A Cluster Analysis of Cotton P.Lantjng Strategiesintbe Namoi Valley

A Cluster Analysis of Cotton P.lantjng Strategiesintbe Namoi Valley

G Kaine-:Jones Centre For Water Policy Research University ofNew England Annidale NSW2351

and

YSimpson ·Department of AgIicultura1 Economics and Business ManageIIlent UniversitYQf New England Annidale NSW 2351

Agricultural tome 34th Annual Conference ofthe Australian A contributed paper University of Queensland Economics Society, 12 to lSthFebruary 1990, AClnster Analysis of Cotton Planting Strategies in the Natnoi Valley

bt.this,paperth(:; feasibility of clusteranalysisasa technique for .predicting .tbeplanting'strategies of cottonirrigatoIS in the NamOi Va11Qyisexplor~.This .explomtion was undertaken with tbe intention. ofenabling,cventually,tbe demand for irrigation water to be fo~ecast witbgreateraccuracy,and so provide .a technique that woUld assist in the .resolution of the pJ'Oblem of determining announced allOCCltions.

Introduction

The inland 'riversof New South Wa.1eshavebeen, and still are, characterised ,by highly variable, unpredictable streamflgws.This vanabllity generates a range of problems with respect. to the management of irrigation schemeslQc;;lteQ pn these rivets, ,particularly the management ofheadw3terstQrages. Ina manag¢wa,ter system the variabiUty in 'stream tlowsis a detenninantt together with storage capacity and licensed allocations, of the reliability of regulated flows,. Intheeventtbatregulated flows are not .reliabletben problemsarenUsed concemingthe tnaIlageQlent of irrigation ,entetprises on the farm.

The reliability oeregulated flows and tbe management of irrigation enterprises are interdependent. 'Ibemanagement oftheirrigatiQn enterprise iletenninesthe demand for J'Cgtllated flows. This demand, together with the capacity ·of ~beadwatetstQragesand catchment inflows, will govemthe degree tQ which tbedemandfor.andsupply of regulated flows will.coincide,andhence, affects the reliability ofrcgulatedflows.

The efficient JDaIlagement of an irrigationschelllC becomes then. partly dependent upon an accurate assessment oCthe likely demand for regulated flows across a range of reliability scenarios. Given that individual irrigators adopt different management strategies when faced with variable water supply (CWPR: 1989) the accurate assessment of the demand foJ.' water is difficult. The intention in .this study is to investigate theapplicabllity of cluster analysis.'asa. technique forcbaracterising the management strategies forinigators with a view to predicting the demand for regulated flows. The investigation is based upon a mailed SllIVey ofcotton irrigators located in the Namoi Valley in North ..West New South Wales. Background

Thestudycon$ists .ofan.analysisoftbe responses to a survey of cotton inigators located in the Natnoi Valley in Nprth ..West.New South Wales.- The valley is oneol the major cotton producing regions in Australia, and .irrigatedcotton is the ·predominant irrlgatedcropping ienterprisein the valleyintenns ·ofarea. planted and also in. tenns of value of production. The irrigation system servicing the Namoi .consistsoftwoheadwater storages .-.. :Keepit and Split Rock Dams -·andregulated water flows are distributed through natural stream channels (FigUl" 1). Weirs have been constructed .atMollee, WeetaandGunidgera in order to improve stream flow control.

The headwater storages are serviced by catchment area of 43 000 sq kIn, with anannttal discharge.of762.gigalitres (GL) on average. Keepit Dam completedin 1960 has a storage capacity of 425 GL with a planned annual supply of 222 GLon average. Split Rock Dam completed in 1988 bas a storage capacityof397GL with up to 700L available annuaUy on average when used in conjunction with existing storages (CWPR; 1989).

An indication of the varIability that is present in the .system is present in Figure 2in which the storage level in Keepit Damov~r two decades is depicted. Note the lengthy periods over which the storage remained at less than .ftftyper cent of capacity and the rapidity with which substantial rises and falls in the storage level can occur.

Intbe Namoi Valley fUITOW irrigation is used to irrigate cotton crops. In furrow irrigation, water is drawn by siphonstorpumped from, a head channel into parallel furrows which run between the crop rows. Care is needed in landpreparationandiu water application to ensure adequate and even wetting and to avoid over watering (Pigram: 1986).

The supply ofiniganonwater, that is, regulated flow from the river is restricted byilcence. A river licence is granted in tenns ofa volumetric allocation which entitles the licensee to pump up toa s~cified volume of regulated flow from the river. Initially licences were stipulated in terms of area.. However, when water and not land was recognised as the limiting .resource in the system, the original area licences were converted to volumetric licences (at a rate of roughly six megalitresper hectare)...... '" \ \\- •...... Areas under irrlgatf1n ( ..".,- Catchrnentnreas""-' '\ \. "-\

o 20 olO 60 60 krn L =1

Figure 1 Namoi and Gwydir drainage basins, Dorth.western New South Wales

4 tOO'Y.~ttPQr::ttV! 423.000 megall\res

400

300

200

100

1965 1963 1967 ,968 1969

15%

50%

25%

100%

75%

50%

25%

100%

75%

50%

25%

1980 19S1 1982 1983 1984

Figure 2 Keepit Danl storage levels 1965-1984. Source: Pigram (1986.187). 'If'the'supplying authority believes that the volume of water in tbeheadwater,storages is not sufficient to matcb. the licensed volume, then inigators are restricted topumpmg a ~ntage of their licensed entitlement. This restricted percentage, tenned the 'announced allocation' is set at the commencement of each season by the water authority (NSW Departn'1entof Water Resources}. The announced allocation can, vary between .zero and 100 percent olthe licensed entitlement. Irrigators are guaranteed the announced allocation.

