Changes in groundwater irrigation withdrawals due to climate change in Kansas

Warming temperatures increase the evapotranspiration demand of crops, leading to an increase in irrigation and exacerbating water scarcity. Previous research relies on models of irrigation water requirements to understand the potential impacts of climate change, but these models have significant uncertainty and ignore the risk-averse behavior of irrigators. Here we develop regression models to estimate how changes in vapor pressure deficit and precipitation affect groundwater withdrawals for corn, soybeans, and wheat using well-level data from the Kansas portion of the High Plains Aquifer. Withdrawals are expected to increase for all three crops, with the largest increase for soybeans. Even after accounting for the CO 2 improvements in transpiration efficiency, we find that total withdrawals are expected to increase by 5.9% (7.6%) by mid-century under RCP 4.5 (8.5). The increase in withdrawals is expected to accelerate the decline in aquifer water levels and is therefore important to consider when projecting


Introduction
Climate change is expected to create major disruptions to the global food system. Extreme heat is likely to cause significant decreases in agricultural yields (Schlenker and Roberts 2009, Asseng et al 2015, Tack et al 2015 and productivity (Liang et al 2017, Ortiz-Bobea et al 2021. Another concern facing the global food system is the depletion of aquifers. More than 40% of global crop production is supported by irrigation and groundwater accounts for 43% of irrigation consumptive use globally (Siebert et al 2010). Consumption of groundwater exceeds recharge in many areas of the world, leading to persistent depletion of aquifers, especially in agriculturally important areas (Gleeson et al 2012, Famiglietti 2014, Jasechko and Perrone 2021.
Climate change, aquifers, and food are inextricably linked. Irrigation represents a potential adaptation to reduce crop losses from greater extreme heat (Tack et al 2017, Zaveri andLobell 2019). However, the prospects of expansions in irrigated area vary across regions (Elliott et al 2014, Rosa et al 2020, Wang et al 2021. Climate change is also expected to intensify the hydrologic cycle (Huntington 2006, Wild et al 2008, which could cause an increase in water supply available for irrigation in some regions and a decrease in others (Vorosmarty et al 2000, Arnell 2004, Schewe et al 2014, Cuthbert et al 2019. Irrigation water demand will also be affected by climate change through changes in atmospheric water demand, precipitation, and crop water use efficiency due to higher CO 2 concentrations.
There is a large literature that explores different aspects of how climate change is expected to affect groundwater (Taylor et al 2013). Some studies model the impacts of climate change on groundwater levels directly (Loáiciga 2009, Chakraborty et al 2021a.
Previous studies also evaluate changes in evapotranspiration, but are not crop-specific (Sheffield et al 2012, Miralles et al 2014, Trenberth et al 2014. Other studies estimate changes in crop water demand (Urban et al 2017) or irrigation water requirements (Döll 2002, Izaurralde et al 2003, Fischer et al 2007, Pfister et al 2011, Wada et al 2013. Several studies use large-scale integrated assessment models that model projected changes in both water supply and demand, where demand is based on irrigation water requirements (Rosenzweig et al 2004, Blanc et al 2014, Elliott et al 2014, Haddeland et al 2014, Wada and Bierkens 2014. However, different methods of calculating evapotranspiration and uncertainty about crop coefficients can lead to large uncertainty in estimates of irrigation water requirements (Fisher et al 2011, Puy et al 2022. Furthermore, changes in irrigation water requirements may not correspond directly to changes in irrigation withdrawals because the latter depends on producer behavior. Risk averse producers that face a constraint on the rate at which water can be extracted (i.e. the well capacity) may not adjust water withdrawals 1:1 with a change in annual irrigation water requirements.
