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Impact of increased rechargeon groundwater discharge: DEVELOPMENT AND APPLICATION OF A SIMPLIFIEDFUNCTION USING CATCHMENT PARAMETERS

Mat Gilfedder, Chris Smitt, Warrick Dawes, Cuan Petheram, Mirko Stauffacher, Glen Walker

Impact of increased rechargeon groundwater discharge: DEVELOPMENT AND APPLICATION OF A SIMPLIFIEDFUNCTION USING CATCHMENT PARAMETERS

Mat Gilfedder, Chris Smitt, Warrick Dawes, Cuan Petheram, Mirko Stauffacher, Glen Walker

Authors: Mat Gilfedder1, Chris Smitt2, Warrick Dawes1, Cuan Petheram1,3,4, Mirko Stauffacher1, Glen Walker2

1. CSIRO Land and Water, Canberra.2. CSIRO Land and Water, Adelaide.3. Cooperative Research Centre for Catchment Hydrology.4. Department of Civil and Environmental Engineering,

University of Melbourne.

CSIRO Land and Water Technical Report 19/03CRC for Catchement Hydrology Technical Report 03/6MDBC Publication 05/03

Published by: Murray-Darling Basin Commission

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Canberra ACT 2600

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ISBN: 1 876 830 55 7

Cover photo: Arthur Mostead Margin photo: Mal Brown

© 2003, Murray-Darling Basin Commission and CSIRO

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To the extent permitted by law, the copyright holders (including its employees and consultants) exclude all liability to any person for any

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using this report (in part or in whole) and any information or material contained in it.

The contents of this publication do not purport to represent the position of Murray-Darling Basin Commission or CSIRO in any way and are presented

for the purpose of informing and stimulating discussion for improved management of Basin's natural resources.

This work was funded under the Murray-Darling Basin Commission funded StrategicInvestigations and Education projects (SI&E) Grant Number D9004: ‘Catchment characterisationand hydrogeological modelling to assess salinisation risk and effectiveness of managementoptions’. We acknowledge the advice and feedback received from members of the ProjectSteering Committee.

Funding from the National Dryland Salinity Program (Stage 2), Project CLW29: ‘Predicting thecombined environmental impact of catchment management regimes on dryland salinity’ for theinitial development of the G parameter is also acknowledged.

Thanks also to Dr Tom Hatton (CSIRO Land and Water, Perth) and Dr Rob Argent (University ofMelbourne) for taking the time to provide helpful review comments of the draft manuscript.

Acknowledgements

I M P A C T O F I N C R E A S E D R E C H A R G E O N G R O U N D W A T E R D I S C H A R G E

i

Executive summary

I M P A C T O F I N C R E A S E D R E C H A R G E O N G R O U N D W A T E R D I S C H A R G Eii

The objective of the present report is todevelop a simple approach towardsestimating the response of groundwatersystems to changes in recharge that arisefrom changes in land use. The emergentproperties of a groundwater system areexamined using scaling arguments, bycombining the effect of aquifer properties intoa single dimensionless groundwater systemsimilarity parameter (G).

The expansion of areas of saline land, andrising river system salinities is occurring inmany parts of Australia. Such environmentalchange has increased the need for an abilityto predict the effects of salinity into thefuture. Without this predictive capability,management strategies will continue to try totreat symptoms caused by salinity ratherthan develop preventative and more effectivemanagement solutions.

The timing of salinity changes in response toland use changes is not well understood.While changes in land use may causerelatively rapid changes in surface run-off andevapotranspiration, the time lag betweenrecharge to groundwater systems and theirsubsequent discharge to surface water canbe much longer. Since groundwaterdischarge is the main pathway by which saltis moved into streams, understanding thetime lags between management change andgroundwater change is paramount.

Unfortunately there is a lack of detailedmeasured data at catchment and regionalscales, even in the well-studied parts ofAustralia’s dryland regions. This fact alonemeans that any suitable approach at thislarge scale must be simple.

A dimensionless similarity parameter (G) isintroduced in this report, which simplifies thecharacterisation of a groundwater system bycombining transmissivity, specific yield,recharge, length and head. G can bevisualised as a measure of the ratio of thesystem’s ability to fill (tV) compared to itsability to drain (tH). As such, G gives anindication of the state of balance of agroundwater system.

A simple approach incorporating G is used toestimate groundwater system response timesfor five case studies under different increasedrecharge scenarios. This approach offers animportant step towards a more rigorousestimate of catchment’s overall response tochanges in land use for their componentgroundwater systems. This approach hadthree main steps:

1. The time to drain (tH) factor was scaled togive a baseline response (i.e. where nosurface discharge occurs) to an increasein recharge.

2. G was then used to obtain an estimatedresponse, by scaling this baselineresponse. For G < 4, the groundwaterresponse time was faster than thebaseline response (because surfacedischarge allowed faster change to a newequilibrium).

3. The estimated response was thenconverted into a 50% response time(which was then used to parameterise thedischarge function in Eq. 21). Thiscorrection process relied on the goodcorrelation (r2 = 0.92) between theestimated response and modelledFLOWTUBE predictions for several casestudy catchments.

This study has shown that there is a strongrelationship between variations in G and groundwater system behaviour. The plan-viewshape of a system and the slope-profile alsoimpact upon groundwater system response tochanges in recharge. The analysis has demonstrated that there is a relationship between G and the time to surface discharge in response to increased recharge. Therefore,in the absence of more detailed hydrogeologicaland hydrological data, G provides a tool tosimplify investigation of catchment behaviour.

This report investigates the response of both generic and case-study groundwater systems to increased recharge. Further workis required to test how such systems willrespond to reafforestation or other rechargereduction strategies.

