TIlE HlE

ACOMPARATIVE STUDY UFHlE Al'PUCATION OF

TWOCATC HM ENT IWlDELS TO TIlE BAIIAK RIVER BASIN

LOMIIOK ISLAND-INDONESIA

B, KADARISMAN

AThesisSubmitted10 theSchool of GraduateStudies

inPartialFulfilmentof the Requirements for theDegre eof Masterof Engine ering

FACULTYOFENGINEERING AND APPLIEDSCIENCE MEMORIALUNIVERSITYOFNEWFOUNDLAND

OCTOBER,1993

STJOliN'S NEWFOUNDl.AND CAN AD A

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ISBN0-315-86609- 8

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Abstract

Acom monproble min waterre source s planning inEa~lcrnIlldlll...·si.l.IMnkul ,lrly inthe Province ofWest NusaTcnggarn(NTDl.is the lackof strcamtt ow

rnua.

IIIt:"'l1l'ra l the availab le runo ff data donOIcoverperiods of more than tinedl'l' <ltkand an.'t1lkn insufficientfordesign purposes. Rainfalldata,however. canhaverecords111:\[ arcIWlI

or threedecades in length.Toextend thelengthoftheSlrt:;1I11 1l11Wrecor ds,rainfallIJilia may betransformedintostrcemnowsusing a catchmentrainfall.runoffmill!..'!.TWll co nceptual catchme ntmodels.the Tan kModelamiMoc k'sMudd.arcIJrtll"'I~'l1fur this transformation ofrainfall into runoff.Both modelsrcsquire1Ilc;J1lareal pn..'Cil'ililliu lI;mt!

eva potran sp irationas inputs.Tl1eT ankModelrequiresdlilyinpu ts values,whileMuck' , Mod el-oqutresmo nt hly inputvalues. Twovananoe softheTa nkMudd(l."tlllflgur.uiIlU' with threeandfourlank components) werestudied.

Threeyear data periods(1973-1975)were employed furcalib ration,:U1dthc subsequent three yearperiods (1976-1979)wereusedforvcnflc ation.By a tria laml errormethod,a setof parametenfo rthefou rcompo nentTankModelwe reobtaine d '101I suggestedformode lling daily runoffof the BabakRiver.The model withthreeumks did notgiveagoodrepresen tationoflowne ws.By thesame method,a set of paramete rs

fortheMockModel wereobtained;theseare consideredsatisfactoryfor monthly flow mudell ing.Mock' sModelis considered suitable for preliminarywaterresources studies.

where monthly time stepsarcappropriate. The choiceofasuitable model varieswith the purposesand tneavailability of data.Additional raingaugesin the basinare recommended 10improvethe resultsof themodel.Forbasinslocated neartheBabak Riverbasinandfor basinswithsimilarcatchmentcharacteristics. theobtainedparameters fornOlhtheTankModeland Mock'sModelcanbeused asinitialvalues.

iii

Acknowledgm ent

IwouldlikeCoextend m) sincere thanksto mysupervisor,Dr.L.M.lye. furall his academic guidance throughoutmy program here.I wouldalsolike tothankMs.

SU~H. RichterandDr.A.Robertson.who offeredsuggestions andencouragement duringmythesis preparation.Iam alsograteful10 SeanaKozarforherassistance in editing thisthesis.

My appreciation isalsoextendedtotheGovernmentof Canada throughthe CanadianInternationalDevelopmentAgencyfor providing methefunding 10study OIl MemorialUniversityof Newfoundland.My-aanks arealso extended10the Director General of WaterResourcesDevelopment.Ministryof PublicWorkofIndonesia .for allowingmeto pursuemy studies here.

Finally,I acknowledge the supportof my wifewardandmytwochildren Alii andSony fortheir patience duringmystudyhere.

Conte nts

Ackno ",,·led ~ment

Contents Ltst of Tables ListufFigures ,\hh~via t ions

J Introduction.

I.I lMckgruund I.::! AvailableData. 1.3 ObjectivesoftheStudy 1.4 Outline oftheThesis•. .

2 Descriptionof StudyArea 2.1 StudyArea andLand Use 2.2 ClimateandHydrology .. 2.3 Sourcesof Data, ..

3. Rainfalt-Runnff Models .1.1 General... ••.,

: 1.2

^{Tank Model .. . ..}

, .

viii

xl

10 10 10

3.2 .1 The 5tTUClUreof theTank Model 3.2.2 The behaviourof the Tank Model 3.3 Theoreticalbasisofthe TankModel

3.3 .1 Simp leTank Model .. 3.3 .2 Storage Type Model. . . . 3.3.3 SeriesStorag eTypeModel 3A Mock'.. Model.

3.4.1 SoilMoistur e .

3.4.2 GroundwaterStorageand Runoff. 3.4.3 Storm Runoff.

3.5 ModelInputs... 3.5.1Preci pitation 3.5. 2 Evapotranspiration

3.5.3 ActualEvapotranspi rationEstimates

J Methodology

4.1 DeterminationofLagTime 4.2 TankModelCalibration .

4.2.1Runoff Generation . 4.2.2 DeterminationoftheInitialParametersof

theTankModel 4.2.3 Trialand Error Calibration 4.2.4 AutomaticCalibration . 4.3 Mock 'sModelCalibration...

4.3.1 Runoff Generation...

4.3.2 Initial Parame tersfo r Calib ration 4.4 Verificatio n, •.

4.4. 1GraphicalCriteria .

4.4.2 Nume rical Criteria.

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vi

5. Resultsand Discussion 56

5.1 Tank Model(fourlankcomponents) 56

5.2 Tank Model(three tankcomponents) 66

5. ~. Mock'sModel. 67

5,4 SensitivityAnalysis 7}

5.5 Compari sonbetweenthe Tank ModelandMock'sModel . 77

6 Conclusionsand Recommendatlons 80

Refere nces 83

AppendixA:Compute r Program forMock'sModel 85 Appt'ndix B:Sprea ds heetComputationfor the TankModel 90 AppendixC:Results ofthe TankModel(four tanks) 93 Appt'ndixD : Resultsofthe TankModel(threetanks) 109

Uibliogr a ph y 132

vii

List of Tab les

1.1 Available Dataforthe BabakRiverBasin... 2.1 LandUse ofBabakRiverBasin(1985) 3.1 Potential EvapotranspirationEstimates (Epl 5.1 TankModelParameters Obtained..

:5.2 ResultsofTankModelCalibrationbasedon NumericalCriteria

:5.3 ResultsorTank Model Verificationbasedon Numerical Criteria •.

5.4 Parameters ofMock'sModel. 5.S ResultsofMod e'sModelCalibrationbased on

NumericalCriteria •. . . . • . .

5.6 Results ofMoc k'sMod elverification based on Numerical Criteria .. .•. . ..•. . . ..

JII 57

, ,,

n n

viii

Li st of Figures

J.I BabakRive r Basin

3. 1 TankModel Structure 12

3.2 TankModelCharacteri stic s . 14

3,3 Tank ModelTypes JA Mock'sModelDiagram

4.1 Cross CorrelationAnalysi sResult. 4.2 SingleTankComponentAdjustmen tGuidelines 4.3 SingleandTwo TankComponentsAdjustment

Guidelines

4.4 Two TanksLowFlo w AdjustmentGuidelines 4.5 Mock'sModelItera tiveProcedur e 4.b Detailed CalculationforSoilMoisture(SM)and

Soil Storage(55) .

5.1 TankModel(four tanks) Calibration>1975/1976 5.2 TankMode l (fourtanks)Verification-197611977.

S.3 Mock' sModelCalibration- 1973·1976 5.4 Mock' sModelYeri flcation.1976-1979 5.5 SensitivityAnalysisoftheTankModel (fourtanks)

17

22 34 41

42

49

5\

58 6\

68 70 75

5.6 SensitivityAnalysisoiMod'sMtldel .., 5.7 Comparison oftheTdf.kMoJcI{fourtanksland

Mock's Model Results

"C DitjcnAi r

Fig.

Kccarnatan

krn!

krnhr' mm day'

MI.

