Model uncertainty covariance quantification using Expectation-Maximization algorithms in ensemble Kalman and particle filters (invited talk)

MANUEL PULIDO

Paris

Workshop; Model uncertainty covariance quantification using Expectation-Maximization algorithms in ensemble Kalman and particle filters; 2019

Institut Henri Poincare

One standard methodology to estimate physical model parameters from observations in data assimilation techniques is to augment the state space with the parameters. This methodology presents an overall success when estimating deterministic physical parameters. On the other hand,  the posterior density  model error covariances or stochastic parameters posterior distribution within the augmented state approach collapses in both ensemble Kalman filters and particle filters. To overcome this intrinsic limitation, we introduce  statistical learning methods that combines the  Expectation-Maximization (EM) algorithm with sequential Monte Carlo and ensemble Kalman filters to estimate statistical parameters that give the maximum of the observation likelihood given a set of observations. A batch EM algorithm and an online EM algorithm  that work with particle filters and ensemble Kalman filters are introduced. Both methods take approximations to  avoid the need of smoothing, using the innovation likelihood in the former and neglecting the influence of current observations in the summary statitistics in the latter. Numerical experiments with the 40 variable Lorenz-96 system will be shown, in which the method is applied to infer model error covariances from noisy observations. The methods are able to converge using the perturbed observation ensemble Kalman filter and the variational mapping particle filter with a good  accuracy under moderate observational noise. The proposed methods show promising results and ongoing work is focused on the extension of the methodology for very  high-dimensional geophysical models.