Water Conservation with Managed Aquifer Recharge under Increased Drought Risk

Abstract

Economic analysis of managed aquifer recharge (MAR) typically focuses on identifying the quantity of water to add cost-effectively to natural rates of recharge. However, to the extent that MAR is successful, higher groundwater levels or at least slower depletion are likely to influence crop choice and groundwater pumping dynamics. Using a landscape-level model, we maximize farm net returns taking into account MAR and on-farm surface reservoir storage, crop choice, and the impacts of drought on groundwater use in Eastern Arkansas, USA, over 120 years. We find that drought frequency (risk) has a stronger influence on groundwater pumping and MAR use compared with drought severity. There is evidence of a substantial slippage, the percentage of the increase in groundwater use with versus without MAR divided by the MAR use, under a range of MAR cost and drought scenarios. Total slippage ranges from about 32 to 75% of total MAR water, indicating that only 68–25% of the MAR water raises groundwater levels. Even if the costs of MAR are relatively high and slippage is present, the total net returns to farms in this region are higher, and the variability in those returns are less with MAR.

Appendices

Appendices

Appendix A. Estimation of Return Flow and Correct Withdrawal Coefficients

The depth to the water, H_f, initial saturated thickness, b_f, and hydraulic conductivity, K_f, of the Alluvial aquifer varies across the landscape, as shown in Table 6 (ANRC 2018). The natural recharge, NR_f, and storativity, S_f, values come from the USGS (Clark and Hart 2009; Reitz et al. 2017). The irrigation method influence substantially returns flow coefficients. Conventional irrigation can have a return flow coefficient of 50%, whereas drip irrigation has a coefficient of <1% (Dewandel et al. 2008). Here, we estimate the return flow coefficient, α, with an assumption that n (n = 2000) sites use only groundwater for irrigation initially.

The change in groundwater level at the cell, f, depends mainly on groundwater pumping, GW_f, natural recharge, NR_f, the size of the aquifer, A_f, and storativity, S_f. Thus, the average change in groundwater level for the study area can be expressed as

$$\overline {H_f} (t + 1) = \frac{1}{n}\mathop {\sum}\limits_{f = 1}^n {\left( {H_f(t) - \frac{{{\mathrm{NR}}_f(t) - (1 - \alpha ){\mathrm{GW}}_f(t)}}{{A_fS_f}}} \right)}.$$

(4)

The average groundwater level falls about 0.25 feet (0.08 m) annually between 1994 and 2016 in the study region (ANRC 2006, 2017). Groundwater pumping, GW_f, was estimated based on the 2017 Cropland Data Layer, the required irrigation water use per unit area of crop, and the current level of irrigation in the region (Poch-Massegú et al. 2014; Edward 2016). The estimated return flow coefficient is equal to 29%.

Appendix B. Surface Water Availability for MAR, the Distance to Recharge Sites and Water Conveyance Costs

Storing excess surface water underground through MAR is a viable alternative in the region. Only excess water withdrawals are legal from Arkansas’ rivers (ARNC 2014). Arkansas state laws indicate that excess water is any water that is 25% or greater than the average annual yield from a watershed determined by ARNC (2014). Arkansas has ~8.6 million acre-feet/year (AFY) (10,608 million m³/year) excess surface water and most of which are in Arkansas and White Rivers. Based on the maximum injection rate, we estimated that the maximum amount of water that could be used for MAR in the study area is only about 2 million AFY (2467 million m³/year), which is about four-times lesser than the excess surface water.

The water conveyance costs from rivers, e.g., Arkansas and White Rivers, to recharge sites principally comes from energy cost (FEMA 2016; Falconer et al. 2017). The cost is estimated as a function of the distance from rivers to recharge sites that are based on the distance to nearest major rivers, the amount of water used through MAR, and energy price. The distances come from comparing recharge well locations with the river network distribution in the NHD (USGS 2019). In the main text, we describe how to account for MAR spatially. Herein, we assume that excess surface water is always available for MAR even in the driest year because the amount of excess surface water is much higher than the amount of water that could be used for MAR.

