/// <summary>
/// Evaluate the state vector at the given point.
/// </summary>
virtual void EvaluatePointwiseState(
const PhysicalConstants & phys,
const Time & time,
double dZp,
double dXp,
double dYp,
double * dState,
double * dTracer
) const {
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();
// The Brunt-Vaisala frequency
const double dNbar = dG / sqrt(dCp * m_dT0);
// Base potential temperature field
const double dTheta0 = m_dT0;
double dThetaBar = dTheta0 * exp(dNbar * dNbar / dG * dZp);
// Set the uniform U, V, W field for all time
dState[0] = m_dU0;
dState[1] = 0.0;
dState[3] = 0.0;
// Set the initial potential temperature field
dState[2] = dThetaBar;
// Set the initial density based on the Exner pressure
double dExnerP = exp(-dG / (dCp * m_dT0) * dZp);
double dRho = dP0 / (dRd * dThetaBar) * pow(dExnerP,(dCv / dRd));
dState[4] = dRho;
}
/// <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 reference state at the given point.
/// </summary>
virtual void EvaluateReferenceState(
const PhysicalConstants & phys,
double dZp,
double dXp,
double dYp,
double * dState
) const {
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();
// Base potential temperature field
double dThetaBar = m_dTheta0 * exp(m_dNbar * m_dNbar / dG * dZp);
// Set the uniform U, V, W field for all time
dState[0] = m_dU0;
dState[1] = 0.0;
dState[3] = 0.0;
// Zero gravity case
if (dG == 0.0) {
static double dT0 = 300.0;
dState[2] = dT0 * pow(dP0, (dRd / dCp));
dState[4] = dP0 / (dRd * dT0);
// Stratification with gravity
} else {
// Set the initial density based on the Exner pressure
double dExnerP = (dG * dG) / (dCp * m_dTheta0 * m_dNbar * m_dNbar);
dExnerP *= (exp(-m_dNbar * m_dNbar / dG * dZp) - 1.0);
dExnerP += 1.0;
double dRho = dP0 / (dRd * dThetaBar) * pow(dExnerP,(dCv / dRd));
dState[4] = dRho;
// Set the initial potential temperature field
//dState[2] = phys.PressureFromRhoTheta(dThetaBar * dRho);
//dState[2] = (dThetaBar * dRho);
dState[2] = dThetaBar;
}
}
/// <summary>
/// Evaluate the state vector at the given point.
/// </summary>
virtual void EvaluatePointwiseState(
const PhysicalConstants & phys,
const Time & time,
double dZp,
double dXp,
double dYp,
double * dState,
double * dTracer
) const {
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();
// Base potential temperature field
double dThetaBar = m_dTheta0 * exp(m_dNbar * m_dNbar / dG * dZp);
// Set the uniform U, V, W field for all time
dState[0] = m_dU0;
dState[1] = 0.0;
dState[3] = 0.0;
dState[3] = sin(M_PI * dZp / m_dGDim[5]);
// Set the initial density based on the Exner pressure
double dExnerP = (dG * dG) / (dCp * m_dTheta0 * m_dNbar * m_dNbar);
dExnerP *= (exp(-m_dNbar * m_dNbar / dG * dZp) - 1.0);
dExnerP += 1.0;
double dRho = dP0 / (dRd * dThetaBar) * pow(dExnerP,(dCv / dRd));
dState[4] = dRho;
// Set the initial theta field
//dState[2] = phys.PressureFromRhoTheta(dThetaBar * dRho);
//dState[2] = (dThetaBar * dRho);
dState[2] = dThetaBar;
}
