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/***********************************************/
/**
* @file griddedTopography2AtmospherePotentialCoefficients.cpp
*
* @brief Estimate interior and exterior potential coefficients for atmosphere above digital terrain models.
*
* @author Christian Pock
* @author Daniel Rieser
* @date 2013-10-16
*/
/***********************************************/
// Latex documentation
#define DOCSTRING docstring
static const char *docstring = R"(
Estimate interior and exterior potential coefficients for atmosphere above digital terrain models.
Coefficients for interior $(1/r)^{n+1}$ and exterior ($r^n$) are computed.
The density of the atmosphere is assumed to be (Sjöberg, 1998)
\begin{equation}
\rho_0\left(\frac{R}{R+h}\right)^\nu,
\end{equation}
where $R$ is the radial distance of the ellipsoid at each point, $h$ the radial height above the ellipsoid,
$\rho_0$ is \config{densitySeaLevel} and \config{nu} $\nu$ is a constant factor. The density is integrated
from \config{radialLowerBound} and \config{upperAtmosphericBoundary} above the ellipsoid.
The \config{radialLowerBound} is typically the topography and can be computed as expression at every point
from \configFile{inputfileGriddedData}{griddedData}.
)";
/***********************************************/
#include "programs/program.h"
#include "base/legendreFunction.h"
#include "parser/dataVariables.h"
#include "files/fileGriddedData.h"
#include "files/fileSphericalHarmonics.h"
#include "misc/miscGriddedData.h"
/***** CLASS ***********************************/
/** @brief Estimate interior and exterior atmospheric potential coefficients above digital terrain models.
* @ingroup programsGroup */
class GriddedTopography2AtmospherePotentialCoefficients
{
public:
void run(Config &config, Parallel::CommunicatorPtr comm);
};
GROOPS_REGISTER_PROGRAM(GriddedTopography2AtmospherePotentialCoefficients, PARALLEL, "Estimate interoir and exterior atmospheric potential coefficients above digital terrain models", Grid, PotentialCoefficients)
/***********************************************/
void GriddedTopography2AtmospherePotentialCoefficients::run(Config &config, Parallel::CommunicatorPtr comm)
{
try
{
FileName fileNameOutExterior, fileNameOutInterior, fileNameInGrid;
ExpressionVariablePtr expressionLower;
Double rho, ny, upperBoundary, factor;
UInt minDegree, maxDegree;
Double GM, R;
readConfig(config, "outputfilePotentialCoefficientsExterior", fileNameOutExterior, Config::OPTIONAL, "", "");
readConfig(config, "outputfilePotentialCoefficientsInterior", fileNameOutInterior, Config::OPTIONAL, "", "");
readConfig(config, "inputfileGriddedData", fileNameInGrid, Config::MUSTSET, "", "Digital Terrain Model");
readConfig(config, "densitySeaLevel", rho, Config::DEFAULT, "1.225", "[kg/m**3]");
readConfig(config, "ny", ny, Config::DEFAULT, "680", "Constant for Atmosphere");
readConfig(config, "radialLowerBound", expressionLower, Config::DEFAULT, "data0", "expression (variables 'L', 'B', 'height', 'data', and 'area' are taken from the gridded data");
readConfig(config, "upperAtmosphericBoundary", upperBoundary, Config::DEFAULT, "11000", "constant upper bound [m]");
readConfig(config, "factor", factor, Config::DEFAULT, "1.0", "the result is multiplied by this factor, set -1 to subtract the field");
readConfig(config, "minDegree", minDegree, Config::DEFAULT, "0", "");
readConfig(config, "maxDegree", maxDegree, Config::MUSTSET, "", "");
readConfig(config, "GM", GM, Config::DEFAULT, STRING_DEFAULT_GM, "Geocentric gravitational constant");
readConfig(config, "R", R, Config::DEFAULT, STRING_DEFAULT_R, "reference radius");
if(isCreateSchema(config)) return;
// read rectangular grid
// ---------------------
std::vector<Double> lambda, phi, radius;
Matrix topo;
if(Parallel::isMaster(comm))
{
// read rectangular grid
// ---------------------
logStatus<<"read grid from file <"<<fileNameInGrid<<">"<<Log::endl;
GriddedDataRectangular grid;
readFileGriddedData(fileNameInGrid, grid);
MiscGriddedData::printStatistics(grid);
// evaluate upper and lower height
// -------------------------------
logStatus<<"evaluate expression for lower boundary"<<Log::endl;
