Methods Note/

A New Method for Estimating Rechargeto Unconfined Aquifers Using Differential RiverGaugingby Andrew M. McCallum1, Martin S. Andersen2,3, and R. Ian Acworth2,3

AbstractIn semiarid and arid environments, leakage from rivers is a major source of recharge to underlying unconfined

aquifers. Differential river gauging is widely used to estimate the recharge. However, the methods commonlyapplied are limited in that the temporal resolution is event-scale or longer. In this paper, a novel method ispresented for quantifying both the total recharge volume for an event, and variation in recharge rate during anevent from hydrographs recorded at the upstream and downstream ends of a river reach. The proposed methodis applied to river hydrographs to illustrate the method steps and investigate recharge processes occurring in asub-catchment of the Murray Darling Basin (Australia). Interestingly, although it is the large flood events whichare commonly assumed to be the main source of recharge to an aquifer, our analysis revealed that the smallerflow events were more important in providing recharge.

IntroductionRecharge estimates are critical for the management

of water resources in semiarid and arid environments (deVries and Simmers 2002; Scanlon et al. 2006). In suchenvironments, leakage from rivers (as well as channelsand wadis) is a major source of recharge to the underlyingunconfined aquifers (Rushton 1997). Differential rivergauging, where the difference in river flow between suc-cessive cross sections is calculated, is widely used to esti-mate the recharge from rivers (Scanlon et al. 2002; Kalbuset al. 2006). Many studies have made use of this methodwith good results (Ruehl et al., 2006; USGS, 2008; Harteand Kiah, 2009 ), and when compared to other methods(e.g., hydrometric, seepage meters) it has been found togive the best estimate of recharge to unconfined aquifers

1Corresponding author: Connected Waters Initiative, Uni-versity of New South Wales, Sydney, NSW, Australia;a.mccallum@wrl.unsw.edu.au

2Connected Waters Initiative, University of New South Wales,Sydney, NSW, Australia.

3 National Centre for Groundwater Research and Training(NCGRT), Australia.

Received July 2012, accepted February 2013.© 2013, National Ground Water Association.doi: 10.1111/gwat.12046

from rivers (Cey et al. 1998; Kaleris 1998). As theonly data required are recorded river hydrographs attwo locations, which in most countries worldwide arereadily available, the method is a powerful tool to thehydro(geo)logist.

As the timing of peak flow at the upstream gauge isdifferent from that at the downstream gauge, the differen-tial river gauging method can provide the total rechargevolume for an event but not the variation in recharge rateduring an event. The temporal resolution of the method isconsequently assumed to be event-scale or longer (Scan-lon et al. 2002). Therefore, while the average rechargerate can be computed if the event duration is known,the variation in recharge rate during an event cannotbe determined. From the perspective of catchment-scalewater resource management this is acceptable, however,when the temporal aspect of recharge processes is of con-cern, or when comparison with continuous measurementsof recharge is required (e.g., from hydrometric methods),the limitation that the temporal resolution is event-scaleor longer becomes important.

To our knowledge, only one study has used a differ-ential river gauging method to estimate the variation inrecharge rate during an event in addition to total rechargevolume. Opsahl et al. (2007) established the relationship

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for all flow events between transit time (i.e., the lagbetween peak flow at the upstream and downstreamgauges) and peak flow at the upstream gauge. This rela-tionship was then used to adjust the downstream data toan equivalent data set which could be directly comparedwith the upstream data for each flow event. However,there was uncertainty in the established relationship,which would likely increase if the method were appliedto regulated reaches in semi-arid or arid environmentswhere flow regimes are highly erratic and episodic.

In this paper, a novel method is presented whichallows for estimating the total recharge volume for anevent, as well as the variation in recharge rate duringan event from hydrographs recorded at upstream anddownstream ends of a river reach. The proposed methodis applied to river hydrographs from the Namoi River toillustrate the method steps and complete a preliminaryinvestigation of the recharge from the river to the aquiferin the Maules Creek Catchment, a sub-catchment of theMurray Darling Basin (Australia).