.Asmentioned befort\vmability iathe inflow ofwater lnto the heoowaterstoragesraises significant problems for managing water resources in the Namoi Valley. This is reflected in the shift fron1 area to volumetric licensing. and in tbe necessity for the Department of Water Resources to resort to procedures such as 'announced allocations' which effectively vary the ~ntit1ements of licensees in accordance with the ~ariabiUty incatchm·enirun off. As inflows from the catchment over the irrigation season cannot bepredictr.d.the department is limited when detennining the announccxlallocation tathe volumethatis in storage at tbeopenillgoftheseason {less dead storage and cany~over requirements for ,the $llbsequentseasan).Thisrelianceon minbnum supplies, togetberwiththe variability of demand forimgation water and the guarantee on the delivery of announcedalIocauQn .fOrces the Deparunenuo adopt a con~ativeponcywithrespect to announced allocations.

OrQundwaterresourc~s in the valley are extensively developed and are subject to strict amtro'~ due to an accelerated ~ssiQll insllbsurface water levels which bas resulted in the faUureofsomcshallowstoclcbores and wells (Pi gram: 1986, 190). .Access to groundwater islice.nsed and the extt'actionrates orb<>res is regUlated. Aswithrlver licences only a proportion of the licensed entitlement is.usualIy available in. a season. River and·bQre licences in the NamOi Valley :maybe issued f'Qfconjunctive or non~Qnjunctive use. ACOI)junctive: licence means thatboreentitlement'.mayonly be usedto.meet the difference. :if any, between theannouncedallocanon and entitlement on the river licence. The bore licence is l\supplementaryentitlement totherlver licence.Wbete the licences are notisslled for conjunctive usetberiver and bore licences can be operated independently. :Fornon:-eonjuncrlve users the total availableentidementis the sum of tht river and bore entitlements. For conjunctive users the total available entitlement is sirnplythe river entitlement.

The Ucensingrestrictionsplaceanupper limit on the area that can be developed for inigatioo.on apropeny. as only that area of lan4 for which there issuffacientreliable water (given croprequh'ements) can be developed forinigation purposes1• In response to these entit1~mentrestriction$and in, order to increase manllgerial flexibility, substantial investment basocc\lI'nXi inon~fann storages. More lhanbalf()f·~·inigatorslnthe Nanloi Valley :have ,on .. farm .stotage rC$elVoirs (Pigram: t986). On~f~ ,storages enable irrigatQr$tocollec:tand,~set~twater. ilierebY'improving·,lhc· efficiency of 'Water use.· 'lbey alSQ allow tbe collection Qfminfall tun .. off from tbepropertyand; thepllmping of untegul~ted or; surplus liver ,flows when such flows iaredeclat'edby thc:Depanmcntof Water: ResolUCcsas 'off,.allocauontflows(that is, not regulated).. The volllmesof 'off allocation' :f1ow pumped intoon.. farmstQrage 3fC Dot counted toward the licensed !entitlC11lent Qtannouncedallocation.

This, ability tostorerun-offsutplusflowsand tailwater introducesS()meadditional Dexibilityin fann management since it alloVl$,irrigationpn demand asirrjgatioo 'water,nee4 not be Qtderedpreeisely in advance of when :required but ordered for 'arrivaiSOlUcwbat earlietthan required and stored in readiness for application when .1.lppropriate~ Further. waterwbichhas .been .()rd~redand is not required due to irainfall prlor,toanivalcan b~ pumpedamdstottdfor'lajerusc.

On..;iann$tOOtgesimprov~management' fle,ubUityandby enablingtllestoring ofwlwatel:', run~ffanc:tsurplusfl()wsCQnferad~greeof independence on the irrigator by reducing dep:ndence on licensed entitlements.

BcforeproceedingtotbeanaIysis, the hnpactofentitlement$ and on-farmstQragesonthe irrigators plzmting decision needs.to addresset.LTheplanting declsion.is crucial as this 'dcclsionciefines 'tbeboundarywithin wbichsubsequent,irrigationand. management d~sionsmustbernade.Genera11yspealdngttheavai1abilitYofwater ortbeilrea oflat\J develQPed for irrigation are the liIllitingreSQUrccs constraining tbeplanting decision, provide(iooUQnprjce$are satisfactory. In .the event that water availability is the limitiqg f~t()f, the individpal irrigator must choose between plantingtbeareailiat '.can.befully irrigated given 'river ~. boreallocanons for the season and the volume available mon .fiu'nt ~ge;. ;and theareadevelopedfor irrigation, or :sor.llC gamble in between.

