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

IIn recent years, there has been a growing interest in applying data assimilation (DA) methods, originally designed for state estimation, to the model selection problem. In this setting, Carrassi et al. (2017) introduced the contextual formulation of model evidence (CME) and showed that CME can be efficiently computed using a hierarchy of ensemble-based DA procedures. Although Carrassi et al. (2017) analyzed the DA methods most commonly used for operational atmospheric and oceanic prediction worldwide, they did not study these methods in conjunction with localization to a specific domain. Yet any application of ensemble DA methods to realistic geophysical models requires the implementation of some form of localization. The present study extends the theory for estimating CME to ensemble DA methods with domain localization. The domain-localized CME (DL-CME) developed herein is tested for model selection with two models: (i) the Lorenz 40-variable mid-latitude atmospheric dynamics model (L95); and (ii) the simplified global atmospheric SPEEDY model. The CME is compared to the root-mean-square-error (RMSE) as a metric for model selection. The experiments show that CME improves systematically over the RMSE, and that this skill improvement is further enhanced by applying localization in the estimate of the CME, using the DL-CME. The potential use and range of applications of the CME and DL-CME as a model selection metric are also discussed.