Power Spectra of Physics-Based and Data-Driven Ensembles

Power spectra are evaluated for a range of ensemble systems run at the European Centre for Medium-Range Weather Forecasts (ECMWF). These spectra allow us to chart and compare the spatial–temporal evolution of ensemble spread and error, and to evaluate the impact of model and observational changes. We investigate whether differences between spread and error indicate issues of reliability or other deficiencies. In agreement with previous studies, for ensembles made with the physics-based model, extratropical variances (of 250 hPa geopotential height) saturate quickly at small scales, while planetary scale errors are far from saturated at day 10. At intermediate lead-times, forecasts are over-dispersive at synoptic scales. Tropical errors (for 200 hPa velocity potential) grow most rapidly over the first day, but are not fully saturated even by day 40. Tropical differences between spread and error at scales below 500 km are thought to reflect a need for more observations of tropical (divergent) winds, rather than a lack of reliability. Forecast variances in a “near perfect twin” ensemble suggest there is the potential to improve predictive skill by 5 days. Error variances highlight the substantial observational and modeling developments required to ensure that such forecasts are reliable. The impact of a recent system upgrade (which includes a change to the formulation of model uncertainty) and results from an experiment where additional radio occultation observations are assimilated, demonstrate that progress can be made when developments are focused on synoptic scale uncertainty and error-growth. Power spectra for two prototype data-driven ensembles show similar spatial–temporal evolution at large scales to that of the physics-based model; one has better overall reliability, and the other has reduced error. At smaller scales, the prototypes display a tendency for small-scale forecast variance and error to increase with lead-time beyond their theoretical limits. With the speed and breadth of ensemble development, these results illustrate the potential utility of power spectra diagnostics for comparing and developing ensemble systems.