Our work is different from previous literature in that we study how climate change affects irrigation withdrawals while implicitly accounting for producer behavior. Our study combines location-specific data on irrigated water withdrawals for corn, soybeans, and wheat with fine-gridded (4 km) weather data in the Kansas portion of the High Plains Aquifer. Kansas provides an ideal application for the model because of the available records on water withdrawals over a long period that is not common in other areas (Foster et al 2020). We utilize these unique data to estimate how withdrawals are affected by weather shocks and then project the impacts of climate change by mid-century while accounting for the effect of higher CO 2 concentrations on improved transpiration efficiency (TE). Several studies project future groundwater levels and production in the High Plains Aquifer, but none of these projections incorporate the impacts of climate change (Steward et al 2013, Haacker et al 2015, Steward and Allen 2016, Mrad et al 2020. Our results illustrate the importance of incorporating climate change into these projections of future resource conditions.

Data
Well-level data on the depth of water applied and crop grown is obtained from the Water Information Management and Analysis System of the Kansas Department of Agriculture from 1991 to 2014. These three crops represented approximately 88.30% of the total irrigated area in Kansas in 2017 according to the Census of Agriculture. To avoid the influence of outliers, wells are excluded that reported irrigation on less than 40 acres or greater than 500 acres or that reported a depth applied outside the 1st and 99th percentiles.
Daily weather data are from the Parameterelevation Regressions on Independent Slopes Model. We calculate cumulative precipitation and the average vapor pressure deficit (VPD) separately for the pre-season and irrigation season. For corn, soybeans, and wheat, the pre-seasons are February-May, March-June, and September-February and the irrigation seasons are June-August, July-September, and March-May, respectively. VPD is the difference between saturation and actual vapor pressure, where the minimum temperature is used to approximate the dew point. Daily climate projections for 18 climate models are from the downscaled Coupled Model Intercomparison Project obtained from the US Geological Survey Geo Data Portal. We bias-correct the model projections to match our historical data (Hawkins et al 2013). Further details on the data are provided in section A1 of the SI appendix.

Regression model and projections
Regression models are frequently used by recent literature to quantify the impact of climate change on agricultural outcomes (Ortiz-Bobea and Tack 2018, Perry et al 2020, Diffenbaugh et al 2021, Ortiz-Bobea et al 2021. Using a regression model with data on actual irrigation water applied implicitly accounts for producer behavior because the coefficients reflect how producers adjust irrigation in response to changes in weather and not just how crop water requirements change. Our regression model to explain irrigation water applied W itj from well i in year t for crop j is specified as where VPD s itj is the average VPD in either the preseason (pre) or the irrigation season (irr), PPT s itj is the cumulative precipitation, α ij are well-level fixed effects used to control for time-invariant heterogeneity like soil quality, t is a linear time trend, and ε itj is the error term. Regression models are estimated separately for each crop as denoted by the j subscript for each parameter. We cluster the standard errors by year to account for heterogeneous variances and spatial correlation in the error.
Projections of water use by mid-century incorporate a CO 2 adjustment to account for the increase in TE in all crops and an increase in radiation use efficiency (RUE) in the C3 crops (soybeans and wheat). We follow the method used in previous literature that makes an adjustment to future VPD values based on the model of crop water demand in the agricultural production systems simulator (Urban et al 2017). The projected future irrigation water use is a weighted average of the water use with the CO 2 adjustment and water use without the adjustment to account for the fact that only transpiration will be affected by higher CO 2 concentrations and not evaporation (Wei et al 2017) (see SI appendix, section A2 for further details).
To estimate the percent change in projected depth applied, we predict the depth applied with the regression model using average historical weather and compare it to the prediction using average projected climate data. The trend is held constant at 2006 to isolate the effect of climate change on depth applied. We decompose the total change in depth applied by three potential drivers: (i) precipitation, (ii) temperature, and (iii) CO 2 . To isolate the contribution of changes in precipitation, we simulate the percent change in irrigation water by using projected precipitation and historical temperature (i.e. VPD) and CO 2 concentration. The temperature effect uses projected temperature to calculate VPD in the future, but holds constant precipitation and CO 2 concentration at historical levels. The CO 2 effect applies the CO 2 adjustment to VPD with future CO 2 concentrations, but uses historical (1991-2014) VPD and precipitation. To aggregate across crops, we calculate the weighted average irrigation water applied using the share of acres irrigated for each crop from the county-level 2017 Census of Agriculture.
