On the filtering properties of ensemble averaging for storm-scale precipitation forecasts

For an ensemble of precipitation forecasts, the ensemble mean (ENM) is generally more skillful than any of the ensemble members as verified against observations. A major reason is that the averaging filters out non-predictable features that the ensemble members fail to agree on. Previous research has shown that the non-predictable features occur at small scales, in both numerical forecasts and Lagrangian persistence nowcasts. Hence, it is reasonable to postulate that the unpredictable features filtered through ensemble averaging would also occur at small scales. In this study, the exact range of scales affected by the averaging process is determined by comparing the statistical properties of precipitation fields between the ENM and the individual ensemble members from a Storm-Scale Ensemble Forecasting (SSEF) system.

The filtering effect of ensemble averaging results in an intensity bias for the ENM forecasts. Ebert (2001) proposed to correct empirically the ENM forecasts by recalibrating the intensities in the ENM using the probability density function (PDF) of rainfall values from the ensemble members. This procedure, called probability matching (PM), leads to a new ensemble mean, the Probability Matched Mean (PMM). The PMM appears more realistic and yields better skill as evaluated using traditional metrics. However, we demonstrate that despite the PMM having the same PDF of rainfall intensities as the ensemble members, the spectral structure and spatial distribution of the precipitation field differs from that of the members. It is the lesser variability of the PMM fields at small scales that causes the better scores of the PMM.

References

Ebert, E. E., 2001: Ability of a poor man's ensemble to predict the probability and distribution of precipitation. Monthly Weather Review, 129, 2461-2480.