Non-renewable groundwater use and groundwater depletion: a review

Before providing definitions and concepts about groundwater per se, it is good to first define the different dimensions of human water use, as it is excessive water use that ultimately results in the depletion of groundwater resources. Water use is a general term that encompasses water demand, water withdrawal and consumptive water use (Döll et al 2012, De Graaf et al 2014).

Water demand is the water that is needed by a specific sector, e.g. domestic, agriculture or industry, to optimize its activities. Domestic demand contains water needed for drinking, cooking, toilet flushing, bathing and watering the garden. Agricultural water demand consists of irrigation water needed for crop growth and livestock feeds, and water directly needed for livestock, i.e. primarily drinking water. Industrial water demand consists of process water for manufacturing and cooling water needed to support production processes. Note that water demand for processing animal products is included in industrial water demand (see Flörke et al 2013). Often, water demand is separated into net water demand, i.e. the water demand that is actually needed, and gross water demand including losses. For instance, net water demand for irrigation would be the difference between potential crop transpiration and actual crop transpiration without irrigation. Gross water demand is then equal to net water demand plus the percolation and evaporation losses that occur during water transport and water application during irrigation.

Water withdrawal is the amount of water that is taken from surface water or groundwater to satisfy gross water demand. In case water availability is sufficient, water withdrawal is equal to gross water demand. In case water availability is not sufficient, water withdrawal is equal to water availability. In this case one has a water gap equal to gross water demand minus water availability. Note that in certain analyses (e.g. Yates et al 2005), recycling of water is taken into account (mostly in the industrial sector). In this case water withdrawal can also be smaller than gross demand as part of the demand is met from the recycled water. In addition, in some water scarce regions, deficit irrigation often takes place and water is supplied less than optimally leading to reduced gross water demand.

Consumptive water use is the amount of withdrawn water that is lost due to evaporation (including crop transpiration). The remaining part, i.e. water withdrawal minus consumptive water use, is called return flow to groundwater and/or surface water and is available for water use elsewhere but subject to water quality concerns or wastewater treatment in many cases. Note that even if water availability is sufficient, consumptive water use is not the same as net water demand because net water demand only includes the useful part of the evaporated water and not the evaporation losses due to e.g. transport.

In quite a few papers, including those written by the authors of this review, the terms fossil groundwater and non-renewable groundwater and depletion are used interchangeably, while they are not strictly the same. We will provide definitions here and illustrate these with some schematics. Table 1 summarizes the various definitions introduced. Similar definitions were given previously by Margat et al (2006, table 1 therein), Margat and Van der Gun (2013, section 4.6 therein), Gleeson et al (2015) and Jasechko et al (2017).

2.2.1. Fossil groundwater

The term 'fossil' in fossil groundwater pertains to groundwater of a certain age that surpasses human history. With 'age' we mean the time that has passed since a drop of groundwater has recharged, i.e. since a drop of water from rainfall or from river bed leakage has entered the groundwater body. The age at which groundwater is called 'fossil' is not strictly defined. We follow Jasechko et al (2017) who define all groundwater that pre-dates the beginning of the Holocene (approximately 12 000 years B.P.) as fossil. Gleeson et al (2015) further subdivide the non-fossil groundwater (younger than 12000 BP) into modern groundwater (younger than 50 years) and young groundwater (between fossil and modern). We will also follow this suggestion.

The occurrence of fossil groundwater greatly varies between groundwater systems. Figure 1 provides three schematic examples of groundwater systems showing lines of equal groundwater age, or isochrones. Figure 1(a) is an archetypical phreatic groundwater system with a free groundwater surface is present, called the water table. In case of a humid to semi-humid climate, i.e. long-term precipitation is larger than long-term potential evaporation, a hydrologically active groundwater body develops that drains to the surface water system. If the aquifer is homogeneous and isotropic, i.e. hydraulic conductivity is the same everywhere and independent of direction, then the isochrones are almost horizontal, except close to the surface water. In this case, a simple equation describing groundwater age as a function of depth can be derived (Ernst 1973, Broers 2004):

$$\begin{eqnarray}&&t=\displaystyle \frac{nD}{R}\,\mathrm{ln}\left(\displaystyle \frac{D}{D-z}\right).\end{eqnarray} \tag{ 1 }$$

With t groundwater age (years), n drainable porosity (−), R recharge (m yr⁻¹), D aquifer thickness (m) and z depth below water table (m). This shows that theoretically, very old and thus fossil groundwater is present even in this most elementary groundwater system, but only close to the bottom of the aquifer. Obviously, in reality aquifers are heterogeneous and anisotropic while recharge rates are generally not homogenously distributed across the surface. So, although groundwater age generally increases with depth, groundwater ages for a given depth may vary considerably.

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Figure 1(b) shows the same aquifer, but now in a semi-arid to arid climate, where long-term average precipitation is smaller than long-term potential evaporation. In this case, water tables are deeper and the aquifer is only occasionally recharged following short periods of heavy rainfall and from leaky streams. In such systems, groundwater reserves are relicts from times that recharge was much larger. Examples are the Nubian aquifer in Africa (Margat and Van der Gun 2013) that was last recharged during the African Humid Period between 15 and 5 ka BP (Claussen et al 2017). In this system, the groundwater age reflects the system with larger recharge of the past. Equation (1) still applies, but with D and z with respect to the palaeo-water table and the time since the termination of the humid period added. In case of the Nubian Aquifer, there is also evidence of alternating dry and wet periods over the last 200 ka (Castañeda et al 2009) and probably before as dating with krypton isotopes revealed groundwater ages of order 10⁶ years from samples taken at 1200 m depth from the Nubian aquifer system (Sturchio et al 2004).

Figure 1(c) provides an example of a confined aquifer system with a phreatic system on top. Confined aquifers can be recharged from humid areas where deeper permeable geological layers, e.g. sand stones, limestone, or unconsolidated gravelly or sandy deposits, are in contact with the surface. If these recharge areas are at topographically higher levels than the larger part of the aquifer, the groundwater is under pressure and will rise above the surface when punctured by a well (artesian well). The location of a groundwater sample from such an aquifer may well be several tenths to hundreds of km away from the recharge location, resulting in very old groundwater ages. An example is the Great Artesian Basin in Australia, where groundwater ages are found to vary between 20 Ka and 1.5 Ma based on chlorine 36 dating (Torgersen et al 1991). Note that the aquitard, i.e. the less permeable layer on top of the confined aquifer, may also be partly leaky, which would in the case of over pressure bring the fossil groundwater much closer to the surface where it will mix with the younger groundwater in the phreatic aquifer above. In fact, Jasechko et al (2017) showed that fossil groundwater, with an age of over 12 ka, is the dominant groundwater type below 200 m depth, for most aquifers around the world.

2.2.2. Non-renewable groundwater

2.2.3. Groundwater depletion

Following Margat et al (2006), we define groundwater depletion as the prolonged (multi-annual) withdrawal of groundwater from an aquifer in quantities exceeding average annual replenishment, leading to a persistent decline in groundwater levels and reduction of groundwater volumes. In case there is virtually no groundwater recharge occurring, non-renewable groundwater withdrawal leads to almost indefinite depletion and is also called groundwater mining (table 1). We note that this definition is a steady-state view on groundwater depletion. In reality, increased withdrawal in the dry growing season often causes large depletion rates, followed by partial recovery of the water table from subsequent recharge in the wet season. Also, multi-year variability in dry and wet years may cause periods of depletion to alternate with periods of recovery (Scanlon et al 2012a). In this case a fluctuation pattern of groundwater storage change is superimposed on a long-term declining trend. Our definition of groundwater depletion pertains to that long-term trend.

By definition, groundwater depletion can occur in aquifers with renewable and non-renewable groundwater resources (figure 2). Figure 2 (upper left) shows and example of groundwater withdrawal in a humid system with renewable groundwater. Some groundwater is first taken out of storage, creating a depression cone, but after a while all of the pumped groundwater consists of capturing recharge that would otherwise have ended up discharging to the stream (see also section 2.3). Groundwater withdrawal leads to (dynamically) stable groundwater levels and is therefore physically sustainable⁵ . If the well is not too deep, most of the groundwater that is pumped will be young groundwater. Figure 2 (upper right) shows an example of a phreatic aquifer in a semi-arid to semi-humid climate where pumping exceeds the long-year average recharge from streams and rainfall events. Here, groundwater can in principle be still renewable (if pumping stops, recovery could occur in a time scale of years to decades), but over-exploitation leads to depletion. In terms of age, the groundwater pumped will be young or modern. As the water table declines under persistent over-exploitation, the water pumped will become progressively older and be called fossil at some point. Figure 2 (lower left) shows the situation that non-renewable (and fossil) groundwater is pumped from a confined aquifer, but at rates that are smaller than the aquifer's recharge. If withdrawal from the aquifer exceeds recharge, groundwater is depleted (Figure 2 lower right).