Methodology

Theoretical BackgroundThe mass balance for a river reach is defined as (based

on Lerner et al. 1990):

Qu + Qi + Qf = Qd + Qo + Ea + �S

�t, (1)

where Qu is flow at the upstream end of the reach, Q i isflow into the reach (e.g., tributaries), Q f is river-aquiferflux (n.b., a positive value indicates a mass gain to river;conversely, a negative value indicates a mass loss fromriver), Qd is flow at the downstream end of the reach, Qo

is flow out of the reach (e.g., surface water diversions),E a is evapotranspiration from the reach, and �S

�t is thechange in channel storage with time. All components ofthe mass balance have dimensions L3/T.

If �S�t is assumed negligible, which is a reasonable

assumption for analysis at the event-scale or longer time-scales, Equation 1 simplifies to:

Qf = Qd − Qu + Qo − Qi + Ea. (2)

Equation 2 is the commonly used equation in thedifferential river gauging method for estimating the river-aquifer flux (i.e., recharge). It has the limitation that thetemporal resolution is event-scale or longer, and so therecharge rate for shorter time-scales cannot be determined.An alternative approach is thus required.

Proposed MethodStarting from the same mass balance approach (i.e.,

Equation 1), the recharge rate at shorter time-scalescan be estimated, without making assumptions about�S�t , from hydrographs recorded at the upstream anddownstream ends of a river reach. The physical basisbehind the proposed method is that although a flow

event spreads out with time as it travels between theupstream and downstream gauges, the mass remainsthe same if no recharge from the river occurs. It istherefore possible to create equivalent hydrographs bytime-shifting the recorded hydrographs. These can thenbe compared to check for mass conservation. This can bedone by shifting the downstream hydrograph backward intime, the upstream hydrograph forward in time, or somecombination. For the sake of illustrating the method, E a,Q i, and Qo have been assumed to equal zero.

The proposed method consists of eight steps asoutlined below: These were scripted in Matlab (thevariable names are in parentheses).

1 Select flow event to be analyzed (between start and enddate/time) for upstream and downstream hydrographs(i.e., Qu,d).

2 Create cumulative hydrographs by integrating thehydrographs (i.e., CumQu,d).

3 Create normalized cumulative hydrographs by dividingthe maximum values in the cumulative hydrographs(i.e., NorCumQu,d).

Note: if scripting these steps recreate normalizedcumulative hydrographs by discretizing on the y-axis(i.e., between 0 and 1) rather than on the x -axis (i.e.,between start and end date/time).

4 For each value of the cumulative normalized flowcurve on the y-axis, calculate the value at a chosenpoint between CumQu and CumQd on the x -axis(e.g., midpoint). This gives a time-shifted normalizedcumulative hydrograph (i.e., NorCumQ t).

Note: if scripting these steps recreate the time-shiftednormalized cumulative hydrograph by discretizing onthe x -axis (i.e., between start and end date/time) ratherthan on the y-axis (i.e., between 0 and 1).

5 Create time-shifted cumulative hydrographs by multi-plying by the maximum values in the cumulative hydro-graphs (i.e., CumQt

u,d).6 Create time-shifted upstream and downstream

hydrographs by differentiating the cumulative hydro-graphs

(Qt

u,d

).

7 Create a time series of river-aquifer flux (n.b., a nega-tive value indicates recharge from river to aquifer) bysubtracting the downstream from upstream hydrograph:

Qtf = Qt

d − Qtu. (3)

8 Repeat Steps 4 to 7 with different time-shifted nor-malized cumulative hydrographs between the limits ofshifting the downstream hydrograph backward in timeand shifting the upstream hydrograph forward in timeto give a range of possible time series of river-aquiferflux.

Field ExampleA reach of the Namoi River in New South Wales,

Australia (Figure 1) was investigated using the method.

