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 fact, the barrier of building and maintaining TLMs and adjoints of the global coupled system has, so far, proved insurmountable.

As an alternative to traditional TLMs, in this paper, we create ensemble-based TLMs (ETLMs) and test their ability to propagate both climatological and flow-dependent parts of hybrid error covariance models. Our tests demonstrate that rank deficiency limits the utility of unlocalized ETLMs. We construct and test high-rank, time evolving, flow adaptive localization functions using recursive application of short-duration ETLMs, each of which is localized using a static localization. We evaluate performance of the ETLM models in a series of progressively complex models, including one-dimensional wave dispersion, low-resolution version of the global weather model, and coupled dynamics of the atmospheric and oceanic boundary layers.

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*email: frolovsa@gmail.com
*Preference: Oral