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DETERMINATION OF SUSTAINABLE GROUNDWATER YIELD: A SYSTEMS MANAGEMENT APPROACH BASED ON THE MINIMUM

GROUNDWATER BALANCE

Dr J.J.P. Vivier

AGES Gauteng Consulting, Pretoria, Gauteng, South Africa; email: kvivier@ages-group.com

Abstract The determination of a sustainable groundwater yield is a complex and challenging task. There is a high degree of uncertainty associated with most aquifer parameters such as recharge from rainfall and aquifer storativity, especially in fractured aquifers. This leads to analysts often taking a very conservative and risk averse approach in determining the “sustainable” yield for boreholes. The problem with this approach is that groundwater can be considered as impractical or not an option, due to the low and conservative yields. Potential well fields also become too expensive to develop. The concept of sustainability does not only cater for the environment, but also for people (social) and the economy (business). A popular method to determine groundwater sustainability is the groundwater balance (also known as the groundwater budget) method. This method has come under scrutiny as it is proposed that capture zone method is a more conservative and technically correct approach. Two of the most important parameters in determining long-term borehole yield namely, recharge and storativity are unknown and unknowable at the time of well field development. At best, qualified guesses can be made with regard to these two parameters. This makes the capture method impractical as boreholes have to be drilled and tested first and capital spent before any planning can be done. In this paper, it was shown that the risk averse approach in determining borehole yield will result in the most expensive groundwater development option. The principle of sustainability requires that environmental, social and economic considerations be taken into account. By following a risk averse approach, which would be the most expensive, the principle of sustainability is violated and it cannot be claimed that the borehole yield is “sustainable”. Due to the exponential relationship between risk and cost, a no risk approach would be infinitely expensive. It was shown that due to the uncertainties, it is actually impossible to determine the sustainable yield of a borehole. The objective should rather be to develop a sustainable groundwater management plan. This can be achieved by following a systems management approach based on the minimum groundwater balance. The minimum groundwater balance approach makes use of e.g. hydrocensus data to determine a minimum groundwater balance for a system of aquifers based on recharge at a minimum level of assurance .e.g. lower 95th percentile rather than making use of the mean annual precipitation (MAP). The potential effects of storativity is neglected at this stage. The systems management approach was applied on a case study to demonstrate the application where some risk was taken for a limited period of time while monitoring takes place. Proactive warning systems would alert decision-makers when to develop new aquifers which are predefined based on the minimum groundwater balance method. The difference is that in the case of the risk averse approach, should it come to light that the recommended abstraction rates were wrong in the sense that it is too low, the capital is spent and cannot be recovered. In the case of the systems approach, where slightly risky abstraction rates are recommended for a limited period of time, additional well fields can be developed well in advance, before any negative environmental impacts can occur. 1. INTRODUCTION One of the biggest challenges that faces groundwater development and management in South Africa, is the reliability of the resource. The presence of hard rock aquifers over large parts of the country complicates the groundwater supply option. The hard rock aquifers are associated with highly variable transmissivity values, recharge and yields. Boreholes that “dry up” have left decision-makers and groundwater users opting for alternative sources. Hydrogeologists face challenges in this regard as they have to deal with uncertainties that are usually high. There is a high degree of uncertainty associated with

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most aquifer parameters such as recharge from rainfall and aquifer storativity, especially in fractured aquifers. This leads to analysts often taking a very conservative approach in determining the sustainable yield for boreholes. This type of approach often results in groundwater being neglected as a water supply option due to overly conservative borehole yield estimates which inflate the cost of well field development. By following a systems approach aimed at reducing uncertainty, this problem can be managed to arrive at a sustainable groundwater management plan for an aquifer or aquifer systems rather than trying to determine a sustainable yield for a borehole, which is considered as an impossible task. 2. OBJECTIVE The objective of this investigation was to determine whether a yield can be determined for an aquifer system that conforms to the principle of sustainability. 3. THE PRINCIPLE OF SUSTAINABILITY Decision-making in environmental management must be based on the principle of sustainability that is also known as the triple bottom line (represented by PPP for People, Planet and Profit). Sustainable development was first described by the Brundtland Commission in 1987 as; “development that meets the needs of the present without compromising the ability of future generations to meet their own needs” (Brundtland, 1987).

