Optimal Filtering in Mass Transport Modeling From Satellite Gravimetry Data

Monitoring natural mass transport in the Earth's system, which has marked a new era in Earth observation, is largely based on the data collected by the GRACE satellite mission. Unfortunately, this mission is not free from certain limitations, two of which are especially critical. Firstly, its sensitivity is strongly anisotropic: it senses the north-south component of the mass re-distribution gradient much better than the east-west component. Secondly, it suffers from a trade-off between temporal and spatial resolution: a high (e.g., daily) temporal resolution is only possible if the spatial resolution is sacrificed. To make things even worse, the GRACE satellites enter occasionally a phase when their orbit is characterized by a short repeat period, which makes it impossible to reach a high spatial resolution at all. A way to mitigate limitations of GRACE measurements is to design optimal data processing procedures, so that all available information is fully exploited when modeling mass transport. This implies, in particular, that an unconstrained model directly derived from satellite gravimetry data needs to be optimally filtered. In principle, this can be realized with a Wiener filter, which is built on the basis of covariance matrices of noise and signal. In practice, however, a compilation of both matrices (and, therefore, of the filter itself) is not a trivial task. To build the covariance matrix of noise in a mass transport model, it is necessary to start from a realistic model of noise in the level-1B data. Furthermore, a routine satellite gravimetry data processing includes, in particular, the subtraction of nuisance signals (for instance, associated with atmosphere and ocean), for which appropriate background models are used. Such models are not error-free, which has to be taken into account when the noise covariance matrix is constructed. In addition, both signal and noise covariance matrices depend on the type of mass transport processes under investigation. For instance, processes of hydrological origin occur at short time scales, so that the input time series is typically short (1 month or less), which implies a relatively strong noise in the derived model. On the contrary, study of a long-term ice mass depletion requires a long time series of satellite data, which leads to a reduction of noise in the mass transport model. Of course, the spatial pattern (and therefore, the signal covariance matrices) of various mass transport processes are also very different. In the presented study, we compare various strategies to build the signal and noise covariance matrices in the context of mass transport modeling. In this way, we demonstrate the benefits of an accurate construction of an optimal filter as outlined above, compared to simplified strategies. Furthermore, we consider both models based on GRACE data alone and combined GRACE/GOCE models. In this way, we shed more light on a potential synergy of the GRACE and GOCE satellite mission. This is important nor only for the best possible mass transport modeling on the basis of all available data, but also for the optimal planning of future satellite gravity missions.