Multi-scale modeling of Earth's gravity field in space and time

Since 2002, the GRACE mission has been providing an unprecedented view of the Earth's gravity field spatial and temporal variations. The gravity field models built from these satellite data are essential in order to study the mass redistributions within the Earth system. Often, they are modelled using spatial functions, such as spherical harmonics, averaged over a fixed time window. However, the satellite sampling naturally leads to a trade-off between the achievable spatial and temporal resolutions. In addition, the gravity variations are made of local components in space and time, reflecting the superimposition of sources. With the final aim to better estimate gravity variations related to local processes at different spatial and temporal scales, and adapt the temporal resolution of the model to its spatial resolution, we present an attempt at 4D gravity field modelling using localized functions in space and time. For that, we develop a four-dimensional wavelet basis, well localized in space and time and orthogonal in time. We then analyze the inverse problem of 4D gravity field estimation from GRACE synthetic inter-satellites potential differences along the orbit, and its regularization in a Bayesian framework, using a prior knowledge on the mass sources. We then test our approach in a simplified synthetic test setting, where only one mass source is present: hydrological mass variations over Africa during the year 2005. Applying a purely regional approach, we are able to reconstruct, regionally, the water height signal with a ≈2.5 cm accuracy at 450 km, 21 days resolution. We test the influence of the geophysical prior on this result, and conclude that it cannot explain alone the residuals between original and reconstructed mass signal. redIn contrast, an ideal test case with a perfect adequacy between the 4D basis and the synthetic data, without approximations nor regularization in solving the normal system, leads to a significantly improved reconstruction of large-scale, seasonal water variations, at the millimetric level of a few % of relative accuracy. The performances of the regional test are likely significantly limited by the block-diagonal approximation of the normal system and the scales selection in the regional 4D basis.