Mathematics of Planet Earth

Today is my father’s birthday. If he were alive he would be 110 years old! My father, Steve Basor, was born to immigrant parents in Lead, South Dakota, in 1903 but left there when he was very small with his parents who returned to live in the tiny village of Dunave, Croatia (then part of the Austrian empire). He went to the local village school, helped with the family farm, and then after living in Argentina for five years, returned to the United States in 1931. He settled in Watsonville, California, and farmed in the Pajaro Valley, close to the Monterey Bay. Watsonville had a large population of Croatians, most from the Konavle Valley, and almost all were involved in farming. My father was an apple grower, as were many of his friends and relatives. It was from him that I got my love of farming and also my love of mathematics. He knew many math facts, games, and puzzles that he taught to me when I was young. The following tells how the two interests combined.

The Pajaro Valley is ideally suited for agriculture. When my father farmed one could see acres and acres of fruit trees, but these were slowly replaced by crops of vegetables, berries, and flowers. In fact, the Pajaro Valley and the nearby Salinas Valley produce nearly half of the 2 billion pounds of strawberries grown in the United States annually. The water source for the valley is a confined underground aquifer, which is slowly being depleted. Estimates for the overdraft vary, but the amount of water being used each year is between 125% and 150% of the sustainable yield. The overdraft creates a problem of salt water intrusion along the coast, making many coastal wells unusable, and lowers the water table over the entire valley.

In January of 2011, AIM held a Sustainability Problems workshop, with the goal of bringing together mathematicians and industry representatives to work on a variety of sustainability problems, including renewable energy, air quality, water management, and other environmental issues. It seemed to me that it might be possible to get berry growers to team with the mathematicians to help with the overdraft problem. I still have farming ties in the valley and asked Driscoll’s, whose associated growers are the largest supplier of fresh berries in North America, whether they were interested. To my delight, the Driscoll’s representatives agreed to come to the workshop.

So three Driscoll’s employees teamed up with nine applied mathematicians to evaluate how various water and land management techniques could be utilized by landowners and growers to work towards balancing aquifer levels. During the week of the workshop and with followup activity in an AIM SQuaRE program, the team has made significant progress in the creation of a virtual farm model to study alternative crop management strategies and their effect on water usage and profit. The model uses an optimization framework (with over 200 constraints) to maximize profit while meeting a water budget constraint. According to Dan Balbas, Vice President for Operations for Reiter Affliated Companies, (a Driscoll’s associated grower), “the results of the optimization program validated much of what the growers thought before and gave validation and new information to our crop growing strategies.” The team also investigated a surface water analysis to understand feasible ways to capture rainfall for reinfiltration (or recharging) into the aquifer.

Driscoll’s has also spearheaded a community effort to help solve the overdraft problem. Pajaro Valley community members are working in smaller groups on a number of additional strategies, including the determination and promotion of best practices for irrigation and the identification of the most promising areas in the valley for aquifer recharge projects (a fluid flow problem!). The community effort to solve the water problem is a remarkable model for bringing together groups with very different goals and experiences and finding common ground.

I am pleased to report that the SQuaRE group is back at AIM this week and should have a future report very soon about progress, including the recharge efforts.

Estelle Basor
AIM