292 A.M. McCallum et al. Groundwater 52, no. 2: 291–297 NGWA.org

Figure 1. Location of the Namoi Catchment (main figure) within the Murray Darling Basin and Australia (inset figures). Alsoshown are Maules Creek Catchment and the upstream (Boggabri) and downstream (Turrawan) gauging stations. The arrowsadjacent to the rivers show the flow directions. Also shown is the location of the geological cross section A to A′ shown inFigure 2.

The Namoi River is the main river in the Namoi Valley,and is a tributary to the environmentally and politicallysensitive Murray Darling Basin. The alluvial aquifersalong the river have one of the highest groundwaterabstraction levels in Australia.

The selected reach of the Namoi River runs fromsouth to north for 34 km through the semiarid MaulesCreek Catchment. Beneath and to the east of the river is apalaeochannel up to 120 m deep, filled with alluvial claysand permeable sands and gravels (Figure 2). The gentlysloping plains of the catchment, which consist mostly ofHolocene clay and silt rich vertosols, are 200 to 250 mabove sea level (Figure 3a). The Namoi River is incisedinto this flood plain up to a depth of about 8 m (Figure 3b).Further geological details can be found in McCallumet al. (2013).

Owing to groundwater abstraction for flood irrigationwithin the catchment, the groundwater levels have beenlowered such that the reach is now predominately losingduring both low- and high-flow conditions (McCallumet al. 2013). Recharge from the river is now a major

source of water for the ongoing groundwater abstraction(Giambastiani et al. 2012). Understanding and quantifyingthe recharge to the unconfined aquifer is thus an importantstep in the management of the water resource.

Government-operated gauging stations at theupstream (Boggabri) and downstream (Turrawan) endof the reach record river stage which is post-processedto give river flow (DNR 2011) (see Figure 1). For thispaper, hourly data from the stations were used. The riveris regulated at Keepit Dam, approximately 50 km south-east of the upstream gauging station. Between the twostations, there is a major tributary, Maules Creek. Whilethis creek has perennial pools about 10 km upstream fromits confluence with the Namoi River (Rau et al. 2010),the creek is ephemeral and rarely flows between thepools and the confluence (Andersen and Acworth 2009).For this reach of the Namoi River, evapotranspirationcan be assumed negligible compared to the magnitude ofthe other components (McCallum et al. 2013).

The proposed method was applied to the gaugingstation data in two stages. First, a flow event from

Figure 2. Schematic geological cross section for Maules Creek Catchment (A to A′ in Figure 1). The red dashed vertical linesshow where lithological borehole information is available. Elevation is shown in meters above the Australian Height Datum(m AHD).

NGWA.org A.M. McCallum et al. Groundwater 52, no. 2: 291–297 293

(a) (b)

Namoi River

Figure 3. Photograph of (a) flood plain and Namoi River facing north and (b) Namoi River and river banks at low-flowconditions facing south.

13 December to 26 December 2008 (i.e., ∼14 d) wasselected to illustrate the method step-by-step. Second,high-flow events (i.e., greater than 1.5 GL/d) between thewater years 2000 and 2010 were analyzed (n.b., GL isGigalitre, e.g., 1.5 GL/d = 1.5 × 106 m3/d; the water yearruns from October to September). In this way statisticsof flow in the Namoi River and recharge in the MaulesCreek Catchment were created for each flow event (i.e.,cumulative flow volume at the upstream gauge, eventduration, total recharge volume, and variation in rechargerate during event). The start and end date/time wasdefined as the date/time corresponding to the lowest flowat the upstream gauge in the 7 d prior to/following arecorded flow of 1.5 GL/d. As the data set was large (i.e.,a decade of hourly data at two gauges), the analysis wasautomated using a Matlab script.

Results and Discussion

StepsThe eight steps outlined in the methodology are

illustrated in Figure 4 and discussed below:1. Hydrographs for the upstream and downstream

gauges for the selected flow event show that the down-stream hydrograph (gray line) has a smaller and laggedpeak flow as compared to the upstream hydrograph (blackline). The upstream hydrograph peaked at 26.4 GL/d whilethe downstream hydrograph peaked at 22.5 GL/d. Therewas a lag of 18 h between the peaks.

