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

Quantifying uncertainties is a key aspect of data assimilation systems since it has a large 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 additive Gaussian noises and use both inflation and localization to avoid filter degeneracy and compensate for misspecifications. This introduces different stochastic parameters which need to be carefully estimated in order to get a reliable estimate of the latent state of the system. A classical approach to estimate unknown parameters in data assimilation consists in using state-augmentation, where the unknown parameters are included in the latent space and are updated at each iteration of the EnKF. However, it is well-known that this approach is not efficient to estimate stochastic parameters because of the complex (non-Gaussian and non-linear) relationship between the observations and the 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 fails to estimate high-dimensional systems due to the curse of dimensionality. The strengths of these two methods are gathered in the proposed algorithm, where the PF first generates the particles that estimate the stochastic parameters, then using the mean particle the EnKF generates the members that estimate the geophysical variables. This generic method is first detailed for the estimation of parameters related to the model or observation error and then for the joint estimation of inflation and localization parameters. Numerical experiments are performed using the Lorenz-96 model to compare our approach with state-of-the-art methods. The results show the ability of the new method to retrieve the geophysical state and to estimate online time-dependent stochastic parameters. The algorithm can be easily built from an existing EnKF with low additional cost and without further running the dynamical model.