Acknowledgements i

Executive summary ii

1. Introduction 11.1 Objective and outline 2

2. Scaling the groundwater equations 22.1 Dimensionless G parameter 4

3. Steady-state surface discharge 53.1 Steady state results 53.2 Summary of steady-state investigation 6

4. Transient response to land use changes 74.1 Groundwater modelling 74.2 Transient state results 74.3 Summary of transient modelling 9

5. Groundwater system case studies 105.1 Calculating G for the case studies 115.2 Groundwater response—case studies 115.3 Groundwater response—overall comparison 125.4 Predicting case study response 13

6. Discussion 15

7. Conclusions 16

8. References 17

Table of contents


iii


iv


The expansion of areas of saline land, andthe rising salinities of river systems haveincreased the need for an ability to predictthe likely environmental effects into the future(PMSEIC 1999). Salinity is a surfaceexpression of hydrological change togroundwater systems. Therefore, anunderstanding of groundwater systems, andtheir responses to land use change, shouldlie at the core of any method used to predictchanges in land and stream salinisation intothe future.

Regional or catchment scale methods musttake into account the fact that features ofsalinity are related to the scale and type ofgroundwater systems, which can varysignificantly both within and betweencatchments. As such, the first step inprediction at a regional or catchment scalewill involve the disaggregation of thelandscape into smaller components thatexhibit similar behaviour in terms of theirhydrology and salinity processes (Gilfedderand Walker 2001). An approach currentlyfavoured in Australia is the classification ofgroundwater flow systems at a range ofscales (local, intermediate and regional)which are also related to the topographicaland hydrogeological processes leading tosalinity in each system (Coram et al. 2000).This classification offers a systematiclandscape disaggregation, useful at anational or regional scale.

The second important step is theidentification and simplification of relevantlandscape characteristics to predictgroundwater response to land use change.The complexity of these methods must below, because of the paucity and irregularity ofavailable data at the catchment scale.Previous research has examined relationshipsat a catchment scale betweenevapotranspiration and vegetation type withrespect to rainfall (Holmes and Sinclair 1986;Zhang et al. 2001). The complement of this isthat the non-evaporated component ofrainfall (runoff + recharge = yield) will alsofollow the inverse relationship. This has beenused to investigate the relationship between

rainfall and yield, with changes in land use forcatchments in the Murray-Darling Basin(Bradford and Zhang 2001). It has also beenused to study the effects of strategicreafforestation over part of the Murrumbidgeecatchment in New South Wales (Vertessyand Bessard 1999). The investigation of howthis relationship might relate to groundwaterrecharge has also been reviewed byPetheram et al. (2002), who looked atpossible relationships between groundwaterrecharge and vegetation type for a range ofsoil types with respect to rainfall.

The third step is to predict the timing ofgroundwater response, following a change in recharge. The previous studies mentioneddid not attempt to look at the temporalresponse of catchments to land use change.Instead they were based on the assumptionof long-term mean annual condition, at asteady state. However, the effect of changesin land use on catchment yield is notinstantaneous. While the evaporated andrun-off components may respond relativelyquickly to a land use change, increasedrecharge to a groundwater system may notnecessarily express itself as a correspondingincrease in surface discharge for many years.The timing of effects of a large-scale land usechange on catchment yield will be differentfor a range of groundwater systems within a catchment. This timing is very important. It affects the physical and economic viabilityof possible management options, sincegroundwater discharge is the process whichmobilises salt to the land surface and also tosurface water bodies. Dawes et al. (2001)considered relationships between catchmentyield and land use, using a two-parametergroundwater discharge function as anestimate of the expected shape of theresponse for each of the three groundwaterflow system types. This work identified theneed for further, more scientifically rigorousinvestigation of discharge behaviour, thattakes into account the characteristics andimpacts of the groundwater system.

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1. Introduction

1.1 Objective and outline

The objective of this report is to develop a simpleapproach to estimate the response groundwateremergent properties of a groundwater systemare examined using scaling arguments, bycombining the effect of aquifer properties into asingle dimensionless groundwater systemresponse similarity parameter (G).

• The first part of this report usesdimensional analysis to derive agroundwater system scaling argumentthat is used to obtain G. Some features of G are then explored of for both steadystate and transient scenarios. The steadystate component looks at changes withgroundwater system parameters, andalso aquifer shape and profile.

• The second uses the FLOWTUBEgroundwater model to investigate theeffect of these changes on the temporalresponse of an idealised groundwatersystem systems to changes in rechargethat arise from changes in land use.

• The third part investigates the modelledbehaviour of five case studies toincreased recharge. A simple approachthat uses G is developed, to estimatetransient groundwater system responsefollowing increased recharge.


2

Dimensional analysis is a mathematicaltechnique that can be applied to complexphysical systems to help determinerelationships between variables. Byidentifying the factors involved in a physicalsituation, dimensional analysis can be usedto form a relationship between them. Thus, it can be used to combine several variablesinto a single parameter to simplify the inter-comparison of different groundwatersystems. Examples of this include theReynolds number for viscous flow, andFroude number for open channel flow.

This type of analysis allows the simplificationof a range of aquifer properties into a singlesimilarity parameter (G) for a groundwatersystem. The first step in this analysis is totake a control volume within a groundwatersystem (Figure 1).

2. Scaling the groundwaterequations

Figure 1. Mass balance variables for control volumewithin a groundwater system. R is recharge, h0 and h1

are aquifer thickness, L is length, x is distance alongthe aquifer, and the Q terms are groundwater flowinto and out of the control volume.


3

The mass balance equation for the controlvolume in Figure 1 can be expressed as:

, (1)

where Q is flow, R is recharge, w is the width,S is specific yield, h is groundwater head, x isthe distance along the groundwater system,and t is time. Substituting Darcy’s Law intoequation (1) yields:

, (2)

where T is aquifer transmissivity (= kd), k is hydraulic conductivity, and d is aquiferthickness (it is assumed that d does notchange with time).

We assume that for the upper boundarycondition x = 0 is a groundwater divide or thatthere is no groundwater recharge from upslope.

, (3)

where hsurface is the ground surface elevation,and where x1 and x2 are defined by:

, (6)

where Qmax is the aquifer discharge capacity.