Figure 1 The three components of sustainability (modified after Vivier, 2006) The concept of sustainability may be described through the triple bottom line representation, encompassing the environment, technology and development and social aspects (Figure 2 3; Gibson, 2001; Vivier, 2006). It is important to note that any decision that is made based on the sustainability principle has to conform to the three very different spheres of environmental management, technological development and social development. Social development contains four sub-components that are important in environmental decision-making. These include; political, economic, legal and management aspects (Figure 1). The principle of sustainability is also encapsulated in the National Water Act (NWA, 1998) and in the National Environmental Management Act (NEMA, 1998).

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4. THE PROBLEM OF YIELD DETERMINATION IN FRACTURED AQUIFERS Historically, safe yields were determined for aquifers which were subjected to a process of drilling and pump testing. A safe yield for an aquifer was historically defined as “the amount of water that can be withdrawn from it annually without producing an undesired effect”(Todd, 1959). Today, this principle has been replaced by sustainable yield. But what does it mean? In general, groundwater specialists have to make recommendations based on short duration aquifer tests that are then applied in the long-term. Sustainability would suggest that the recommendation should not adversely affect people or the environment now and in the future. The result is that more often than not, groundwater specialists are risk averse and make overly conservative recommendations. 5. CONSERVATISM VS UTILIZATION POTENTIAL The problem with a risk averse approach, is that it can become uneconomical or impractical to make use of groundwater resources. It is often neglected that economics form part of the sustainability principle. For instance, consider an engineer that has to design a bridge that would be able to withstand a 1:1000 year flood and the maximum conceivable seismic event that could happen. The result would be that the bridge would be infinitely expensive. There is a risk-cost relationship in engineering design where cost is exponentially higher with a lowering in risk (Figure 2, Freeze et al. 1990). Similarly, if a risk averse approach to groundwater development is followed, it would mean that the most expensive alternative to develop a well field is chosen. This would violate the sustainability principle as economics should be taken into account. This aspect will be illustrated later in a case study example.

Figure 2 Graphic representation of risk vs. cost (Freeze et al. 1990) What is required, is an optimal design where risk and cost is managed to within e.g. a minimum acceptable risk, which would result on an acceptable or minimum cost. 6. GROUNDWATER DEVELOPMENT AND ENVIRONMENTAL IMPACTS Groundwater abstraction would always result in a lowering of the water table in an unconfined aquifer or a lowering in the hydraulic head in a confined aquifer. In a natural, groundwater system where no previous abstraction has taken place, any abstraction from boreholes would impact on the groundwater balance and would reduce the head in a specific area in the aquifer. This would reduce discharge to base flow or evapo-transpiration (ET) zones, which will have an environmental impact. Environmental impacts are also risks to a groundwater development program that should be factored in the design. If a design is sought with no environmental impacts, then no groundwater development is

