The aquifer response to pumping is simulated using the Theis analytical solution for the transient aquifer pressure response due to a pumping well (Eq. ). In order to use the Theis solution, permeability values (k in m² units) are converted to hydraulic conductivity (K) using assumed values of water density (ρ), gravitational acceleration (g in m s⁻²), and dynamic viscosity (μ) at 20 °C (Eq. ). 1K=k⋅ρ⋅gμ=10log(k)×107[ms-1] Saturated thickness (b) is defined by the difference between well depth and water depth in the time step being modeled, b=hwell(t)-hwater(t), and aquifer transmissivity (T in m² s⁻¹ units) is calculated as a product of hydraulic conductivity and saturated thickness (T=Kb). (Note that the definition of b may be slightly different from the conventional definition used for confined aquifers (depth from the water table to the bottom of the confining unit).) Aquifer transmissivity and storativity along with well pumping rate are used in the analytical Theis solution to calculate drawdown in Eq. (), which assumes homogeneous, isotropic aquifer properties (storage, hydraulic conductivity, and saturated thickness). Laterally, we assume no-flow boundaries between grid cells. Groundwater head recovery during the non-pumping period was not simulated – e.g., by using superposition in time to represent recovery by simulating an equivalent injection rate after 100 d. We assume that the cone of depression around each well created during the 100 d of pumping mostly re-equilibrates to an initial, horizontal state (minus the volume depleted) during the non-pumping period of the year (265 d of no pumping), which is a reasonable assumption given the 100 d pumping period considered in this study (see more details in the Supplement). The Theis approach, as presented in Eq. (), describes the pressure response to pumping at any time since pumping began and at any distance from the pumping location. 2s=Q4πTW(u), where s is drawdown (m), Q is well pumping rate or well yield (m³ s⁻¹), T is the aquifer transmissivity (m2s-1), and W(u) is the well function. The well function W(u) in the analytical solution of Theis Eq. () is an exponential integral Ei and for small values of u can be approximated by the infinite series in Eq. (). 3W(u)=-0.5772-ln⁡(u)+u-u22⋅2!+u33⋅3!-⋯, where u is defined by Eq. (). 4u=r2S4Tt, where r is the radial distance from pumping source (m), S is aquifer storativity assumed to be equal to aquifer porosity in this study (–), T is aquifer transmissivity (m2s-1), and t is the time since pumping started. Uniform length and time units must be used for Theis Eqs. () and () for u. The value of W(u) in Superwell is determined using a conditional statement based on the u value. For very large u values, representing either early time or large r, the well function is set to zero W(u)=0; for intermediate values of u, the well function is determined from a lookup table u:W(u) whose values are sourced from ; and for small values of u, W(u) is approximated by the first four terms of Eq. ().

A radial distance of 0.28 m, representing negligible well diameter, is used to determine transient drawdown at the well head that is used for determining the pumping cost and pumping rate feasibility. Drawdown is calculated at 10 d increments, and the average drawdown over the 100 d period is used for pumping cost calculations. To account for the well interference of adjacent wells on the drawdown of a central well, we calculate the distance to adjacent wells (radjacent) using the well area of the central well (Awell) in Eq. () and determine the additional drawdown they contribute. 5radjacent=2×r=2×Awellπ Drawdown for adjacent wells (sadjacent) is calculated at radjacent, and then additional drawdown due to adjacent wells is added to the drawdown of the pumping well (stotal=swell+6⋅sadjacent) to account for the additional drawdown due to well interference. The user can specify the number of adjacent wells – i.e., four wells indicate square packing and six wells indicate circular packing; the results here assume circular packing of wells. Notably, the range of well spacings, pumping rates, and the pumping period of 100 d result in marginal additional drawdown but are accounted for completeness. Thus, the total pumping lift (hlift in Eq. ) used for calculating the energy cost of pumping is the sum of the average drawdown at the well (swell), the additional drawdown from the nearest wells, and the depth to water (hwater) before pumping starts. 6hlift=swell+6⋅sadjacent+hwater A notable limitation of the Theis analytical solution is the assumption that saturated thickness remains constant during pumping, which is only applicable to confined aquifers. For our application, we represent pumping in unconfined aquifers (also called phreatic) where the saturated thickness changes in response to pumping. The Jacob approximation provides a means to use the Theis result to calculate the equivalent drawdown in an unconfined aquifer (Eq. ). 7sc=su-su22b⇒-su22b+su-sc=0⇒su=b±b1-2scb, where su is the drawdown in the unconfined aquifer (in this case the drawdown at the well with interference), sc is the drawdown in a confined aquifer from Eq. (), and b is the saturated thickness. Drawdown in unconfined aquifers (su) can be calculated by solving the quadratic equation su=-beq±beq2-4ac2a, where a=-1/(2b), beq=1, and c=-sc from Eq. (). Superwell first calculates the drawdown for a confined aquifer and then converts it to an equivalent drawdown for an unconfined aquifer using Eq. ().