2. The cumulative flow for the upstream gaugewas 85.7 GL while for the downstream gauge this was74.8 GL, that is, during the analyzed flow event, 85.7 GLentered the catchment and 74.8 GL left the catchment. Thedifference between these curves at the final time step (i.e.,10.9 GL) is equal to the total recharge volume for theevent.

3 and 4. When the cumulative hydrographs arenormalized, they still follow the s-shape but becomedimensionless, varying between 0 and 1 (solid lines). Thetime-shifted normalized cumulative hydrograph also fol-lows the s-shape, is dimensionless, and varies between 0and 1 (dotted line). The dotted line is midway between the

solid lines (i.e., shifting both the downstream hydrographbackward in time and the upstream hydrograph forwardin time).

5. The time-shifted cumulative hydrographs forupstream (black line) and downstream (gray line) gaugeshave the same final values as the originals (i.e., 85.7 and74.8 GL) but are shifted in time.

6. The difference between the curves at the final timestep is equal to the total recharge volume for the event(i.e., 10.9 GL). The time-shifted downstream hydrograph(gray line) has a smaller peak flow as compared tothe time-shifted upstream hydrograph (black line). Thepeak flows are no longer lagged. By time-shifting therecorded hydrographs, the hygrographs are therefore nowcomparable.

7 and 8. From the time-shifted hydrographs, a time-line of the recharge can be estimated (dotted line). Sincedifferent time-shifted normalized cumulative hydrographsare possible (i.e., Steps 4 and 8 above), the timing ofrecharge cannot be determined exactly (cf. dotted lineand solid lines). However, the variation in recharge ratecan be bounded by the upstream and downstream limits(solid lines).

Recharge in Maules Creek CatchmentThe results of applying the method to field data are

shown in Figure 5. Each mark on the figure representsa recharge event that occurred sometime during thewater years 2000 to 2010. As would be expected, thetotal recharge volume over an event increases withincreasing cumulative flow volume at the upstream gauge(Figure 5a). The total recharge volume ranges from 0.3to 34.7 GL, while the cumulative flows range from 3.5 to188.9 GL. The correlation between total recharge volumeand cumulative flow is high (i.e., r = 0.97). The slopeof the line of best fit (∼ 0.2) is the total rechargevolume expressed as a ratio of cumulative flow. Thescatter about the line indicates that the total rechargevolume is dependent on other variables (e.g., antecedentgroundwater level), in addition to the cumulative volumeof the flow event.

The cumulative flow is dependent on two variables:the duration of the flow event and the variation in recharge

294 A.M. McCallum et al. Groundwater 52, no. 2: 291–297 NGWA.org

Q

NormCumQ

CumQ

CumQ

Qt

Qt

NormCumQ

NormCumQ

Q

u

Qt

f

Qt

f

Qt

f

d

CumQ

CumQ

Figure 4. (1) Flow event hydrographs for upstream (blackline) and downstream (gray line) gauges. (2) Cumulativehydrographs for upstream (black line) and downstream(gray line) gauges. (3, 4) Normalized cumulative hydrographsfor upstream (black line) and downstream (gray line) gauges.Also shown is the time-shifted normalized cumulative hydro-graph (dotted line). (5) Time-shifted cumulative hydrographsfor upstream (black line) and downstream (gray line) gauges.(6) Time-shifted flow event hydrographs for upstream (blackline) and downstream (gray line) gauges. (7, 8) Rechargeusing time-shifted normalized cumulative hydrograph (dot-ted line). Also shown are the upper and lower bounds of therecharge (black and gray lines).

rate during the event. There is a clear relationship betweenthe total recharge volume for the event and the eventduration (Figure 5b). The duration of flow events rangefrom 4 to 71 d. While the correlation is high (i.e., r = 0.97)between the total recharge volume and event duration, theamount of scatter for events with durations less than 20 d

