Distributed Forcing of Forecast and Assimilation Error Systems

Temporally distributed deterministic and stochastic excitation of the tangent linear forecast system governing forecast error growth and the tangent linear observer system governing assimilation error growth is examined. The method used is to determine the optimal set of distributed deterministic and stochastic forcings of the forecast and observer systems over a chosen time interval. Distributed forcing of an unstable system addresses the effect of model error on forecast error in the presumably unstable forecast error system. Distributed forcing of a stable system addresses the effect on the assimilation of model error in the presumably stable data assimilation system viewed as a stable observer. In this study, model error refers both to extrinsic physical error forcing, such as that which arises from unresolved cumulus activity, and to intrinsic error sources arising from imperfections in the numerical model and in the physical parameterizations.