Groundwater Management Tools: Analytical Procedure and Case Studies. MAF Technical Paper No: 2003/06. Prepared for MAF Policy by Vince Bidwell

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1 Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies MAF Techicl Pper No: 00/06 Prepred for MAF Policy by Vice Bidwell ISBN No: ISSN No: 7-66 October 00

2 Disclimer While every effort hs bee mde to esure the iformtio i this publictio is ccurte, the Miistry of Agriculture d Forestry does ot ccept y resposibility or libility for error or fct omissio, iterprettio or opiio which my be preset, or for the cosequeces of y decisios bsed o this iformtio. Ay view or opiios expressed do ot ecessrily represet the officil view of the Miistry of Agriculture d Forestry. The iformtio i this report d y ccompyig documettio is ccurte to the best of the kowledge d belief of the cosultt ctig o behlf of MAF Policy. While the cosultt hs exercised ll resoble skill d cre i the preprtio of iformtio i this report, either the cosultts or MAF Policy ccept y libility i cotrct, or otherwise for y loss, dmge, ijury, or expese, whether direct, idirect or cosequetil, risig out of the provisio of iformtio i this report. Requests for further copies should be directed to: Publictio Adviser MAF Iformtio Bureu P O Box 56 WELLINGTON Telephoe: (0) 7 00 Fcsimile: (0) 7 This publictio is lso vilble o the MAF website t Crow Copyright - Miistry of Agriculture d Forestry

3 Cotets Pge Executive Summry Itroductio Sectio A Groudwter Mgemet: Best Prctice Guidelie. The Mgemet Objective. Cocepts of Sustible Yield.. A Miscoceptio.. Groudwter Budgets.. Dymic Storge. Scle of Abstrctio Effects. Limittios of Dt d Iformtio.. Qutifyig Rechrge.. Geohydrologicl Iformtio.. Piezometric Dt.. Abstrctio.5. Coclusios bout Groudwter Resource Dt 5. Moitorig Methods Groudwter Levels the Key Idictor Ld Surfce Rechrge Abstrctio 5 6. Adptive Mgemet Wht is Adptive Mgemet? Alyticl Tools for Adptive Mgemet 6 Sectio B The Eigemodel Method 7. Eigemodel New Nme 7. Assumptios 7.. The Mgemet Objective 7.. Cuses of Evirometl Effects 7. Dymic Behviour of Aquifers 8.. Lier Storge the Buildig Block of Dymic Respose 8... Computtiol Equtios 9...Stedy-stte Coditios 9... Storge Residece Time d Eigevlue 9... Combitios of Lier Storges 0.. The Aquifer s Complex Lier System 0. Eigemodels.. Assumptios v i

4 ... Dymics of Rechrge Processes...Ld Surfce Rechrge Ptter...Aquifer Properties...Dymic Effect of the Vdose Zoe.. Model Structure... Chrcteristics of Eigemodel.. Equtios for Spredsheets...Predictio Equtio... Prmeter Reltioships.. Model Clibrtio...Objective Fuctio 5...Prmeter Costrits 5... Iitil Prmeter Vlues 5...Clibrtio Procedure 5 5. Aquifer Chrcteristics d Eigemodel Prmeters Eigevlues of Simple Aquifer Sigificce of Eigevlues Effect of Horizotl Scle Effect of Aquifer Boudries Effect of Geologicl Properties Relevce of the Gi Coefficiets Effect of Loctio d Boudries Estimtig Aquifer Stortivity The Bse Prmeter d River Rechrge 8 6. Cse Histories Motuek Aquifer Prelimiry Assessmet with Limited Dt Assessmet with Additiol Dt Cetrl Plis Aquifer, Cterbury Prelimiry Assessmet with Idividul Short Records Ressessmet with Combied Short Records Assessmet with Loger Time Series 6...Assessmet with Combied Loger Series 7. Applictio to Groudwter Mgeme t Sustible Limits to Groudwter Alloctio Short-term d Log-term Effects of Abstrctio Alysis of Aquifers with Ukow Abstrctio Cse Study: Effects of Groudwter Abstrctio o the Hlswell River Reltioship betwee Groudwter Level d Stremflow Eigemodel Predictios of Low Flow A First Look t sustible yield A Tool for Adptive Mgemet 7.6. Updtig the Eigemodel for Rel-time Forecstig 7.7. Forecstig the Effects of Abstrctio ii

5 8. Summry of Good Prctice 8.. Estimtio of Ld Surfce Rechrge 8.. Whe to Use the Eigemodel Method 8.. The Trsitio to More Complex Models Appedix I: Coferece Pper o Eigemodel Theory 5 Appedix II: Eigemodel Mthemtics for Spredsheet Implemettio 5 List of Appedices: Pge Appedix I: Coferece pper o eigemodel theory Appedix II: Eigemodel mthemtics for spredsheet implemettio List of Tbles: Pge Tble : Summry of eigemodel results for the Motuek Aquifer 0 Tble : Eigemodel results for 5 yers dt, Cetrl Cterbury Plis, for idividul clibrtio t ech loctio 5 Tble : Eigemodel results for 5 yers dt, Cetrl Cterbury Plis, for simulteous clibrtio t ll loctios 6 Tble : Eigemodel results for 8 yers dt, Cetrl Cterbury Plis, for idividul clibrtio t ech loctio Tble 5: Eigemodel results for 8 yers dt, Cetrl Cterbury Plis, for simulteous clibrtio t ll loctios iii

6 List of Figures: Pge Figure : The lier wter storge elemet 8 Figure : Vribles d prmeters for eigemodel ssumptios Figure : Eigemodel structure Figure : Results heder from eigemodel spredsheet exmple Figure 5: Loctio of observtio wells i the Motuek Aquifer 9 Figure 6: Eigemodel results for short dt record t Rossiters Well, Motuek Figure 7: Eigemodel results for Wrtts Well, Motuek Figure 8: Eigemodel results for Rossiters Well, Motuek Figure 9: Eigemodel results for Horrells Well, Motuek Figure 0:Loctio of observtio wells d river gugig sttio i the Cetrl Cterbury Plis 5 Figure :Eigemodel results for the 5-yer record t well L5/06 7 Figure :Eigemodel results for the 5-yer record t well L6/009 8 Figure :Eigemodel results for the 5-yer record t well M5/080 9 Figure :Eigemodel results for the 5-yer record t well M6/055 0 Figure 5:Eigemodel results for the 8-yer record t well L5/06 Figure 6:Eigemodel results for the 8-yer record t well L6/009 Figure 7:Eigemodel results for the 8-yer record t well M5/080 5 Figure 8:Eigemodel results for the 8-yer record t well M6/055 6 Figure 9:Reltioship betwee groudwter levels d low flow i the Hlswell River 8 Figure 0:Eigemodel predictios t idictor well for low-flow effects 9 Figure :Compriso of stdrdised well records for the droughts of 997/98 d 998/99 0 Figure :Effect o groudwter level of specified wter lloctio Figure :Eigemodel forecsts t idictor well for low-flow effects iv

