Analysis in the following sections expands on previous work by including consideration of recharge water from reservoir reoperation, evaluation of recharge water sourcing, cropland characteristics and groundwater hydrology for a site-specific setting and demonstrating a hydro-economic optimization approach that simulates separate decisions for land access and water delivery in the performance of Ag-MAR.The regional-scale analysis is conducted for a semi-arid part of California, USA that has conditions fairly common for many parts of the globe. The two groundwater sub-basins in the study area are part of the much larger Central Valley groundwater system with an interfingered assemblage of alluvial and flood-basin deposits of local maximum depth exceeding 1,000 ft . Many of the sub-basin boundaries shown in Fig. 2a are arbitrarily based on surface-water features, and the southern boundary has recently been adjusted northward to accommodate governance considerations for current groundwater management efforts . The 525,000-acre study area has a mix of urban , agricultural , wetland and undeveloped rangeland land uses . Over 90% of the total water use in the study area is supplied by groundwater . Moreover, square pot plastic approximately 41% of the agricultural acreage is planted as vineyards and orchards . This investment in perennial crops hardens water demand and intensifies groundwater extraction during droughts. The spatial distribution of recent water levels indicates localized depressions from extractions far exceeding groundwater recharge . Groundwater levels have dropped as much as 60 ft over the past several decades so that surface water frequently becomes disconnected from saturated groundwater and drains into the subsurface. The lower reaches of the Cosumnes River, in the central part of the study area , are dry 85% of the time .
New regulations for sustainable groundwater management in California require that this chronic lowering of groundwater levels and depletion of storage be addressed through active measures . While restoration of surface-water base flow in the study area may not be required because impact occurred before implementation of the regulations, there is interest in maintaining, and possibly improving, groundwater support of surface-water flows . Consistent with recent analysis , local stakeholders are interested in harvesting runoff from high-precipitation events for recharging groundwater. One option is reoperation of Folsom Reservoir to release extra water in advance of significant rain events alone could achieve a potentially significant amount of aquifer recharge using some of the 140,000 ac of croplands in the study area . This work presents a planning-level analysis of what might be possible. While infrastructure construction costs are not considered, the results of this work might encourage further evaluation of necessary investments.A retrospective analysis is conducted to evaluate the range of improvements in groundwater system state that might have occurred for the study area from an Ag-MAR recharge program. Recharge water is from simulated reoperation of Folsom Reservoir with delivery through the Folsom South Canal consistent with capacity limitations over a 20-year period that covers water years 1984 through 2003 . The timing and amounts of surface water delivered to croplands for recharge application is prescribed by a linear programming model that combines available information regarding surface water and groundwater hydrology with the spatial distribution of croplands. Groundwater recharge is simulated with a groundwater/surface-water model that incorporates existing land uses, surface-water deliveries and groundwater demands over the period considered .This analysis applies a formulation of simulation-optimization to MAR.
Previous work includes Mushtaq et al. who simulated unsaturated flow from individual recharge basins and applied nonlinear programming to identify optimal loading schedules for maximizing recharge volume. Marques et al. included decisions for recharge area allocation and water volume application as part of a two stage quadratic programming analysis that maximized crop profits. Hao et al. used a genetic algorithm to maximize recharge volume while meeting constraints on groundwater elevations. To the best of the authors’ knowledge, the approach presented here is new in that it combines elements of recharge basin and groundwater hydraulics with economic considerations at a regional scale. The foundation of the linear programming approach is based on the study area hydrology which is adapted to include economic considerations regarding land use. A hydrologic formulation is presented as an explanatory step in developing the full hydro-economic formulation.The formulation objective, Eq. , maximizes the volume of water recharged over the planning horizon subject to a set of operational constraints. The total volume of water recharged in any period t cannot exceed the water available for recharge , which is derived from a reoperation of Folsom Reservoir to provide additional water during November through March each year. The reoperation is performed by maximizing reservoir releases during the aforereferenced months while maintaining expected levels of service for flood control, water supply and hydropower generation . The levels of service are maintained with a set of optimization constraints that include downstream requirements for minimum environmental flows and water supply as well as the reservoir operation rule curve. The analysis is based on a perfect foresight formulation which provides an upper bound for recharge water available from the reservoir. A static upper bound on the volume of water recharged at a particular location , is based on local infiltration capacity and field berm height through an analytical ponding and drainage model described in the Appendix. Equations and dynamically constrain the magnitude of recharge decisions as a result of a cap on groundwater elevation to avoid water-logging of soil. This constraint is tied to the buildup and redistribution of recharged water as a result of groundwater flow and is described further in the Appendix.
