Distributions and convergence of forecast variablesin a 1,000-member convection-permitting ensemble

GEORGE CRAIG; MATJAZ PUH; CHRISTIAN KEIL; TOBIAS NECKER ; JUAN RUIZ; MARTIN WEISSMANN; TAKEMASA MIYOSHI

QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY

JOHN WILEY & SONS LTD

Lugar: LOndres; Año: 2022

0035-9009

The errors in numerical weather forecasts resulting from limited ensemble size were explored using 1,000-member forecasts of convective weather over Ger-many at 3-km resolution. A large number of forecast variables at different lead times were examined, and their distributions could be classified into three categories: quasi-normal (e.g., tropospheric temperature), highly skewed (e.g.precipitation), and mixtures (e.g., humidity). Dependence on ensemble size was examined in comparison to the asymptotic convergence law that the samplingerrordecreasesproportionaltoN−1/2forlargeenoughensemblesizeN, independent of the underlying distribution shape. The asymptotic convergence behavior was observed for the ensemble mean of all forecast variables, even for ensemble sizes less than 10. For the ensemble standard deviation, sizes of up to 100 were required for the convergence law to apply. In contrast, there was no clear sign of convergence for the 95th percentile even with 1,000 members. Methods such as neighborhood statistics or prediction of area-averaged quantities were found to improve accuracy, but only for variables with random small-scale variability, such as convective precipitation.KEYWORDSensemble, forecast uncertainty, probability distribution1INTRODUCTIONWeather is by nature unpredictable, and especially on the convective scale where errors grow rapidly(Lorenz,1969; Hoheneggeret al.,2006; Leonciniet al.,2010; Clarket al.,2010;Keilet al.,2014;Craiget al.,2021). But even when deterministic forecasts are inaccurate, useful information can often be obtained in the form of probabilities. In a highly non-linear system like the atmosphere, the probability distribution is oftenThis is an open-access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.© 2022 The Authors.Quarterly Journal of the Royal Meteorological Society published by John Wiley & Sons Ltd on behalf of the Royal Meteorological Society.Q J R Meteorol Soc. 2022;1–19.wileyonlinelibrary.com/journal/qj1