Torsten Mayer-Gürr

Combined satellite gravity field model GOCO01S derived from GOCE and GRACE

[1]xa0The satellite-only gravity field model GOCO01S is a combination solution based on 61 days of GOCE gravity gradient data, and 7 years of GRACE GPS and K-band range rate data, resolved up to degree/order 224 of a harmonic series expansion. The combination was performed consistently by addition of full normal equations and stochastic modeling of GOCE and GRACE observations. The model has been validated against external global gravity models and regional GPS/leveling observations. While low to medium degrees are mainly determined by GRACE, significant contributions by the new measurement type of GOCE gradients can already be observed at degree 100. Beyond degree 150, GOCE becomes the dominant contributor. Correspondingly, with GOCO01S a global gravity field model with high performance for the complete spectral range up to degree/order 224 is now available. This new gravity model will be beneficial for many applications in geophysics, oceanography, and geodesy.

Deriving daily snapshots of the Earth's gravity field from GRACE L1B data using Kalman filtering

[1]xa0Different GRACE data analysis centers provide temporal variations of the Earths gravity field as monthly, 10-daily or weekly mean fields. These solutions are derived independently for each time span, i.e., no correlation between the analyzed batches is considered. Following this procedure, an increase in temporal resolution is accompanied by a loss in accuracy. To avoid this problem, a new approach is followed, which takes into account the temporal correlations of the gravity field variations thus enabling the enhancement of the temporal resolution up to daily snapshots. The GRACE Level-1B (L1B) instrument data processing is performed within the framework of a Kalman filter estimation procedure, where the information about the temporal correlation patterns can be derived from geophysical models. The WaterGAP hydrological model was analyzed to derive the required information in terms of an empirical auto-covariance function. First results are presented and compared to GFZ-RL04 monthly and weekly gravity field solutions.

ITG-GRACE: Global Static and Temporal Gravity Field Models from GRACE Data

More than 4 years of GRACE data were used to determine the gravity field model ITG-Grace03 s. The solution consists of three parts: a static high resolution model up to a spherical harmonic degree of 180, temporal variations up to degree 40 and the full variance-covariance matrix for the static solution. The temporal gravity field variations are parameterized by continuous basis functions in the time domain. The physical model of the gravity field recovery technique is based on Newton’s equation of motion, formulated as a boundary value problem in the form of a Fredholm type integral equation. The principal characteristic of this method is the use of short arcs of the satellite’s orbit in order to avoid the accumulation of modeling errors and a rigorous consideration of correlations between the range observations in the subsequent adjustment procedure.

Gravity Field Recovery from GRACE-SST Data of Short Arcs

The signal content in the low-low SST observables of the gravity field twin-satellite mission GRACE (Gravity Recovery And Climate Experiment) varies in the space domain depending on the roughness of the gravity field features. On the one hand, the maximum degree of the spherical harmonic expansion has to be selected as high as possible to bring out the maximum of gravity field information out of the data. On the other hand, an increasing maximal degree deteriorates the stability of the normal equations to solve for the gravity field parameters. Therefore, a trade-off is necessary between the selection of a maximal degree adequate for representing the signal content in the observables, on the one hand, and a maximal degree which can still be recovered without causing instabilities, on the other hand. We propose to integrate the global gravity field recovery with regional gravity field refinements tailored to the specific gravity field features in these regions: In a first step, the gravity field only up to a moderate safely determinable degree is recovered; the specific analysis features tailored to the individual gravity field characteristics in areas of rough gravity field signal will be modelled subsequently by space localizing base functions in a second step. In a final third step, a spherical harmonic expansion up to an (in principle) arbitrary degree can be derived based on a numerical Gauss — Legendre - quadrature procedure without any stability problems. The procedure will be applied in a first example to observations of a GRACE simulation scenario to test the potential capabilities of the approach. A second application demonstrates the determination of a global gravity field model and regional refinements based on low-low SST data of the GRACE twin satellite mission for the August 2003 observations.

Gravity Field Recovery and Validation by Analysis of Short Arcs of a Satellite-to-Satellite Tracking Experiment as CHAMP and GRACE

A procedure for gravity field determination is presented based on the analysis of short arcs of low flying satellites as CHAMP and GRACE. The analysis technique can be applied to high-low as well as to low-low satellite-to-satellite tracking in a consistent way. The method allows to recover the global gravity field of the Earth, combined with a regional gravity field refinement in regions with rough gravity field features. To detect regional residual signals in the observations a preprocessing step is being applied based on the energy balances along the short arcs. This procedure will be applied as well as the validation of the regional gravity field refinement in a post-processing step. First results are presented by using Post-processed Science Orbits (PSO) of CHAMP for a region with rough gravity field features. To demonstrate the applicability to a tailored low-low satellite-to-satellite tracking experiment the procedure is applied to a GRACE simulation scenario.

