Bayesian optimization for parameter estimation of a local particle filter

抄録

The 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. 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 strong nonlinear observation operator, it is possible to estimate the analysis with higher accuracy than the local ensemble transform Kalman filter by setting the inflation factor  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  and  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. As a result, the BO estimated  and  with higher accuracy than random sampling and was robust to changes in the observations to a certain extent. In addition, it was important to adopt the kernel functions and the acquisition functions tailored to the characteristics of the problem to improve the estimation accuracy of the BO.

This study clarified that the BO contributes to improving the practicality of the LPF and suggested what approach should be adopted when the number of estimated parameters increases. By developing this technology, the prediction accuracy of heavy rainfall is expected to improve in the future. The usefulness of the BO will eventually be proven in atmospheric model experiments aimed at the practical application of the LPF.