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For deep confined aquifers with little to no surface water interaction (figures 1(b), 2 (lower rows)), the degree of groundwater depletion is only dependent on the balance between recharge and withdrawal. However, groundwater depletion of phreatic aquifers under humid to semi-humid conditions also depends on groundwater-surface water interaction. This fact is often neglected in studies (including the authors' first: Wada et al 2010), that wrongfully assume that the maximum allowable withdrawal rate that is physically sustainable is equal to groundwater recharge. This is called the 'water budget myth' by Bredehoeft (1997) and we refer to e.g. Sophocleous (1997), Alley and Leake (2004) and Zhou (2009) for critical comments on and reviews of the subject. In this section, we describe groundwater-surface water interaction and its consequences for physically sustainable groundwater withdrawal. In a classic paper, Theis (1940) explained the source of groundwater pumped and our explanation is based on his work and later explanations by e.g. Alley et al (1999), Bredehoeft (2002) and Konikow and Leake (2014).

Under pristine conditions we can divide the interactions between streamflow and groundwater into two main categories: gaining streams where groundwater discharge is contributing significantly to streamflow (figure 3(a)) and loosing streams where groundwater is replenished by infiltrating water from the stream which adds to the recharge from precipitation (figures 3(b) and (c)). The category 'loosing streams' can be sub-divided into two subcategories; connected losing streams (figure 3(b)), when the groundwater level and river bed are connected and infiltration rate varies with difference in groundwater and river levels, and disconnected losing streams (figure 3(c)), where the groundwater level is not connected to the river bed, and infiltration loss from the stream mainly depends on river level and quickly becomes constant at greater groundwater depths. This can be readily seen by calculating sensitivities of the infiltration flux to surface water and groundwater levels using Darcy's law in figures 3(b) and (c). Denoting I the infiltration flux, s the surface water level and h the groundwater level, it follows that in case of a connected stream (figure 3(b)) the infiltration flux is equally sensitive to s and h: $\tfrac{\partial I}{\partial s}=\,\tfrac{\partial I}{\partial h}$ ≡ constant, while in case of a disconnected stream we have (figure 3(c)): $\tfrac{\partial I}{\partial s}\propto \tfrac{1}{h}$ and $\tfrac{\partial I}{\partial h}\propto \tfrac{s}{{h}^{2}}.$

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Draining, connected losing and disconnected losing streams may occur simultaneously at different locations within one catchment, or at the same location at different times of the year. Gaining streams are dominant in (semi-)humid climates and wet periods, and in the lowest parts of a catchment where groundwater that infiltrated higher up in the catchment convergences to. Losing streams are typical for climates and periods when potential evaporation is large enough to evaporate most of the rainfall and for locations higher up in the catchment with very permeable soils. The start of groundwater withdrawal may reverse the flow of rivers from a gaining to a losing stream.

What happens to groundwater-streamflow dynamics under groundwater withdrawal is schematically depicted in figure 4. We start in figure 4(a) with the pristine situation of a gaining stream. Figures 4(b)–(d) show what happens under increasing withdrawal rates. These figures may pertain to one location where withdrawal rates are increasing over time, or multiple locations with similar hydrogeological setup with different withdrawal rates. Note that the following description is done from the perspective of constant meteorological forcing and withdrawal rates, which in reality of course will fluctuate over the years and between years. It thus provides a long-term average perspective on groundwater-surface water interaction.

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Figure 4(b) shows a withdrawal regime where the withdrawal rate (q₁) is limited. Just after withdrawal starts, the main source of water to a well comes out of groundwater storage of the aquifer. When time passes, the water table starts to develop a gradient towards the pumping well and part of the groundwater recharge, that otherwise would have supplied water to the stream, now contributes to the pumped water (figure 4(b.1)). Consequently, groundwater discharge (GD in figure 4) to the stream is reduced. Also, evapotranspiration (E in figure 4) from groundwater dependent vegetation will decrease due to falling groundwater levels. The deeper the water table, the larger the contribution of reduced groundwater discharge and reduced evaporation (together termed increased capture⁶ ) to pumped water becomes, until a new equilibrium is reached where all pumped water comes out of capture (see figure 4(b.2)) and groundwater levels stabilize. Thus, withdrawal rate q₁ is physically sustainable. Under limited withdrawal rates, groundwater discharge will remain positive and the stream remains a gaining one, albeit with lower streamflow.

If the withdrawal rate is higher than in figure 4(b) (q₂ figure 4(c)), groundwater level decline is larger, evaporation is further reduced, and groundwater discharge may shift to surface water infiltration making the stream a losing stream (figure 4(c.1)). However, as long as the groundwater level and river are connected, the contribution of recharge from the infiltrating river water increases with falling groundwater levels. Due to this negative feedback, a new equilibrium will be reached even under q₂, where all pumped water comes from captured recharge, streamflow infiltration and decreased evapotranspiration (figure 4(c.2)). Consequently, withdrawal rate q₂ is still physically sustainable.

If the withdrawal rate is even higher (q₃ figure 4(d)) and groundwater levels drop below the river bed, groundwater gets disconnected from the stream. This situation can be seen as a critical threshold, as the stream recharge rate remains almost constant when groundwater levels drop further (or more precisely, approaches a constant flux with declining groundwater levels). The negative feedback that limits water table decline in case of a connected stream is no longer present, which induces an acceleration of water table decline and successive reduction of evaporation. Moreover, if the withdrawal rate becomes higher than the maximum stream infiltration rate and the recharge over the depression cone (as often the case in areas with intensive groundwater dependent irrigation), the excess rate of withdrawal comes out of the aquifer storage. As a result, groundwater levels will continue to decline and groundwater storage is persistently being depleted (figure 4(d.2)).

To conclude, similar to evaporation where in a drying soil two stages of evaporation can be distinguished: an energy limited stage where evaporation remains more or less constant and a water limited stage where evaporation deceases in time with diminishing soil moisture a (Philip 1957, Richie 1972), we can also define two stages of groundwater withdrawal in phreatic aquifers: stage 1 (figures 4(b) and (c)) where groundwater is connected with the surface water system, groundwater depletion is limited, and groundwater withdrawal mostly diminishes streamflow and evaporation—one could further distinguish stage 1a and stage 1b by distinguishing gaining and loosing streams-, and stage 2 (figure 4(d)) where further withdrawal in excess of recharge and (constant) stream water infiltration mainly leads to groundwater depletion and does not further impact streamflow.

The actual response time for the water levels to reach a new equilibrium in stage 1 withdrawal depends on hydrogeological properties and dimensions of the aquifer and boundary conditions (river levels, distance well from the stream) and can sometimes be multiple decades (Konikow and Leake 2014). Given that groundwater withdrawal for irrigation often occurs in semi-arid areas with little to no precipitation surplus during the growing season (Wada et al 2010), stage 2 is prominent for these regions and progressive groundwater depletion is the rule. We also note that in many regions of the world groundwater is pumped from deeper (semi-)confined aquifers (De Graaf et al 2017, figure 1(c)). Under confined conditions groundwater-streamflow interaction only occurs for the larger rivers that are deep enough to penetrate the confining layer. Also, because storage coefficients of (semi-)confined aquifers are much smaller than the drainable porosity of phreatic aquifers, hydraulic head declines in (semi-)confined aquifers are often much larger than water table declines in phreatic aquifers.

