudeOfMoonsNode = MathFuncs.Angle(LongitudeOfMoonsNode);
this.LongitudeOfLunarPerigee = 334.3837214 + 40.66246584 * yearsSince1900 + .111404016 * additionalDays + .004641834 * doubleHour;
this.LongitudeOfLunarPerigee = MathFuncs.Angle(this.LongitudeOfLunarPerigee);
this.LongitudeOfSun = 280.1895014 - .238724988 * yearsSince1900 + .9856473288 * additionalDays + .0410686387 * doubleHour;
this.LongitudeOfSun = MathFuncs.Angle(LongitudeOfSun);
this.LongitudeOfSolarPerigee = 281.2208569 + .01717836 * yearsSince1900 + .000047064 * additionalDays + .000001961 * doubleHour;
this.LongitudeOfSolarPerigee = MathFuncs.Angle(LongitudeOfSolarPerigee);
this.LongitudeOfMoon = 277.0256206 + 129.38482032 * yearsSince1900 + 13.176396768 * additionalDays + .549016532 * doubleHour;
this.LongitudeOfMoon = MathFuncs.Angle(LongitudeOfMoon);
// the following calculations are based on the Manual Of Harmonic Analysis and Prediction of Tides by Paul Schureman
// I, from Schureman p156 first equation. Values for each degree of longitude of Moon's node given in Schureman table 6.
double N = MathFuncs.DegreesToRadians(LongitudeOfMoonsNode);
double IRadians = Math.Acos(.9136949 - .0356926 * Math.Cos(N));
this.Schureman_I = MathFuncs.Angle(MathFuncs.RadiansToDegrees(IRadians));
// little V, Schureman p156. Values for each degree of longitude of Moon's node given in Schureman table 6.
double vRadians = Math.Asin(.0897056 * Math.Sin(N) / Math.Sin(IRadians));
this.Schureman_v = MathFuncs.RadiansToDegrees(vRadians); //v
// epsilon, Schureman p 156, third equation. Values for each degree of longitude of Moon's node given in Schureman table 6.
double epsilonRadians = N - 2.0 * Math.Atan(.64412 * Math.Tan(N / 2.0)) - vRadians;
this.Schureman_e = MathFuncs.RadiansToDegrees(epsilonRadians);
// used for node factor calculations
double NUP = Math.Atan(Math.Sin(vRadians) / (Math.Cos(vRadians) + .334766 / Math.Sin(2.0 * IRadians)));
this.DNUP = MathFuncs.RadiansToDegrees(NUP);
// used for node factor calculations
double NUP2 = Math.Atan(Math.Sin(2.0 * vRadians) / (Math.Cos(2.0 * vRadians) + .0726184 / (Math.Sin(IRadians) * Math.Sin(IRadians)))) / 2.0;
this.DNUP2 = MathFuncs.RadiansToDegrees(NUP2);
// P is the mean longitude of the lunar perigee reckoned from the lunar intersection.
// Equation 191, Schureman p 41
this.Schureman_P = MathFuncs.Angle(this.LongitudeOfLunarPerigee - this.Schureman_e);
}
/// <summary>
/// Calculate node factors that are used to modify the amplitude of each tidal constituent
/// </summary>
/// <param name="epochStartYear">The epoch start year</param>
/// <param name="epochStartJulianDay">The epoch start day</param>
/// <param name="halfEpochLengthInHours">One half of epoch length in hours</param>
private void CalculateNodeFactors(int epochStartYear, int epochStartJulianDay, int halfEpochLengthInHours)
{
CelestialLongitudes middleOfEpochLongitudes = new CelestialLongitudes(epochStartYear, epochStartJulianDay, halfEpochLengthInHours);
///CalculateCelestialLongitudes(epochStartYear, epochStartJulianDay, halfEpochLengthInHours);
double N = MathFuncs.DegreesToRadians(middleOfEpochLongitudes.LongitudeOfMoonsNode);
double I = MathFuncs.DegreesToRadians(middleOfEpochLongitudes.Schureman_I);