Generally, with land salinisation it would beexpected that up-gradient recharge exceedsthe discharge capacity. Once this isexceeded, the groundwater system can onlycarry so much flow, hence it is expected thatthe aquifer flow will be greater at x1 than at x2.As there is a time lag for increases in the up-gradient recharge to reach x1, it is expectedthat x1 would respond by moving up thesystem, but x2 would remain relatively fixed.

The following dimensionless variables fordistance, thickness and time are defined as:

, (7)

, (8)

, (9)

where ∆h is the difference in groundwaterelevation between the upslope end and theoutlet of the system, and T

–is a

representative transmissivity of the system(such as mean transmissivity).

We also define the following non-dimensionalvariables:

, (10)

, (11)

where T*(x) is a transmissivity shape-factor,w*(x) is a width shape-factor, and w– is arepresentative width (such as mean width).

A constant head has been used for the lowerboundary condition since the system is likelyto feed into a surface water feature.

, (4)

where h1 is the groundwater head at the systemoutlet, and L is the length of the system.

The area of surface discharge is where thegroundwater system is assumed to beincapable of carrying all of the up-sloperecharge. We assume for this report that thisoccurs only in the area x1 to x2. For this area:

, (5)


4

By substituting equation (7-11) into equation (2), we obtain:

, (12)

, (13)

where G is analogous to the dimensionlesssimilarity parameter TH/QD2 used byO’Loughlin (1981), who used the parameterto determine the steady-state extent ofhillslope seepage areas. Seepage occurredwhere this parameter was exceeded by ageometric function (ratio of planformgeometry factor to slope profile factor).

We also define a non-dimensional flux:

, (14)

2.1 Dimensionless G parameter

Another way of conceptualising G is as theratio of two time factors. The first of these isthe time factor for groundwater discharge (tH).This time factor is related to the lateral drainingof an aquifer and can be expressed as:

, (16)

The second of the time factors is that forgroundwater response to recharge (tV). This isrelated to the vertical filling of an aquifer inresponse to recharge and can be expressed as:

, (17)

The ratio of these two time factors provides adimensionless parameter for the groundwatersystem:

, (18)

This type of analysis allows the simplificationof a range of aquifer properties into a singlesimilarity parameter (G) that gives a measureof the ratio of the system’s ability to fillcompared to its ability to drain. As such, Ggives an indication of the state of balance ofthe groundwater system, which can be usedto determine how well a system is likely tocope with a given rate of recharge withoutdischarge to the surface.

and for groundwater systems expressingland salinisation it is expected that:

, (15)

∆

Figure 2. Position of surface discharge. Node atposition x1 (where the recharge up-slope from x1 isequal to the discharge capacity at x1 ).

Figure 3. Steady-state effect of groundwater systemshape on position of surface discharge: divergent,parallel and convergent (the legend gives the ratio of‘width at outlet:width at top’).


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3. Steady-state surfacedischarge

The G parameter can be used to identifygeneralised surface discharge behaviourfor a groundwater system at steady state. As a first part of investigating groundwatersystem sensitivity, G was calculated for a range of recharge scenarios for anidealised groundwater system. Thisidealised system had: 20 nodes, each 250 m apart; constant aquifer thickness of 20 m with the top of the aquifer at theground surface; initially a constant surfaceslope (four per cent); uniform aquiferproperties and recharge; and width wasvaried for different scenarios.

A steady-state analysis was undertaken for a range of recharge values to estimate wheresurface discharge is likely to occur along thegroundwater system. This was done bydetermining the upper-most node where the‘recharge volume upslope of the node’exceeds the ‘discharge capacity at the node’(given by Darcy’s Law) for a range ofrecharge scenarios (Figure 2, equation 19):

, (19)

where the left side of equation 19 is therecharge volume upslope of x1, and the rightside is the aquifer capacity at x1. Where w isthe system width, and T is the transmissivity. This calculated x1 provides a simple way ofinterpreting how a groundwater system’saquifer discharge capacity varies with respectto changes in recharge (by using G).

3.1 Steady state resultsFor this example, aquifer properties (k, S, d ),and the surface slope were uniform throughoutthe groundwater system. The effect of changingthe groundwater system shape was investigatedby using a range of convergent, parallel anddivergent cases. Each case was identified bythe ratio of ‘system width at the outlet’ to the‘width at the top’ (for a trapezoidal shapedsystem). Figure 3 shows these cases asseparate curves; each curve presents thechanging position (x) of surface dischargeagainst the G for a particular steady-staterecharge. Generally, as G decreases (due toincreased recharge), the position where surfacedischarge occurs also moves up along thesystem. The threshold value of G for whichsurface discharge begins to occur for aconvergent system was significantly greater (i.e. lower recharge) than for the divergent case.


6

Figure 4. Steady-state effect of groundwater systemprofile on position of surface discharge; convex (+),constant, concave (-). (the legend indicates thecurved profiles given by equation 20).

A similar investigation was undertaken to seethe effect of changing the slope profile of thegroundwater system along its length. Theprofile was made convex and concave bychanging the elevation of the initial constantslope (upper elevation 200 m, lower elevation10 m) example by adding an amountdetermined by:

, (20)

where x* is given in equation (7), and A is ascaling variable which was varied (between–50 and +50) to provide a range of convexand concave profiles. Figure 4 shows thevariation in the position of surface dischargewith changing recharge for different slopeprofiles (constant slope case (bold), andconcave (A<0) and convex (A>0)groundwater systems). For a concave profilethe aquifer discharge capacity is exceededfor higher values of G, while for a convexprofile the discharge capacity is exceededonly for much lower values of G.

3.2 Summary of steady-stateinvestigation

This steady-state exercise reinforces theargument that while G is a parameter forassessing similarity between groundwatersystems, the importance ofdivergence/convergence (plan view), andchanges in slope profile (convex/concave inelevation view), also play an important role isthe sensitivity of surface discharge tochanges in recharge. Both the shape and theprofile of a groundwater system will havesignificant impacts on where surfacedischarge may occur for a given scenario.Concavity increases the value of G wheresurface discharge began to occur. A G withno surface discharge is likely to be greaterthan unity (as high as five in this case). Thetemporal response of these relationships isexplored in more detail in the next section.

