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/***********************************************/
/**
* @file griddedTopography2PotentialCoefficients.cpp
*
* @brief Estimate potential coefficients from digital terrain models.
*
* @author Torsten Mayer-Guerr
* @date 2011-11-01
*/
/***********************************************/
// Latex documentation
#define DOCSTRING docstring
static const char *docstring = R"(
Estimate potential coefficients from digital terrain models.
Coefficients for interior $(1/r)^{n+1}$ and exterior ($r^n$) are computed.
)";
/***********************************************/
#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 potential coefficients from digital terrain models.
* @ingroup programsGroup */
class GriddedTopography2PotentialCoefficients
{
public:
void run(Config &config, Parallel::CommunicatorPtr comm);
};
GROOPS_REGISTER_PROGRAM(GriddedTopography2PotentialCoefficients, PARALLEL, "Estimate potential coefficients from digital terrain models", Grid, PotentialCoefficients)
/***********************************************/
void GriddedTopography2PotentialCoefficients::run(Config &config, Parallel::CommunicatorPtr comm)
{
try
{
FileName fileNameOutExterior, fileNameOutInterior;
FileName fileNameInGrid;
ExpressionVariablePtr expressionUpper, expressionLower, expressionRho;
Double factor;
UInt minDegree, maxDegree;
Double GM, R;
readConfig(config, "outputfilePotentialCoefficients", fileNameOutExterior, Config::OPTIONAL, "", "");
readConfig(config, "outputfilePotentialCoefficientsInterior", fileNameOutInterior, Config::OPTIONAL, "", "");
readConfig(config, "inputfileGriddedData", fileNameInGrid, Config::MUSTSET, "", "Digital Terrain Model");
readConfig(config, "density", expressionRho, Config::DEFAULT, "2670", "expression [kg/m^3]");
readConfig(config, "radialUpperBound", expressionUpper, Config::DEFAULT, "data0", "expression (variables 'L', 'B', 'height', 'data', and 'area' are taken from the gridded data");
readConfig(config, "radialLowerBound", expressionLower, Config::DEFAULT, "0", "expression (variables 'L', 'B', 'height', 'data', and 'area' are taken from the gridded data");
readConfig(config, "factor", factor, Config::DEFAULT, "1.0", "the result is multiplied by this factor");
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;
std::vector<Double> lambda, phi;
Matrix rLower, rUpper, rho;
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 upper and lower height"<<Log::endl;
VariableList varList;
addDataVariables(grid, varList);
expressionUpper->simplify(varList);
expressionLower->simplify(varList);
expressionRho ->simplify(varList);
std::vector<Double> radius(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();
rLower = rUpper = rho = 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);
rUpper(i,k) = radius.at(i) + expressionUpper->evaluate(varList);
rLower(i,k) = radius.at(i) + expressionLower->evaluate(varList);
rho(i,k) = expressionRho->evaluate(varList);
}
});
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))
if(Parallel::size(comm) > 1)
logStatus<<"broadcast data"<<Log::endl;
Parallel::broadCast(rUpper, 0, comm);
Parallel::broadCast(rLower, 0, comm);
Parallel::broadCast(rho, 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) = std::remainder(lambda.at(i+1)-lambda.at(i), 2*PI);
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, snmExt, cnmInt, snmInt;
if(!fileNameOutExterior.empty()) cnmExt = Matrix(maxDegree+1, Matrix::TRIANGULAR, Matrix::LOWER);
if(!fileNameOutExterior.empty()) snmExt = Matrix(maxDegree+1, Matrix::TRIANGULAR, Matrix::LOWER);
if(!fileNameOutInterior.empty()) cnmInt = Matrix(maxDegree+1, Matrix::TRIANGULAR, Matrix::LOWER);
if(!fileNameOutInterior.empty()) snmInt = Matrix(maxDegree+1, Matrix::TRIANGULAR, Matrix::LOWER);
Parallel::forEach(phi.size()-1, [&](UInt i)
{
const Matrix Pnm = LegendreFunction::integral(std::sin(std::min(phi.at(i), phi.at(i+1))),
std::sin(std::max(phi.at(i), phi.at(i+1))), maxDegree);
// const Matrix Pnm = LegendreFunction::compute(std::sin(0.5*(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
if(!fileNameOutExterior.empty())
{
Matrix fExt(lambda.size()-1, maxDegree+1);
for(UInt k=0; k<lambda.size()-1; k++)
if(rho(i,k) && (std::fabs(rUpper(i,k)-rLower(i,k)) > 0.001))
{
const Double term = factor * rho(i,k) * GRAVITATIONALCONSTANT/GM * R*R*R;
const Double r1R = rLower(i,k)/R;
const Double r2R = rUpper(i,k)/R;
Double r1RnExt = term * std::pow(r1R, minDegree+3);
Double r2RnExt = term * std::pow(r2R, minDegree+3);
for(UInt n=minDegree; n<=maxDegree; n++)
{
fExt(k,n) = (r2RnExt-r1RnExt)/((2.*n+1)*(n+3.));
r1RnExt *= r1R;
r2RnExt *= r2R;
} // for(n)
} // for(i)
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));
}
} // if(!fileNameOutExterior.empty())
if(!fileNameOutInterior.empty())
{
Matrix fInt(lambda.size()-1, maxDegree+1);
for(UInt k=0; k<lambda.size()-1; k++)
if(rho(i,k) && (std::fabs(rUpper(i,k)-rLower(i,k)) > 0.001))
{
const Double term = factor * rho(i,k) * GRAVITATIONALCONSTANT/GM * R*R*R;
const Double Rr1 = R/rLower(i,k);
const Double Rr2 = R/rUpper(i,k);
Double r1RnInt = term * std::pow(Rr1, minDegree-2.);
Double r2RnInt = term * std::pow(Rr2, minDegree-2.);
for(UInt n=minDegree; n<=maxDegree; n++)
{
if(n != 2)
fInt(k,n) = (r2RnInt-r1RnInt)/((2*n+1)*(2.-n));
else
fInt(k,n) = term * std::log(rUpper(i,k)/rLower(i,k))/(2*n+1);
r1RnInt *= Rr1;
r2RnInt *= Rr2;
} // for(n)
} // for(i)
for(UInt n=minDegree; n<=maxDegree; n++)
for(UInt m=0; m<=n; m++)
{
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));
}
} // if(!fileNameOutInterior.empty())
}, comm);
if(!fileNameOutExterior.empty()) Parallel::reduceSum(cnmExt, 0, comm);
if(!fileNameOutExterior.empty()) Parallel::reduceSum(snmExt, 0, comm);
if(!fileNameOutInterior.empty()) Parallel::reduceSum(cnmInt, 0, comm);
if(!fileNameOutInterior.empty()) 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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