To quantify the uncertainty in our projections, we estimate 1000 bootstrap replications of the projections from each of the 18 climate models-giving a total of 18 000 replications for each RCP scenario. The total uncertainty reflects the uncertainty across all 18 000 replications. The regression uncertainty represents the uncertainty across 1000 replications that are first averaged across climate models. The climate uncertainty represents the uncertainty across the 18 different climate models after averaging across the 1000 replications for each climate model. We use a wild bootstrap technique that is clustered by year.
Water balance equations are used to estimate the change in water level. Butler et al (2016) developed a methodology to estimate the parameters of the water balance equation using observed data on water levels and aggregate pumping. Butler et al (2020) discuss the implications of this approach for improving our understanding of the specific yield of aquifers. The water balance equation is written as where ∆WLg is the average change in water level in Groundwater Management District (GMD) g in scenario r, Q r g is the total quantity of groundwater pumped, and λg and ρg are parameters estimated by Butler et al (2018) for each GMD using historical data on pumping and changes in water levels. We estimate the average historical change in water level by using the average quantity of water pumped centered on 2006 (1996-2016) (2018). To project the future change in water level, we scale Q H g by the average percent change in water applied for the respective district under the RCP scenarios and plug this into equation (2).

Regression results
Water withdrawals-measured in depth of water applied-are observed for 25 127 different wells between 1991 and 2014 (SI appendix, figure A1), giving 119 181 observations for corn, 15 226 for soybeans, and 12 822 for wheat (see SI appendix, figures A2-A4 for summary statistics). Coefficients from the regression generally have the expected signs and the models explain 56%-70% of the variation in depth applied (table 1). An increase in average VPD by 0.1 kPa during the irrigation season, increases the depth applied by 10.7 mm for corn, 17.8 mm for soybeans, and 10.9 mm for wheat. Pre-season VPD has smaller effects and is only statistically significant for corn. An additional 1 mm of precipitation during the irrigation season decreases irrigation depth applied by 0.32 mm for corn, 0.32 mm for soybeans, and 0.15 mm for wheat. Pre-season precipitation has about half the effect on depth applied as irrigation season precipitation for corn and soybeans. For wheat, the effect of pre-season precipitation is slightly larger than the effect in the irrigation season because the pre-season includes irrigation requirements in the fall. The depth applied for all crops has decreased over time-holding weather constant-but none of the trends are statistically significant.

Effects of climate change on depth applied for each crop
The depth applied is projected to increase by 3.1% (4.1%) for corn, 18.8% (23.7%) for soybeans, and 3.0% (4.1%) for wheat under RCP 4.5 (8.5) (panel A of figure 1). The depth applied increases the most for soybeans because it is the most sensitive to changes in VPD during the irrigation season and the CO 2 effect is positive for soybeans. Most of the uncertainty is due to differences in projections across climate models. Accounting only for the uncertainty of the regression model, the 95% confidence interval does not include zero for corn and soybeans (panel A figure 1). The variation across climate models is much Note: The dependent variable is the depth of water applied (mm). Standard errors clustered by year are in parenthesis. * , * * and * * * indicate significance at 10, 5, and 1 percent levels. larger-ranging between −6.6% and 15.2% for corn (SI appendix, figure A5). We decompose the total change in depth applied for each crop into (i) precipitation, (ii) temperature, and (iii) CO 2 effects (panel B of figure 1). We find that an increase in temperature is the main driver of the future increase in water withdrawals, while precipitation has a small impact. Increases in temperature that increase VPD are projected to increase depth applied by 7.6% (10.4%) for corn, 15.1% (19.1%) for soybeans, and 5.6% (7.6%) for wheat under RCP 4.5 (8.5). Changes in precipitation are projected to decrease the depth applied for corn and wheat because pre-season precipitation is projected to increase. The depth applied for soybeans is expected to increase because precipitation during the irrigation season for soybeans is projected to decrease more than the increase in pre-season (SI appendix, figure A7).
