Abstract
Abstract. Several alternatives have been proposed to shift the paradigms of water management under uncertainty from predictive to decision-centric. An often-mentioned tool is the response surface mapping system performance with a large sample of future hydroclimatic conditions through a stress test. Dividing this exposure space between acceptable and unacceptable states requires a criterion of acceptable performance defined by a threshold. In practice, however, stakeholders and decision-makers may be confronted with ambiguous objectives for which the acceptability threshold is not clearly defined (crisp). To accommodate such situations, this paper integrates fuzzy thresholds to the response surface tool. Such integration is not straightforward when response surfaces also have their own irreducible uncertainty from the limited number of descriptors and the stochasticity of hydroclimatic conditions. Incorporating fuzzy thresholds, therefore, requires articulating categories of imperfect knowledge that are different in nature, i.e., the irreducible uncertainty of the response itself relative to the variables that describe change and the ambiguity of the acceptability threshold. We, thus, propose possibilistic surfaces to assess flood vulnerability with fuzzy acceptability thresholds. An adaptation of the logistic regression for fuzzy set theory combines the probability of an acceptable outcome and the ambiguity of the acceptability criterion within a single possibility measure. We use the flood-prone reservoir system of the Upper Saint François River basin in Canada as a case study to illustrate the proposed approach. Results show how a fuzzy threshold can be quantitatively integrated when generating a response surface and how ignoring it might lead to different decisions. This study suggests that further conceptual developments could link the reliance on acceptability thresholds in bottom-up assessment frameworks with the current uses of fuzzy set theory.
Highlights
Imperfect knowledge is a defining feature of water resources management
Taken in 5-year periods (610 time series), the values all lead to flood control reliabilities superior to 0.97, which is above any considered acceptability threshold
Applying a fuzzy threshold would be straightforward for a deterministic response surface, with each performance value on the exposure space being mapped to a degree of acceptability between 0 and 1
Summary
Imperfect knowledge is a defining feature of water resources management. As a prime example, the uncertain availability of water at any given time drives human interventions such as building storage capacities or levees. To address the uncertain future in water systems, the dominant paradigm has been to optimize investments or management plans according to probabilistic estimates based on past observations, assuming that the underlying processes are stationary. A well-established alternative is to rely on some form of prediction of those processes through climate modelling and downscaling. Such an approach has its own limitations, . Greenhouse gas emission pathways depend on policy choices which are not predictable, while climate models and downscaling processes have structural uncertainties (Prudhomme et al, 2010; Mastrandrea et al, 2010; Kay et al, 2014). A discrete set of projections may not be suited to find the hydroclimatic thresholds beyond which a system fails to reach its target (Culley et al, 2016)
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