State and Stochastic Parameters Estimation with Combined Ensemble Kalman and Particle Filters

Abstract

Quantifying uncertainties is a key aspect of data assimilation systems since it has alarge impact on the quality of the forecasts and analyses. Sequential data assimilation algorithms,such as the Ensemble Kalman Filter (EnKF), describe the model and observation errors as additiveGaussian noises and use both inflation and localization to avoid filter degeneracy and compensatefor misspecifications. This introduces different stochastic parameters which need to be carefullyestimated in order to get a reliable estimate of the latent state of the system. A classical approachto estimate unknown parameters in data assimilation consists in using state-augmentation, wherethe unknown parameters are included in the latent space and are updated at each iteration of theEnKF. However, it is well-known that this approach is not efficient to estimate stochastic parametersbecause of the complex (non-Gaussian and non-linear) relationship between the observations andthe stochastic parameters which can not be handled by the EnKF. A natural alternative for non-Gaussian and non-linear state-space models is to use a particle filter (PF), but this algorithm failsto estimate high-dimensional systems due to the curse of dimensionality. The strengths of thesetwo methods are gathered in the proposed algorithm, where the PF first generates the particles thatestimate the stochastic parameters, then using the mean particle the EnKF generates the membersthat estimate the geophysical variables. This generic method is first detailed for the estimation ofparameters related to the model or observation error and then for the joint estimation of inflationand localization parameters. Numerical experiments are performed using the Lorenz-96 model tocompare our approach with state-of-the-art methods. The results show the ability of the new methodto retrieve the geophysical state and to estimate online time-dependent stochastic parameters. Thealgorithm can be easily built from an existing EnKF with low additional cost and without furtherrunning the dynamical model.