4.1 Groundwater modelling

The relationship between G and the temporalresponse of a groundwater system torecharge change was investigated. A simplegroundwater flow model was used to modelthe same idealised groundwater system as forthe steady-state case (see §3 of this report).Groundwater heads and discharge fluxes forthis system were simulated using theFLOWTUBE model (Dawes et al. 1997,2000). FLOWTUBE was developed as asimplified model, which is easier toparameterise than some of the more complexconventional models (such as TOPOG-IRM,MODFLOW, or MIKE-SHE). This makes it auseful tool to apply to many of the drylandgroundwater systems that do not have muchavailable hydrogeological data.

FLOWTUBE is a simple mass balance modelthat uses a finite difference solution toDarcy’s Law to estimate the flux of waterbetween any two points. Groundwater flow ismodelled only in one-dimension, that is in thedirection of flow, only a single conductingaquifer layer is considered, and it is assumedthat the boundaries of each flow strip areknown, and they do not change over thelength of any simulation run. At the bottomend of the tube a flux loss was calculated byspecifying a constant head 500 m below thedown-slope end of the tube. Vertical diffuserecharge is allowed to vary in FLOWTUBEboth spatially, across the groundwatersystem, and temporally, changing as thesimulation proceeds. The value is allowed tobe either positive, implying water addition, ornegative, implying a net extraction. There arethree options for vertical recharge input.Vertical recharge rates were specified, withthe same value at each node. When head ata node becomes artesian, surface dischargecan occur, although this is moderated by amaximum surface discharge capacityparameter in FLOWTUBE. This parameterenables the area of surface discharge tomove back up through the groundwater

system, rather than being contained at asingle point above a system constriction.

FLOWTUBE was used to investigatefunctional behaviour and response of agroundwater system under a range ofrecharge scenarios and with variation inaquifer parameters.

4.2 Transient state results

The similarity parameter G was used in thesteady-state to identify surface discharge.Under transient state analysis, G’srelationship to the temporal response ofgroundwater systems will now be examined.As for the previous section, three groups ofgroundwater system scenarios weresimulated:

1. parallel sides, constant slope

2. divergent/convergent sides, constant slope

3. parallel sides, convex/concave slope profile.

An idealised groundwater system (same asfor §3) was used as input into theFLOWTUBE groundwater model. The timingof the groundwater response patternfollowing a step increase in recharge wasthen investigated. The aim of this exercisewas to investigate how the variation inrecharge and aquifer parameters affected thetiming response of a single groundwatersystem and its characteristic dimensionlesssimilarity parameter (G).

4.2.1 Simple case: parallel sides andconstant slope

FLOWTUBE was used to model theresponse of a groundwater system to a stepincrease in recharge. This scenario is basedon obtaining equilibrium under nativevegetation (recharge = 1 mm/yr) and thenrunning a series of separate scenarios with a range of recharge rates. The time in the

4. Transient response to land usechanges


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Figure 5. The groundwater system response overnormalised time. Each curve is for a different rechargescenario from an initial 1 mm/yr to 2, 5, 10, 20, 40,100 mm/yr at tH*=0).

Figure 6. Normalised groundwater system responseto a range of increased recharge (from 1 mm/yr to 2,5, 10, 20, 40, 100 mm/yr), for different hydraulicconductivity (K), and porosity values, over normalisedtime. G varies left to right from 0.061–6.147.

Figure 7. Effect of groundwater system shape on theresponse of the groundwater system over time, for two different recharge increases (from 1 to 2 mm/yr,and from 1 to 20 mm/yr) for convergent, parallel anddivergent cases of an otherwise identical system(legend gives the ratio of width at outlet:width at top).


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x-axis has been normalised by the ‘time todrain’ (tH in equation 16), such thatnormalised time, tH* = t / tH. The resultspresented start at the time of clearing, tH*=0.

The groundwater system response to achange in recharge is shown by a normalisedrecharge:discharge ratio. This ratio isnormalised so that the ratio is zero immediatelyfollowing a change in recharge, and returns toa value of one once a new equilibrium isreached. As such, the results shown in thefollowing figures give a relative response andnot an absolute one. Figure 5 shows themodelled groundwater system response to arange of different recharge scenarios.

For relatively minor increases in recharge, themodelled groundwater system discharge iswholly contained within the aquifer—there isno discharge to the land surface. When thiswas the case, all curves with G>4 collapsedto a single curve, and formed the baselineresponse for the groundwater system (whichis the case in Figure 5 for G = 6.14). For thebaseline case, no surface discharge occurredfor scenarios where G>4. However, for higherrecharge values, surface discharge began tooccur. This was indicated by a departure fromthe baseline curve as the system was able toreach an equilibrium by discharging directly tothe surface. As G decreased (i.e. higherrecharge) below four in this case, the time toreach a new equilibrium was reduced.

The next stage in this process was to modela range of scenarios for a range of differentaquifer properties for a groundwater systemwith the same dimensions. Hydraulicconductivity and porosity were both alteredand FLOWTUBE was used to run a range ofrecharge values for each. The results areshown in Figure 6, with the response plotted

against dimensionless time. Note that thecurves collapse together in a similar patternto that in Figure 5, again with a baselineresponse occurring when G>4.

4.2.2 Groundwater system shape:convergence and divergence

G does not incorporate changes in the widthof the groundwater system. As a result, theimplications of convergence/divergence mayneed to be considered. FLOWTUBE wasused to model two additional groundwatersystem shapes, using identical aquiferproperties and groundwater system slopes.As expected, the relationship between G andthe normalised time to surface dischargechanged. Figure 7 shows the variation in thebaseline (no surface discharge) groundwatersystem response for convergent, parallel anddivergent cases. This figure reveals littledifference between responses.

