How much water could be pumped
from an aquifer and still remain
sustainable?


Victor M. Ponce and Janaina Da Silva


07 February 2018



Abstract. The concepts of safe yield and sustainable yield of groundwater are analyzed and compared in the context of a hydrologic balance. All recharges and discharges are duly accounted for. Since groundwater is a flow, not a volume, tapping the nearly horizontal natural recharge may arguably compromise the rights of other users in the vicinity, including natural ecosystems, wetlands, and baseflow. It is surmised here that vertical recharge, i.e., the recharge originating in local precipitation, is the only recharge that may be freely tapped for capture by groundwater to avoid encroachment on established rights.

A methodology to evaluate vertical recharge is developed and tested. The methodology is based on the cybernetic hydrologic balance of L'vovich (1979), including the definition of a groundwater recharge coefficient. This coefficient represents the fraction of precipitation that reaches the water table; therefore, it may be used to evaluate and assess sustainable groundwater yield. Any amount of groundwater capture over and above the vertical recharge would have to demonstrate, by means of suitable ecohydrological and baseflow studies, that it does not significantly affect established rights.


1.  INTRODUCTION

The question of how much water could be pumped from an aquifer and still remain sustainable has no straightforward answer. At first, the decision seems to be one related to hydrogeology. A careful examination, however, reveals a host of other issues, among which some of the more significant are: How does the decision affect surface vegetation? How does it affect the relation between surface and groundwater? How does it affect pertinent water rights? How does it affect land subsidence and salt-water intrusion? (Ponce, 2006).

In the past two decades, it has become patently clear that the sustainability of an aquifer has little to do with its hydrogeologic properties (Alley et al., 1999). Instead, the focus is now seen to be on ecosystem conservation and established water rights (Ponce, 2014). This paradigm shift follows from the realization that groundwater is not a volume to be mined, but rather a flow to be acknowledged. In his seminal paper on hydrogeology, Theis (1940) wrote:

"All ground water of economic importance is in the process of moving from a place of recharge to a place of discharge. Under natural conditions, prior to the development of wells, aquifers are in a state of dynamic equilibrium. Discharge by wells is a new discharge superimposed upon a previously stable system, and it must be balanced by: (a) an increase in recharge, (b) a decrease in discharge, (c) a loss of storage, or (d) a combination of these."

In this article, we endeavor to make the case for the quantification of groundwater sustainability. We focus on the interdisciplinary nature of the problem. Detailed hydrologic studies at the watershed/basin scale will assist in determining appropriate quantities for individual cases.


2.  GROUNDWATER FLOW EXPLAINED

Groundwater flow is extremely complex, varying in space (in three dimensions) and time (through various spans). Aquifers may be broadly classified as: (a) confined or unconfined, and/or (b) quaternary (alluvial) or tertiary (fractured rock) (Ponce, 2006). An assessment of sustainability will depend largely on the type of aquifer and the associated problem scale; it is very likely to transcend hydrogeology to encompass a gamut of related fields (Ponce, 2007). In this article we focus primarily on unconfined, predominantly alluvial aquifers of local or regional size, as a first approximation to the analysis.

At the outset, we acknowledge that all groundwater is constantly in motion from a zone of higher potential to a zone of lower potential, with the ultimate fate of groundwater being the nearest ocean. However, depending on the terrain's geomorphology, groundwater could eventually exfiltrate as the moisture of wetlands or the baseflow of rivers (Fig. 1). It is clear that surface water and groundwater are indeed intrinsically connected: Groundwater may actually become surface water in space and time, and vice versa. It follows that exploitation of groundwater could eventually affect the surface water and other components of the hydrologic cycle in the vicinity (Ponce, 2014).

a hydrologic budget that considers both surface water and groundwater
Wikimedia Commons

Fig. 1  The constant motion of groundwater flow.

