The impact of model-error correlation on regional data assimilative models and their observational arrays

Data assimilative models often minimize a penalty functional that measures model adjustment and model-data misfit. The penalty functional builds assumptions about model error into the analysis. Usually, errors from different parts of the model (e.g., dynamics and boundary conditions) are presumed to be uncorrelated. This is clearly not a valid assumption in regional models where uncertain large-scale forcing affects open-ocean boundary conditions. In this study, calculations with a regional wind-driven inverse model provide a specific example where model error from uncertain wind stress is correlated with model error from uncertain open boundary conditions. This physically realistic scenario motivates development of a more general penalty functional that includes model-error correlation. In fact, model-error correlations must be included in order to meet the objective of making the open-ocean boundaries behave like the open ocean. Statistical issues for the generalized inverse model are described in the context of objective analysis. Implications for array design are addressed. For data assimilative models that incorrectly neglect model-error correlation, data should not come from open-ocean boundary regions. Rather, data should come from the interior of the regional domain. There is no such restriction on data placement for the assimilative model that correctly accounts for model-error correlation.