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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Volume 21, issue 6
Hydrol. Earth Syst. Sci., 21, 2967–2986, 2017
https://doi.org/10.5194/hess-21-2967-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Hydrol. Earth Syst. Sci., 21, 2967–2986, 2017
https://doi.org/10.5194/hess-21-2967-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 19 Jun 2017

Research article | 19 Jun 2017

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

Simon Matte1, Marie-Amélie Boucher1, Vincent Boucher2, and Thomas-Charles Fortier Filion3 Simon Matte et al.
  • 1Dept. of Applied Sciences, Université du Québec à Chicoutimi, 555, boulevard de l'Université, Chicoutimi, G7H 2B1, Canada
  • 2Dept. of Economics, Université Laval, 1025, avenue des Sciences-Humaines, Québec, G1V 0A6, Canada
  • 3Québec Government Direction of Hydrologic Expertise, 675, boul. René Lévesque Est., Québec, G1R 5V7, Canada

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 over-forecasting could help improve both the quality and the value of forecasts.

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In this study we set the basis of an alternative framework to replace the popular cost-loss ratio for the economic assessment of flood forecasting systems. The C-L ratio implicitly considers the decision maker to be risk-neutral, whereas it is rarely the case in real-life emergency situations. Instead of the cost-loss ratio, we propose using a utility function. We show that the decision-maker’s level of risk aversion is a crucial factor in the assessment of the economic value of flood forecasts.
In this study we set the basis of an alternative framework to replace the popular cost-loss...
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