To further compound the complexity of the problem, we recognize that a groundwater analysis suffers from a decided limitation:  The size of the control volume is not fixed. Since all groundwaters are connected, defining the limits of a control volume is accordingly an arbitrary exercise. Unlike surface water, which is constrained to the applicable watershed/basin boundary, there is no similar boundary for groundwater flow. Pumping without limit will generally result in an ever increasing size of the cone of depression (Prudic and Herman, 1996; Ponce and Vuppalapati, 2015).

Echoing Theis' statement, we reiterate that groundwater is not a volume, but a flow. An arbitrarily defined control volume will have: (1) inflow (recharge), (2) outflow (discharge), and (3) stored volume of groundwater (water filling the soil or rock voids). Pumping constitutes an external demand, with its discharge originating in any or all of the three components mentioned above. Under this optic, three scenarios are possible (Fig. 2):

  1. A pristine system, in its natural condition, in dynamic equilibrium, in the absence of pumping;

  2. A developed system, where the amount of pumping is equal to the increase in recharge (captured recharge) plus the decrease in discharge (captured discharge).

  3. A depleted system, where an additional fraction of the pumped discharge is actually being extracted from the stored volume. In this case, aquifer depletion takes place, with the size of the cone of depression (Ponce, 2006) increasing progressively in time.

groundwater balance

Fig. 2  Pristine, developed, and depleted groundwater systems.

In a typical groundwater system, recharge consists of all flow entering the control volume. This amounts to:

  1. The natural (equilibrium or pristine) nearly horizontal recharge, entering along the upstream boundary in the absence of pumping;

  2. The captured (nonequilibrium or induced) nearly horizontal recharge (Sophocleous, 1997), entering along the upstream boundary in the presence of pumping;

  3. The captured nearly horizontal discharge, converted into recharge as a direct result of pumping; and

  4. The vertical recharge, defined as the fraction of precipitation that reaches the top of the control volume (i.e., the groundwater table) within the timeframe of analysis.

Note that in a highly developed system, the vertical recharge may include amounts of artificial groundwater replenishment, rejected recharge, or return flows (Ponce, 2007).

Discharge from the control volume consists of:

  1. The natural, nearly horizontal discharge, in the absence of pumping; or the residual nearly horizontal discharge, in the presence of pumping, exiting along the downstream boundary (Fig. 2); and

  2. Deep percolation, i.e., the fraction of precipitation that leaves the control volume as a net vertical discharge (positive flux) at its bottom, joining deeper groundwaters.

Amounts of deep percolation are largely intractable and generally considered to be a relatively small fraction of precipitation (a global average of about 2%) and, therefore, negligible on practical grounds (L'vovich, 1979). In other words, deep percolation is the (small) fraction of precipitation that is effectively lost from the surface waters. Figure 3 shows a schematic of the various fluxes relevant to groundwater flow.

groundwater balance

Fig. 3  Inputs and outputs in an aquifer's control volume.


3.  SUSTAINABLE USE OF GROUNDWATER

The central issue of sustainability is the question of how much water to pump from an aquifer and still remain sustainable (Alley et al., 1999). In the typical case, aquifer replenishment is slow, taking decades, if not hundreds or thousands of years. Thus, it follows that excessive pumping of groundwater may lead to depletion and the consequent lack of sustainability. A depleted aquifer is one that cannot recover fast enough to continue to be of use; therefore, it is unsustainable.

Since an aquifer can be readily depleted through excessive pumping, it may be argued that the solution is to leave the aquifers alone and use only surface waters. Unlike groundwaters, the recycling time of surface water is a global average of 11 days (L'vovich, 1979; Ponce et al., 2000); therefore, all surface waters are sustainable when judged against groundwaters. This approach, while apparently logical, does away with the practice of groundwater pumping established for the past century in developed societies. We argue here that this extreme solution is politically incorrect. Groundwater use cannot and should not be altogether suspended; rather, it should be regulated with the aim to manage, mitigate, and/or minimize depletion in order to meet the challenge of sustainability.