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possible. What is important is that the environmental impacts should be within acceptable limits. It is important that Hydrogeologists co-operate with other environmental specialists e.g. wetland, aquatic ecology etc to ensure that all important environmental impacts are accounted for. 7. BOREHOLE AND AQUIFER YIELDS The yield of an aquifer is a complex aspect which relies on the transmissivity, storativity, recharge and boundary conditions of the system. In groundwater investigations, the yield of an aquifer is determined by both the yield of a borehole and collectively, the yield of the whole aquifer which could contain a number of boreholes. The collective yield of all the boreholes in an aquifer is constrained by the recharge within the aquifer boundaries. It is common practice by Hydrogeologists to aim and determine the sustainable yield of an aquifer by estimating a recharge rate as a fraction of the mean annual precipitation (MAP) across the surface area of the aquifer and subtract the outflows e.g. groundwater component of base flow, existing abstractions etc. This is the groundwater balance or water budget approach that has been criticized as the yield of a borehole is constrained by a decrease in discharge and an increase in recharge with time (Bredehoeft et al, 1982, Seward et al. 2006). It is proposed that the principle of borehole capture rather be used. When a borehole is pumped, a capture zone develops which depends on the transmissivity, storativity and pumping duration. The capture zone is different from the cone of depression in that all the water particles in the cone of depression will not actually flow to the borehole whereas the capture zone will capture all particles. The cone of depression depends on recharge as well (Van Tonder, 2010). This means that the volume of water that can flow to a borehole could be less than the recharge. In unconfined aquifers, the transmissivity decrease with time as well with a lowering in the water level. A review on the water balance and capture zone approaches found that both these methods should be employed when groundwater management decisions are made and that the groundwater balance approach cannot be rejected outright nor can it be used in isolation (Zhou, 2009). The problem with both the groundwater balance and borehole capture zone approaches is the lack of information. In fractured aquifers, we can analyse and derive the transmissivity, storativity and boundary conditions from aquifer tests, but we cannot determine the exact location of these boundaries. Recharge and storativity which are both critically important parameters cannot be determined and is usually at best based on a qualified estimate. From a practical consulting point of view, capital has to be spent on drilling of boreholes only to find that the aquifer cannot sustain the yield. This leads to client dissatisfaction and opting to make use of surface water alternatives. It is proposed that both the groundwater balance and capture zone approaches be followed in a practical and tiered approach. Before a groundwater development program is initiated it is important to calculate a minimum groundwater balance as it would be senseless to develop boreholes and determine capture zones oif the aquifer is already over-utilised. 8. THE MINIMUM GROUNDWATER BALANCE APPROACH AND DECISION-

MAKING In a natural, steady-state situation, the groundwater balance equation for the model is given by: ∆S = R - ET - BFG (1) Where S is the groundwater storage, R the recharge, ET the evapo-transpiration and BFG the groundwater component of base flow. In an unnatural system, the groundwater balance equation changes to (Figure 3): ∆S = R - ET - BFG-QA (2)

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Figure 3 Conceptual model of the groundwater balance. Where QA is the anthropogenic abstractions influences that can result in outflows to boreholes or inflows from dams etc. The major challenge faced by a groundwater analyst utilising either the groundwater balance approach or the capture zone approach is the uncertainty associated with the recharge value and the storativity of an aquifer. When utilising the groundwater balance approach to determine an initial potential yield it is common practice to assume a negligible storativity and estimate only the aquifer recharge. However through simplification the groundwater yield estimates are often more conservative. It is important to note that at this stage of the project development it is not about the actual aquifer parameters and the technical detail, but about decision-making on how to develop and manage the aquifer system in a practical way. The reality is that we will never have all the data we require to make perfect decisions (Vivier, 2011). In a decision-making making process, an iterative approach to groundwater development and sustainable yield determination is required that would ensure that over-utilisation of the resource does not take place while it is still practical and economical to develop the resource. The problem with both the groundwater balance and capture zone approaches to determine the sustainable yield of a borehole, is that it is actually impossible to determine either without stating a statistical significance. Aquifer parameters such as transmissivity, storativity and recharge changes spatially while recharge changes temporally as well. In the case of unconfined aquifers, transmissivity also changes with time. It is however possible to make conservative assumptions for the purposes of decision-making to determine the minimum groundwater balance. In this approach, the aim is not to determine the actual groundwater balance as it is accepted that this would be an impossible task. It is however possible to determine the minimum volume of groundwater that can be expected following a systems approach in the decision-making process. In the minimum groundwater balance approach the lowest recharge is used on the smallest known aquifer boundary areas. The recharge rate is also not determined from the MAP, but on an assured lower 5th or 2nd percentiles of rainfall. The minimum groundwater balance approach is based on the minimax principle of decision-making (Vivier, 2011). Based on this principle, it is accepted that it is impossible to determine the actual groundwater yield of an aquifer however based on conservative assumptions, the minimum yield can be determined (Figure 4). Consider, for instance, that a water supply project demands a yield of 10 ℓ/s and the minimum groundwater balance indicates that the

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minimum expected yield based only on recharge is 40 ℓ/s then there is a sound basis to make recommendations to develop the aquifer. It is important to note that at this stage, the yield of the boreholes are unknown and it is also not the objective to determine borehole yields. If it were the case that the required demand would be 10 ℓ/s and the minimum groundwater balance indicate that e.g. only 2 ℓ/s could be available, then there is no need to try and determine borehole yields. Once the initial boreholes are developed and monitoring information becomes available, then the actual yield of the aquifer can be determined over time. This is called envelope tracking in the decision-making process.

