Timing Groundwater Protection: An Optimal Control Analysis of Annual Floors versus Terminal Targets for Irrigated Cotton in Lubbock County, Texas
This study employs a discrete-time optimal control model to demonstrate that while annual groundwater pumping floors in Lubbock County, Texas, successfully prevent stock depletion below a 90% target without altering cumulative pumping or mean acreage, they significantly reduce net present value by $1.0 to $13.5 million and are highly sensitive to yield multipliers and cotton prices rather than initial storage levels.
Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer
In the vast, flat expanse of the Texas High Plains, beneath the cotton fields of Lubbock County, lies a hidden reservoir of water that has sustained agriculture for generations. This underground lake, known as the Ogallala Aquifer, is not a lake in the traditional sense but a massive layer of porous rock and sand holding ancient water. For farmers, this water is the difference between a bountiful harvest and a dry field. However, the water is being pumped out much faster than nature can refill it. This creates a difficult economic puzzle: how can a community use a finite resource today without destroying the ability to use it tomorrow? The answer often depends on the specific rules written by regulators. Some rules set a final goal, requiring that a certain amount of water remains in the ground at the end of a long period, like a savings account that must have a specific balance when a child turns eighteen. Other rules are stricter, demanding that the balance never drop below a certain line at any point during those years. While both rules might allow the same total amount of water to be used over time, they force farmers to make very different choices about when to pump and when to conserve.
A recent study by Patrick Nyenkan at Texas Tech University explores exactly this dilemma, using a computer model to simulate twenty years of cotton farming in Lubbock County. The researcher built a detailed digital version of the local agricultural economy, incorporating real data on how much water cotton needs to grow, the costs of farming, and the actual hydrology of the aquifer. The model tested two different sets of rules against three different weather scenarios: a series of wet years, a series of dry years, and a mix of both. In one scenario, the model was told only to ensure that 90% of the initial water remained after twenty years, allowing the level to dip low in the middle of the period as long as it recovered by the end. In the other scenario, the model was forced to keep the water level above that 90% mark every single year, acting as a strict floor that could never be crossed.
The results reveal a subtle but significant trade-off between immediate income and long-term stability. When the model was allowed to dip the water levels in the middle of the twenty-year period, farmers could pump more water early on, generating higher profits in the short term. When the strict annual floor was applied, the total amount of water pumped over the full twenty years remained exactly the same, and the average amount of land planted with cotton did not change. However, the timing of that pumping shifted. Under the strict rule, farmers had to delay using the water, pumping less in the early years to ensure the level never dropped too low. This delay meant that the money earned from those early crops was pushed further into the future. Because money earned today is worth more than the same amount earned later, this shift reduced the total value of the farm's income over the twenty years. In the wettest scenarios, this cost was relatively small, amounting to a reduction of about 0.2% in total value. In the driest scenarios, the cost was higher, reaching up to 2.7%, which translated to a loss of between one and thirteen million dollars in present value terms.
The study also uncovered how much the value of water depends on the weather and the profitability of the crop. In the wettest simulated years, the water was so valuable that the rule limiting its use acted as a tight constraint, with the model valuing an extra acre-foot of water at nearly four hundred dollars. In the dry years, however, the water was not the limiting factor; the lack of rain made farming unprofitable regardless of how much water was available. In those dry conditions, the value of the water dropped to about thirty-seven dollars per acre-foot, and the strict rules had almost no effect on how much water was actually used because farmers simply chose not to irrigate. This suggests that the cost of protecting the aquifer is not a fixed number but changes depending on whether the weather is kind or harsh.
Perhaps the most striking finding concerns the data used to build the model. The researcher compared experimental results from small research plots, where scientists carefully control every variable, with actual yield data from the entire county. The county data showed that real-world farmers produce about two-thirds of the cotton per acre that the research plots predict. More importantly, the county data was too noisy to tell researchers exactly how much more cotton a farmer gets for every extra drop of water they apply. The numbers were so scattered that the model could not identify a clear relationship between water and yield using county records alone. When the researcher adjusted the model to reflect these lower, real-world yields, the results changed dramatically. In the dry weather scenarios, the model showed that it was no longer profitable to irrigate at all, regardless of the rules. The farmers in the simulation simply stopped pumping water and planted dryland cotton instead. This suggests that the high profits seen in the initial models were likely an overestimate, and that in reality, the decision to irrigate is often driven more by the price of cotton and the quality of the soil than by the strictness of the water rules.
The study concludes that while strict annual rules do protect the water level from dipping too low in the middle of a planning period, they come with a price tag in the form of reduced economic returns. The timing of protection matters just as much as the final goal. If the goal is simply to have water left at the end, farmers can use it freely in the beginning. If the goal is to keep the water level steady every year, farmers must save their water for later, which lowers the total value of their harvest. The research does not offer a single recommendation for what the rules should be, but it clarifies the cost of different approaches. It shows that the value of water is not constant; it rises and falls with the weather and the market. Ultimately, the study serves as a reminder that managing a shared resource requires understanding not just how much is left, but when it is used, and that the rules we choose today will shape the timing of our harvests for decades to come.
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