Exploring the structure of time‐correlated model errors in the ECMWF data assimilation system

Abstract

Model errors are increasingly seen as a fundamental performance limiter in both Numerical Weather Prediction and Climate Prediction simulations run with state‐of‐the‐art Earth‐system digital twins. This has motivated recent efforts aimed at estimating and correcting the systematic, predictable components of model error in a consistent data assimilation framework. While encouraging results have been obtained with a careful examination of the spatial aspects of the model error estimates, less attention has been devoted to the time correlation aspects of model errors and their impact on the assimilation cycle. In this work we employ a Lagged Analysis Increment Covariance (LAIC) diagnostic to gain insight in the temporal evolution of systematic model errors in the ECMWF operational data assimilation system, evaluate the effectiveness of the current weak constraint 4D‐Var algorithm in reducing these types of errors and, based on these findings, start exploring new ideas for the development of model error estimation and correction strategies in data assimilation.

The relationship between two methods for estimating uncertainties in data assimilation

“…Errors in the observations, background, and analysis tend not to be largely different from each other; in some sense, the assimilation homogenizes the errors. This is more of an issue when 3CH is used in its broader context of using alternative data sets. Though unaccounted‐for biases can be an issue in general for both methods, DA residuals benefit from various levels of bias correction: (i) applied to the observations either offline (e.g., Haimberger, 2007) or online, as in variational procedures (e.g., Dee, 2005, and references therein); and (ii) applied to the background (underlying model) as in weak‐constraint variational applications (e.g., Bonavita, 2021, and references therein). DBCP benefits from these automatically and, as long as 3CH constructs its data sets from the same residuals used in DBCP, the effect should be similar in 3CH. Unknown cross‐covariances in the context of the present work would be a manifestation of lack of optimality in the underlying DA.…”

“…Though unaccounted‐for biases can be an issue in general for both methods, DA residuals benefit from various levels of bias correction: (i) applied to the observations either offline (e.g., Haimberger, 2007) or online, as in variational procedures (e.g., Dee, 2005, and references therein); and (ii) applied to the background (underlying model) as in weak‐constraint variational applications (e.g., Bonavita, 2021, and references therein). DBCP benefits from these automatically and, as long as 3CH constructs its data sets from the same residuals used in DBCP, the effect should be similar in 3CH.…”