Abstract
Abstract. 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.
Highlights
Mathematical models represent hydrological and other geophysical systems
The particle filter is an ensemble-based sequential data assimilation method that consists of a forecast and an analysis step
The final water content state estimated with the particle filter agrees with the synthetic truth in a narrow band, while the mean of the ensemble propagated without data assimilation is far-off
Summary
Mathematical models represent hydrological and other geophysical systems. They aim to describe the dynamics and the future development of system states. Moradkhani et al (2005a) suggested the perturbation of the parameters using Gaussian noise with a zero mean after the resampling step They used an unweighted variance of the ensemble modified with a damping factor such that the ensemble spread does not become too large. Further development of the resampling for parameter estimation was done by Moradkhani et al (2012) and Vrugt et al (2013) They used a Markov chain Monte Carlo (MCMC) method to generate new particles. The particle filter with covariance resampling is able to estimate state and parameters in case of a difficult initial condition without additional model evaluations, which are necessary for MCMC methods
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