Negative recharge decisions are prevented with Eq. .Cropland area use for recharge as a function of funding is presented in Fig. 10a,b. These are the results of parametric analysis using Eq. . Differences between the results for hydroeconomic analyses and the reference curves occur because, as indicated by the curves for individual crop categories , some of the more expensive land is brought into use before all of the least expensive land has been used. This result is driven by variation in infiltration rate across the study area which is controlled by the shallow geology and the interconnectedness of high conductivity sediments at depth used in the ponding model of Eq. . Figure 11 shows the spatial distribution of land use for two different levels of funding. For low amounts of funding, land is brought into use where there is a combination of cheaper land and higher infiltration rates in an effort to maximize the product of decision variables RA and D. This observation is consistent with the steep slope of recharge volume as a function of funding for land use at low funding levels . Spatial distribution of the recharge water cumulative depth per year is presented for the maximum funding and land use in Fig. 13. The values are generally within a reasonable range based on currently available information on crop inundation tolerance; however, large plastic planting pots constraints could be added to control cumulative water application as necessary. Figure 14 indicates the increase in groundwater storage from recharge using all of the cropland . Recharging over the 20-year planning period used 36% of the WAR . Simulation of the optimal recharge scenario with the groundwater model indicates the most of the water remains in the groundwater system ; however, appreciable amounts exit to surface water or flow across sub-basin boundaries . Additionally,the recharge provides enough base flow to support flow in the Cosumnes River throughout the 20-year simulation except during a 5-year drought from 1987 through 1992. Table 2 presents results for a range of recharge funding levels. Volumes discharging to surface-water and flowing to other sub-basins increase with the volume recharged since head buildup from adding water to the system is more pronounced. Comparison of the recharge volume results from the hydroeconomic analysis for cost set No. 1 with reference curves from the initial capture analysis indicates the effect of including study area hydrogeology in the analysis . High infiltration rate sites are selected preferentially, even when the amount of recharge area is limited by funding, and plot on the left side of the hydro-economic curve. These sites drain quickly and the results plot above the reference curves . Only few such sites are within the footprint of the cropland and, when greater amounts of land are used for recharge, the additional sites drain slower and plot below one or both of the reference curves. The result is a recharge capture curve for the study area that is shallower in slope than the reference curves. Therefore, the spatial variability in infiltration rate magnifies the diminishing returns to scale already occurring as a results of the temporal variability of the water source. More recharge could be achieved, and the study area capture curve moved higher on the plot, if the berm heights around the cropland were increased.
The linear programming results obtained can help develop guidance on where such capital investment might be most valuable. Reformulating the Lagrange multiplier for Eq. in terms of the berm height indicates where and how much additional water could be recharged over the planning horizon if berms were raised from 1–2 ft . This result provides a high estimate of what might be possible since some perennial crops may be unable to accommodate the increased ponding depth; nevertheless, this information provides guidance for where efforts might be best spent increasing berm heights. The values for Lagrange multipliers based on increasing berm height by 1 ft are low in the northern portion of the study area because little cropland is present . Given the high infiltration rates of the deeper geology in the north , recharge potential would be much better for a gravel pit since it would provide additional land area and also penetrate the low hydraulic conductivity soil layer included in this analysis. Cropland present in one of the northern model elements with high-infiltration rate was used to simulate the potential effect of repurposing a gravel pit for recharge. A total of 570 ac in crop categories 2, 3 and 4 were used to simulate gravel pits by increasing the hydraulic conductivity of the soil layer to match the underlying geology and increasing the berm height to 20 ft . Figure 16a,b summarizes the results of gravel pit simulation at the maximum annual funding level. Recharging over the 20-year planning period uses 50% of the WAR . Most of the water remains in the groundwater system with amounts similar to the previously presented results exiting to surface-water and flowing across sub-basin boundaries . Allocation is skewed towards the gravel pits and provides enough base flow to support continuous flow in the Cosumnes River throughout the 20-year simulation including during the previously mentioned 5-year drought. This approach could entail representing cropland managers as individual profit maximizing agents along with the groundwater management agency charging fees for groundwater pumping and providing rebates for recharge. This approach would relax the assumption of uniform land use rents for each crop category and include a more likely dispersion of land use costs across the study area. It is unclear if the aggregate effect of net metering with modest pumping fees would significantly differ from the work presented here since the influence on rational profit maximizers of a net rebate, rather than a payment for using land for recharge, may be similar. However, the effect of net metering combined with a cash flow constraint applied to water management operations could impose limits on a program for improving groundwater system conditions. Given the regulatory requirement for improved groundwater system state, these changes could drive pumping fees higher and influence the behaviors of profit maximizing land managers. It may also be possible to explore improving groundwater conditions through water banking operations where capital investments and operations costs would be paid by a client, or clients, external to the sub-basins. Management policy questions would include: how much water would be left in-place to benefit the groundwater system and the longevity of withdrawal rights . Details of the policy decisions would likely have implications for the amount of infrastructure investment a water banking client might be willing to make. Either the cash flow or water banking approach might be modified to encourage recharge in areas where it is most needed.