Measuring the decision support value of probabilistic forecasts

It is widely believed that probabilistic forecasts provide greater decision support value than deterministic forecasts. The need for probabilistic information is unarguable. At issue is whether or the skill of a probabilistic forecast system matches or exceeds the skill of deterministic forecast system, which it is intended to replace. Investigations of this question are muddied by the fact that the accepted skill measures for deterministic forecasts are incompatible with the accepted skill measures for probabilistic forecasts.

We shall introduce an extension of a proven measure of deterministic forecast skill, the Peirce Skill Statistic, which also applies to probabilistic forecasts. This skill statistic provides a way to directly compare the skill of a probabilistic forecast system and a deterministic forecast system. Using interpretations from decision theory, we shall show that the extended Peirce Skill Statistic is directly related to the value of the forecasts for decision support.

These ideas will be illustrated by examples of probabilistic forecasts for the SFO Marine Stratus Forecast System.