Pumping during each annual period is simulated as 100 d of pumping in each year, similar to , followed by 265 d of recovery. The choice of a constant pumping period followed by an off period was a compromise between approximating representative well operations, computational efficiency, and reasonable annual total groundwater production volumes per well. Groundwater wells are seldom operated continuously on long yearly scales. Instead, wells are used intermittently to provide supply to end uses such as irrigation, industrial operations, or municipal water supply. Since groundwater is predominantly used for agriculture, 100 d periods reasonably approximate the seasonality associated with crop production, while also producing reasonable unit cost estimates for other applications such as industrial or municipal use. Besides being unrealistic, constant pumping could also underestimate unit costs as the total pumped volume to well cost ratio would be inflated by year-round operation.

Recharge rates are important in determining pumping requirements and groundwater storage levels for a region. We take gridded long-term annual averaged recharge rates from and , regrid them to match Superwell's grid using an area-weighted approach, and adjust the ponded depth targets and depth to groundwater based on recharge rates. We implement the effect of recharge in two ways: (1) to incorporate the response in shallow subsurface that potentially reduces the pumping requirement (currently set to 20 % of total recharge) and (2) in deep storage that increases groundwater stocks on longer timescales to potentially reduce depth to groundwater. The relative contribution to shallower parts compared to deeper parts of the aquifer can be controlled by the user, where recharge rates determine the magnitudes of ponded depth target reduction and depth to groundwater reduction. User-controlled checks have been put in place to prevent fully eliminating the ponded depth target from shallow recharge contributions (such as a threshold depth ratio of 0.75, making the ponded depth target never fall below 75 % of its original value due to shallow recharge adjustment). Although never activated in the current default settings, the processing also allows passing on “leftover” shallow recharge (not used to reduce ponded depth target) to deep groundwater storage to maintain recharge accounting. However, recharge contributions to deep parts of the aquifer do not exceed annual pumping volumes (avoiding groundwater accumulation) to ensure cost accounting for each simulated grid cell. Including recharge dynamics into Superwell enables accounting for the impacts of varying contributions to groundwater from the surface on pumping dynamics and cost accounting, including under alternative climate change impact scenarios. Varying sub-annual, gridded groundwater costs under climate impacts, as enabled by the incorporation of recharge components (that alter the pumping requirements and deep aquifer storage level), could be a valuable resource for hydro-economic models and studies exploring groundwater's role in enabling water and food security globally.

Well pumping rate and recharge-adjusted ponded depth target determine the well area, which has important unit cost implications. Well area, in combination with grid cell area, determines the number of wells in a grid cell and the subsequent capital and maintenance cost requirements which share a significant portion of total and unit costs of supplying groundwater (Fig. ). The initial pumping rate is determined from a range of candidate pumping rates spanning from 10 to 1500 gallons per minute (or 0.00063 to 0.09463 m³ s⁻¹). The upper bound is informed by the typical upper range for irrigation wells , while the lower bound represents a practical lower end for irrigation and other applications, beyond which very high, uneconomical unit costs were observed. The range of candidate pumping rates is used to perform an iterative evaluation of all candidate rates whenever the well pumping rate needs to be determined. This evaluation happens both during the selection of an initial pumping rate in the first year of the pumping phase and when the pumping rate needs to be reduced to prevent well dewatering, if the current pumping rate exceeds the aquifer capacity.