To implement MAR, farmers have to transport the excess surface water from rivers to recharge sites and inject them into the aquifers during nonirrigation periods. The injected water can then be recovered for irrigation during subsequent irrigation periods. Costs will vary by distance and lift (raising the water through a pipe above the level of rivers). We describe how to account for spatial variation of the MAR cost based on site-specific information e.g., groundwater level, hydraulic conductivity, saturated thickness, and storativity in the main text. Here, we only present the spatial differentiation in costs of MAR based on the costs of surface water conveyance from water sources to cells/recharge sites—surface water conveyance cost is the function of lift head and friction losses due to the mainline length, MAR, and energy cost.

The water conveyance costs include variable energy costs for pumping additional acre-feet of water for MAR, and capital costs for piping and standard recharge system (e.g., extraction/injection well, booster pumps, control systems, operation and maintenance, monitoring and assessment). Since the fixed cost is largely unknown, we simulate the model with a range of the fixed cost that comes from the capital costs of existing and planned irrigation projects in Arkansas. The initial cost of capital equipment and operating supplies was provided by the U.S. Department of Agriculture—Agricultural Research Services personnel and Eley-Barkley Engineering and Architecture, Cleveland, MS. The fixed cost is assumed to be identical for all the recharge sites and the cost is the sum of the costs of investment and operation and maintenance, excluding water conveyance cost of a typical recharge system. The variable cost for pumping additional acre-feet of water for MAR is estimated as below.

The energy cost, $c_f^{{\mathrm{ar}}_{{\mathop{\rm{var}}} }}(t)$, is computed based on the cost needed to convey water from the point of diversion from a river to the recharge site, f, in the year, t. The energy is the total energy needed to pump water a given distance and lift along the mainline. Thus the cost can be expressed as

$$c_f^{{\mathrm{ar}}_{{\mathop{\rm{var}}} }}(t) = p_eE_f(t),$$

(5)

where p_e is the price of electricity ($/kWh) and E is the energy consumed in kWh. We have

$$E_f(t) = tp_f(t) \times ({{\rm output}\,{\rm power}}),$$

(6)

where tp_f (t) is time (hours) in the year, t, and output power (kWh) is the power per unit time. One gallon of irrigation water weight about 8.34 pound (999.35 kg/m³). One horsepower provides 33,000 foot-pounds (438,768 m kg) of work per minute. Thus, the output power is

$${{\rm Output}\,{\rm power}}_f(t) = \frac{{8.34q_f(t){\mathrm{TDH}}_f(t)}}{{33,000}} = \frac{{q_f(t){\mathrm{TDH}}_f(t)}}{{3957}},$$

(7)

where TDH_f(t) is the total dynamic head losses, which is equal to the sum of the head losses and friction losses. q_f(t) is the pumping rate at the cell, f, in the year t.

The hours of pumping in year t, tp_f (t), necessary to pump amount of water (acre-feet), MAR_f (t), is computed as (1 foot is 10 inches [0.305 m], 1 acre-inch is 27,154 gallons [102.79 m³] and 1 h is 60 min)

$$tp_f(t) = \frac{{{\mathrm{MAR}}_f(t) \times 27,154}}{{q_f(t) \times 60 \times 12}}.$$

(8)

We convert the output power from horsepower to kilowatts by multiplying 0.746. Combining the relationships in Eqs. (5)–(8) and assuming that efficiency of a typical pumping plant is 0.75, we can rewrite the, c_ef(t), as

$$c_f^{{\mathrm{ar}}_{{\mathop{\rm{var}}} }}(t) = p_e \times 0.0095 \times {\mathrm{MAR}}_f(t) \times (H_{{\mathrm{hf}}}(t) + \frac{{L_f}}{{100}}),$$

(9)

where L_f is the distance from the surface water source to recharge site, f.

To account for the incremental energy costs for the length and lift of additional mainline system, we use Hazen–Williams formula to estimate H_hf(t), for a pipe of 100 feet (30.5 m) in length

$$H_{{\mathrm{hf}}}(t) = K_f\frac{{\left( {\frac{{q_f(t)}}{{C_f}}} \right)^{1.852}}}{{D_f^{4.87}}} \times L_fa,$$

(10)

where K_f is a constant, C_f is the roughness factor, D_f is the inside diameter. For a representative surface water conveyance system, we select K_f = 1046, C_f = 140 (for PVC pipe), and D_f = 10 inches, which is often used for a pump with a capacity of q_f = 1225 gallons/min (1975 AFY [4.64 m³/min]). We assume that the distance between the rivers water level and the centerline of the abstraction pump is 10 feet (3.05 m). As a result, the variable water conveyance cost is roughly $0.038 per 1 mile ($0.019/km) of a mainline per acre-foot of MAR water.

