Aggregation in bottom-up vulnerability assessments and equity implications: The case of Jordanian households’ water supply
Introduction
Water resources modeling and management can be hampered by the difficulties to anticipate the future state of a given water system. The economic, demographic or geopolitical upheavals of human societies are drivers of water demand fraught with deep uncertainties (Maier et al., 2016), while climate change challenges the assumption of hydro-climatic stationarity under which water systems could be designed (Milly et al., 2008). At the same time, model-based planning under such uncertainties also needs to consider the fairness of any policy recommendation, based on distributional outcomes of uncertain futures (Hallegatte and Rozenberg, 2017, Jafino et al., 2021).
Complementary approaches exist to assess and plan water systems under uncertainty. The most common relies on building a discrete set of scenarios to explore internally coherent, representative sets of future trajectories for climate, economic growth, land use or demographics (Riahi et al., 2017). Such scenarios are built upon different categories of projections, often informed by models. Such approaches are often called “top-down” (Mastrandrea et al., 2010, Brown and Wilby, 2012), or forward-oriented (Maier et al., 2016).
Another group of approaches, often called “bottom-up”, flip the procedure instead focusing on the robustness of current decisions to deeply uncertain assumptions, reducing reliance on predictive approaches or probabilistic assumptions. Bottom-up approaches have been used across a diverse set of methodologies including inverse climate impact response functions (Füssel et al., 2003, Marcos-Garcia et al., 2020), robust decision making (Lempert et al., 2006, Lempert, 2019), info-gap (Ben-Haim, 2006), or decision-scaling (Brown and Wilby, 2012), often in combination with other methods. Instead of calculating the impacts of projected changes on different performance indicators, inverse approaches generally seek to identify the range of possible changes that can lead to adverse outcomes, and thus usually expand the range of uncertainty in comparison to classic scenarios (Maier et al., 2016). They do not seek to find the impacts of specific conditions, but the conditions that lead to specific impacts on a system’s performance. This range of conditions typically supports the construction of a response function or surface (Prudhomme et al., 2010): possible conditions are sampled through a few stressor variables, which define an exposure space. System performance is simulated over this exposure space with a computer-based model. An acceptability threshold then divides the domain of performance values into acceptable and unacceptable sub-sets. This allows one to draw acceptable and unacceptable sub-spaces of the exposure space, which are further used to compare the robustness of different policies and interventions, based on their respective areas.
Importantly, water systems are inherently complex and entail a number of actors with diverse objectives that are often conflicting (Loucks and van Beek, 2017). In particular, assessments using some form of robust or inverse approach have been considering increasingly large numbers of stakeholders or objectives, such as in Poff et al., 2016, Culley et al., 2016, Trindade et al., 2017, Kim et al., 2019 and Gold et al. (2019). But each considered objective aggregates the stakes of multiple water users belonging to the same category of water use; e.g. households supplied by the same utility, farmers from the same irrigation scheme. Whereas in reality, users can experience differential impacts based on physical, geographic, and socioeconomic characteristics. Thus response surfaces can be substantially different among water users of a same category. This was illustrated in Hadjimichael et al. (2020) with the disparities of vulnerability profiles among farmers in the Colorado River Basin, showing the need for case-by-case analysis. For systems with a large number of actors, model aggregation risks hiding potential inequalities and undermining the relevance of the vulnerability assessment and public support for selected policies.
Eventually though, if a group of water users is very large, case-by-case assessments become impractical, requiring some form of aggregation to evaluate system-wide performances. For example, intermittent water supply systems can involve large numbers of households with very unequal access to water. In such cases, aggregation remains necessary to quantify the unequal vulnerabilities of different segments of the population. A key issue at the heart of distributional assessments and fairness considerations is the adequacy of the aggregation method (Jafino et al., 2021).
Aggregation does not only shape the description of a problem, but also the preferred policies to solve it. Aggregation of potentially misaligned individual preferences is thus arguably central to political theory, and more explicitly at the heart of social choice theory (Arrow, 1951). A strictly egalitarian worldview such as J. Rawls’ maximin principle could consider a policy choice as fair if it maximizes the outcome for the worse-off individual among a group (Rawls, 1970). A more utilitarian worldview, as often found with average-based performance indicators, would seek to maximize the sum of individual outcomes, accepting that better and worse outcomes even each other out.
In the present paper, the question of aggregation specifically applies to robustness of water availability, understood as the acceptable share of the exposure space. Our goal is thus to explore how aggregation among the same type of water users affects response surfaces and policy recommendation in an inverse or bottom-up framework. We analyze a range of aggregation choices, translating different attitudes towards inequalities, and how it can affect response surfaces and the policy recommendation of a bottom-up assessment. Furthermore, in a similar manner to the inverse paradigm of the response function itself, we identify the aggregation ranges that lead to preferring one policy over another, to support equity and trade-off analysis under uncertainty within a group of similar water users.
In Section 2, the conceptual methodology of the paper presents how to parameterize the aggregation and to identify the aggregation ranges that lead to certain policy preferences. Section 3 presents the studied system – the Jordanian household water supply – using the Jordan Water Model (Yoon et al., 2021), and describes the experimental design to apply an inverse approach using the model. Results are detailed in Section 4, followed by a discussion regarding their potential implications and shortcomings.
Section snippets
Methodology
We explore multiple approaches to vary the aggregation level of a response function, in order to assess (i) the distribution of acceptable outcomes among a large group of water users and (ii) the effect of such aggregation choices on the policy recommendation. Just as the inverse approach looks for the conditions that lead to certain outcomes, here the question is what levels or types of aggregation lead to certain options being favored over others.
The proposed methodology relies on a simple
Case study: the Jordanian water system
As a prime example of a tense water situation and looming uncertainties, the country of Jordan (Fig. 4.a) faces a widening gap between dwindling freshwater resources and rapidly increasing demand, with difficult trade-offs among water uses (Whitman, 2019, Yoon et al., 2021). With an overall dry climate ranging from Mediterranean to arid, Jordan relies on limited natural freshwater resources (Gunkel and Lange, 2012). Its almost exclusive source of surface water, the Jordan River Basin, is shared
Results
Across the 72 simulations, sampling 9 levels of groundwater availability decline and 8 levels of population growth, average water use declines are as expected along with average water per capita (Fig. 5a). The average consumption only gets below the acceptability threshold of 40 L/cap/d in the most extreme combinations of groundwater reduction and population growth. To trace the frontier between acceptable and unacceptable subspaces, linear interpolation is performed for each of the 800
Significance
Even within the same category of water users, aggregation choices can lead to different preferences when comparing possible policies in a water system. This can be particularly relevant for bottom-up methods in water vulnerability assessments, as those commonly rely on limited numbers of acceptability thresholds in order to establish policy preferences under uncertainty.
This study shows how different aggregated response functions can be obtained using a multi-agent hydro-economic model for
CRediT authorship contribution statement
Thibaut Lachaut: Conceptualization, Methodology, Model development, Formal analysis, Writing. Jim Yoon: Model development, Writing. Christian Klassert: Model development, Writing. Amaury Tilmant: Conceptualization, Supervision, Writing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
We thank staff in the Jordanian Ministry of Water and Irrigation (MWI), Water Authority of Jordan (WAJ), Jordan Valley Authority, Ministry of Agriculture, and Department of Statistics for provision of data and reports for the analysis. We are particularly grateful for support provided by Dr. Hazim El-Naser, Ali Subah and Susan Kilani at MWI, and Refaat Bani Khalafat at WAJ. We also thank Steve Gorelick for bringing comments and advice to this paper; Samer Talozi, Yazzan Haddad, Marwan Shamekh
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