A Localized Weighted Ensemble Kalman Filter And Its Application

A geophysical system is a non-linear/non-Gaussian system.In order to obtain an accurate forecast state through a geophysical model,two conditions must be met: one is an accurate initial state of the model,and the other is an accurate physical law.Data assimilation technology can improve the quality of the initial state of the model,but currently widely used operational data assimilation methods ——the variational method and the ensemble Kalman filter method both have linear(weakly nonlinear)/Gaussian assumptions,and can only provide first-order or second-order moment information of the probability density function,which cannot meet the requirements of real geophysical systems.This paper focuses on the theoretical research and practical application of nonlinear/non-Gaussian data assimilation methods ——particle filters: using the particle filter as framework and the ensemble Kalman filter as proposal density,a new local weighted ensemble Kalman filter is proposed and improved;Based on the local weighted ensemble Kalman filter,a nonlinear/non-Gaussian ocean data assimilation system is constructed;constructing model error covariance to advance the practical application of the particle filters with proposal density;In order to apply particle filter to high-dimensional systems and avoid filter degeneracy,a new local particle filter with the ensemble Kalman filter as proposal density ——the local weighted ensemble Kalman filter is proposed in this paper for the first time combining the localization technology and proposal density technology.Based on a weighted ensemble Kalman filter,the main idea is to extend the scalar weight of each particle into a vector weight,and limit the impact of longdistance observations through localization function.The new method is tested in simple chaotic models of different dimensions and the two-layer quasi-geostrophic model.The results show that the method is suitable for high-dimensional numerical prediction models,which indicates its potential for practical applications.In some cases,it can even provide better performance than the ensemble Kalman filter and the local particle filter.Aiming at the filter degeneracy in the real geophysical model applications,this paper proposed a modified local weighted ensemble Kalman filter.Firstly,the scalar proposal weights in the local weighted ensemble Kalman filter are generalized to vectors,and the marginal probability density of each variable is calculated to overcome the degeneracy of the proposal weights.Secondly,in order to reduce the computational cost of tuning parameter,a selection scheme of localization parameters is proposed.The experimental results in the low-dimensional simple model show that the modified local weighted ensemble Kalman filter can effectively overcome the filter degeneracy and obtain better analysis results than the original method.Finally,the adaptive observation error inflation,γ parameter and improved likelihood weight calculation are introduced into the modified local weighted ensemble Kalman filter.These improvements have laid the foundation for the application of the modified local weighted ensemble Kalman filter to real data assimilation systems.In this paper,the particle filter has been applied to a real ocean assimilation system using real observations for the first time.A modified local weighted ensemble Kalman filter ocean data assimilation system is established and the performance of the system is verified and evaluated.The performance of the modified local weighted ensemble Kalman filter is comprehensively compared with the ensemble Kalman filter and local particle filter.Data assimilation experiments were performed based on the regional ocean model ROMS,and assimilated sea surface temperature,sea surface height,Argo temperature and salt profile,and CTD temperature and salt profile.For observed variables,the performance of the modified local weighted ensemble Kalman filter is comparable to the ensemble Kalman filter.For unobserved variables,the modified local weighted ensemble Kalman filter provides more accurate predictions than the ensemble Kalman filter because the latter only considers the mean and covariance(first-and second-order moments),while the former considers the higher-order moments of the probability density function.In this ocean data assimilation experiment,the results obtained by the local particle filter were not ideal,which also verified that the low efficiency of the local particle filter in weakly nonlinear systems.Aiming at the model error covariance matrix required in the particle filters with proposal density,this paper proposes an improved spectral factorization method to decompose the mode error covariance matrix.This method first obtains the eigenvalues of the local model error covariance matrix through spectral decomposition,then removes the nagative variance introduced by localization,and applies the dimensionless correlation matrix two times to improve the correlation length scale of the covariance matrix.The experimental results in the spectral model of the twolayer primitive equation show that the improved spectral decomposition method is conducive to improving the assimilation results,which also provides some reference for the real application of the improved spectral decomposition method.