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An Ensemble-Based Four-Dimensional Variational Data Assimilation Scheme. Part I: Technical Formulation and Preliminary Test

ABSTRACT

Applying a flow-dependent background error covariance (B matrix) in variational data assimilation has been a topic of interest among researchers in recent years. In this paper, an ensemble-based four-dimensional variational (En4DVAR) algorithm, designed by the authors, is presented that uses a flow-dependent background error covariance matrix constructed by ensemble forecasts and performs 4DVAR optimization to produce a balanced analysis. A great advantage of this En4DVAR design over standard 4DVAR methods is that the tangent linear and adjoint models can be avoided in its formulation and implementation. In addition, it can be easily incorporated into variational data assimilation ...

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