The errors in numerical weather forecasts resulting from limited ensemble size are explored using 1,000‐member forecasts of convective weather over Germany 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 sampling error decreases proportional to N−1/2 for large enough ensemble size N, 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.

<p>Accurate precipitation forecasts at kilometre scales are still a key challenge for convective scale ensemble prediction systems. We assess the spatial forecast skill-spread relationship for summer convection in 2021 and address the impact of considering model uncertainties from two physics parametrisations -- microphysics and planetary boundary layer turbulence -- together with initial and lateral boundary conditions uncertainties. To investigate their flow dependence all analyses are done conditionally to strong and weak synoptic convective forcing cases.<br />It is found that the spatial skill-spread relationship is highly dependent on synoptic forcing and the current operational ensemble forecasts are spatially underdispersive especially during weak synoptic control, whereas a good agreement is found during strong synoptic control. Case studies during weak synoptic control demonstrate that perturbations in the planetary boundary layer contribute to improving forecast skill and increase spread at small scales while microphysical perturbations contribute to spread increase across all scales. Overall, the combination of both perturbations seems to combine their individual impacts and thus benefits the spatial skill-spread relationship at most times and scales.</p>

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