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Hybrid error covariance models that blend climatological estimates of forecast error covariances with ensemble-based, flow-dependent forecast error covariances have led to significant reductions in forecast error when employed in 4DVAR data assimilation schemes. Tangent linear models (TLMs) designed to predict the differences between perturbed and unperturbed simulations of the weather forecast are a key component of such 4DVAR schemes. However, many forecasting centers have found that TLMs and their adjoints do not scale well computationally and are difficult to create and maintain—particularly for coupled ocean–wave–ice–atmosphere models. In this paper, the authors create ensemble-based TLMs (ETLMs) and test their ability to propagate both climatological and flow-dependent parts of hybrid error covariance models. These tests demonstrate that rank deficiency limits the utility of unlocalized ETLMs. High-rank, time-evolving, flow-adaptive localization functions are constructed and tested using rec...

Localized Ensemble-Based Tangent Linear Models and Their Use in Propagating Hybrid Error Covariance Models