double NU = MathFuncs.DegreesToRadians(middleOfEpochLongitudes.Schureman_v);
double XI = MathFuncs.DegreesToRadians(middleOfEpochLongitudes.Schureman_e);
double P = MathFuncs.DegreesToRadians(middleOfEpochLongitudes.LongitudeOfLunarPerigee);
double PC = MathFuncs.DegreesToRadians(middleOfEpochLongitudes.Schureman_P);
double SINI = Math.Sin(I);
double SINI2 = Math.Sin(I / 2.0);
double SIN2I = Math.Sin(2.0 * I);
double COSI2 = Math.Cos(I / 2.0);
double TANI2 = Math.Tan(I / 2.0);
// Equations are from Schureman pp 25-45
double EQ197 = Math.Sqrt(2.310 + 1.435 * Math.Cos(2.0 * PC));
double EQ213 = Math.Sqrt(1.0 - 12.0 * TANI2 * TANI2 * Math.Cos(2.0 * PC) + 36.0 * TANI2 * TANI2 * TANI2 * TANI2);
double EQ73 = (2.0 / 3.0 - SINI * SINI) / 0.5021;
double EQ74 = SINI * SINI / 0.1578;
double EQ75 = SINI * COSI2 * COSI2 / 0.37988;
double EQ76 = Math.Sin(2.0 * I) / 0.7214;
double EQ77 = SINI * SINI2 * SINI2 / 0.0164;
double EQ78 = (COSI2 * COSI2 * COSI2 * COSI2) / 0.91544;
double EQ149 = COSI2 * COSI2 * COSI2 * COSI2 * COSI2 * COSI2 / 0.8758;
double EQ207 = EQ75 * EQ197;
double EQ215 = EQ78 * EQ213;
double EQ227 = Math.Sqrt(0.8965 * SIN2I * SIN2I + 0.6001 * SIN2I * Math.Cos(NU) + 0.1006);
double EQ235 = 0.001 + Math.Sqrt(19.0444 * SINI * SINI * SINI * SINI + 2.7702 * SINI * SINI * Math.Cos(2.0 * NU) + 0.0981);
// Node factor calculations from Schureman p 25
this.Constituents[Constants.M2].NodeFactor = EQ78;
this.Constituents[Constants.S2].NodeFactor = 1.0;
this.Constituents[Constants.N2].NodeFactor = EQ78;
this.Constituents[Constants.K1].NodeFactor = EQ227;
this.Constituents[Constants.M4].NodeFactor = EQ78 * EQ78;
this.Constituents[Constants.O1].NodeFactor = EQ75;
this.Constituents[Constants.M6].NodeFactor = EQ78 * EQ78 * EQ78;
this.Constituents[Constants.MK3].NodeFactor = EQ78 * EQ227;
this.Constituents[Constants.S4].NodeFactor = 1.0;
this.Constituents[Constants.MN4].NodeFactor = EQ78 * EQ78;
this.Constituents[Constants.NU2].NodeFactor = EQ78;
this.Constituents[Constants.S6].NodeFactor = 1.0;
this.Constituents[Constants.MU2].NodeFactor = EQ78;
this.Constituents[Constants._2N2].NodeFactor = EQ78;
this.Constituents[Constants.OO1].NodeFactor = EQ77;
this.Constituents[Constants.LAMBDA2].NodeFactor = EQ78;
this.Constituents[Constants.S1].NodeFactor = 1.0;
// equation 207 not working.
//this.Constituents[Constants.M1].NodeFactor = EQ207;
this.Constituents[Constants.M1].NodeFactor = 1.0;
this.Constituents[Constants.J1].NodeFactor = EQ76;
this.Constituents[Constants.MM].NodeFactor = EQ73;
this.Constituents[Constants.SSA].NodeFactor = 1.0;
this.Constituents[Constants.SA].NodeFactor = 1.0;
this.Constituents[Constants.MSF].NodeFactor = EQ78;
this.Constituents[Constants.MF].NodeFactor = EQ74;
this.Constituents[Constants.RHO1].NodeFactor = EQ75;
this.Constituents[Constants.Q1].NodeFactor = EQ75;
this.Constituents[Constants.T2].NodeFactor = 1.0;
this.Constituents[Constants.R2].NodeFactor = 1.0;
this.Constituents[Constants._2Q1].NodeFactor = EQ75;
this.Constituents[Constants.P1].NodeFactor = 1.0;
this.Constituents[Constants._2SM2].NodeFactor = EQ78;
this.Constituents[Constants.M3].NodeFactor = EQ149;
// equation 215 is not working.
