A New Localized Particle Filter Based on Gaussian Process Regression for High Non-linear Observation Operators in data assimilation

In data assimilation(DA), various types of observations can be assimilated. Highly nonlinear observation operators are very common in geoscience, which goes against the linear and Gaussian assumptions of the Kalman filter. Particle filters are promising and possible solutions to non-linear issues in DA because they do not rely on Gaussian assumptions. However, traditional particle filters cannot be applied in high dimensional systems. As a method based on Bayes theory and Monte Carlo approximation, particle filters require numerous particles to represent the distribution of high-dimensional model states, which is called the curse of dimensionality. Because of this, it is prohibitive for realistic DA applications. In this study, a new local particle filter was proposed to deal with both the nonlinearity of observation operators and the dimensionality of particle filters. Localization methods are frequently used in Ensemble-type methods to solve the issues caused by limited ensemble size in high dimensional models. In this research, localization is applied to overcome the curse of dimensionality in particle filters. For the non-linear issue in observation operators, Gaussian process regression (GPR) is used to estimate the uncertainty of non-linear observation operators. At each update, the surrogate is adaptively trained and refined by current observations and model states. When the model states are transferred to the observation space, the surrogate can give the information about estimations and the corresponding uncertainty. A Lorenz model (1996) with 40 variables is used to evaluate the performance of this proposed local particle by conducting a set of experiments with different settings including the number of particles, the impact of localization scales, etc. To test its ability to deal with nonlinear issues, a highly nonlinear observation operator is designed and used in experiments. LETKF and local EAKF are two benchmarks in this research. The results show that the new method has a stable performance with high accuracy and it outperforms the two benchmarks. More importantly, for the non-linear case in this study, the new method only uses 25 particles to achieve a good performance. Although only the Lorenz model is considered in this study, it is highly likely to apply the proposed method to other models.