Data assimilation strategies for state-dependent observation error variances

Abstract

The Ensemble Kalman Filter (EnKF) and 4D‐Var Data Assimilation (DA) approaches require that a fixed observation error variance be specified for each observation. To highlight the need to consider the state dependence of observation error variances, we prove that the error variance of unbiased observations of bounded variables tends to zero as the unknown true value of the variable approaches the bound. How then, should state‐dependent observation error variances be specified for the EnKF and 4D‐Var? In an idealized system, three distinct strategies for choosing the observation error variance R are considered: (a) choose R to be the ensemble mean of the observation error variances associated ..