7 Executive Summry This report ddresses issue of groudwter mgemet tht ws idetified by regiol coucil stff, s prt of project coducted by Miistry of Agriculture & Forestry d the Miistry for the Eviromet for ecourgig d esurig effective d efficiet wter lloctio i New Zeld. The issue is how to mge groudwter lloctio uder coditios of icresig bstrctio d imperfect, but developig, kowledge of the resource. The overll objective is to miti sustibility of the groudwter resource i terms of cceptble evirometl effects. The first prt of this report is drft Best Prctice Guidelie, which sets the cotext of the ture of the groudwter resource, qulity d vilbility of dt, d pproprite resource mgemet pproch. A recommedtio from the wter lloctio project ws tht dptive pproch to groudwter mgemet ws required, d tht there ws eed for pproprite lyticl tools to support this pproch. A compio report ddresses the origi d philosophy of dptive mgemet i wter resources. The secod prt of the report is cocered with the developmet d demostrtio of suitble lyticl method, d guidelies for its implemettio, which supports the recommeded dptive mgemet strtegy. The eigemodel method is cocered primrily with the mout of wter stored i quifer, d how this respods to rechrge d bstrctio. The resultig iformtio bout groudwter levels c be relted to evirometl effects such s low flow i strems, for exmple. It is whole quifer pproch d does ot purport to be suitble for detiled ivestigtio of locl effects cused by bstrctio stresses. These problems require other well estblished modellig techiques, d their comptibility with the eigemodel method is discussed. The issue of sprse dt is ddressed by the simplicity of the lyticl formt, which ebles idetifictio of fudmetl properties of quifer storge, sometimes from oly oe observtio well record. Implemettio of the procedure is idelly suited to spredsheet softwre. These simple models c lso be expressed i form tht icorportes cotiul moitorig of groudwter levels for rel-time forecstig s decisio support for dptive mgemet. Severl demostrtios with observed dt from two quifer systems re preseted to illustrte the cpbilities of the procedure. v

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9 Itroductio This report hs bee commissioed s result of two-yer project coducted by Miistry of Agriculture & Forestry d the Miistry for the Eviromet, to ecourge d esure efficiet d effective wter lloctio i New Zeld. Oe of the outcomes of tht project ws the idetifictio of issues i groudwter mgemet, s result of survey of regiol coucils d cosulttio with the Regiol Groudwter Forum of coucil groudwter scietists. These issues iclude: Kowledge bout quifer ofte follows demd o the groudwter resource; Alloctio decisios, with potetil log-term effects, must be mde o the bsis of iformtio tht is perceived to be isufficiet; The mout of iformtio bout quifer my icrese with time, but my ever hve icluded the stte of zero demd A dptive mgemet pproch ws suggested for optiml decisio-mkig whe both demd d iformtio re icresig with time. This report presets pproch to groudwter ssessmet d lloctio tht ebles the pplictio of reltively simple lyticl methods tht re pproprite to the vilbility of dt. This pproch is derived from the sme mthemticl theory s groudwter modellig softwre, such s MODFLOW, so tht comptibility with these methods is iteded where there re sufficiet dt for more refied lyses. The groudwter lloctio issues tht re ddressed i this report re bsed o wholequifer poit of view tht ccouts for time-vryig evirometl effects such s chges to the low-flow regime of strems. There re of course other effects such s strem depletio d slt wter itrusio, which my be cused primrily by short-term locl groudwter demd. There re estblished lyticl methods for ssessig these ltter effects, d the iterfce betwee these methods d the ew pproch will be discussed. The report is preseted i two prts. Sectio A describes Best Prctice Guidelie for groudwter mgemet, which is iteded to be geerl frmework for lysig d resolvig issues of groudwter lloctio. Sectio B provides detiled descriptio of oe method of lysig groudwter resource for the purpose of supportig the dptive mgemet pproch proposed i Sectio A. MAF Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies

10 Sectio A Groudwter Mgemet: Best Prctice Guidelie. The Mgemet Objective The mout of groudwter stored i quifer t y istt of time depeds o the dymic reltioship betwee rechrge iputs, through the overlyig ld surfce d from rivers, d outflow to surfce wters d pumped bstrctio. Aquifer storge provides buffer betwee highly vrible, climticlly-drive rechrge processes d the less vrible outflow tht supports surfce wter ecology. Abstrctio of groudwter for hum use, d some kids of ld use chges, lters the dymic blce betwee turl rechrge d the stte of surfce wters. The resource mgemet objective is to determie the regime of bstrctio tht results i cceptble evirometl effects.. Cocepts of Sustible Yield.. A MISCONCEPTION Occsiolly, there ppers i the medi sttemet to the effect tht...we must coserve groudwter for our grdchildre.... This my rise from cocept of groudwter s sttic, fiite body of wter, which is mied by y bstrctio. Wht should be pssed o to future geertios re the beeficil results of well-mged, dymic wter resource system... GROUNDWATER BUDGETS Oe resource mgemet pproch is to ttempt to estimte ll the iput d output compoets of the groudwter budget, d the mke decisio bout wht c be sfely llocted for bstrctio o sustible bsis. I prctice, it is very difficult to mesure idepedetly the qutity of rechrge from rivers or the turl outflow from quifer to surfce wters, for exmple. Selectio of the rechrge proportio to be used s sustible yield c become rbitrry choice tht my ber o reltio to the effects of bstrctio... DYNAMIC STORAGE The mout of groudwter preset i quifer t y istt of time depeds o the recet (moths or yers) history of climticlly-drive rechrge processes, turl outflow to surfce wters, d bstrctios for hum use. The rechrge processes re highly vrible through the ld surfce, d less so for river rechrge. Nturl outflows re less vrible th the rechrge history, becuse of the smoothig effect of groudwter storge, d bstrctio is potetilly mesurble d mgeble. This is the picture of dymic wter storge respodig to iflows tht hve vryig degrees of rdomess. At most loctios, this wter storge is itimtely coected to the surfce wter eviromet d the ecology hs dpted to the locl regime of turl vribility of wter supply. Abstrctio of groudwter for hum use lters the regime of vribility, d therefore ffects the turl eviromet. The coceptul bsis for mgemet should be uderstdig of system behviour rther th budgetry pproch. Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies MAF

