Localized ensemble-based tangent linear models and their use in propagating hybrid error covariance models

High-rank, time-evolving, flow-adaptive localization functions are constructed and tested using recursive application of short-duration ETLMs, each of which is localized using a static localization. Since TLM operators do not need to be semipositive definite, the authors experiment with a variety of localization approaches including step function localization. The step function localization leads to a local formulation that was found to be highly effective.

In tests using simple one-dimensional models with both dispersive and nondispersive dynamics, it is shown that practical ETLM configurations were effective at propagating covariances as far as four error correlation scales.