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IIn recent years, there has been a growing interest in applying dataassimilation (DA) methods, originally designed for state estimation, to themodel selection problem. In this setting, Carrassi et al. (2017) introduced thecontextual formulation of model evidence (CME) and showed that CME can beefficiently computed using a hierarchy of ensemble-based DA procedures.Although Carrassi et al. (2017) analyzed the DA methods most commonly used foroperational atmospheric and oceanic prediction worldwide, they did not studythese methods in conjunction with localization to a specific domain. Yet anyapplication of ensemble DA methods to realistic geophysical models requires theimplementation of some form of localization. The present study extends thetheory for estimating CME to ensemble DA methods with domain localization. Thedomain-localized CME (DL-CME) developed herein is tested for model selectionwith two models: (i) the Lorenz 40-variable mid-latitude atmospheric dynamicsmodel (L95); and (ii) the simplified global atmospheric SPEEDY model. The CMEis compared to the root-mean-square-error (RMSE) as a metric for modelselection. The experiments show that CME improves systematically over the RMSE,and that this skill improvement is further enhanced by applying localization inthe estimate of the CME, using the DL-CME. The potential use and range ofapplications of the CME and DL-CME as a model selection metric are alsodiscussed.

Estimating model evidence using ensemble-based data assimilation with localization - The model selection problem