## Abstract

The Environment Agency of England and Wales uses its calibrated regional models to estimate the reduction in river flows resulting from proposed groundwater abstractions. Where there is no regional model, analytical equations can produce quick initial estimates of river flow depletion. However, users often want more confidence in their estimates by representing more faithfully their understanding of the real river–aquifer system. This paper shows that, when using a numerical model designed to predict river flow depletion, it is important to include adjacent catchments and intermittent streams and less important to include river elevations and variations in transmissivity with groundwater head. Recharge does not usually need to be included unless part of the river becomes disconnected or dry. Therefore, for rivers where stream length is constant and transmissivity variations are small, it is valid to use a ‘no-recharge’ depletion model, which can be built quickly (within a month). A case study on the River Leith in NW England illustrates the use of such a model to assess the ecological impact of two groundwater abstraction licences under the European Union Habitats Directive.

The Environment Agency, the environmental regulator of England and Wales, manages groundwater resources via abstraction licenses. Abstraction from aquifers almost certainly results in some reduction or depletion in river flows (Rushton 2002) and, before granting a licence, Environment Agency hydrogeologists will estimate this depletion from the rivers flowing over the aquifer.

Under natural conditions, aquifers are in a state of approximate dynamic equilibrium, with recharges equal to discharges, but when a well begins pumping, it disturbs this equilibrium. Initially the well gets all its water from aquifer storage, but as the cone of depression spreads out, it intercepts other sources of water such as rivers, lakes, wetlands or the sea. Eventually a new dynamic equilibrium is reached when all the water for the abstraction comes from either a decrease in the natural discharges to these sources or an increase in the natural leakage from them (Theis 1940; Sophocleous 2002). This paper focuses on the situation, common in the UK, where baseflow depletion is the long-term source of water for a pumping well.

The best predictors of river flow depletion due to groundwater abstraction are regional groundwater models because they are a synthesis of current understanding and have been tested against observed heads and flows. In England and Wales there are regional models for most of the major aquifers (Whiteman *et al.* 2012), many of which are used to assess the spatial and temporal impacts of groundwater abstraction (Shepley & Soley 2012; Soley *et al.* 2012). Where there is no regional model, analytical approaches can be used, such as the Environment Agency's IGARF (Impact of Groundwater Abstraction on River Flows) spreadsheet tool (Kirk & Herbert 2002; Environment Agency 2004). This includes three analytical equations (Theis 1941; Hantush 1965; Hunt 1999) to estimate the flow depletion in up to two infinite, straight, parallel rivers. Analytical approaches like IGARF provide quick initial estimates of river flow depletion, but fail to take into account the real geometry of multiple rivers, the nature of intermittent streams, variations in recharge or heterogeneous transmissivity (Rushton 2002; Jackson 2004).

Users often want greater confidence in their estimates than analytical solutions can provide and would prefer to represent their understanding of the real river–aquifer system in a numerical model (Soley *et al.* 2012). However, they would like to do this more quickly than the one to three years it usually takes to build a regional model in the national groundwater resources modelling programme of England and Wales (Whiteman *et al.* 2012).

This paper illustrates how a numerical model can be developed quickly (within a month) by including only mechanisms that are essential for predicting river flow depletion rates. The first part of this paper (the modelling investigations) identifies which these essential mechanisms are. These investigations showed, for example, that all rivers hydraulically connected to a pumping well should be included in a depletion model whereas recharge can often be ignored. The second part of the paper (River Leith case study) describes how a rapidly built, numerical model incorporating only the crucial mechanisms was used to assess the ecological impacts of two groundwater abstraction licences on the River Leith in Cumbria, NW England.

## The modelling investigations

In this section the crucial mechanisms for simulating groundwater depletion are investigated. This study was undertaken originally as part of a project by the British Geological Survey (BGS) and the Environment Agency (Jackson *et al.* 2008). The work followed two previous studies on the impact of groundwater abstraction on river flows: the development of IGARF (Environment Agency 2004) and the work by Parkin *et al.* (2007) with neural networks. This paper describes five series of simulations that were used to investigate the influence of the following mechanisms: single and multiple river catchments (series 1); recharge (series 2); the length of intermittent streams (series 3); stream elevation (series 4); and variations in transmissivity with head (series 5).