Thc:cnoice. aCme 'individualinigatof will depend on, amongst other things, experience, attitude tC)w.aros'rlskand, possibly ,cotton prices. For example, an inigator may gamble on the $Cason being average, conserving one .megalitre per hectare ofwaterfromtailwater 8l1d .ron..oftand ·pulllpingtheequivalentofan additionalmegalitre of water pe.r hectare ~surplus·oroff.. al1ocationflows. Such a choice entails planting an area to cotton roughly tbirty:percent greater than that 'which can be fully irrigated with cenainty (assuming the .crop. mt~s 6~S ~ga.titteS of wt\tetperhectareina normal season)" .If cotton prices are high.:theinigator:Jnay:be wiUil\gto.thensk

Sbould thesr:uon'~ ·.dry,Ol" should the tailwateran(lrun~ffs'tppliesbe lower than .anticlpatedtorsbould'.thesurplus flow not eventtlate,thenthe. irrigator'wjllbe foreedtoset a.sid~; .1and..Al~tivcIYf shoutd,the anticipated,additionalsuppli~ eventuate, then tho tetumS 'tQtheenterprise ~y well be.thiny pet centgrea.ter than if.tbe gamble had not ·been talc~~ 'ClearlYU1e~isroont for a variety ·of choices or strategies to be adopted. The intention. in this :study is to explOl'e·the possibili~of predicting ,the stra.tegi~that in:igatoJ;'S rnayadopt

The technique :involv~ .assessingcertainstrucu.mll characteristics ·ofhrigationpropei.1ies. OllWbich infonnati<'lPis ,readily .available.in thebeliefthatthesech~cterlstics impose stIQng constraints lIpontherange ofpl~ting' ·strategi~· available to theirrjgator. Asa consequence,inigatQrS with properties exhibiting similar structural cbaracterisncswill, it is be!ieved,ailoPtsbnilarpI1\llningstrategiC$.Sbouldiliisbe the ease"then the opportunity ex,ists to predict the planting strategies ofhrigators. and so. the demand for ,irrigation water.

The data usedinlhcanaivsis wascollectedfro11l a mail .slllVcyquestiQnnaire ·of cotton .inigatorsin. the Nam6i Valley.. The .slll'Vey was conductedbytbeCentre for WatetPolicy Researchatthet]niversityof New England ,in 1988 and fonnedpartof a project ~ertaken at the Centrc which was supported bytbeNew South Wales Departnlentof Water Resources and :tbeNamoiCorton Co-operabvc. The project involved examining various,managementoptions~ted With the commissioning ofSplit Rock Dam and the findings of the .project are reported in A Study ofReliabilitY ol~Vater Supply tDrlTTigared Cotton in tlaeNamoi Valley.

The S\U'\'~ was intended to gailieriufonnation on a range of issues of interest. to the Centre. 1ml ;ators were questioned about the characteristics of their Pnlpertiesand water licences, the. it' planting strategies and, the factors influencing their choice of planting strategy .. Inaddition,inigators were asked to supply detailsconceming their in..crop unganonstrategies.wbole fann 'strategies and farm development strategies. The X'esponses tQwequesti.ons concerning the characteristics of properties and licences. pl~dpg. strategies and the chQice of strategy are of interest .here~ With regard to the characterlsdcsofpropertiesnntl water licensing details concerning size of river and bore Ucen«s..fannstoragc and .bore.capacities, lotal area and .i;U'ea developed forirtigation were l;qUestedi :Inaddition.infornmtion concenting conjunctive use was requested. Irrigators ~rereque$ted to list. the factors that. influence their cotton ptanting strategy,in order of irnportanecif possible,Cottonpricestanl1Qunced allocations, financial capacity to absorb riSk andexpettationsconcerning weatber conditions 'we~ some oCthe factors ;that were $uggcs~~

With~ttoplandngstrategies.itrigators were requested toindieate the m:eas·thatthey would plant tocOUOn lor different combinations of announcedailocations,SQil moisture profiles,volulllCs inQn~fann .stotageandcotton. 'prices. In addition, the ateaactvAlly planted to··e'

Responses wete 'reeeivedfrom f()rty.;fourirrigators, .toughly half of the irrigators in the N~i Va11c~y. The tesponsestotherequestconcerningpropertY3nd licensing chil1i.

.SummarystatisuCS·Qftbe data a.."C presented ill Tables land2\< The substantial ranges cQveredbytbc data-is apparentirQm Table t. The degree ofvariability intbcdata is also quite;, high as evidencedbythehigb.valth;;s for the .coefficientof variation. .InTable 2 the correlation$between.tbe variables are reported. There area. few quitcsuongcorrcla.tions whichls .notsurprising. Riverlice~ is highly correlated with the conjunctive use variable ..$id ~veloped~ Bore licenceisbighly COl"felated with the conjunctive use variable and ·bore capacity while fann stOOlgeis .strongly correlated with develQped .area.. 0l1\l'8Cteristic t Minimum Maximum M¢an S02 CV3

River IJcence 123 13488 2034 2763 1..36 Bore Licente 0 8'795 1 tOI 1646 1.49 Bore·eap.clty 0 130 15 23 1.52 Conjunctive 123 13488 2426 2947 1.21 FannStorage, 0 12800 621 1532 2.47 Pevelopcxl Area 97 4656 675 841 L2S -- 1 VallJCSe,,~lntentl$ of the units in lbofirst ~t1on oftbc survey. 2 Standardl>eviltiQn$" 3eoerGcicntQ( Vail{iOO .. Source:' Derived from CWPR (Pers.Comrn.).

Table 2:Correlationsbetweenc:haracteristies"

River Bo~ Use Bore Flll1ll Developed Licence Licence ,Capacity Storage Area

River Licence 1.00 Bore,Lkence 0.63 1.00 U$C 0.93 0.17 1.00 BoteCapa.city ·<0 0.70 0.77 0.67 1.00 Farm StQfage 0.52 O~91 Q.80 0.73 tOO t>evelopedAlQ 0.90 0.79 0.91 0.80 0.73 1.00 SOilMoistul'e ·0.14 -0.11 .. 0.20 0.00 -0.11 -0 .. 09

SQlUce: Derlved from CWPR (Pe(S.Comm.).

