Improved Regional Mass Change Estimation Using Slepian Functions in a Kalman Filter Framework

Abstract Satellite gravimetry, such as data from the Gravity Recovery and Climate Experiment (GRACE) and its successor GRACE-FO (Follow-On), provides insights into temporal variations in Earth’s gravity field, which are linked to mass redistribution processes like ice sheet melting and groundwater depletion. However, measurement noise and limited spatial resolution require filtering techniques to extract meaningful signals. In this context, Slepian functions—optimal basis functions for spatially localized signal representation—offer a way to mitigate signal leakage and improve regional mass change estimates. In addition, integrating Slepian functions within a Kalman-filter framework enables simultaneous filtering and localization of the dataset. Following the work of Wöhnke et al. (Int J Geomath. 16:2, 2025), who combined radial basis functions with a Kalman filter in a closed-loop simulation, a similar setup has been developed that incorporates Slepian functions into the Kalman filter. We test this setup with simulated gridded water storage estimates for a region in central Europe, based on the European Space Agency (ESA) Earth System Model (ESM) as well as realistic GRACE-like noise. The differences between the simulated observations and results from the closed-loop simulation of the Slepian functions and Kalman filter are compared with results from applying the Kalman filter alone, as well as with the simulation presented in Wöhnke et al. (Int J Geomath. 16:2, 2025). The comparison indicates that Slepian functions perform similarly to radial basis functions, and generally better than using a Kalman filter only.