The design of an optimal filter for monthly GRACE gravity models

Abstract

S U M M A R YMost applications of the publicly released Gravity Recovery and Climate Experiment monthly gravity field models require the application of a spatial filter to help suppressing noise and other systematic errors present in the data. The most common approach makes use of a simple Gaussian averaging process, which is often combined with a 'destriping' technique in which coefficient correlations within a given degree are removed. As brute force methods, neither of these techniques takes into consideration the statistical information from the gravity solution itself and, while they perform well overall, they can often end up removing more signal than necessary. Other optimal filters have been proposed in the literature; however, none have attempted to make full use of all information available from the monthly solutions. By examining the underlying principles of filter design, a filter has been developed that incorporates the noise and full signal variance-covariance matrix to tailor the filter to the error characteristics of a particular monthly solution. The filter is both anisotropic and nonsymmetric, meaning it can accommodate noise of an arbitrary shape, such as the characteristic stripes. The filter minimizes the mean-square error and, in this sense, can be considered as the most optimal filter possible. Through both simulated and real data scenarios, this improved filter will be shown to preserve the highest amount of gravity signal when compared to other standard techniques, while simultaneously minimizing leakage effects and producing smooth solutions in areas of low signal.

Estimation of mass change trends in the Earth’s system on the basis of GRACE satellite data, with application to Greenland

“…Such a difference is about 3 orders of magnitude smaller than the expected signal and, therefore, would have a negligible effect on the estimates obtained. This conclusion is fully consistent with the findings of Klees et al (2008), who applied a similar filtering procedure in the context of monthly solutions. Unfortunately, the procedure described above leads to a contamination of the bias component y (k) 1 with strong concentric ringing artifacts around the poles.…”

“…Conceptually, it is somewhat similar to the Wiener-type filter for post-processing monthly gravity field solutions proposed earlier by Klees et al (2008). Such a filter is based on statistically optimal estimation principles and makes use of the full noise and signal covariance matrices.…”

“…The factor l −1 j in front of the term on the right-hand side of Eq. (10) compensates for the neglection of covariances in the spatial domain by forcing a smoothness of the signal (Klees et al 2008;Liu et al 2010). The rest of the right-hand side of Eq.…”

“…Therefore, a proper post-processing of the results is required. To that end, we use a statistically optimal Wienertype filter, inspired by the one designed for monthly gravity field solutions (Klees et al 2008). The basic idea is to regard the estimated parameters y as a realization of a stochastic process Y.…”

The impact of common versus separate estimation of orbit parameters on GRACE gravity field solutions

“…The critical point of filtering is, however, how much signal is accidentally damaged by the filtering process. More recent publications on the topic (Kusche (2007), Klees et al (2008)) make use of approximations of the signal covariance to protect the signal during the filtering process.…”