Wells are installed under an assumption to have high but reasonably sustainable pumping rates. Here, sustainable means that the initial pumping rate will be viable for more than just a few years. Candidate pumping rates are screened by simulating drawdown for 2 years of constant pumping. Total drawdown and drawdown fractions (ratio of drawdown to screened aquifer saturated thickness) are then calculated at t=2 years for all candidate pumping rates. A hard limit of 80 m is used for the absolute drawdown, and 0.4 is used for the maximum drawdown fraction that limits the drawdown to 40 % of saturated aquifer thickness. Pumping rates must satisfy both drawdown criteria to be considered viable. The largest viable pumping rate is used to establish the initial pumping rate which drives pumping over years until it can no longer satisfy the drawdown criteria. A new viable pumping rate is determined in subsequent years when the pumping rate needs to be reduced due to aquifer depletion. The reduced pumping rate also reduces the well area, which in turn adds more wells in the same grid cell. This increases infrastructure costs due to installation of new wells while reducing energy costs per well due to the reduced pumping rate. The pumping phase terminates if the lowest pumping rate is not viable.

One of the key contributions of Superwell is tracking energy and non-energy costs of pumping groundwater emerging from well characteristics and volumes pumped under hydrogeological controls. These controls include grid-specific hydrogeological conditions, aquifer properties, well hydraulics, and decision constraints of pumping regimes that emerge from user-defined pumping scenarios. This section describes energy, capital, and maintenance cost calculations, along with unit cost calculation under model controls, constraints, and scenarios.

The cost phase uses well attributes and pumping phase outputs to calculate the total cost of groundwater extraction and eventually the unit costs of pumping. The total cost for each year of pumping is the sum of the annual energy, capital, and maintenance costs (Eq. ): 8Ctotal,yr=Cenergy,yr+Ccapital,yr+Cmaintenance,yr. Pumping cost (Eq. ) is defined by the total energy (kilowatt hours, kW h) required to pump the annual volume of groundwater from a grid cell multiplied by the country-specific energy cost rate for electricity (er, USD 2016 kW h⁻¹) sourced from . 9Cenergy,yr=Energyyr⋅er,country The energy required to pump groundwater is calculated using Eq. (). 10Energyyr=ρw⋅Hyr⋅Qyr⋅tpumping1000η, where ρw is the specific weight of water (assumed to be 9800 kg m⁻³); Hyr is the distance (m) that water has to be lifted during pumping in a given year and is the sum of the water depth (hwater,yr) plus the average total corrected drawdown (savg,yr); Qyr is the pumping rate in the given year; tpumping is the 100 d pumping period in hours (2400 h); and η is the well efficiency, assumed to be 0.7.

Capital cost associated with the installation of the well is represented by an amortization-based cost accounting approach that estimates annual payments on a loan issued over the well lifetime using Eq. (). 11Ccapital=Cinstall(1+i)n×i(1+i)n-1, where i is the interest rate on the loan assumed to be 0.1, n is the loan duration currently equal to the well lifetime to distribute loan payments over the lifetime of a well, and Cinstall is the installation cost defined by Eq. (). 12Cinstall,yr=cu,aquiferClass⋅hwell,yr, where well unit cost (cu,aquiferClass, USD m⁻¹) is a function of the WHYMAP aquifer classification and the hwell,yr is the well depth in a given year. The well unit cost has three values reflecting costs of installing a well in easy (USD 50 m⁻¹), normal (USD 82 m⁻¹), and complex (USD 164 m⁻¹) aquifers. Well depth unit costs are sourced from . Annual maintenance costs are calculated based on the current installation cost (i.e., well depth) with an annual assumed fraction of 7 % (Cmaintenance,yr=0.07⋅Cinstall,yr) to represent increasing maintenance costs for deeper wells. A few examples of maintenance costs are pump maintenance or replacement, flushing of fines from the well to maintain pumping capacity, and descaling of precipitates from the well screen .

