Model error covariance estimation in particle and ensemble Kalman filters using an online expectation–maximization algorithm

COCUCCI, TADEO J.; PULIDO, MANUEL; LUCINI, MAGDALENA; TANDEO, PIERRE

QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY

JOHN WILEY & SONS LTD

Año: 2020

0035-9009

The performance of ensemble-based data assimilation techniquesthat estimate the state of a dynamical system from partial ob-servations depends crucially on the prescribed uncertainty ofthe model dynamics and of the observations. These are notusually known and have to be inferred. Many approaches havebeen proposed to tackle this problem, including fully Bayesian,likelihood maximization and innovation-based techniques. Thiswork focuses on maximization of the likelihood function via theexpectation-maximization (EM) algorithm to infer the modelerror covariance combined with ensemble Kalman filters andparticle filters to estimate the state. The classical application ofthe EM algorithm in a data assimilation context involves filteringand smoothing a fixed batch of observations in order to completea single iteration. This is an inconvenience when using sequentialfiltering in high-dimensional applications. Motivated by this, anadaptation of the algorithm that can process observations andupdate the parameters on the fly, with some underlying simplifi-cations, is presented. The proposed technique was evaluated andachieved good performance in experiments with the Lorenz-63and the 40-variable Lorenz-96 dynamical systems designed torepresent some common scenarios in data assimilation such asnon-linearity, chaoticity and model misspecification