Geopotential Model ( Spanish version)


Program objectives

The GPS receivers allow calculating the ellipsoidal heights, but when you need to obtain heights referred to mean sea level, these ellipsoidal heights must be converted into orthometric heights by subtracting geoidal heights. Here you need to compute geoidal heights for a site by entering its geographical latitude and longitude. At this point, it is the application and utility of this computer program. You can compute the geoid height for any location on the globe from a spherical harmonic expansion of the earth disturbing potential, to degree and order 360. These geoidal heights are referred to the Geodetic Reference System 1980 (GRS80).

Another important application of this program is the calculation of theoretical gravity anomalies. Because of the gravity anomalies are given in a limited area cannot resolve the long wavelengths of the gravity field. Then, a geopotential model is needed for the computation of these long wavelengths, which represents a smooth approximation of the geoid for the local area under study. Thus, this program allows the computation of the free-air anomalies referenced to the geopotential model, computing the difference between the observed free-air anomalies and the anomalies predicted by this model, these differences could be used in a FFT integration procedure to obtain the undulation of the geoid.

Program description

The GEOSAT program and its files, which are needed to run this application, are enclosed into a ZIP file named "geodesy.zip". When you have got the ZIP file and you have uncompressed this file, you must have three files named geosat.exe, geosat.dat and model.dat. The file named model.dat contains fully-normalized, unitless spherical harmonic coefficients and their standard deviations, for the gravitational model complete from degree 2 order 0 to degree and order 360. This file contains 65338 records and each record is in the format:

(n,m,Cnm,Snm,SigmaCnm,SigmaSnm) --- FORMAT(2I4,2E20.12,2E16.8)

where n is the degree, m is the order, (Cnm,Snm) are the harmonic coefficients and (SigmaCnm,SigmaSnm) are 1-sigma errors in the harmonic coefficients. The file geosat.exe contains a program (in FORTRAN code for PC) for the computation of point values of the geoid height and gravity anomaly, also it is possible make these computations for a grid point data. This option and all program capabilities are controlled by parameters enclosed in the file named geosat.dat. This file is in the free format and contains the parameters:

(NOPT,NMAX,NX,NY,DX,DY,LAT,LONG)

The description of all parameters is as follows:

NOPT = With value 1 makes the computation of point values of the geoid height, gravity anomaly and deflection of the vertical (with both components). With value 0 makes the same for a grid data points. With value 2 performs the computation for the point values listed in a file named input.dat. This file is an ASCII file with the latitude and longitude of the computation points. At the final of the computation, we obtain a new file named output.dat which contains the results: the geoid undulation in the points listed in the file input.dat.
NMAX = Selects maximum degree and order to be considered in the geopotential model.
NX = Number of points data in the grid for x-axis (šE longitude). This value is only taken into account if NOPT = 0.
NY = Number of points data in the grid for y-axis (šN latitude). This value is only taken into account if NOPT = 0.
DX= Distance increment between the values in x-axis. Units are in degrees. Only equidistant points are taken into account.
DY= Distance increment between the values in y-axis. Units are in degrees. Only equidistant points are taken into account.
LAT,LONG = Geographical coordinates for the origin point of the grid (only when NOPT=0).

The file geosat.dat contains values for all mentioned parameters and the above description in spanish language. These values are an example to obtain the geoid height and gravity anomaly for NMAX = 360.