Correlation between System and Observation Errors in Data Assimilation

Abstract

AbstractAccurate knowledge of two types of noise, system and observational, is an important aspect of Bayesian filtering methodology. Traditionally, this knowledge is reflected in individual covariance matrices for the two noise contributions, while correlations between the system and observational noises are ignored. We contend that in practical problems, it is unlikely that system and observational errors are uncorrelated, in particular for geophysically motivated examples where errors are dominated by model and observation truncations. Moreover, it is shown that accounting for the cross correlations in the filtering algorithm, for example in a correlated ensemble Kalman filter, can result in significant improvements in filter accuracy for data from typical dynamical systems. In particular, we discuss the extreme case where the two types of errors are maximally correlated relative to the individual covariances.