11 . Scle of Abstrctio Effects The theory of groudwter wells shows tht the piezometric effect of groudwter bstrctio propgtes wy from the well i rdil directio, d tht this effect decreses i mgitude with distce. Most pplictios of this theory re directed to estimtig the effects of drwdow from well, i terms of iterferece with other wells or ifluece o strem-quifer iterctio. The distce scle of these ivestigtios is usully up to few kilometres, d the time scle is up to few moths. These methods re well estblished d re ot cosidered y further i this report. However, it is importt to relise tht these pplictios of well theory limit the estimtio of effects to mgitudes tht re sigifict or re prcticlly mesurble. Ay bstrctio from quifer hs effect tht evetully propgtes throughout the whole quifer. This effect my be lowerig of piezometric levels or iduced dditiol rechrge from river. The effect from y oe well my be ifiitesiml i terms of prcticl mesuremet, but the cumultive log-term effects of my wells c be very sigifict. The result is tht every user of groudwter from quifer is cotributor to evirometl effects such s reductio of low flows i strems or slt wter itrusio, which re determied by turl outflow to surfce wters t the whole-quifer scle. MAF Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies

12 . Limittios of Dt d Iformtio.. QUANTIFYING RECHARGE Aquifers hve two sources of rechrge: through the ld surfce, d from rivers. Ld surfce rechrge c be estimted from wter blce models to ccurcy suitble for most resource mgemet decisios. River rechrge is very difficult to estimte, d it c be very expesive to coduct mesuremets of sufficiet qulity d frequecy for useful resource ssessmet... GEOHYDROLOGICAL INFORMATION Groudwter models usully require iformtio bout the ture of quifer boudries d the quifer properties of trsmissivity d stortivity. The ltter re sometimes estimted from pumpig tests, but these re subject to high degree of vribility d my ot be pproprite for quifer-scle pplictio. For these resos, quifer properties ted to become model prmeters for clibrtio by mes of vilble piezometric dt. Idetifyig the ture of quifer boudries c sometimes be difficult, especilly for quifer-river boudries i lluvil quifers. Poor defiitio of boudries hs sigifict effect o the relibility of mthemticl groudwter model... PIEZOMETRIC DATA Mesuremet of groudwter levels i observtio wells provides high qulity dt bout the dymic behviour of quifer, i terms of its vlue s resource. For ssessmet of the whole-quifer resource, legth of record is geerlly more importt th umbers of wells observed. The pricipl dt limittio i my res is legth of record... ABSTRACTION Most use of groudwter is cotrolled by the resource coset process. However, these cotrols re usully specified s mximum rtes d volumes. There re few dt bout ctul bstrctio from quifers, but this situtio is likely to improve s implemettio of wter meterig is dvced..5. CONCLUSIONS ABOUT GROUNDWATER RESOURCE DATA The high qulity dt bout quifer tht re reltively esy to cquire, re estimtes of ld surfce rechrge d observtios of groudwter level. It would be desirble to use lyticl methods tht c build o these stregths. Idequte dt bout curret bstrctios, d the geerl pucity of observtios i my quifers, suggests tht mgemet of these quifers should proceed i mer tht llows for chges i strtegy s more iformtio becomes vilble. Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies MAF

13 5. Moitorig Methods 5.. GROUNDWATER LEVELS THE KEY INDICATOR Groudwter level, s moitored t observtio wells, is the most importt idictor of the stte of the resource i terms of vilbility for use d the likely effects o the eviromet. Evirometl effects, such s the low-flow regime of strems d slt wter itrusio, re determied primrily by piezometric levels i the coectig quifers. The dymic vribility of groudwter levels t observtio wells locted throughout quifer hs some compoets commo to ll the wells. This mes tht eve oe well, suitbly locted, c provide sigifict mout of iformtio bout the overll stte of the resource. The best loctios re furthest from outflow boudries to surfce wters, becuse the mplitude of level vritio is gretest i reltio to mesuremet oise d other iflueces. It is lso desirble to select sites tht re less likely to be ffected sigifictly by locl bstrctio, or locl rechrge from surfce irrigtio d flood evets i strems perched bove the quifer. The vlue of groudwter level observtios icreses more with legth of record th with umber of observtio sites, becuse of the commo dymic compoets. 5.. LAND SURFACE RECHARGE The defiig chrcteristic of quifer s groudwter resource is its dymic behviour s leky storge for turl rechrge. This behviour c be determied from the observed respose of groudwter levels to ld surfce rechrge, becuse the ifluece of river rechrge is usully tteuted to stedy piezometric effect withi few kilometres of the rechrge zoe. Ld surfce rechrge is estimted s the soil-wter drige compoet of soil-plttmosphere processes t the ld surfce, i respose to climte. There re umber of wter blce models vilble, but these re ot critiqued i the preset report. The emphsis here is o ecessry d sufficiet spects of these models: Wter blce must be clculted o dily bsis, d the totlled to the selected time itervl such s moth; Prticulr crop-soil combitios, c be expressed s wter-holdig cpcity; Oly sigifict res (s percetge of totl) of prticulr soil-crop combitio eed be cosidered. The strogest rechrge sigl for lysis of quifer comes from witer rechrge whe bstrctio (for irrigtio) is lest. Therefore, estimtio of ld surfce rechrge eed ot tke bstrctio ito ccout, for iitil ssessmet, eve if the quifer is ot i virgi stte. 5.. ABSTRACTION Abstrctios re limited to mximum rtes d volumes by mes of the resource coset process, but this iformtio is ot directly useful for mgemet. There is icresig tred to requirig sigifict wter users to meter their bstrctios. For the purpose of mgig groudwter for sustible use, bstrctio dt recorded s mothly volumes would usully be dequte. MAF Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies 5

