Aggregation in bottom-up vulnerability assessments and equity implications: The case of Jordanian households’ water supply

Highlights

• The method allows to handle equity among water users in response surface assessments.

• Aggregation choices are tested through percentile sampling and generalized means.

• A multi-agent model of Jordan tests supply enhancement and redistributive policies.

• Aggregation choices massively shape assessment results for Jordanian households.

• Aggregation intervals corresponding to specific policy preferences can be quantified.

Abstract

Bottom-up methods for water resources modeling rely on acceptability thresholds to find, through a response surface, which deeply uncertain futures lead to system failure. They commonly treat water users as aggregate actors, which may preclude analysis of the equity impacts of interventions. This paper explores how aggregation choices for large groups of water users lead to different policy recommendations in response surface assessments. Two aggregation methods with varying parameters are considered: percentile satisfaction targets and generalized mean. A 2-dimensional stress-test assessment across groundwater availability and population is applied to household water supply in Jordan. The study compares six different policies covering supply enhancement and rebalancing, using a country-wide multi-agent model that characterizes households across socioeconomic strata. For different aggregation levels, policies are ordered by their associated robustness index. Results show that aggregation choices strongly determine policy preference. A focus on the most vulnerable households favors the equalization of access to water, in terms of regional allocation and weekly supply durations, as it substantially reduces robustness disparity. Combined policies with additional resources allow to withstand higher levels of stress under most aggregation choices. Preferences defined by aggregation intervals provide a finer understanding of trade-offs among water users and may improve deliberation over equity under deep uncertainty.

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.