J. Kusche

Mass variation in the Mediterranean Sea from GRACE and its validation by altimetry, steric and hydrologic fields

The seasonal seawater mass variation in the Mediterranean Sea is estimated between April 2002 and July 2004 from GRACE and altimetry data and from hydrologic and oceanographic models. A smoothed spatial averaging kernel is applied to each field, in order to obtain comparable basin averages. The GRACE seawater mass corrected for the leakage of continental hydrology and the filtered steric?corrected altimeter sea level have similar annual amplitude and phase. To restore the magnitude of the GRACE?derived water mass signal we apply a scaling factor to the smoothed annual amplitude. The estimated scaled mass signal has an annual amplitude of 52 ± 17 mm peaking in November. We combine the seawater mass variation with the Mediterranean freshwater deficit and obtain a net flow at the Strait of Gibraltar with annual amplitude of 60 ± 25 mm/month (0.06 Sv) and maximum in September.

Regional high-resolution spatiotemporal gravity modeling from GRACE data using spherical wavelets

We determine a regional spatiotemporal gravity field over northern South America including the Amazon region using GRACE inter-satellite range-rate measurements by application of a wavelet-based multiresolution technique. A major advantage of this method is that we are able to represent the Amazon hydrological signals in form of time series of detail signals with level-dependent temporal resolution: the coarser structures generally require only ten days, whereas the medium and finer details are computable from one month of data. To this end, we employ the basic property of multiresolution representations, which is to split a signal into detail signals, each related to a specific resolution level and computable from data covering a specific part of the spectrum. Our results, which for the first time fully exploit the spatial and temporal resolutions of GRACE data in modeling Amazon hydrological fluxes, are in good agreement with hydrological models and GPS-derived height variations.

Multiresolution representation of a regional geoid from satellite and terrestrial gravity data

In this paper we present results from modeling the Earth’s gravitational field over the northern part of South-America using spherical wavelets. We have applied our analysis to potential data that we derived from CHAMP using the energy balance method, and to terrestrial gravity anomalies. Our approach provides a regional correction to the EGM96 reference gravity field, expressed in various detail levels, which are partly determined by the satellite data and partly by the terrestrial data.

Stochastic model validation of satellite gravity data: A test with CHAMP pseudo-observations

The energy balance approach is used for a statistical assessment of CHAMP orbits, data and gravity models. It is known that the quality of GPS-derived orbits varies and that CHAMP accelerometer errors are difficult to model. The stochastic model of the in-situ potential values from the energy balance is therefore heterogeneous and it is unclear if it can be described accurately using a priori information. We have estimated parameters of this stochastic model in an iterative variance-component estimation procedure, combined with an outlier rejection method. This means we solve simultaneously for a spherical harmonic model, for polynomial coefficients absorbing accelerometer drift, for sub-daily noise variance components, and for a variance parameter that controls the influence of an a-priori gravity model (EGM96). We develop here, for the first time, a fast Monte Carlo variant of the Minimum Norm Quadratic Unbiased Estimator (MINQUE) as an alternative for the fast Monte Carlo Maximum Likelihood VCE that we have introduced earlier. In this way, spurious data sets could be indicated and downweighted in the least-squares estimation of the unknown parameters. Using only 299 days of CHAMP kinematic orbit data, the quality of the estimated global gravity model was found com-parable to the EIGEN-3P model. Monte Carlo Variance Components Estimation appears to be a valid method to estimate the stochastic model of satellite gravity data and thus improves the least squares solution considerably.

Comment on “On the steric and mass‐induced contributions to the annual sea level variations in the Mediterranean Sea” by David García et al.

[1] Garcia et al. [2006] (hereafter referred to as GCDVG) present an analysis of mass-induced sea level variation (SLVmass) of the Mediterranean Sea based on satellite altimetry, ocean modeling and Gravity Recovery and Climate Experiment (GRACE) gravity measurements. In particular, GCDVG find consistency between altimeter sea level variations corrected for steric effects and changes in oceanic mass derived from Gravity Recovery and Climate Experiment (GRACE). GCDVG show that the annual cycle of the sea level variability (SLVtotal) is dominated by changes in its steric part (SLVsteric) and that the basin average of mass (SLVmass) is maximum in February. They conclude that, when the sea level is rising (falling) the Mediterranean Sea is actually losing (gaining) mass. [2] GCDVG appear to use an unrealistically large estimate of steric sea level variability (SLVsteric) and neglect changes in continental water storage that can significantly affect GRACE measurements over the Mediterranean Sea. These issues are examined in turn below by reviewing relevant individual basin averages of the Mediterranean Sea in comparison to results of other studies. In particular, while also finding consistency between altimetry and GRACE measurements, Fenoglio-Marc et al. [2006] (hereafter referred to as FKB), in a similar study of the Mediterranean Sea, find steric effects only accounting for about 60% of the total annual sea level variability and the annual cycle of SLVmass having a maximum in November.

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.

Assessment of the Results of VLBI Intra-Technique Combination Using Regularization Methods

Various important aspects should be taken into account in the combination of different space geodetic techniques. Consistency of models and standards, quality checks of solutions from individual Analysis Centers (AC), proper scaling of these solutions within the combination process, usage of rigorous combination methods and quality checks of the final combined solution are some of those. In this study, variance component estimation (VCE) is implemented to obtain optimal scaling (weighting) factors for the VLBI (Very Long Baseline Interferometry) intra-technique combination on the basis of normal equations. Afterwards, we apply a Tikhonov-type regularization method to stabilize a combined solution by imposing additional constraints about the solution. The regularization parameters are calculated with two different methods, variance component estimation and generalized cross-validation. The results show that the use of regularization significantly reduces the effect of instability in combined normal equation systems and provides more reasonable results.

Towards an optimal combination of satellite data and prior information

With the CHAMP and GRACE satellite gravity missions and the upcoming GOCE mission, millions of gravity-related observations are being released to the geodetic community. In order to provide an optimal gravity model in a statistical sense, it is common practice to combine satellite-only normal equations with prior information derived from terrestrial data or from previous satellite missions in the form of an existing gravity model. The weighting could be derived from formal error estimates, but more often these are adjusted based on heuristics like inspection of the residuals or of subset solutions. In recent years, rigorous approaches based on variance component estimation techniques have been developed and enjoy increasing popularity. At the same time, these techniques aim to provide more realistic error assessments of the combination solutions.