Volume based methods directly estimate the change in stored groundwater volume over time. These methods are generally the most accurate, because they implicitly take account of increased capture that may occur during groundwater withdrawal (see section 2.3). Konikow (2011) provides global estimates of groundwater depletion based on a large number of regional estimates using volume-based methods. Examples of volume-based methods are:

3.1.1. Volume change estimates based on hydraulic head data

3.1.2. Volume change estimates based on remote sensing with Gravity Recovery and Climate Experiment (GRACE)

3.1.3. Volume change estimates based on (global) groundwater models

Water balance methods compute the groundwater withdrawal rates and compare these with recharge rates. In case withdrawal rates are larger than recharge, groundwater depletion is assumed to occur. The problem with water balance methods is that they typically include diffuse recharge from soils but ignore recharge from water bodies and streams (i.e. focused recharge). Also, they do not account for increased capture (see section 2.3) of streamflow and evaporation (Theis 1940, Konikow and Leake 2014). As recharge is difficult to measure and groundwater withdrawal rates are largely unknown, large-scale hydrological models often use water balance methods to assess groundwater depletion. Here, two methods are discussed, one using hydrological models and one using a combination of remote sensing information and models.

3.2.1. Depletion estimates based on (global) hydrological models

Many hydrological models have a loss term denoting recharge to (deeper) groundwater or they model groundwater as a simple reservoir with a storage-outflow relationship (e.g. Van Beek et al 2011). If groundwater withdrawal data are available, groundwater depletion is estimated by subtracting withdrawal rates from recharge rates and setting depletion equal to the difference if negative. In this case, return flow to groundwater from irrigation is added to recharge rates

$$\begin{eqnarray}&&\begin{array}{l}{\rm{d}}{\rm{e}}{\rm{p}}{\rm{l}}{\rm{e}}{\rm{t}}{\rm{i}}{\rm{o}}{\rm{n}}=\,{\rm{\min }}\left({\rm{r}}{\rm{e}}{\rm{c}}{\rm{h}}{\rm{a}}{\rm{r}}{\rm{g}}{\rm{e}}({\rm{n}}{\rm{a}}{\rm{t}}{\rm{u}}{\rm{r}}{\rm{a}}{\rm{l}}+{\rm{r}}{\rm{e}}{\rm{t}}{\rm{u}}{\rm{r}}{\rm{n}}\,{\rm{f}}{\rm{l}}{\rm{o}}{\rm{w}})\right.\\ \left.\,\,\,\,\,-\,{\rm{w}}{\rm{i}}{\rm{t}}{\rm{h}}{\rm{d}}{\rm{r}}{\rm{a}}{\rm{w}}{\rm{a}}{\rm{l}},0\right).\end{array}\end{eqnarray} \tag{ 2 }$$

The first global assessment of groundwater depletion using this method was published by Wada et al (2010) (figure 5(d)) using the global hydrological model PCR-GLOBWB (Van Beek et al 2011, Wada et al 2011). Assessments were made at 30 arc-minutes resolution, which required downscaling of country-based withdrawal data from IGRAC (www.igrac.net). This was done by calculating surface water availability and total gross water demand using PCR-GLOBWB and attributing country-based groundwater withdrawal proportional to the difference between gross water demand and surface water availability. As pointed out by Konikow (2011), this approach does not properly account for increased capture, leading to an over-estimation of groundwater depletion. Wada et al (2012a) acknowledged this by using a correction factor based on the volume-based estimates collected by Konikow (2011). In later work (De Graaf et al 2014, Döll et al 2014) groundwater depletion was calculated with water use schemes that explicitly included surface-groundwater interaction and return flows leading to lower estimates of global groundwater depletion than reported by Wada et al (2010).

3.2.2. Based on remote sensing of fluxes (+ models)

One of the effects of groundwater depletion is land subsidence (Galloway and Burbey 2011). It is caused by decreased pore pressure as a result of head decline and subsequent consolidation of (mostly) soft sediments, such as can be found in deltas, valley fills, floodplains and former lake beds. Examples of land subsidence as a result of groundwater withdrawal can be found in e.g. Mexico City (Ortega-Guerrero et al 1999), California (Amos et al 2014), China (Chai et al 2004), the Mekong Delta (Minderhoud et al 2017), Iran (Motagh et al 2008) and Jakarta (Hay-Man Ng et al 2012). Estimates of land subsidence rates use geodetic methods. Traditionally this has been surveying, but lately remote sensing methods such as GPS, airborne and space borne radar and lidar are frequently applied. Also, a number of studies mentioned use a combination of geomechanical modelling (e.g. Ortega-Guerrero et al 1999, Minderhoud et al 2017) and geodetic data to explain the main drivers of land subsidence. Mostly these have been combined in a forward approach, whereby a geomechanical model is driven with known groundwater head declines or withdrawal rates and validated with the geodetic data. A few papers (e.g. Zhang and Burbey 2016) use a geomechanical model together with a withdrawal data and geodetic observations to estimate hydraulic and geomechanical subsoil properties. However, there are no studies known to us that attempt to reconstruct groundwater depletion itself from inverse modelling of land subsidence. This would however be an interesting new and possibly accurate way to estimate groundwater depletion rates at high relative resolution and large spatial extent. Figure 4(f) shows an example of modelled and observed head declines from Minderhoud et al (2017).

Thus far, at the global scale, several studies have attempted to estimate groundwater withdrawal based on two different approaches: country reporting/inventories and modelling.

4.1.1. Country reporting and inventories

4.1.2. Hydrological modelling

As explained in section 3, global estimates of groundwater depletion can be divided into water balance methods and volume-based methods.

4.2.1. Water balance methods

Global estimates of groundwater depletion are mostly limited to water balance methods (Wada 2016). Postel (1999) provides one of the earliest estimates of 200 km³ yr⁻¹ (contemporary), which is based on extrapolated country statistics. Most water balance methods however rely on global hydrological models (Bierkens 2015). Earlier model studies (e.g. Vörösmarty et al 2005, Rost et al 2008, Hanasaki et al 2010, Wisser et al 2010, Pokhrel et al 2012a, 2012b, Yoshikawa et al 2014) used the difference between human water demand of agriculture, industry and households and surface water availability as a proxy for 'non-renewable or non-local water resources', resulting in estimates ranging from 400 to 1700 km³ yr⁻¹ (around year 2000). Here, it is important to note that 'non-renewable or non-local water resources' are not further specified and may consist of a combination of non-renewable groundwater withdrawal, water diversion and desalinated water. As a result, these estimates vary substantially between studies.

The first model-based global estimate of groundwater depletion was produced by Wada et al (2010). They reported that global groundwater depletion increased from 126 (±32) to 283 (±40) km³ yr⁻¹ from 1960 to 2000. The analysis was limited to sub‐humid to arid climate zones to avoid overestimation arising from increased capture of discharge and enhanced recharge due to groundwater withdrawal (Bredehoeft 2002). Later, Wada et al (2012a, 2012b) applied a correction factor to constrain the original groundwater depletion estimate (Wada et al 2010) by regionally reported numbers, producing a 30% lower estimate (204 ± 30 km³ yr⁻¹). Döll et al (2014) combined hydrological modelling with information from well observations and GRACE satellites, and simulated focused groundwater recharge from surface water bodies in dry regions, while Wada et al (2010, 2012a, 2012b) included only diffuse recharge. Moreover, Döll et al (2014) applied a deficit irrigation scheme (assuming an irrigation gift of 70% of the maximum water requirements) to constrain their agricultural water withdrawal and estimated global groundwater depletion to be 113 km³ yr⁻¹ (average of 2000–2009). Pokhrel et al (2015) used an integrated hydrologic model, which explicitly simulates groundwater dynamics and withdrawal within a global land surface model, and estimated a global groundwater depletion of 330 km³ yr⁻¹ (year 2000). The most recent study by Hanasaki et al (2018) estimated a non-renewable groundwater withdrawal of 182 (±26) km³ yr⁻¹ (year 2000). Although global estimates are quite different between these studies, the regional hotspots of groundwater depletion are quite consistent with those found by Wada et al (2010): California's Central Valley and the High Plains aquifer in the United States, the North China Plain, western India and a part of eastern Pakistan, central Mexico, Iran and the Middle East. We refer to table 3 and figure 6 for a more extensive overview of global estimates.

