Model uncertainty estimation in data assimilation for multi-scale systems with partially observed resolved variables
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Model uncertainty quantification is an essential component of effective Data Assimilation (DA), although it can be a challenging task for complex partially observed non-linear systems with highly non-Gaussian uncertainties. Model errors associated with sub-grid scale processes are of particular interest in meteorological DA studies; these are often represented through Stochastic Parameterizations of the unresolved process. Many existing Stochastic Parameterization schemes are only applicable when knowledge of the true sub-grid scale process or full observations of the coarse scale process are available, which is typically not the case in real applications. We present a methodology for estimating the statistics of sub-grid scale processes for the more realistic case that only partial observations of the coarse scale process are available. The aim is to first estimate the conditional probability density of additive model errors given the state of the system, from which samples can be generated to simulate model error within any ensemble-based assimilation framework. Model error realizations are estimated over a training period by minimizing their conditional variance, constrained by available observations. Special is that these errors are binned conditioned on the previous model state during the minimization process, allowing for the recovery of complex non-Gaussian error structures. We demonstrate the efficacy of the approach through numerical experiments with the multi-scale Lorenz 96 system. Various parameterizations of the Lorenz 96' model are considered with both small and large time scale separations between slow (coarse scale) and fast (fine scale) variables. Results indicate that both error estimates and forecasts are improved with the proposed method compared to two existing methods for accounting for model uncertainty in DA.
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