Appendix C. Drought Indices

We use the PDSI to determine whether a year is a drought year. PDSI index provides information on the severity and intensity of drought. PDSI values are negative during dry years and positive during wet years (NOAA 2018). The smaller PDSI value, the more severe the drought, for example, PDSI values within a range of −0.5 to −1.0 are for incipient drought years, −1.0 to −2.0 for mild drought years, −2.0 to −3.0 for moderate drought years, and −3.0 to −4.0 for severe drought years (NOAA 2018) (Figs. 3–6).

Fig. 3

PDSI value for the baseline scenario. Drought frequency is 43%, 52 drought years out of 120 years. The average PDSI in drought year is −2.36 (moderate drought) as the PDSI during the most recent driest period, 2010–2012, in Arkansas. The average PDSI over a 120-year time horizon is −0.43. This synthetic 120-year PDSI was created by repeating the historical PDSI in the last 30 years in Arkansas, for four successive 30-year periods

Fig. 4

PDSI value for increase in frequency (scenario 1). Drought frequency is 60%, 72 drought years out of 120 years. Average PDSI in drought year is −2.36 (moderate drought) as the PDSI during the most recent driest period, 2010–2012, in Arkansas. The average PDSI over a 120-year time horizon is −0.74. This synthetic 120-year PDSI was created by repeating the historical PDSI in the last 30 years in Arkansas, for four successive 30-year periods

Fig. 5

PDSI value for increase in severity (scenario 2). Drought frequency is 43%, 52 drought years out of 120 years. Average PDSI in drought year is −3.32 (severe drought) as the PDSI during the driest period, 1954–1956, in the record in Arkansas. The average PDSI over a 120-year time horizon is −0.87. This synthetic 120-year PDSI was created by repeating the historical PDSI from 2005 to 2014, the most recent long dry period in Arkansas, for twelve successive 10-year periods

Fig. 6

PDSI value for increase in both frequency and severity (scenario 3). The increased drought frequency is 60%, 72 drought years out of 120 years. Average PDSI in drought year is −3.32 (severe drought) as the PDSI during the driest period, 1954–1956, in the record in Arkansas. The average PDSI over a 120-year time horizon is −1.31. This synthetic 120-year PDSI was created by repeating the historical PDSI from 2005 to 2014, the most recent long dry period in Arkansas, for twelve successive 10-year periods

The annual irrigation water use by crops for normal and drought years is shown in Table 7.

Table 6 Descriptive statistics of the model data across the sites of the study area

Appendix D. Descriptive Statistics of the Model Data Across the Sites of the Study Area and Model Parameters

Crop prices come from the average of crop prices from 1977 to 2016 (USDA-NASS 2018a). We use these average prices to reflect long-term prices. A model with stochastic prices is computationally infeasible with ample spatial and temporal detail. The assumption of constant prices is to preserve the focus on economics of MAR over a long time horizon. Crop production costs excluding irrigation cost, crop irrigation requirements are obtained from the Division of Agriculture with the University of Arkansas (UARK 2018). The irrigation costs include costs of labor, fuel, lube and oil, and poly-pipe for border irrigation plus the levee gates for the flood irrigation of rice, purchase and maintenance costs of the wells, pumps, gearheads, and units cost (e.g., energy cost) to lift a volume of unit of irrigation water (Martin et al. 2010). A standard well (i.e., the well depth is 36.56 m or less [120 foot or less]) requires about 0.037 l of diesel per cubic meter (12 gallons of diesel per acre-foot), and a deep well (i.e., the well depth is between 36.56 and 73.15 m [120–240 feet]) requires about 68 l (18 gallons) of diesel per acre-foot (Hogan et al. 2007). Pumping an acre-foot of water from an on-farm reservoir requires about 6 gallons (0.018 l/m³) of diesel. EIA (2015) indicates $0.99 per liter ($3.77/gallon) of diesel, and to account for oil and lube for irrigation equipment, we add 10% to the fuel costs (Hogan et al. 2007) (Table 8).