The investigations used models A, B and C, which were set up as shown in Figure 1 and Table 1 using the finite difference groundwater model, ZOOMQ3D (Jackson 2001). All three models have a single layer with a base elevation of 0 m, a uniform grid of 250 m square cells and no-flow boundaries on all four sides. Model A is 5 km square and includes one river, which runs from north to south along the centre of the model (*x*=2500 m) with the river stage elevation at 100 m and river bed at 99 m. The abstraction well is one grid cell (250 m) away from the river. Model B has two additional river catchments, identical to model A, on each side of the central river. Model C is the same as model A except that the river is 1 km shorter at its upstream end.

Table 2 summarizes the mechanisms investigated, the models used and the input parameters for each series of the investigations. Model A was used to represent flow depletion from a single river in series 1, 2 and 5, model B to represent the influence of multiple rivers in series 1, 2 and 4, and model C to investigate the effect of stream length in intermittent streams in series 3. Transmissivity was held constant in series 1–4 at 500 m^{2}/day. The influence of varying transmissivity as a function of hydraulic head was investigated in series 5 to represent firstly unconfined conditions and secondly the variation of hydraulic conductivity with depth. For all model runs the storage coefficient was 10% and the river conductance was 2500 m^{2}/day. River conductance is known to depend on grid size (Rushton 2007) and the value used here was calculated for a specific grid size of 250 m using the following relationship:
where *K*=river bed hydraulic conductivity (1 m/day); *L*=length of reach (250 m, i.e. model cell size); *w*=width of river (10 m); *b*=river bed thickness (1 m).

The river flow depletions were obtained by taking the difference between the river flows for a run with abstraction and the corresponding run without abstraction. Each model was run with the abstraction well pumping at a constant rate and the leakage rates (to or from the river) at each node added to produce a total flow rate for the whole river. Then the model was re-run without the abstraction and the new total flow rate for the river was calculated. The depletion rate is the difference between these two total flow rates. This was repeated at each model time step.

### Series 1: single and multiple river catchments

Series 1 compares the river flow depletion rates from the single river model (model A) and the three-river model (model B) to investigate whether including multiple rivers is a crucial mechanism for predicting river flow depletion. Apart from the model size and the number of rivers, all other parameters in models A and B are the same (Table 1). The upper part of Table 3 summarizes the runs for series 1. Three runs use model A (A1.1, A1.2 and A1.3), each with a different abstraction rate, and three use model B (B1.1, B1.2 and B1.3). The run numbers comprise a letter showing the model used, the series number and the run number. So run A1.2 refers to model A, series 1, run 2.

Figure 2 shows the variation of river depletion with respect to time from the single river model (run A1.1) and from the central river in the three-river model (run B1.1) for an abstraction of 5 Ml/day (5000 m^{3}/day). Until about 200 days the depletion rates are the same in both the single-river and the three-river model. However, after this, the depletion for the central river of the three-river model (dashed line) is less than for the single river model (solid line). This is because in the single-river model the river is the only long-term source of water and so the cone of depression continues to spread until all the pumped water comes from this river. In the three-river model the cone of depression initially spreads out in the same way, accessing only the central river but at around 200 days it reaches the two outer rivers and their flows start being depleted by the abstraction. Beyond 200 days the depletion from the central river in run B1.1 continues to rise, but more slowly than for the single-river in run A1.1 because water is being provided by the two outer rivers. Eventually after about 2800 days a new dynamic equilibrium is reached for both models and the long-term depletion rates remain at a constant maximum value. These are 5 Ml/day for the single river and 4.66 Ml/day for the central river in run B1.1 (Fig. 2). The drawdown values at the mid-point of each river at dynamic equilibrium are 10.54 m at the single river for run A1.1 and, for run B1.1 they are 10.53 m at the central river and 0.1 m at the left-hand river.

The long-term depletion rates for all the runs in the series are shown in Table 3. For the runs using the single river model, the long-term depletion rate is always 100% of the abstraction rate because in the long-term there is nowhere else for the pumping well to get its water from. The three-river model is more realistic and allows depletion from the central river and the two rivers beyond it. For abstractions of 5 and 10 Ml/day, the depletion rates from the central river are 4.66 and 9.32 Ml/day respectively (93.2% of the pumping rate). This means that the total depletion from the two outer rivers is 0.34 and 0.68 Ml/day, respectively (6.8% of the pumping rate). Therefore ignoring these outer rivers would have significantly underestimated the impacts on them and overestimated the impact on the central river.

