A Mathematical Approach to California’s Water Woes
Severe drought and climate change have adversely affected groundwater aquifers globally, and an Illinois Institute of Technology researcher is working to help the California’s agriculture industry redistribute the dwindling natural resource.
Igor Cialenco, professor of applied mathematics, has earned a along with Mike Ludkovski, professor of statistics and applied probability at University of California, Santa Barbara, to develop a mathematical solution to groundwater distribution.
“There is a real risk of exhausting groundwater supplies in parts of the world unless an equitable and adaptive water allocation mechanism is implemented—one that balances multiple objectives while preserving economic viability,” Cialenco says. “Until now, groundwater management has been extensively studied by resource economists, hydrologists, and environmental scientists, but there is no underpinning mathematical theory to describe desirable water allocations.”
California is among the first states to shift toward regional groundwater planning and is anchored by the California Sustainable Groundwater Management Act (SGMA) of 2014, which mandated the creation of Groundwater Sustainability Agencies to oversee yearly water budgets. The related Groundwater Sustainability Plans have forced stakeholders to consider aquifer replenishment, consumption, and conservation, but also trading water rights among themselves. At the same time, environmental demands of preserving and protecting ecosystems heightened the importance of multi-year planning.
SGMA provides a multi-decade contour of how much water is available to consume and the majority of the new groundwater management agencies provide rule-based individual pumping limits and allow the trading of allocations through bilateral transactions in groundwater permits.
Cialenco says this challenging, multidisciplinary problem requires accounting for the inherent volatility of future precipitation and basin supplies, the conflicting objectives of different stakeholders, and extensive policymaking. The modeling framework must be stochastic, dynamic, and optimal. He says that the aim of the framework is to develop the fundamentals of these new water markets, leveraging methods from stochastic games, financial engineering, and stochastic control.
“To be clear, our goal is not to ‘gamify' water allocation or to support financial trading of water,” he says. “Rather, we set out to develop a mathematically rigorous analysis of water allocation and price formation.”
Cialenco says the biggest challenge is to develop models that are relevant to policymakers and stakeholders, based on existing data, yet are tractable and mathematically rigorous.
“We are thrilled to be at the forefront, pioneering this area of research and laying the foundation for future studies,” he says. “A diverse group of graduate and undergraduate students will be involved in all aspects of the project, from calibrating models using real data, developing a computationally feasible algorithm to solve complex control problems, and studying what is the impact of cooperative/non-cooperative between stakeholders in achieving more sustainable management practices. Initially, we will focus on California groundwater management, thanks to the availability of rich datasets. However, the developed method can also be applied to other affected aquifers, as groundwater depletion is a universal problem that we aim to address through scalable and adaptable solutions.”
Disclaimer: Research reported in this publication is supported by the National Science Foundation under Award Number DMS-2407549. This content is solely the responsibility of the authors and does not necessarily represent the official views of the National Science Foundation.