10 In SUtnmary,me data to be used in the analysis exhibited a substantial degree of variation intenns·of property and UcensingcbantcteriS~:lCs and intenns of.irrigationstrategies. The responses to tr; qncstionrequestinga listing o€the factors lnfluencing the planting decision clearly indicated.thru: the ,price ofcoUonandannounced allocation were the pri.n(;ipalfactors infiuencingthedeci.sion. Consequently ,the responses to the questions on couonpianting .strategyshouldreasonablyreflectacroal decisions as these questions were constructed lntennS of cotton price and announced allocation.

SimU.rityMeasures,Fador and Cluster Analysis

Cluster analysisisa.generic tenn for a, variety of procedures that can be used to classify similar enudes .into,clusters or groups. That is. a sample of entities is .re-organisedinto relatively homogeneous groups (AldenderferandBlashfield: 1984, 7). Clustermetbods ate based on simple troles of thumb- and. different methods will yield different cluster solutions.to,tlle sam~ data set. While clusteranalysisseeksstructuTe. it does impose structure in the sense that clusters will virtually always be formed. The root problem in cluster analysis is detennining when clusters atc'rear and not imposed.

The objective of clustering can be characterised as detenmningthatnumber Qfclusters (of individuals).thatensures each individual belongs to one cluster only. All indivi(!uals in one cluster.shQuld be dissimilar to individuals in other clusters. Clusters fonn where tbereare signlrlC.'Ult diff'erencesbetweenindiViduals(Duran and.O~DeU! 1974, 1).

Thef(llJrultion ufclusters is predicated on two assumptions. One, that the characteristics selected ~relevant to the desired cluster sQlution;and two, that the units ofmeasuring similarityarelvalidt (Duran and O·Dell: 1974, 31). The first .assumption means that only what are believed to be the relevant characteristics of individuals have been chosen as the basis' for classifying individuals as similar. The second means that these characteristics are ~suredappropriately, and that an appropriate scale or ·similarity coefficient· has been selected for measuring the .similarity between individuals across these characteristics.

In this stlldy the selection of relevant characteristics was limited to those supplied by the S1,l1Vey. The responses to .the question concerning factors that influenced the planting deciSion indicated that the price 0). ·t:otton and water allocation were paramount. Consequently, details .concerning water licensing and the area of land developed for .irrigation(as an upper bound on area) were considered relevant for classifying properties assinillar.Reganiingrneasurement of the property and the licensing characteristics the use

11 of hectares andmegulittes.respectlvely seemed quite appropriate, though measure~ such as .entitl~tnents..in.megalitres perdeveloped bectare may well be worth investigating in future researcb.

The choice of an appropriate similarity measure or coefficient was quite difficult, .partieularlyas Jbereare a few guidelines to assist in making this choice (Aldendederand Blashfield: :1984. 61). The similarity between individuals can be decomposed into three parts: shape, which is the pattern of dips and rises across variables; scatter, which is the spread ofyaluesaround the average; and elevation, which is the mean score of the case over all variables (AldenderferandBlashfield: 1984, 23). Measures of similarity such as the correlation coefficient describe shape but ignore elevation. With respect to the property characteristics. shape and elevation are important as both reflect differenc~s in resource constraings. The Euclidean distance was selected as the nleasure of similarity as this mct\SUl'e is sensitive to shape and to elevation. This measure is defined as:

K dij = II (Xik .. Xjk)2 11/2 k=l

Where dij is the distance or similarity between individuals i and j, and %ik is the value for individual i. A desirable property of this measure is that more distant values receive a greater implicit weighting through the squaring of differences, thereby improving the likelihood that diSSimilar strategies would be discovered. Although this measure is scale sensitive (Everitt: 1980, 17) this disadvantage was thought to be acceptable in this study as the variables representing characteristics (excepting bore capacity) arr measured in the same scale. The lower the score, the more similar the individuals.

Having settled upon a similarity metric, the next step in the methodology is to select the appropriate (hopefully) clustering technique. A clustering technique that attempts to impose tight, hypersphericnl clusters on the data was thought desirable. Remember that the strategy clusters will be assessed on the data for the members of a particular clustering on property characteristics. The hypothesis is that since members of a 'property· cluster are similar, tbenplanting strategies should be similar for members of that cluster.

Intuitively t if such a technique cannot successfully contradict the hypothesis then a technique that seeks to impose less compact. irregularly shaped groupings on the data is unlikely to be successful. Furthennore, the necessity for compact, hyperspherical groupingsQn the characteristics data arises because of the interpretation of characteristics a.~ constraints on the range of strategies available to the irrigator. Clearly, the less

12 constrained tbeinigatorsare 'by water availability and developed arca,thegreater is the potential foruniquely :individual strategies to be adopted. In tenns of this study it is critical that variations in strategy attributable ,to ·differences. in property characteristics be distinguishable front variations due to indlviduarspreferences. llence, the need for co~pact grouping acrosS characteristics. The possibility that less restrictive groupings might generate similar resu1t$ is an area, forfurtberresearch.

