A concept for the estimation of high-degree gravity field models in a high performance computing environment

Abstract

The determination of global gravity field models by the combination of complementary observations within a joint adjustment is a computationally expensive task. Global gravity field models are typically parameterized by a finite series of spherical harmonic base functions. The effort to compute the set of coefficients depends on the one hand on the maximum degree of the spherical harmonic expansion and on the other hand on the number of observations and their stochastic characteristics. The main result of this contribution is a computation scheme for the rigorous (i.e. avoiding computationally motivated approximations) estimation of high-degree gravity models. A conjugate gradient based iterative solver is implemented in a high performance computing environment allowing to estimate hundreds of thousands to millions of unknown parameters. To perform the computations in a reasonable time, the solver is designed to operate on thousands of computing cores. A flexible design is considered to process an arbitrary number of observation groups. For each group a variance component can be estimated to derive a data adaptive weighting factor. The combined solution results from the weighted joint inversion of all observation groups, which might be provided in terms of preprocessed normal equations (e.g. from satellite gravity field missions like GRACE or GOCE) or in terms of observations like datasets of point-wise terrestrial gravity field information. A small-scale closed-loop simulation (250000 unknowns, spherical harmonic degree and order 500) for the estimation of the Earth’s gravity field serves as proof of concept. Normal equations derived by observations from three satellite missions and 15 datasets of point-wise measurements (gravity anomalies and along-track altimetry) are combined in the gravity field adjustment. The simulation study i) verifies the implementation, ii) analyzes the computational effort of the individual steps involved and iii) leads to the main conclusion that the rigorous least-squares solution can be determined in a reasonable amount of time.