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Water balance methods are subject to considerable uncertainty owing to errors in biophysical, climate and socio-economic inputs and parameters of the global hydrological models used, as well as ignoring increased capture from simplified assumptions about groundwater-surface interaction (see section 2.3). Of particular interest, next to the uncertainty about global groundwater withdrawal, are the resulting large uncertainties in simulated global groundwater recharge, especially since observed recharge rates are rarely available at the scale used in global hydrological models. Natural replenishment of groundwater occurs predominantly from precipitation (i.e. diffuse recharge) and from surface water bodies such as ephemeral streams, wetlands or lakes (Scanlon et al 2006, Crosbie et al 2012, Taylor et al 2013). Modelled global estimates of diffuse recharge range from 11 000 to 17 000 km³ yr⁻¹, equivalent to 30%–40% of the world's renewable freshwater resources (IGRAC GGIS, Döll and Fiedler 2008, Wada et al 2010, Wada and Heinrich 2013, De Graaf et al 2014, 2017, Hanasaki et al 2018). These modelled global recharge fluxes tend not to include focused recharge, which can be substantial in semi-arid environments, while preferential flow processes and the profound seasonality of recharge are equally underrepresented. Isotopes may be one way of improving recharge concepts uses in global hydrological models (Jasechko et al 2014). Wada and Heinrich (2013) estimated additional recharge from irrigation to be 500 km³ yr⁻¹ globally, which is less than 5% of the global diffuse recharge, but can be substantial over arid environments.

4.2.2. Volume-based methods

As excessive groundwater withdrawal and associated depletion are highly localized, regionally parameterized and calibrated groundwater flow models (volume based methods) generally provide the better estimates of groundwater storage change (Konikow 2011, Aeschbach-Hertig and Gleeson 2012). However, in order to properly calibrate a regional groundwater model, sufficient in situ observations such as groundwater levels and streamflow data are needed, which are often not available, in particular in developing countries. In recent studies, GRACE-derived total terrestrial water storage changes have been increasingly applied to quantify groundwater depletion at regional scales (volume based methods). Table 4 lists recent studies that estimate groundwater depletion for various regions. These studies primarily use volume-based or partly indirect geodetic methods using regionally available data. For the North China Plain (NCP) and the California's Central Valley, both regional calibrated groundwater models and GRACE-derived approaches provide groundwater depletion estimates, while for the other regions (Northwest Sahara, Arabian, Guarani, Northern India, Bangladesh, Colorado River Basin, Canning Basin and MENA) mostly GRACE-derived estimates are available given a lack of in situ groundwater levels and regional groundwater models.

Scanlon et al (2012a) and Cao et al (2013) simulated the spatiotemporal variability in groundwater depletion across the North China Plain (NCP) and the two major aquifer systems in the US (California's Central Valley and High Plains Aquifer Systems) respectively, building a multilayer, heterogeneous and anisotropic flow model using MODFLOW (Harbaugh et al 2000). The US Geological Survey manages a dense network of groundwater level data across the country (>800 000 wells), which makes it possible to construct locally calibrated and robust groundwater models for the US. The simulated groundwater depletion estimates by Scanlon et al (2012a) are mostly consistent with available GRACE-derived groundwater depletion estimates (Famiglietti et al 2011, Scanlon et al 2012b). For the NCP, the groundwater depletion estimates produced with groundwater models (Cao et al 2013) substantially differ from those obtained using GRACE (Feng et al 2013, Huang et al 2015, Gong et al 2018). Huang et al (2015) indicated that the NCP aquifer system is highly complex, where shallow groundwater declines faster than deep groundwater, but shallow groundwater storage recovers quickly. Representing this type of complex aquifer system remains challenging even for regional groundwater models. In addition, coarse spatial resolution and noise contamination inherent in GRACE data still pose a challenge estimating groundwater depletion. Moreover, using in situ groundwater level observations, Shamsudduha et al (2012) showed that groundwater depletion estimates for the humid tropics (e.g. Bangladesh) derived from GRACE gravity estimation may be subject to large uncertainties due to highly seasonal water storage changes in other hydrological compartments.

Future projections of groundwater depletion rely on hydrological model simulations that are subject to large uncertainties. Future model simulation requires climate projections from General Circulation Models or Regional Climate Models, and future socio-economic and land use change scenarios. Future land use change including agriculture is particularly important as global hotpots of groundwater depletion overlap with the areas with intensive irrigation. As land use change is heavily affected by factors such as population growth, associated food demands, economic development and international food trade, statistical extrapolation based on historical groundwater depletion rates is likely not suitable to project future groundwater depletion. Thus far, only few studies are available that attempt to assess future groundwater depletion (table 2). The first global study was produced by Wada et al (2012b) who projected future groundwater depletion based on the combination of three climate and socio-economic scenarios. Their results showed that global groundwater depletion is projected to increase from 204 (±30) km³ yr⁻¹ in 2000 to 295 (±47) km³ yr⁻¹ by 2050. Yoshikawa et al (2014) found a much higher depletion volume under a consistent expansion of irrigated areas and projected global groundwater depletion to reach ~1150 km³ yr⁻¹ by 2050. They, however, used a globally medium population growth scenario (0.9% yr⁻¹) to extrapolate the future irrigated area change, which is rather high (from 2.7 in 2000 to 3.9 million km² in 2050), as the expansion of irrigated areas has been slowing down in many countries. Wada and Bierkens (2014) quantified the fraction of the consumptive blue water use that is met from non-sustainable use of groundwater and surface water. They projected global total and non-renewable groundwater withdrawal and depletion to increase from 952 and 304 km³ yr⁻¹ in 2010 to respectively 1621 (±128) and 597 (±85) by the end of this century. For climate and socio-economic change they used a business as usual scenario based on the latest Representative Concentration Pathways (RCP6.0) and Shared Socioeconomic Pathways (SSP2). These future projections show that, apart from an intensification of a number of current hotspots, groundwater depletion is likely to expand to other regions such as Africa, other parts of Asia, and South America where significant increase in population (>2 billion), food production and economic development are expected. In developed economies such as the US, the annual rate of groundwater depletion in the High Plains Aquifer is estimated to have already peaked at 8.25 km³ yr⁻¹ in 2006 followed by projected decreases to 4 km³ yr⁻¹ in 2110 (Steward and Allen 2016). This indicates that we can expect a rapid increase in groundwater depletion in developing economies and gradual decrease in developed economies such as the US. We stress, however, that projecting future demand is notoriously difficult leading to large differences between projections and models (Wada et al 2016a) and improvements are desperately needed. This would mean going beyond the current practice of using relatively simple statistical modelling of relationships between socio-economic data and water withdrawal data, possibly using more advanced behavioural modelling based on machine learning and agent-based modelling (Aerts et al 2018, Mason et al 2018).

The perpetual use of non-renewable groundwater will eventually result in complete exhaustion of groundwater stocks. This raises the question: 'How long will it last?'. In order two answer this question two underlying questions need to be answered: (1) 'How much groundwater is there?' and (2) 'What will be the future withdrawal rates?'. As groundwater is not a global common pool, these questions will result in different answers depending on region and even location. As has been shown in previous studies (Gleeson et al 2015, Richey et al 2015a), there is enormous uncertainty in estimates of global groundwater stocks as well as in regional assessments. Moreover, scenarios about future water demand are still under development, while projections under the same scenario are extremely variable between global models (Wada et al 2016a). This makes the question 'How long does it last' a wicked problem. In this review, we will focus on the first question only.