Figure 4 The minimum groundwater balance approach with envelope tracking (Vivier, 2011). The problem with the minimum groundwater balance approach is that it could lead to a risk averse approach where the most expensive groundwater development option is chosen or the groundwater option is rejected as impractical. To solve this problem, the minimum groundwater balance is used within a systems management approach to not only determine but optimize the sustainable yield of an aquifer. 9. A SYSTEMS MANAGEMENT APPROACH TO DETERMINING SUSTAINABLE

YIELD From the groundwater yield determination problem described earlier, it can be accepted that it is impossible to determine the sustainable yield for a borehole without long term monitoring. This is due to the fact that when a borehole is drilled and tested in fractured hard rock aquifers, apart from a qualified guess, there is no way to determine the storativity and the recharge. A superficial way to solve this problem, is to follow a risk averse approach in which the groundwater yields from boreholes are recommended at a very low rate to aim and obtain supply that can last virtually “forever” (steady-state approach). This approach is seemingly safe and will protect the environment as well as the borehole yield, let alone the reputation of the groundwater specialist. The problem is that it would result in the most expensive groundwater development option possible (Figure 2) thus violating the sustainability principle (Figure 1). It is much more expensive to drill and equip e.g. 10 boreholes each abstracting at 1 ℓ/s when there is a possibility of drilling 5 boreholes each abstraction 2 ℓ/s (Figure 2). A sustainable yield can be determined for a well field by following a systems approach. The aim is not to determine the sustainable yield of a single borehole but rather to develop a sustainable management plan for a system of well fields.

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Systems1 thinking is the understanding of how components in complex systems influence each other as a whole (Sterman, 2000; Sterman, 2002). It can be regarded as viewing problems as parts of a system rather than considering specific parts of outcomes of individual components. It is increasingly used in decisions regarding sustainable development (Nooteboom, 2007) and solving complex problems. There are two views of general problem solving. The historical view is that of cause-and-effect or event-orientated analysis. The systems view is more complex and consists of components connected via interaction pathways with feedback loops, which allows for non-linearity (Figure 5).

Figure 5 Schematic representation of the event-orientated and systems or feedback loops. The use of the systems management approach is illustrated on a case study of the water supply to the Middelburg Town in the Eastern Cape Province (AGES,2010). The objective is to supply an additional 40 ℓ/s to the town from groundwater resources. To obtain the required future supply of 40 ℓ/s and using the risk-averse approach, boreholes would be recommended at very low abstraction rates of typically 2 ℓ/s/borehole or 10% of the tested yields, even if the pump tests indicated yields of up to 20 ℓ/s (Figure 6). The problem with this approach is that due to the risk-cost relationship, it drives costs up and violates the sustainability principle (Figure 2). The engineering design of infra-structure has to take cognisance of not only risk but also cost. Due to the fact that sustainability is not only defined by environmental considerations, but also by development and the economy (Brundtland, 1987), sustainable yield is not the lowest possible yield. The terminology used for sustainable yield in the groundwater papers evaluated in this investigation (Seward et al. 2006 and Zhou, 2009) neglects development and economic effects and only concentrates on the yield of a single borehole. Following this type of approach would lead to the most expensive groundwater development possible. Sustainable yield in terms of the definition of sustainability (Section 3, Figure 1) can only be defined if economic considerations are accounted for. Terminology such a safe yield should be used rather than sustainable yield when considering borehole yields without taking cognisance of the cost implications

1 A system is defined as a group of things that are connected to work together (Oxford English Dictionary, 2006). A group or combination of interrelated, interdependent, or interacting elements forming a collective entity (Collins English Dictionary, 2006).

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Figure 6 Graphic representation of a well filed with “sustainable yield” from a steady-state approach (20 boreholes at 2 ℓ/s/borehole = 40 ℓ/s).