In runs B1.1 and B1.2 the long-term depletion rate from any of the three rivers is proportional to the abstraction rate. As described above, the central river is depleted by 93.2% of the abstraction rate (Table 3) and the two outer rivers together by 6.8% of the abstraction rate. This proportionality between the river depletion rate and the groundwater abstraction rate arises from the way river–aquifer interactions are represented. In the ZOOMQ3D model used here, flow either way between the river and the aquifer (river leakage) is linearly related to groundwater head when the groundwater head is above the river bed. The same representation is used in MODFLOW (McDonald & Harbaugh 1988). A detailed analysis by Rushton (2007) suggests that this representation is correct because the relationship between head and flow should approach linearity for this condition.

For run B1.3, however, where the abstraction is higher (40 Ml/day), the long-term depletion rate from the central river is less as a percentage of the abstraction (91.9%, 36.77 Ml/day). Consequently a larger proportion of water is coming from the two more distant rivers (8.1%, 3.23 Ml/day). The reason for this is that the three nodes nearest to the borehole on the central river become disconnected (the groundwater head is below the river bed) and there is no longer a linear relationship between the river leakage and the groundwater head. In fact the modelled river leakage at a disconnected node should approach a constant value (Rushton 2007) and the depletion rate is limited. This behaviour was also noted by Shepley & Soley (2012).

Series 1 shows that including all the rivers that are hydraulically connected to the pumping well is a crucial mechanism in a flow depletion model. If multiple rivers are not included, the impacts on rivers beyond the nearest river can be significantly underestimated. Hence it is important to follow usual good practice and, as far as possible, define the boundaries of the model using the physical extent of the aquifer. Since the impacts of pumping can readily spread into adjacent catchments, it is not acceptable to select a stable groundwater divide between two catchments as a model boundary.

The smaller the catchment and the larger the hydraulic diffusivity, that is, transmissivity/storativity (*T/S*), the more important it is to include the more distant rivers because the cone of depression will reach them more quickly. The effect of catchment size was tested by repeating the runs in series 1 with a three-river model that was double the size of model B but the same in every other respect. The two outer rivers in the smaller model experienced about twice as much depletion as in the larger model. Series 5 describes the effects of transmissivity.

### Series 2: without recharge

Series 2 uses the three-river model (model B) without recharge (Table 2) to investigate how important recharge is when predicting river flow depletion. The lower part of Table 3 gives the long-term depletion rates for series 2. For abstractions of 5 and 10 Ml/day, the river depletion for models with and without recharge is the same (within the accuracy of the model's numerical solver). However, for abstractions of 40 Ml/day, the run without recharge has a lower depletion (36.58 Ml/day, run B2.3) than the run with recharge (36.77 Ml/day, run B1.3). As noted in series 1, some river nodes became disconnected in run B1.3 and this happens sooner in the same run without recharge (run B2.3), which results in less depletion from the central river (91.5% rather than 91.9%) and more from the outer rivers.

Series 2 shows that recharge is not a crucial mechanism in a river flow depletion model when river leakage is linearly related to the groundwater head (see also Shepley & Soley 2012). This is not the same as saying that river flows are independent of recharge because clearly, the larger the recharge is, the higher the discharge to the connected rivers. However, although recharge affects the *magnitude* of river flows, it does not affect the *difference* in river flows due to a groundwater abstraction.

Recharge does, however, need to be included if the disconnected length of the river changes because the river leakage and groundwater head are then not linearly related. Series 3 illustrates other circumstances where it may be important to include recharge.

### Series 3: the length of intermittent streams

There are many intermittent streams on the outcrop of the Chalk aquifers in England where a stream rises on the unconfined aquifer and its length varies seasonally as the water table intersects different parts of the river. Series 3 tests how important variations in stream length are for predictions of depletion.

The runs in series 3 use model C (Figure 1c), and Table 2 summarizes the model parameters. Unlike series 1 and 2, there is no inflow at the northern (upstream) end of the river. The model was first run to steady state with a uniform recharge rate of 1 mm/day and the resulting heads were used as initial conditions for the runs in series 3.

