Ensemble mean forecast skill and applications with the T213 ensemble prediction system

Ensemble forecasting has become the prevailing method in current operational weather forecasting. Although ensemble mean forecast skill has been studied for many ensemble prediction systems (EPSs) and different cases, theoretical analysis regarding ensemble mean forecast skill has rarely been investigated, especially quantitative analysis without any assumptions of ensemble members. This paper investigates fundamental questions about the ensemble mean, such as the advantage of the ensemble mean over individual members, the potential skill of the ensemble mean, and the skill gain of the ensemble mean with increasing ensemble size. The average error coefficient between each pair of ensemble members is the most important factor in ensemble mean forecast skill, which determines the mean-square error of ensemble mean forecasts and the skill gain with increasing ensemble size. More members are useful if the errors of the members have lower correlations with each other, and vice versa. The theoretical investigation in this study is verified by application with the T213 EPS. A typical EPS has an average error coefficient of between 0.5 and 0.8; the 15-member T213 EPS used here reaches a saturation degree of 95% (i.e., maximum 5% skill gain by adding new members with similar skill to the existing members) for 1-10-day lead time predictions, as far as the mean-square error is concerned.