Figure 8. Effect of slope profile on groundwater systemresponse for a: concave, constant and convex profile fortwo increased recharge scenarios (from 1 to 2 mm/yr,and from 1 to 20 mm/yr). (A is a variable in equation 20).

Figure 9. Effect of the depth of unsaturated zone(above the aquifer) on normalised groundwater systemresponse, for two increased recharge scenarios (from1 to 2 mm/yr, and from 1 to 20 mm/yr).


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Effect of changing groundwatersystem profile

While G includes overall gradient, it does notconsider any deviation from a constantgradient, as would be the case with changesin the surface profile of groundwater system.Additional scenarios have been modelled usingFLOWTUBE with groundwater system profileschanged using equation 20: convex andconcave profiles (Figure 8). For the baselineresponse (no surface discharge), the concaveprofile responded more slowly than the othercases. Interestingly, although the convex profileresponded more quickly in the early stagesthan the constant slope system, the overalltime to equilibrium was almost identical.

Effect of increasing the unsaturated zone

The effect of the depth of unsaturated zoneabove the aquifer was also considered. Thiswill not affect the equilibrium dischargeconditions, but will affect the timing of theresponse to recharge change, since aquiferheads will need to increase to a higher levelbefore surface discharge can occur.

The modelled groundwater system was alteredto make the aquifer deeper. For the previousmodelling scenarios, the aquifer was 20 mthick with an upper boundary at the groundsurface. Two additional runs were carried outwhere the depth from the ground surface tothe upper boundary of the aquifer was 10 mand 20 m. Figure 9 shows the groundwatersystem response for each of the threemodelled aquifer depths following a change inrecharge at tH*=0 from 1 mm/yr to 2 mm/yr forthe idealised groundwater system. The deeperaquifer system responded more slowly thanthe system that was at the ground surface.

4.3 Summary of transientmodelling

The FLOWTUBE modelling of a range ofidealised groundwater flow systems hasbeen a useful exercise in investigating thesensitivity of system response to increasedrecharge.

For the scenarios that were investigated inthis section, there were only relatively minordifferences in the response time as a resultof changing the convergence/divergence,slope profile, or the depth of theunsaturated zone. These factors are likelyto alter the distribution and occurrence ofsurface discharge, but their effect on theoverall response time is likely to be lessthan other attributes such as length,transmissivity, recharge, and porosity.

The next section of this report investigatesfive groundwater system case studies, anduses them to develop a simple method forpredicting groundwater system responsefunction curves without modelling.

This section of the report describes themodelled results from several case studiesaround Australia. The case study groundwatersystems are introduced, G is estimated foreach of them, and the modelled FLOWTUBEresponses to increased recharge are shown.

While the behaviour of these systems is notcompletely understood, they provide the bestand most rigorous hydrogeological data setswhich we have available. As such, these

case studies are a logical next-step in thedevelopment and validation of any newapproach to predicting the effects of land usechange on the groundwater response.

The general location of the case studiesdescribed in this report is shown in Figure10. Table 1 then gives an overview of someof their attributes, as used within theconstraints of a simplified approach that willneed to be applied more widely.


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5. Groundwater system casestudies

TABLE 1. General case study attributes.

Case study State Groundwater Mean Area Length Main land useflow system rainfalltype range(GFS) [mm/yr] [ha] [km]

Kamarooka VIC Local 427 10,000 4.5 Cropping & grazing

Billabong NSW Local/ 700 300,000 52 CroppingIntermediate

Popes SA Local 520 18,000 4.25 Cropping & annual pasture

Kyeamba NSW Intermediate 650 60,200 68 Pasture & some cropping

Brymaroo QLD Local 670 1,370 4.4 Cropping & perennial pasture

Figure 10. Approximate location of case studies.

Figure 11. Kamarooka modelled FLOWTUBEgroundwater system response to different amounts ofrecharge. Increase from 1 mm/yr recharge at time=0.

show the normalised groundwaterresponse for four recharge scenariosagainst time. In each case, thegroundwater system was ‘primed’ byrunning the model for 1,500 years at 1 mm/yr of recharge, so that it was inequilibrium (recharge=discharge). Recharge was then increased (shown on x-axis as time=0) to the current rechargerate (ranging between 15 to 25 mm/yr,depending on the case study). There arethree other curves on each figure, whichcorrespond to an increase from 1 mm/yr to 50%, 25% and 12.5% of currentrecharge rates.

Figures 11 to 15 show the return of the groundwater system to equilibrium. The y-axis shows the return of thegroundwater system to equilibrium following the recharge increase.

Figure 12. Billabong modelled FLOWTUBEgroundwater system response to different amounts ofrecharge. Increase from 1 mm/yr recharge at time=0.

TABLE 2. Simplified case study attributes used to calculate G (from equation 18).

Case study K Thick Specific Length Head Recharge tH tV Gyield drop min/max

[D] [S] [∆h] [R]# [SL2/T] [∆h S/R] [tV/tH](m/d) (m) (m) (m) (mm/yr) (yr) (yr)

Kamarooka 1 20 0.06 4,500 24 2.45 166 588 3.5315.06 166 96 0.57

Billabong 10 10 0.05 52,000 168 3.13 3,704 2,684 0.7225 3,704 336 0.09

Popes 0.05 25 0.01 4,250 137 3 396 457 1.1524 396 57 0.14

Kyeamba 10 20 0.1 68,000 261 2.63 6,334 9,924 1.5721 6,334 1,243 0.20

Brymaroo 2 30 0.02 4,400 51 2.5 17.7 408 23.0820 17.7 51 2.88

5.1 Calculating G for the case studies

G was calculated for the case studies discussedin the previous section. Currently availableinformation and data on the hydrogeologicaland catchment attributes were used. Wherethere was a large range in a given attribute, a value close to the mean value was used.

Table 2 shows the attribute values used to estimate G for each of the case studies.Since G varies with catchment recharge, it has been given for both the pre and postchange periods for each case study.