Of the range of clustering techniques that were evaluated (Simpsoil: 1989). density se~h,complete Unkageand Ward's method. were retained for fUlal examination. Each technique is based on plausible, though very differentcl\lsteringrul~sandeach was biased toward the fonnationof byperspherical clusters. The literature offers little in the way of guidance as .to rules for choosing an apPI'()priate technique prior to the conunencementof analysis. The intuitive appeal of the 'natural' clustering approach that density reflects (Simpsom 1989, .34):is extremely:powerful, while 'there is comfort in the rather more popular methods of complete linkage and Ward's method.

Hierarchical methods such as complete and Wardts Were designed and developed to fonn hietarehies, that is., a graded. sequence of rank.~ratherthan to search and locate an opthnal nutn»erQfclusle1'$.The shape of the dendrogram(bie~hy)isof DlOIe impQrt tbanisthe sb.\tisticaisigniticanceof the clustering implied at any particular levelofbrancbing. Oensitysearchonthe other band, is .designed to locate an optimal O)r()adly speaking) clustering of the data.O.n the basis ofthis difference in design ;andthepowerful intuitive appeal of the notionof'naturaltclu:~teYstthe density ~archtechniquewassettled upon as the most appropriate clustering technique. Wanttsmethodand complete linkage were retained for thc'purpose of validation.

Prior to the application of the clustering technique to the data onproper1yand licensing characteristics thcdata was analysed by means ofprincipal.c()nlponents,a form of factor anaIysis~ Th'~Ie were two reasons forconductirtgsuch an analysis. First. in the original data the cOJTClation between variables (characteristics) were found to be quite high. The simple. correlation coefficients being of the order of 0.7 or higher for the most part. :R.easonably bigh correlations sucb as these raises diffizulties inasse$sing .the relative lmportanceofeacb characteristic in the fonnation. of clusters. Througb. factQranalysis soroeassess1ll~ntcan 'be made for the importance of characteristic$ by examiningtbe weightingeachcbaracterlsncreceives in the significant factors. Second, an examination ·of tbefactQrs(principal components) themselves may provide useful infonnation on the felationsbi'psbetween characteristic$. The employment of factor analysis .is described in ·more detail·jn :Simpson (1989, 3~37). ,Analysis and 'llesults

Tbc,:fesultsofthe factor analysis of the property charac~risticsarep~sentedand discussed,f()IlQwedby cluster analysis using the density ;search technique!' A comparison is then tt1adc with the cIUStefSobtained using Ward's JDethodandcompletc linlcage.

Factorana1y~s(principalcomponents) fonns linear combinations of varlablC!S .insuch a way that the explanation of the varlancepresentinthedataismaxUnisedhythe ,tninimal number of combinations. Factor analysis wasP¢"011l1ed usingtheprincipalcolllponents ter;:hnique available 'in the SPSSX(Norusis: 1985). 'The Kalset.. Meyer-Olkin measure of sampling a4equacy which indicates tbeoveral1smtabllity of the data fQrfactoringproduced an ,excellent score(fable3)~ .Banlett'stestof sphericity of the daUlt which indicates the likelihood that the ~rrelationmatri1t is. an identity matrix and so, .not suitable for factor analysis,. clearly indicates the matrix is ,not an identity matrix.

Having assessed' the suitability .()f the data for factoring tbeprincipal components analysis wrusthen ,undertaken. The results of thisanalysls are reported in Tables 3 and 4. In the first tab1e. statistics on the extractedfactorsarerewrted.andtheresultsclearly indicate that the ·first .principlec()Jllponent ·explaills virtually 'all ,the variation ,in tIle data. The fU'St comwnent captures some eight!percent'()fthevarl~bilityinthepropeny characteristics, tllc$eCOPdcoDlpOnentcapturlng ·an·additionaltVielvepercent. The eigenvaluesn:ported in Table4c;learlyindiCatetbat only the.fustcomponent should be l.'etained.as significant. The resultwa$ CQnfinnedby Catell'sscreetest which is presented in Figure 3 (N'orusis: 131). The scree test involves :retaining. those components which do not form pan ,of tbescreeof debris lying atthe base of.a slo~~Again onlythefirstcomponent appe81'$significant.

The extent to wbicbthe rewnedcomponentrept'esents each property characteristic is also reported in Table 4. 'The component is highly correlated with eachc~eristicandscores oncom.Qlunalityare alsohigb. The latter are the proportion of the variance of the characteristic described by the retained component. The table .also contains values for smnplingadequacy for each property characteristic and the loadings or weights on each characteristic for the fJI'Stprincipalcomponent. Tberocasuresofsampling adequaCY, (Norusis; l29-.-130) indicate the extent to whichconelations between pairs ofvarlables are described byothervariables~ The results I1lQge from 'middling' to 'marveUous',again indicating ·that. factor analysi$ is appropriately applied. The weights are the coefficients on each characteristic .in the f1l'Stprincipal comptlnentinterms of the .original values of the cbara~.!stics.Th~eweights .~in fact correlations andean be tested for significance (l{outs()yiat\~'d5: 1918). All weights meet the criterion for significance. Table 3: Summary statistics lorractoranalysis.

, EactorSmlisij,,~ }actor Eigenvalue Variance Cwnulative

I 4.82 'SO.5 80.4 ,2 0.70 11.7 92.1 3 0.29 4.2 96.9 4 0.09 1.5 98.4 5 0.07 1.2 99.6 6 0.03 0.4 100.0 SamplinKStatisties

I{aiser.. Meyer..()lkin 3 0.78 Bartlettf sTest4 341.87

lPetcentnge ofdata v~ explained byibe factor or principal component 2cumulatiVQpercentage of data. variance explained s'AvaIueof O.Sis ~meri~" 0.7'middlingt (Norusis: 129). 4ProbabiUtythat matrix is an identity matrix is lesstban 0.0001.