NTB

P3SA-NTB WMO

Abb reviat ions

Degree inCentigrade

Directorate General ofWaterResourcesDevelopment

(undertheMinistry of PublicWorks ofIndonesia) Figure

Sub District Sq uar e Kilo metres Kilometre perhour Milllmetres per day Millimetre Mount

Wes tNusaTenggara Province Wa te r ResourcesDevelopmentPlannin g Study World MeteorologicalOrganization

xi

Chapter I

Introdu ction

1.1Background

Water resources plannersin Lombok Island.as wellas inotherislands in E:lslcrn Indonesia,faceproblems withregar d to theavailabilityIIfstreamflo w(bill. Dillyfew river basinshavesubsta ntialco ntinuous records(Ifstreamflow.fo,loslhavedata fur"

shortperiodornone at all.TheGo vernmentofIndonesia (lhroughIhcMinistryofPuhlic Works)beganinslalling streamflowmeasurement instrumentstluringthecarty11)71k . Financialdifficulties and natural disasters. suchasfluods, ho weve r,h,,\o..k·tIIn discontinuitiesin the recordsinseveralyears.Onthe other hand,rainfalldataMe availablefor longe r period s of recor d ,due10 the factthatraint'a11 mcasure memis simple r andrequireslessskilled labour.

This thesisconcentrateson the Babakpi-erbasin which..hares IhC!iCrunotf data problems.TheBabakRiverbasininLombokIsland (Fig.1.1)hasseveralycus(If streamflowobservation,Fromanengineeringpoint ufview,suchashnrt periodof recordis insufficientforwaterresourcesplanning.An irrigationproject.forexample.

requiresatleast20yearsormoreyearsof recordedstrea mflowdatain order10 deter mine the yieldreliably.Forwat e r resourcesplanningpurposes,alackof.\ trc;t11100 W

~(a:)F";;~

-=--.J V C-J ~ -

Sesaot •

SlI,anadi Pe'sil

Lom bo kSt,~ it

o

Gebon{l

Pron{l{l a,al a

ClimateStat ion RainfallStation Runo ff Station River

Ma~tang

Ung k uk U m e

Kopang

o

Fig . 1.1:BabakRiverBasin

data can lead to eitheran underestimationor overestimationoftill'projectcostor.

conversely,anunde restimatio n or overe stimationof thesize of thetar g e t servicearea.

To solvetheproblemofthe shortageofrunoff data, transfonuationofrainfalldillOiuuo runoff data is required .Catchmentmodellingisone of severa lmethods 10<ll'l'llllllllh h suchtransform ation.

The purpose of thisthesi s isto carryouta detailedassessment of a dailycall..-hmcnt model as appliedto theBabakRiver basin,andcomparetheresultswith"monlhly model.Th e model usedistheTank Model(Sugawara, 196 1,19 b7),\I~ingeitherdaily or monthly timesteps,The reasons for the choice of thismodel arc:(I )the modelhas beenused for severalrive r basins in Indonesia withgood succe ssand (2)becauseIll'its simplicity,where all mathematicaloperationscanbe performon«pocketcalculator.

makes themodelsuitableforareaswithlimited computerfacilitic~,suc h as thecasein Lo mbok.

Asaco mpariso n, Mock'sModel(Whichis designedformon thlytime steps \ln ly) was also used,Itis consideredsuitable forpreliminaryplanningin whichmonthly Ilows is more importantthandaily flows.Moc k'sModel ischosen becauseitW,ISucvc!o"l ..d ba sed on the particularfeatu resoftheIndo ne si an climate,ThLs modelhasbeenadopled by the Ministryof Public WorksofIndonesiaandisrec omme nded for usclIUOUghUllt thecountry,especially forirrigationplanning (lJitjcnAir,1985).

1,2 Ava ilable Data

Collection and observationof runoff data from the Dabak Riverat Gcbongwas

underta ken from 197]until1985.Severalyearsof dataaremissing. However.six complete years of dataare available.The catchmen tareaupstreamofthe gaugingstation is194km",Rainfalldata in the basinare availablefortheperiodfrom1970to1989.

However ,theserecordsshow some discontinuityand some missingdatafor several years. Thisis usually causedby themalfunctioningof the rainfallgauging instruments or byachange of the gauge location.Inaddition,climatic data areavailablefromthe neareststation (Kopang),foranine year period. Theavailabledataarcpresented in Table1.1.

1,3 ObjectivesoftheStudy

Tileobjectivesof the studycan be statedas follows:

I. Tn obtain suitable parametersofthe TankModel for the Babak River Basin,which can beusedto transformthe dailyrainfall dataintodailyrunoff data.Bysumming lip the dailyrunoffdata, the monthly runoff datacan be obtained for comparison withthemonthly model.

2. To obtain theparametersofMock's Model for the Babak Riverbasin, which can be usedto transformthe monthlyrainfalldata into the monthly runoff data. 3. To compare the monthlyresultsof both modelsand makerecommendations to the

agencies and professionals concerned withwaterresources developmentin Lombok Island and other IslandsinEastern Indonesia .

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1.4 OutlineortheThesis

The backgroundof the thesis has beenpresentedintheprevioussectionalong with the objectivesof thestudy.Thenext chapterdescribesthe studyarea.Theoretical considerations ofthemodels arediscussedin Chapter3.Themethodology usedfor calib rationand verifica tion is discussed inChapter4.The summary ofthe resultsanda discussiondescribedareinChapter5.Finally, theconclusionsandrecommendationsof thestudyarepresentedinthe Chapter6. The appendicescanbefound afterthe references.

Chapter 2

Description of Study Area

2.1 St udyAre aand Land Use

The Babak Riveris located in LombokIsland.Indonesia(Pig.1.1).Thisregionlies just southof the equator. between8.5"and 8.7"Souih Latitudeandbetween116" and 116.5~EastLongitude.The head waters arelocatedon thesouth westernside ofMt.

Rinjani (elevation3726 m).The totalcatchmentareais286km¹(or approximatelyfive percentof the whole island),whichmakesitthe secondlargestbasinonthe island.The main land uses ofthe basinare presentedin Table 2.I.

Table 2.1:Land Use of Babak RiverBasin, (1985)

No TypeofLand Use Percentage

I Horticulture 35

2 Paddy fields 28

3 Forests 32

4 Villages 5

The pop u lationof Kecamatan Narmada and KceamatanMantang, the twosubdistricts withinthebasin.is92,516 (1985) .Thepopulationis employedmainlyin the agricultural

industry. There arealso minor employment opportuni ties in trade, government administra tionand private services.

2.3 Clim ateandHydrology

The basin hasatropicalclimatewithtemperatu res rangingfromabout25" to29" C.

The dailywind speedislight , averag ing 5 km/hr. There aretwodistinctseasons,awet season anda dry season.The wetseasonis fromNo vember to April andthedryseason isfromMay to October.Theclimateisstro nglyin fluencedby altitude.Precipitatio nin the lower basin is considerably less than in the uppe rbasin.Sevenrainfallgauges arein operationbothwithinand around thebasin. The lengt hsofrecordvaryfrom threeyears to more tha n twent y years.

Rainfallinthisregion displaysa diversespatia lpattern,Down streamof theriver basin,forexample,atGC11lng, themean annual rainfall is1496mm; the highest reco rded was 215 2mm,thelowestwas 876 mm.Inthecentralpartofthebasin, the mean annualrainfallis 2051mm;the highest recordedwas 2726mm,the lowest was 1064mm. Upstream,where the elevationis highe r,themean annual rainfallis 2418

1ll111;thchighest recordedwas 4125mm; thelowest recordedwas 1415mm.

2.2 SourcesofData

The dataforthisstudy wereob tainedfrom the sources listedbelow.

I. HyurologySection(NTBProvincialWat erReso urces Division) providedthe rainfall nodclimatedata.

•. Southlom bokIrrigationProject providedtheruooffdata.

3. NTB RegionalOffice of theCentruBureau ofSunsucs provided the populatio n data,aswell asthe land uSC: data.

4. NTB WaterResource s Development PlanningStudylP3S,\-NTDl,Division ofthe Provincialware, Resource-Serviceprovidedthegauginglocations,SOIll~ctiuune data, andalso somerunoff data.

Chapter 3

Rainfall- Runoff Models

3. 1 General

This chapterdiscusses tworainfall runoffmodels whichareusedto transformrainfall dataintostrca mllowsdata forthe Babak River . Thefirst modelisthe Tan k Model.a lumped-conce ptualmodel whichis based on dailyrainfalldata.The secondmodelis Muck'sMode l.alsoalumped-conceptual model,butMock' sMCNieluses monthlydata

as itsinput.TheTankModel i'l categorizedas a conceptual catchment modelwhichhas nolimitationson itsuse eitheringeographical areaor inthesize ofbasin.Mock'sModel isalsoaconceptualmodel;the usc50farhasbeenlim ited 10 Indonesia.Theinp ut rc...[uirements for both modelsarediscussed atthe end of thischap ter.