Ignoring the effect of CO 2 overstates the increase in withdrawals for corn and wheat. An increase in the concentration of CO 2 increases TE of all crops and increases RUE in the C3 crops, soybeans and wheat (SI appendix, section A1). For corn, the increase in CO 2 concentration alone leads to a decrease in depth applied of 3.7% in RCP 4.5. This causes the increase in depth applied to be overstated by 3.8 percentage points if the CO 2 effect is ignored for corn (SI appendix, figure A9). The higher CO 2 concentration leads to an increase in depth applied by 4.1% in RCP 4.5 for soybeans and a small decrease for wheat. The difference in results between soybeans and wheat occurs because soybeans have a smaller improvement in TE than wheat.

Effect of climate change on total water withdrawals and aquifer depletion
Aggregating withdrawals across crops (figure 2) indicates that total withdrawals are projected to increase by 5.9% (7.6%) under RCPs 4.5 (8.5). The change in water withdrawals under RCP 4.5 has a 95% confidence interval of 4.8%-7.1% when accounting for uncertainty from the regression model and averaging across climate projections. Variation across climate models gives a larger band of uncertainty, between -3.9% and 18.4%. Corn represents the dominant share of the area (64%) with the remaining fairly evenly split between soybeans (19%) and wheat (17%), so the overall change in water withdrawals mostly reflects the change in withdrawals for corn.
The change in withdrawals varies between less than 2% in some counties in WC and greater than 10% in some counties in SC under RCP 4.5 (panel (A) of figure 3). The regional variation is driven by differences in climate projections and differences in cropping patterns. Precipitation is expected to increase the most in the SW district (SI appendix, figures A6-A8). Precipitation in the summer months is projected to decrease in the SC district and parts of other districts. VPD is also projected to increase the most in the SC and NW districts and soybeans are a larger share of crops in the SC district. Total water withdrawals are expected to increase by 2.2% (3.4%) in WC and 10.1% (12.5%) in SC under RCP 4.5 (8.5) and the increase in withdrawals are significant at the 5% level for all districts.
The increase in water withdrawals accelerates the decline in groundwater levels. Historically, the annual rate of aquifer decline has been the largest in the SW district (0.68 m) and the rate of decline is projected to increase due to climate change to 0.75 m (0.78 m) under RCP 4.5 (8.5) (panel (C) of figure 3). The rate of decline is also projected to increase in NW and WC districts, but not as large of a change as in the SW district. The largest change in water level is projected to occur in the SC district that has historically been the closest to aquifer sustainability. Water levels have historically decreased annually by 0.06 m in SC, but are projected to decrease by 0.26 m (0.31 m) under RCP 4.5 (8.5).

Robustness of climate change impacts
We model depth applied as a linear function of VPD and precipitation because the irrigation requirement is evapotranspiration demand minus effective precipitation. To assess the robustness of our results, we show results if we allow a nonlinear relationship between depth applied and the weather variables using natural cubic splines with three knots or if we replace VPD with reference ET calculated using the reduced-set Penman-Monteith method (SI appendix, Figure 3. The spatial impact on water withdrawals and changes in aquifer water levels. Panel A shows the projected change in water withdrawals by county under RCP 4.5 and RCP 8.5, respectively. Panel B shows the projected change in water withdrawals aggregated for each Groundwater Management District. Panel C shows the annual changes in water level for each Groundwater Management District historically (red) and by mid-century under RCP 4.5 (green) and 8.5 (blue). Dots indicate the mean effect and whiskers show the 95% confidence interval due to regression uncertainty. figure A10). The results in figure A10 do not include a CO 2 correction so that they are comparable across all specifications since our CO 2 correction is not readily applied to the Penman-Monteith calculation.