14 6. Adptive Mgemet 6.. WHAT IS ADAPTIVE MANAGEMENT? The compio report to the preset oe (Lowry, 00 ) provides comprehesive descriptio of the ture of dptive mgemet i the cotext of mgig groudwter resources i New Zeld. Mteril is quoted from tht report, i this sectio, s mes of describig the role of lyticl methods tht support mgemet.... dptive mgemet develops mgemet polices s experimets tht test the resposes of ecosystems to chges i people s behviour.... shll be thought of s mgig the people who iterct with the ecosystem, ot mgemet of the ecosystem itself. Adptive mgemet is process of lerig while doig. The emphsis is o coopertive mgemet by stkeholders who eed to uderstd the resoig behid the possible rge of outcomes. The role of models is see s expressig the collective uderstdig of the prticipts bout how the groudwter system opertes, ssessig the ucertities, d predictig the effects of vrious mgemet ctios. 6.. ANALYTICAL TOOLS FOR ADAPTIVE MANAGEMENT The lyticl tools tht support dptive mgemet require t lest the followig chrcteristics: Coceptul plusibility to the stkeholders, which mes tht the physicl bsis d ssumptios c be clerly preseted Ability for implemettio i rel-time mode cosistet with the time scle of dptive decisio-mkig Suitble for use with the vilble dt. It is ulikely tht y oe lyticl method would meet ll these requiremets i ll situtios, d therefore it is desirble tht pproprite methods re, coceptully, upwrdly comptible i terms of dt vilbility d scles of time d spce. I prcticl terms this mes tht method cocepts c be preseted to stkeholders s beig cosistet d pproprite views of physicl relity. Lowry, T, Bright, J (00): Groudwter Mgemet Tools: Drft Guidelie for Groudwter Alloctio Mgemet. Licol Evirometl Report No 56/ 6 Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies MAF

15 Sectio B The Eigemodel Method. Eigemodel New Nme As cler d coveiet lbel for the pproch preseted i this report, we hve coied the me eigemodel. The term eige- is Germ word tht is log estblished i mthemticl theory, for which it hs the meig of chrcteristic. The eigemodel pproch is derived from the prtil differetil equtios of groudwter flow by mes of mthemticl cocepts clled eigevlues d eigevectors (e.g. Shuquillo, 98), but hs ot previously hd specific me. Slo (000) pplied the theory to groudwter dischrge t ctchmet scle.. Assumptios.. THE MANAGEMENT OBJECTIVE The mout of groudwter stored i quifer t y istt of time depeds o the dymic reltioship betwee rechrge iputs, through the overlyig ld surfce d from rivers, d outflow to surfce wters d pumped bstrctio. Aquifer storge provides buffer betwee highly vrible, climticlly drive rechrge processes d the less vrible outflow tht supports surfce wter ecology. Abstrctio of groudwter for hum use, d some kids of ld use chges, lters the dymic blce betwee turl rechrge d the stte of surfce wters. The resource mgemet objective is to determie the regime of bstrctio tht results i cceptble evirometl effects... CAUSES OF ENVIRONMENTAL EFFECTS The eigemodel method for quifer mgemet depeds o three ssumptios: Rechrge through the ld surfce overlyig quifer c be estimted from wter blce models bsed o climtic dt d ld-use prmeters Most of the temporl vritio i piezometric levels throughout quifer is cused by temporl vritios i ld surfce rechrge, together with the effects of pumped bstrctio Evirometl effects, such s the low-flow regime of strems re usully relted to piezometric levels i the quifer. I summry, if the dymic respose of quifer to ld surfce rechrge is qutified the evirometl effects c be relted to bstrctive demd o the quifer. Ech of the bove fctors d the cocepts of dymic respose will be explied i more detil. Shuquillo, A (98): A eigevlue umericl method for solvig ustedy lier groudwter models cotiuously i time. Wter Resources Reserch 9: Slo, WT (000): A physics-bsed fuctio for modelig trsiet groudwter dischrge t the wtershed scle. Wter Resources Reserch 6():5-. MAF Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies 7

16 . Dymic Behviour of Aquifers.. LINEAR STORAGE THE BUILDING BLOCK OF DYNAMIC RESPONSE The cocept of lier wter storge elemet is illustrted i Figure. We will exmie the dymic behviour of this simple elemet i some detil, becuse complex lier systems re lysed s ssemblies of this bsic uit. Subsequetly, we will show tht the dymic respose of quifer to rechrge c be lysed s complex lier system. Iflow I(t) h(t) Storge S(t) = h(t)/g Outflow O(t) Figure : The lier wter storge elemet The wter blce of the lier storge elemet (Figure ) c be writte s differetil equtio: ds( t) = I( t) O( t) () dt Sice this is lier wter storge, the outflow O(t) is proportiol to the mout of stored wter S(t). This reltioship c be expressed with proportiolity costt k s: By substitutig equtio () ito equtio (): O ( t) = ks( t) () ds( t) ks( t) = I( t) () dt The trsitio from equtio () to equtio () is quite sigifict. Equtio () is mthemticl sttemet of the wter budget without y other kowledge bout processes, wheres equtio () icorportes kowledge bout the process expressed s the dymic prmeter k. Equtio () o loger ivolves the outflow O(t). A further step is to icorporte the reltioship betwee wter depth h(t) d storge S(t) i the form: h ( t) = g S ( t) () 8 Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies MAF

17 The costt g, clled the gi, could icorporte the cross-sectiol re of the storge d other properties such s porosity of the storge medium, for exmple. By combiig equtios () d (): dh( t) kh( t) = gi ( t) (5) dt Equtio (5) provides the reltioship betwee temporl vritios i wter depth h(t) d temporl vritios i wter iflow I(t). Equtios of this kid re the reso tht groudwter mgemet c be coducted without kowig ll the rechrge d outflow qutities, becuse these re substituted for by kowledge of dymic behviour. Now we exmie some of the prcticl implictios of equtio (5).... Computtiol Equtios I order to use equtio (5) i spredsheet clcultio with time-series dt, solutio of this differetil equtio is required for time itervls of?t. For the cse where the iput I(t) is verged over the time itervl from t -?t to t d the output h(t) is the istteous vlue t the ed of the itervl, the solutio is: h = h bi (6) for which: = exp( k t) b = g t = t [ exp( k t) ] (7) Equtio (6) is differece equtio suitble for use i spredsheet with dt observed t discrete time itervls. The coefficiets d b re relted to the process properties k d g by the reltioships (7).... Stedy-stte Coditios If the lier wter storge receives stedy iput of I s, the h = h - = h s. If these vlues re substituted oto equtio (6): h h s s = h s bi b = I ( ) s s (8) The rtio b/(-) is clled the stedy-stte gi (ssg). This cocept will be used i the eigemodel ssessmet of groudwter resources.... Storge Residece Time d Eigevlue The residece time of wter storge is defied s the rtio of storge volume to me flow. I the cse of sigle lier storge, the outflow is lwys relted to storge by the coefficiet k, s show by equtio (). Therefore the residece time T R of sigle lier storge is /k. MAF Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies 9