In run C3.1 recharge continues at the same rate as that used to produce the initial conditions (1 mm/day). This represents wet conditions when the river is flowing over its whole length (a perennial stream). In run C3.2 there is no recharge. This represents dry conditions when heads and river flows are falling and some of the river is drying up (an intermittent stream). In both runs the abstraction is 5 Ml/day and the depletion rate is calculated, as before, by comparison with the same run without any abstraction. The solid line in Figure 3 shows that the depletion rate for the perennial stream (run C3.1) rises to a maximum of 5 Ml/day and is similar to that for run A1.1 in series 1. The long-dashed line in Figure 3 shows that the depletion rate for the intermittent stream (run C3.2) is the same as for the perennial stream for about 800 days. Then in the run with abstraction, the river nodes begin to dry out, the river gets shorter and the depletion rate falls. The short-dashed line in Figure 3 shows the number of dry nodes in run C3.2 (with abstraction). As more nodes go dry, the stream length continues to reduce until, after 1417 days, all 17 nodes are dry. However the nodes in the corresponding run without any abstraction do not go dry and so the depletion continues until about 5500 days (Fig. 3). The heads have then fallen to the same elevation as the river stage and so the river flows are zero.

These results show that the changing length of an intermittent stream is another essential mechanism for properly estimating flow depletion. The predictions with regional models made by Soley *et al.* (2012) show the same thing. In the investigations in this paper, it was 800 days before river nodes began to dry up but shorter (and more realistic) times are likely with modified parameter values.

Series 2 showed that, when the disconnected length of the river varies, river leakage is no longer linearly related to groundwater head and so recharge needs to be included in a depletion model. In series 3 changes in the length of dry sections of the river also result in non-linear behaviour and again recharge should be included.

### Series 4: stream elevation

Series 4 uses the three-river model (model B) to investigate how the relative elevation of rivers affects their depletion rates. The parameters in this series are the same as in series 2 except that the initial groundwater heads are 150 m throughout the model domain (Table 2). The only difference between the three runs in this series are the elevations of the three rivers (Table 4). In the base run (B4.1) the river stage elevations of all three rivers are set at 100 m above datum, whereas in the other two runs the two outside rivers are raised to 110 m (run B4.2) or lowered to 90 m (run B4.3). In all cases the river bed is 1 m below the river stage.

The depletion rates for all three runs are identical so the elevation of a river is not a crucial mechanism and does not need to be included unless it affects any other crucial mechanisms, for example the timing when sections of a river become disconnected or dry (series 2 and 3).

### Series 5: variations in transmissivity with head

All the runs in the previous four series have constant transmissivity whereas series 5 looks at how depletion is affected when transmissivity varies with groundwater head. The single river model (model A) is used to investigate firstly unconfined conditions, where transmissivity varies with saturated thickness, and secondly where hydraulic conductivity varies with depth (VKD). VKD is a key mechanism in many Chalk aquifers in England (Rushton & Rathod 1980). Rushton *et al.* (1989) describe transmissivities varying between 76 and 200 m^{2}/day as the water table fluctuates by 12 m in southern England, which gives rise to the characteristically high variation in Chalk stream flows. Winter to summer flow ratios can easily be 10:1 or more.

Runs A5.1 and A5.2 (Table 5) have the same initial transmissivities, 400 m^{2}/day, but the hydraulic conductivities and initial saturated thicknesses are different by a factor of 4. The long-term depletion rates are equal to the abstraction (5 Ml/day) in all the runs in this series (Fig. 4), because the single river model (model A) is being used. However, the depletion rate in run A5.2 (red line, Fig. 4) with the higher hydraulic conductivity rises more slowly than in run A5.1 (solid black line). This is because, as pumping depresses the groundwater heads, the transmissivity falls more quickly in the run with the higher hydraulic conductivity (A5.2). This lower transmissivity results in a deeper cone of depression that spreads out more slowly and so run A5.2 accesses more water from storage and less from the river (red line) than the run with lower hydraulic conductivity (solid black line).

