24 . 3 Forecasting Mesoscale Uncertainty :

All types of end users who must make weatherdependent decisions stand to benefit greatly from knowing the expected accuracy of a particular forecast a priori. Forecast accuracy varies both spatially and temporally as a result of initial state and model errors, which change as the atmospheric flow evolves. Probabilistic weather forecasts derived from numerical weather prediction (NWP) ensembles can provide crucial information about the expected forecast uncertainty. It has been theorized that ensemble spread should provide a measure of forecast uncertainty (Kalnay and Dalcher 1987; Murphy 1988; Houtekamer 1993), such that high (low) spread events correspond with high (low) forecast errors. The traditional approach to quantifying this so-called spreadskill relationship has involved finding the correlation between a measure of ensemble spread and the accuracy of a particular determinstic forecast. However, using the simple statistical arguments outlined by Houtekamer (1993, hereafter H93), there exists a theoretical limit to the strength of this type of correlation (Whitaker and Loughe 1998). From Eq. (33) in H93, the correlation between the standard deviation of perfect ensemble forecasts (σ) and the absolute error of the ensemble mean (|Ē|) is limited by the temporal spread variability. As the temporal variability in spread (β) increases, so does the spread-error correlation. In the upper limit of spread variability,