18 If there is o iput to the storge, the the iitil cotets will be reduced to hlf i time equl to 0.69T R. For this sigle lier storge, cosidered s dymic system, the eigevlue is equl to k d hs the dimesios of /time.... Combitios of Lier Storges Sigle lier storges, ech with differet vlues of k d g, c be itercoected ito etworks to form complex lier systems. The mthemticl techiques of eigevlue lysis c be used to covert y etwork ito prllel set of lier elemets. The resultig eigevlues provide the k vlues of the elemets. This is the pproch tht we use to lyse the dymic behviour of quifers by mes of eigemodels... THE AQUIFER AS A COMPLEX LINEAR SYSTEM Our pproch to ssessmet d mgemet of groudwter is bsed o two-dimesiol cocept of quifers, i which groudwter flow is essetilly horizotl. Most pplictios of umericl models, such s MODFLOW, re for problems of this kid. I these umericl models, the horizotl extet of the quifer is divided up ito (usully) rectgulr cells. Sets of equtios re geerted which specify the reltioship betwee the piezometric heds o the cell corers, groudwter flow through the cell, bstrctio d rechrge i ech cell, d quifer properties of trsmissivity d stortivity. These sets of equtios tht re the core of umericl model re ctully the mthemticl descriptio of complex lier system, give the ssumptios iheret i the -D cocept of quifer. It is possible to covert these sets of equtios ito the mthemticlly equivlet eigevlue-eigevector form but there my be little computtiol dvtge. The reso for this is mily due to the bility of the umericl model to simulte loclised vritios i rechrge d bstrctio, which is the stregth of these models. However, this modellig cpcity demds pproprite levels of dt. For my groudwter resource ssessmets these dt re ot vilble, d pplictio of the umericl modellig pckges my be ipproprite. If we re prepred to scrifice some of this modellig flexibility the the eigevlue-eigevector lysis c yield models tht re simple, hve lower dt requiremets, d re suitble for implemettio i spredsheets. These re our eigemodels. 0 Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies MAF

19 . Eigemodels The coferece pper i Appedix I, bout the eigevlue pproch to modellig quifers, provides the theoreticl bsis for this sectio... ASSUMPTIONS Figure illustrtes the cocepts d mthemticl symbols used i the followig discussio. Ld Surfce Rechrge P(x,y)R(t) River h(x,y,t) r(x,y) u(x,y,t) Aquifer T(x,y), S(x,y) Se Figure : Vribles d prmeters for eigemodel ssumptios... Dymics of Rechrge Processes There is fudmetl differece i the resposes of piezometric levels i quifer to chges i river rechrge d ld surfce rechrge. Time-vryig piezometric effects er river, tht re ssocited with chges i river rechrge, re rpidly tteuted with distce from the river ito the quifer. The time lg for piezometric effect lso icreses with distce from the river. Chges i ld surfce rechrge cuse reltively rpid piezometric effects everywhere i the quifer, d the mgitude of these effects icreses with distce from the fixedhed boudries of the quifer. Therefore we ssume tht t y observtio well, the piezometric effect of river rechrge r(x,y) is costt vlue for tht loctio d tht temporl vritios i piezometric hed u(x,y,t) re cused by the effects of ld surfce rechrge d time-vryig bstrctio. The vlidity of this ssumptio improves with distce from river rechrge sources.... Ld Surfce Rechrge Ptter Ld surfce rechrge is ssumed to hve fixed sptil distributio, but the overll mgitude vries with time. This is expressed mthemticlly by sttig tht the rechrge R LS (x,y,t) t time t for loctio x, y is give by: R LS ( x, y, t) = P( x, y) R( t) (9) where P(x,y) is sptil distributio ptter d R(t) is time-vryig mgitude. This mes tht the output from oe wter blce model my be quite stisfctory for regio with MAF Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies

20 vryig mouts of rifll becuse the sptil vritios re icorported ito the eigemodel clibrtio, s will be show lter.... Aquifer Properties There re o ssumptios required bout the vritio of trsmissivity T(x,y) d stortivity S(x,y) throughout quifer. The geologicl structure my be quite heterogeeous. However, the ssumptio of -D groudwter flow mes tht piezometric levels i res with sigifict verticl compoet of groudwter flow my be less well estimted.... Dymic Effect of the Vdose Zoe Ld surfce rechrge must trvel through the usturted regio (vdose zoe) betwee the ld surfce d the groudwter before it hs y piezometric effect. Rechrge ito the top of the vdose zoe displces wter from the bottom of the zoe ito the groudwter surfce, by mes of hydrulic wve propgtio. This process itroduces time dely d some tteutio of the estimted ld surfce rechrge sigl. We iclude dditiol lier storge i the eigemodel to ccout for this effect. This storge elemet c lso ccout for the dymic effect of groudwter perchig bove quitrd s it leks ito semi-cofied quifer... MODEL STRUCTURE A eigemodel of the dymic behviour of quifer c be represeted s set of lier storges coected i prllel, s show i Figure. The dymic effect of the vdose zoe is represeted by sigle lier storge i series with the prllel set. R(t) Vdose zoe k v (x,y) k k k g (x,y) g (x,y) g (x,y) u(x,y,t) Figure : Eigemodel structure... Chrcteristics of Eigemodel The eigemodel structure show i Figure hs some importt chrcteristics tht re relevt to prcticl pplictios:. The dymic prmeters k, k..., which re the eigevlues of this lier system, re the sme t ll loctios i quifer. This property ebles trsfer of these prmeter vlues from loctios with good dt to other loctios with poorer dt. Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies MAF