The discussion then shifts to the components of the groundwater balance. Where should the pumped water come from? We note that there is a caveat in the hydrologic balance. The water extracted by pumping could be either:

  • Consumptive, when none of the pumped water returns to the aquifer; or

  • Partially nonconsumptive, when a certain fraction of the pumped water returns to the aquifer at some point in time or space.

Irrigated agriculture is the classical example of consumptive use, particularly when the drainage waters (drainage is ostensibly a necessity in arid/semiarid regions) are collected and removed from the premises via surface flow (Fig. 4). Other uses (domestic or industrial) may be totally or partially consumptive, depending on the local situation.

groundwater balance

Fig. 4  Irrigation canal (left) and drainage canal (right), Wellton-Mohawk irrigation, Arizona.

While the concept of sustainable yield has only been recently recognized (Alley et al., 1999), the admittedly older concept of safe yield has been around for nearly a century. Lee (1915) defined "safe yield" as the limit to the quantity of water which can be withdrawn from an aquifer, regularly and permanently, without dangerous depletion of the storage reserve. He noted that water permanently extracted from an underground reservoir reduces the volume of water passing through the basin by way of natural channels, i.e., the natural discharge. To illustrate the existence of this natural discharge, Lee observed that heavy pumping would commonly result in the drying up of springs and wetlands (Ponce, 2014). Thus, he distinguished between a theoretical safe yield, equal to the natural recharge, and a practical safe yield, a lower value which takes into account the need to maintain a residual discharge (Fig. 2). According to Lee, the residual discharge must be ascertained and deducted from the theoretical safe yield in order to obtain the practical safe yield. Over the past two decades, the latter has morphed into sustainable yield, which reaches beyond hydrogeology.

How much should the residual discharge be when assessing sustainable yield? In cases when the captured discharge must be minimized due to the existence or claims of downstream water rights (i.e., springs, wetlands, and baseflow), it follows that very little or none of the nearly horizontal recharge could be captured without encroachment on the rights of others. Under nonequilibrium conditions, pumping one-hundred percent of the natural recharge could theoretically result in the capturing of up to 50% of the natural discharge (Fig. 2). At the asymptotic limit, i.e., under near equilibrium conditions, any amount of capture would come from discharge and possibly encroach upon established downstream rights.

This bleak picture is somewhat ameliorated when it is recognized that the vertical discharge, i.e., the fraction of local precipitation that manages to reach the water table, is not specifically included in the determination of (nearly horizontal) recharge. Thus, a resolution of the conflict of rights between surface water and groundwater would be the capture of any of the vertical recharge. This shift from capturing nearly horizontal to capturing vertical recharge is predicated upon the fact that nearly horizontal recharge is regional and beyond, while vertical recharge is essentially local. Under this spatial optic, all vertical recharge could be subject to capture. Moreover, basing the determination of sustainable yield solely on vertical recharge is likely to put to rest the argument that capture by pumping could negatively affect neighboring ecoystems and surface waters.


4.  THE CYBERNETIC HYDROLOGIC BALANCE

Ir order to properly quantify vertical recharge and, therefore, gain a handle on sustainable groundwater yield, we resort to L'vovich's cybernetic hydrologic balance, an approach better suited for yield hydrology than the conventional one (L'vovich, 1979; Ponce, 2018).

In L'vovich's approach, annual precipitation is separated into two components (Fig. 5):

            
P  =  S  +  W
            
(1)

in which S = surface runoff, i.e., the fraction of runoff originating on the land surface, and W = catchment wetting, or simply, wetting, the fraction of precipitation not contributing to surface runoff.

L'vovich's water balance

Fig. 5  The cybernetic hydrologic balance (L'vovich, 1979).

In turn, wetting is separated into two components:

            
W  =  U  +  V
            
(2)

in which U = baseflow, i.e., the fraction of wetting which exfiltrates as the dry-weather flow of streams and rivers, and V = vaporization, i.e., the fraction of wetting returned to the atmosphere as water vapor.