Table 4: Summary statistics for significant ;factors.

Otaracteristic Correlation Communality Weights! MSA2,3 - River Licence 0.87 0.76 0.397 0.69 Bore Licence 0.90 0.82 0.411 0.81 Conjunctive 0.92 0.85 0.420 0.72 fann StQrage 0.87 0.76 0.397 0.77 !lore Capacity 0.85 0.72 0.388 0.81 Developed Area 0.95 0.91 0.434 0.93

lAvalue.ot 0.37 or greater is signiflqult for both Pearson Correlation and Burt ..Banks Test (Koutsoyiannis: 1978). 2Measul'eOC sampling adequacy. 3See dlc thintnoteto Table 3. ))1 ,,{

<'ti" t .~ "~ 'I.

5.0

4.5

4.0

3.5

3.0 t4 ...,0 2.5 ~ % ttl ....Q 2 .. 0 fat 1.. 5

1.0

0.5 0,0 . a 2 4 5 6 7 FACTOR

Figure 3: eaUel's s\!ree test ,for significant factors. ,As only one significant component was extIactei!frolD the data, interpretation is difficult. :B8$ica1lyas the valueofeachcbaracterlstic increasestbe value of the component increases. Hence a high component SCOre for an individualpropenyreflects high volume licensing and a large developed areate1ative to a property with a lower factor score.

UnfPttuntlt~lythescorescannotbe used to distinguish clearly between .river only or bore only licensed properties,. otto distinguish conjunctive from non-conjunctive licensing. Tboughthe factor analysis was less informative than was expected with regard to interpretation, tberesulting 'Pl'()perty scores for the first principal component were used in the cluster analysis.

Using Clustan (Wishart: 1987) the Euclidean distance measure was used to calculate a sitnilarity matrix of the properties, based on the fIrSt. component scores obtained in factor analysis. Densitysearc:h (Wishart: 1987) was then used to produce cluster of properties with similar.characteristics. The density procedure classified tbe forty-three properties in

the sample intosixc:lusters of 6,5l 8, 3, 10 and 11 individuals respectively. The dendrogram illusttating tbeclusterlng .hierarchy is presented in Figure 4. Employing the upper tail rule (Aldenderferand Hlashfield: 1984) seven clusters may be present Appal'ently Property 2Smay well be treated asa single case cluster. This is .not-surprising as this property exhibited characteristics radically differentftom any other'property~

The characteristics of the properties in. each cluster are summarised in Table Sand the clustersarep~sentedgrapbically in FigureS. The dendrogram,statisticaiand graphical summaries oftbe clustering analysis clearly indicate that six clusters, and probably seven. are present in the data. On the evidence it appears quite likely that the cases constituting the cluster ofthree properties represent poor samples of·additional clusters.

In Table 5 the mean and. coefficient of variation of the property characteristics for the members of each cluster are presented. In addition tests statistics on the degree of variation present in each cluster are presented. 'The F statistic indicates whether the variance of the dataonpropel1ycharacteristics for the members of a particular cluster is significant, given the variance of the data for the whole sample. With the exception of the cluster of three properties, the scores Qnthe F statistic did not exceed the relevant critical value for any of the property characteristics in any of me clusters. Consequently with the one notable excepdonnone of the. clusters formed presented. a significant degree of variation across cluster members. 21 43 33 iTittt. .~ip!l) 10 30 1. 38 12 34 29 20 26 27 ,. 31 24- • 19 IS 3!S 42 16 4 3 13 2 S 25 eYct.t I 3 CO!"" 32 14 3'1 8 28 '0 36 41 9 39 23 11 7 17 22 • " ,. 1 ~1 3. 0.001 2 41 31 0 .. 002 .3 41 A 0.002 I. r" 9 0 .. 002 '1 ~ ~IIIIII.I.·IIIIIIIIIIIIIIII1.111~ 5 '1 U12 0.003 H111111111 6 lot 24 0 .. 003 • 41 28 0 .. 003 ? ..• I I I I I I I I I I I I I I I 1 1 I I I I J I I I I J J J I I f 1 I I .. 8 '1 39 O.QOi. 9 .l&- .iISj '1 D.PD' • .... 10 41 "19 0 .. 00'1 L;.. (JQ : I II I III J I I I 1 1 I I I I I I I I I I I I I I I I I t I I .. 11 40 23 0 .. 009 C "'I 1.2 1.0 29 0.009 ft 13 40 1S 0.010 · f:- 14 40 :5 0.tJ10 1$ 40 11 i). OlD : I I I I I I I ( I I I I I I I I I I :t J I J I • 1_ 21 42 '0.013 r ~ II .~ 17 21 :: 0 .. 01.'5 18 21 1.7 O.OU. a 19 4O 20 0.0145, ~... 20 40 3S 0.016 ::. 21 1.0 13 0.0i.:7 • c...: 22 21 43 0 •.01a - 41 I I I 1- I "I I I I I I f I I I II .. C. 2.l 40 7 0.020 · g 2' 21 16 0.021 c.. 25 21 !I 0 .. 022 "'I 26 21 22 0.037 C • 2' 10 26 0 .. 0" ~ 21S to 32 0 .. 05' · I I II. II I I I I '4 29 10 36 0.:060 · '" .. i3 30 10 30 0 .. 066 n II. 6 0.071 .. 32 10 '7 0.0'1...... 33 14 18 0 .. 099 .. 34 11. 1 0 .. 116 a. 35 14 37 0.145 .. .. 36 33 I- 1' .. 167 37 33 25 96 .. 544 .. 38 40 21 0 .. 021 I 39 41 40 0.Ot2 .. ~': 4O 10 14 '1.053 .. I .. U. 10 41 0 .. 054 I: 1 .. [ 42 10 33 5 .. 460 · ~ ...... ,...... ~ ...... 1.• 6 .------...... ------,

LEGEND 0.8 • .cluster 1 o cluster 2 a cluster.3 • • A elusler 4 • a cluster 5 o 000o 0 A OO -0.8

-1.2. '00 000 000 000

FigureS: Clusters un property characteristics. ....