Run A5.3 includes the variation of hydraulic conductivity with depth, but has the same initial transmissivity and initial saturated thickness as run A5.2 with no VKD (Table 5). In the run with VKD (A5.3), the transmissivity is more sensitive to the drawdown in heads so the depletion rate rises more slowly (dashed black line) than in the run without VKD (A5.2, red line). The maximum difference between the depletion rates for all these runs is about 0.17 Ml/day or less than 4% of the abstraction rate.

Although unconfined conditions and variable hydraulic conductivity with depth (VKD) give rise to non-linear behaviour with respect to groundwater head, the effect on the river flow depletion rates in these investigations was small. However for a shallower Chalk or limestone aquifer, VKD could lead to larger variations in transmissivity. In practice, analytical solutions such as the IGARF spreadsheet can be used with the highest and lowest anticipated transmissivities to check whether the errors from ignoring the variation in transmissivity are likely to be significant.

## River Leith case study

The River Leith is a tributary of the River Eden in Cumbria in NW England (Fig. 5), which flows over the Carboniferous Limestone and Millstone Grit and then onto the highly permeable Penrith Sandstone aquifer. The River Leith is part of the River Eden SAC (Special Area of Conservation). This in turn is part of the Natura 2000 network of protected areas, which were set up to ensure the survival of Europe's most valuable species and habitats (Council of European Communities 1992, Article 3). The River Leith requires action under two pieces of European legislation. Firstly the Habitats Directive (Council of European Communities 1992) requires that all abstraction licences are reviewed to assess whether they could have an adverse impact on the ecological integrity of Natura 2000 sites. Secondly the Water Framework Directive (Council of European Communities 2000) requires that groundwater bodies are at ‘good’ status by 2015 (Whiteman *et al.* 2012).

The Environment Agency reviewed the ecological impact of two licensed groundwater abstractions located to the north of the River Leith, Figure 5b, on two designated fish species, salmon and bullhead. The abstraction to the east began pumping in 1970 and the one to the west in 1997. The review was based on two main issues, firstly the physical habitat available in the river and secondly the estimated flow depletion due to the abstractions. Field studies indicated that, where the river is connected to the sandstone aquifer (from about 2 km upstream of Cliburn gauging station to the confluence with the River Lyvennet, Fig. 5b), there is only a small amount of suitable habitat (cobbles and riffles) available for bullhead and juvenile salmon. Estimates of the flow depletion in the River Leith using a ‘no-recharge’ depletion model are described below.

### The ‘no-recharge’ depletion model

The modelling investigations above show that recharge can be ignored in a model designed to estimate river flow depletion, unless it causes variations in the length of the stream that is disconnected (series 2) or dry (series 3), or in the transmissivity (series 5) or in other non-linear behaviour with respect to groundwater head. No reaches of the River Leith dry up and, although the river is known to be disconnected in its upper reaches, this is a permanent state and so does not result in non-linear behaviour with respect to groundwater head. The aquifer is locally unconfined, but the error introduced by assuming that the transmissivity is constant was shown to be small (less than 5%) compared with other uncertainties in the system. A ‘no-recharge’ depletion model was built (Fig. 6) using MODFLOW (McDonald & Harbaugh 1988), comprising three layers, a uniform grid of 500 m square cells and no-flow boundaries on all four sides. The groundwater pumping was from layer 2. The model included the main rivers that are in hydraulic connection with the aquifer, the Eden and its four main tributaries (Fig. 5a). The stage elevations of all the rivers were set at 0 m, the river bottom elevations at −1 m and the initial groundwater heads at 0 m.

As noted at the start of the modelling investigations section, the depletion rate is the difference between the river leakage for a run with abstraction and the corresponding run without abstraction. In the Leith model the initial heads are equal to the elevation of the river stage so the river leakage without abstraction is zero and the depletion rate is simply the river leakage for the abstraction run. This cuts the number of runs to estimate depletion by half.

