A nonlinear dynamical perspective on model error: A proposal for non-localstochastic-dynamic parametrization in weather and climate prediction models

wdConventional parametrization schemes in weather and climate prediction mo dels describe the effects of subgrid-scale processes by deterministic bulk formulae which depend on local resolved-scale variables and a number of adj ustable parameters. Despite the unquestionable success of such models for w eather and climate prediction, it is impossible to justify the use of such formulae from first principles. Using low-order dynamical-systems models, a nd elementary results from dynamical-systems and turbulence theory, it is s hown that even if unresolved scales only describe a small fraction of the t otal variance of the system, neglecting their variability can, in some circ umstances, lead to gross errors in the climatology of the dominant scales. It is suggested that some of the remaining errors in weather and climate pr ediction models may have their origin in the neglect of subgrid-scale varia bility, and that such variability should be parametrized by non-local dynam ically based stochastic parametrization schemes. Results from existing sche mes are described, and mechanisms which might account for the impact of ran dom parametrization error on planetary-scale motions are discussed. Proposa ls for the development of non-local stochastic-dynamic parametrization sche mes are outlined, based on potential-vorticity diagnosis, singular-vector a nalysis and a simple stochastic cellular automaton model.