Observed Characteristics of Representation Error

Elizabeth Satterfield* and Daniel Hodyss*, David D. Kuhl**, Craig H. Bishop*
Naval Research Laboratory, Monterey, California, USA
*Naval Research Laboratory, Monterey, California, USA, **Naval Research Laboratory, Washington, DC, USA

Data assimilation schemes blend observational data, with limited coverage, with a short term forecast to produce an analysis, the best estimation of the atmospheric state. Appropriately specifying error statistics of the observational data and short term forecasts is necessary to obtain an optimal analysis. Errors associated with sub-grid scale features of the model, or errors of representation, are often poorly accounted for. Since models are only capable of representing a filtered true state, the background error does not contain errors associated with the inability of relatively coarse grids to resolve small-scale features, or errors of representation. Such terms must be included in the observation error covariance matrix.

In what follows we attempt to bridge the gap between the use of statistical methods to estimate the observation error covariance and the more theoretical error of representation studies by analyzing the dependence of estimation methods on ensemble variance and latitude. We perform a detailed analysis of the Desroziers and Höllingsworth-Lonnberg methods, illustrating that they can recover terms associated with error of representation, along with additional model error terms. We investigate the structure of representation error using 6-hour ECMWF forecasts to attribute spatial dependence of estimated variances to error of representation. Thus, we outline a procedure by which one could use statistical methods to diagnose representation error. Finally, we discuss the use of ensemble variance as a predictor of representation error and how our findings could be used to form a flow dependent observation error covariance model.

*email: Elizabeth.Satterfield@nrlmry.navy.mil
*Preference: Oral