Applying Sequential Monte Carlo Methods into a Distributed Hydrologic Model: Lagged Particle Filtering Approach with Regularization

Abstract

Data assimilation techniques have received growing attention due to their capability to improve prediction. Among various data assimilation techniques, sequential Monte Carlo (SMC) methods, known as "particle filters", are a Bayesian learning process that has the capability to handle non-linear and non-Gaussian state-space models. In this paper, we propose an improved particle filtering approach to consider different response times of internal state variables in a hydrologic model. The proposed method adopts a lagged filtering approach to aggregate model response until the uncertainty of each hydrologic process is propagated. The regularization with an additional move step based on the Markov chain Monte Carlo (MCMC) methods is also implemented to preserve sample diversity under the lagged filtering approach. A distributed hydrologic model, water and energy transfer processes (WEP), is implemented for the sequential data assimilation through the updating of state variables. The lagged regularized particle filter (LRPF) and the sequential importance resampling (SIR) particle filter are implemented for hindcasting of streamflow at the Katsura catchment, Japan. Control state variables for filtering are soil moisture content and overland flow. Streamflow measurements are used for data assimilation. LRPF shows consistent forecasts regardless of the process noise assumption, while SIR has different values of optimal process noise and shows sensitive variation of confidential intervals, depending on the process noise. Improvement of LRPF forecasts compared to SIR is particularly found for rapidly varied high flows due to preservation of sample diversity from the kernel, even if particle impoverishment takes place.