Mathematicians help California drought-weary berry growers address water issues


WASHINGTON, D.C. — It’s just not summer without a piece of strawberry shortcake.

Just as synonomous are those joys we associate with water: sparkling swimming pools, cooling mists of summer hoses and the scent of warm pavement suddenly accosted by raindrops.

As much as these two images fit snugly in sentimental minds, they do not coexist in California’s berry farmlands, which reportedly produce 80 percent of the nation’s strawberries. According to the U.S. Geological Survey, “In 119 years of recorded history, 2013 was the driest calendar year for the state of California.”

Serious concern

To be sure, California, and specifically coastal Central California, is never overflowing with water in any year, but recent, yearly water supply needs caused serious concern.

In January 2014, California’s snowpack, which normally provides about one-third of the water used by California’s cities and farms, was measured at 12 percent, the lowest for January in more than a half-century of record keeping.

Calif. Gov. Jerry Brown declared a drought emergency for the state, long before the “dry season,” which usually occurs during the summer months. Then, April 1, the California Department of Water Resources measured water content of statewide snowpack at 32 percent of normal for that time of year.

California’s water managers saw the result as truly foreboding, since April typically is considered the snowpack’s peak, when snow and ice begin to melt into streams and reservoirs, and conditions were only expected to worsen.

Taking action

Drought conditions like these, occurring annually, prompted policymakers, conservationists, geologists, hydrologists, farmers and business owners to creatively address the state’s water problems. And, in an interesting turn, mathematicians factored into this mix with one of the most unique perspectives of all.

John Eiskamp, owner and president of JE Farms, describes the Pajaro Valley in Central Coastal California as the “berry capital of the world.”

Strawberries reign supreme, followed by raspberries and then blackberries, but ultimately, it’s a berry world in his Santa Cruz County.

“This is an agricultural area,” he said. “It’s the driver of the economy. It provides the majority of the jobs. It provides the majority of the support industries that are here for agriculture — the companies that sell the product, the supplies, and the inputs that we growers use to produce the crops.”

Good stewards

So, water shortage issues — even for berries that aren’t the thirstiest crops by a long shot — still need water to produce saleable, harvestable fruit. According to Eiskamp, agriculture represents 85 percent of the valley’s water usage, but because of that the growers know they must be good stewards of the limited water supply.

Not surprisingly, they already have explored various crop rotation and water conservation strategies. However, this problem only worsens as each year passes.

So, in 2011, a National Science Foundation-funded math institute, the American Institute of Mathematics (AIM) in Palo Alto, Calif., got involved in what they describe as an “optimization problem.”

One of eight NSF-funded math institutes, AIM brings 800 mathematicians from around the world to Palo Alto each year to study a “whole variety of programs,” according to its deputy director, Estelle Basor.

Small research groups with “applied” objectives come for weeklong stints, modeling neural effects related to migraine headaches, more efficient medical imaging or, in this case, improved water use in drought-stricken areas.

Math research

Additionally, the institute spends even more time on its initial focus of “pure math” research.

““So many aspects to farming are difficult,” Basor said. “There are so many unknowns — weather, what other people are doing in other countries, pests, and supply and demand. I’m not sure that a lot of the public actually realize the risks involved.

“So, if we (mathematicians) can just help smooth out some of the decision-making process and help solve a few of the problems that growers might have, I think it’s a really good step forward.”

With that in mind, Basor talked to Driscoll Associates, familiar to many as purveyors of of Driscoll’s berries, and invited them to participate in an institute workshop that brought together 30 mathematicians from around the world to discuss sustainability problems.

Nine of the participants worked on the berry problem,along with three industry representatives. These collaborators then formed a smaller group to focus on the water supply’s confined aquifer and its chronic overdraft of water that had persisted over many years.

“We were given a list of possible changes that could happen in terms of crop rotation, fallowing land, looking at developing recharge areas to capture rainfall to reduce the amount of water that’s being taken out of the aquifer or the ground water region,” said Katie Fowler, an associate professor of mathematics at Clarkson University in Potsdam, N.Y., and member of this math team.

Getting technical

She explained how they could look at the problem simplistically by just considering crops’ water consumption and different planting strategies.

But, more sophisticated, elegant modeling included soil properties, precipitation data, topography and run-off measurements. With essentially two tiers of data, they could create a model that minimized aquifer impact and found ways to recharge it naturally.

“The approach is an example of ‘multi-objective optimization,’” she said. “We’ve developed three performance metrics. A person is going to want to try to make as much profit as possible using the least amount of water while meeting market demands. And those (goals) are naturally competing. So our most recent work has been toward offering a set of possible solutions with a clear description of those trade-offs.”

Another researcher, Lea Jenkins, an associate professor in mathematical sciences at Clemson University, describes the model as “stochastic,” which means values of variables are random, versus “deterministic,” when a problem has parameters with fixed values.

“This problem is about math,” said Dan Balbas, vice president of operations for Reiter Affiliated Companies, a grower for Driscoll’s, and who attended the 2011 workshop. “You’ve got a given resource, so how do you maximize it to maintain sustainability and do the right thing from an economic and environmental standpoint, marrying the two.”

Bringing in others

Interestingly enough, as the mathematicians talk about their process thus far, they admit that while they have collaborated with a variety of players in this issue, they still need to bring in sociologists and environmental economists to improve their model. A better future for berries

So, this team of mathematicians has now created models that help identify which crops to plant where and when.

With iPad in hand, growers like Eiskamp and Balbas can go to the fields connecting to wireless tensiometers in real time to essentially tell them when plants have been watered sufficiently, minimizing waste and ensuring fertilizers stay in the root zone where plants can most efficiently access them and keep from contaminating the water aquifer.

“The thing the math institute best did was shed light on per-unit of water—what is the best crop to grow?” Balbas said. “We found that raspberries — from a per-unit-of-water standpoint — were a better crop, so we’ve grown the raspberry program a little bit.”

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  1. Just on another blog I read these words from an agricultural scientist: “When you pray for rain, just make sure you can take care of what you get.” The main problem is that (in summer) about half the rain evaporates immediately and the rest often is lost because the soils have lost of their retention capabilities they used to have prior to intensive farming, tilling, ploughing and decimating microbial life by the billions (!) per cubic inch through herbicides and fertilizers etc. That being said though I am still amazed how little e.g. a method like “Design of Experiments” is being used in agriculture. A few years back I hinted at a young agronomist fresh from college that “Design of Experiments” might be a useful tool to which he dismissively quipped “Of course we design our experiments”. Well, that stands to reason in the agricultural community at large …


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