5.2 Groundwater response—case studies

This section presents the modelled resultsfrom each case study. Figures 11 to 15

# Recharge is initially 1 mm/yr and changed to the increased rate given in this column at t = 0.


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Figure 17. Modelled groundwater system responsefor each case study to increased recharge fromequilibrium at 1 mm/yr, to a new rate of 12.5% ofcurrent rates (between 2.5-3.5 mm/yr).

Figure 16. Modelled groundwater system responsefor each case study to an increase in recharge fromequilibrium with 1 mm/yr, to current recharge rates(between 15–25 mm/yr).


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Figure 14. Kyeamba modelled FLOWTUBEgroundwater system response to different amounts ofrecharge. Increase from 1 mm/yr recharge at time=0.

Figure 15. Brymaroo modelled FLOWTUBEgroundwater system response to different amounts ofrecharge. Increase from 1 mm/yr recharge at time=0.

Each of the case studies (Figures 11 to 15)show a similar style of response to that of theidealised modelled system (see Figure 5). Therapid response to large changes in rechargecan be seen clearly in the first four casestudies as a result of discharge to the surface.

5.3 Groundwater response—overall comparison

This section compares the modelled responsesof each case study to increased recharge:

• First, the responses for each case studyare shown as figures for two scenarios.

• Second, this modelled time for responseis used to calibrate a prediction methodusing G without modelling.

�

Figure 13. Popes modelled FLOWTUBE groundwatersystem response to different amounts of recharge.Increase from 1 mm/yr recharge at time=0.

Two scenarios are shown: (i) response tochange from 1 mm/yr to current rechargerates; and (ii) response to change from 1 mm/yr to 12.5% of current rates (referredto as ‘minimum’ rates in the figures).

• The response to a change fromequilibrium with a recharge of 1 mm/yr tocurrent recharge rates (ranging between15-25 mm/yr) is shown in Figure 16.

• The response to a change fromequilibrium with a recharge of 1 mm/yr, toa relatively minor increase in recharge rate(12.5% of current recharge rates) isshown in Figure 17.

The different response times for theincreased recharge for each of the casestudies is shown in Table 3. This table showsthe time taken for 50% and 90% of a returnto equilibrium (this corresponds to 0.5 and0.9 on the y-axis of Figures 16 and 17). Inthe absence of measured field data for arange of case study sites, these modelledresponse times have been used assurrogates for ‘reality’. These modelledresponse times form the basis for calibratinga non-modelling approach to groundwaterresponse characterisation in the next sectionof the present report.


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TABLE 3. Modelled response times for increase in recharge from 1 mm/yr to a new recharge rate.

Groundwater system New recharge G Time for Time forrate 50% response 90% response(mm/yr) (yr) (yr)

Kamarooka 2.5 3.53 64 10415 0.57 14 51

Billabong 3.1 0.72 88 20725 0.09 17 251

Popes 3 1.15 40 6824 0.14 10 15

Kyeamba 2.6 1.57 205 45821 0.20 36 92

Brymaroo 2.5 23.08 4 1520 2.88 4 10

5.4 Predicting case studyresponse

This section of the report describes theformation of a method to generate responsecurves from simple catchment attributes. A three part method is outlined which usesthe results of FLOWTUBE modelling of fivecase studies. This method is used togenerate parameters for a two parameterresponse function.

Response function

A simple model of response to change wasused that weights changes in recharge tochanges in discharge, according to a timescale and rate of change (Dawes et al. 2001).The model is a two parameter logisticfunction and assumes independent annualrecharge pulses, that the response is linearand additive, that recharge from year to yearis not correlated, and that the dischargeresponse is not hysteretic:

, (21)

Parameterising the response function

A three step approach was used to predictthe response of a groundwater system to anincrease in recharge. This involves:

(i) estimating the baseline response time (no surface discharge)

(ii) scaling this response time using G topredict estimated response time (to shorten response due to surfacedischarge)

(iii) Correcting this estimated response time(using the relationship derived in thisreport from FLOWTUBE modelling) toobtain a 50% response time (t half) which is used to generate a response functionusing equation (21).

[e.g. to predict Popes case study responseto recharge change from 1 to 24 mm/yr (seeFigure 13) by: (i) predicting the 1 to 3 mm/yrbaseline response time; (ii) scaling this downto the shorter time of the 1 to 24 mm/yrresponse), and (iii) correcting this estimateusing the relationship which was derived inthis paper’s FLOWTUBE modelling of thecase studies.]

The first part of this approach is to predictthe baseline response time (i.e. for a scenariowith no surface discharge). Fromobservations of the FLOWTUBE modelling,this time has been estimated as 40% of thetime factor related to the lateral draining of anaquifer (tH, from equation 16).

The second part of this approach is to scalethis baseline response time using G to predict

where thalf is the time when 50% of theresponse has occurred, and tslope gives theslope of the central portion of the curve. Thetslope parameter has been estimated byassuming that it is directly proportional to thalf.For the current examples, tslope has been setas 25% of thalf. This is considered areasonable first guess.

D(t) = 1

—— — 1 + exp{(thalf - t)/tslope}

�

Figure 18. Modelled time for 50% of the response torecharge change, as a function of estimated responsetime (given in equation 22).

Figure 21. Groundwater system response predictedusing the G parameter, for Popes (Eyre Peninsula,South Australia), to different amounts of recharge.Recharge increased from 1 mm/yr at time=0.


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the estimated response time due to surfacedischarge occurring. From observations ofmodelled FLOWTUBE responses, and fromthe steady state analysis (in §4) a baselineresponse will occur when G > 4. When G < 4,the estimated response time is shorter thanthis. A linear scalar has been used to reducethe estimated baseline response time by G / 4for cases where G < 4 (e.g. for baselineresponse of 100 years: G = 10 gives anestimated response of 100 years; G = 4 gives100 years; G = 2 gives 50 years, and G = 0.5gives 12.5 years). The estimated responsetime (x-axis in Figure 18) is taken as:

, (22)

The third part of this approach is to correct theestimated response times using the relationshipderived from FLOWTUBE modelling of the fivecase studies. This relationship for the casestudies is shown in Figure 18, and provides thethalf parameter for the logistic curve (equation21). The significant finding is that there is highcorrelation between the estimated responseand the results for the FLOWTUBE modelling(Figure 18). As such, the estimated responsetime has been corrected using equation (23)(trendline from Figure 18).