Additional steps are required to calculate the evolution of annual infrastructure costs when wells are deepened or their pumping rates are reduced to prevent violation of the drawdown thresholds (Sect. ). The cost phase tracks annual costs associated with wells as they are added and deepened. Increased costs from deepening wells are represented by an amortized loan over the well lifetime (20 years) for the additional depth added. During the time step of deepening, these costs are added to the next n years, currently set to a well lifetime of 20 years. If the well pumping rate must be reduced to prevent exceedance of the drawdown limit, the number of wells in the grid cell is increased to compensate for the reduced production per well. The cost array tracks each new addition of wells from their own reference time, and those wells are replaced at the end of each well's lifetime (n) interval. If they are deepened, the additional cost is applied as a loan for that specific group of wells over the lifetime of the well.

Unit costs are calculated to express the economic burden of groundwater extraction capacity by taking into account both extraction volumes and their associated costs. Unit cost of pumping groundwater is the ratio of the total cost incurred for pumping groundwater and the total volume pumped within a grid cell in each year. Total costs of pumping from a well (Ctotal,yr) is multiplied by the number of wells in a grid cell (nwells) to obtain total annual costs of pumping groundwater from all wells within a grid cell for each pumping year (CGW,yr). This is shown in Eq. (). 13CGW,yr=Ctotal,yr⋅nwells,yr The number of wells is determined by the area of the grid cell divided by the area served by one well (nwells=Agrid/Awell), where area served by a well is estimated by well yield (Q), pumping duration in a year (pumping days converted to seconds), and ponded depth target (dp) as shown in Eq. . 14Awell=Q⋅tpumpingdp,target The total volume pumped by each well is based on the annual well yield multiplied by the duration of pumping in a year (number of pumping days in a year). The total volume pumped by all wells is then the product of the volume pumped per well and the number of wells. 15Vpumped,yr=Q⋅tpumping,yr⋅nwells,yr The unit cost of producing groundwater is a key attribute of cost curves. Unit cost (cunit) is calculated as a fraction of total cost incurred by pumping groundwater and total volume pumped within a grid cell in each year as shown in Eq. (). 16cunit=CGW,yrVpumped,yr The unit cost relation in Eq. () is also applicable to other spatial and temporal scales; for example, unit costs could also be calculated for basins on a decadal pumping scale. Superwell currently calculates unit costs on a finer resolution (annually for each 0.5° grid cell), which could be upscaled later in post-processing using the spatial mappings (grid, basin, country, region, continent) provided with the model.

Figure a highlights the relationship between aquifer properties and well yield (also referred to as pumping rate). Hydraulic conductivity (K) and transmissivity (T) exhibit a direct relation with well yield, confirming that aquifers with both higher hydraulic conductivity and greater saturated thickness can support higher pumping rates, agreeing with well theory . As noted by the Theis Eq. (), transmissivity and storativity (reflective of porosity) determine the drawdown response of a well at a given pumping rate. Consequently, when storativity remains constant, aquifers characterized by higher saturated thickness and hydraulic conductivity can support higher pumping rates compared to thinner and lower-conductivity aquifers.

Well yield and well area have a direct relationship in Superwell varied by annual pumping requirement as a result of varying ponded depth targets due to recharge (Fig. b). This relationship implies that as the well yield decreases, well area decreases, with smaller well areas for larger ponded depth targets. Reduced well yield results in an increase in number of wells in a grid cell and an increase in unit capital cost due to the need for more wells. Note that well yield and well area are variable and subject to change over time due to aquifer depletion or management strategies that aim to reduce depletion. As aquifer storage declines due to pumping (i.e., depletion), well yield is adjusted accordingly to meet the dynamic conditions and well area is adjusted to achieve the net ponded depth target.

