Covariance resampling for particle filter - state and parameter estimation for soil hydrology

Particle filters are becoming increasingly popular for state and parameter estimation in hydrology. One of their crucial parts is the resampling after the assimilation step. We introduce a resampling method that uses the full weighted covariance information calculated from the ensemble to generate new particles and effectively avoid filter degeneracy. The ensemble covariance contains information between observed and unobserved dimensions and is used to fill the gaps between them. The covariance resampling approximately conserves the first two statistical moments and partly maintains the structure of the estimated distribution in the retained ensemble. The effectiveness of this method is demonstrated with a synthetic case - an unsaturated soil consisting of two homogeneous layers - by assimilating time-domain reflectometry-like (TDR-like) measurements. Using this approach we can estimate state and parameters for a rough initial guess with 100 particles. The estimated states and parameters are tested with a forecast after the assimilation, which is found to be in good agreement with the synthetic truth.