Cummulative Geoid Errors for GRIM5-S1 and Predictions for CHAMP and GRACE
Present models for the mean gravity field of the Earth are derived from combinations of various space and ground based data which have been gathered over the past several decades. These data include terrestrial and space based satellite tracking (like SLR, Doris, PRARE or GPS), conventional gravimetry over land and satellite altimetry over the oceans. The accuracy of the mean gravity models is currently limited by the heterogeneity of the data quality and origin and the lack of global coverage with uniform accuracy. The estimates of the global temporal variabilty of the Earth's gravity field are presently limited to the longest wavelengths resp. to the first few spherical harmonics of the geopotential or to certain selected frequency regimes. Earth System Science disciplines like oceanography, hydrology, glaciology or solid Earth sciences however have a strong need for a global coveraged, high resolution and homogenously high quality data set to improve their appropiate science applications.
These applications are limited by the relatively poor knowledge of the geoid, the area of equal geopotential near the surface of the oceans. Current gravity models like GRIM5-S1 are able to determine this area with an accuracy of about 40 cm with a spatial resolution of about 500 km. The CHAMP satellite will give an improvement of one order of magnitude for this wavelength (rf. figure below)!
Due to its mission profile and high accuracy caused by the dedicated instrumentation, a further quantum leap in the accuray of the Earth's gravity model is feasible with GRACE: the mm-Geoid! The anticipated geoid height errors derived from 30 days GRACE data is shown in the following table:
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Since the two GRACE satellites are separated in orbit by only a few hundred kilometers along-track, the errors due to media effects are small as compared to space- or ground-based tracking. This also ensures the homogeneity of data quality over the mission lifetime of 5 years. Non-gravitational forces caused by drag or solar radiation pressure will be eliminated using high accuracy accelerometers onboard each satellite. The orbit position will be continuously and accurately determined by geodetic qualified GPS receivers, which can be externaly calibrated by dedicated Laser Retroreflectors integrated on each satellite.
The orbits of the two satellites, which are dependent on the integrated effect of the mass distributions and movements in the Earth system, are influenced by these effects at slightly different phases and will therefore be perturbed slightly differentially. This perturbation difference will cause changes in the inter-satellite range, which is measured very precisely (< 1 µm/s) by the K-Band ranging equipment. These differential measurements can be used to monitor higher frequency contents of the gravitational signal resp. to improve higher resolution estimates of the Earth's gravity field.
The following figure shows the accuracy of present (GRIM5-S1) and future (CHAMP, GRACE) geoid determination (simulation results):