3.2 TankModel

TheTankModelwasdevelopedbySugawara(1961.19 67)based on the analysisof data collected from seve ralJapaneserivers.Duringtheearlystagesofdevelopment,the modelwasde si gnedas eithera simple orastora getank model.A simpletank model consistsof only onetankwithone sideoutlet atthebottom.A storagetypemodel consistsof atank witheuheroneormoresideoutlets aboveth~bottom andonebottom

outlet.Later, a combinatio nof simpleand storagelan k models.arranged eisner~ria\ly or in parallelwas used. Thenext few sectionsdiscusstheTa nk Moddand[he hasic meory underlyin gthe model.

3,2.1The structure of theTankModel

TheTankModel is asimple modelwhichconsistsofseveraltanks.verticallyordcrcrl eitherin series,paralleloracombination. Fig.3.1(a) ,showsaserieslypeofmeTank Modelwhich isusedinthis study.Theinput(whichrepresentsancquivalcnrvalueIll' meanbasinrainfal l)entersthefirst tank.Someof theaccumulatedwaterwillnow throughthe sideoutlet andsomewillinf iltra tedownintothesecondtank. l'hcproc ess isrepeatedforeachofthelower tanks.

Evapotranspirationfromthe basinis takenintoacco untby cxtractingaslk:cilied amountofwater fro mthefirst lank.or fromthelowertankifthere isnowater available inthe firsttank.The calculateddischargeisthesumof the outflowsfromeachnmk.

From Fig .3.1(b) ,it canbeseenthatthe model alsorepresentsthezonalgroundwater profile.

3.2.2 Thebehaviourof theTankModel

-,'

Inspiteof thesimplicityofits structure.thebehaviouroftheTank..~odelis quite complex andvarious typesof responseshavebeende scribedbased on several typesof rainfallinput.Considerfo rexample,aTankModelwhichconsistsofthreetanks, arranged vertically asshow ninFig.3.2.Thefirst tank outputis relatedto direct runoff,

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o -oSO o ~ ~oo

000

t go

^{0 0 00}

0 ° -:. 0

o

c-, 0

0 -0

OJ oOa a

'o000 00

o a

while thesecond and thethird tankoutputsarerelatedtointer mediate andbase.:11\1\\

respecti vely.Fouralternativeinputsand(heirresponsesaregivenbelow(~ug;\w;lraet al.•1984).

a. Low Precipitatio n

If inputs representinglowprecipitation are addedinto the model.the water accum ulatio ninthe firsttwotankswillnot reach (helc..-etofthe sideoutletas sho wnill Fig.3.2(a).Therefore,the ra infallwillinfiltrate downintothethirdtankwitho utany outflowfro mthefirs tandsecondtanks. Consequen tly,the stora ge in (liethirdtankwill sho wlittle changeduetoadd it ionalinfil trationfromthe secondlan k.Becausethestorage remains approximately constan t.theouttlowfro mthethirdtankwillhave httlc change.

Thestorageinthe thi rdtank corresponds10groundwate rstorag e.In:1 real riverbasin, base flowsarenearlyconstantbecause thereis a largeamount ofground waterstorage.

Accordingly.if thereislowprecipitationoverthe basin,therewillbelittlechange inthe riverflows.

b. Moderate Precipi tation

If inputsrepresen ting moderate precipitatio nare introducedinto themod el,thewater storageinthefirsttank willnotreachthelevelofthesi deoutlet.hut thewaterle vel in thesecondtank will rise tothelevelabove theside outlet assho wn inFig.3.2 (hI.

Therefore,therewillbe a dischargefromthe secondtank.Accordingly ,ifmoderate precipitationoccursovertheriverbasin,the riverdischarg ewillincrease slo wly and then willgraduallydecrea se.

13

Low Ptecipili1UOIl MOO. '. lI1 P/tl;,p,lluo n He ' "tP'ec,p'latl on Ve<t H" ""vR" In!. 11 to" SI'lO'tOur'l>on

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-J ~[ J= 7 -

8 ^tJ=-C}-b;}

t:1 ^{, . ,} ~ 8~

^lbl

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Fig.3.2: Tank Modelcharacteri stics.(a)Low precipitationwin causeincreasingstorageinthe firstandsecond tank,but the water level willnorreach theside:outlet level, and waterwill infiltrate to the:thirdtank and cause alittlechangeinthe storage anddischarge (romthethirdtank.(b) Moderateprecipitation will leadto anincreaseinstorageinthe secondtank.

withoutlet discharge; (c)Heavy precipitationwill increasestoragein thefirstandsecond

Ian".

Large dischargewilloccur fro mthefirst tank,the nreducequickl yto intermed iatedischargefrom thesecondtank;(d) VerylI\:a~ yrainfall fora shun duration will increa sestorage inthefirsl tankand producedischargefromlt,butnowaterwillbedischargedfromIhesecond lank.

4:. Heavy PrKipilatlon

Ifinputsrepresen tingheavyprecipitatio nare added 10 the modelasshown in Fig.

3.2(el. thestorageinlhefirst and secondtanks will rise upquickl y.exceedingthe level ofthe sideoutlet.Asaresult.thedischargewill also increase quickly.Thedischarge comes mainlyfromthesideoutletofthefirsttank,whichrepresent sthesurfacenU....·li.

The amountwillbe large.bUIitwillreduce quicklyumilrhere maining dischargelakes theform ofintermediate flows.Similarly.ina realbasm,ifheavy precipitationIl\: CUr<i.

thedischarge in theriver will increaserapidlytoreachthe peak discharge ,then"Iuick' y reduceto the intermediate discharge level.

d.VeryheavyrAinfallwith a sho rt duratlon

Iftheinput represents veryheavyrainfall with ashort duration,theTank Mudd wouldappearas showninFig.3.2(d). Therewillbedischarge fromthefinll<lnk withoutintermediateflow fromthesecondtank.Overtime.however.thecundililln would revert 10theconditionof (c).and withintermedia te flow fromthe ....·cund lank.

In some cases.forvery heavy rainfallwithashonduration,however.onlysurfaceflows appear. without intermediateflows.

3.3Theoreticalbasis

or

Ihe Tank Model 3.3.1 SimpleTankModel.

The simple TankModel. also called the exponentialtype model,consistsof a lank with a sideoutletat thebottom.This modelisbased onthehypothesis thatthedischarge from atankisproportional to thestorage depth abovetheoutlet.Considerforexample ,

15

a simple Tank Modelwitha storage height of h(r) as shown inFig. 3.3(a).The flow q(t) canbe writte nas follows:

q(t) =h{t) a (3.1)

where:'1(f)isthe out flow(mm/day).h(l)isthe storage height (mm) anda isthe outlet coefficie nt(day').Assuming, thaithereisno add itionalwaterin the tank,fromtime t

=

0tot=Ior (At

=

I) ,thedecreasingstorageheightfromheighthgat timet=O to heighlhJattime 1= l is Ah,the re fo rethe outflowqcan be expressedas:

-.«

^(3.2)

Theminussignmeansthat the dischargeisanoutflow.Iftheinitia l outflow isq~,with respect to equation3. 1,thewaterstorageandoutflowwilldecreaseexponentiallywith dall.~ingtime.Thus, equation3.1 canbe writte n:

q(t) •qo exp (-(l t)

where;q,⁼qatt=O.

Iff/" =It0',a constantflow,the storagevolumewilldrain out afte rtimeT.

(3.3)

(3.4)

16

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^iltl

IbI

TankMod el Types.fal Simple Tank Model

Fi9·s~~~age

^TypeTank Model:Ie)Series

St~rage

~b ;pe

Tank Model withitsParamet ersNotati on s

t cI

11

whereTIS thetime requiredfordepleting thestorage volume.Tis calledthetime ftm.rtant,whichis usedfor determining the initial parametersof the Tank Model.Incase thcreis additionalinput(p) eitherfrom precipitationor infiltrationfromthepreceding lank. theoutflow(q)isa specialcaseof the unit hydrogra ph.Sugawara(196 1)solved therelationship betweenthe input (p) andoutput(q)fromsuchtankasfollows:

q( t)·

[ p

^{(e-sla.e-U ds}

whereq(I) isoutflow, s is afunct ion ofstorage andQ'is anoutlet coefficient.

(3.5)

3.3.2 Stor ageTypeModel

The storagetype model is basedon the hypothesisthai both dischargeand inflftration arc functionsof the storedwater.Fig. 3,3(b),shows the storagetypemodel.If the heightofthe storage in the tank ish(tJ,andh(tJ

<

HI'there isno outflo w fromthe tank.

