Convergence of forecast distributions in a 100,000-member idealised convective-scale ensemble

Tempest, Kirsten I.; Craig, George C. und Brehmer, Jonas R. (2022): Convergence of forecast distributions in a 100,000-member idealised convective-scale ensemble. In: Quarterly Journal of the Royal Meteorological Society, Bd. 149, Nr. 752: S. 677-702

Abstract

Many operational weather services use ensembles of forecasts to generate probabilistic predictions. Computational costs generally limit the size of the ensemble to fewer than 100 members, although the large number of degrees of freedom in the forecast model would suggest that a vastly larger ensemble would be required to represent the forecast probability distribution accurately. In this study, we use a computationally efficient idealised model that replicates key properties of the dynamics and statistics of cumulus convection to identify how the sampling uncertainty of statistical quantities converges with ensemble size. Convergence is quantified by computing the width of the 95% confidence interval of the sampling distribution of random variables, using bootstrapping on the ensemble distributions at individual time and grid points. Using ensemble sizes of up to 100,000 members, it was found that for all computed distribution properties, including mean, variance, skew, kurtosis, and several quantiles, the sampling uncertainty scaled as n-1/2 for sufficiently large ensemble size n. This behaviour is expected from the Central Limit Theorem, which further predicts that the magnitude of the uncertainty depends on the distribution shape, with a large uncertainty for statistics that depend on rare events. This prediction was also confirmed, with the additional observation that such statistics also required larger ensemble sizes before entering the asymptotic regime. By considering two methods for evaluating asymptotic behaviour in small ensembles, we show that the large-n theory can be applied usefully for some forecast quantities even for the ensemble sizes in operational use today.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Physik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 530 Physik
• ISSN: 0035-9009
• Sprache: Englisch
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 491502892
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 257899354