Understanding the relationship between streamflow forecast skill and value across the western US

Abstract. Accurate seasonal streamflow forecasts are essential for effective decision-making in water management. In a decision-making context, it is important to understand the relationship between forecast skill – the accuracy of forecasts against observations – and forecast value, which is the forecast's economic impact assessed by weighing potential mitigation costs against potential future losses. This study explores how errors in these probabilistic forecasts can reduce their economic “value,” especially during droughts, when decision-making is most critical. This value varies by region and is contextually dependent, often limiting retrospective insights to specific operational water management systems. Additionally, the value is shaped by the intrinsic qualities of the forecasts themselves. To assess this gap, this study examines how forecast skill transforms into value for true forecasts (using real-world models) in unmanaged snow-dominated basins that supply flows to downstream managed systems. We measure forecast skill using quantile loss and quantify forecast value through the potential economic value framework. The framework is well-suited for categorical decisions and uses a cost-loss model, where the economic implications of both correct and incorrect decisions are considered for a set of hypothetical decision-makers. True forecasts are included, made with commonly used models within an ensemble streamflow prediction (ESP) framework using a process-based hydrologic modeling system, WRF-Hydro, and a deep-learning model, Long Short-term Memory Networks, as well as operational forecasts from the NRCS. To better interpret the relationship between skill and value, we compare true forecasts with synthetic forecasts that are created by imposing regular error structures on observed streamflow volumes. We assess the sensitivity of skill and value from both synthetic and true forecasts by modifying fundamental properties of the forecast-error in mean and change in variability. Our findings indicate that errors in mean and change in variability consistently explain variations in forecast skill for true forecasts. However, these errors do not fully explain the variations in forecast value across the basins, primarily due to irregular error structures, which impact categorical measures such as hit and false alarm rates, causing high forecast skill to not necessarily result in high forecast value. We identify two key insights: first, hit and false alarm rates effectively capture variability in forecast value rather than error in mean and change in variability; second, the relationship between forecast skill and value shifts monotonically with drought severity. These findings emphasize the need for a deeper understanding of how forecast performance metrics relate to both skill and value, highlighting the complexities in assessing the effectiveness of forecasting systems.