Flexible forecast value metric suitable for a wide range of decisions: application using probabilistic subseasonal streamflow forecasts

Streamflow forecasts have the potential to improve water resource decision-making, but their economic value has not been widely evaluated, since current forecast value methods have critical limitations. The ubiquitous measure for forecast value, the relative economic value (REV) metric, is limited to binary decisions, the cost–loss economic model, and risk-neutral decision-makers (users). Expected utility theory can flexibly model more real-world decisions, but its application in forecasting has been limited and the findings are difficult to compare with those from REV. In this study, a new metric for evaluating forecast value, relative utility value (RUV), is developed using expected utility theory. RUV has the same interpretation as REV, which enables a systematic comparison of results, but RUV is more flexible and better represents real-world decisions because more aspects of the decision context are user-defined. In addition, when specific assumptions are imposed, it is shown that REV and RUV are equivalent, hence REV can be considered a special case of the more general RUV. The key differences and similarities between REV and RUV are highlighted, with a set of experiments performed to explore the sensitivity of RUV to different decision contexts, such as different decision types (binary, multi-categorical, and continuous-flow decisions), various levels of user risk aversion, and varying the relative expense of mitigation. These experiments use an illustrative case study of probabilistic subseasonal streamflow forecasts (with lead times up to 30 d) in a catchment in the southern Murray–Darling Basin of Australia. The key outcomes of the experiments are (i) choice of decision type has an impact on forecast value, hence it is critically important to match the decision type with the real-world decision; (ii) forecasts are typically more valuable for risk averse users, but the impact varies depending on the decision context; and (iii) risk aversion impact is mediated by how large the potential damages are for a given decision. All outcomes were found to critically depend on the relative expense of mitigation (i.e. the cost of action to mitigate damages relative to the magnitude of damages). In particular, for users with relatively high expense of mitigation, using an unrealistic binary decision to approximate a multi-categorical or continuous-flow decision gives a misleading measure of forecast value for forecasts longer than 1 week lead time. These findin