Moving beyond the cost–loss ratio: economic assessment of streamflow forecasts for a risk-averse decision maker

Abstract

Abstract. A large effort has been made over the past 10 years to promote the operational use of probabilistic or ensemble streamflow forecasts. Numerous studies have shown that ensemble forecasts are of higher quality than deterministic ones. Many studies also conclude that decisions based on ensemble rather than deterministic forecasts lead to better decisions in the context of flood mitigation. Hence, it is believed that ensemble forecasts possess a greater economic and social value for both decision makers and the general population. However, the vast majority of, if not all, existing hydro-economic studies rely on a cost-loss ratio framework that assumes a risk-neutral decision maker. To overcome this important flaw, this study borrows from economics and evaluates the economic value of early warning flood systems using the well-known Constant Absolute Risk Aversion (CARA) utility function, which explicitly accounts for the level of risk aversion of the decision maker. This new framework allows for the full exploitation of the information related to a forecasts' uncertainty, making it especially suited for the economic assessment of ensemble or probabilistic forecasts. Rather than comparing deterministic and ensemble forecasts, this study focuses on comparing different types of ensemble forecasts. There are multiple ways of assessing and representing forecast uncertainty. Consequently, there exist many different means of building an ensemble forecasting system for future streamflow. One such possibility is to dress deterministic forecasts using the statistics of past error forecasts. Such dressing methods are popular among operational agencies because of their simplicity and intuitiveness. Another approach is the use of ensemble meteorological forecasts for precipitation and temperature, which are then provided as inputs to one or many hydrological model(s). In this study, three concurrent ensemble streamflow forecasting systems are compared: simple statistically dressed deterministic forecasts, forecasts based on meteorological ensembles, and a variant of the latter that also includes an estimation of state variable uncertainty. This comparison takes place for the Montmorency River, a small flood-prone watershed in southern central Quebec, Canada. The assessment of forecasts is performed for lead times of 1 to 5 days, both in terms of forecasts' quality (relative to the corresponding record of observations) and in terms of economic value, using the new proposed framework based on the CARA utility function. It is found that the economic value of a forecast for a risk-averse decision maker is closely linked to the forecast reliability in predicting the upper tail of the streamflow distribution. Hence, post-processing forecasts to avoid overforecasting could help improve both the quality and the value of forecasts.

Water Temperature Ensemble Forecasts: Implementation Using the CEQUEAU Model on Two Contrasted River Systems

“…A decision therefore can be made based on knowledge of the risk associated with this decision. In fact, it was recently shown that the level of risk aversion of a decision-maker is a key factor in assessing the comparative benefits of forecasting systems for decision-making [57]. In the case of a fully deterministic forecast, that notion of risk is much more difficult to assess and to communicate to the decision-makers, although they are usually aware of its existence [58].…”

Develop a coupled agent-based modeling approach for uncertain water management decisions

“…To fit the CL model into the proposed ABM framework, we modify the above CL model following the concept of Tena and Gómez (2008) and Matte et al (2017) which added the perception of risk into the decision-making process. We define " " as the expected cost of taking management action that will potentially increase the gross economic profit and " " as the expected opportunity loss of not taking such management action.…”

“…CL modeling has been widely used in estimating the economic value of weather forecasts (Keeney, 1982;Lee and Lee, 2007;Murphy, 1976;Murphy et al, 1985). Tena and Gómez (2008) and Matte et al (2017) incorporated the Constant Absolute Risk Aversion theory in CL modeling to evaluate risk perception of decision makers since the original CL model assumes a risk-neutral decision maker. They used a parameter, Arrow-Pratt coefficient, to represent "risk-averse" and "risk-seeking" decision makers but did not specify how this parameter could be determined.…”

Do users benefit from additional information in support of operational drought management decisions in the Ebro basin?

“…CC BY 4.0 License. users in weighing the costs and probability of losses, but has its limitations as different users may make different decisions depending on their levels of risk averseness, though this can be incorporated through a function of risk aversion (Quiroga et al, 2011;Matte et al, 2017).…”

“…A more realistic distribution of risk averseness can be developed using for example the Constant Absolute Risk Aversion Utility Function (Matte et al, 2017;Quiroga et al, 2011), though this will require extensive survey data to determine how risk averseness is distributed among farmers.…”