The integrated model is composed of independent disciplinary models that each conform to and are linked within the Open Modeling Interface (OpenMI) Standard . The linked model consists of four components with the input–output mappings shown in Fig.  with one exogenous component: climate. The lowest common unit of analysis across all modeling components operates at the county level, of which there are 12 in GMD3, and the models conduct their simulations and exchange data over this set of 12 polygons. The components operate on an annual time step over the 100-year horizon from 2013 to 2112. For each year of the simulation, the socioeconomic impact model requests (see R1 in Fig. ) the crop acreage from the crop choice model and crop yield from the crop production model, which also requests the crop acreage from the crop choice model. The crop choice model in turn requests (R2) the saturated thickness and depth to water from the groundwater model (for the previous year), which triggers the groundwater model to simulate the previous year and provide the data (D3). The crop choice model then calculates the acreage data for the current year and provides them (D4) to the crop production and socioeconomic impact models. The crop production model then calculates the yields and water use (D5) for the year and provides them to the socioeconomic impact model (D6) and groundwater model (D7), respectively, allowing them to calculate their outputs for the year.

The socioeconomic impact model uses cash flow at time t (CFt), also referred to as “gross profit”. CFt = revenue (i.e. price ⋅ yield) - costs (fixed costs + variable costs + lift costs). Based on CFt, the net present value (NPV) is the discounted CFt, calculated as Σ (CFt/(1 + Kt))t where K is the discount rate on investments (set at 4 %) and t is a counter for the year, starting with 1 in 2013. In this model and in the crop choice model, all monetary variables are in inflation-adjusted 2013 dollars. Many economic impact models also estimate economic multiplier effects using Impact Analysis for Planning (IMPLAN) . IMPLAN produces direct, indirect, and induced impacts on total economic activity, value-added activity, and employment. Our linked CNH model focuses on community impacts that yield employment opportunities to support a stable population base. Over the years, as agricultural production has become increasingly mechanized and technologically based, farms have consolidated, creating larger farms with fewer employees . This has led to considerable population decline in most rural-farming-dependent communities in the Great Plains region. Even though wealth creation from farming is important, from a community development standpoint, this wealth is most important when it translates to jobs and population. In western Kansas, IMPLAN estimates that it takes about USD 1 million CFt to produce 1.2 full-time equivalent (FTE) employees, of which 0.88 FTE are directly tied to crop production agriculture and 0.32 FTE represent indirect and induced employment. There are slight variations between CFt for irrigated cropland and nonirrigated cropland, which are detailed in Table  in Appendix A2.

To estimate the population impact of this employment, we conducted a cross sectional time series analysis with panel-corrected standard errors (TSCS) from 1970 to 2010, where the time increments are every 5 years (1970, 1975, 1980, etc.), the cross sections are the 12 counties of GMD3, and the error terms are both heteroskedastic and serially correlated (AR1). yi,t=βnxi,t+ϵi,t, where ϵi,t = υi,t + ρϵi,t-1. In this 40-year TSCS regression model, the independent variables are each county's employment levels (no. of employees) in agriculture, manufacturing, construction, health care, government services, and education, while the dependent variable is each county's total population. We obtained US Census population data and Bureau of Economic Analysis employment data from . This equation explained 92 % of the variance in total population in these counties during this time period (see Appendix A1 for model results). We multiplied the regression coefficient for agricultural employment (2.15) by the IMPLAN's employment multiplier to calculate the impact on population (2.15 ⋅ (.88) = 1.88 people). Thus, each USD million CFt from crop production in GMD3, supports an additional 0.88 FTE and 1.88 residents in region. Given the connection between agriculture and value-added meat production, we assign the other 0.32 FTE emanating from indirect and induced employment impacts to the coefficient for manufacturing (.32 ⋅ 1.33 = .43 people). Taken together this suggests that each USD 1 million in CFt from crop production supports 1.2 additional jobs and 2.3 more people living in the region.

The crop choice component is an iterative positive mathematical programming (PMP) model that simulates farmers' allocation of arable land to different crops in each county. The model operates on an annual time step, with each execution predicting farmers' choices in a single growing season.

An annual horizon reflects the fact that farmers competitively extract water from a common pool, leaving no individual incentive to conserve stocks that can be withdrawn by other users in future periods .

A separate instance of the model was calibrated to data from each county in the study region. Each county model simulated acreages for irrigated and nonirrigated plantings of the five dominant in crops in the region: wheat, corn, sorghum, soybeans, and alfalfa. Nonirrigated production of soybean and alfalfa is unfeasible given regional hydroclimatology and so are only included as irrigated crops. Thus, eight crop categories were modeled. The models were calibrated to the 2006–2008 average of observed acreages, yields, and prices for the eight crops by county, the most recent period for which comprehensive county-level data are available from the National Agricultural Statistics Service (NASS). Expected crop yields are simulated within the model from water response functions in , which were calibrated to yield data from NASS and weather data from the Kansas Weather Data Library.