Figure 5. (a) Total recharge volume vs. cumulative flow.(b) Total recharge volume vs. duration of event. (c) Totalrecharge volume vs. maximum rate of recharge. Largenatural flow events are shown as circles, and small naturalflow events and dam-release events are shown as crosses. Theillustrative flow event in Figure 3 is plotted in as a single datapoint, with a total recharge of −10.9 GL, cumulative flow of85.7 GL, duration of 14.5 d, and maximum rate of rechargeof −3.3 GL/d.

is significant, indicating that other important factors areat play.

When total recharge volume is plotted against maxi-mum rate of recharge during the event the data group intotwo distinct populations (Figure 5c). On the one hand,there are data which lead to total recharge volumes ofapproximately 10 GL or less but have varying and largerecharge rates of more than 3 GL/d (shown as circles). Onthe other, there are data which lead to total recharge vol-umes of upwards of 30 GL but have recharge rates of lessthan 1 GL/d (shown as crosses).

Recharge from the Namoi River in the MaulesCreek Catchment during high-flow conditions is thereforedue to two distinct processes. Comparing the two datapopulations with the raw hydrographs reveals that thecircles correspond to large natural flow events whilethe crosses correspond to small natural flow events anddam-release events. The threshold between these twopopulations is approximately 4 GL/d. The large naturalflow events with large rates of recharge do not necessarilylead to large total recharge volumes for individual events.On the other hand, the small natural flow events and dam-release events, while having relatively small flow rates andrelatively small rates of recharge, have potential to leadto large volumes of recharge.

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Over the analyzed decade, twice as much rechargeoccurred due to small natural flow events and dam-release events than the large natural flow events (193 vs.82 GL). This interesting fact has implications for waterresource management. There is a widespread perceptionthat because of the natural occurring cycles of droughtand flood within semi-arid environments, large flowevents are predominately responsible for replenishmentof groundwater resources via recharge from rivers tounconfined aquifers. For the studied decade in the studiedcatchment, this was not the case. The analysis presentedhere suggests that the smaller flows are more significant.This could have significance on the design of dam releaseevents so as to optimize recharge to the groundwater.This is presently an under-researched area of watermanagement (cf. Zammouri and Feki 2005).

McCallum et al. (2013) present data which showthe annual groundwater abstraction for Maules CreekCatchment between 1985 and 2005 varied from 5.4to 17.9 GL/year with an average annual abstraction of10.9 GL/year. The recharge of 10.9 GL recorded by thedifferential river gauging in the illustrative exampletherefore represents approximately the volume abstractedduring the average irrigation year. In the case of thisevent, recharge from the river from a single flow eventwas sufficient to meet the average irrigation demand.However, as a consequence, the downstream river flowwould be reduced by the recharged volume, therebyimpacting the downstream users of surface water as wellas the environment. Furthermore, for the analyzed decade,only six flow events had estimated total recharge volumesequal to or greater than 10.9 GL (see Figure 5a), while theremaining 46 events had an average total recharge volumeof only 2.8 GL, indicating that the irrigation demandwould on average exceed the recharge from the river.

Method LimitationsThere are a number of limitations associated with

the proposed method. First, gauging data can haveinherent uncertainties in accuracy. Oftentimes, due tothe difficulty of creating accurate rating curves, thedata quality can be poor for very low- and very high-flows. How this uncertainty is propagated into the resultsshould be assessed on a site-by-site basis. Understandingthe uncertainties involved is imperative to properlyinterpreting the results (Schmadel et al. 2010).

Second, following on from the previous limitation,the range of recharge volumes and rates that can be cal-culated directly depends on the uncertainty and recordingfrequency in the gauging data (Scanlon et al. 2002). Thiscreates a constraint on the spatial and temporal resolu-tion of the method. As the recharge volume must besignificantly higher than the uncertainties associated withthe gauging station measurements, the distance betweenthe gauging stations must be sufficiently large to overcomethis issue (Kaleris 1998). The lag between hydrographpeaks that can be resolved depends on the frequency of thecollected data. In the illustrative example, the lag of 18 hwas able to be resolved as hourly data were available. This

may pose a limitation for different catchments. Again,these issues should be considered on a site-by-site basis.