Figure c shows a relation between transmissivity (T=Kb) and Jacob-corrected drawdown for unconfined aquifers at the well head for a range of well yields. This figure reinforces the relation in Fig. a that higher transmissivity allows for higher well yields and vice versa. Further, as transmissivity decreases over time due to a reduction in aquifer saturated thickness, the drawdown for a given well yield increases as lower transmissivity results in more drawdown near the well to extract the same quantity of water. This explains the indirect and nonlinear relation between decreasing transmissivity and increasing drawdown. Figure c also reflects our assumption that drawdown cannot exceed the absolute drawdown threshold of 80 m. Notably, the screening process of selecting viable well yield is designed to select initial drawdowns closer to the upper limit of 80 m or 40 % of initial saturated thickness to maximize well yields initially. The fractional drawdown limit of 40 % means some locations could become non-viable with drawdowns below the 80 m absolute drawdown limit if the drawdown of those wells under the lowest pumping rate of 0.00063 m³ s⁻¹ is more than 40 % of the aquifer's current saturated thickness.

Unit costs (USD m⁻³) are observed to be higher at lower well yields and greater water depths (Fig. d). Non-energy costs per unit groundwater pumped are higher for wells that produce less volume, resulting in changes to observed unit costs. For example, for two wells of the same depth (i.e., having identical non-energy costs per well) in aquifers that support different well yields, the well in the lower capacity aquifer would have a higher unit cost because the non-energy cost per unit groundwater pumped would be higher. At the grid cell scale, lower yield wells also have smaller areas served (Fig. b), which results in a greater number of wells (and thus higher non-energy cost). Larger water depths also increase unit costs and total cost per well due to the higher energy costs needed to lift a unit of groundwater.

Assuming the number of wells remains constant, larger water depths require more energy to extract a certain volume of groundwater, leading to higher annual energy costs per well (Fig. e). Higher well yields also result in higher energy costs per well as more volume is extracted over the annual pumping period. Both of these relationships, as shown in Fig. e, can be explained by Eq. ().

Figure f shows that non-energy costs (capital and maintenance) are dependent on well depth and aquifer class, which represent the ease of installing a well and its associated costs. The interest rate for amortization of installation costs, maintenance costs, and well lifetime affect the non-energy costs but are kept fixed for this documentation. This panel also shows increasing non-energy costs with increasing well length (where the “tuning-fork” like separation is due to the well-deepening feature of the model). The deepest wells in the most complex hydrogeological conditions have the highest non-energy costs.

The challenge in building global groundwater extraction unit cost curves is partly attributed to characterizing aquifers that are economically, hydrogeologically, and environmentally feasible for production. Before showcasing Superwell results about groundwater extraction and associated costs, our processing of input datasets suggests that 5.22×106 km³ of groundwater is initially available in storage globally. Here, available groundwater, estimated using Eq. (), refers to the amount of water present in storage, not necessarily what is feasible or practical to produce. Estimating the initial groundwater availability aids in setting an absolute upper bound to the volume available for pumping in each grid cell. Figure  shows this availability expressed as ponded depth by normalizing available volume with grid cell area (Vavailable/Agrid). This normalization removes the influence of grid cell area on the volume calculation and shows groundwater availability as if it was extracted and pooled on the land surface directly above storage. 17Vavailable=∑i∈E(b⋅Agrid⋅ϕ)i⟹dp=Vavailable/Agrid, where Vavailable is the global available groundwater volume (m³), i is each grid cell in all grid cells E, b is saturated thickness (aquifer thickness - depth to water, m), Agrid is areal extent of grid cell (m²), ϕ is porosity, and dp is the ponded depth of groundwater (m).