21 . Although the umber of prllel elemets is theoreticlly lrge, i prctice oly few elemets re required. Our experiece is tht for dt t mothly time itervls oly three eed be cosidered.. The smllest eigevlue k hs the most ifluece o log-term dymic behviour, d the other, lrger, eigevlues ccout for the more rpid respose of piezometric hed to chges i rechrge.. The lrger eigevlues re more likely to be sigifict er fixed-hed boudries, becuse they c ccout for the rpid dymics of the shorter drige pths i these regios. 5. The vdose zoe dymic prmeter k v does vry with loctio, but its effect is usully less sigifict th the smllest eigevlue, so it c be eglected (set to rbitrry lrge vlue) durig the iitil stge of model clibrtio. 6. The gi coefficiets g i (x,y) do deped o loctio... EQUATIONS FOR SPREADSHEETS... Predictio Equtio Differetil equtios, similr to equtio (), c be writte for ech of the compoets of the eigemodel structure show i Figure but these would ot be suitble for direct solutio i spredsheet. We eed differece equtio, similr to equtio (6), which c be used with discrete time-series dt such s mothly totls of rechrge d mothly vlues of groudwter levels. Equtio (6) is first-order differece equtio, becuse it hs oly oe coefficiet. The four-compoet structure of Figure will yield fourth-order differece equtio by use of mthemticl techique clled the method of trsforms (i this cse, z-trsforms). The developmet of the equtio is show i Appedix II, d the resultig form is: u hˆ = u u u u br b R b R = u r ( x, y) (0) where h is the predictio of the observed piezometric hed h.... Prmeter Reltioships The prmeters i d b i of equtio (0) do ot hve obvious physicl meigs, becuse they re derived from the more physiclly relevt prmeters k i d g i (x,y) by the mthemticl trsformtio processes. The prmeters i equtio (0) re lso iterdepedet, which c be problem for model clibrtio, d it is difficult to set meigful iitil tril vlues durig clibrtio. Therefore, clibrtio is coducted o the z-trsform model, which hs prmeters i d ß i, d these vlues re coverted to the i d b i of the differece equtio by the followig reltioships (developed i Appedix II) i the spredsheet: MAF Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies

22 b b b = = = = ( ) ( ) ( ) = = ( )( β β β ) ( )( β β β β β β ) ( )( β β β ) = () () The clibrted vlues of i d ß i re lso coverted to the equivlet eigemodel prmeters k i d g i (x,y) by the reltioships: k l = t g ( x, y) ( ) l ( ) l ( ) l ( ) β k = t ( x, y) k = t k v ( x, ) = g = g y ( ) ( ) β = = β t ( ) () () Equtios () to () re show bove oly for the purpose of illustrtig the lyticl process, d re lredy embedded i the exmple spredsheets. Figure shows the results heder from exmple spredsheet. Eigemodel for Well M5/080 Storge residece times Aquifer Dtum (msl) LSR effect GWL bse ssg R T T T Tv properties N/A 0.6 Eigemodel k k k kv g g g prmeters N/A Trsform Alph Bse Alph Bet Alph Bet Alph Bet Obj. f. model Differece b b b equtio Figure : Results heder from eigemodel spredsheet exmple The prmeter vlues for the trsform model, i the shded lie, hve bee obtied by clibrtio d the other prmeter vlues hve bee clculted by mes of equtios () to ()... MODEL CALIBRATION Eigemodels expressed i spredsheet form re clibrted by use of the Solver routie i the Tools meu of Microsoft Excel. There re o problems with hvig missig dt i the timeseries of observed piezometric hed, other th some loss of iformtio, becuse the objective fuctio i the spredsheet igores blks. Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies MAF

23 ... Objective Fuctio The Tools user-form prompts for Trget Cell, d this should be set to the cell Obj. f. show by drk shdig i Figure, d the optio Mi selected. The objective fuctio is the sum of squres of the model error. This error is clled oise N d is defied s the differece betwee the observed d predicted vlues of piezometric levels: N = h hˆ (5)... Prmeter Costrits I the Subject to costrits box of the user-form, the Trsform Model prmeters (shded lie) should be set s follows: Alph-prmeters: >=0, <= Bet-prmeters: >=0 Bse: o costrit... Iitil Prmeter Vlues All the Trsform Model prmeters should be set to hve iitil vlue of zero. This coveiet settig is oe of the dvtges of coductig clibrtio o the z-trsform versio of the eigemodel.... Clibrtio Procedure The differece equtio prmeters re rrged i prticulr order i the spredsheet to fcilitte stepwise clibrtio procedure tht miimises mbiguity d istbility of prmeter vlues. The Solver tool should be pplied successively to the followig selectios of prmeters show i the shded lie of Figure : Bse Bse, Alph, Bet Bse, Alph, Bet, Alph, Bet Bse, Alph, Bet, Alph, Bet, Alph, Bet The best of the bove selectios plus Alph The bove groupigs re bsed o selectig, i stepwise mer, prmeters i order of their likely effect o vritios i piezometric levels. The iclusio of Alph is to pply the vdose zoe elemet to the best groudwter model. MAF Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies 5

24 5. Aquifer Chrcteristics d Eigemodel Prmeters I order to use the prmeter vlues of the eigemodel to ssist with ssessmet of groudwter resource, it is importt to pprecite the meig of these prmeters i terms of the physicl chrcteristics of quifer. We will be cocered primrily with the eigevlues k i d the gi coefficiets g i (x,y), show i Figure. The vlues of these prmeters re provided by the eigemodel clibrtio procedure described i Sectio EIGENVALUES OF A SIMPLE AQUIFER Although the eigemodel theory c be pplied to y quifer, useful isight is obtied by cosiderig the eigevlues of rectgulr-shped quifer with homogeeous properties of trsmissivity T d stortivity S. The horizotl dimesios re L x, L y, d there is fixedhed boudry o ll edges (such s surfce wter boudry ll roud the quifer). This simple cse c be solved lyticlly, d the geerl formul for the eigevlues is: π T i kij = S Lx i, j =,,K j L y (6) We ow exmie some of the implictios of equtio (6) for groudwter ssessmet Sigificce of Eigevlues The reltive mgitudes of the eigevlues give by equtio (6) depeds o the squres of the itegers,,... This mes tht the secod eigevlue is t lest four to five times the mgitude of the first, depedig o the reltive mgitudes of L x d L y. The storge residece time (Sectio..) of quifer, which is the iverse of the eigevlue, will therefore be domited by the first eigevlue. The lrger eigevlues c be importt for more ccurte simultio of the dymics of piezometric respose, but they do ot cotribute very sigifictly to wter storge Effect of Horizotl Scle Equtio (6) sttes tht the eigevlues re iversely proportiol to the squre of the horizotl dimesios. This mes tht, for exmple, quifer 6 km by 0 km hs four times the storge residece time (iverse of eigevlue) of quifer 8 km by 5 km tht hs similr geologicl properties d boudry coditios Effect of Aquifer Boudries Equtio (6) hs bee derived for idel simple quifer tht dris to ll four boudries (fixed hed). If this quifer is squre, L x = L y = L, d the first eigevlue is: π T k SL = (7) If the quifer dris oly to two opposite boudries, this is equivlet to the -D cse where L x = L d L y? 8, i which cse equtio (6) gives: 6 Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies MAF

