Predicting uncertainty in forecasts of weather and climate

The predictability of weather and climate forecasts is determined by the pr ojection of uncertainties in both initial conditions and model formulation onto flow-dependent instabilities of the chaotic climate attractor. Since i t is essential to be able to estimate the impact of such uncertainties on f orecast accuracy, no weather or climate prediction can be considered comple te without a forecast of the associated flow-dependent predictability. The problem of predicting uncertainty can be posed in terms of the Liouville eq uation for the growth of initial uncertainty, or a farm of Fokker-Planck eq uation if model uncertainties are also taken into account. However, in prac tice, the problem is approached using ensembles of integrations of comprehe nsive weather and climate prediction models, with explicit perturbations to both initial conditions and model formulation; the resulting ensemble of f orecasts 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 e nsemble perturbations have been developed. Special emphasis is placed on th e use of singular-vector methods to determine the linearly-unstable compone nt of the initial probability density function. Methods to sample uncertain ties in model formulation are also described. Practical ensemble prediction systems for prediction on timescales of days (weather forecasts), seasons (including predictions of El Nino) and decades (including climate change pr ojections) are described, and examples of resulting,probabilistic forecast products shown. Methods to evaluate the skill of these probabilistic foreca sts are outlined. By using ensemble forecasts as input to a simple decision -model analysis, it is shown that probability forecasts of weather and clim ate have greater potential economic value than corresponding single determi nistic forecasts with uncertain accuracy.