/// <summary>
/// Calculate the geopotential and temperature at the given point.
/// </summary>
void CalculateGeopotentialTemperature(
const PhysicalConstants & phys,
double dEta,
double dXp,
double dYp,
double & dGeopotential,
double & dTemperature
) const {
// Get some constants
const double dG = phys.GetG();
const double dCv = phys.GetCv();
const double dCp = phys.GetCp();
const double dRd = phys.GetR();
const double dP0 = phys.GetP0();
const double dae = phys.GetEarthRadius();
const double df0 = 2 * phys.GetOmega() * sin(m_dRefLat);
//const double df0 = 0.0;
const double dbeta0 = 2 * phys.GetOmega() * cos(m_dRefLat) / dae;
//const double dbeta0 = 0.0;
const double dLy = m_dGDim[3] - m_dGDim[2];
// Horizontally averaged temperature
double dAvgTemperature =
m_dT0 * pow(dEta, dRd * m_ddTdz / dG);
// Horizontally averaged geopotential
double dAvgGeopotential =
m_dT0 * dG / m_ddTdz *
(1.0 - pow(dEta, dRd * m_ddTdz / dG));
// Horizontal variation geopotential function
double dXYGeopotential = 0.5 * m_dU0 *
((df0 - dbeta0 * m_dY0) * (dYp - m_dY0 -
m_dY0 / m_dpiC * sin(2 * m_dpiC * dYp / dLy)) +
0.5 * dbeta0 *
(dYp * dYp - dLy * dYp / m_dpiC * sin(2 * m_dpiC * dYp / dLy) -
0.5 * dLy * dLy / (m_dpiC * m_dpiC) * cos(2 * m_dpiC * dYp / dLy) -
dLy * dLy / 3 - 0.5 * dLy * dLy / (m_dpiC * m_dpiC)));
double dExpDecay = exp(-(log(dEta) / m_dbC) * (log(dEta) / m_dbC));
double dRefProfile1 = log(dEta);
double dRefProfile2 = 2 / (m_dbC * m_dbC) * log(dEta) * log(dEta) - 1.0;
// Total geopotential distribution
dGeopotential = dAvgGeopotential + dXYGeopotential*
dRefProfile1 * dExpDecay;
// Total temperature distribution
dTemperature = dAvgTemperature + dXYGeopotential / dRd *
dRefProfile2 * dExpDecay;
}
/// <summary>
/// Evaluate the state vector at the given point.
/// </summary>
virtual void EvaluatePointwiseState(
const PhysicalConstants & phys,
const Time & time,
double dZ,
double dLon,
double dLat,
double * dState,
double * dTracer
) const {
// Radius
double dR = dZ + phys.GetEarthRadius();
// Calculate parameters
double dT0 = 0.5 * (ParamT0E + ParamT0P);
double dConstA = 1.0 / ParamLapseRate;
double dConstB = (dT0 - ParamT0P) / (dT0 * ParamT0P);
double dConstC = 0.5 * (ParamK + 2.0)
* (ParamT0E - ParamT0P) / (ParamT0E * ParamT0P);
double dConstH = phys.GetR() * dT0 / phys.GetG();
// Computed quantities
double dScaledZ = dZ / (ParamB * dConstH);
// Calculate tau values
double dTau1 =
dConstA * ParamLapseRate / dT0
* exp(ParamLapseRate / dT0 * dZ)
+ dConstB
* (1.0 - 2.0 * dScaledZ * dScaledZ)
* exp(- dScaledZ * dScaledZ);
double dTau2 =
dConstC * (1.0 - 2.0 * dScaledZ * dScaledZ)
* exp(- dScaledZ * dScaledZ);
double dIntTau1 =
dConstA * (exp(ParamLapseRate / dT0 * dZ) - 1.0)
+ dConstB * dZ * exp(- dScaledZ * dScaledZ);
double dIntTau2 =
dConstC * dZ * exp(- dScaledZ * dScaledZ);
// Calculate utility terms
double dRRatio;
if (m_fDeepAtmosphere) {
dRRatio = dR / phys.GetEarthRadius();
} else {
dRRatio = 1.0;
}
double dInteriorTerm = pow(dRRatio * cos(dLat), ParamK)
- ParamK / (ParamK + 2.0) * pow(dRRatio * cos(dLat), ParamK + 2.0);
// Calculate temperature
double dTemperature = 1.0
/ (dRRatio * dRRatio)
/ (dTau1 - dTau2 * dInteriorTerm);
// Calculate hydrostatic pressure
double dPressure = phys.GetP0() * exp(
- phys.GetG() / phys.GetR()
* (dIntTau1 - dIntTau2 * dInteriorTerm));
// Calculate hydrostatic density
double dRho = dPressure / (phys.GetR() * dTemperature);
// Velocity field
double dInteriorTermU =
pow(dRRatio * cos(dLat), ParamK - 1.0)
- pow(dRRatio * cos(dLat), ParamK + 1.0);
double dBigU = phys.GetG() / phys.GetEarthRadius() * ParamK
* dIntTau2 * dInteriorTermU * dTemperature;
double dRCosLat;
if (m_fDeepAtmosphere) {
dRCosLat = dR * cos(dLat);
} else {
dRCosLat = phys.GetEarthRadius() * cos(dLat);
}
double dOmegaRCosLat = phys.GetOmega() * dRCosLat;
if (dOmegaRCosLat * dOmegaRCosLat + dRCosLat * dBigU < 0.0) {
_EXCEPTIONT("Negative discriminant detected.");
}
double dUlon = - dOmegaRCosLat +
sqrt(dOmegaRCosLat * dOmegaRCosLat + dRCosLat * dBigU);
double dUlat = 0.0;
// Calculate velocity perturbation
double dUlonPert;
double dUlatPert;
EvaluatePointwisePerturbation(
phys, dZ, dLon, dLat,
dUlonPert, dUlatPert);
dUlon += dUlonPert;
dUlat += dUlatPert;
// Store the state
dState[0] = dUlon;
dState[1] = dUlat;
dState[2] = phys.RhoThetaFromPressure(dPressure) / dRho;
dState[3] = 0.0;
dState[4] = dRho;
}