Therefore,thevalue of HIis analogousto the initial lossforsoilmoisture retention. This type of tankisusuallyused in the top or secondposition .For thestoragetype tank,the outflowoftI(t)and theinfiltrationiff)can be expressed as follows (Sugawara cited in Summ a,1987):

(3.6) i(t)..h(t)0:

0

18

where110andIIIarethecoefficient ofthe bottom andside lluikt express....d;1\unitsuf day01andH,isthe heightoftheside outlet.These ecuadou s howethel'l,ndili\'lI\that l,'tl

>

u;

3.3.3 Ser iesStorageTypeModel

The series storage type model usedin this study(klltlleli ..verticallyurc.ll'f\.'tl configuration.as shownin Fig.3.3(e) .This structu recorrespo ndstothe1111\:11structure of theunderground waterprofile asmentioned earlier.Thisstructure alsu explicitly representsthe threecomponents of discharge: high.intermediate. andbaseFlows . 'lbe se ries storagetype modelisthetype thatis mostoftenused for low nnwan<l lysisor 11000analysis.Thecomplete mathematicaldescriptionuftheseriesstoragetYI)CllItl\h,:l.

however,is very complexsinceitconsistsofseveraltankswlurnon-tmcur l'qu;\liuns.

3.4 Mock'sModel

Mock(1973) developedarainfallrunoff modelbasedonhisexperienceinan.dy,-ing hydrolog icaldatainIndonesia.Themodel isbasedon tile Themthwaitc WaterBalance Model(1948)withsomemodificatio nsandadditional componentsandparameters.The changes are:theutilization of Penman' smethodinsteadofThormbwaitc'smethodfur the calculat ionofpotentialevapotranspiration,additionalcomponents of basenow lind stormrunoff , and a modificationinthecalculationof actualevapotranspiration. Inthis thesis, however, theactualevapotranspirationiscalculated basedon the recent modificati ons proposed by theInstituteofHyd raulicEngineering Banc.l ung(1991).

19

3.4.1SoilMoisture

Two properties of soil moisturewhich are relevantto Mock'sModel are Soil Moisture CapacityandSoilMoistureSurplus.

a.SoilMolsture Ca pacity

Soilmoisture capacity is defined as the capability of the soil to retainwater.

Dependingon the type and structureof soil and thetype of vegetationgrowingin the surface, the soil moisturecapacitycanrange from one ortwo centimetres per30 cc nu mcrrcs depth forsandy soil toten centimetresor more for clay [Thornthwaiteand Mather,1957).porIndonesia.where the soiltypeisvolcanic,thesoilmoisturecapacity rangesfrom200 to300 mm.This valueis comparable to other volcanic regions suchas CostaRica (Calvo,1986) . The soilmoistureduringanygivenmonthis determined by thesoil moisture of the preceding month,minus the water loss overthaimonth.The waterloss isdefined as the differencebetweentheprecipitation andthe actual evapotranspiration. In the eventthatthe differenceis greaterthan zero, the water loss is equal tozero since theamount of precip itationcan meetthe requirementsfor evapotranspiration.If,however,thedifference isless than zero, the soilmoistureof that particular month willdecrease.Thismeans thatIhe availableprecipitationfailsto supply thepotentialneeds of the vegetation.

h.SoilMoisture Surp lus(w aterSur plus)

Watersurplusis definedasthe excessof water availablefor runoff andinfil tration . IIoccursmainlyduring the rainyseason,whenprecipitation is always greate rthan

20

evapotranspiration.The values ofthewater surpluscanbeoblo"\inl'\lbysimple calculation.with precipitation treatedasaninput. potentialcvapotroll1s;Jiration3Soutp ut.

and soilmoisture as )\ reserve whichcanbedrawnonandrdi!:l"tl{wheneverthe precipitationis la"'6erthanevapotranspirationandl!:lt.-;oilmoisturevalucsbelowiu capacity).

3.4.2 GroundwaterStorageand Runoff

The calculatedrunoffisderivedfromthreemodelcomponents:base Flow,direct runoff and stormrunoff(Fig3.4).Tocalculate lherunoff fromthe mood.thefolluwing working assumptions are made(Mock.1973).

a. Theinfiltrationshouldbeproportional to themonthlywatersurplus.Inurucr tu determinetheinfiltration rate,the coefficientofinliltrntioncanbeesliuliltedhy consideringthegeologicalstructure andtopographyof the basin.Acrossdu.:ck uf this calculation canbeperformedbyeitherchecking thenw.imum storagevalue derivedfrom the calculationorby comparing thecalculated water surpluswiththe actualrunoff.

b. Thegroundwaterflowsintothe surfacestrea marcproportionaltothestoragevolume

21

PrecipItation

Evapotranspiration Precipitation

l_! __ ~

~ ~m Runorl

IfWS .. 0

'Me

I ~. w,,~, ^'"1_ "'"' ----'~ I ~ O i ,." """ ,II

~

Infiltration

Groundwater storaQlllVnl

L ^....,

'--- - - - -- -- -

Monthlyriverd ischarllll

sMC:SOil Moisturll Capacily sM:SoilMoisture

Fig.3.4:Mock'sModel Diagram

wsiwarersorercs

22

(.\.7)

v

=....1..

2.

where:0isassumedtobeaconsaruwith thetime:diff..:rcnli.d.ll=:Imonth."is theflow(mmJmo nth) intosurfacestreams and V (mm)isth..:groundwaterstorage.c.

Inthecasewhere the reisno infiltra tion.the recessionofgroundwaterIh 'W5fulluws {he principle

q,=

s,

X'

(.un

whereKis assumed 10beaconstantwith thelime differential At='Imonth.The re latio nship betweenaandKisgive nbyMock(1973) as :

K=(l-a) (1...a)

('-K)

a=~ (J.Wl

In real itytherecessionflowsdo notexactlyfollow theabove form ulaasKirH;rcascs withtime.This meansthat the groundwaterflowsfasterthanits assumed va lueat 2J

the beginningand moreslowly over time .

d. Thestorage volume(VJis calculatedas follows(Mock.1973):

(3.11)

where1istheinfiltrationattimetandq,./isthe outflow at timet-t.Fromequation3.7, equation3.11 becomes:

V"~V +~l

I I+Q ll t I-l 1+a

For .1.t=1 month. then

(3.12)

V,"

Simplifyi ng,itcan be writtenas:

1-a 1•a V,-I + 1

1•a

(3.13)

V,'"K

v,.•

+

t

^{(l+K)I (3.14)}

whereV,isthegroundwaterstorage attimet.andKisthe monthly recession coefficient.

The base flowsare calculatedbasedonthedifferencesbetween the infiltration andthe changes in groundwate rstorage. IIcan beexpressedas follows:

24

Q,

~ ~

^(qt-l+q/>

^at

=IAt-(V' _l-V,)

•IAr-AV

(.1.15)

whereQ,isthe base flow at timeI.Thedirect runoff iscalculated fromthedifference betweenthe watersurplusandtheinfiltratio n. The calculatedrunoffisasuuunationof thedirect runoffand the baseflow. Intheeventthat thesoilmoisture isbelowcapacity, aniterativeprocedureisrequired to obtain the soilmoistureandsoilstorageattuneI.

This procedure is discussed in detailin Chapter4.

3.4.3 Storm Runorr

The stormrunoffcomponent of the model was proposedbyMock(197]).and is basedon the pheno menonthat during the dry season when thereisnowate r surplus.

some direct runoffoccursas a result ofstormrainfall. Theamountorthestormrunoff isassumed to be a small percentageofthe totalprecipitation.Inthemodelcalculation, the perce ntageof the impermeablelayeris adoptedastherepresentationofthatportion of the basin whichproducesthedirectstorm runo ff.The factthatsomeofthe precipitation directly becomesrunoff, causesthe soilmoisturedeficit to increaseand decreases thewater surplusespeciallyin the earlypartof the wet season.Areasonable approachfordealingwiththemagnitudeofstormrunoffcan beobtainedby comparing observed floodflows duringthedryseasonto the baseflow.

25

3.5 Model Inputs

The model inputs for the Tank Model are daily meanareal precipitatio n.

evapotranspiration and dailyrunoff data. Mock'sModelmakeuseof the same kinds of inputsbutona monthly basis.Aslightdifference in Mock' sModel is theintroductio n of theestimatedactual evapotranspirationwhichis influencedbythe availabilityof the monthlysoil moisture.