Results allowing nonlinearity indicate larger increases in depth applied, but the 95% confidence intervals of the nonlinear estimates include the point estimates of the linear model. The results are similar using either VPD or Penman-Monteith ET, which highlights an advantage of our regression approach to modeling changes in water withdrawals-our results are not sensitive to different formulas to represent ET. Changes in VPD are highly correlated with different calculations of ET and the regression coefficient represents a data-driven translation between VPD and water withdrawals.
Results are also robust to using only later years in the regression analysis. In the early 1990s, water withdrawals were reported primarily using estimates of withdrawals based on the number of days pumping and the pumping rate. Water meters were adopted throughout the 1990s, typically as a requirement from GMDs. Most of the adoption of water meters had occurred by 2000 and producers had some experience properly using a meter. Therefore, the accuracy of the withdrawal data improved after 2000. Table  A2 in the SI appendix shows regression coefficients if we use the period 2000-2014 to estimate the models instead. Coefficients are similar to the results from the full sample in table 1. Using these coefficients to calculate the projected change in total water withdrawals (SI appendix, figure A11) gives similar results to using the full sample, but slightly larger increases in projected withdrawals.

Discussion
This study combines water withdrawal records from 25 127 wells between 1991 and 2014 and gridded weather data to estimate how plausibly random weather shocks affect irrigation water withdrawals. Producers change their water use due to weather shocks in ways that may not correspond with irrigation water requirements. For example, we find that an additional 1 mm of precipitation during the irrigation season decreases the depth applied by about 0.3 mm. While a mechanistic crop model might not predict a 1:1 relationship between precipitation and depth applied due to runoff, a mechanistic model would likely indicate a larger relationship between precipitation and crop water requirements than our regression results. One reason that producer withdrawals do not exactly correspond to irrigation water requirements is that irrigation is a form of risk management. Producers do not know the entire irrigation season's weather when making irrigation decisions, so applying more water than the irrigation requirement reduces the risk of large yield penalties from applying too little water. The incentive to apply additional water to reduce risk is stronger when producers are constrained in the instantaneous rate that they can extract water (i.e. the well capacity). Our results emphasize the importance of accounting for producer behavior when modeling the impact of climate change on water withdrawals rather than relying on estimates of irrigation water requirements.
We then apply the model of water withdrawals to climate change projections. Results indicate that the depth applied is expected to increase by 3.1% (4.1%) for corn, 18.8% (23.7%) for soybeans, and 3.0% (4.1%) for wheat under RCP 4.5 (8.5) by mid-century. Corn is the most commonly irrigated crop in the region, so overall withdrawals are expected to increase by 5.9% (7.6%), even after accounting for CO 2 improvements in TE. This is consistent with most previous studies that have found climate change increases irrigation water requirements in most regions of the world (Izaurralde et al 2003, Fischer et al 2007, Wada et al 2013, Haddeland et al 2014. However, some crop models indicate a decrease in irrigation water requirements (Elliott et al 2014). Most of the increase in withdrawals are due to the increase in temperature that increases evapotranspiration demand. Changes in precipitation are expected to result in small changes in withdrawals.
Elevated levels of CO 2 in future climatic scenarios are known to increase TE, since increased CO 2 concentration leads to a partial closure of stomata (Lammertsma et al 2011). Reduced stomatal space for gas exchange under elevated CO 2 lowers water lost per unit of carbon intake by the plants and hence increases TE or water use efficiency (Policy et al 1993), until leaves are exposed to optimum temperatures (Hatfield and Dold 2019). Accounting for changes in TE due to higher CO 2 concentrations is important to avoid overstating the impact of climate change on withdrawals. We find that withdrawals are predicted to be 45% smaller for corn when accounting for the CO 2 effect.
