Possibilistic response surfaces combining fuzzy targets and hydro-climatic uncertainty in flood vulnerability assessment

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 stress-test response surface; mapping system performance to a large sample of future hydro-climatic conditions. Dividing this exposure space between success and failure requires clear performance targets. In practice, however, stakeholders and decision-makers may be confronted with ambiguous objectives for which there are no clearly-defined (crisp) performance thresholds. Furthermore, response surfaces can be non-deterministic, as they do not fully capture all possible sources of hydro-climatic uncertainty. The challenge is thus to combine two different types of uncertainty: the irreducible uncertainty of the response itself relative to the variables that describe change, and the fuzziness of the performance target. We propose possibilistic surfaces to assess flood vulnerability with fuzzy performance thresholds. Three approaches are tested and compared on a un-gridded sample of the exposure space: (i) an aggregation of logistic regressions based on α-cuts combines the uncertainty of the response itself and the ambiguity of the target within a single possibility measure; (ii) an alternative approximates the response with a fuzzy analytical surface; and (iii) a convex delineation expresses the largest range of failure specific to a given management rule without probabilistic assumptions. To illustrate the proposed approaches, we use the flood-prone reservoir system of the Upper Saint-François River Basin in Canada as a case study. This study shows that ambiguity can be effectively be considered when generating a response surface and suggests how further research could build a possibilistic framework for hydro-climatic uncertainty.