3.5.1Precipitation

Mea ndailyandmonthly arealprecipitationare the majorinputsfortheTank and Mock 'smodel ,respectively.Therainfalldatacan be obtainedfro m the stations which arc locatedwithin thebasin itselforobtainedfrom the additionaldata atthe nearest suuion outsidethe drainagearea.Due to the variabilityof rainfall,itis desirable to IIhlain themean areal rainfall usingdata fromseve ralstations.'lh e mean areal precipitation can becalculated usingthe arithmeticmean method.the ThiessenPolygon method.theisohyetal methodorusingmultiple regressionanalysis.In principlethe mean arealprecipitation is given as follows:

(3.16)

where:

I'~isthemeanarealrainfall I~is theobservedrainfallat stationi

26

W, isthe weightingfacto r coefficient ofstationi nisthe number of observedrainfallsta tions

Thediffere nce inIheresult obtainedwhe ther usingthe Thi•.-sscn "olygon 11I<:11100,th<.·

ari th meti c mean, thelsohyetalmethod, ormultiplereg res sionitnillysisdep,..'"m.1slinthe weighting facto rgive n to each station by eachmethoo.Thiessen ' sPlllygOll methudgives the weighting factoras:

w

_,

.5

₀ ...••.\4-'.'

~

^{lJ. 17)}

whereais thetotal catc hmentarea anda,is area of polygoni.

The arithmeticmean givesthe sameweightingfactorforL"VCrystation , since Ihemean arealprecipitation is an average ofthetotalrainfallat a particular uuilIIflime.

Therefo re, theweightingfac toris given as:

C\.IK)

where IIis the numberof rainfallstations.

The isohyetal method givesthe weightir.gfactoras:

(3.19)

whereAjisthe area betweentwo successiveisohyets ,Aisthe 101;,1catchment andI',is

27

theaverage rainfallbetweentwosuccessivelsonyets.

Themultiple regressionmethod givesthe weightingfactorfor each stationbased on the equation:

(3.20)

where:Y isthedependentvariable(runoff) in mm/day X,.Xl , X. areindependen t variables(rainfall depth)in mm flu.fl" 13.arethe regressioncoefficients

The valuesoffl"^fll'....13.arcthe regressioncoefficient of eachrai nfall station. The wcighting factor foreach stationis appro ximately:

(3.21)

Inthecase wheretherainfall dam are almostthe sameforeachstation , the arithmetic meanis a specialcase of themultipleregressionmethod.

Eachmethodgivesan approximationof the mean rainfallfor a given time.Each methodhas itslimitatio ns.due to the factthat it is impossib leto measu rerainfallat every point in the basin.In thisthesis.the four methodswere evaluated.Theresults arevery similar,except forthe munipteregressionanalysis. In theC.l..eoftheres ult ofthe .nultip!eregressionana lysis. thestationslocatedoutsidethe basin have higherweighting factor than thestationslocated withinthebasin.Thisresult seemphysicall y unlikely.

28

Sincetheresultsfro mtheother three methods arealmostsimilar.henceforsimpli\:ilY.

the arithmeticmeanwasused in this lbesis.

3.5.2 Evapotranspiration

The other input variablefor both theTankMo..Jet amIMud,'s,..h...1I:1is evapotranspiration.In!histhesis.Penman'smcthodisUS4.'dtocalculatethe !lOIl.'1uial evapotranspiration.Thismethodha s been selectedbecauseit isconsidered10besuitable fortropicalregionssince itusestemperatureandclimaticdata suchashumidity,sunslunc dumtton. latitudeand windspeed. The generalformulation"11'penman's method is expressed as follows (Mock .1973) :

11•R(1 -,)(0.18+0.55 5 )-B( 0.56-o.o92/t'd) CU21 (0.1•0.9S )

D..0.35(tQ -t'd)(J: ..0.01w)

where:

Epis the potential evapotranspirationinmmHJO/d ay

A istheslopeof the vapour pressure curveatmean air temperatureinmmHJOItiay B is the blackbodyradiation atmeanair temperatureinllllllHlJ/day eoisthe saturated vapour pressureatmeanairtemperature innunHg ed::::;rh x eois thcactual vapourpressureinmmHg rhistherelatuve humidityin%

29

1/isan expressionof dryin gpoweror netradiationin romHlOfday

R is thesolarradi ationon a horizontal surf ace abovetheatmosphere inmmH₂0 /day.

Tls the reflectioncoefficient (Albed o)

S isthetheratioofactual to possiblehours of brightsunshinein % kis the coefficientofroughnessfor the evapo rating surface wisthe windspeedattwo metreheight in miles/day

The evapotranspirationvaluescalculatedusing Penman 's methodarepresentedinTable 3.1.

Table3.1; Potentia lEvapotranspira tion Estimates (Ep)

tnihts study.thevalues ofthe pote ntial evapotranspirationareusedas negativeinput for theTank Model.Theevapotra nspira tionissubtracted from the toptank ,andifthetop tank isempty,fromthe secondtank.Ifboth tanks are empty, evapotranspirat ionis subtracted fromthethirdtankand soon.The problem iswhether thevaluevariesornot accurdingtothetank fromwhere evapotranspirationissubtracted. Ilmay berelatedto theavailabilityofsoil moisture.Inthisthesis , the evapotran spirationis assumedto be equalto thepotentialevapot ranspirationthroughoutthe year.Thisisbec ausethe values oftheactu al eva potranspiration have beenimplicitly takeninto acco untbythe Tank Model's coefficient(i.c.lumpedwithtankcoefficients).

Mock 'sModelwhichconsiderstheso ilmoistureeachmonth,usestheactual cvapotran spinuionasnegativeinput.Theactual evapotranspirat ion is discussed in the nextsection.

30

3.5.3ActualEvapotran spiration Est imates

Actual evapotranspirationshouldbeequaltopotentialevapotranspiration duringthe rainy season whenthe soil moisturereachesitscapacity.Duringthedryseason, when rainis sparse,soil moisturedecreasesand theactual evapotranspiration should he lower thanthepotentialevapotranspiration.A method tocalculatethe actualevapotranspiration

was proposed byThomrhwaiteandMather (1957)based onthehypothesisthatina particularmonth.where theprecipitationislessthantbepotentiall".>va pot r.mspir.lti\1I1, the actual evapotranspirationisequaltothe precipitationplus the aroountofwaterdrawn fromlhesoilmoisturestorage.Mock (1973) proposed an approachforcalculatingthe actualevapotranspirationusingthe termlimitedCI'U{HJlrtJllSpirmillll.rhis is calculatedas follows:

0.23)

wheretJ£is the differencebetween the pote ntial andactualeva potranspiration(Ea)in mm/month.Ep isthe potential evapotranspirationin rom/month,disthe numberofmys per monthwhenthesurface isdry andm istheestimationofnonvegetative so ilin percent units.Mock alsofound a general rclationshipbetweenthedrysurfacedaysand thenumberof rainydays for Indones ia.The relationshipisexpressedas:

d

,, %

(18-n) 0.2<1'

31

wherenis the number of rainydays. The equation (3,23) can be rewrtnenas:

(3.25)

In practice, ho wever, estimatesform aredifficultto find. To avoidthis drawback,a slightmodificationof Mock'sModel was proposedby theInstituteofHydraulic Engineering Bandung (l991). Itisbased onthe hypothesisthat the rate of the evapo transpirationis proportional to tile amountofthe remaining water in the soilas postulatedbyThcmthwaite and Mather(1955)and Budyko (1948,citedin Nguyenand Ikrndtson, 1986).If the soilmoisture contentisonequarterof the total capacity, for example.then therateof evapotranspirationwillbeone quarterof the potential evapotranspiration.Thus,

& =SS:CEp

(3.26)

whereSMCis the soilmoisturecapacityandSMisthe soil moisture contentfor a particularmont h. A chartsummarizingthe iterativecalculationsis presentedinthe methodologysectionalongwith a summary oftheentire Mock'sModelprocedure. In this thesisthe actualevapotranspiration was calculatedusing theevaporation equation ,L!6.

32

Chapter 4 Met hodo logy

Thischap te r discusses themethodus ed inthe proces sof calib mtioa andvcnficatkm oftherainfall-runoffmodels.Before thecatchment modelswere applied .thelaglime betw ee nthe occurrenceofrainfalland runoffmust bedetermine dnrsr.To obtai nIhe parameters ofIhecatchmentmodels,thetrialand errormethodwas usedfor bo t hUle Tan kandMoc k'sMod el. Perevaluation ofth eresult. the criteriausedwere those used bytheWorldMeteorol ogical Organization(WMO),(1986),

4.1 Determi natio nofLag Time

Thelag timebetweenthe occurrence ofrainfall inthe basin andtherunoff occ urrencein the gaug ing sta tio nwas calculatedusingcross co rrelation analysis.Cross corr elat ionanalysisis a statist icalproc eduretoobtain the correlation between IWIl concurrenttime seriesat vari o uslagtimes.Forrainfallandrunoffda ta,thehighc.~t coefficie ntshowsthe appro p ria telagtime bet weenthe rainfa ll in thebasinandtile occu rrenceof runoff at thega ugingstatio n.Theresultofthe analysis ispresented inFil:

4.1.