For reference purposes, at Middelburg, the surface water option is estimated to be in the order of R300 million capital cost2 and a high operating energy cost as water has to be lifted at a head of 300 m and pumped across a minimum distance of 30 km. A conceptual calculation was done for groundwater development at Middelburg using estimated groundwater development and infra-structure capital costing with the same reference (Table 1). Operational costs were neglected to simplify the comparison. The conceptual capital costing assumed that there are a number of options for groundwater development that ranges from extreme ends by choosing a high risk approach where 2 boreholes at 20 ℓ/s/borehole is used vs. choosing 20 boreholes at 2 ℓ/s/borehole associated with very low risk (risk-averse) of failure (Table 1). The unit costs were assumed to be the same. The cost graph indicates an exponential increase in costs with lowering in abstraction rate per borehole (Figure 7). The problem with the risky approach is that if the analyst is wrong, then the groundwater resource could be depleted but at a low infra-structure capital cost of R10.6 million. The problem with the risk-averse approach is that if the analyst is wrong and higher abstraction rates were possible then a total of R106 million of tax payer’s money was unnecessarily spent. In this, the risk-averse approach is more problematic than the risky approach in that if it is wrong, then the money cannot be retained, but in the risky approach, there are still options to expand the well fields as long as there is a time limit with monitoring imposed in the groundwater management plan. If an optimal approach is taken, then groundwater can be supplied at around R 45 million, which is much more cost-effective than the surface water option. The problem is that there is uncertainty with regard to the sustainability of the pumping rates of boreholes, which could result in future failures in borehole yield. The interest of the surface water alternative at a capital cost of R300 million would amount to around R 30 million per year. The payback on the groundwater option would be 1.5 or in the worst case 2 years, which is a good financial option. The discussion will be confined to the groundwater supply problem to illustrate the application of the systems approach based on the minimum groundwater balance to develop a sustainable groundwater management plan. With a systems approach, the groundwater supply problem is initially considered as a combination of transient, non-sustainable well fields that are initially stressed to determine the actual yields possible. This is done within a larger framework of additional well fields that are brought online as information becomes available through monitoring (Figure 8). This approach does not only consider groundwater and the environment but also economics. The groundwater supply problem is differentiated in terms of spatial and temporal components and does not aim to determine a sustainable yield per borehole that can last forever (Figure 8).

2 Base date 2010.

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Table 1 Middelburg: Conceptual comparative costs for groundwater development following various options.

No No of

boreholes

Yield per borehole

(ℓ/s/borehole)

Cost of boreholes

(R mil)

Cost of infra-structure (R

mil) Total capital cost (R mil)

Total yield (ℓ/s)

Unit capital cost over 20 year period

(R/m3)

1 2 20 R 0.60 R 10.00 R 10.60 40 R 0.42

2 4 10 R 1.20 R 20.00 R 21.20 40 R 0.84

3 8 5 R 2.40 R 40.00 R 42.40 40 R 1.68

4 16 2.5 R 4.80 R 80.00 R 84.80 40 R 3.36

5 20 2 R 6.00 R 100.00 R 106.00 40 R 4.20

Figure 7 Middelburg groundwater development options vs. cost. The groundwater development is done at an initial solution that is expected to be near-optimal, but scaled on the higher risk and lower cost side of the curve (Figure 9). It is accepted that recharge, aquifer boundaries, geological interactions and storativity is unknown and unknowable at this stage and that the minimum overall water is abstracted based on the minimum groundwater balance approach. The reason that the minimum groundwater balance approach is taken and not the capture approach is that we can use the minimum groundwater balance approach and based on hydrocensus information, plan ahead before any new boreholes are drilled an tested. With the capture method, new boreholes have to be drilled and tested, meaning capital has to be spent before we can take a stab at determining the potential yield of an aquifer. Using the minimum groundwater balance and systems management approach, conservative qualified calculations and estimations were used to determine the initial conditions for abstraction for each well field. This would entail using a slightly higher initial abstraction rate for the boreholes that were tested. This abstraction rate of 8 ℓ/s is still significantly lower than the tested yield which was at 20 ℓ/s to 30 ℓ/s for actual field borehole tests (AGES, 2010) but sufficient to stress the system so that information with regard to the aquifer storage and recharge can be determined. This is the slightly risky approach where the risk is managed by limiting the time and allow for monitoring. This approach is in line with the adaptive management proposed by Seward et al, (2006).