25 k π T = (8) SL If the quifer dris to oly oe boudry, it c be show tht: k π T = (9) SL Compriso of equtios (7) to (9) shows tht chgig oly the boudry coditios of this simple quifer results i eight-fold vritio of storge residece time Effect of Geologicl Properties The rtio T/S ppers i ech of the bove equtios for the eigevlues of the homogeeous quifer. Alysis of heterogeeous quifers by eigevlue methods hs the potetil to provide estimtes of the lrge-scle vlue of this rtio, if quifer geometry d boudries re well defied. However, it is ulikely tht this vlue would be the sme s properties derived from pumpig tests, becuse the up-sclig process is quite complex. It is worth otig tht the T/S vlue ppers oly to the first power i the bove equtios, d the likely effect of geologicl properties eeds to be kept i perspective with the effects of horizotl scle d quifer boudries. 5.. RELEVANCE OF THE GAIN COEFFICIENTS The gi coefficiets g i (x,y) t ech well loctio ot oly idicte the reltive sigificce of the quifer eigevlues t tht loctio, but c lso provide iformtio bout quifer boudries d stortivity. The totl stedy-stte gi ssg(x,y) t loctio is give by: ( x y) g ( x y) d c lso be derived from the differece equtio (0) s: ssg ssg, = i, (0) i ( x, y) b b b = () The verge piezometric effect of ld surfce rechrge (LSR effect i the eigemodel results), h (x,y), is give by: ( x y) ssg( x y) R h, =, () where R is the log-term verge of the rechrge mgitude series R(t) Effect of Loctio d Boudries The vlue of ssg(x,y) is zero t fixed-hed boudries, d icreses with distce from those boudries. This property c be used, for exmple, to idicte whether river is iterctig directly with quifer or is perched bove the groudwter surfce. I the ltter cse, the vlue of h (x,y) will be reltively lrge. MAF Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies 7

26 5... Estimtig Aquifer Stortivity If the vilbility of dt llows, the plot of h (x,y) would permit estimtio of the verge thickess, H, of the quifer tht is occupied by the verge mout of wter origitig from ld surfce rechrge. This verge mout of wter c be resobly estimted by mes of the verge rechrge R d the verge storge residece time /k. The the lrge-scle quifer stortivity S is give by: S R k H = () I cses where there re few observtio well records, there is pproximtio tht my be useful. This relies o the ssumptio tht the shpe of the groudwter surfce uder stedystte coditios is prboloid, which degeertes to prbol for -D groudwter flow. The verge height of prboloid is /9 the mximum height. The correspodig rtio for prbol is /. If the vlue of h (x,y) is kow for well tht is furthest from fixed-hed boudry the, s first pproximtio, the verge thickess H is hlf this mximum vlue. 5.. THE BASE PARAMETER AND RIVER RECHARGE The Bse prmeter vlue i the eigemodel results (Figure ) is the piezometric effect of river rechrge r(x,y) t the prticulr well loctio, which is ssumed to be stedy. If there re sufficiet loctios with piezometric records, these bse vlues c provide mp of the river rechrge effect s dditiol set of iformtio bout the quifer. This piezometric surfce could be used to estimte the qutity of river rechrge if vlues of trsmissivity re vilble. However, it would be simpler to express river rechrge s proportio of ld surfce rechrge, which is more ccurtely clculted, by mes of the reltive piezometric grdiets, becuse the trsmissivity i both cses is the sme. 8 Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies MAF

27 6. Cse Histories I ech of the followig cse studies, the oly sources of dt re: Dily vlues of ld surfce rechrge estimted from wter blce model. These re summed to mothly totls for use with mothly groudwter level dt. Records of groudwter (piezometric) level from few observtio wells, either t dily or mothly time itervls. Reprits of portios of topogrphicl mps re show, to illustrte the loctio of observtio wells d the scle of the quifer. Detils of the wter blce model d geologicl iformtio bout the quifers re ot preseted here. 6.. MOTUEKA AQUIFER 6... Prelimiry Assessmet with Limited Dt Figure 6 shows the results of eigemodel clibrtio with oe yer of dily dt for Rossiters Well (Figure 5). This is good set of dt becuse there is sigifict ld surfce rechrge evet tht hs cused strog piezometric respose i the quifer. 0 km Wrtts Rossiter Horrells Figure 5: Loctio of observtio wells i the Motuek Aquifer The results (Figure 6) show tht oly oe eigevlue ws required to provide good fit (R = 0.9) to the dt. The importt result is tht the storge residece time (T ) is oly dys. This mes tht the cotributio of ld surfce rechrge is ulikely to be dequte becuse hlf of this storge is lost by turl drige i bout 5 dys (0.69 ). Therefore, this quifer ppers to be primrily trsport medium for river rechrge. Now we exmie the dditiol iformtio provided by the use of five yers of dily dt for the three observtio wells show i Figure 5. MAF Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies 9

