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A new approach to quantifying and comparing vulnerability to drought

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Abstract

In this study we develop an “inference modeling” approach to compare and analyze how different disciplines (economics, political science, and behavioral science/environmental psychology) estimate vulnerability to drought. It is thought that a better understanding of these differences can lead to a synthesis of insights from the different disciplines and eventually to more comprehensive assessments of vulnerability. The new methodology consists of (1) developing inference models whose variables and assertions incorporate qualitative knowledge about vulnerability, (2) converting qualitative model variables into quantitative indicators by using fuzzy set theory, (3) collecting data on the values of the indicators from case study regions, (4) inputting the regional data to the models and computing quantitative values for susceptibility. The methodology was applied to three case study regions (in India, Portugal and Russia) having a range of socio-economic and water stress conditions. In some cases the estimates of susceptibility were surprisingly similar, in others not, depending on the factors included in the disciplinary models and their relative weights. A new approach was also taken to testing vulnerability parameters by comparing estimated water stress against a data set of drought occurrences based on media analysis. The new methodologies developed in this paper provide a consistent basis for comparing differences between disciplinary perspectives, and for identifying the importance of the differences.

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Notes

  1. Working definitions of susceptibility, water stress and drought-related crisis are adapted from Alcamo (2001). (1) Susceptibility: the capability of an individual, community, or state to resist and/or recover from crises brought about by environmental stress. (2) Water stress: the intensity of a change in water resources that (a) involves an undesirable departure from long-term, undisturbed conditions, (b) is of short duration, (c) is directly or indirectly influenced by society, and not only the result of natural geologic factors. (3) Drought-related crisis: an unstable or crucial time or state of affairs in which a decisive and undesirable change is impending or occurring, and which requires extraordinary emergency measures to counteract.

  2. Another case study of interest would have been an arid or semi-arid region in Africa where susceptibility is high because of low income and because of scarce water resources. Unfortunately, an African region was outside the scope of this study.

  3. For example, since much of the water in the Volgograd–Saratov region comes from outside with the large flow of the lower Volga, the indicator “withdrawals to availability ratio” will always indicate that the level of water stress is low (because the Volga always provides a source of water for those that live near it). This however underestimates the impact on drought on inhabitants that live too far from the Volga to exploit its waters during a drought. For these inhabitants, a better indicator of water stress would be, for example, the percentage of area in the region experiencing high water stress.

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Acknowledgments

This paper sums up key results of the project “Security diagrams: An innovative approach for estimating risk to extreme climate events”. This project was funded under the DEKLIM research programme of the German Ministry of Education and Research (BMBF). The Indian, Russian and Portuguese data analyzed in this paper have been collected by Kavi Kumar (Madras School of Economics, Chennai, India), Valentina Pavlova (Moscow State University, Russia), Eldar Kurbanov (Mari State Technical University, Russia), and Patrícia Nortista (Euronatura, Portugal), respectively, and have been kindly made available by the Potsdam Institute for Climate Impact Research, University of Kassel and Adelphi Research.

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Author notes

  1. Lilibeth Acosta-Michlik

    Present address: Université Catholique de Louvain, Louvain, Belgium

  2. Frank Eierdanz

    Present address: Faculty of Psychology, University of Kassel, Kassel, Germany

  3. Richard Klein

    Present address: Stockholm Environment Institute, Stockholm, Sweden

Authors and Affiliations

  1. Center for Environmental Systems Research, University of Kassel, Kassel, Germany

    Joseph Alcamo, Frank Eierdanz & Dörthe Krömker

  2. Potsdam Institute for Climate Impact Research, Potsdam, Germany

    Lilibeth Acosta-Michlik & Richard Klein

  3. Adelphi Research, Berlin, Germany

    Alexander Carius & Dennis Tänzler

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  1. Joseph Alcamo
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Correspondence to Joseph Alcamo.

Appendix: Using fuzzy set theory to quantify susceptibility to drought

Appendix: Using fuzzy set theory to quantify susceptibility to drought

It is difficult to specify a precise mathematical model of susceptibility for several reasons, e.g.:

  • Thresholds of susceptibility are poorly understood (e.g., At what annual income is susceptibility “low”?).

  • The relationship between susceptibility and its determinants is often non-linear. (e.g., As income increases, susceptibility tends to decrease. However, above a certain income, increasing income is unlikely to further decrease susceptibility.)

  • Different determinants of susceptibility interact in complex ways. (e.g., Health status and educational attainment both influence susceptibility. They are also related to each other in ways difficult to quantify.)

Hence in this paper we have proposed the alternative approach of developing linguistic models and using fuzzy set theory to translate inexact linguistic statements into quantitative estimates. Here we briefly explain how fuzzy sets are used for this translation, for example how they can be used to translate statements such as ‘high’ and ‘low’ into numerical values. For instance, consider an inference model containing the statement “if income is high, susceptibility is low”. Our first problem is to define “high” and other levels of income. Using typical binary logic, “high” and “low” incomes are by necessity defined with unrealistically sharp boundaries (left side of Fig. 9). In contrast, fuzzy logic permits us to specify a fuzzy boundary for these income levels (right side of Fig. 9). The Y axis of the fuzzy logic diagram runs from 0 to 1 and expresses the “degree of membership” or “degree of belief” in a particular value of a variable. Thus, an income of, say 5,000 US$ per year does not have to be defined as “high” or “low” but can be a “member” of both categories, having a certain degree of membership in each category.

Fig. 9
figure 9

Translation of linguistic statements into numerical data using binary and fuzzy logic

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In the inference models in this paper, several “fuzzy indicators” are combined together to make up a consistent set of rules. Consider the simplified example in which a model consists of two independent variables income and intensity of conflicts, each having two possible values, “low” and “high”, and one dependent variable susceptibility which can take the values “low”, “medium” or “high”. These can be combined into a model with four rules:

  • rule 1: If income is high and the intensity of conflicts is low then susceptibility is low

  • rule 2: If income is high and the intensity of conflicts is high then susceptibility is medium

  • rule 3: If income is low and the intensity of conflicts is high then susceptibility is high

  • rule 4: If income is low and the intensity of conflicts is low then susceptibility is medium

Each of the variables in this model would have membership functions of the type shown on the right side of Fig. 9 which define their meaning of “low”, “medium” and “high”, as appropriate.

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Alcamo, J., Acosta-Michlik, L., Carius, A. et al. A new approach to quantifying and comparing vulnerability to drought. Reg Environ Change 8, 137–149 (2008). https://doi.org/10.1007/s10113-008-0065-5

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