Gerrit Austen

Analysis of the Earth’s Gravitational Field from Semi-Continuous Ephemeris of a Low Earth Orbiting GPS-Tracked Satellite of Type CHAMP, GRACE or GOCE

The aim is to present and to examine an algorithm for the orbit analysis of a low-Earthorbiting GPS-tracked satellite to determine the spherical harmonic coefficients of the Earth’s gravitational field. By means of Newton’s interpolation scheme the accelerations acting on the satellite are derived from the satellite’s GPSpositions x(t k ), y(t k ), z(t k ) or position differences Δx,(t k-1 k ), Δy(t k-1 k ), Δz(t k-1 k ). This is done in a quasiInertial Reference Frame to avoid frame accelerations. The acceleration vector is balanced due to Newton’s equation of motion by the gravitational force vector, namely the gradient of the gravitational potential. The coordinates of the gradient of the gravitational potential, which are given in a Cartesian representation, also have to be transformed to the quasi-Inertial Reference Frame. The resulting equation system is then solved by means of a Gauss-Markov model. In order to get a more stable solution for higher resolutions a regularization method (Tikhonov, Kaula) can be applied.

Mapping Earth’s Gravitation Using GRACE Data

This article describes an approach for global mapping of the Earth’s gravitational field developed, tested and successfully implemented at the Geodetic Institute of the Stuttgart University. The method is based on the Newtonian equation of motion that relates satellite-to-satellite tracking (SST) data observed by the two satellites of the Gravity Recovery And Climate Experiment (GRACE) directly to unknown spherical harmonic coefficients of the Earth’s gravitational potential (geopotential). Observed values include SST data observed both in the low-low (inter-satellite range, velocity and acceleration) and the high-low (satellites’ positions) mode. The low-low SST data specific for the time being to the GRACE mission are available through a very sensitive K-band ranging system. The high-low SST data are then provided by on-board Global Positioning System (GPS) receivers. The article describes how the mathematical model can be modified. The geopotential is approximated by a truncated series of spherical harmonic functions. An alternative approach based on integral inversion of the GRACE data into the geopotential is also formulated and discussed. The article also presents sample numerical results obtained by testing the model using both simulated and observed data. Simulation studies suggest that the model has a potential for recovery of the Stokes coefficients up to degree and order 120. Intermediate results from the analysis of actual data have a lower resolution.

Use of High Performance Computing in Gravity Field Research

In the light of the three geoscientific satellite missions CHAMP, GRACE and GOCE the overall scientific aim is to achieve an automatism for the recovery of the Earth’s gravity field respectively the physical shape of the Earth, namely the geoid. Furthermore, an improved understanding of the spatial and temporal variations of the geoid is of great benefit for the study of the dynamics of the Earth’s lithosphere and upper mantle, global sea level variations, ocean circulation and ocean mass and heat transport, ice mass balance, the global water cycle and the interaction of these phenomena. This involves the determination of up to a hundred thousand unknown coefficients of the corresponding series expansion model from data sets which amount to several millions of observations provided by the satellites. The resulting system of equations which has to be solved for such an analysis cannot be evaluated without simplistic assumptions or within a satisfying time frame on personal computers due to hardware limitations. Consequently this challenging problem has to be tackled by means of high performance computing strategies. Only adoption of parallel programming standards such as MPI or OpenMP in conjunction with highly efficient numerical libraries allows for successfully accomplishing the demands of gravity field analysis. Indeed, the huge amount of data provided by satellite sensors, together with a high-resolution gravity field modeling, requires the determination of several ten thousands of unknown parameters and leads to the assignment that this problem is a true “challenge of calculus”.

Efficient Satellite Based Geopotential Recovery

This contribution aims at directing the attention towards the main inverse problem of geodesy, i.e. the recovery of the geopotential. At present, geodesy is in the favorable situation that dedicated satellite missions for gravity field recovery are already operational, providing globally distributed and high-resolution datasets to perform this task. Due to the immense amount of data and the ever-growing interest in more detailed models of the Earth’s static and time-variable gravity field to meet the current requirements of geoscientific research, new fast and efficient solution algorithms for successful geopotential recovery are required.