Bayesian optimization in parameter estimation for a local particle filter

抄録

The particle filter (PF) is a powerful data assimilation method that assumes neither linearity in the time evolution of errors nor Gaussian error distributions. However, the number of required particles, which increases exponentially with the dimensionality of a dynamical system, becomes a bottleneck when the PF is applied to numerical weather prediction (NWP) models. The local particle filter (LPF) realizes the PF method in high-dimensional systems through localization, but it has high parameter sensitivity and is difficult to operate stably. However, when a nonlinear observation operator is used, it is possible to estimate the analysis with higher accuracy than is possible with the local ensemble transformation Kalman filter by setting the weight inflation factor tau, which smooths the weights among the particles, and the localization scale r to their optimal values. Therefore, an efficient parameter estimation method is required.

The Bayesian optimization (BO) is a method that efficiently optimizes black-box functions with high computational costs. In this study, the BO was used to estimate the values of tau and r that minimize the root mean square error between the observation and the forecast in the Lorenz-96 40-variable model. As a result, the one-dimensional BO could estimate the optimal weight inflation factor with all observation sets. However, the observation sets that could estimate the optimal weight inflation factor stayed at 34% and the ones that could estimate the localization scale stayed at 97% in the two-dimensional BO. An investigation into the cause of this performance degradation revealed that excessive exploration near the boundary, which became significant as the dimension of the parameter space increased, was the cause. Additionally, a need to adequately set the Lipschitz constant depending on the problem formulation was identified.

This study is one of precious study solving systematically a limit of the BO performance and that cause in data assimilation. The obtained insight suggests two improvement methods in applying the LPF to the practical NWP system: (1) preventing excessive exploration near the boundary with the virtual derivative sign observation method, and (2) estimating the Lipschitz constant with the GP-LCA method. This study clarified problems and the applicability of the BO in data assimilation and provided a direction for future research.