Efficient Formulation and Implementation of Data Assimilation Methods

Dear Colleagues,

Data Assimilation is the process by which imperfect numerical forecasts are adjusted according to real, noisy observations. In general, two families of methods are well-known in the data assimilation context: variational- and ensemble-based methods. In the context of ensemble data assimilation, the moments of the background error distribution are estimated via the empirical moments of an ensemble of model realizations. The resulting ensemble covariance matrix is well-known to be
flow-dependent and therefore, the estimated background-error correlations are driven by the physics and the dynamics of the numerical model. In operational data assimilation, model runs are computationally expensive, which implies that only a small ensemble size is feasible. Consequently, sampling errors impact the estimated background-error correlations and therefore, analysis innovations are poorly estimated by the ensemble covariance matrix. Likewise, in variational data assimilation methods, the actual state of a system is forecasted via the posterior mode of the error distribution. The assimilation process can be performed sequentially via the three dimensional variational (3D-Var) cost function or, given an assimilation window, for multiple observations, the four dimensional variational (4D-Var) cost function can be considered. In the last case, adjoint formulations are required, the computation of which is not trivial in practice. In recent years, the scientific community has centered its efforts on providing assimilation schemes wherein, information brought by ensemble members and optimization features of variational methods are exploited in order to reduce the impact of sampling errors over innovations and to provide efficient and practical implementations of robust data assimilation methods.

Papers are welcome on all aspects of ensemble data assimilation, including, but not restricted to:

• Covariance matrix estimation in ensemble-based methods.

• Ensemble 4D-Var data assimilation.

• Parallel implementation of ensemble methods for data assimilation.

• Domain localization in ensemble-based methods.

• Ensemble data assimilation in highly non-linear models.

• Ensemble-based methods for non-Gaussian data assimilation.

• Efficient and practical implementations of ensemble-based methods.

• Adjoint-free ensemble-based methods for 4D-Var data assimilation.

Dr. Adrian Sandu
Dr. Elias D. Niño-Ruiz
Dr. Haiyan Cheng
Guest Editors

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