//this.Constituents[Constants.L2].NodeFactor = EQ215;
this.Constituents[Constants.L2].NodeFactor = 1.0;
this.Constituents[Constants._2MK3].NodeFactor = EQ78 * EQ78 * EQ227;
this.Constituents[Constants.K2].NodeFactor = EQ235;
this.Constituents[Constants.M8].NodeFactor = EQ78 * EQ78 * EQ78 * EQ78;
this.Constituents[Constants.MS4].NodeFactor = EQ78;
}
/// <summary>
/// Calculate the phases of all constituents of the theoretical equilibrium tide, for the start of the epoch
/// </summary>
/// <param name="epochStartYear">Year of epoch start</param>
/// <param name="epochStartJulianDay">day of epoch start</param>
/// <param name="epochStartHour">hour of epoch start</param>
/// <param name="halfEpochLengthInHours">One half of epoch length in hours</param>
private void CalculateEquilibriumPhases(int epochStartYear, int epochStartJulianDay, int epochStartHour, int halfEpochLengthInHours)
{
// get celestial longitudes for start of the epoch
CelestialLongitudes startOfEpochLongitudes = new CelestialLongitudes(epochStartYear, epochStartJulianDay, epochStartHour);
double S = startOfEpochLongitudes.LongitudeOfMoon;
double P = startOfEpochLongitudes.LongitudeOfLunarPerigee;
double H = startOfEpochLongitudes.LongitudeOfSun;
double P1 = startOfEpochLongitudes.LongitudeOfSolarPerigee;
double T = MathFuncs.Angle(180.0 + epochStartHour * (360.0 / 24.0)); // hour angle of mean sun at place of observation
// get values based on longitude of moon's node, these are calculated from the middle of the epoch.
CelestialLongitudes middleOfEpochLongitudes = new CelestialLongitudes(epochStartYear, epochStartJulianDay, halfEpochLengthInHours);
double NU = middleOfEpochLongitudes.Schureman_v; //v
double XI = middleOfEpochLongitudes.Schureman_e; //e
double NUP = middleOfEpochLongitudes.DNUP;
double NUP2 = middleOfEpochLongitudes.DNUP2;
// now fill in the equilibrium phases of the Harmonic Constituents.
// equations from The Manual of Harmonic analysis and Prediction of Tides by Paul Schureman page 22.
this.Constituents[Constants.M2].EquilibriumPhase = MathFuncs.Angle(2.0 * (T - S + H) + 2.0 * (XI - NU));
this.Constituents[Constants.S2].EquilibriumPhase = MathFuncs.Angle(2.0 * T);
this.Constituents[Constants.N2].EquilibriumPhase = MathFuncs.Angle(2.0 * (T + H) - 3.0 * S + P + 2.0 * (XI - NU));
this.Constituents[Constants.K1].EquilibriumPhase = MathFuncs.Angle(T + H - 90.0 - NUP);
this.Constituents[Constants.M4].EquilibriumPhase = MathFuncs.Angle(4.0 * (T - S + H) + 4.0 * (XI - NU));
this.Constituents[Constants.O1].EquilibriumPhase = MathFuncs.Angle(T - 2.0 * S + H + 90.0 + 2.0 * XI - NU);
this.Constituents[Constants.M6].EquilibriumPhase = MathFuncs.Angle(6.0 * (T - S + H) + 6.0 * (XI - NU));
this.Constituents[Constants.MK3].EquilibriumPhase = MathFuncs.Angle(3.0 * (T + H) - 2.0 * S - 90.0 + 2.0 * (XI - NU) - NUP);
this.Constituents[Constants.S4].EquilibriumPhase = MathFuncs.Angle(4.0 * T);
this.Constituents[Constants.MN4].EquilibriumPhase = MathFuncs.Angle(4.0 * (T + H) - 5.0 * S + P + 4.0 * (XI - NU));
this.Constituents[Constants.NU2].EquilibriumPhase = 2.0 * T - 3.0 * S + 4.0 * H - P + 2.0 * (XI - NU);
this.Constituents[Constants.S6].EquilibriumPhase = 6.0 * T;
this.Constituents[Constants.MU2].EquilibriumPhase = 2.0 * (T + 2.0 * (H - S)) + 2.0 * (XI - NU);
this.Constituents[Constants._2N2].EquilibriumPhase = 2.0 * (T - 2.0 * S + H + P) + 2.0 * (XI - NU);
this.Constituents[Constants.OO1].EquilibriumPhase = T + 2.0 * S + H - 90.0 - 2.0 * XI - NU;