As noted above, the crop choice model is not calibrated to a specific year, but rather to the mean outcome during the base period. Calibrating to a specific year would “overfit” the model so that it replicates that single year, but does a poor job with the years before or after that one year. The mean approach does not give an exact fit for any single year but makes the model match better with the data cloud.

There is a long history of increasing crop yields due to genetic improvements in plant varieties p. 46. Considering this history and the continued investment in plant genetics by industry and governmental agencies, the crop choice model assumes that yields will continue to improve into the future based on the noncompounded percentage growth rates estimated from time series regression of western Kansas yields for irrigated and nonirrigated plant varieties from 1974 to 2009 (see Appendix A3, Table A2) . The average annual improvements in yield range from a high of 1.28 % for irrigated corn to a low of 0.55 % for dryland wheat and 0.53 % for irrigated sorghum. Crop production costs, excluding irrigation, were obtained from Kansas State University Extension enterprise budgets and were increased over time at noncompounded percentage rates in proportion to yields based on a regression analysis of budget and yield data using 2006–2012 observations. While base-level yields and costs were calibrated to 2006–2008 data, growth percentages were applied to adjust the initial simulation year to correspond to 2013. The cost of irrigation water was calculated separately based on the energy costs from pumping lifts . Details on the model development and calibration methods are in , , and .

The crop production component projects grain yield and irrigated water by using the erosion–productivity impact calculator (EPIC) model . EPIC simulates daily crop growth by representing three major processes: (1) phenological development, (2) dry matter production and partitioning to plant tissues resulting in growth, and (3) economic yield. The model reproduces the results of irrigation, fertilization, tillage, variety selection, alternative production calendars, etc. Plant growth is estimated from intercepted solar energy and plant leaf area. Daily dry matter is accumulated for the growing season as controlled by heat units or environmental conditions (typically freeze events for summer crops), and yield is estimated using a total-biomass-to-grain ratio. EPIC is able to simulate multiple crops because it embodies a generic plant model that can be parameterized to represent different species.

We previously calibrated the model for use in western Kansas and further refined the parameters to support nonirrigated cropping for this study. The model component, developed in an earlier effort and implemented using the simple model wrapper , has an embedded set of simulated output data from EPIC collected by executing the model for all combinations of the relevant inputs (soil, crop, management, weather). The component operates over a set of (independent) polygons of variable size, accepting inputs for soil type, weather station, and crop and providing outputs for yield and water use.

Each simulated year's weather is determined by a random draw from meteorological records between 1985 and 2012. We build the likelihood of climate change into our simulation about the future of GMD3. ECHAM5 climate change models for the High Plains region suggest future regional warming and a gradual increase in extreme weather events, pointing toward a less suitable climate and thus reduced yields for agricultural production . To model this climatic progression, we weight the weather data from 1985 to 2012 such that years of below-average dryness will, over 100 years, gradually become 25 % more likely to occur than they are now. We find that this captures both the prolonged periods of drought that are likely to become typical, while allowing for shorter-lived periods of plentiful precipitation.

We compared the statistics of the original 27 years of weather data the our 100-year simulation where the drier years gradually became 25 % more likely. The average maximum temperature increased from 20.09 to 20.14 ∘C, the average total precipitation declined from 477.83 to 458.58 mm, while the relative humidity declined from 63.95 to 63.63 %.

The groundwater modeling component provides estimates of groundwater storage and the changes in storage due to pumping and natural hydrologic processes. This model is linked to the crop production and economic crop choice model using OpenMI , and operates on the common county-level scale. Conservation of mass requires that recharge minus extractions is equal to the annual change in storage: Recharget-Extractiont=Storaget+1-Storaget. This groundwater model integrates these spatially and temporally variable components of the hydrologic cycle to provide these fluxes on the common county-level aggregation scale, which are consistent with the scales of previous studies in the study region .

Specific steps used to prepare groundwater data follow. Storage is obtained from groundwater observation wells, kriging across wells to give a surface of saturated thickness, multiplying by specific yield to give water content, and integrating across the aquifer area within a county . Recharge is obtained by spatially integrating results from

It is important to note that the recharge component is kept consistent throughout this study. Given the relatively thick soil units throughout much of the region , recharge rates are low and may take decades or longer to reach saturated groundwater . This is consistent with , who noted that groundwater pumping usually has little impact on the recharge.