The initial groundwater availability exhibits considerable spatial heterogeneity stemming from the underlying hydrogeological properties. The ponded depth of available groundwater in Fig.  shows that regions with thick aquifers and high porosity (Fig. ) are associated with higher groundwater availability. Higher ponded depths are observed across a wide range of hydroclimates spanning from tropical (Amazon) to arid regions (Sahara, central Australia), suggesting a stronger hydrogeologic control than climate on total groundwater in storage. Similarly, regions with low ponded depths do not strictly coincide with arid regions. For example, the Congo and southern India show low storage despite having high annual precipitation. Instead, low storage is more closely associated with thinner aquifers with low porosity.

Estimates of total groundwater storage are highly uncertain due to lack of hydrogeological data at a global scale , with quantifications varying by over an order of magnitude (1 to 60×106 km³) depending on the methodology followed ; see Table . While our estimate falls within the range noted in the literature, it is highly conditional on the input datasets described earlier. Despite uncertain estimates of aquifer properties and global groundwater availability, calculating available groundwater from the best-available data sources still offers some value. In the absence of such an estimate, modelers of integrated water–energy–land dynamics would have no credible means to limit groundwater depletion from storage .

Across the six scenarios modeled in this study, Superwell delineates mean pumped groundwater at 0.7×106 km³ globally (ranging between 0.13 and 1.2×106 km³). This amounts to a quantity of extractable volume that represents only 14 % of globally available groundwater (5.22×106 km³); see Table . This represents the upper bound of groundwater volume that could be pumped under constraining factors such as screening criteria, ponded depth target, depletion limit, pumping rate, and aquifer properties among other controls. Extractable volume is driven by constraining factors within each scenario and does not reflect actual demand-driven extraction in aquifers.

Well yield – or pumping rate – reflects grid-specific hydrogeological properties (Eq. ), impacts extractable groundwater volumes, and determines the energy costs per well and non-energy costs (number of wells) per grid cell which affect unit groundwater cost (Eq. ). Figure a shows optimized well yield averaged over the pumping duration of a cell. Optimization here implies the selection of maximum well yield that location-specific aquifer properties can support. The mapped results are presented as averaged well yield over the pumping duration because pumping rate can be reduced as a result of violating the drawdown criteria (see Sect.  for details). Most regions have well yields less than 2000 m³ d⁻¹ (367 gpm; Fig. a). Some cells were skipped due to screening criteria or their inherent aquifer properties that precluded viable pumping rates. These areas predominantly lie in high-altitude mountainous areas, boreal forests, and rainforests, as well as areas with rocky terrains, low saturated thickness, or low permeability.

Figure b shows global groundwater pumped volumes under the moderate-depletion (25 %) scenario at the end of the pumping period expressed as ponded depth. Incidentally, many regions currently experiencing water stress around the world coincide with regions showing high groundwater extraction (high availability) within the scenario's constraints . These areas include parts of aquifers in proximity to mountain ranges such as to the east of the Andes, certain pockets in Africa, central and south Asian river basins such as the Indus Basin, and central and western parts of Australia, among others. It is important to note that the extracted volumes of groundwater here only are reflective of the volumes that could be pumped considering aquifer properties, hydrogeological controls, and scenario design and not volume associated with actual historical multisector demand-driven consumption of groundwater.

The evolution of global groundwater pumping over time differs across scenarios mainly driven by defined recharge-adjusted ponded depth targets and depletion limit criteria. Figure c and d show how model scenarios influence temporal patterns of global groundwater production. Extractable groundwater becomes exhausted at comparatively steeper rates in initial years under scenarios with lower depletion limits due to some cells reaching exhaustion early in the simulation period. Alternatively, in scenarios with higher ponded depth targets, groundwater is pumped at proportionally higher rates, resulting in higher volumes pumped early on, which, in all cases, results in earlier termination of pumping compared to their lower ponded target counterparts.

Geophysical aspects contributing to energy costs are primarily packaged into the energy required for pumping groundwater from a certain depth at a certain rate over a defined period. Pumping energy required by a given well depends on the initial groundwater depth, the amount of drawdown at the well during pumping, and decline in water depth due to depletion caused by groundwater extraction (Eq. 10). This pumping energy, as shown in Fig.  for each grid cell globally in a moderate-depletion scenario, represents a culmination of various dynamics pertaining to well yield and unit lift (Eq. ) during the pumping phase of Superwell simulations and primarily drives the spatial variability in energy costs in a country.