28 6... Assessmet with Additiol Dt The eigemodel results d simultio plots for Wrtts, Rossiters d Horrells observtio wells (Figure 5) re show i Figures 7 to 9. The relevt prmeter vlues from these results re summrised i Tble. Tble : Summry of eigemodel results for the Motuek Aquifer Observtio well Wrtts Rossiters Horrells Eigevlues (d - ) 0.60, Residece time (d) 99 5 LSR effect (mm) GWL bse msl (mm) Eigemodel fit R At Rossiters d Horrells, there is oly oe sigifict eigevlue d it is similr for both loctios, s re the storge residece times (iverse of the smllest eigevlue). This similrity is expected from quifer dymics (Sectio 5..). These vlues re lso comprble to the eigevlue of 0.05/d (residece time of dys) determied from the short dt record (Sectio 6..). The well t Wrtts exhibits ppretly omlous vlue for the smllest eigevlue, of 0.0/d. This could be cused by piezometric respose to the djcet Motuek River, which reflects the storge chrcteristics of the river ctchmet rther th the quifer. This sigl is likely to be rpidly dmped with distce from the river d therefore ot detected t the other wells. The lrger eigevlue t this well (0.60/d) is order of mgitude greter th the first eigevlue of y of the wells, which is typicl (Sectio 5..). The verge piezometric effect of ld surfce rechrge (LSR effect) is similr for Wrtts d Rossiters (7 mm, 68 mm). This idictes tht the Motuek River is ot fixed-hed boudry er Wrtts, otherwise the LSR effect would be reltively smller. Horrells Well hs the lrgest vlue of LSR effect (50 mm), d this suggests tht it is further from fixed-hed outflow boudries. This my suggest the presece of o-flow boudry to the south of this well. The GWL bse d the LSR effect t Horrells c be compred with the bed level d stge of the Motuek River s prt of y ivestigtio of the ture of the coectio betwee river d quifer. This is ot icluded i the preset cse study. Compriso of the verge piezometric heds (GWL bse LSR effect) t the three wells idictes groudwter flow to the southest qurter. The eigemodel fit (R ) is poorest t Wrtts (0.5) becuse of the ifluece of the Motuek River, d becuse the eigemodel trets river effects s costt. The fit improves with distce from the river t Rossiters (0.75) d Horrells (0.85). The primry source of model error ppers to be the low piezometric hed durig summer drought, whe bstrctios re high. These periods re idicted (Figures 7 to 9) by piezometric levels (GWL) below the GWL bse vlues. 0 Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies MAF

29 The coclusios from this eigemodel ssessmet of the Motuek quifer re s follows: There is isufficiet quifer storge to crry-over ld surfce rechrge from witer moths through the dry sprig-summer period; The quifer is trsport medium for river rechrge, which is the primry wter resource; The coectio betwee the Motuek River d the quifer is probbly ot directly iterctive, but the ture of this coectio is very importt for mgig bstrctio from the quifer, i terms of the mgitude of the resource Rossiters 00 GWL (mm) bove me se level Observed GWL Simulted GWL Ld surfce rechrge Ld surfce rechrge (mm/d) J-8 Mr-8 Apr-8 Ju-8 Aug-8 Oct-8 Dec-8 Eigemodel for Rossiters Well Storge residece times Aquifer Dtum (msl) LSR effect GWL bse ssg R T T T Tv properties N/A N/A.7 Eigemodel k k k kv g g g prmeters 0.05 N/A N/A Trsform Alph Bse Alph Bet Alph Bet Alph Bet Obj. f. model Differece b b b equtio Figure 6: Eigemodel results for short dt record t Rossiters Well, Motuek MAF Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies

30 Wrtts Observed GWL Simulted GWL Ld surfce rechrge GWL (mm) bove me se level Ld surfce rechrge (mm/d) 6000 J-8 Ju-8 Dec-8 Ju-85 Dec-85 Ju-86 Dec-86 Ju-87 Dec-87 Ju-88 Dec-88 0 Eigemodel for Wrtts Well Storge residece times Aquifer Dtum (msl) LSR effect GWL bse ssg R T T T Tv properties N/A.8 Eigemodel k k k kv g g g prmeters N/A Trsform Alph Bse Alph Bet Alph Bet Alph Bet Obj. f. model Differece b b b equtio Figure 7: Eigemodel results for Wrtts Well, Motuek Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies MAF

31 6000 Rossiters 00 GWL (mm) bove me se level Observed GWL Simulted GWL Ld surfce rechrge Ld surfce rechrge (mm/d) J-8 Ju-8 Dec-8 Ju-85 Dec-85 Ju-86 Dec-86 Ju-87 Dec-87 Ju-88 Dec-88 Eigemodel for Rossiters Well Storge residece times Aquifer Dtum (msl) LSR effect GWL bse ssg R T T T Tv properties N/A.88 Eigemodel k k k kv g g g prmeters N/A Trsform Alph Bse Alph Bet Alph Bet Alph Bet Obj. f. model Differece b b b equtio Figure 8: Eigemodel results for Rossiters Well, Motuek MAF Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies

32 GWL (mm) bove me se level Horrells Observed GWL Simulted GWL Ld surfce rechrge Ld surfce rechrge (mm/d) 0 0 J-8 Ju-8 Dec-8 Ju-85 Dec-85 Ju-86 Dec-86 Ju-87 Dec-87 Ju-88 Dec-88 Eigemodel for Horrells Well Storge residece times Aquifer Dtum (msl) LSR effect GWL bse ssg R T T T Tv properties N/A N/A.68 Eigemodel k k k kv g g g prmeters 0.0 N/A N/A Trsform Alph Bse Alph Bet Alph Bet Alph Bet Obj. f. model Differece b b b equtio Figure 9: Eigemodel results for Horrells Well, Motuek Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies MAF

33 6.. CENTRAL PLAINS AQUIFER, CANTERBURY Figure 0 shows the loctio of four observtio wells i the Cetrl Cterbury Plis, which will be the bsis of the ext cse study. The Cetrl Plis quifer is much lrger th the Motuek quifer, d the dymic behviour c be dequtely described by the use of mothly vlues of piezometric hed. The ld surfce rechrge is still estimted from dily wter blce model but the results re summed to provide mothly totls. The piezometric dt re i uits of metres (rther th millimetres s for the Motuek dt). L5/06 M6/055 M6/055 L6/009 Hlswell River 0 km Figure 0: Loctio of observtio wells d river gugig sttio i the Cetrl Cterbury Plis Figure 0 lso shows the loctio of flow gugig sttio o the Hlswell River. The reltioship betwee stremflow d piezometric levels i the quifer will be exmied i Sectio Prelimiry Assessmet with Idividul Short Records Figures to show the simultio results d prmeter vlues for the four wells (Figure 0), bsed o five yers of mothly dt for This is quite short dt record for quifer of this size, give the climtic vribility of the Cterbury Plis. The results re summrised i Tble. Tble : Eigemodel results for 5 yers dt, Cetrl Cterbury Plis, for idividul clibrtio t ech loctio Observtio well L5/06 L6/009 M5/080 M6/055 Eigevlues (mth - ) N/A , 0.9 Residece time (mth) N/A LSR effect (m) N/A GWL bse msl (m) N/A Eigemodel fit R N/A MAF Groudwter Mgemet Tools: Alyticl Procedure d Cse Studies 5