The first two policy scenarios use two separate Kansas water conservation statutes to model different policy approaches for achieving a 10 to 20 % reduction in irrigation. The Kansas Groundwater Management District Act contains provision K.S.A. 82a-1036, which allows the Chief Engineer to designate an “Intensive Groundwater Use Control Area” (IGUCA) to implement corrective control provisions reducing the permissible groundwater withdrawal based upon relative dates of priority of such rights (this statute also allows for a rotating schedule; ). Thus, this first scenario takes at least 20 % of fields out of irrigated crop production based on senior versus junior water rights. This is modeled by reducing by 20 % the acreage assigned to irrigation in each county. We assume that this acreage will be returned to dryland production. The second policy scenario emanates from K.S.A. 82a-1041(d)(1), which allows adjacent water users in a region to create “Local Enhanced Management Areas” (LEMAs). Under this statute, if a large consensus of irrigators in a contiguous area agree to limit water use by a prescribed percentage then that reduction becomes a legally enforceable limitation on all irrigators. Currently, there is one LEMA restricting irrigation in Kansas, located in Sheridan and Thomas counties, which are north of GMD3. LEMAs have two advantages over the IGUCA approach. First, it is a bottom-up process, where irrigators in an area agree to the restrictions through a consensus among themselves instead of regulations set centrally by the chief engineer. The work of suggests that this is a better institutional design for managing common pool resources. Second, this represents a “shared pain” approach; an approach that is preferred by irrigators over the enforcement of junior versus senior water rights. We operationalize the LEMA policy scenario by assuming that irrigators in GMD3 agree to create a LEMA that doubles the interval between irrigation applications, thus slowing the rate of water application by about 12 % across the management district. Based on previous research, we do not anticipate that either of these scenarios will produce a sustainable outcome. Rather, the focus here is on the effects of restrictions on farmers' NPV and the local communities.

Table  reports the results of simulations for scenarios 1 and 2 compared to the baseline analysis. Removing 21 % of fields from irrigation based on junior water rights means there is an immediate reduction in the number of irrigated acres in all the crop varieties; however, irrigated corn only decreases by 18 000 ha (300 000 ha in the baseline to 282 000 ha in junior rights scenario). The crop choice model suggests that the bulk of acres taken out of irrigated production will move to dryland corn (an increase of 106 000 ha in 2013 over the baseline) production. By contrast, doubling the irrigation interval has little appreciable impact on crop choices in GMD3 compared to the baseline. For scenario 1, the maximum number of acreage for irrigated corn tops out in 2063 at 329 000 ha compared to 350 000 in 2055 in scenario 2. Interestingly, under scenario 2, the number of acres under irrigation increases incrementally from 741 to 811 000 ha in 2070 (not shown). This pattern is consistent with previous research noting that farmers use their water savings on more fields to increase their capital returns.

Scenarios 3–5 follow this same pattern.

Both scenarios improve the lifespan of the aquifer by 10 to 15 years, but neither comes close to achieving aquifer sustainability given the very slow rate of recharge in most of GMD3. Both approaches produce similar types of outcomes for CFt and employment. The NPV by 2060 is USD 11.3 billion for the junior rights scenario and USD 12.1 billion for the LEMA scenario, compared to USD 13.3 billion for the baseline. Interestingly, in the long term, communities in GMD3 benefit from conservation. Extending the life of the aquifer in both scenarios leads to more people being employed by the direct and indirect impacts of production farming (an average of 340 to 400 workers a year by 2112).

Given that neither of first two policy options achieves sustainability, we explore the relationship between water conservation and the associated socioeconomic consequences for the farmers and communities in GMD3. To do so we simulated the implementation of a LEMA across GMD3 that incrementally increases the interval for irrigation by 3X (a 26 % reduction compared to 2014 usage), 4X (a 35 % reduction), and 6X (a 48 % reduction). We focus on the LEMA policy approach because it is a theoretically more pleasing policy prescription (see arguments above and Ostrom's work; ). Significantly, increasing the interval by 6X stretches to the maximum limit the marginal utility of irrigation for the purpose of assuring increased crop yields. Thus, after the 6X point, the LEMA approach begins to lose its policy integrity.

Tripling the irrigation interval for irrigated corn production gradually increases the acres in production from 300 000 ha in 2013 to a peak of 376 000 ha by 2071. Dryland corn, which in the baseline analysis becomes the most predominant crop after 2080, only surpasses irrigated corn in acres planted in 2110, at the end of the 3X simulation. Given the large variation in yields and revenues associated with dryland corn production, policies that reduce dependence on this high-risk crop are desirable. The 3X scenario tends to benefit the communities of GMD3, as the number of additional people employed due to the direct and indirect impacts of production agriculture increases from fewer than 1000 in 2013 to 1940 in 2112. Similarly, the number of people living in the region because of direct and indirect economic impacts from irrigation and dryland farming increases from 2000 in 2013 to 4200 in 2112.

Disappointingly, increasing the irrigation interval by 4X or 6X does not produce sustainable outcome for the aquifer. A total of 6 of the 12 counties under the 4X scenario and 2 of 12 counties under the 6X scenario still end the simulation with average saturation depths of 15 m or less. There is also an economic cost to irrigators to achieve this level of water savings. The NPV in 2060 shrinks to USD 9.5 billion for 4X scenario and USD 7.6 billion for the 6X scenario. On the positive side, after an initial decline in employment and population early in the simulation, both rebound to levels just above the baseline.