Energy costs in Fig. a account for electricity as the energy source to pump groundwater, introducing an influence of variable electricity rates of each country (Fig. S24) on energy costs of groundwater pumping. Higher mean energy costs are observed in parts of North America, central Asia, and northern and southern extents of Europe, whereas some parts of Africa, South America, and Oceania have lower mean energy costs. As Superwell separately calculates the energy required to pump groundwater (kW h) before applying electricity rates (USD kW h⁻¹) from to calculate energy costs (USD), see Eq. (), there is flexibility to estimate costs for alternative energy sources for regions which may have different fuel mixes.

Non-energy costs are influenced by the aquifer class (Fig. S1), well depth (Fig. S19), and parameterization choices for accounting capital and maintenance costs over the well lifetime and loan period. Each of the components of non-energy costs are impacted by exogenous assumptions along with model dynamics. For instance, installation costs are highly influenced by the hydrogeological complexity of the aquifer and the well depth, capital costs are sensitive to the interest rate to account for cost incurred over the lifetime of a well, and maintenance costs are subject to maintenance cost factor (7 % in this version) to account for wear and tear on the pump and need for periodic cleaning or flushing of the well casing. High non-energy costs in regions such as parts of North America, Eurasia, eastern Africa, southwestern India, and southeastern parts of Australia correspond to areas with considerable hydrogeologic complexity and deeper wells incurring high capital and maintenance costs.

The evolution of costs over time, along with the evolution of volume pumped (as shown in Fig. ), is tracked for each grid cell in each pumping period (yearly in the version of ). Figure c shows global annual total costs per well averaged over all grid cells, and Fig. d shows total costs for one individual grid cell over model pumping years. The upward trend in capital, maintenance, and energy costs of pumping is attributed to a combination of factors. Specifically, the increasing depth of pumped groundwater, larger drawdown from pumping, increasing well depth, and variable aquifer thicknesses ceasing pumping over time as depletion limits are hit. The rapid decline in global average costs (Fig. c) after ≈200 years is due to grid cells going out of production, as can be seen in Fig. c (but note that Fig. c is normalized by number of wells).

The impact of model features pertaining to changing well characteristics over time (including well deepening, well replacement, and well addition) on the total cost of groundwater extraction is demonstrated using costs of a single grid cell in Fig. d. Capital and maintenance costs remain constant until well deepening, well replacement, or well addition happens. Energy costs rise over time as water table depth decreases due to depletion but temporarily drop when/if well deepening occurs, which increases aquifer transmissivity and reduces drawdown for the same pumping rate. Well deepening is used as a first preference when drawdown constraints are violated; the increase in capital and maintenance costs and a decrease in energy costs in year 16 represent the impact of well deepening. The cost of deepening is spread over the well lifetime (20 years in the version of ). The rise in costs in year 20 is due to wells being replaced upon reaching their pre-defined lifetime of 20 years. The period between year 20 and year 36 represents paying off the costs incurred due to both well replacement in year 20 and well deepening in year 16. Pumping rate is reduced as a second preference after violating the drawdown criteria. This occurs in year 48 because the deepening in year 16 extended the well to the full aquifer depth. The reduction in pumping rate results in addition of new wells (with smaller well areas) to compensate for the reduced annual production per well. The addition of wells causes non-energy costs to rise; however, energy costs drop because the reduced pumping rate results in less drawdown and less total lift for the pumps.

The unit cost of groundwater extraction, calculated as a ratio of the total cost of groundwater extraction and the total volume produced, offers crucial insights into the economic feasibility of groundwater production. Figure  shows the mean unit cost over the simulation duration. Hot spots of unit cost are widely distributed over the world, showcasing pronounced heterogeneity due to variability in total groundwater production and drivers of associated costs. Unit cost captures in a single metric the impacts of hydrogeological conditions and model constraints manifested through the production efficiency of aquifers along with physical and economic considerations of infrastructure required for pumping.