According to Shiklomanov (1993) groundwater encompasses 30% of total fresh water storage and over 98% of the non-frozen fresh water storage on land. Given the limited knowledge about the subsoil (Bierkens 2015), estimates of total groundwater volume are, however, extremely uncertain as testified by the different estimates shown in table 5 that range between 1 and 60 km³ globally. Recent studies (Gleeson et al 2015, Richey et al 2015a) have reviewed extensively earlier estimates of global groundwater volume. Our review is largely based on these assessments. Generally, all estimates rely on the assumption that the free pore space below the water table is filled with water and that porosity diminishes according to a certain function with depth (either by layer or exponentially). The general equation to estimate the volume (with A total aquifer area, n porosity, z depth, d_gw depth to groundwater and x location within an aquifer):

$$\begin{eqnarray}&&V=\displaystyle {\int }_{A}\displaystyle {\int }_{{d}_{{\rm{gw}}}}^{\infty }n\left({\bf{x}},z\right){\rm{d}}z\,{\rm{d}}{\bf{x}}.\end{eqnarray} \tag{ 3 }$$

The oldest estimate (Vernadskiy 1933) is also the largest and equals 60 million km³; however, this number covers depths to 5 km at which it is highly unlikely that any extractable fresh groundwater can be found and is therefore considered to be on the high side. Another earlier estimate is from Nace (1969). This estimate (7 million km³) has long been assumed to be on the low side because of the low porosity assumed (1%). Also, the arbitrary multiplication with a factor 5 makes this estimate questionable. The estimate of Korzun (1978) (23.4 million km³) is generally seen as the most acceptable one as testified by its appearance in multiple text books on global water resources (e.g. Shiklomanov 1993). Recently, using a much more data-intensive approach, Gleeson et al (2015) arrived at a surprisingly similar estimate, which should increase confidence in Korzun's textbook estimate. At the same time Gleeson et al (2015) state that not all of this groundwater will be of sufficient quality to be useable. Moreover, because porosity and permeability are low at large depths, it would most likely be technically infeasible to extract the groundwater in sufficient quantities to be of use. Following this reasoning, Richey et al (2015a) arrived at much lower volumes of extractable groundwater (1.1 million km³) assuming that for most aquifers the saturated thickness from which groundwater can be withdrawn is on average 200 m (following Margat and Van der Gun 2013). Their results match considerably better with volume estimates from regional aquifer studies. This, however, negates that sometimes multiple aquifers systems are stacked on top of each other that collectively may amount to much more extractable groundwater. Moreover, regional studies generally focus on the shallower systems that are more easily exploited and sampled. Based on the hydrogeological parameterization of a global groundwater model (i.e. De Graaf et al 2015, 2017), De Graaf (2016) provides an intermediate estimate of groundwater in sedimentary basins of 6 million km³.

The current consensus seems to be that the global groundwater storage amounts to approximately 23 million km³. However, the physical limit that matters is the extractable and useable volume. The useable volume depends on the quality (mostly salinity) of the groundwater, with the fresh groundwater volume being less than half of the total according to Shiklomanov (1993). The extractable volume depends on four important parameters: (1) the depth at which the groundwater should be pumped, i.e. how deep the filter and pump should be installed; (2) the static head in the well compared to the surface level which determines the amount of lift that is needed; (3) the drainable porosity or storage coefficient of the layer from which groundwater is pumped which determines the volume extracted per m head decline; (4) the permeability of the aquifer which determines the maximum yield (m³ s⁻¹) that can be achieved by the well, which should be sufficiently high to support the water demand by e.g. irrigation. It should therefore be concluded that in order to assess globally and regionally extractable and useable groundwater volumes, equation (3) will not suffice and a global groundwater flow and transport model is needed. At the time of writing this review, there is only one model available that can simulate global groundwater flow and withdrawal (De Graaf et al 2017). The hydrological schematization underlying this model is, however, quite rudimentary and needs improvement. Table 6 provides an overview of global datasets that are currently available to parameterize global groundwater flow and transport models. Again, they are not yet sufficiently detailed for accurate regional and global estimates and would require updating using smart combinations of geological maps, regional groundwater model studies, data from observation wells and bore logs.

We conclude this section by stating that the parameters that determine the volume of extractable groundwater may be only partly of a technical nature, since they are also subject to economic laws. Similar to oil, the technical efforts suffered to extract groundwater highly depend on the economic value of the water when used (Burt 1964, Gisser and Sanchez 1980). If high enough, an increasing economic value of water will spark innovations that would enlarge the volume of usable groundwater that can be extracted.

In section 3 we have already introduced the effects of groundwater depletion on land subsidence, as it makes it possible to monitor depletion using geodetic observations. Land subsidence has quite a number of detrimental effects, such as damage to infrastructure (underground pipes, roads, bridges, building) and increased flood risk by subsidence-related dike failure and lower surface levels (Sato et al 2006). We will not repeat what was written in section 3, but instead will add some more information about the processes behind land subsidence by groundwater withdrawal. Subsidence occurs because a release of pore pressure causes water carrying layers to be compacted under the weight of the overlying sediments, or because the water table falls below clay or peat layers, which results in shrinking of these materials. Part of the land subsidence is elastic. This means that if groundwater heads and/or water tables would be restored to the old values, the land would rise again. There is also a part that is inelastic, either by irreversible shrink, mineralization and oxidation of organic materials, or by a rearrangement/resettling of grains (Galloway et al 1998, van Asselen et al 2009). The problem with inelastic subsidence is not only that land elevation cannot be restored to its original value, but also that the storage capacity of the aquifer is compromised, which means that it is not possible to recover full storage after groundwater withdrawal stops. Inelastic subsidence is often considered as plastic instantaneous deformation (e.g. Leake and Galloway 2007) which may be appropriate for sandy deposits. If, however, clay and peat layers are present (as in many subsiding regions), inelastic compaction is time dependent and results in secondary compaction or creep (Minderhoud et al 2017). Creep is believed to be the cause of prolonged subsidence, even when withdrawal has stopped. For instance, when the city of Tokyo drastically reduced groundwater withdrawal rates to cease subsidence, subsidence still continued for years, albeit at a much slower rate (Sato et al 2006).

A meteorological drought is defined as a prolonged period with below-normal precipitation. (Tallaksen and van Lanen 2004). If persistent enough, a meteorological drought will propagate through the hydrological system by causing abnormally low soil moisture contents and evaporation (agricultural drought), reduced groundwater recharge and low water tables (groundwater drought) and finally declining groundwater discharge to streams resulting in extremely low streamflow (hydrological drought) (Wilhite and Glantz 1985, Tallaksen and van Lanen 2004). As excessive groundwater withdrawal affects groundwater discharge, it may therefore also enhance hydrological drought (Wada et al 2013). The Ganges River Basin, home to over 400 million people, includes the aquifers with highest groundwater depletion rates around the word (Gleeson et al 2012). In recent years, the Ganges Basin is experiencing widespread reduction of summer streamflow. A recent study by Mukherjee et al (2018) reports that severe groundwater depletion is the likely cause of this summer flow drying due to decreasing groundwater contribution to streamflow over the region. Decreasing summer flows trigger other environmental problems, such as degrading water quality due to reduced dilution of pollutants and pathogens and higher water temperatures. Also, the subsequent reduction of surface water flows in turn lead to potential water deficits for agricultural production downstream, resulting in further groundwater depletion over large agricultural regions (Scanlon et al 2012a, 2012b). This increased groundwater withdrawal compensates, albeit temporarily, for decreased surface water availability (Taylor et al 2013).

Another consequence of groundwater depletion is the contribution to global sea level rise. Deep fossil groundwater has been isolated from the current hydrological, atmospheric, and ocean balance and cycle for hundreds to thousands of years, depending on storage volume, recharge, and discharge rates (see section 2.2). Withdrawal of this groundwater will thus redistribute water stored on land to the hydrological cycle and contributes to additional ocean storage and sea-level rise.

Sahagian et al (1994a) were the first to try to estimate the contribution of terrestrial water storage change to global sea‐level variation. The main components of this positive and negative contribution are impoundments behind reservoirs (negative), groundwater depletion (positive), wetland loss (positive) and changes of water levels in lakes and endorheic basins (negative or positive). Subsequent estimates of the sign and magnitude of this terrestrial component differ greatly (Chao 1994, Gornitz et al 1994, Greuell 1994, Rodenburg 1994, Sahagian et al 1994b) and have been subject to considerable debate. This resulted in the IPCC fourth assessment report (IPCC 2007) neglecting the contribution of non‐frozen terrestrial waters to sea‐level variation, due to its perceived uncertainty and the assumption that negative contributions such as impoundments behind dams compensate for positive contributions such as groundwater depletion. Subsequent studies (Postel 1999, Gornitz 2000, Huntington 2008, Milly et al 2010, Church et al 2011) differ mostly in their estimates of the contribution of groundwater depletion, due to methodological differences, i.e. based on limited country estimates versus based on global hydrological modelling.

