Spatial optimization nodels for water supply allocation

Authors: Alan T. Murray (1), Patricia Gober (2, 3), Luc Anselin (1), Sergio J. Rey (1), David Sampson (3), Paul D. Padegimas (1), Yin Liu (1)
in Water Resource Management, DOI 10.1007/s11269-012-0013-5


Fig. 1 Water sources by large providers in metropolitan Phoenix

Climate change is likely to result in increased aridity, lower runoff, and declining water supplies for the cities of the Southwestern United States, including Phoenix. The situation in Phoenix is particularly complicated by the large number of water providers, each with its own supply portfolio, demand conditions, and conservation strategies. This paper details spatial optimization models to support water supply allocation between service provider districts, where some districts experience deficits and others experience surpluses in certain years. The approach seeks to reconcile and integrate projections derived from a complex simulation model taking into account current and future climate conditions. The formulated and applied models are designed to help better understand the expected increasingly complex interactions of providers under conditions of climate change. Preliminary results show cooperative agreements would reduce spot shortages that would occur even without climate change. In addition, they would substantially reduce deficits if climate change were to moderately reduce river flows in Phoenix’s major source regions, but have little effect under the most pessimistic scenarios because there are few surpluses available for re-allocation.


The results obtained from the developed spatial optimization model reflecting regional cooperation in water supply management across the Phoenix metropolitan area demonstrate the insights possible from a modeling based analysis approach. It is foreseeable that the introduction of demand management strategies will be necessary in the face of future climate change, but also it is possible to significantly reduce deficits in some cases. By taking full advantage of all the water that is available as well as establishing cooperation between water districts, as opposed to the practice of conserving surpluses for future use but not distributing extra water when available to those districts in need, it is possible to stretch the available supply of water to ensure that the impacts of water shortages are minimized.

In every scenario, the results pointed to clear benefits of regional cooperation, whether it is the complete avoidance of deficits over a period of time (Scenarios 1 and 2), to a reduction of total deficits across the region (Scenarios 3 and 4). Effective policy implementation could lead to the employment of a trading strategy that embodies the benefits demonstrated in this paper. It is clear in each scenario presented in this paper that Phoenix and its ability to transfer water either in from or out to other districts appears inevitable. As the largest city in the region by almost four times, it will clearly be an important factor in water resource management. While it is assumed in this paper that water transfers are possible by simply recharging subsurface aquifers by one district and pumping out water by another, there may be a need for conveyance infrastructure to successfully implement an effective water sharing strategy in the region. Whether it be by manmade infrastructure or natural aquifers, in the case of the Phoenix metropolitan region, it is obvious that the city of Phoenix must be completely intertwined with the water network of the region.

The linear program presented in this paper is a foundation for effective water management and is, in the form presented, adaptable to accommodate different weighting schemes. While it may be possible to re-allocate water across the region in a more equitable manner than weighting by population of each provider district, it is evident that as it stands, this model is effective for demonstrating the potential gains of any region with multiple, independent water providers, through optimal water re-allocation. The potential to change the weighting mechanism will be important for future work, which may include a cost structure for transfer transactions, measures of social benefit achieved by water re-allocation, or economic gains related to water availability. Decision rules about who does and does not share access to relevant conveyance infrastructure may also be included in future applications. While different potential decision rules and weighting mechanisms will likely vary by application, the foundation for multi-district water re-allocation modeling presented here clearly demonstrates the potential benefits of such a system.


This article is based on work supported by the National Science Foundation under Grant No. SES-0345945, Decision Center for a Desert City. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

(1) GeoDa Center for Geospatial Analysis and Computation, School of Geographical Sciences and Urban Planning, Arizona State University

(2) School of Geographical Sciences and Urban Planning, Arizona State University

(3) Decision Center for a Desert City, Arizona State University