One of the key advantages of Superwell is to be able to define groundwater extractability at specific cost thresholds for each grid cell (Fig. b). In this example, the global median unit groundwater cost (USD 0.123 m⁻³) is used as the threshold to determine the pumped groundwater volume below the cost threshold at each grid cell. We find that groundwater produced under a global median unit cost of USD 0.123 m⁻³ amounts to 0.436×106 km³, representing only 8.3 % of the total available groundwater and 56.6 % of the total volume produced in a moderate-depletion scenario. As demonstrated by the patterns in Fig. b, Superwell can indicate regions where groundwater is more economical to extract or where it may be more expensive due to various factors, including but not limited to water depth, recharge, hydrogeological parameters, and energy cost of groundwater production. This illustrates the importance of local hydrogeology, pumping scenario, and energy cost in influencing the hydro-economic viability of groundwater production.

Complex human and Earth system interactions could be modeled in a class of models identified as integrated human–Earth system models, such as GCAM . Water supply in GCAM is determined from competing cost curves between renewable surface water , groundwater resources , and desalinated water. Each water basin in GCAM undergoes a water price interaction between nonrenewable groundwater (supplied by Superwell derived cost curves), renewable water, and desalinated water to incrementally withdraw water starting from the cheapest source of water. Each unit of water that is further withdrawn causes price increases to account for the potential costs of river rerouting, dam construction, or transportation of renewable water and the increased costs for extracting deep nonrenewable groundwater. As the price of water extraction increases, a resultant increase in price across end-use sectors occurs, decreasing the profitability of agricultural commodities and increasing the cost of non-agricultural water-demanding sectors (such as municipal water) which may cause production shifts to more economically and environmentally favorable conditions . Such interactions are possible in other modeling frameworks as well with appropriate integration of cost curves derived from Superwell.

In an initial pilot application, Superwell was integrated with a national-scale farm agent-based model of irrigation cropping decisions in the continental United States CONUS;. In the agent-based model, ≈50000 farm agents are deployed across the continental United States at 1/8° resolution (following the North American Land Data Assimilation System grid), with the farms considering irrigation water allocation decisions under changing hydrologic conditions. The farms are treated as profit-maximizing firms, determining cropped areas based on crop prices, production costs (including the costs of producing water for irrigation), crop irrigation needs, and irrigation water availability. The farm agents adopt a positive mathematical programming approach , calibrated to historical data of cropped areas, water availability conditions, and economic conditions. In the pilot application, the farm agent-based model is integrated with two hydrologic sub-models that capture surface water and groundwater availability and cost, with Superwell providing the latter capability.

To align with the spatial delineation of farm agents, Superwell is implemented at 1/8° resolution over the continental United States, with each grid cell assumed to represent an independent groundwater system. The coupled farm ABM–groundwater model abstracts an agricultural groundwater wellfield onto each grid cell, with individual wells uniformly dispersed over the grid cell following Superwell's methodology around designing well spacings that will accommodate sufficient pumping for agricultural needs. For each grid cell, Superwell is run prior to model integration, generating ≈50000 pre-processed groundwater cost curves.

The cost curves from Superwell in turn serve as a simple lookup table for each farm to track the evolution of groundwater costs and availability over time. In a coupled simulation, the model keeps track of cumulative groundwater production for each grid cell, with the associated point on the groundwater cost curves providing farm agents with the availability and cost of groundwater at that particular state. These inputs from the groundwater cost curves serve as inputs to the farm's cropping decision problem, with the unit cost of groundwater input as a production cost variable and the groundwater production capacity as a resource constraint in the agent's profit-maximization formulation. The Superwell approach serves as a compact and efficient simulator of groundwater cost and response for effective incorporation into the CONUS-scale agent-based model that allows for dynamic agent response to changing groundwater conditions, adding only trivial computational cost and software complexity to the integrated model design.