The mean error measures forecast bias, whereas the mean square error confounds several attributes of forecasts such as bias, conditional bias, and skill [ Murphy and Epstein, 1989]. Inasmuch as bias can always be eliminated, the most essential performance attribute is skill, measured by the Bayesian correlation score that varies monotonically with the economic value of forecasts [ Krzysztofowicz, 1992a]. No such measure is reported by Seo and Smith [1992], but the correlation coefficient computed by French et al. [1994] can be taken as an approximate measure of skill. And with respect to the correlation coefficient, the model forecasts improved only marginally upon the advection forecasts. This implies that the cloud physics, satellite data, and surface data add little predictive information beyond that contained in the trajectory of storm dynamics estimated from radar scans.
The overall conclusion which emerges from these studies is twofold. First, the integration of observations from several sensors with physically based models does offer some potential for improving rainfall predictions. Second, within the confinements of the current models, the potential gains appear to be small. This conclusion must be viewed as tentative, given the limited testing of the models. It nonetheless corroborates the general notion held by many atmospheric scientists that progress in short-term mesoscale rainfall prediction will be laborious and slow [ John Cahir, personal communication, 1992]. And in the near term, the greatest gains in flash flood forecasting will come primarily from advantages of the radar technology itself, while the rainfall prediction problem continues to present formidable research challenges. Besides novel models for convective and frontal storms, there is a great need for thorough verification studies on large and independent data sets, using comprehensive performance measures [ Murphy, 1993].