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This chapter describes a novel approach for the treatment of model error ingeophysical data assimilation. In this method, model error is treated as adeterministic process fully correlated in time. This allows for the derivationof the evolution equations for the relevant moments of the model errorstatistics required in data assimilation procedures, along with anapproximation suitable for application to large numerical models typical ofenvironmental science. In this contribution we first derive the equations forthe model error dynamics in the general case, and then for the particularsituation of parametric error. We show how this deterministic description ofthe model error can be incorporated in sequential and variational dataassimilation procedures. A numerical comparison with standard methods is givenusing low-order dynamical systems, prototypes of atmospheric circulation, and arealistic soil model. The deterministic approach proves to be very competitivewith only minor additional computational cost. Most importantly, it offers anew way to address the problem of accounting for model error in dataassimilation that can easily be implemented in systems of increasing complexityand in the context of modern ensemble-based procedures.

Deterministic treatment of model error in geophysical data assimilation