Annual report - 2007

This grant began in September 2007. The following items are studied (in fact we started preparing software and doing various simulations which are possible even without actual data from the GOCE mission, see below):

The diminished resolution of solutions for variations of the gravity field from the Gravity Recovery And Climate Experiment (GRACE) around September 2004 was related to the short orbit repeat cycle of R/D = 61/4 for the GRACE A/B satellites (R = 61 satellite’s nodal revolutions per D = 4 synodic days). Similar situations were encountered in GRACE’s past orbit and may be encountered in its future free fall. We use recent models of atmospheric density to estimate minimum and maximum drag and the orbit decrease of GRACE, providing a warning of possible future degradation. Our analysis serve as a warning for orbit choice of GOCE for its measutring phases (the case of 16/1 repeat orbit). We are in close scientific contacts with the project manager Rune Floberghagen, ESA. The goal is to select repeat orbit with long repeat period and optimum ground track density.

The team is in the position to estimate and evaluate global gravity field parameters derived from satellite missions from gradiometry as well as orbitography and their combination/stabilization with selected ground based gravity data by different approaches including direct inversion with full var/cov information. A second emphasise has been newly put on the spectral approach using lumped harmonic coefficients. Instead of estimating these coefficients from a Fast Fourrier Transformation over the measurement data our strategy will be based on a rigorous Least Squares estimation for the coefficients, that has lead to more stable results when concerning data gaps and discontinuities (gaps do not have to be filled). Further advantage can be taken when additional external data from the polar regions, other satellite missions (GRACE) or external gravity models (EGM07) will be added to regularize results. Moreover the approach offers a faciliate manner to solve for lumped harmonic frequencies from the in-situ data even in situations where the number of orbital revolutions (?) within (or close to) a repeat cycle orbit (?) is below twice the maximum bandwith (2 Lmax) of the model resolution. In this case order-wise correlations between frequencies arise that cannot generally be taken care of by Fast Fourrier methods (Nyquist- criterion). Such a situation could possibly occure if the ground-track density during the envisaged measurement epoch doesn't supply sufficiently high coverage due to low-order resonance phenomena (16/1) or the given time-frame is too short befor/after solar eclipses. Although this is not a highly probable scenario, by concerning the order-wise correlations between the lumped harmonic frequencies still stable solutions can be processed by our software. The prototyps (matlab) have been tested and shall be implemented in a higher order programming language (f95).

The team has experiences in gravity field estimation of CHAMP & GRACE data as well as with its evaluation. For the resonance analyzis of GRACE data some improvements in the reduction of orbital elements by luni-solar disturbances are under discussion together with our Collegues at NOAA. The 'Encke-Method' i.e. the solution of a differential equation shall be used to split non-graviational forces from the inclination and to estimate the resonant lumped harmonics due to gravity. For GRACE and GOCE gravity field processing this method could become highly interesting, since in both cases the observables have to be de-alliased from luni-solar, tidal and other forces. Further studies are on the way.

The calibrated GOCE gravity gradient observables can be used to determine the static field of the Earth gravity potential. Due to the huge amount of observational data on one hand and the complexity of the geopotential model on the other hand a solution for the parameters remains a highly demanding computational task. An alternative method has been developed to minimize the necessary workload concerning parameter estimation. A test has been initiated to verify or condemn whether the matrix inversion can be carried on with single numerical precision numbers and the corresponding result meets sufficient accuracy. This could double the amount of parameters and therefore significantly raise the final model resolution. A closed loop gravity gradient simulation has been established with the result that a full parameter recovery can be accomplished at orbital height down to accuracy requirements (residuals below 10^-4 meter geoid height) – but it seems not sufficient at sealevel (1-2 cm geoid height residuals). Further test are required.

 

Item 3. Comparison of detailed satellite and terrestrial data
(responsible person: Pavel Novák)

Despite the current large progress in global gravity field modeling, high accuracy and resolution local/regional models of the geoid/quasi-geoid to be used for geodetic height transformations must still rely on combination of global (spaceborne) and local (ground and/or airborne) gravity data. This situation will not change even after the GOCE data will be released. Most of the current techniques for regional gravity field modeling is based on a weighted combination of harmonic geopotential coefficients and observed local gravity data (ground anomalies, airborne disturbances). In an alternative approach, ground, airborne and spaceborne observables could be combined directly in derivation of a unique and frequency-seamless model of the geopotential, thus also of the gravimetric geoid/quasi-geoid. The GOCE data represented by selected components of the gradiometric tensor will offer a completely new spaceborne data type with unprecedented properties, both in terms of their spatial distribution and namely spectral content. It will be very interesting to include this data type to other gravity field observables available over the territory of Central Europe in an attempt of derivation of the most accurate regional gravity field model to-date. Besides the main aim of this project represented by a surface for height transformation, the combination of the GOCE data with other available gravity information will be used for testing the quality of the solution, thus also of the GOCE-based component, with a help of high-precision and resolution GPS/leveling data in the region. For this purpose, a regional database of gravity, elevation, density and GPS/leveling data has been compiled. Relevant experiences for the project of a similar kind were obtained while using currently available CHAMP and GRACE observables and their corresponding observations for regional gravity field modeling.

 

Item 4. Detection of hidden impact (meteoritic) structures on the Earth surface (responsible person: Jaroslav Klokocnik)

Can the second gravity derivatives derived from GOCE gradiometer measurements be used to identify impact craters on the Earth still hidden under rain forests, deserts, seas and similar places? About 150 large impacts are already known for sure. In accord with opinion of various astronomers and geologists, there are many impact structures still hidden and waiting to be revealed. Sufficiently precise and dense GOCE data may lead to a great progress in this direction.

The concept is based on the mascon approach; crater is a mascon, generating a signal which might be measurable by GOCE. For the first rough informative estimate, we consider only the component Vzz,= 2 GM/r3 (where M is the mass of the impact crater, r its distance from the measuring instrument (i.e. height of flight of GOCE, and G is the universal gravitational constant).
We assume GOCE at height 250 km (on circular orbit). The measuring precision of GOCE gradiometer, stated by ESA, is about 3 miliEötvös (0.003 E) for frequency range 5-100 mHz. To be conservative, we take ? = 0.010 E as a typical measuring accuracy of the second derivatives from the GOCE gradiometer.