More recent work on global groundwater depletion (Wada et al 2010, Konikow 2011, Wada et al 2012b) suggests an increase of a positive contribution to sea‐level rise during the last decade as a result of a rise in groundwater depletion. For instance, Wada et al (2012b) project an increase of the contribution of global groundwater depletion to sea level rise from 0.57 (±0.09) mm yr⁻¹ in 2000 to 0.82 (±0.13) mm yr⁻¹ towards 2050. The increase is primarily driven by growing water demand during the last century, but is also affected by decreased water availability and groundwater recharge, and larger evaporative demand from agricultural areas due to changes in precipitation patterns and higher temperatures. Other studies report the contribution of groundwater depletion to global sea level rise in the order of 0.3–0.9 mm yr⁻¹ for around the year 2000 (Wada et al 2010, Konikow 2011, Döll et al 2014, Pokhrel et al 2015, De Graaf et al 2017, Hanasaki et al 2018). In response to these more recent studies, the terrestrial contribution to sea-level change was again included in the sea-level chapter of the fifth IPCC report (IPCC 2013).

The aforementioned estimates assume that nearly 100% of groundwater extracted eventually ends up in the oceans. A recent study by Wada et al (2016) used a coupled climate-hydrological model simulation to show that only 80% of groundwater depletion ends up in the ocean, while the rest is recycled by local precipitation. The resulted contribution of groundwater depletion to global sea level rise eventually amounts to 0.02 (±0.004) mm yr⁻¹ in 1900 and increased to 0.27 (±0.04) mm yr⁻¹ in 2000, which indicates that existing studies have substantially overestimated the contribution (Wada et al 2016b). To add to this, a study by Reager et al (2016) used more than 12 years of GRACE gravity estimates to show that over the period 2002–2014 the positive contribution of groundwater depletion of 0.38 mm yr⁻¹ was more than offset by a negative contribution of water stored on land (−0.71 mm yr⁻¹) as a result of increased precipitation due to climate variability or change. Wang et al (2018), however, published estimates of a strong positive contribution (0.295 mm yr⁻¹) from water loss from endorheic basins of which about 40% was attributed to groundwater. The work of Wada et al (2016), Reager et al (2016) and Wang et al (2018) show that the issue of the contribution of groundwater depletion to sea-level rise is far from resolved.

In the top 100–500 m of the of larger aquifer systems we can expect groundwater to be fresh (concentration of total dissolved solids TDS smaller than 1 g l⁻¹). Below these depths groundwater is most likely brackish (TDS 1–10 mg l⁻¹), saline (TDS 10–35 mg l⁻¹) or hyper-saline (> 35 mg l⁻¹), where the origin of natural high salinity groundwater can be either marine or terrestrial (Van Weert et al 2009, Margat and Van der Gun 2013, Van Engelen et al 2018). In some aquifers or regions, brackish or saline groundwater can occur at shallow depths. In these regions, groundwater pumping, due to a decrease in groundwater pressure below the pumping well screen, can lead to upconing of the fresh-salt groundwater interface resulting in salinization of groundwater resources. Van Weert et al (2009) provide a global inventory of regions where brackish and saline groundwater can be found at intermediate or shallow depths.

The pumping of groundwater has led to the progressive salinization of groundwater in many parts of the world, particularly in coastal aquifers, as testified by a large number of case studies described in e.g. Custodio and Bruggeman (1987) and Post et al (2018). The process of upconing of a salt-fresh groundwater interface under an individual wells or drains has been studied extensively. Earlier work (Bear and Dagan 1964, Dagan and Bear 1968, Schmorak and Mercado 1969, Strack 1976) and subsequent extensions (e.g. Reilly and Goodman 1987, Garabedian 2013) provide analytical solutions to the upconing elevation of the fresh-salt groundwater interface and the critical pumping rates that lead to salinization of the well. These studies show that, if the fresh-salt water interface is not too far below the well screen, upconing and well contamination occurs rather quickly (order of years). They also show that return of the salt water cone to its original state may take an order of magnitude longer (decades), especially when groundwater recharge is small.

These analytical studies all assume a sharp boundary between fresh and salt groundwater, which generally results in optimistic estimates of the effects of pumping on salinization. If hydrodynamic dispersion is taken into account, a brackish transition zone will develop that has a larger area of influence of brackish upconing then a sharp interface (Reilly and Goodman 1987, Zhou et al 2005, Jakovovic et al 2016) and creates a gradual increase in concentrations of pumped groundwater (Reilly and Goodman 1987, Werner et al 2009). Also, the development of a brackish transition zone makes the decay of salinity after pumping has stopped much slower. Thus, numerical models including hydrodynamic dispersion and experimental results indicate that in case salt groundwater is present closely below the well screen, groundwater withdrawal may not only result in well shutdown within a short period of time, but will also render groundwater unsuitable for use over a large area around the well (several km², Jakovovic et al 2016) for prolonged periods (several decades, Zhou et al 2005).

In conclusion, areas with intensive groundwater withdrawal and shallow saline groundwater (Van Weert et al 2009), most prominently coastal aquifers, are very sensitive to irreversible salinization of fresh groundwater resources, which is likely to become a global problem (Custodio 2002, Konikow and Kendy 2005). This is further supported by a sensitivity study by Ferguson and Gleeson (2012), who find that the impact of groundwater withdrawal on coastal aquifers is more significant than the impact of sea-level rise for a wide range of hydrogeologic conditions and withdrawal intensities. Despite the global importance of salinization by groundwater withdrawal and reported cases of imminent salinization (Custodio and Bruggeman 1987, Post et al 2018), there are hardly any regional-scale projections of aquifer salinization under future developments of groundwater withdrawal, with Mabrouk et al (2018) as a recent exception.

Groundwater withdrawal has impact on streamflow, groundwater levels and evaporation (figure 4) and as such on groundwater dependent ecosystems (GDEs), i.e. ecosystems with organisms that depend on groundwater discharge or the proximity of a water table. Eamus et al (2015, 2016) divides GDEs into three classes: (1) GDEs that reside within groundwater itself (e.g. stygofauna in caves, fissures); (2) GDEs requiring the surface expression of groundwater (springs, lakes, streams, wetlands) and (3) GDEs dependent upon the availability of groundwater within the rooting depth of vegetation (e.g. woodlands; riparian forests). In earlier work, Foster et al (2006) used a classification based on their geomorphological setting (aquatic, terrestrial, coastal) and associated groundwater flow mechanism (deep or shallow). Their insightful figure 1 is reproduced here (figure 7) and shows that classes A–D fit into category 2 of Eamus et al (2015) and class E into category 3. Recent overview papers about global GDEs are given by Eamus et al (2015) (monitoring) and Rohde et al (2017) (policy and management). Doody et al (2017) provide a framework for continental-scale mapping of GDEs using remote sensing and expert knowledge. Of interest to mapping GDEs is the global groundwater depth map provided by Fan et al (2013) based on a 30 arc-second steady state global groundwater model. From this map Fan et al (2013) estimate that ~15% of the land surface (not including the large lakes) is covered by areas that receive persistent groundwater discharge (lakes, marshes, swamps, fens, springs, streams), ~2% by less frequently inundated wetlands (floodplains an fens) and 5%–15% with the water table depth within the rooting depth of upland plants.

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From figures 4 and 6 we can deduce that for cases A–D the effect of groundwater withdrawal on GDEs is most prominent during stage 1 withdrawal, while both stage 1 and stage 2 withdrawal affect case E. When discussing the effect of groundwater withdrawal on GDEs we will distinguish between aquatic ecosystems (C and D in figure 7) and terrestrial ecosystems (A, B and E in figure 7). It should, however, be noted that this subdivision is partly arbitrary as GDEs such as marshes and swamps possess elements of both.

