Improving the particle filter for data assimilation in hydraulic modeling by using a Cauchy likelihood function

Abstract

Over the recent decades, particle filter (PF)-based data assimilation has been adopted to improve hydrodynamic simulation due to its wide applicability and effectiveness for nonlinear and non-Gaussian models. The particle weighting is the core procedure to combine the observations and simulations within the PF framework, in which the Gaussian likelihood function (GLF) is commonly used to update weight values. However, there are some widely acknowledged challenges within the GLF-based PF. Among them, the excessive dispersion problem occurs when the standard deviation of the Gaussian likelihood is small, which may even cause filtering failures. Unfortunately, this issue has not been sufficiently addressed in the hydrology community. More attention needs to be paid to the likelihood function since the errors of the observed water stage (represented by the standard deviation) from hydrometric stations are usually small. This study focuses on the form of the likelihood function and parameter tuning within the particle weighting procedure of the PF for data assimilation. The limitations of using the common GLF were clarified and a novel Cauchy likelihood function (CLF) was proposed and tested in both a synthetic and a real-world case study using a PF-based hydraulic model. Comparisons showed that the CLF-based PF can effectively relieve the problem of excessive dispersion within the GLF-based PF framework, resulting in more stable and more accurate results. These findings not only provide another option for the selection of likelihood function within the PF framework, but also offer reliable evidence for improving hydraulic modeling by incorporating high-precision observations using the data assimilation technique.