this.Constituents[Constants.LAMBDA2].EquilibriumPhase = 2.0 * T - S + P + 180.0 + 2.0 * (XI - NU);
this.Constituents[Constants.S1].EquilibriumPhase = T;
double I = MathFuncs.DegreesToRadians(middleOfEpochLongitudes.Schureman_I);
double PC = MathFuncs.DegreesToRadians(middleOfEpochLongitudes.Schureman_P);
double TOP = (5.0 * Math.Cos(I) - 1.0) * Math.Sin(PC);
double BOTTOM = (7.0 * Math.Cos(I) + 1.0) * Math.Cos(PC);
double Q = MathFuncs.Arctan(TOP, BOTTOM, 1);
this.Constituents[Constants.M1].EquilibriumPhase = T - S + H - 90.0 + XI - NU + Q;
this.Constituents[Constants.J1].EquilibriumPhase = T + S + H - P - 90.0 - NU;
this.Constituents[Constants.MM].EquilibriumPhase = S - P;
this.Constituents[Constants.SSA].EquilibriumPhase = 2.0 * H;
this.Constituents[Constants.SA].EquilibriumPhase = H;
this.Constituents[Constants.MSF].EquilibriumPhase = 2.0 * (S - H);
this.Constituents[Constants.MF].EquilibriumPhase = 2.0 * S - 2.0 * XI;
this.Constituents[Constants.RHO1].EquilibriumPhase = T + 3.0 * (H - S) - P + 90.0 + 2.0 * XI - NU;
this.Constituents[Constants.Q1].EquilibriumPhase = T - 3.0 * S + H + P + 90.0 + 2.0 * XI - NU;
this.Constituents[Constants.T2].EquilibriumPhase = 2.0 * T - H + P1;
this.Constituents[Constants.R2].EquilibriumPhase = 2.0 * T + H - P1 + 180.0;
this.Constituents[Constants._2Q1].EquilibriumPhase = T - 4.0 * S + H + 2.0 * P + 90.0 + 2.0 * XI - NU;
this.Constituents[Constants.P1].EquilibriumPhase = T - H + 90.0;
this.Constituents[Constants._2SM2].EquilibriumPhase = 2.0 * (T + S - H) + 2.0 * (NU - XI);
this.Constituents[Constants.M3].EquilibriumPhase = 3.0 * (T - S + H) + 3.0 * (XI - NU);
double R = Math.Sin(2.0 * PC) / ((1.0 / 6.0) * (1.0 / Math.Tan(0.5 * I)) * (1.0 / Math.Tan(0.5 * I)) - Math.Cos(2.0 * PC));
R = MathFuncs.RadiansToDegrees(Math.Atan(R));
this.Constituents[Constants.L2].EquilibriumPhase = 2.0 * (T + H) - S - P + 180.0 + 2.0 * (XI - NU) - R;
this.Constituents[Constants._2MK3].EquilibriumPhase = 3.0 * (T + H) - 4.0 * S + 90.0 + 4.0 * (XI - NU) + NUP;
this.Constituents[Constants.K2].EquilibriumPhase = 2.0 * (T + H) - 2.0 * NUP2;
this.Constituents[Constants.M8].EquilibriumPhase = 8.0 * (T - S + H) + 8.0 * (XI - NU);
this.Constituents[Constants.MS4].EquilibriumPhase = 2.0 * (2.0 * T - S + H) + 2.0 * (XI - NU);
for (int index = 0; index < Constants.ConstitutentArraySize; index++)
{
this.Constituents[index].EquilibriumPhase = MathFuncs.Angle(this.Constituents[index].EquilibriumPhase);
}
}
/// <summary>
/// this is the derivative of the RateOfChange function, it returns the acceleration of the tide
/// Same units (probably feet or meters) per hour per hour as the amplitude
/// </summary>
/// <param name="hours">hours since epoch start</param>
/// <returns>the acceleration of the tide</returns>
public double AccelerationOfChange(double hours)
{
return(-1 * Amplitude * NodeFactor * (Math.PI / 180) * Speed * (Math.PI / 180) * Speed * Math.Cos(MathFuncs.DegreesToRadians(Speed * hours + EquilibriumPhase - Phase)));
}
/// <summary>
/// Calculate the height of this constituent. Same units (probably feet or meters) as the amplitude
/// </summary>
/// <param name="h">the number of hours since the start of the epoch that the equilibrium phases are based on.</param>
/// <returns>the height of this harmonic constituent</returns>
public double Height(double hours)
{
return(Amplitude * NodeFactor * Math.Cos(MathFuncs.DegreesToRadians(Speed * hours + EquilibriumPhase - Phase)));
}
