Bayesian optimization for parameter estimation of a local particle filter

Particle filter (PF) is a powerful data assimilation method that does not assume the linearity in the time evolution of errors or Gaussian error distributions. However, the number of particles required increases exponentially with the dimensions of the dynamical system, which is a bottleneck when applying the PF to numerical weather prediction (NWP) models. Local particle filter (LPF) realizes the PF in high-dimensional systems by the localization, but it has high parameter sensitivity and is challenging to operate stably. On the other hand, when using a nonlinear observation operator, it is possible to estimate the analysis with higher accuracy than the local ensemble transformation Kalman filter (LETKF) by setting the weight inflation factor, which smooths the weights among particles, and the localization scale, to the optima. Therefore, an efficient parameter estimation method is required.Bayesian optimization (BO) is a method for efficiently solving optimization problems of black box functions with high computational costs, and is used for parameter optimization of neural networks. Therefore, we estimated the weight inflation factor and localization scale that minimize the root mean square error between the observations and the forecasts (RMSE(o vs. f)) in the LPF using the BO in the Lorenz-96 40-variable model (L96). As a result, the BO was able to model the response surface with high accuracy and estimate the weight inflation factor and localization scale with accuracy equal to or better than random sampling (RS). In addition, this result was robust to changes in the observation set. However, as the number of parameters to be estimated increased, the BO did not always obtain estimations close to the optima, depending on the observation set.This study has clarified that the BO contributes to improving the practicality of the LPF, and it has also provided suggestions on how the BO should be developed in the future. Since the LPF can estimate high-precision analysis even in strongly nonlinear phenomena, the development of the technology in this study is expected to improve the accuracy of heavy rainfall prediction in the future. The BO will be helpful in atmospheric model experiments for the practical application of the LPF.