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Figure 8 Systems approach to sustainable groundwater development and management at Middelburg (40 ℓ/s at 5 ℓ/s/borehole = 8 boreholes).

The approach entails that according to the level of knowledge at the time, there are three different aquifer types at Middelburg:

1. The existing Municipal Aquifer with long-term monitoring of water levels and abstraction rates. High level of information/knowledge and high confidence. It is known that over-abstraction takes place with that water levels and borehole yields that declined over time.

2. New aquifers that were evaluated in terms of potential that were pre-determined using the minimum groundwater balance approach and where drilling and testing was done. Although qualified estimates were done, the actual recharge, storativity and long-term groundwater behaviour is unknown and can only be determined through future monitoring.

3. New aquifers that were evaluated in terms of potential based on the minimum groundwater balance approach and where no drilling and testing was done. The minimum groundwater potential or balance indicates that it could be a viable future options for groundwater development. The papers evaluated in this investigation that condemn the groundwater balance approach deny the opportunity to follow this step. This is due to the fact that these papers were compiled from an academic and research perspective that counteracts decision-making due to practical and economic considerations and hence fails to arrive at a sustainable solution (Bredehoeft et al. 1982; Seward et al. 2006).

The systems management approach employing the minimum groundwater balance method is described below (Figure 8, Figure 10):

1. The aquifer would initially be operated at a near-optimal solution that is on the medium to high risk and medium to low cost side of the curve – for a limited period of time (Figure 9).

2. The time limit for the recommended abstraction rates would be 1 to 2 years, which is a short enough period to prevent large scale over-abstraction and unacceptable negative environmental impacts. In the case of Middelburg, this decision point would be to abstract 5 boreholes at 8 ℓ/s each to obtain 40 ℓ/s (Figure 8).

3. Monitoring is done (using automated and manual systems) to prove or disprove the feasibility of the abstraction rates during this time.

4. If the abstraction rates are sustainable, then no unnecessary costs were incurred and the system can continue to operate on recommended abstraction rates. If not, the next one, two or more aquifer areas can be developed well in advance (1 to 2 years) – as determined by the minimum groundwater balance. Monitoring is critical and will be used as early warning systems to pre-detect excessive decline in groundwater heads with time before it can occur.

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5. The abstraction rates at the initial two aquifers can then be reduced that would allow recovery once the third and fourth aquifers are developed and ready for use.

6. The same process can be re-iterated until the optimal (i.e. sustainable) solution is found with time. This approach means that if the recommendation is correct, then the most cost-effective option was chosen from the start and if it is wrong, management measures can be pro-actively put in place to prevent over abstraction. In the case of the risk averse approach, should it be realized with monitoring that the water levels do not decline as expected and that borehole and well field yields could have been higher, it is too late and the capital has already been spent. By following this approach, a sustainable groundwater management plan can be implemented rather than aiming to determine the sustainable yield of a single borehole. The borehole yields can be obtained iteratively with time without incurring undue high costs from the start. By also incorporating the economy in the approach, the groundwater management plan would adhere to the principle of sustainability and become a practical way to supply water to the project.

Figure 9 Risk-cost and reliability relationship with expected near optimal solution. Middelburg sustainable groundwater development and management plan The sustainability of groundwater at Middelburg will depend on how the resources are developed and managed. A phased and systems management was compiled based on the minimum groundwater balance approach. The purpose of the management plan is not to manage a single borehole to ensure only a small decline in water level, but rather the collective management of all the aquifers for a cumulative sustainable supply of the system. The sustainable management plan also accounts for the economics of the resource development and aim to prevent over-expenditure due to a risk-averse approach (Figure 7, Table 1). By following this approach, some aquifers can be stressed in the short-term while new aquifers are developed and then allowed to recover. It is shown that instead of the 40 ℓ/s additional water supply, groundwater should be able to support and additional supply of 70 ℓ/s would be feasible from groundwater resources.