, (23)

It was assumed that this relationship will holdmore widely, and thus may be used to correctthe estimated response times for other casestudies in a predictive sense without furthermodelling, with some degree of confidence.Further work on a greater number of casestudies is required to strengthen theconfidence in a relationship of this type.

Figure 19. Groundwater system response predictedusing the G parameter, for Kamarooka (Victoria), todifferent amounts of recharge. Recharge increasedfrom 1 mm/yr at time=0.

This three step approach was used togenerate the following groundwater responsefunctions for the five case studies (Figures19 to 23). These are the same scenarios asfor the FLOWTUBE modelling results (seeFigures 11 to 15). There is good correlationbetween this approach and the FLOWTUBEmodelling results for the case studies.

Figure 20. Groundwater system response predictedusing the G parameter, for Billabong (New SouthWales), to different amounts of recharge. Rechargeincreased from 1 mm/yr at time=0.

= 0.4 tH * G/4 (for G≤4 )= 0.4 tH (for G>4)

thalf = 2.107 [estimated response time]0.641

Large parts of Australia have a lack ofdetailed hydrogeological data on which tobase future predictions of changes in landand river salinity. There is a need for relativelysimple approaches to determine the effect ofland use changes on the timing of salinityexpansion or remediation at a regional orcatchment scale. The simplified approach to characterising groundwater systemspresented in this report is a step towards this end.

The simplification of groundwater systemresponses is a necessary step towardscatchment or regional-scale prediction of theeffects of land use change on the timing ofchanges in groundwater discharge. This leadson from the simplified modelling approachesused by groundwater models such asFLOWTUBE, which allow groundwater systemsto be conceptualised one-dimensionally.Surface hydrologists have already tackled thistype of simplified approach.

The scaling argument approach that wasused in this report provides an approach forcharacterising groundwater systems. It canbe seen that the modelled groundwatersystem response is affected by aquiferproperties and the amount of recharge.These properties have been combinedthrough the use of a dimensionless similarityparameter (G) to reduce the complexity ofthe characterisation. G provides a measureof the ratio of a groundwater system’s abilityto drain compared to its ability to fill. What isclear from this study is that while there is a

strong relationship between variations in G and groundwater system behaviour, theinfluences of shape (in plan view) and slopeprofile also exert some effect on groundwatersystem response to changes in recharge.

The sensitivity of modelled groundwaterresponse to assumptions underlying theFLOWTUBE model is also important. Theexact determination of how the maximumsurface discharge capacity at a node which isspecified as a model input influences themodelled response, particularly with referenceto the actual area discharging rather than thedischarge volumes. Also, in areas whereclimatic variability (e.g. episodicity of rechargeevents) is more significant, the notion of usingmean recharge values becomes more tenuous.If the recharge event recurrence interval issimilar to the groundwater system responsethen the approximations will break down. Theaccuracy of this type of approach is difficult toverify, because of the long time scales involved,and also because of the lack of detailed actualmeasurements for different groundwatersystems. As such, our ability to predictgroundwater system response will depend onour knowledge of how actual hydrogeologicalparameters vary within and between systems.

This report has described the transientresponse of both generic and real case study groundwater systems to increasedrecharge. The logical next step is to look at how such systems will respond toreafforestation or recharge reductionstrategies (Smitt et al. 2003).

6. Discussion

Figure 22. Groundwater system response predictedusing the G parameter, for Kyeamba (New SouthWales), to different amounts of recharge. Rechargeincreased from 1 mm/yr at time=0.


15

Figure 23. Groundwater system response predictedusing the G parameter, for Brymaroo (Queensland), todifferent amounts of recharge. Recharge increasedfrom 1 mm/yr at time=0.


16

The main conclusions from this report are:

• Groundwater system characteristics canbe simplified using a dimensionlesssimilarity parameter (G). G is acombination of transmissivity, specificyield, recharge, length and head, and canbe visualised as a measure of the ratio ofthe system’s ability to fill (tV) compared toits ability to drain (tH). As such, G gives anindication of the state of balance of agroundwater system.

• A simple three step approach has beendeveloped to generate normalisedgroundwater system response curvesfollowing an increase in recharge:

(i) The time to drain (tH) factor is scaledto give a baseline response (i.e. whereno surface discharge occurs) to anincrease in recharge.

(ii) G is then used to scale this baselineresponse. From the case studies, it appears that for G < 4, thegroundwater response time is lessthan the baseline response (becauseof surface discharge allowing fasterchange to a new equilibrium).

(iii) This estimated response is thencalibrated against the FLOWTUBEmodelled predictions of the time for50% of the groundwater response toan increase in recharge (see Figure18). This time is then used in a two-parameter logistic curve (seeequation 21) as the thalf parameter togenerate a response curve over time.

Other conclusions from this report are:

• Analysis of steady-state groundwatersystems shows a clear relationshipbetween G and the position of surfacedischarge within an idealised groundwatersystem. However, this relationship alsovaried with the shape (convergence,divergence) and profile (convex, concave)of the groundwater system.

• Analysis of transient groundwater systemresponse to changes in recharge showeda relationship between G and the timefrom an increase in recharge to the timeof surface discharge. Scenario modellinghighlighted the effect of system shapeand profile on this relationship. Therelationship was more affected byconvergence than divergence, and moreaffected by concavity than convexity.

Predictions of groundwater response timesare an essential part of predicting likelyeffects of land use change on stream salinityand salt loads into the future. In the absenceof detailed hydrogeological and hydrologicaldata at a regional scale, simple methods areneeded. The G parameter provides a toolthat can help simplify the investigation ofcatchment behaviour. It will help improve theprediction of groundwater system responseswithout the use of process-based models.