19 TableS: ,SlJmDl~"Y statistics ,of ·clpsters.

},KU.l:'tiKTYCH.AR./t{·TERIS~I1P Ouster! Rivet Bore, Fann Bore Developed Licence Licence Conjunctive Storage Capacity Area ONE2,3 F 0.26 0.17 0.12 O~O6 O~19 O~O3 T 0.23 0.47 0.24 0.04 0.46 ~.08 .. Mean 2351.66 1423.83 2675.67 606.17 30.3.3 687.17 , CV 0.60 OA7 0.38 0.52 0.. 50 0.20 Cases 6 'tWO F 0.65 0.66 0.08 0.01 0.27 O~O9 T 0.49 0.39 2.69 O~18 OAO 0.61 Mean 3128.19 1628.39 4657.19 590~OO 20.60 831.20 Cases 5 TaREE F 0.04 0.15 0.04 0.19 0.12 0.21 T 0.97 0.66 1.38 0.21 0.45 0.08 Mean 1489.37 678.75 1630.00 416.00 11~g7 644.00 CV 0.. 31 0.95 0.35 1.43 0.70 0.60 Cases 8 FOUR F 4.05 3.07 0.. 67 11.15 6.85 2~52 T l.39 1.62 3.81 0.67 0.96 1.96 Mean 9806.66 5778.00 11639.;66 4092.99 75.S) '3293.66 CV 0.57 0.50 0.21 1.25· 0.82 OA1 Cases 3 FIVE F 0.04 OJ2 (t03 0.01 OJ6 0.06 T 2 ..21 LOS 3.24 0.67 0.53 lA6 Mean 821.99 499.00 888.59· .345.70 20.30 371.89 CV 0.67 1.15 0.53 1.. 18 0.91 0.56 Cases 10 SIX F 0.01 0.06 0.01 0.00 0.02 0.00 T 4.13 2.16 5.38 10.35 4.64 8.2l Mean 740AS 265.09 740.45 52.90 2.09 181.12 CV OA2 1,,46 0 ..42 1.04 1.39 0.33 Cases 11 lS~ ~t tor ~plamltion of symbols. and measures. :2lbccritical'va!ue for F isapprodmatety 3.0. lThe- critical value forT is appro~imately 1.9 T'heTstatistic Was calculated to test whether the means for the sample were significantly diffctentfiom the means for the clusters. Tberesults indicate that the clustering procedure hasgencratcda $Ct ofreladvelycompactt weU defined, sphericalgroupingsofsiroilar iplOpemes~ Having ~stllblished that well defmedgroupings of similar properties 'bad been 'produced~tbexneans of the property characteristics for each cluster were i,nspected and .companm in order to intetpret th~natute of the gtOtlPings.1lte rUSt andSC!COnd clusters in Table 5 both consistof.properties .exl\ibitingaverage l~vels of licensing .forboth. river and boJ:c licences.neara:v~gc stOJ'age capacities on ·{annand borecapacjties~ The s<:patation ofthe.clus~e($isclearlyonthebasisof whethetthebo.re licences were issued for COlljuncP.V~ use or not TheptOpertiesinclust~ onehavecOIlJunctive licences wbile those .inclu$tertwoh~ve, non.-conJunctive licences~ This is reflected :in the higber mean ,~velop;da.reaforthesecond group relatiwt to the firs~

Thefifth,·~" sixtb elusterscotl$ist ofrelat:Velysmalterpropenies in terms oflicensing and clevd~, area.. The separation.betweentht~~clusters 'i$on tbcbasis·ofbothconjunctive liccnsing'ancl()n,~fann .sto~gc capacity. The properties .inthcsixth duster 'possess conjunctivc·liC

The :~rtiesintbe thitdclusterpossess characteristics midway between those Qfthe (U'St twoC1u$tetsandt1lt~~, last twoclusters~ These properties possess smaller river 'and bore licences than dotbose iilclu$terooc~ The licensing is p;edonlinantlyoouJuncnve.On fann iStOlllg~ are also smaller than thosc forpropmies in the farst cluster.thouWa the developed artais of tbesame .magnitude.