Runoff (i.e., total runoff) is the sum of surface runoff and baseflow:

            
R  =  S  +  U
            
(3)

Combining Eqs. 1 to 3:

            
P  =  R  +  V
            
(4)

Equations 1 to 4 constitute a set of water balance equations. Four water balance coefficients may be defined: (1) runoff coefficient, (2) baseflow coefficient, (3) wetting coefficient, and (4) recharge coefficient.

The runoff coefficient is:


            R
Kr  =  _____
            P

(5)

The baseflow coefficient is:


             U
Ku  =  _____
            W
(6)

The wetting coefficient is:


             W
Kw  =  _____
             R

(7)

The groundwater recharge coefficient is:


             U
Kg  =  _____
             P

(8)

Figure 6 shows runoff and baseflow coefficients calculated by Ponce and Shetty (1995), based on data reported by L'vovich (1979). It is seen that in five all cases, runoff and baseflow coefficients increase with annual precipitation.

[Click on either image to display]
Runoff coefficients.
(a)
    
Baseflow coefficients.
(b)
Fig. 6 (a) Runoff coefficients and (b) baseflow coefficients, for the following data:
1. Africa: evergreen sclerophyll forests and scrub.
2. Africa: mountain conifer forests.
3. North America (Canada); subarctic forests (taiga).
4. South America: wet evergreen forests in the mountains.
5. Asia (india): semideciduous forests in the mountains (Western Ghats).

5.  EXAMPLE APPLICATION

The methodology described in the previous section is applied herein to data from the Sarada river basin, upstream of Anakapalli, in Andhra Pradesh, India (Fig. 7). The basin is positioned between the Eastern Ghats and the eastern coastline of India, and features a subhumid climate (Ponce et al., 2000), with a drainage area of 1,980 km2.

anakapalli
Wikimedia Commons

Fig. 7  Geographical location of Anakapalli, in Andhra Pradesh, India.

Eleven (11) years of rainfall-runoff data are analyzed. The precipitation data consists of a daily rainfall hyetograph and the runoff data consists of the hydrograph measured at the basin outlet. The annual hyetographs are used to calculate annual rainfall P (mm). Each annual hydrograph is integrated to obtain runoff R (mm). Surface runoff S (mm) is obtained by hydrograph separation using established principles (Ponce, 2014). The matrix of P-R-S is used to run online water balance 2.

Figure 8 shows the tabular results of the online program, where the groundwater recharge coefficient Kg is given in Col. 11. Figure 9 plots Kg vs mean annual precipitation P, in ascending order of precipitation. Despite the apparent noise in the data, the general trend is for an increase in Kg with an increase in P.

Sarada data table

Fig. 8  Cybernetic hydrologic balance for Sarada river basin data.

Sarada results

Fig. 9  Groundwater recharge coefficient vs mean annual precipitation, Sarada river basin data.


6.  RECHARGE COEFFICIENTS AND SUSTAINABLE YIELD

The vertical groundwater recharge is the fraction of precipitation that reaches the groundwater table. Given mean annual precipitation, and, for that matter, given any annual precipitation, the recharge coefficient may be interpreted as the amount of water that could be captured by pumping while assuring a sustainable yield. Ostensibly, this strategy does not compromise any part of the (nearly horizontal) recharge or discharge. Note that the conversion of discharge to recharge (in a control volume) has been a point of contention in groundwater resource evaluations for many decades (Kazmann, 1956).

For any one watershed/basin, the recharge coefficient should be evaluated following the cybernetic hydrologic balance described herein (Ponce, 2018). Given the natural hydrologic variability, in any one year, the sustainable groundwater yield, i.e., the permissible amount of capture, could be practically based on the amount of precipitation occurring in the previous year. Amounts of artificial replenishment, rejected discharge, and/or return flows, if any, may be added to the (natural) vertical recharge at this time (Ponce, 2007).


