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

In recent years, there has been increased interest in applying data assimilation (DA) methods, originally designed for state estimation, to the model selection problem. In this setting, previous studies introduced the contextual formulation of model evidence, or contextual model evidence (CME), and showed that CME can be efficiently computed using a hierarchy of ensemble-based DA procedures. Although these studies analysed 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, very high-dimensional geophysical models requires the implementation of some form of localization. The present study extends CME estimation to ensemble DA methods with domain localization. Domain-localized CME (DL-CME) developed in this article is tested for model selection with two models: (a) the Lorenz 40-variable midlatitude atmospheric dynamics model (Lorenz-95); and (b) the simplified global atmospheric SPEEDY model. CME is compared to the root-mean-square error (RMSE) as a metric for model selection. The experiments show that CME systematically outperforms RMSE in model selection skill, and that this skill improvement is further enhanced by applying localization to the CME estimate using DL-CME. The potential use and range of applications of CME and DL-CME as a model selection metric are also discussed.