Thelag timewiththehigh est correlationcoefficientiszero .Thismeans th a tthe runo ffoccu rsonthesamedayastherainfall. Due to {he systemoftherainfall

observationin thebasin (tod ay's rainfallamount is basically thetotalrainfall from7.00 am previousday to 7.00am today) ,thelagti me is therefore,actuallyequalto one day.

II I

Fig. 4.1: Cross CorrelationAnalysisResult

4.2 TankModel Calibration

Generaldiscussionsofthe Tank.Model werepresentedin Chapter3.The following sectio ns provideamore detaileddiscussionof themodel,because to calibrate the Tank Model,anunderstand ing of thestruc tureofthe Tank Modelis important,Assum ingthat the configuratio nis a verticallystructuredstorage type model,the tanks can belabelled A.B,C and Drespect ively. The relevantcomputat ionsfor themode lare give nin the followingsections.

34

4.2.1 RunoffGeneration

a.Com putat ionofWa ter Stora ge

The inputsrepresentingthe meanarealprecipitatio n are added directlyto the top ta nk.

Theabst ractionduetoev apotran sp iration is assum edto takeplacesimultaneously.The storage intheto ptank.be forethe runoffcalculatio n. is:

(4.1)

whereSAmisthestorageof lankAaltimeI,SUA''''Jisthestorag ebalance oflank A ;11 time(1-1),P~Iis the meanarealprecipitatio n at time(I)an d1'"/is theevapotranspir a tion attime t.

Inthecasewheretheamount ofprecipi tationcannot supplythe evapotranspiration requirementandIhefirst tankcontains insuflicicntwaterforevapotran spiratio n.the evapotranspira t ionrequirement willbetakenfro mthelower lank (secondtank).Inthe casewhe rethesecondtankalsocontainsin sufficie nt wate r for evapo transpiration . water willbeextracted fromthethirdtank. Thesameprocedure canbe appliedtothefourth tankifthethirdtank also failsto meet th erequirement. The storageequation(wh ichis the same forthesecond.thirdand fourt htanks)canbe expressedas:

35

(4. 2)

where;SBfIJisthestorageof W1kBattime t,S88"'/Jisthestoragebalanceof tankBat lime(I-I),QAO,./is!heinfiltrationfromtank A andEOIIJislheevapotran spirationthat may have (0bedeductedfromtankB.SBBm isthestorage balanceof tank Battimer, whichisdescribedinthefollowingsectio n.

h. Com p urauc nof Runoff

Theruno ffandinfiltration fromeachtankarecalculatedbylakingintoaccountthe storageoftheindividualtanh inthefollowing way.FortankA:

OA21~1'" (SAl e)-HA2 1xA2

OAlw • ^{(SAlt) -HAllxAl} OAOw.,SAw xAO

(4.J)

whereQA 2lUisthedischarge fromtheupper oullet oftankAattimet,QM.isthe dischu gefromtheloweroutlet oftankAattimetandQAO/l₁repre sents theinfiltration

rr om

tank Aattimet.112,AlandAO,re spectively, arethecoefficien ts oftheuppe r, lowerandbonom outlets oftankA.HA lis the he ight ofloweroutletandHA2isthe heightoftheupperoutlet.

Thesora g ebalance ofthe tanksA.B,C andDattimetcanbeex pressed.as follo ws:

36

SBAlel ..SAl t l -QA2w -QAl_ltl- QA0 1tI SBBle! .. SBrt) - OBlw -^OBOw SBCrel =SCw-OClfel -OC O(tl SBDlt l= SDw -ODlrt^!

These storage balancevalues are usedastheinitialconditionsfor lime(1+ 1).

(4.·q

Inasimilar fas hion.thedischarge from thesecond, third andfo urthtankscallbe expressed as follows:

OCr r! ..(s e_rtl-HC1.) xCI

Thetotalrunoffisthe summationofthedischarge s from each lank.

(4.5)

4.2.2 Dete r minati on or the Initial Parameters of the Tank Model

Intheap plicationof the TankModel. there is no exactform ula foraccurate ly determiningits parameters.This is because the parameters dependuponthesoil structures, geologicalfeatures,landuse within the basinandthe river courseitself.Two approximationsofthe parametershavebeensugges tedforinitial calculations.Bothsets of thesuggestedparametersandtheirrespectivede rivation s are givenbelow.

37

a. SuggestedParametersbased on theAnalysis ofSeveralJapan eseRivers These parametersare based on Sugawara research (1980):

Top tank(First tank).

Dullet Coefficients Heightof thelower runoff outlet Heightoftheupperrunoffoutlet SecondTank

OuueiCoefflcienrs Heightoftherunoffoutlet Thirdlank

Outlet Coefficients Height oftherunof f outlet Fourthlank

Outlct Coc ffi cients

0.1·0.5 day'

to

·20 30- 60

0.03 ·0.1 day-' 0-50

0.001•0.005day' 0-30 0.0005-0.005dati

These abovevaluesreprese ntgeneral cases for Japaneseriver basins,however, theycan beusedastlte initialparametersforriver basinsoutsideoflap-..nwhichhave similar climate.Basedonthese:values,hydrographsofthecalculated andobservedrunoffare compared,thentheparametersare adjustedas requiredbasedon vis ual comparisons of

ue sc

two hydrographs .Thisrequires numeroustrials,since each valueof theparameters has tobeadjustedindividually. The initialstoragevaluesforthefirstand secondtanks arctaken as cqualtozero.This impliesthatthe startin gtimeforsimulationshouldbe inthedriestperiodoftheyear.

b.Initial Pantml'lersbased onIhe Relationshi pbetween theCatchmentArea and IheTime Coustent

ThemethodproposedbySugawaraetal. .(1984)usesthe characteristics of aSimple 38

Tank Model.AsdiscussedinChapter 3,for a SimpleTankMod el. Tis a timeconstant and T::: I/a.The derived ais simplydividedin two,for the bouornand side outletof thetop tank.The summation of coefficientsofthe lower ta nkistaken asIlrof the summation of the coefficientsof the upper tank,whereristheratiobetweenthe summationof the coefficients of the uppertank overthelower lank.Basedonthe analysisofseveralJapanese rivers,anempiricalformulaforca lculating thetimeco nstant isgiven as:

T- O.15 { A.

whereTis the time constantand A isthe catchmentarea (km²),For riversoutsideof Japan, someadj u s tments arc likelytobereq uired.Inadditio n,lhe initialparameters should be wellbalanced andin harmony,which meanstha! theparametermust satisfy thefollowingguid elines:

I.The ratio betweenthe sideoutletcoefficient to the infiltration coefficient inthe first.

second and thirdtanks should be in close agreement (i.e.AI/AO .. HIIBO..

Clt CD).

2.The ratiobetween the sum of theside outletcoefficients and infiltration coefficients of thetop tankto the second and to the third tank should beinclose agreementwith the squareof itsratio(AI+AO : 81+80

recommended value of ris5 (Sugawara et al.,1984),Inthisthesis,thefirst set of guidelinesfor theinitialpara meters wasused withadjustments based on the calculated andobservedhydrographs.

39

4.2.3TrialandError Calibra tion

Once the initia lparameters havebeen selected. they must be adjustedto ensure that Ihc finalmodel gives a good representationof catchmentresponse.Thisprocess is called calibration. The adjust mentsofthe tank coefficients depend on whichpan of the hydrogra phs dono t match . Forexample.ifthepeakflowsdo not match then coefficients of thetop tankshouldbeadjusted.If the base flows donot match,thenthecoe fficient ofthe thirdandfourtankshouldbeadj usted.The basic principleforcalibrating the Tank Modelis based on the procedure suggested bySugawara (1980).Moredetailson the principles underlying the calibrationsare givenin the accompanyingdiagramspresented inPig.4.2to Fig.4,4.

4.2.4AutomaticCalibration

Despitethefac tthatthetrialanderror methodis usuallyused10calibratethe Tank Model, therehave beenthr eeattempts to developanau tomaticcalibrationmethod. The mcthodsdevisedbyMaruyama,etal.,(197'), Sugawara (1979)andOzaki (1980)are presented below.

a, Manlyama,et al.,(1975)

Maruyamaattempted to determinethe parametersof theTankModelbyusingno n linear optimization.The Powell ConjugateGradientMethodwas emp loyed inorder to derive the optimumparame ters.Theworkingprincipleofthismethod involves the minimization of the objectivefunc tionwi thregard tothe unknownvariables.In general the objective functionFocanbewritten as follows:

40

Decrease the coelh <:ien t 01 Ihetower run oll outlet .nd Iheinfili rat ion outl ei.