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Figure 10 Middelburg groundwater development and management phases with yield. 10. CONCLUSIONS The challenge that Hydrogeologists face in determining the sustainable yield for boreholes has led to the adoption of risk averse approaches in recommending borehole yields in fractured aquifers. A popular method to determine groundwater sustainability is the groundwater balance (also known as the groundwater budget) method. This method has come under scrutiny as it is proposed that capture is a more conservative and technically correct approach. Where the groundwater balance approach typically makes use of an assumed recharge rate over an aquifer surface area to determine a volume, the capture method relies on the aquifer parameters and boundaries as well as pumping time to determine a “sustainable” borehole yield. Two of the most important parameters in determining long-term borehole yield namely, recharge and storativity are unknown and unknowable at the time of well field development. At best, qualified guesses can be made with regard to these two parameters. In this paper, it was shown that the risk averse approach in determining borehole yield will result in the most expensive groundwater development option. The principle of sustainability requires that environmental, social and economic considerations be taken into account. By following a risk averse approach, which would be the most expensive, the principle of sustainability is violated and it cannot be claimed that the borehole yield is “sustainable”. Due to the exponential relationship between risk and cost, a no risk approach would be infinitely expensive. It was shown that due to the uncertainties, it is actually impossible to determine the sustainable yield of a borehole. The objective should rather be to develop a sustainable groundwater management plan. This can be achieved by following a systems management approach based on the minimum groundwater balance approach. The minimum groundwater balance approach makes use of e.g. hydrocensus data to determine a minimum groundwater balance for a system of aquifers based on recharge at a minimum level of assurance .e.g. 5th percentile of rainfall rather than making use of the mean annual precipitation (MAP). The potential effects of storativity is neglected at this stage. From a practical perspective, this method is better than the capture approach because it can be done in the planning phase without the requirement to drill new boreholes and hence spend capital. The systems management approach was applied on the Middelburg Town Water Supply Case Study. Based on the minimum groundwater balance approach, apart from the sub-minimum of two new aquifers

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that were developed, an additional 3 potential aquifers have been identified that have sufficient development potential but which are as yet undeveloped. The objective was to supply an additional 40 ℓ/s to the town from groundwater resources. The surface water alternative would have a capital cost of R300 million. A series of options were evaluated that ranged from a risk averse option where 20 boreholes would be developed at a yield of 2 ℓ/s/borehole to a high risk option where 2 boreholes would be developed at 20 ℓ/s/borehole. The actual borehole yields were generally high and ranged between 20 ℓ/s to 30 ℓ/s. The risk averse approach was the most expensive at R106 million and the high risk approach was the most cost effective at R10.6 million. A risk averse approach does not provide sustainable groundwater yields as it violates the principle of sustainability. Based on the systems management approach, a sub-optimal option was chosen on the risk side of the curve (i.e. slightly risky) with 5 boreholes abstracting at 8 ℓ/s/borehole. The systems management approach aimed at stressing the aquifer somewhat but for a limited period of time of 1-2 years so that maximum information could be obtained through monitoring. Should monitoring proactively indicate that e.g. a borehole yield would be too high, additional well fields that were predetermined can be developed in advance. The difference is that in the case of the risk averse approach, should it come to light that the recommended abstraction rates were wrong in the sense that it is too low, the capital is spent and cannot be recovered. In the case of the systems approach where slightly risky abstraction rates are recommended for a limited period of time, additional well fields can be developed well in advance, before any negative environmental impacts can occur. By following the systems management approach based on the minimum groundwater balance, a sustainable groundwater management plan can be developed that adheres to the principle of sustainability. It also allows for groundwater to be developed in a practical way that would make groundwater a more feasible option while reducing uncertainties associated with recharge and storativity. 11. RECOMMENDATIONS Based on the findings of this study, the following recommendations are made:

• The use of the term sustainable yield for a borehole should be redefined as it is not possible to determine a sustainable yield for a borehole.

• Sustainable groundwater management plans should be developed based on the systems management approach based on the minimum groundwater balance method.

• The risk averse approach in groundwater yield determinations should be avoided as it discourages the use of groundwater as a resource.

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