Convergence of forecast distributions on the synoptic scale

Abstract Sampling uncertainty exists in probabilistic weather forecasting due to the constraint of the ensemble size. Recent work with large ensembles for convective‐scale numerical weather prediction has shown that a convergence of sampling uncertainty with ensemble size proportional to was found in the limit of large ensemble size. We investigate whether similar results are also obtained for global ensembles, where synoptic‐scale weather systems play a greater role. To do this, the 50‐member Integrated Forecasting System ensemble from the European Centre for Medium‐Range Weather Forecasts is analysed for a 15‐day run in the summer of 2021 at a grid point in central Germany. Using the neighbourhood method to increase the effective ensemble size, characteristic convergence proportional to was seen in the variables of temperature at 2 m and 500 hPa, total accumulated precipitation and the relative humidity. The nature of convergence was similar to convective‐scale studies, where less than 10 members were needed for the mean and between 50 and 100 were needed for the standard deviation, although more members were needed to see convergence in any of the quantiles. The neighbourhood method was proven to be useful for quantities with large variability on small spatial scales, including the 2 m temperature and the total accumulated precipitation. Furthermore, two complementary operational forecasting statistics relevant to detecting extreme events were tested, the extreme forecast index (EFI) and shift of tails (SOT). The EFI converged with less than 10 members, whereas the SOT did not, due to the EFI being calculated from the entire range of the climatology distribution and the SOT using an extreme quantile in its calculation that is likely not well defined with a 50‐member ensemble. Although the spatio‐temporal variability of synoptic weather systems is different from that of convection, one is able to use the same asymptotic convergence framework to evaluate ensemble size required.