5.5.1. Aquatic ecosystems

5.5.2. Terrestrial ecosystems

Groundwater as a natural resource has a number of properties that make it special. Some important ones are:

• (1)  
  Ownership is often poorly established or groundwater is jointly owned by the land owners sitting on top of the aquifer (Moench 1992, Theesfeld 2010). This entails that without a permit system in place, anyone with the capital to install a production well on his/her land is allowed to use it (Famiglietti 2014), although legally established limits may apply.
• (2)  
  Groundwater can be both a renewable as well as a non-renewable resource, which calls for a different economic analysis (Halvorsen and Layton 2015).
• (3)  
  Extraction (i.e. withdrawal) costs are not constant per unit extracted as assumed in many economic analyses and increase with groundwater depth (e.g. Gisser and Sánchez 1980, Negri 1989, Foster et al 2015).
• (4)  
  The benefits of groundwater withdrawal are for the individual user, while the costs of the exploitation are (partly) borne by all the users of the same aquifer system. This occurs because groundwater withdrawal may lead to water table (or head) decline in parts of the aquifer that do not underlie the individual user's land, thus leading to increased extraction costs for others, often called pumping externalities (Negri 1989). So, just as with many other common pool resources groundwater may suffer from the tragedy of the commons (Hardin 1968, Müller et al 2017). Note, however, that the largest groundwater decline will occur at the location where groundwater is being pumped.
• (5)  
  Groundwater is often not exactly a common pool resource. First of all, it is not a fully non-exclusive resource (Gisser and Sánchez 1980), because generally only the owners of land overlying the aquifers can access the groundwater it contains. Second, the degree to which groundwater can be seen as a common pool depends the hydrogeological properties of the aquifer. For instance, groundwater withdrawal from a homogenous sedimentary confined aquifer with large transmissivity results in a large radius of influence of the pumping wells. Such an aquifer thus resembles a common pool. On the other hand, a granite aquifer with isolated pockets of high secondary permeability cannot be seen as a common pool.
• (6)  
  Being (partly) a common pool resource entails that the costs of groundwater pumping surpass the direct withdrawal costs (i.e. the well construction costs and energy costs to lift water above the ground). Rogers et al (1998) list these additional costs that, when not accounted for, hamper the efficient use of groundwater: opportunity costs resulting from depriving other more profitable types of water use (now and in the future), environmental externalities, such as the costs of ecosystem deterioration due to lowering water tables and diminished low flows; and economic externalities, for instance increased extraction costs for future users due to groundwater level decline or wells drying up and becoming stranded assets (Perrone and Jasechko 2017).
• (7)  
  Another property that arises from the common pool characteristic of groundwater is so-called 'strategic externality' (Negri 1989). This means that what a groundwater user does not extract today, is likely to be extracted by a rival user today or tomorrow. This property frustrates any incentives to forego current pumping and leave groundwater in the ground for future use.

Economic theories that seek to optimize groundwater use should take account of these special properties of groundwater resources. Hereafter, we provide an overview of past research on optimal groundwater withdrawal and depletion.

When examining approaches used to analyse optimal groundwater withdrawal, one can distinguish between papers by economists that use sophisticated mathematical analyses but relatively simple aquifer representations, e.g. bathtub models or single cell aquifers, and papers by hydrogeologists that use more realistic numerical models of groundwater flow and withdrawal (including groundwater-surface water interaction) in combination with (mostly numerical) tools from operations research and economics (see Harou et al 2009, MacEwan et al 2017 for a more elaborate classifications).

6.2.1. Economic analyses with simple aquifer models

Most of the economic literature that is concerned with optimal groundwater use regards groundwater as temporary non-renewable resource, where it is expected that, at least for some period into the future, groundwater pumping will exceed groundwater recharge, leading to groundwater depletion and head decline. The question then is to find an optimal future trajectory of pumping rates such that the present economic value of groundwater use is maximized (e.g. Burt 1964, 1966). The pumping rates in such an optimal trajectory typically decrease over time to the groundwater recharge rate or until the aquifer is physically depleted.

Within the literature on optimal withdrawal rates over time (called inter-temporal efficiency), the following distinctions are important (Gisser and Sánchez 1980, Negri 1989): the first is controlled (inter-temporally efficient) withdrawal rates (Gisser and Sánchez 1980) versus pumping rates under full competition (Gisser and Mercado 1973). In case of controlled withdrawal, the assumption is that a single owner or all groundwater users collectively adopt a withdrawal trajectory that maximizes the present economic value of the groundwater resource. Free competition typically occurs in case there are many users of a single common resource. Under free competition, individual groundwater users cannot assume that water left in the ground is available for him/her next year, as it may be used by his/her neighbour. This stimulates individual users to forego on inter-temporal efficiency and maximize current net return by increasing withdrawal such that current marginal revenue equals marginal withdrawal costs. The second important distinction that is made pertains to the access to the groundwater resource (Negri 1989). In case of non-exclusive access, everyone that is able is allowed to use the resource. This is can be compared to fisheries without quota for instance. Exclusive access means that only a limited number of potential users are able to access the resource, with a single user or owner of an aquifer's groundwater as a limiting case. Access to groundwater is often limited to the landowners sitting on top of the aquifer, and as such is by definition exclusive. Some large aquifer systems, however, such as the Gangetic plain aquifer, underlie regions with a very larger number of small farms, with each farmer using its groundwater. Such a case could be seen as intermediate between exclusive and non-exclusive access of a common resource.

The basis for much of the work on optimal groundwater depletion is found in Hotelling (1931). This work is more relevant for absolutely non-renewable resources such as oil and mineral resources, although water is mentioned in this paper. Hotelling assumed that resources are exclusive and its volume known and introduces the inter-temporal efficiency as the extraction rate that maximizes the present value of the resource over the time period till complete depletion. An important result is that the percentage change in net-price of the resource per unit of time should equal the discount rate. This entails that the change in extraction rate per unit time is inversely proportional to the change in price per unit time, following the demand curve. He also shows that this depletion trajectory is inter-temporally efficient. Hotelling also analysed the case of a monopoly, where the optimal extraction trajectory and associated price depend on the demand function.

6.2.1.1. Exclusive access and controlled withdrawal

Burt (1964, 1966, 1967) in a series of papers laid the foundation of the theories of optimal groundwater withdrawal over time. The work has similarities with that of Hotelling (1931) for a monopolist extractor, except for the fact that groundwater is recharged and the extraction costs are not constant, but increase with decreasing stock (increasing costs of pumping with deeper water tables or heads in the wells). The results equally apply to a single user or the total withdrawal of multiple users of a single aquifer that fully cooperate to follow the same pumping strategy. Burt used dynamic programming to find withdrawal trajectories that maximize the present value of groundwater use over time. The dynamic maximization problem in Burt's papers and later additions thereof has the following basic form:

$$\begin{eqnarray}&&\mathop{\max }\limits_{q(t)}\left\{{\int }_{0}^{\infty }\left[r\left(q\right)-c(q,h)\right]{e}^{-it}dt\right\}\,\end{eqnarray} \tag{ 4a }$$

subject to:

$$\begin{eqnarray}&&\displaystyle \frac{dh}{dt}={h}_{0}+\displaystyle \frac{1}{An}\left(q\left(t\right)-R\right).\end{eqnarray} \tag{ 4b }$$

The first equation denotes the present value of the profit made by exploiting the groundwater, with q(t) the withdrawal rate over time [L⁻³ T⁻¹], r(q) the revenue [US$ T⁻¹] that is made by using the groundwater (e.g. market value of crop yield), c(q,h) the withdrawal costs [US$ T⁻¹] that depend on the depth of the water table or water in the well (h [L]) and i is the discount rate [T⁻¹]. The second equation is the water balance of the aquifer with h₀ [L] the initial groundwater depth before withdrawal starts, R the recharge rate [L³ T⁻¹], A [L²] the area of the aquifer and n specific yield or storage coefficient [−].

An important result from Burt (1964) is that intertemporal efficiency is achieved if, at every moment in time, the net return (revenue minus costs) from a marginal unit of extracted groundwater is equal to the present value of that marginal unit if it remains in the ground. Negri (1989) calls this marginal value the shadow price of a unit groundwater and shows that it can be considered as the present value of avoiding future pumping costs by leaving groundwater underground. In Burt (1966), the work is extended by including stochastic groundwater recharge and in Burt (1967) by increasing the withdrawal costs by the value of groundwater as a contingency stock against years with reduced recharge. Adding the contingency value yields an optimal withdrawal trajectory that results in reduced groundwater depletion. Dominico et al (1968) and Burt (1970) used simple aquifer models to analyse a situation where an institutional regulator allows groundwater mining up to a certain time and subsequently limits groundwater withdrawal equal to groundwater recharge. Here, the timing of stopping groundwater overuse is determined that maximizes the present value of both the non-renewable and renewable groundwater. The associated volume of non-renewable water extracted is called the optimal mining yield. Dominico et al (1968) also introduced the concept of 'economic limit' as the volume of non-renewable groundwater that can extracted until marginal costs exceed marginal revenue from groundwater use. Finally, Brown and Deacon (1972) extended the original analysis of Burt (1964) by considering optimal groundwater withdrawal under conditions of economic growth, the inclusion of delayed return flows, the conjunctive use of groundwater and surface water and groundwater recharge. Results show that both depletion and present value increase under economic growth. Also, optimal groundwater withdrawal rates increase with artificial recharge, and decrease when surface water is available. As expected, when farmers use both surface water and groundwater, increasing the price of surface water increases optimal groundwater withdrawal rates, leading to a larger depletion.