For C3 crops like soybeans and wheat, elevated CO 2 increases RUE which counters the effect of increases in TE. We find that elevated CO 2 results in a small decrease in depth applied for wheat and an increase in depth applied for soybeans. The difference in results is explained by the higher temperatures during the soybean irrigation season causing a smaller improvement in TE because a higher VPD leads to increased stomatal opening (Hatfield andDold 2019, Roby et al 2020). In the case of wheat, the higher TE improvement (10.6%/100 ppm; SI appendix, section A2) could be through the impact of elevated CO 2 leading to reduced stomatal closure accompanied by a cooler irrigation season with lower VPD levels of around 0.9 kPa (SI appendix, figure A4). Soybeans are exposed to a hotter summer irrigation season with an average VPD of 1.4 kPa (SI appendix, figure A3). The higher atmospheric pressure from higher VPD is known to increase stomatal opening to ensure the crop canopy temperature is maintained at levels lower than the critical threshold, through a mechanism called transpiration cooling (Julia and Dingkuhn 2013, Jagadish et al 2021. Due to the higher VPD of the irrigation season, soybeans have a smaller improvement in TE (5.3%/100 ppm; SI appendix, section A2).
The central and southern portions of the High Plains Aquifer have been significantly depleted (Scanlon et al 2012, Steward et al 2013, Haacker et al 2015, Steward and Allen 2016. Furthermore, the production of grains has already peaked in Kansas and Texas (Mrad et al 2020). Yet projections of future water and production conditions do not account for the impact of climate change on withdrawals (Steward et al 2013, Haacker et al 2015, Steward and Allen 2016, Mrad et al 2020. The increase in water withdrawals is projected to increase the rate of aquifer depletion by mid-century. The largest impact on aquifer depletion is expected to occur in the SC district that has historically been closest to aquifer sustainability. The SC district has a historical rate of annual depletion of 0.06 m, but this is expected to increase to 0.26 m by mid-century under RCP 4.5. There have been several recent local stakeholderdriven efforts to extend the life of the aquifer in Kansas (Perez-Quesada and Hendricks 2021). One program decreased withdrawals by roughly 26% (Drysdale andHendricks 2018, Deines et al 2019), though the impacts on aquifer levels in the long run may be smaller since the reductions were primarily achieved through more efficient irrigation that reduced return flows (Deines et al 2021). The projected increase in water withdrawals is important for water managers across the High Plains Aquifer and other similar climatic regions globally. An increase in irrigation withdrawals due to climate change implies that the economic gains from dynamically optimal irrigation management are larger than when ignoring climate change (Quintana Ashwell et al 2018). Furthermore, our results emphasize the importance of measuring water withdrawals to understand how withdrawals could change in the future.
While our results provide important insights for water management in a changing climate, there are also several limitations of our work. First, while regression models produce similar results as crop simulation models for the effects of climate change on crop yield (Liu et al 2016), a limitation of our regression model is that it does not explicitly account for complex nonlinear relationships between weather, soil, and vegetation that affect soil moisture (Rodriguez-Iturbe et al 1991, D'Odorico et al 2000. Future research could utilize machine learning or artificial intelligence to model these relationships (Sun and Scanlon 2019, Chakraborty et al 2021a, 2021b. Second, our projections do not account for potential producer adaptation by switching crops or adopting new technology (Rising andDevineni 2020, Sloat et al 2020). Third, we quantify how climate change is expected to affect water withdrawals, but do not account for the effects of climate change on aquifer recharge or return flows. Fourth, changes in irrigation withdrawals could have feedback effects on the local climate (Bonfils and Lobell 2007). An important topic for future research is to incorporate behavioral models of irrigation withdrawals like we develop in this study into integrated assessment models that allow for feedback within the system.

Data availability statement
The data that support the findings of this study are openly available at the following URL/DOI: historical water withdrawal data are available at https:// geohydro.kgs.ku.edu/geohydro/wimas/, historical daily temperature and precipitation data are available at https://prism.oregonstate.edu/, and projected daily temperature and precipitation data are available at https://labs.waterdata.usgs.gov/gdp_web/.