Credible Interval Temperature Forecasting: Some Experimental Results

Abstract

This paper describes the results of an experiment involving credible interval temperature forecasts. A credible interval is an interval of values of the variable of concern, in this case maximum or minimum temperature, accompanied by a probability which expresses a forecaster's ?degree of belief? that the temperature will fall in the given interval. The experiment was designed to investigate the ability of fore-casters to express the uncertainty inherent in their temperature forecasts in probabilistic terms and to compare two approaches (variable-width and flied-width intervals) to credible interval temperature forecasting. Four experienced weather forecasters participated in the experiment, which was conducted at the National Weather Service Forecast Office in Denver, Colorado. Two forecasters made variable-width, fixed-probability forecasts using 50% and 75% intervals, while the other two forecasters made fixed-width, variable-probability forecasts using 5°F and 9°F intervals. On each occasion the forecasters first determined a median, and the variable-width and fixed-width intervals were then centered at the median in terms of probability and width, respectively. The results indicate that, overall, the medians determined by the forecasters were good point forecasts of maximum and minimum temperatures. Further, a comparison of the average errors for the forecasters? medians with the average errors for the medians derived from climatology reveals that the forecasters were able to improve greatly upon climatology. The variable-width credible intervals were very reliable in the sense that the observed relative frequencies corresponded very closely to the forecast probabilities. Moreover, the variable-width intervals were more reliable and much more precise than the corresponding climatological forecasts. The fixed-width intervals, on the other hand, were assigned probabilities that were, on the average, larger that the corresponding relative frequencies. In summary, the results indicate that weather forecasters can use credible intervals to describe the uncertainty contained in their temperature forecasts. The implications of these experimental results for probability forecasting in general and temperature forecasting in particular are discussed.