Evaluation of ensemble forecast uncertainty using a new proper score: Application to medium-range and seasonal forecasts

Forecast verification is important across scientific disciplines, as it provides a framework for evaluating the performance of a forecasting system. In the atmospheric sciences, probabilistic skill scores are often used for verification, as they provide a way of ranking the performance of different probabilistic forecasts unambiguously. In order to be useful, a skill score must be proper: it must encourage honesty in the forecaster and reward forecasts that are reliable and have good resolution. A new score, the error-spread score (ES), is proposed, which is particularly suitable for evaluation of ensemble forecasts. It is formulated with respect to the moments of the forecast. The ES is confirmed to be a proper score and is therefore sensitive to both resolution and reliability. The ES is tested on forecasts made using the Lorenz '96 system and found to be useful for summarizing the skill of the forecasts. The European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble prediction system (EPS) is evaluated using the ES. Its performance is compared with a perfect statistical probabilistic forecast: the ECMWF high-resolution deterministic forecast dressed with the observed error distribution. This generates a forecast that is perfectly reliable if considered over all time, but does not vary from day to day with the predictability of the atmospheric flow. The ES distinguishes between the dynamically reliable EPS forecasts and the statically reliable dressed deterministic forecasts. Other skill scores are tested and found to be comparatively insensitive to this desirable forecast quality. The ES is used to evaluate seasonal range ensemble forecasts made with the ECMWF System 4. The ensemble forecasts are found to be skilful when compared with climatological or persistence forecasts, though this skill is dependent on the region and time of year.