VariableList varList;
addDataVariables(grid, varList);
expressionLower->simplify(varList);
radius.resize(grid.heights.size());
for(UInt i=0; i<radius.size(); i++)
radius.at(i) = grid.ellipsoid(Angle(0), grid.latitudes.at(i), grid.heights.at(i)).r();
topo = Matrix(grid.latitudes.size(), grid.longitudes.size());
Single::forEach(grid.latitudes.size(), [&](UInt i)
{
for(UInt k=0; k<grid.longitudes.size(); k++)
{
evaluateDataVariables(grid, i, k, varList);
topo(i, k) = expressionLower->evaluate(varList); // Topography
}
});
grid.cellBorders(lambda, phi);
for(UInt i=0; i<phi.size(); i++)
phi.at(i) = grid.ellipsoid(Angle(0), Angle(phi.at(i)), 0.).phi(); // geocentric
} // if(Parallel::isMaster(comm))
Parallel::broadCast(topo, 0, comm);
Parallel::broadCast(radius, 0, comm);
Parallel::broadCast(lambda, 0, comm);
Parallel::broadCast(phi, 0, comm);
// precompute integral_sin, integral_cos
// -------------------------------------
Matrix cosm(lambda.size()-1, maxDegree+1);
Matrix sinm(lambda.size()-1, maxDegree+1);
for(UInt i=0; i<lambda.size()-1; i++)
{
cosm(i,0) = lambda.at(i+1)-lambda.at(i);
for(UInt m=1; m<=maxDegree; m++)
{
cosm(i,m) = (std::sin(m*lambda.at(i+1)) - std::sin(m*lambda.at(i)))/m;
sinm(i,m) = -(std::cos(m*lambda.at(i+1)) - std::cos(m*lambda.at(i)))/m;
}
}
// computing quadrature formular
// -----------------------------
logStatus<<"computing quadrature formular"<<Log::endl;
Matrix cnmExt(maxDegree+1, Matrix::TRIANGULAR, Matrix::LOWER);
Matrix snmExt(maxDegree+1, Matrix::TRIANGULAR, Matrix::LOWER);
Matrix cnmInt(maxDegree+1, Matrix::TRIANGULAR, Matrix::LOWER);
Matrix snmInt(maxDegree+1, Matrix::TRIANGULAR, Matrix::LOWER);
Parallel::forEach(phi.size(), [&](UInt i)
{
// const Matrix Pnm = LegendreFunction::integral(std::sin(phi.at(i+1)), std::sin(phi.at(i)), maxDegree);
const Matrix Pnm = LegendreFunction::compute(std::cos(0.5*(PI-phi.at(i+1)-phi.at(i))), maxDegree)
* std::fabs(std::sin(phi.at(i+1))-std::sin(phi.at(i))); // integral cos(phi) dPhi
const Double H0 = radius.at(i);
const Double term = factor * rho * GRAVITATIONALCONSTANT/GM *R*R*R;
Matrix fExt(lambda.size(), maxDegree+1);
Matrix fInt(lambda.size(), maxDegree+1);
for(UInt k=0; k<lambda.size(); k++)
{
const Double r1R = (1.+upperBoundary/H0);
const Double r2R = (1.+topo(i,k)/H0);
Double r1RnExt = term * std::pow(1.+upperBoundary/H0, 3.+minDegree-ny);
Double r2RnExt = term * std::pow(1.+topo(i,k)/H0, 3.+minDegree-ny);
Double r1RnInt = term * std::pow(1.+upperBoundary/H0, 2.-minDegree-ny);
Double r2RnInt = term * std::pow(1.+topo(i,k)/H0, 2.-minDegree-ny);
for(UInt n=minDegree; n<=maxDegree; n++)
{
if (n == ny-3.)
fExt(k,n) = term/(R*R*R) * std::pow(1./R, n) * std::pow(H0, ny) * std::log((H0+upperBoundary)/(H0+topo(i,k)));
else
fExt(k,n) = (r1RnExt-r2RnExt) * std::pow(H0/R, n+3.)/((2.*n+1.)*(3.+n-ny));
fInt(k,n) = (r1RnInt-r2RnInt) * std::pow(H0/R, 2.-n)/((2.*n+1.)*(2.-n-ny));
r1RnExt *=r1R;
r2RnExt *=r2R;
r1RnInt /=r1R;
r2RnInt /=r2R;
}
}
for(UInt n=minDegree; n<=maxDegree; n++)
for(UInt m=0; m<=n; m++)
{
cnmExt(n,m) += Pnm(n,m) * inner(cosm.column(m), fExt.column(n));
snmExt(n,m) += Pnm(n,m) * inner(sinm.column(m), fExt.column(n));
cnmInt(n,m) += Pnm(n,m) * inner(cosm.column(m), fInt.column(n));
snmInt(n,m) += Pnm(n,m) * inner(sinm.column(m), fInt.column(n));
}
}, comm);
Parallel::reduceSum(cnmExt, 0, comm);
Parallel::reduceSum(snmExt, 0, comm);
Parallel::reduceSum(cnmInt, 0, comm);
Parallel::reduceSum(snmInt, 0, comm);
// save potential coefficients
// ---------------------------
if(Parallel::isMaster(comm) && !fileNameOutExterior.empty())
{
logStatus<<"write potential coefficients to file <"<<fileNameOutExterior<<">"<<Log::endl;
writeFileSphericalHarmonics(fileNameOutExterior, SphericalHarmonics(GM, R, cnmExt, snmExt));
}
if(Parallel::isMaster(comm) && !fileNameOutInterior.empty())
{
logStatus<<"write potential coefficients (interior) to file <"<<fileNameOutInterior<<">"<<Log::endl;
writeFileSphericalHarmonics(fileNameOutInterior, SphericalHarmonics(GM, R, cnmInt, snmInt, TRUE));
}
}
catch(std::exception &e)
{
GROOPS_RETHROW(e)
}
}
/***********************************************/
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