F'inally.the fourtbclusterconsistsof the three 'outlier' properties. These properties are substanually larger properties than any others in the sample. They .have high volume~ conjunctive licences and large on ..fann. storages. Tbedeveloped area is correspondingly gteat,et,', io.. r thestlhtee, ,pt'Qpem,es," 11ti,S, cluster a, ppear.s, to,' represc,Rt .atJea5t one and probabi~Jtwoclusterspresentin tbepopulationofirrlgators lnthe Namoi V leywhicllare 'poortyreprcscntcd inthesam,ple. The validity of the clusters was tested by applying complete linkage and Ward's method. Virtually identical clusters were foaned by these p~l1res. tn Table oSlltllma.ry statisucs foreacbcluster according to planting .strategy a.reptesented~ Ofrnost "interestistbe, F ratio whichmeasUfesthevananee 'oCstratcgies for each cluster :"Iati~ :'0 tbevariancefor 'the sample asa wbole.Exceptmg the,threctncDlbet group (cluster ,four) the ratios are $lusfytnglysma11.. In~pection ·t)ftbevalnes for the means for each strategy 'reveals that th~area. ;plantedto cottQn declines with decreasing water avail.bilityand decreasing price. and thlspattemholds for ~achof 'the clusters. TI:lese resultssuggest··that lnigationptopcrties canbe,sensiblygtOUped. aecordirtgto sbnilarlties 'in propenyand licensingebaracteristics. Funher. tberesults indicate that such groupings do ~present a classification of ~es acconUllgto sinU!arity inplantingst;nUegies.

Table': Statistical $ummary for planting.strategies.

STR.ATEGY

.60%. AllocauC)n 100% Allocation 2Qtl,A1~ ctu.ster ,$500 $300 $250 5500 ,S300 S2SO !SOO 5300 $2SO I.~ 01'iB. F 0.11 0.14 0.26 0.10 0.13 0.25 0.. 17 0.20 0.07 Mctn 543 543 385 5S3 553 .38S 342~ 338 208 TWO P O~2t 0,,06 0.14 0.39: 0.10 O.HS O.OS 0.02 0.02 Mean 616 454 334 6S4 484 3$4 .324 354 2S4 1'HREE F 0.21 O.ll 0.04 .0.19 0.09 0.04 o.n QJ3 0.02 MeIn 398 '326 132 390 324 144 28S 242 9S FOUR f 5.33 6.80 11.01 ·4;22 '6.64 11.0S 1,53 12.01 6.64 Mean 2200 1940 1553 2347 19S1 15S3 1940 1450 3017 ..FlVB F 0.05 0.03 0.03 0.05 0.03 0.04 0.03 0.03 0.01 MC*1 230 207 163 262 214 173 197 148 106 SJX. F 0.00 0.01 0.01 0.00 0.01 0.01 0.01 0.01 0.00 Meat) UP 115 90 128 124 109 84 71 SS Conclusion

A combination of facto{anaJ,ysisand cluster :analysis ,has been used in this study to group irrigation properties on the basis of land and water licencechRrd.Cleristics. Tbegroupings obtained were Judged, t() have been formedort;l 'plausible and sensible basis. Subsequently. ana.ysis on, data describing the planting strategies of cotton irrigators 'indicated 'that membetsof each of the clusters }JtOducet1 t.~the fustpbase of the analysis foUovvt'jstatisticalty similarplantingstrRtegies.

Withreganltothe fundamental .management problems faced by both the 'Department of Water "Resources.in detenniningannounced allocations., and inigato(S with respect to their co-ttonplannngdecisiOll. the application Qfthe J;e$lllts of a cluster analysis may improve the precision with wbichseasonal allocations are detennined. Iftbewatet authority has information on property and licensing characteristics and survey responses concerning pl~ting strategies fora sample of .inigatorsthen clusters of ,similarirrigatol"smay be fol'tlled. The planting strategies. of irrigators not included in the survey may then be predicted on the basis of allocating these irrigators atnongst the varlousclusterson ule basisof.tbe characteristics of theirpropertie$~ benceamoreaccuratcmappingofplanting intentions' and demand for irrigation water across the popuJationofirrigators might be obtained, leading togreaterpreclsion in matching predicted watersnpply and. demand. Also. as irrigators invest in sttUcturalthange (for example byexpandingon·,farm.$torage) the impact of this investment on demand for irrigation water could be assessedbyre.. allocating irrigators between the relevant. clustersolutioll5..

The scope for further study ,is substantial. A similar study using a more appropriate survey over&. tnorerepresentativesample of irrigators is clearly necessary~ Also. an :interesting study would be to apply the results of a morethorOl,lgh cluster analysis ofinigators in the Namoi Valley to the .managed. irrigation ~ystem and assess the usefulness .ofthep1'QCedure to see if it cart, in fact, act as a .usefulmanagement tool for the Department of Water Resources.

References

Aldenderfer, M.S., Blashfield, R.K. (1984). Cluster Aruzlysis. Sage University Press, USA. CWPR. (1989). AStudy 0/ Reliability o/Water Supply for/rrigated Cotton in the Nomoi Valley. University of New England, Annidale. 1)utan,B.. S., O·Oen. P.L. (1974). Cluster Analysis: A Survey. Springer-Verlag. Heidelberg. Everitt,B. (1980). C/uster.Analysis. Heinemann Educational Books, London.

Koutsoyiamtis, A~ (1973). Theory o/Econometrics. The Macmillan Press Ltd. UK. Norusis. (1985). SPSSXUsersManual. IvlcGraw-HiU, USA. Pigram. J.J. (1986)_ Issues in the Management ()/ Australia's Water Resources . .Longmans, Cheshire •. Melbourne. Simpson, Y. (1989). A clUster analysis .0/ cottonplantingstraregies in the NamoiValley. Unpublished BAgEe dissertaion. Depanment of Agricultural Economics and Busin.essManagement. UNE, Armidale. Wishart. D. (1987). Clustan Users Manual. Computing Laboratory, University of St Andrews, Scotland.