Parameter estimation beyond the augmented state approach: Expectation-Maximization algorithm

PULIDO M

Munich

Simposio; 6th International Symposium of Data Assimilation; 2018

ne 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 parameters. On the other hand, the collapse of the parameter posterior distribution found in both ensemble Kalman filters and particle filters  is a major contention point when one is interested in estimating model error covariances or stochastic parameters. To overcome this intrinsic limitation, I will give an overview on a statistical learning method that combines the  Expectation-Maximization (EM) algorithm with an ensemble Kalman filter to estimate statistical parameters that give the maximum of the observation likelihood given a set of observations. Numerical experiments with toy models will be shown, in which the method is applied to infer model error covariances and deterministic and stochastic physical parameters from noisy observations in coarse-grained dynamical models. The algorithms are able to identify an optimal stochastic parameterization with a good  accuracy under moderate observational noise. The proposed EnKF-EM is a promising statistical learning method for estimating model error and for constraining stochastic parameterizations in high-dimensional geophysical models.