Figure 6 shows the structure of the ‘no-recharge’ depletion model in plan and cross-section. Table 6 shows the best estimate model parameters that were used for the baseline run and their plausible ranges that were used for the sensitivity runs. River conductances were estimated from river width, river bed thickness, river bed permeability, vertical hydraulic conductivity of the aquifer (*K*_{v}) and the length and thickness (*d*) of the cells below the river. They were compared with a review of the conductances used in models of several sandstone aquifers in the UK, where the range was 50–1000 m^{2}/day (Rushton 2003). The conductances used in the Leith model are specific to a grid size of 500 m since conductance values are known to depend on grid size (Rushton 2007). Values of hydraulic conductivity, transmissivity and storage were based on the Environment Agency's hydrogeological investigations for the Habitats Directive assessment of the Leith and previous work by Lovelock *et al.* (1975) and Price *et al.* (1982).

The models were all time-variant with no recharge and were run until they reached a new equilibrium, that is, a new steady-state condition. For the baseline run the abstraction wells get most of their water by depleting baseflow to the largest river (River Eden) and the nearest river (River Leith). The long-term depletion rates from each river as a percentage of the total abstraction for the best estimate parameters (baseline run) are River Eden 41%, River Leith 33%, Rivers Eamont & Lowther 21% and River Lyvennet 5% (totalling 100%).

The outputs from typical regional models in the UK include groundwater heads and river baseflows, and these models are ‘calibrated’ by comparing their outputs with field measurements. As stated above, this model provides direct outputs of the river flow depletion rates from the run with abstraction. So unlike a standard model (where the outputs are river flows), the depletion model cannot be compared against observations. This is because field measurements of depletion rates (the difference between the flow in the river with a groundwater well pumping and what it would have been without) do not exist. This means that more reliance than usual must be placed on sensitivity analysis.

Sensitivity runs were carried out based on the plausible ranges of the input parameters shown in Table 6. These yielded a range of modelled depletion rates for the River Leith. Setting the river conductances to their lowest values produced the lowest depletion rates from the River Leith (11% of the abstraction), whereas high river conductances or low aquifer transmissivities produced the highest depletions (49% of the abstraction). When transmissivity is low, the distance between the pumping well and river providing the water has a larger influence and it is easier for a pumping borehole to obtain its water from a nearby river compared with a distant one. Long-term depletion rates occur when the system is at steady state, so these are independent of changes in storage coefficient. Storage does, however, influence timing, and increasing the storage coefficient by a factor of 10 increased the time taken to reach dynamic equilibrium (steady-state) by about two years.

This ‘no-recharge’ depletion model was quick to build (about 10 days), model runtimes were less than 2 minutes and the whole process from conceptualizing the system to final results took less than 25 working days. Having identified which rivers are most likely to be impacted by the abstractions and the likely range of the flow depletion for the River Leith, ecologists used the analysis below to consider whether these impacts were large enough to adversely affect the habitat for salmon or bullhead.

### Impacts on ecology

Figure 7a shows flow duration curves for flows on the River Leith at Cliburn gauging station (Fig. 5b) against the guideline flow for salmon. This study was conducted when there was only one year's flow data available from Cliburn (from November 2003 to December 2004), so it was adjusted using the river flow data from Temple Sowerby gauging station (Fig. 5b) between 1976 and 2004 to produce a synthetic flow record for Cliburn from 1976 to 2004. The current flow duration curve at Cliburn (black line in Fig. 7a) was derived from this synthetic long-term record.

This current flow duration curve includes the full effects of the depletion due to the two groundwater abstractions because both have been pumping long enough (more than five years) for the river–aquifer system to have reached dynamic equilibrium. Therefore, adding the modelled depletion rates back in to the current flow duration curve (black line) gives a high and a low predicted flow duration curve for no groundwater abstraction (red and green lines). The red line shows the highest flows that can be expected if the two abstractions ceased (by adding 49% of the current abstraction rate) and the green line shows the lowest flows that can be expected (by adding 11% of the current abstraction). The two flow duration curves are not the same as fully naturalized flow duration curves because other influences such as the impact of quarrying, other groundwater abstractions and discharges from sewage treatment works are not taken into account.

Depths and velocities were measured at five sites on the river and used to derive guideline flows for each of the protected species, 9.14 Ml/day for salmon and 3.52 Ml/day for bullhead (ATKINS 2005, 2007). River flows below these guideline values are likely to limit the habitat for the two species. If pumping from the two wells stopped, the highest anticipated river flows would be above the salmon guideline for 80.4% of the time and so would be below it for 19.6% of the time or on average 72 days per year, point A on Figure 7a. The lowest anticipated river flows would be below the guideline for on average 74 days per year, point B. Environment Agency ecologists concluded that neither of these flow regimes, even with the groundwater abstractions turned off, would provide suitable flow habitat for juvenile salmon in most years. Considering also the limited amount of riffle habitat on the depleted reach, referred to at the beginning of this section on the River Leith case study, it was concluded that the two groundwater abstractions themselves would not cause adverse impact to the integrity of the designated site for salmon.

