How many members are necessary to reduce errors in ensemble spread in hydrometeorological forecasts?

Ensemble prediction is commonly used to assign uncertainty to numerical weather prediction forecasts, but it has long been recognized that numerical weather prediction ensembles often suffer from being underdispersive. Another long-standing problem is the lack of correlation between forecast spread and model skill. It has been hypothesized that these problems might be alleviated if there were enough ensemble members to sample from the full set of possible outcomes. Here, we explore whether this is possible by utilizing forecasts of precipitation, snow water equivalent, and temperature from the 200-member West-WRF large ensemble produced by the Center for Western Weather and Water Extremes (CW3E) for the winter season (December-March) of 2021-2022 over the California hydrologic region. The West-WRF 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. Model skill is assessed by comparing to daily data from The University of Arizona (UA) snow product for snow water equivalent and Parameter-Elevation Relationships on Independent Slopes Model (PRISM) dataset for precipitation and temperature. Stronger relationships between ensemble spread and skill are found when more members are used. To understand this, we explore how much the ensemble spread in each month captures the observational spread. We will determine the minimum number of ensemble members needed to obtain an ensemble evenly sampling the observational spread across the various subregions and as a function of forecast month. We will also emphasize differences between normal conditions and days of meteorological interest when there were atmospheric rivers impacting the region. We will also explore whether postprocessing has an effect by using quantile matching and a spread correction. With this, we will provide recommendations as to how many ensemble members are needed to produce a useful large ensemble with and without post-processing.