Possibilistic response surfaces: incorporating fuzzy thresholds into bottom-up flood vulnerability analysis

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.

BAYESIAN MAGNETOTELLURIC INVERSION USING METHYLENE BLUE STRUCTURAL PRIORS FOR IMAGING SHALLOW CONDUCTORS IN GEOTHERMAL FIELDS

In geothermal exploration, magnetotelluric (MT) data and inversion models are commonly used to image shallow conductors typically associated with the presence of an electrically conductive clay cap that overlies the main reservoir. However, these inversion models suffer from non-uniqueness and uncertainty, and the inclusion of useful geological information is still limited. We develop a Bayesian inversion method that integrates the electrical resistivity distribution from MT surveys with borehole methylene blue data (MeB), an indicator of conductive clay content. MeB data is used to inform structural priors for the MT Bayesian inversion that focus on inferring with uncertainty the shallow conductor boundary in geothermal fields. By incorporating borehole information, our inversion reduces non-uniqueness and then explicitly represents the irreducible uncertainty as estimated depth intervals for the conductor boundary. We use Markov chain Monte Carlo (McMC) and a one-dimensional three-layer resistivity model to accelerate the Bayesian inversion of the MT signal beneath each station. Then, inferred conductor boundary distributions are interpolated to construct pseudo-2D/3D models of the uncertain conductor geometry. We compared our approach against a deterministic MT inversion software on synthetic and field examples and showed good performance in estimating the depth to the bottom of the conductor, a valuable target in geothermal reservoir exploration.

Possibilistic response surfaces: incorporating fuzzy thresholds into bottom-up flood vulnerability analysis

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 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 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 hydro-climatic conditions. Incorporating fuzzy thresholds therefore requires articulating uncertainties that are different in nature: 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 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 theoretical development should link the decision-making under deep uncertainty framework with the existing experience of fuzzy set theory, notably for hydro-climatic vulnerability analysis.

NIEPEWNOŚĆ NAUKI A DZIAŁANIE, CZYLI – PROBLEMY Z EVIDENCE – BASED POLICY

The purpose of this article is primarily to introduce the topic of scientific uncertainty to the wider context of economics and management. Scientific uncertainty is one of the manifestations of irreducible uncertainty and reflection on it should enable better decision making. An entity that bases its operation on current scientific research, which depreciates over time and ultimately leads to erroneous decisions, is referred to as the “loser”. The text indicates estimation of potential scale of this problem supplemented by an outline of sociological difficulties identified in the analysis of the process of building scientific statements. The article ends with a sketch of the answer to the question “how to act in the context of scientific uncertainty?”.

Temperature variability implies greater economic damages from climate change

A number of influential assessments of the economic cost of climate change rely on just a small number of coupled climate–economy models. A central feature of these assessments is their accounting of the economic cost of epistemic uncertainty—that part of our uncertainty stemming from our inability to precisely estimate key model parameters, such as the Equilibrium Climate Sensitivity. However, these models fail to account for the cost of aleatory uncertainty—the irreducible uncertainty that remains even when the true parameter values are known. We show how to account for this second source of uncertainty in a physically well-founded and tractable way, and we demonstrate that even modest variability implies trillions of dollars of previously unaccounted for economic damages.