Tuesday, 15 January 2002: 4:29 PM
Stochastic forecast models for nonlinear deterministic systems
Given a perfect model, an accurate weather forecast will require an accurate estimation of the initial state. It is shown that even under the ideal conditions of a perfect model, unlimited computer time and infinite past observations of a deterministic nonlinear system, uncertainty in the observations makes exact state estimation impossible (Judd & Smith 2001, Physica D 151, 125--141). Nevertheless, shadowing trajectories, that is, model trajectories consistent with the observations to within observational error, form a set of indistinguishable states which, in turn, provide an efficient method for constructing ensembles with an optimal assessment of observational uncertainties. When the models are not perfect, however, the set of indistinguishable states may be empty. This suggests the introduction of a stochastic term into models of deterministic dynamical systems; the implications of using such pseudo-orbits in ensemble forecasting is discussed. While the resulting stochastic models cannot be expected to produce desirable statistics, like an accountable probability density forecasts, alternative aims such as bounding the verification appear within reach. The bounding box produced by the operational ECMWF ensemble forecast is examined in this light.