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

wdConventional parametrization schemes in weather and climate prediction models describe the effects of subgrid-scale processes by deterministic bulk formulae which depend on local resolved-scale variables and a number of adjustable parameters. Despite the unquestionable success of such models for weather and climate prediction, it is impossible to justify the use of such formulae from first principles. Using low-order dynamical-systems models, and elementary results from dynamical-systems and turbulence theory, it is shown that even if unresolved scales only describe a small fraction of the total variance of the system, neglecting their variability can, in some circumstances, lead to gross errors in the climatology of the dominant scales. It is suggested that some of the remaining errors in weather and climate prediction models may have their origin in the neglect of subgrid-scale variability, and that such variability should be parametrized by non-local dynamically based stochastic parametrization schemes. Results from existing schemes are described, and mechanisms which might account for the impact of random parametrization error on planetary-scale motions are discussed. Proposals for the development of non-local stochastic-dynamic parametrization schemes are outlined, based on potential-vorticity diagnosis, singular-vector analysis and a simple stochastic cellular automaton model.