Third, the differential river gauging method thereforegives an estimation of fluxes over a selected reach lengthand is thus not sensitive to small-scale heterogeneities inthe recharge (Kalbus et al. 2006). This, however, is oftennot a significant limitation as large-scale measurementsoften provide a better estimation of the recharge thanpoint-scale measurements (Cey et al. 1998). This couldthus be considered an advantage rather than a limitation.The relationship between at-point measurements andchannel-reach measurements needs further investigationin any case (de Vries and Simmers 2002).

Fourth, as the differential river gauging methodgives the net exchange of water between the river andaquifer between gauging stations, it is conceivable thatsmall-scale inflows and outflows can occur simultane-ously, leading to no net exchange of water between riverand aquifer (McCallum et al. 2012). Where needed, theinflows, outflows, and net exchange can be distinguishedby combining the differential river gauging method withtracer tests (e.g., Ruehl et al. 2006).

Finally, and perhaps most importantly, while Step7 refers to the “river-aquifer flux,” this needs to beinterpreted with an understanding of the specific riverhydrology. Conceptualizing the interaction as simplybeing between two reservoirs (i.e., river and aquifer)may be too simplistic. River-aquifer interactions occur atdifferent spatial and temporal scales, which superimposeon one another, causing dynamic and complex patterns ofinteraction (Angermann et al. 2012). Furthermore, thereare often various intermediate stores and flows which canimpact on the results as they operate on time-scales ofweeks to months after the peak event flow (e.g., returnflow from bank storage, interflow within the unsaturatedzone, flow from draining pools on the floodplain, and soon). These need careful consideration on a site-by-sitebasis. For example, the computed total recharge volumemay not represent actual recharge but potential rechargeonly due to the presence of perched aquifers (Lerneret al. 1990) or bank storage (Lambs 2004).

These five limitations are in common with differentialriver gauging methods generally. Further work is requiredin applying the proposed method to a variety of hydro-geological settings, as well as comparing the estimationsof total recharge volume and variation in recharge ratewith other techniques of estimating recharge from riversto unconfined aquifers (e.g., seepage meters, heat as anatural tracer).

ConclusionsBy applying this method to hydrographs recorded at

the upstream and downstream ends of a river reach, onecan estimate the total recharge volume for a flow event,as well as the variation in recharge during the event. Theproposed method overcomes the significant limitation inpreviously used differential river gauging methods that

296 A.M. McCallum et al. Groundwater 52, no. 2: 291–297 NGWA.org

assume the temporal resolution must be event-scale orlonger.

Applying the method to field data allowed forstatistics of flow in the Namoi River and recharge inthe Maules Creek Catchment to be generated for eachflow event (i.e., cumulative flow volume, event duration,total recharge volume, variation in recharge rate). Thestatistical data were useful in revealing that two rechargeprocesses are occurring during high-flows: (1) largenatural flow events with larger rates of recharge and (2)small natural flow events and dam-release events withsmaller rates of recharge but with the potential for largertotal recharge volumes.

The method can be readily transferred to othercatchments worldwide where river flows are beingmonitored.

AcknowledgmentsFunding for the research was provided by the Cot-

ton Catchment Communities CRC (Projects 2.02.03 and2.02.21). In-kind funding was provided by the NationalCentre for Groundwater Research and Training, an Aus-tralian Government initiative, supported by the AustralianResearch Council and the National Water Commission.Gabriel Rau helped with the drafting of Figures 1 through5. Ian Cartwright, Peter Engesgaard, and four anonymousreviewers provided thoughtful comments on a draft of thepaper. Erin McCallum reviewed the paper for readability.

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