7.  SUMMARY AND CONCLUSIONS

The concepts of safe yield and sustainable yield of groundwater are analyzed and compared in the context of a hydrologic balance. All recharge and discharge fluxes are duly accounted for. Since groundwater is a flow, not a volume, tapping the nearly horizontal natural recharge may arguably compromise the rights of other users in the vicinity, including natural ecosystems, wetlands, and baseflow. It is surmised here that vertical recharge, i.e., the recharge originating in local precipitation, is the only recharge that may be freely tapped for capture by groundwater to avoid encroachment on established rights.

A methodology to evaluate vertical recharge is developed and tested. The methodology is based on the cybernetic hydrologic balance of L'vovich (1979), including the definition of a groundwater recharge coefficient. This coefficient represents the fraction of precipitation that reaches the water table; therefore, it may be used to evaluate and assess sustainable groundwater yield. Any amount of groundwater capture over and above the vertical recharge would have to demonstrate, by means of suitable ecohydrological and baseflow studies, that it does not significantly affect established rights.

The online calculator online water balance 2 rounds up the analysis.


ACKNOWLEDGMENTS

The authors wish to recognize Donna Tisdale and the people of the community of Boulevard, in southeast San Diego County, California, for their support of theoretical and applied research in groundwater sustainability throughout the past 12 years. The Sarada river basin data used in this study was provided by Dr. Y. R. S. Rao, National Institute of Hydrology, Roorke, India.


REFERENCES

Alley, W. M., T. E. Reilly, and O. E. Franke. 1999. Sustainability of groundwater resources. U.S. Geological Survey Circular 1186, Denver, Colorado, 79 p.

Kazmann, R. G. (1956). "Safe yield" in ground water development: Reality or illusion? Journal of the Irrigation and Drainage Division, American Society of Civil Engineers, Vol. 82, No. IR3, November, Paper 1103.

Lee, C. H. (1915). The determination of safe yield of underground reservoirs of the closed-basin type. Transactions, American Society of Civil Engineers, Vol. LXXVIII, Paper No. 1315, 148-218.

L'vovich, M. I. 1979. World water resources and their future. Translation from Russian by Raymond L. Nace, American Geophysical Union.

Ponce, V. M., and A. V. Shetty. 1995. A conceptual model of catchment balance: 2. Application to runoff and baseflow modeling. Journal of Hydrology, 173, 41-50.

Ponce, V. M., R. P. Pandey, and S. Ercan. 2000. Characterization of drought across climatic spectrum. Journal of Hydrologic Engineering, ASCE, Vol. 5, No. 2, April, 222-224.

Ponce, V. M. 2006. Groundwater utilization and sustainability. Online article.

Ponce, V. M. 2007. Sustainable yield of groundwater. Online article.

Ponce, V. M. 2014. Effect of groundwater pumping on the health of arid vegetative ecosystems. Online article.

Ponce, V. M. 2014. Engineering hydrology: Principles and practices. Online textbook.

Ponce, V. M. and B. Vuppalapati. 2015. The myth of groundwater resource evaluation. Online article.

Ponce, V. M. 2018. Why is the cybernetic hydrologic balance better suited for yield hydrology than the conventional approach? Online article.

Prudic, D. E., and M. E. Herman. 1996. Ground-water flow and simulated effects of development in Paradise Valley, a basin tributary to the Humboldt River, in Humboldt County, Nevada. U.S. Geological Survey Professional Paper 1409-F.

Sophocleous, M. 1997. Managing water resources systems: Why "safe yield" is not sustainable. Editorial, Ground Water, Vol. 35, No. 4, July-August, 561.

Theis, C. V. 1940. The source of water derived from wells: Essential factors controlling the response of an aquifer to development. Civil Engineering, Vol. 10, No. 5, May, 277-280.


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