Particle Filter with Nudging in Soil Hydrology

Abstract:

The Ensemble Kalman Filter (EnKF) is widely employed in soil hydrology but is challenged by the characteristics of the processes there. These are highly nonlinear and state variables occasionally show sharp fronts and discontinuities across layer boundaries. This leads to sometimes strongly non-gaussian probability distributions, which is at odds with the EnFK's basic assumption. Therefore, we explore particle filters, which are able to handle such situations. However, standard particle filters with resampling suffer from the curse of dimensionality. They are thus not applicable to high-dimensional systems as they are encountered with soil water dynamics. A particle filter that may be able to lift this curse was proposed by van Leeuwen (2010). He introduced a nudging term based on the freedom of the proposal density. This particle filter has been applied in oceanography and showed promising results.

While oceanography focuses on state estimation, soil hydrology in addition aims at parameter estimation. Therefore, we test the applicability of this filter for a one-dimensional test case, where we estimate states and parameters simultaneously. We generate synthetic data that correspond to water content measurements as they would be available from time domain reflectometry (TDR) probes. The results are compared with the true parameters and water contents. Finally, the performance of this filter (with different nudging terms) is compared with an EnKF and a particle filter without nudging.