U

^II

'

^,,_\

, ,

Ollt leaSethe cOllllfic,enl of thitinl illr at,Ofl outllllt.

In creaSlIth lll cOllfficienl of thelowllIrunolloul le t

(.J

(bJ

leJ

- - - Obse/v ed

-.

^{II _...}

~oc'lIlIselhecoefl i(:,enlof I!\elowerfunoll ecneteoe thelOli'u a 'oonout let.

t".creaslIthecoetllc,enl01 Iheml,lt lll lOnou tlet.

~

^IIII

^{- "}

^{,," -,}

Decreasetn,h e,gh!of the. loW" runotl Oullll\

Fig .4.2: Single Tan kComponentAdjustmentGuidelines.lal Lower runoffeouer adjustme nt;/blinfiltratio nadjust monl (cl Heightlowerrunotladjustment.

41

Caleulated

f A

~

roereese thecoaftie,enlof therc werruncn oulle t

Elevate theheight01the tcwernmc ttoutletand 'ne'ea5cs't 5eoe ff<e'ent

oeeeasethecoetncenr01 thc in liltra tiOnoutlet in the upp e'tank

Ibl

lei

- _ _ Observed

R"duea t he he,ghtof \he uppe , runolloUllet

Reducetheheightof the uppe" uno Heouetand eec.easeos ccetuereor

Inc rea se the ccetnerenrct thetnfill,ationcutletin the uppet laf1k

Fig.4.3: Single andTw oTankComponents Adjust mentGuide- lines. (aland(b)Upper and lowe routlet adjust ment ; (e)

Two tanks;mtntraucnoutlet adju stment.

.,

Calculated

Increasetheccetueenr of the runolt outlet;nth el owe r ta nk orredueo its hoight

I.)

ObslllVllll

necrea semeceeue.eu01the rUl'lo/f oullel ll'lthe low"r lank 01mcreaeeusheillht

r. ^{- -} -'"' ^{- -}

Jan Feb Mar Oct No v

Reducetheinitial storagenomtank Whichhaslargeuue. ruano ncurrrow,then trya new outlet eoell icient

Feb Mar Oct Nov

Inc re ase the coefficientfromth etank which haslalge out flow fluc tu at io n,then try a new coefficient

Fig.4.4: Tw oTanksandLo wFlo w Adjustme n l Guide line s . (al Lowertankruno ff adju st ment; {bandc) lowFlow adjus t men t.

43

whereXl•• ••Xl~are the parameters of the TankModel,Q..istheobserved discharge.Q., isthe calculated dischargeand aisa constantassumed tobethe average of the observed discharge.

h. Sugaware (1979)

Sugawara(1979 )introduced feedback procedures for automaticcalibratio nof the Tank Mod eJ.Two methods wereintroduced, thehydrograp hcomparison methodandthe durationcurves compa rison method.Theprocedureis carriedoutby co mparingtWO criteriaobtainedfromtheobservedand calculatedhydrographfromthemodel.Thetwo criteria arcthevolumeofdischarge and the shapeof thehydrograph.The feedback proc ed ure startfromtheinitialmodelparameters,and theparametersare adjusledbased onthetwccn teria.

1:. OZ:lki(1980)

Ozaki (1980)introd uced a method forautomaticcalibrationbased on a non linear dynam icmodel,combinedwiththe use ofthe AkaikeInformation Criteria (Ale).The methodfocussed onthe determinationof the modelstructureand its coefficients.

Inthisthesis,automaticcalibration usingthe Sugawara'smethod was considered.

The obtainedparameters tendedto becomelargerand did notselfcorrec t, thusleading

\0unsatisfactoryresults. Therefore, the trialand errormethod was used here. In fact, using thetrial anderror method ledtoa betterunderstanding ofboththemodel and the

44

catchment response.

4.3 Mock' s Model Calibration

Tocalibrate Mock' sModel,it is firstnecess:lryto understandhow the mode lworks.

Thefollowingsection discussesmonthlyrunoffgenerationusing Mock' sModel.

4.3.1 Runoff Ge neration

The principleof runoffgene rationforMock'sModel is asfollows:

a. PotentialWater Loss (Pc)

Thepotentialwaterloss(Pe)is definedasthedifferencebetweenprecipitationandactual evapotranspiration.This differen ce shows the periods of moistureexcessordeficit.The equationcanbe expressedas:

Pe= P- Ep (4o.S )

where Peis the potentialwater loss, Pisprec ipitationand Ep is potent ial evapotranspiration.

b. SoliStorageandSoilMoistur e

The negative value of the difference between potentialevapotran sp iration and precipitation causes a decrease inthe roil moisture .Parallel withthe decreasedsoil moisture,the roilsto rage also changes .In addition,tiledecrease inthesoilmoister..

causes areciprocal effectinthe actua levapotranspiration .Therefore .these components

45

areinterrelated. In orderto solvethispro blem,an iterativeprocedureisreq uired, by whichthe soilmoisture(SM)and soilstorage(SS)values canbeobtainedat a particular timeI.UnliketheoriginalThom thwaitemethod.which used tables fo r calcu latingthe actual evapotranspiration (Thornthwaite andMather, 1957), Moc kused limited evapotranspirationwhichtakesinto accountthefact orsofnonvegetative surfaceand dry surfacedays. lnthisthesisthe actualevapo transpiration was calculat edbasedon the magnitudeof the soilmoisture fora givenmonth(Institute ofHydrau lic Engineering aandu ng, 199 1). For any particularmonth,thepotentialevapotranspirationwas calculated using Equation 3.21.

c.So il MoistureSur p lus01'WaterSu r plus

water surpluscanbedefined as theexcessofprecipitationoverevapotranspirationby consideringthe amountofsoil moisture.Ifthereis no excess,thewate rsurplusisequal to zero.Ingeneral,thewatersurplus canbecalculatedas:

WS- P - E a (4.9)

whereWSisthewater surplusand(P-Eo )>O.

d.Infil tratio n

Infiltration iscalculated basedonthe watersurplusavailabili tyand istakenintoaccount bythecoefficient ofinfiltration.Itis givenas:

I ..

cor

xWS (4.10 )

46

whereIis theinfiltrationandCOlis the coeffi cientofinfllt ratioo.

e. SterageVolume

The storage volumefor a particutarmon thiscalculatedba~..dOfttheformula pre se nted earlier in Equation3.14 .

r. BaseFlow

Thebaseflo w fora particularmonrhis calculatedbased onthedifferencebetween the incomin g infiltrationandthe differentvaluesrepresentingthestoragevolumeattimeI.

Theformula used toca lculatethe baseflow valueisgiven by Equation 3.15 g. Dir ect Runoff

Thedirect runof f (D RO)is definedasthediffere nce betwee ntheavaililblewater_~llrrlliS andinfiltra tion andcan be calculatedas

DRO·ws-I (4.11)

h. StannRunoff

Duringthedryseason,whenthe water surplusiszero. some amounl of precipitat ion becomes runoff directly.In the calculation discussedearlier.thestormrunoff isfound bytakingintoaccount the percentage oftheimpermea ble lay er.as

SRO=PX IMl.A 14.121

whereSROis directstorm runoff andIMUispercentageof the impermeablelayer.This equationrequirestheconditionthat WS=O.

47

l, TotalRunoff

Thetotal runoff is calculatedby summing up thebase flow, direct runoff and storm runoff.A flow chartofthe MockModel runoffcomputation procedure is presentedin Fig.4.5and Fig. 4.6.

4,3.2InitialPa rametersforCalibr at ion

Similartothe TankModel'scalibration,Mock'sModel calibrationis also conducted bytrial and error.Mock' smodel however,has fewer parameters,andis therefore simpler.Fortheinitial calibration,thefollowingvalues(which are derivedfromseveral Javanese riverbasins)are suggested(Mock,1973):

SoilMoisture Capacity(SMC)=200 - 300 mm Monthlyrecession coefficientK

=

0.25·0.92

The otherparameters,such as the coefficientof infiltration(COl),impermeablelayer (IMl.A)and initial storage(Vo),can be obtained by trying a value andcomparing the calculatedandobservedhydrographs.