7. Conclusions


17

8. References

Bradford, A & Zhang, L 2001, Catchment-Scale Assessment of Land-use Impacts on Water Balance in the Murray-Darling Basin. Technical Report 29/01, CSIRO Land and Water, Canberra.

Coram, JE, Dyson, PR, Houlder, PA, & Evans, WR 2000, Australian Groundwater Flow Systems contributing toDryland Salinity. Bureau of Rural Sciences, National Land and Water Resources Audit, Canberra.

Dawes, W, Gilfedder, M, Walker, GR & Evans, WR 2001, Biophysical modelling of catchment scale surface andgroundwater response to land-use change. In Proceedings of MODSIM 2001, F Ghassemi, P Whetton, RLittle & M Littleboy (eds.), Modelling and Simulation Society of Australia and New Zealand, Canberra,pp.535-540.

Dawes, WR, Stauffacher, M, & Walker, GR 2000, Calibration and Modelling of Groundwater Processes in theLiverpool Plains. Technical Report 5/00, CSIRO Land and Water, Canberra, 40p.

Dawes, WR, Walker, GR, & Stauffacher, M 1997, Model Building: Process and Practicality. In Proceedings ofMODSIM 97, AD McDonald & M McAleer (eds.), Modelling and Simulation Society of Australia, Canberra,pp.317-322.

Gilfedder, M & Walker, GR 2001, Dryland Salinity Risk–A Review of Assessment Methods. Natural ResourceManagement, 4, 2-9.

Holmes, JW & Sinclair, JA 1986, Streamflow from some afforested catchments in Victoria. In Hydrology and WaterResources Symposium, Griffith University, The Institute of Engineers, Australia, Canberra, pp.214-218.

O’Loughlin, EM 1981, Saturation regions in catchments and their relations to soil and topographic properties.Journal of Hydrology, 53, 229-246.

Petheram, C, Walker, G, Grayson, R, Thierfelder, T & Zhang, L 2002, Towards a framework for predicting impacts ofland-use on recharge: A review of recharge studies in Australia. Australian Journal of Soil Research, 40,397-417.

PMSEIC 1999, Dryland Salinity and its Impact on Rural Industries and the Landscape. Occasional Paper No.1,Prime Minister’s Science, Engineering and Innovation Council, Department of Industry, Science andResources, Canberra, 29p.

Smitt, C, Gilfedder, M, Dawes, W, Petheram, C & Walker, G 2003, Modelling the effectiveness of recharge reductionfor salinity management: sensitivity to catchment characteristics. CSIRO Land and Water Technical Report20/03, CRC for Catchment Hydrology Technical Report 03/7, Murray-Darling Basin Commission Publication 06/03, Canberra.

Vertessy, RA & Bessard Y 1999, Anticipating the negative hydrologic effects of plantation expansion: Results from a GIS-based analysis of the Murrumbidgee Basin. In Forest Management for Water Quality and Quantity,Croke, J, & Lane, P (eds.), Report 99/6, Cooperative Research Centre for Catchment Hydrology, Canberra,pp.69-74.

Zhang, L, Dawes, WR & Walker, GR 2001, The response of mean annual evapotranspiration to vegetation changesat catchment scale. Water Resources Research, 37, 701-708.

Integrated catchment management in the Murray-Darling BasinA process through which people can develop a vision, agree on shared values and behaviours, make informeddecisions and act together to manage the natural resources of their catchment: their decisions on the use of land,water and other environmental resources are made by considering the effect of that use on all those resources and onall people within the catchment.

Our valuesWe agree to work together, and ensure that our behaviour reflects that following values.

Courage

• We will take a visionary approach, provide leadershipand be prepared to make difficult decisions.

Inclusiveness

• We will build relationships based on trust andsharing, considering the needs of futuregenerations, and working together in a truepartnership.

• We will engage all partners, including Indigenouscommunities, and ensure that partners have thecapacity to be fully engaged.

Commitment

• We will act with passion and decisiveness, takingthe long-term view and aiming for stability indecision-making.

• We will take a Basin perspective and a non-partisan approach to Basin management.

Respect and honesty

• We will respect different views, respect each otherand acknowledge the reality of each other’s situation.

• We will act with integrity, openness and honesty, be fairand credible and share knowledge and information.

• We will use resources equitably and respect theenvironment.

Flexibility

• We will accept reform where it is needed, be willingto change, and continuously improve our actionsthrough a learning approach.

Practicability

• We will choose practicable, long-term outcomesand select viable solutions to achieve theseoutcomes.

Mutual obligation

• We will share responsibility and accountability, andact responsibly, with fairness and justice.

• We will support each other through the necessarychange.

Our principlesWe agree, in a spirit of partnership, to use the followingprinciples to guide our actions.

Integration

• We will manage catchments holistically; that is,decisions on the use of land, water and otherenvironmental resources are made by consideringthe effect of that use on all those resources and onall people within the catchment.

Accountability

• We will assign responsibilities and accountabilities.

• We will manage resources wisely, beingaccountable and reporting to our partners.

Transparency

• We will clarify the outcomes sought.

• We will be open about how to achieve outcomesand what is expected from each partner.

Effectiveness

• We will act to achieve agreed outcomes.

• We will learn from our successes and failures andcontinuously improve our actions.

Efficiency

• We will maximise the benefits and minimise thecost of actions.

Full accounting

• We will take account of the full range of costs andbenefits, including economic, environmental, socialand off-site costs and benefits.

Informed decision-making

• We will make decisions at the most appropriate scale.

• We will make decisions on the best availableinformation, and continuously improve knowledge.

• We will support the involvement of Indigenouspeople in decision-making, understanding the valueof this involvement and respecting the livingknowledge of Indigenous people.

Learning approach

• We will learn from our failures and successes.

• We will learn from each other.

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