  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.