Figure 7b shows the same black, red and green lines as in Figure 7a against the ecological flow guideline for bullhead. The red and green lines show that without the abstractions, the river flows are below the guideline flow for between 4 and 16 days per year on average, which Environment Agency ecologists considered acceptable habitat.

The Habitats Directive requires that groundwater abstractions at their fully licensed rates are also taken into account. Therefore, two new flow duration curves (the magenta and cyan lines) were constructed by subtracting 49% of the fully licensed abstraction from the ‘no-abstraction highest expected flows’ curve (red line) and 11% of the fully licensed abstraction from the ‘no-abstraction lowest expected flows’ curve (green line). These show that the flows in the Leith would be below the bullhead guideline for on average between 20 and 22 days per year, which Environment Agency ecologists also considered acceptable and so concluded that the two abstraction licences would also have no adverse impact on the integrity of the site for bullhead.

## Conclusions

The Environment Agency has calibrated regional models for most of the major aquifers in England and Wales. They are the best synthesis of how the regional river–aquifer system behaves and should be used as the most appropriate tools for estimating the impact of groundwater pumping on river flows. However, where they do not exist the ‘no-recharge’ depletion model described here provides a rapid means of estimating river flow depletion more accurately than by using analytical approaches.

The investigations in this paper show that a model for estimating river flow depletion due to groundwater abstraction should include all the rivers in hydraulic connection with the aquifer and the correct stream length for intermittent streams. If multiple rivers are not included, the impacts on rivers beyond the nearest river can be significantly underestimated.

On the other hand recharge, variations in transmissivity and correct river elevations are less important. Recharge does not need to be included if the flow either way between river and aquifer (river leakage) varies linearly with groundwater head. However, if the length of the disconnected or dry sections of the river changes, river leakage no longer varies linearly with groundwater head and recharge does then need to be included (series 2 and 3). Seasonal variations in transmissivity, either due to unconfined conditions or where hydraulic conductivity varies with depth, led to small errors in depletion estimates in these investigations (less than 4% of the abstraction rate). However, for a shallower Chalk or limestone aquifer, VKD could lead to larger variations in transmissivity and larger errors in the predicted depletion. Analytical solutions such as the IGARF spreadsheet can be used to estimate the size of these errors to assess whether they are likely to be significant.

As Sophocleous (2002) points out, groundwater pumping gives rise to aquifer drawdown and river flow depletion. Both of these are related to the rate, location and duration of pumping and to the aquifer properties (transmissivity and storage coefficient), but the natural recharge rate is unrelated to any of these parameters and the investigations described in this paper confirm that recharge can often be ignored.

A ‘no-recharge’ depletion model was used to produce rapid estimates of the range of depletion rates from the River Leith in NW England due to two licensed groundwater abstractions. This was done as part of an assessment for the European Union Habitats Directive. Low river conductance values produced the lowest depletion rates (11% of the abstraction rate) and high river conductances and low transmissivity values produced the highest depletion rates (49% of the abstraction rate).

The flow duration curve of current flows on the River Leith and the modelled depletion rates were used to construct predicted flow duration curves where the two groundwater wells were not pumping and also where they were pumping at the fully licensed rate. Environment Agency ecologists compared these curves against ecological flow guidelines for the fish species salmon and bullhead and concluded that the groundwater abstractions were causing no adverse impact on the integrity of this European-designated site.

## Acknowledgments

The authors would like to acknowledge the generous support and guidance of many colleagues in the Environment Agency and in the UK groundwater community over many years and to thank the paper's peer reviewers for their useful comments. The views expressed in this paper are those of the authors, and do not necessarily represent those of the Environment Agency for England and Wales or the Scottish Environment Protection Agency. Jackson, Hughes and Mansour publish with the permission of the Executive Director of the British Geological Survey.

- © The Geological Society of London 2012