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A Role for Modeling, Simulation, and Optimization in an Agricultural Water Crisis

By Eleanor Jenkins and Kathleen Fowler

The authors have been working together since 2011 on a problem to do with agricultural sustainability. What brought them together was a workshop at the American Institute of Mathematics (AIM). For last summer’s SIAM Annual Meeting, they organized a minisymposium, The Mathematics of Sustainability, in which they and others discussed particular aspects of the problem. Here, on the invitation of SIAM News, they tell the story of their ongoing collaboration. 

Water crises in the western U.S. have been making headlines, with recent stories on California and Kansas appearing on PBS, NPR, CNBC, and CNN, as well as in The New York Times, USA Today, and nearly all of the major news outlets. Many of the stories have focused on the impact of the droughts on the local agricultural industry.

The problem is one that’s all too familiar to Estelle Basor. Having grown up in the Pajaro Valley region of California, she knows the strong connections between the region and farming. In “Raspberry Fields Forever,” her contribution to the 2013 Mathematics of Planet Earth blog, Basor gives a synopsis of her family’s farming history and her efforts to help ensure the long-term viability of the agricultural industry in the valley.

Basor also happens to be the current deputy director of AIM (one of the National Science Foundation-supported mathematics institutes). As an organizer of AIM’s 2011 Workshop on Sustainability Problems, she solicited a problem from Driscoll’s, a berry-farming cooperative in California; the problem was to assess the impact of several proposed changes in farming practices on the profitability of the berry farms and the use of groundwater resources.

Photo by M’Liss Hinshaw.
The Pajaro Valley region is responsible for nearly 60% of the strawberries produced in the United States in a given year, and Driscoll’s is one of the main farming cooperatives in the valley. Berries are water-intensive crops, and farmers in California rely heavily on groundwater resources to meet their irrigation needs––meaning that the health of the underlying aquifer is directly tied to their livelihood. Studies have shown that agriculture, along with urban water usage and climate change, has damaged the aquifer in recent decades, causing seawater intrusion along the coast and removing near-shore water supply wells from use. In turn, the cost of water has risen, putting further stress on farmers, who rely heavily on groundwater pumping for irrigation in the face of three consecutive years of below-average rainfall coupled with above-average temperatures.

The Pajaro Valley Water Management Agency, which monitors and regulates the water resources in the region, has worked tirelessly to preserve and manage the available water; part of the agency’s long-term management plan is a proposed irrigation limit for farmers. Operating under this limit will allow for recovery of the depleted aquifer, which currently has significant saltwater intrusion into near-coast drinking water supply wells. The irrigation limit, however, requires farmers to reassess their crop selections and irrigation strategies.

The farmers and Driscoll representatives came to the workshop with several ideas for coping with the reduced water limits, but they needed help in determining which idea, or combination of ideas, would provide the best results for their long-term profitability. With other applied mathematicians and engineers, we collaborated with the representatives to evaluate the possible effects of the proposed changes on water usage and the local farming economy.  Our team, consisting of researchers from academia and industry, brought a truly multidisciplinary approach to the problem.  

The practices suggested by the farmers included fallowing land, varying crop-rotation strategies, building aquifer recharge networks to capture rainfall for infiltration into the basin, and modifying irrigation techniques. In the course of the 2011 workshop, and over the ensuing months and years, we have used a multi-level modeling approach, combining simulation and optimization, to provide insights and offer strategies to farmers in the community. 

To better understand the trade-offs between the various stakeholders in the region, we began by developing a computational farming tool, combining it with optimization algorithms for selecting planting and harvesting strategies over a multiple-year window. We used data provided by the local farmers to formulate the problem, allowing for multiple crops and incorporating constraints to model the planting rules (e.g., the planting or harvesting of crops only in certain months). The objectives for the optimization were to maximize profitability while minimizing water usage, which, based on the crop specifications, can be in opposition. We recently coupled a large-scale, multi-physics farm and groundwater simulator to an optimization suite. This allows us to study more realistic scenarios and accurately model a fully integrated environment. We presented our results to several farmers in the region; they have used our analysis to adjust their crop selection, incorporating crops that are less water intensive, for the near future.

It is clear that mathematics plays a key role in an understanding of critical environmental issues, and in particular of sustainability problems. At the 2011 AIM workshop, the other problems focused on the modeling of systems that provide their own energy, the storage and deployment of energy produced from renewable sources, and the modeling of turbines capable of producing energy from waste heat. Our session at the 2014 SIAM Annual Meeting, the Mathematics of Sustainability, included talks on farming practices, on the design of aquifer recharge networks to replenish depleted water resources, on renewable energy, and on modeling efforts under way for water-quality assessments in the Saint Lawrence Seaway. A common theme is the critical need for interdisciplinary teams from science, engineering, and computational applied mathematics to address such problems, in partnerships with industry, policy-makers, and practitioners. 

Acknowledgments: We have been fortunate to work on a problem that has sustainability as its goal. We are grateful for support from AIM, and Estelle Basor in particular, for giving us the means to gather our team for our annual sessions in Palo Alto. We are also grateful to our main team members, Stacy Howington and Matthew Farthing from the U.S. Army Corps of Engineers, Engineering Research and Development Center, and John Chrispell, from Indiana University of Pennsylvania, for our progress thus far. Tsventanka Sendova of the Michigan State University Department of Mathematics and numerous students––Mark Minick, Matt Parno, Stephen Carter, and Corey Ostrove––have also contributed to this work. We hope to continue our work and apply this analysis to other regions facing similar stresses.  

Eleanor Jenkins is an associate professor in the Department of Mathematical Sciences at Clemson University. Kathleen Fowler is an associate professor of mathematics at Clarkson University.