What is the minimum ensemble size to reduce the uncertainty in the skill of West-WRF hydrometeorological forecasts over California?

Ensemble prediction is used to assign uncertainty to numerical weather prediction forecasts, but numerical weather prediction ensembles often suffer from being underdispersive as well as having a poor relationship between forecast spread and skill. Here, we propose a simple method to identify the minimum ensemble size needed to adequately reduce the difference in deterministic and probabilistic skill scores relative to a large ensemble and to reduce sampling uncertainty for forecasts of precipitation, snow water equivalent, and temperature for the winter season (December-March) of 2021-2022 over ten hydrologic regions in California. We do this for forecasts of precipitation, snow water equivalent, and temperature from the 200-member West-WRF ensemble produced by the Center for Western Weather and Water Extremes (CW3E). This ensemble samples the key sources of forecast uncertainty by utilizing a suite of perturbed initial and lateral boundary conditions, varying model physics parameterizations, and applying a stochastic perturbation to account for unresolved subgrid-scale processes. We determine two minimums: one to reduce computational expense and another that is more accurate. We find that similar numbers of ensemble members (at least ~20-40) are needed to minimize the difference in deterministic and probabilistic skill scores and to reduce sampling uncertainty, but the difference between the computationally inexpensive and more stringent minimum ensemble sizes is smaller to reduce sampling uncertainty. We also explore whether certain meteorological events like extreme precipitation events and atmospheric rivers have an effect on the minimum ensemble size. For instance, the minimum ensemble size needs to be larger in order to forecast extreme precipitation events. Additionally, we will also show whether or not post-processing reduces the minimum ensemble size. Thus, we will provide recommendations as to the minimum number of ensemble members that are needed to produce a useful regional numerical weather prediction ensemble for hydrometeorological prediction with and without post-processing.