4.4 Ver ificat ion

Tileforegoingsection,whichdiscussedthecalibrationmethod, wasto findthe parametersof themodels which canproduce a good fitbetwee nthe calculatedand the measured discharge. Thisis accomplishedby adjusting the parameters,andcheckingthe performanceof themodel based on graphical andnumerical criteria.To restthe parameters,to see whether themodel can producea seriesof runoffsimulations that give

48

No ESlimaleEa= ---~-IculatedEa

SRO·IMLAxP

Fig. 4.5 :Mock'sModel IterativeProcedure.

49

Fig.4.5:(Continued)

50

SM·' ; SoilMoisture atprevious month SM'-5M3-SM-1+SS SM4..5M6..O. 5M2-SMC SM5=5M1"SM-l+Pe S5'=5S4=S55=55 6-551...Pe 552-SMC-ISM·ll;SSJ·O Fig.4.6:Det ail Calculation for Soil Moi sture (SM} andSoil Storage(55)

5'

a goodfit to the observed dischargein a givenyear, a verificationperiodisrequired.In otherwords,the verificationperiod is a necessary testing phase.With respect to the modelperformance,manyresearchers have proposedboth graphicaland numerical criteria.Inth isthesis, four graphical criteria andthree numerical criteria are used to test themodel performance.These are described below.

4.4,1Graph ical Cr iteria

Thegraphicalcriteriaconsistof four graphs,whichcan be usedsubjec tively to evaluatethemodelperformance.Thefourgraphicalcriteria are:

a, Compar ison of Hydrograph s

The hydrographsofthe observed and calculated dischargesareplotted. The plotshows the magnitudeof boththecalculatedandobserved discharge as a function of time.

b. Compariso nofDura tionCurves

Thedurationcurves of thecalculated and observed dischargesare plotted. Theplot shows the magnitude ofthe calculatedand observed dischargesindescending order versusthe percent of time the dischargewas exceeded.If thereare onlysmall discrepancies between thecalculatedand the obse rved discharges, the curveswill appear closetogether.

e. Compariso nofDAily Flows

This graph showsthecomparison of the calculated andobserveddischargein ascending order on a linear scale.Goodsimulateddischarge datawillbecloselyscattered along the lineofperfectagreement.

52

d. ComparisonorDally MaximumFlows

Thisgraphical criterio n isusefulfor checking the magnitude of the high flows between theobserved and the predicteddischarge.

WMO (1986),intheirintercomparisonof rainfall-runoffproject.suggested that the comparison ofhydro graphof the calculated and observeddischargeas the1\lOslimportam criterion.Theduratio n curves compariso nofthe calculatedand observeddischargeis also consideredtobeanimportant criterion.like wise. the scatterdiagram or the daily maximumcalculatedandobserved discharges isalsoconsideredto beextremelyuseful.

These graphical criteria wereusedin boththe calibrationand verificationphasesforboth daily and monthly discharges.

4.4.2NumericalCrite ria

Threenumerical criteriawereusedin thisstud y.TheyarcgiveninWMO (19861.

Thenumericalcriteriaused are:

3. TheNashSutcliffeCoeffici ent,R²

TheNash SutcliffeCoefficientwas proposed byNash andSutcliffe(Nash and Sutcliffe 1972, cited inMartinecandRan ge.1986).The formulais givenas:

(4.13)

t

^{100- 0.1'}

t

^{100- 0.1 '}

R " 1--';'--- - -

53

whereQristhecalculateddischarge,Q~is the observed discharge,Q~istheaverage observed discharge andIIisthe numberof daysof discharge.Itshould benoted however,that for theIntercomparison Project,WMO used the term NTDinstead ofR", butboth equationsare infactidentical.

h.TheDeviathm of theRunoff Volume

Thedeviation oftherunoff volumeis givenas (WMO,1986 citedin Martinecand Rangn,1989):

D"(%) (4. 1 4 )

whereV:,isthevolumeofthe observeddischargeandVristhe volume of thecalculated discharge.WMO referredto thisterm as PD. The criteria ofR¹andD.are considered to be particularlyuseful criteria (WMO,1986),

c. RalioofMeanEr ror to theMean Observed Dischar ge(RME) l11Ccriterionis givenby WMO (1986)as:

(4.1 5)

Itisespeciallyuseful ifthe analysis ofvolumeofthe wateris the mainobjectiverather than analysisof peak flows.Thefollowing values areconsideredideal when assessing

S4

the performanceof amod el (WMO.1986):

R¹orNTD==1. RME "" O. D.orPD

=

^O.

Thecompleteresultsforboth calib rationand verification(usingeithergraphicalor numerical crite ria)are presentedin Chapter5.For thepurposes of this study.the selectednumerical criteriahave been limitedto three. althoughothercri teria are available to measure the performanceofthemodel. Using too many criteria wouldonly serve tu increase the difficulties injud g ing the performanceof the model.

55

Ch a pter 5

Results and Discussion

fhischapterdiscussesthe results ofthecalibration and verificationofthe tworainfall- runof fmodels. The general performanceofthemodels in both thecalibrationand verificationphasesisthe maj orconcernof this chapter. The modelsdiscussedare Tank Modelwithfourtankcc.nponents, TankMoodwith three tank compo nents. andMock's Mood.

S.l Tank Model (four ta nkcomponents)

The sixteenparametersofTankModelas estimatedbytrialanderrorduringthe calibration phaseare presentedinTable 5.1. Thecalibrationperiodwas threeyears, from IQ7:'t/lo;74[01975/1976inclusive.Thecalibration results of 1975/1976 are presentedin

H;;;. 5.1., as an example.Thesefigures compare the observed and calculated hydrog raphs. duration curves, and maxi mumdailyflows .The verificationresults for 1976/77are presented inFig. 5.::!.Theresults based on the numeri calcriteriaofthe dailydata.forboth calibrationand verification phasesare presentedinTable5.2 and 5.3.Thegraphicaland numericalresults for allyearsarepresentedin AppendixC.

Table5.1:TankModelParameters Obtained

Tanks Parameters Notation" Value

FirstTank Upper sideoutletCoefficient A'

o.z:

Lower sideoutlet Coefficient AI 0.15

BottomoutletCoefficient AO 0.~5

Heightof theupper sideoutlet HA2 55 Heightof the lower side outlet HAl 15

Initia lStorage SBAu

o

Second Tank Side outletCoefficient III

o.os

Bottom outletCoefficient

no

11.1

Heightof theside outlct Hili 111

Initial Storage SBB" n

ThirdTank Sideoutlet Coefficient CI 0.00175

Bottom side outletCoefficient cn ^U.(KI2 1---.

Heightoftheside outlet

uc :

111

Initial Storage

snc,

6(Xl

FourthTank SideoutletCoefficient 01 O.tXI2

InitialStorage SODu 6.'iO

").Thenotation refersto Fig. 3.3(c)

Dlscussiom

The followingdiscussionis basedon theresultssummarizedabove.

a. ln general,the estimatedparameters(fromthecalibrationperiod )producedgood resultsin the verificat ion phase. This meansthattheparametersarcsuitable representationsof the simplified mathematicalabsuacucnofthe rainfall-runoff 57

'~ ^{If.; .}

".I) - '/:'

,,,.

U JO ",0 80 \20150180 210

z-o

2"0 300 J.:l\J .550 Dcy Ncmbcrs

Fig,5.1:Tank Model(fourtanks) Calibration ·1975/1976.(a)Prec ipitatio n;(b) ComparisonofObservedandCalculated Hydrographs; (c) Comparison of Observedand Calculated DurationCurves;(d)Comparison of ObservedandCalculatedDaily Flows;

(e)Comparison of Observedand Calculated DailyMaximumFlows.

58

5'J, - - -- --

.. r - - - -- - - - - - --,

,",;..-.,

,.---'/~?.:;;.:

Fig. 5.1: (Continued)

59

I.. ,'

30 Fig.5.1:(Continued)

I" )

Fig.5.2: (Continued)

!J 20 :30 40

cc se rveo Discborqe(mm/ day)

60

so so

~ -o

c. _cD

;,u

,

:!

⁵⁰

"

^'0

0: 30

sc

·'0

"

.o

,

~

~ :0

~~

6 .o

Fig. 5.2:Tan kModel(fourtanks)Verification.197611977.(al Preci pitation ;(hI Comparisonof ObservedandCalculatedHydrographs:(e)ComparisonofObservedand Calculated DurationCurves;(d) Comparisonof ObservedandCalculatedDailyFlows;

(e) Comparison of Observed andCalculated DailyMaxi mum Flows.

61

I )

S

c:.

~ 11)

- - - - . - =

10 ~Q 30 40 50 50 70 SO 90

reo

-,,-,,--- - - - ---,

" oil)

ror

10 20 .30 40

ocserveoDisc hcr c e(m m/dcy)

Fig.5.2:(Continued)

62