Gravity Field Recovery by Analysis of Short Arcs of CHAMP

The gravity field recovery strategy presented here enables the global recovery of the gravity field combined with a regional focus on geographical areas with rough gravity field features in a consistent way. The global gravity field is modeled by a series of spherical harmonics while the regional gravity field features are represented by space localizing base functions of harmonic spline type. The physical model of the orbit analysis technique is based on Newtons equation of motion, formulated as a boundary value problem in form of an integral equation of Fredholm type. The observation equations are established for short arcs of approximately 30 minutes length. The procedure can be applied either globally or regionally to selected geographical regions. For a regional application the coverage with short arcs should be slightly larger than the recovery region itself to prevent the solution from geographical truncation effects. A proper combination and weighting of the normal equations of every arc combined with a tailored regularization allows a stable solution for the field parameters. This procedure can be adapted to the roughness of the regional gravity field features, the discretization of the gravity field and the sampling rate of the observations. A global gravity field solution ITG-Champ01E has been derived based on kinematic orbits covering 360 days from March 2002 to March 2003. Regional gravity field solution have been determined for selected regions with rugged gravity field features.

Do We Need New Gravity Field Recovery Techniques for the New Gravity Field Satellites

The classical approach of satellite geodesy consists in deriving the spherical harmonic coefficients representing the gravitational potential from an analysis of accumulated orbit perturbations of artificial satellites with different altitudes and orbit inclinations. This so-called differential orbit improvement technique required the analysis of rather long arcs of days to weeks; it was the adequate technique for satellite arcs poorly covered with observations, mainly precise laser ranging to satellites. The situation changed dramatically with the new generation of dedicated gravity satellites such as CHAMP, GRACE and – in a couple of months – GOCE. These satellites are equipped with very precise sensors to measure the gravity field and the orbits. The sensors provide a very dense coverage with observations independent from Earth based observation stations. The measurement concepts can be characterized by an in-situ measurement principle of the gravitational field of the Earth. In the last years various recovery techniques have been developed which exploit these specific characteristics of the in-situ observation strategy. This paper gives an overview of the various gravity field recovery principles and tries to systemize these new techniques. Alternative in-situ modelling strategies are presented based on the translational and rotational integrals of motion. These alternative techniques are tailored to the in-situ measurement characteristics of the innovative type of satellite missions. They complement the scheme of in-situ gravity field analysis techniques.

Regionally Refined Gravity Field Models from In-Situ Satellite Data

The satellite mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) will enable the determination of the Earth’s gravity field with unprecedented accuracy, especially regarding the high-frequency part of the gravity field spectrum. To exploit the full potential of the mission, it is advantageous to develop methods to extract as much information out of the given signal as possible. In the approach presented here a global gravity field represented by a spherical harmonic expansion up to a moderate degree is derived in a first step and then refined by regionally adapted high resolution refinements being parameterized by splines as space localizing basis functions. These radial basis functions are designed to reflect the spectral characteristics of the gravity field to be modeled. Another important aspect in the regional gravity field analysis approach is the downward continuation process. In this context, a regionally adapted regularization will be introduced, which assigns different regularization matrices to geographical areas with varying signal content. Regularization parameters individually determined for each region take into account the varying frequency behavior, allowing to extract additional information out of a given data set. If desired, regional solutions with global coverage can be combined to a global solution using quadrature methods. The approach is demonstrated by a simulation scenario that combines a global GRACE solution as reference field with regional refinements calculated from GOCE observations.

An Integrated Global/Regional Gravity Field Determination Approach based on GOCE Observations

GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) is a dedicated satellite gravity field mission to be launched in the year 2006. The payload of GOCE will consist of a GPS receiver for a precise orbit determination and for recovering the long and medium spectral part of the gravity field. The high resolution spectral part of the gravity field will be derived by in-orbit gravity gradients in three spatial directions measured by a gravity gradiometer consisting of six three-axis accelerometers. In this article an integrated gravity field recovery procedure is presented that allows to determine a global gravity field solution with high long and medium wavelength accuracy and to improve this global solution in regions with characteristic gravity field features by an adapted regional recovery procedure. If necessary, several regional solutions with global coverage can be merged by means of quadrature methods to obtain an improved global solution. Simulation results are presented to demonstrate this approach. Due to the improved regionally adapted gravity field solutions this technique provides better global gravity field recovery results than calculating a spherical harmonics solution by recovering the potential coefficients directly.

Global gravity field recovery by merging regional focusing patches: an integrated approach

Usually the gravity potential is modelled by a spherical harmonic expansion. Simulation tests and real-data investigations based on POD (precise orbit determination) and SST (satellite-to-satellite tracking) data demonstrated that the heterogeneity of the gravity field cannot be properly taken into account by base functions with global support. It is preferable to model the gravity field only up to a moderate safely determinable spherical harmonic degree without any regularization to cover the long and medium wavelengths characteristics; the specific detailed features tailored to the individual gravity field characteristics in areas of rough gravity field signal can be modelled additionally by space localizing base functions. In a final step, a spherical harmonic expansion up to a maximum degree, only limited by the most detailed structures of the gravity field, can be derived based on a Gauss-Legendre-Quadrature procedure. This last step can be performed without stability problems and without losing the regional details of the gravity field. The proposed integrated gravity field recovery approach integrates consistently a regional gravity field zoom-in into a global gravity field solution. The technique has been applied to the determination of gravity field models based on SST data of GRACE.