Torsten Mayer-Guerr

Global Gravity Field Solutions Based on a Simulation Scenario of GRACE SST Data and Regional Refinements by GOCE SGG Observations

GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) has the potential of deriving the global gravity field with unprecedented accuracy in the high resolution spectral part. The usual way is to model the gravity field by spherical harmonics up to a degree limited by the numerical stability of the recovery procedure. A disadvantage of this kind of gravity field representation is the lack of flexibility in modeling the inhomogeneous gravity field of regions with variable rough gravity field features. An alternative approach is to determine a global gravity field solution with high long and medium wavelength accuracy, e.g. based on GRACE SST observations up to a moderate degree, and improve this global solution in regions with characteristic gravity field features by an adapted regional recovery procedure. The individual gravity field features in these regions can be modeled by space localizing base functions like spherical spline functions. The advantage of this method is the possibility of adjusting the spline representation and the recovery procedure according to the regional gravity field structures and the specific data distribution. As a first indicator of a rough gravity field the structure of the topography or geophysical apriori information can be used as a criterium. The resolution of the regional gravity field can be further improved by a subsequent iteration step. If neccessary, several regional solutions with global coverage can be merged by means of quadrature methods to obtain a global solution. Simulation results are presented to demonstrate this approach. Due to the regionally adapted recovery strategies this method provides better results than calculating a spherical harmonics solution by recovering the potential coefficients directly.

Improved Resolution of a GRACE Gravity Field Model by Regional Refinements

The available gravity field models derived from data of the GRACE mission (tapley and Reigber (2001)) have provided us with an unprecedented accuracy in gravity field determination. Nevertheless the projected GRACE baseline accuracy has not been achieved yet. One reason out of many could be the insufficient modelling of the satellite data by a global representation by means of spherical harmonics. To extract the signal information present in the satellite and sensor data to full content, it seems reasonable to improve global solutions by regional recovery strategies. Especially in the higher frequency part of the spectrum the gravity field features differ in different geographical areas. Therefore the recovery procedure should be adapted according to the characteristics in the respective area.

A Comparison of Various Procedures for Global Gravity Field Recovery from CHAMP Orbits

We compare selected techniques for recovering the global gravity field from precisely determined kinematic CHAMP orbits. The first method derives the second derivatives by use of an interpolation polynomial. The second procedure is based on Newtons equation of motion, formulated and solved as a boundary value problem in time equivalent to a corresponding integral equation of Fredholm type. It is applied to short arcs of the CHAMP orbits. The third method is based on the energy balance principle. We implement the analysis of in-situ potential differences following Jekelis formulation. The normal equations from the three approaches are solved using Tikhonov-type regularization, where the regularization parameter is computed according to a variance component estimation procedure. The results are compared with the recent satellite-only model EIGEN2 and the first GRACE model GGM01s. All methods provide solutions of the gravity field which represent significant improvements with respect to the reference model EGM96 below degree 50. The quality of the solutions differs only slightly.

Challenges in Deriving Trends from GRACE

The following contribution addresses some of the problems involved with the determination of long-term gravity field variations from GRACE satellite observations. First of all the choice of the time span plays a very important role, especially since it generally is a hard task to derive secular trends from only a few years of satellite data. Another issue, when one is interested in a single trend phenomenon, is the reduction of all other geophysical effects causing long-term gravity field variations. This paper uses the example of trends in continental hydrological water masses for the case of the High Plains aquifer to demonstrate some of the challenges implicated by trend analysis from GRACE.