An international team of more than 2 dozen researchers has found a novel approach to modeling groundwater levels and crop production to forecast future resource availability and yields. The model the researchers developed was inspired by ecology’s Lotka-Volterra equations, a mathematical explanation for the cyclical population dynamics of predator and prey species.
Previous models for forecasting groundwater levels have relied on Hubbert’s curve, an equation with its basis in production rates and demand for a given resource. (The model is named after M. King Hubbert, the geologist who famously predicted in 1956 that crude oil production would reach a peak in the 1970s.) However, the research team behind the new model wanted to develop a method that would couple the dynamics of groundwater withdrawals and crop production. As Assaad Mrad, the lead author on the study and a Ph.D. candidate at Duke University, explained, “we looked at crop production as the predator and groundwater resources as the prey, and we found that [this model] describes the trends in groundwater extraction and crop production rates very accurately. These were the seeds of the project that stemmed from the goal of introducing more rigorous mathematical techniques to [the science of] sustainability.”
“That kind of modeling approach that is drawn from ecology had not really been applied to this kind of physical system before,” said Erin Haacker, an assistant professor of hydrogeology at the University of Nebraska–Lincoln who was not part of the new study. Haacker noted that compared with other hydrologic modeling, which tends to use “a much more physical-based approach” that sets expectations based on physics and checks to see whether they match the data, the model developed by Mrad and his colleagues “uses a really empirical statistical approach” that “fit the [model’s] parameters based on what the observation data told them.”
The paper detailing the innovative methodology was published in the Proceedings of the National Academy of Sciences of the United States of America in October.
Putting Their Ideas to the Test
To test their ideas, Mrad and the other researchers gathered irrigation and crop yield data for Nebraska, Kansas, and Texas. Portions of all three states depend on the Ogallala Aquifer, a vast underground reservoir whose declining stores have been causing concern for years. This massive aquifer underlies parts of eight states in the U.S. High Plains, a region often referred to as America’s breadbasket because of the enormous amounts of grain grown there.
Also called the High Plains Aquifer, the Ogallala supplies water for almost 30% of irrigated crops and livestock in the entire country. The aquifer’s north–south orientation extends through different climates, ranging from hot and dry in the Texas Panhandle to comparatively wet and cool in Nebraska. The crosscutting aquifer allowed researchers to “disentangle the effect of climate on groundwater recharge, crop production, and groundwater extraction,” Mrad said.
The model found that in Texas, crop production initially peaked 9 years after a peak in groundwater withdrawal. After the state began using more efficient irrigation technology, the state’s groundwater extraction and crop production both reached a second peak with an increased lag of 15 years between them. In Nebraska, where higher precipitation replenishes the aquifer at a higher rate, the researchers’ model forecasts that crop production may continue to increase beyond the year 2050. In Kansas, the model projected that the state’s crop production would peak 24 years after its groundwater withdrawals peaked.
“What we found is that [a method based on Hubbert’s curve] is applicable only for cases such as Texas,” Mrad said, “where your groundwater use is very nonrenewable” because of a substantially lower recharge rate. For regions with a higher recharge rate, like Nebraska, Mrad said, “Our studies showed that if you use these methods [based on Hubbert’s curve], you will not get the correct results.”
New Data: Agricultural Technology
Mrad’s model is sensitive to historical improvements in irrigation technology, but he acknowledged that “our projections assume no disruptive technological improvements in the next 30–40 years.”
If such improvements are developed, it may not take long for farmers to start using them. Dana Porter, an agricultural engineer and irrigation specialist with Texas A&M University and Texas Extension, explained that farmers in the Texas Panhandle, where agriculture is a large part of the local economy, have many incentives to adopt better irrigation technologies when they become available. “We’re a semiarid region, so our crop production in this area is water limited,” she said. “There’s an economic advantage to adopting the technology. The aquifer is deep, so it costs a lot to pump it up there, and we want to be as efficient as possible with the water, because a little bit of increase in efficiency can result in a noticeable improvement in yield, especially in a drought year.” Porter was not involved with the new study.
The idea for the new paper originated in discussions at the Ettersburg Ecohydrology Workshop in Germany, a 2018 gathering of 29 experts and graduate students from 11 countries. Mrad was not part of this workshop, but Gabriel Katul, Mrad’s adviser and the second author on the new paper, was one of the experts in attendance.
—Jady Carmichael (@jadycarmichael), Science Writer