Predicting uncertainty in numerical weather forecasts

Abstract The predictability of weather and climate forecasts is determined by the projection of uncertainties in both initial conditions and model formulation, onto flow-dependent instabilities of the chaotic climate attractor. Since it is essential to be able to estimate the impact of such uncertainties on forecast accuracy, no weather or climate prediction can be considered complete without a forecast of the associated flow-dependent predictability. The problem of predicting uncertainty can be posed in terms of the Liouville equation for the growth of initial uncertainty. However, in practice, the problem is approached using ensembles of integrations of comprehensive weather and climate prediction models, with explicit perturbations to both initial conditions and model formulation; the resulting ensemble of forecasts can be interpreted as a probabilistic prediction. Many of the difficulties in forecasting predictability arise from the large dimensionality of the climate system, and special techniques to generate ensemble perturbations have been developed. Methods to sample uncertainties in model formulation are also described. Practical ensemble prediction systems are described, and examples of resulting probabilistic weather forecast products shown. Methods to evaluate the skill of these probabilistic forecasts are outlined. By using ensemble forecasts as input to a simple decision-model analysis, it is shown that that probability forecasts of weather have greater potential economic value than corresponding single deterministic forecasts with uncertain accuracy.