Study area
The Republican River originates in the State of Colorado (CO) and then generally flows east through Nebraska (NE) and Kansas (KS) (Fig. 1). The Republican River Basin (RRB), predominantly underlain by the High Plains Aquifer, extends across an area of 64,500 km2 in CO, NE, and KS. The dominant land uses are grass/pasture and cropland, composing over 45% and 35% of the basin area, respectively, based on the 2008 National Cropland Data Layer. More than 95% of the water withdrawn from the High Plains Aquifer is used for irrigation, and CO, KS, and NE together account for more than 60% of the total withdrawals (Maupin and Barber 2005). In NE and KS, 98% and 85% of the total groundwater irrigation are from the High Plains Aquifer (Hutson et al. 2004).
To efficiently use and manage the water in RRB, the Republican River Compact Administration (RRCA) was formed in 1942 (United States Congress 1943). However, its crossing of multiple political boundaries resulted in conflicts over water access among CO, KS, and NE. Kansas filed a complaint against NE in 1998 and against CO and NE in 2010 for exceeding their water allocations. Recently, variably declining water tables throughout the RRB, a result of intensive irrigation, have been documented using the historical records of groundwater monitoring wells (McGuire 2017). Between 2002 and 2015, the maximum groundwater level decline reached 13.2 m in the RRB.
The RRCA groundwater model
As a result of the Final Settlement Stipulation in the case of KS vs. NE and CO in 2002, a comprehensive groundwater flow model was developed using the MODFLOW code by technical experts from the three states, as appointed by the RRCA committee (RRCA 2003). The purpose of the RRCA model is “… to determine the amount, location, and timing of streamflow depletions to the Republican River caused by well pumping and to determine streamflow accretions from recharge of water imported from the Platte River Basin into the Republican River Basin …” (RRCA 2003). The RRCA model is discretized into a single-layer, uniform, 1-mi grid with 165 rows and 326 columns, of which 30,655 cells are active. Monthly stress period is implemented with two time steps per stress period. The stream package is used to simulate the stream-aquifer interaction and streamflow routing in the modeled area (Prudic 1989). Groundwater recharge and pumping are parameterized in the Recharge and Well packages, respectively. The model was calibrated with historical groundwater levels at monitoring wells and baseflows at stream gauges. The model has been being updated each year with new data. The model files can be downloaded at the RRCA website (http://www.republicanrivercompact.org/), and the simulation period ranges from 1918 to 2015 (accessed on June 8, 2017).
Estimation of irrigation withdrawal
Because observation of irrigation withdrawal was limited, the actual irrigation amount was estimated using other data sources, depending on data availability. In Nebraska, irrigation withdrawal can be estimated with electrical consumption for irrigation. For Kansas and Colorado, irrigation withdrawal is estimated based on irrigated acreages, net irrigation requirements, and application efficiencies (RRCA 2003). To account for the impact of climate variability on irrigation, an estimation of the monthly irrigation withdrawal can be unified as follows:
$$ {Q}_{\mathrm{p}}=\left({K}_{\mathrm{c}}\mathrm{E}{\mathrm{T}}_{\mathrm{r}}-{K}_{\mathrm{p}}P\right)A/{E}_{\mathrm{f}} $$
(1)
where Qp is the monthly irrigation withdrawal (m3/mon), Kc is the crop coefficient, ETr is the monthly reference ET (mm), P is the monthly precipitation (mm), Kp is the effective precipitation coefficient, A is the irrigated area (m2), and Ef is the irrigation efficiency.
ETr is the sum of daily reference ET which is calculated through the Hargreaves equation:
$$ {\mathrm{ET}}_{\mathrm{rd}}=a{R}_{\mathrm{a}}{\left({T}_{\mathrm{max}}-{T}_{\mathrm{min}}\right)}^{0.5}\left({T}_{\mathrm{mean}}+17.8\right)+b $$
(2)
where ETrd is the daily reference ET (mm day−1); Ra is the net radiation (MJ m−2 day−1); Tmin, Tmax, and Tmean are the daily minimum, maximum, and mean temperatures, respectively [°C]; and a and b are constants. The values of a and b are 0.0023 and 0 in the standard Hargreaves equation, respectively (Hargreaves and Allen 2003). To account for spatial variability, a and b are calibrated to match the results calculated with the Penman-Monteith (PM) Evapotranspiration equation (ASCE-EWRI 2005) at Automated Weather Data Network (AWDN) stations (Fig. 1) operated by High Plains Regional Climate Center (https://hprcc.unl.edu/). Data from AWDN stations are used because AWDN stations provide comprehensive weather information needed in the PM equation. After calibration, the values at the stations are interpolated over the RRB domain through kriging. Supplementary Fig. S1 shows the distributions of the deviation of a and b relative to the standard values, respectively.