Table 7 Annual irrigation water use by crops for different drought severity levels

Table 8 Value of economic and irrigation model parameters

Appendix E. On-Farm Reservoir Use and Construction

Without a tailwater recovery system, an acre (0.405 ha) of the reservoir can hold about 16.5 acre-inches per year (1696 m³/year) from natural rainfall (Young et al. 2004). With a tailwater recovery system, a maximum capacity of an acre of the reservoir is 7.5 AFY (9251 m³/year) (Smartt et al. 2002). We use the MARORA tool (Smartt et al. 2002) for estimation of water recovery construction and maintenance costs of an acre of the on-farm reservoir and tailwater system. The significant cost of reservoir construction includes the cost of moving soil, maintenance costs, and re-lift pumping. The reservoir and tailwater recovery system capital and maintenance costs amortize to an annual cost (c_ri) of $377/acre ($931/ha) of the reservoir.

Appendix F. Alternative Irrigation Practice Adoption

The current proportion of producers that use more efficient irrigation practices is <20%, and this proportion increases by about 1% per year (Edward 2016).² Furrow irrigation is the conventional irrigation practice for corn, soybean, and cotton, and the contour-levee flood is the conventional irrigation practice for rice. Alternative irrigation practices (e.g., center pivot, surge irrigation, precision leveling, and poly-pipe with computerized hole selection) to conventional irrigation reduce water use and potentially raise yields. Tables 9 and 10 show the differences in crop yield, irrigation water use, and production cost between conventional irrigation and alternative practices.

Table 9 Adjustment coefficients to water use by crop relative to conventional for alternative irrigation practices

The adjustment coefficients for water use indicates how water applied would change if the irrigation practice is adopted. For example, the coefficient for RISER for corn is 0.60, which means that if corn fields are RISER used, then this would decrease water applied by 40%.

Table 10 Adjustment coefficients to the costs of production by crop relative to conventional for alternative irrigation practices

The adjustment coefficients for costs of production, excluding irrigation pumping costs, indicate how costs would change if the irrigation practice is adopted. For example, the coefficient for RISER for corn is 1.03, which means that if corn fields are RISER used, then this would increase costs of production, excluding irrigation pumping costs by 3.00%.

Appendix G. Length of the Planning Horizon

The results of the analysis are sensitive to the choice of the length of the planning horizon, T. As we reach the 120-year time period, the cumulative gains begin to flatten out and converge to a constant, with an increase in a total net return of less than one million dollars per year. Therefore, extending the time period will give the same substantive result.

Appendix H. Optimal Dynamic Pathways in MAR Use

Examining the quantity of water recharged (Fig. 7), the results show that when the cost of MAR is $0.02/m³ ($20/acre-foot), well below the average pumping cost ($0.03/m³ [$40/acre-foot]), there is significant MAR early in the time horizon. The MAR use reduces the pumping costs and reverses aquifer decline progressively over the time horizon, which leads to a declining trend in the quantity of water recharged through MAR. When the cost of MAR is higher than average groundwater pumping costs, MAR begins at a low level of recharge and gradually rises as the persistent groundwater declines increase the returns to MAR. Under scenarios with increases in drought frequency and severity, the dynamic pathways look broadly similar, but greater drought frequency (scenario 1) leads to a greater increase in MAR use compared with higher drought intensity (scenario 2). Greater drought frequency and intensity only have a slight effect on the MAR use when its cost is $0.03/m³ ($40/acre-foot) or above. At this cost, the results show that farmers increase net returns with adaptive crop management by growing less irrigation intensive crops than by banking groundwater through MAR (Tables 1 and 2).

Fig. 7

The simulated annual optimal amount of water for MAR over 2000 sites for 120 years for three-cost of MAR scenarios and 60% recovery efficiency. Baseline drought frequency is 47%, 52 drought years out of 120 years, and drought intensity is moderate. Increase in drought frequency (scenario 1) represents an increase in drought frequency to 60%, 72 drought years out of 120 years, and drought intensity is moderate. Increase in drought severity (scenario 2) represents an increase in drought intensity scenario; drought frequency is 47%, and drought intensity is severe. Increase in drought frequency, and severity (scenario 3) represents an increased both drought intensity and frequency scenario; drought frequency is 60%, and drought intensity is severe. a MAR cost is $0.02/m³ ($20/acre-foot). b MAR cost is $0.03/m³ ($40/acre-foot). c MAR cost is $0.05/m³ ($60/acre-foot)