6.2.1.2. Exclusive access, controlled withdrawal versus withdrawal under free competition

Gisser and Sánchez (1980) compared the case of controlled withdrawal leading to intertemporal efficiency with free competition, where users use groundwater to maximize current profit at every moment in time. They showed that in case the storage capacity of aquifers is very large or the demand is weakly dependent on price or the costs are weakly dependent on depth, the differences in pumping rates between free competition and controlled pumping are very small. This also means that groundwater depletion and net present value are similar under both withdrawal strategies. Their analysis confirmed an empirical result obtained earlier by the same authors and was also shown to occur in case of a nonlinear demand function (Allen and Gisser 1984). This result has come to be known as the Gisser–Sánchez effect, which has led to quite a lot of debate on the generality of the results, particularly because it seems to suggest the validity of a laisser-faire strategy for groundwater use. Koundouri (2004) provided an extensive review of later studies that looked at the Gisser–Sánchez effect and showed that it seems to hold in the majority of cases except for two. The exceptions are a study by Koundouri (2000) where withdrawal costs become very large as the aquifer is close to full depletion and by Worthington et al (1985), where the relationship between withdrawal costs and head is very nonlinear, which occurs in e.g. an artesian aquifer, and the relationship between revenue and groundwater use is nonlinear, e.g. in case of heterogeneous land use. Similar to many of the above-mentioned analyses, Gisser and Sánchez (1980) disregarded the impact of groundwater depletion on aquatic or terrestrial ecosystems. Esteban and Albiac (2011) included this impact by extending the model of Gisser and Sánchez (1980) with the costs of damage to aquatic ecosystems (called environmental externalities). They showed that for two heavily exploited aquifers in Spain controlled withdrawal does lead to significantly higher present values and less depletion, while adding the costs of environmental externalities further decreases head decline and even leads to recovery of groundwater levels.

6.2.1.3. Partly-exclusive (restricted) access, multiple users and controlled withdrawal

The earlier work on optimal withdrawal pertained to a single owner or multiple owners each following exactly the same pumping strategy (full cooperation). In reality, there may be multiple landowners that not necessarily cooperate and each pursue their individual optimal withdrawal strategy. Negri (1989) used dynamic game theory to analyse two effects. The first is the number of owners sitting on top of the aquifer. His solution allowed analysing the situation between a single and many owners showing that if the number of owners increases and these owners are non-cooperative it will lead to a greater depletion of the resource and a lower net present value per land owner. In case the number of owners is very large, access becomes effectively non-exclusive which leads to complete depletion of the resource. He also analysed the effect of what is called a strategic externality, which means that groundwater users try to capture as much as possible of the groundwater, as it will otherwise be captured by the other users. This was taken into account by allowing the optimal strategy of groundwater users to change dependent how the groundwater depletion develops in time (assuming the same strategies be followed by the other users). Negri (1989) showed that this results in lower present value and larger groundwater depletion. Following Negri's work, Provencer and Burt (1993) introduced and analysed a risk externality, which arises from the fact that if precipitation and groundwater recharge is intermittent between years, a large groundwater stock safeguards against income insecurity of the groundwater users.

6.2.2. Economic analyses using realistic groundwater representations

In order to manage and preferently reduce the use of non-renewable groundwater one can rely on three types of policy instruments (following Theesfeld 2010): (1) regulatory or command-and-control policy instruments; (2) economic policy instruments; (3) voluntary policy instruments. In countries or states where the government owns the water underground, it is possible to use quotas, the bestowal of water rights and the issuing of permits to limit groundwater withdrawal to economically or environmentally sustainable levels. In many countries, however, groundwater is individually or collectively owned by the land owners. In these cases, economic or voluntary instruments could be used.

Economic instruments to reduce or modulate groundwater use have been mentioned already in section 6.2. They can be divided into larger categories of which we mention water pricing, water markets, paying for ecosystem services and subsidies. The effects of taxation or water pricing have been investigated extensively (Höglund 1999, Ørum et al 2010, Dinar et al 2015). Taxation can have different effects, such as: reduce demand (Schoengold et al 2006, Rinaudo et al 2012, Mulligan et al 2014), decrease depletion and increase present value (Bredehoeft and Young 1970); increase investments in water savings technology (Cummings and Nercissiantz 1992, Medellín-Azuara et al 2015); stimulate efficient use of surface and groundwater under environmental constraints (Riegels et al 2013). Water markets have been successfully used to increase the economic efficiency of water use by allowing water to be traded between less-profitable and more profitable uses (Wheeler et al 2014, Xu et al 2018). Necessary requirements for this to work are, among others, a fixed cap on total water withdrawal (e.g. water rights), organized governance to mediate the trade and the infrastructure to move the water between users. Especially the latter is not always in place in case the main source of water is groundwater. Not often mentioned in the economic literature is paying for ecosystem services (Immerzeel et al 2008, Steward et al 2009, To et al 2012). Here, groundwater users are paid the amount of profit, preferable a bit more, that they lose by not extracting a certain volume of groundwater. Alternatively, programs for the buy-back of water rights are setup. If groundwater is a common pool resource, the challenge then is to make sure that sufficient users participate, which is more likely if net revenues drop sharply with increasing depth to groundwater (see Foster et al 2015). Finally, subsidies for investing in water savings technology are thought be of interest to reduce groundwater withdrawal. Quite a number of recent studies, however, indicate that these measures are either ineffective (Scheierling et al 2006) or can even increase consumptive water use (Ward and Pulido-Velazquez 2008). In irrigation, this so-called 'rebound effect' (Sivapalan et al 2014) is generally explained by the fact that saving more water will increase agricultural production (and thus consumptive water use through transpiration).

As is shown by the review above, economic theory suggests that if natural resources such a groundwater are collectively used without governance, it will eventually be depleted. However, based on her own field work and that of Blomquist (1987, 1988), Ostrom (1990) disproved this assumption by pointing out voluntary incentives for sustainable groundwater management. It was found that in many groundwater basins communities of users were able to self-organize themselves, without any central governance, and manage the groundwater resource without depleting it. Apparently, in time, these users had established rules among themselves that rendered the use of a common resource both economically as well as ecologically sustainable. By studying and comparing cases (e.g. in the USA, Nepal, Spain, Japan) of long-time sustainably managed common resources, Ostrom (1990) suggested eight 'design' principles that need to be part of a local self-organizing institution to sustainably govern a common resource. It is important to note that Ostrom (1990) distinguishes between using the resource (e.g. allocating withdrawal on a day-by-day basis) and provision for the resource (e.g. managing long-term groundwater stock, recharge enhancement, land use planning). Collective action for the latter is much more challenging and may require regional governance (Lopez-Gunn 2003).

Ostrom's work constitutes one of the foundations of socio-ecology, studying the interactions between humans and biophysical systems. Similarly, socio-hydrology (Sivapalan et al 2012, Di Baldassarre et al 2013) studies human-water interactions to better understand the evolvement of water resources systems under change (Montanari et al 2013). The rebound effect that results from subsidizing efficient water use (Ward and Pulido-Velazquez 2008) is one of the well-known examples studied in this emerging field. Socio-hydrology states that the concept of economic efficiency is not sufficient to understand the mechanisms behind non-sustainable water use, nor the effects of economic policy thereon. Inspired by related work on coupled human-natural systems modelling (Liu et al 2007), socio-ecological principles (Ostrom 1990) and socio-environmental modelling (Filatova et al 2016), socio-hydrology combines insights from the social sciences, including behavioural economics (Kahneman and Tversky 1979, Camerer et al 2004), with models from complexity theory, such as stylized conceptual models, game theory, machine learning approaches, and agent-based models to describe human-water interactions (Girard et al 2016, Giuliani et al 2016, Li et al 2017). Many of these methods have yet to be applied to the study of sustainable groundwater use, but the first papers start to appear (O'Keeffe et al 2018).