By combining the coefficients, Eq. (1) can be expressed as:
$$ {Q}_{\mathrm{p}}=\alpha \mathrm{E}{\mathrm{T}}_{\mathrm{r}}-\beta P $$
(3)
where α = KcA/Ef and β = KpA/Ef. In Eq. (1), Kc depends on the crop type and growth phase, while the values of A and Kp change with location. The values of α and β vary both in time and space. By neglecting the interannual variability in A, Kc and Kp, α and β become constants for different months in each grid cell. Thus, they can be estimated using historical pumping rates, precipitation, and temperature data in each irrigated cell. The best-fit values of α and β are found using the Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) optimization algorithm (Byrd et al. 1995) with bounds of (0.0, 1.0). Individual α and β values were estimated for each irrigated cell and each month. The calibration period ranges from 1980 to 2009, while irrigation between 2010 and 2015 is used for verification (see Supplementary Materials for the model performance). Irrigation occurs primarily in the summer months and is negligible the rest of the year (Supplementary Table S1). As such, we defined June to September as the irrigation (IRRI) season and the rest months as the non-irrigation (NOIR) season.
Estimation of groundwater recharge
In the RRB, groundwater recharge originates primarily from precipitation and irrigation. Precipitation recharge is estimated with precipitation-recharge curves, while irrigation recharge is considered to be proportional to irrigation. Details follow.
Precipitation recharge
Precipitation recharge is estimated with precipitation-recharge curves (PRCs), as shown in Supplementary Fig. S2. The PRCs, developed based on the results of a soil water balance model CropSim (Martin et al. 1984), transforms annual precipitation into annual precipitation recharge. CropSim is a water-driven point source model that uses weather data in combination with representative system characteristics (crop phenology, soils, management, and irrigation system) to model the daily crop growth and soil water balance. It was used to simulate soil hydrology and generate PRCs with the combinations of five soil types and irrigated and non-irrigated land use types (RRCA 2003).
In the RRCA model, precipitation data were retrieved at the AWDN weather stations in the study area. In order to calculate precipitation recharge, annual precipitation was interpolated to each cell based on the weather station data with the kriging interpolation method. Annual precipitation recharge is then calculated with the PRCs, according to the soil and irrigation types within each grid cell. The irrigated area within each cell is used to apportion the recharge between the irrigated and non-irrigated recharge curves. The annual precipitation recharge was distributed to months using a fixed monthly distribution defined by RRCA.
In this study, we implement two modifications to the precipitation recharge estimation method. First, in the baseline, the PRISM Climate dataset (Daly et al. 1994) is used to re-estimate precipitation recharge. Compared to the interpolation method, the PRISM dataset provides more accurate spatial distribution of precipitation. Meanwhile, the PRISM temperature data is used to estimate reference ET. Second, instead of a fixed monthly distribution of the annual precipitation, we use monthly precipitation from the PRISM dataset.
Irrigation recharge
Irrigated water can be consumed by crops, become runoff, evaporate from the soil, or be stored in the soil, with the remainder recharging groundwater. Irrigation recharge is assumed to be proportional to the gross irrigation amount in the RRCA model (Dewandel et al. 2008). Therefore, changes in irrigation recharge are proportional to changes in gross irrigation withdrawals:
$$ {R}_{\mathrm{i}}={R}_{\mathrm{i}0}{Q}_{\mathrm{p}}/{Q}_{\mathrm{p}0} $$
(4)
where Ri and Ri0 are the projected and baseline irrigation recharge rates, respectively, and Qp and Qp0 are the projected and baseline irrigation withdrawal rates, respectively. The projected irrigation withdrawal rates are estimated using the regression model (Eq. 3) based on temperature and precipitation.
Climate change projections
Projections of future temperature and precipitation are retrieved from the Locally Constructed Analogs (LOCA) statistical downscaled dataset developed by Pierce et al. (2014) for CMIP5 (Taylor et al. 2011). The dataset includes downscaled estimates of daily precipitation and minimum and maximum temperature at 1/16-degree resolution based on the simulation results of 32 GCMs (Supplementary Table S2). The climate data are re-projected to the 1-mi model grid using bilinear interpolation. Each GCM provides historical, RCP4.5, and RCP8.5 data. Changes in monthly precipitation and temperature are calculated between the RCP4.5 or RCP8.5 and mean historical values. A 90-year baseline simulation is constructed through repetition of the RRCA model simulation between 1980 and 2009. The final hydraulic head of a 30-year simulation is used as the initial head for the next 30-year simulation to propagate changes. In the present study, climate change impact is assessed through the comparison of the mean of the future ensemble simulation and the 90-year baseline simulation, in which the future climate impact is isolated from the current trend in the baseline.