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 forcing of the forecast and observer systems over a chosen time interval. Distributed forcing of an unstable system is shown to address the effect on the forecast of model error in the presumably unstable forecast error system, while distributed forcing of a stable system is shown to address the affect of model error in the presumably stable data assimilation system which for this purpose is viewed as a stable observer. Model error is taken to refer both to extrinsic error forcing such as from unresolved cumulus activity and to intrinsic error forcing arising from imperfections in the numerical model and in physical parameterizations