Convergence of forecast distributions in a 100,000 member idealised convective-scale ensemble
07.11.2022
Convergence of forecast distributions in a 100,000 member idealised convective-scale ensemble
An idealised ensemble that replicates key properties of the dynamics and statistics of cumulus convection is used to identify how sampling uncertainty of statistical quantities converges with ensemble size. A universal asymptotic scaling for this convergence was found, which was dependent on the statistic and the distribution shape, with largest uncertainty for statistics that depend on rare events. This is demonstrated in the figure below for a Gaussian distributed model variable, where the sampling uncertainty (y-axis) for 5 quantiles (red lines) indicates that after a certain ensemble size, it begins converging asymptotically (grey lines), and the more extreme the quantile, the more members it requires for this to be the case.
Reference
Tempest, K., G. Craig, and J. Brehmer (2022): Convergence of forecast distributions in a 100,000 member idealised convective-scale ensemble. Under review at Quarterly Journal of the Royal Meteorological Society.