RE GIONAL
rr.oon
FREQUENCY ANALYSIS FORACEIIPROVINCEINI>ONESIA
By
°AODULHANAN AKIIMi\l)
A ThrsisSubmit tedtotheSchoolorGradua teStudies illrartialFulfil ment
o r
tbe Requirem ent sfor(heDegreeorMas1erorEngi n~ring
FACULT YOF ENGI NEERING ANDI\I'I' LIEDSCIENCE
MEMORIAL UNIVERSITYOFNEWFOUNDLAND OCTOBER, 1993
STJOli N'S NEWfOUNDLAN D CANADA
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Abst r act
This thesis discusses tho:development and applicauonIl l'1\\"\1 pTm.:il'.11l1ll1h'Il.h of regionalfloodfrequencyestimationfortherivenin,\cd \pn-vincc,Intl,l/II" IJ.
Thetint method is basedon index-floodapproachesandthe S\.'\:llfltlml'!lul!Ji..II", regressionoffloodquantiles on basincharacteristics approach .
Fortheindex-floodapproaches, Ihe annualmaximumIloods;ItI,.-;,..:h ..ucII"I..'T,' standardizedbythe mean annual tlood of thesue. Fivedifferentim.k",-llnl.w.1 melh' N. l..
were used10derive the~-e: ion alfrequencycurve.Thesearc patrymplc's:11Cllull.l,NI:1H' method, theprobahilityweighted mo ment s method,thestationyC;\rme thud,!l1l1ther,- momentmethod.
For the multiple regressionapproach,the logarithmofeach selected{!u:llltih.'of the annual maximum floods at eachsite ofthenine riverbasinswas regressedtinih correspo nding catchment vari ables. Theleastsquares method wasUSl,.'<!ttl developlh~' multipleregressionequations . The derivedregression~"Iu..lti(Jnswerecorrected lilrhias causedby thelogari thmictransforma tion .
Theflood estimatesobtainedusingtheIWOregional methods wereL'UlIl p,ar~'<!til at-siteestimates and tothoseobtainedfromaprevious study bythernsuuncuf Hydrology(lGH),wallingford(1983 ) forbasins in Jawa andSumatra. The e!>lirnillt:s obtainedby thevariou s methodswerealsocomparedtoeach otherfor hasins:1';11were not used inthe study toshow the variabilityoftheresults.
From aco mparison ofthetworegionalmethods . the lindingsshowed that,III indexfloodapproachesprovidedgreaterconsistencyandsimilarityin the estimatinnIII floodquantile magnitudes.The Lmomemmethod seemed to give thebest co mpromise estimates, whiletheregression approachgavelower estimatesformostsuulons and estimates weresometimesinconsistent. TheestimatesbasedontheIOHstudygave estimates well above theseobtainedin this studvespeciallyfor higherreturn period floods.
Acknowledgments
Iwouldliketoexpresscty mostsinceregraurudc and appre ciationtomy ..upcrvisorDr.L Lyefor his guidanceandadvicethroug houtthe research andthe preparat ion ofthisthesis.
Iwouldalso like 10 express my sincere thank s(0Dr.A.Robertson and Ms.
,1)"S;l1IRichter formany valuablediscussions and usefulsugg estions. Ialsowish\0 [hankMs.SennaKOZ<lr for her assistanceinpreparing thisthesis.
Helpfrom:)lCtechnicalstaff atthe Facult y ofEngineerin g andApplied Sctcncc is also gratefullyacknowledg ed.Theassistance offellowgraduate students is1ll11~tappreciated .
Iwould alsolike totakethisopportunity toacknowledge theIndonesian Governmentand the CanadianInte rnational Develop mentAgencyfor theirfinancial supportduringthe study.
Finally.I would liketo express my sincere thanks andappreci ationtomy wife Marlinda andso ns MuzioHikmahandZaid Ramadhanfortheir supportand encouragementduringmy study.
Content s
Abstract Acknowledg ements Conte nts ListofFigures
List of Ta bles&Abbr eviations Intr odu ct ion
1.1 Gene ralDescription 1.2 Objective oftheThesis L3 Thesis Outline Description of the Study Area
2.1 General Descrip tion 2.2 Locatio nandDrainageBasinsUsed 2.3 SourcesofData
2.4 Region al Hyd rologyand Climate 2.5 Physiographyand'rcpograpny FloodFreque ncyAnalysis
3.1 Data Collection and Analysis 3.1.1Types of Flood Data 3.1.2 Sample Properties 3.1.3CalchmentC haracteristics 3.2 SingleStationAnalysis
iii
iii
viii
II 12 14 16 17 17 IK 211 21
~.2.J PlottingPosition _1.2.2Estima tionofParame ters 3.3 ChoiceofaFrequencyDistri butio n JA Delineatio nofHomogeneo usReg ions 3.5 Estimat ion ofRegionalFJoodQuantiles
3.5. 1IndexFlood Approaches
-'.5.2Logarithmic Regress ionforEachOrApproach 3.6 StudyApproacb
Prelimina ry At-Siteand Regional Analyses
"
23 25 ze
"
.10 30
".1 4.2
4.3
4.4 Introd ucti on
ScreeningoftheFloodflowData. 4.2.1 PWMsand t-Moments 4.2.2 Resu lts
At-SiteFlood Freq uenc y Analysis 4. 3.1Selec tionofBestFittingDistr ib ution 4.3 .2 Results
Selecti onof Regional Freque ncy Distri butio n 4.4 .1Proce d ure ...
4.4.2Results CatchmentCharac te ristics
Resultsof Prelimin aryAnalyse s:Summary Application ofRegiona lEstimat ionTechniques
S. IInde xFloodApproaches 5.1.1Theory 5. 1.2 Dalrymple'sMethod
5.1.3 The NERC Method . . . .. . ... •.
5.IA The\.robabilityWeightedMoments (PWMs)Method 5.1.5 Station Year Approa ch
5.1.6L- Mo ment Method
iv
5.!.7 RI:5Ults
5.18 Results fromtheIOH \lCl::U\Stud~
5.~ TheMUltipleRegressionApproach..
71l
5.~.1 Theory i'J
5.~ .~ RegressionEquationsSelection Criteria 7-l
5.2.3Correctiono(BiasDue to LogarithmicTransformation 7.~
5.2.4 Procedure 7tl
5.~.5Analysisof the LogarithmicRegressionEq uations 77
5.2.6Results of the Multipleregression Study x.~
5.3 Comparisonof At-SiteFlood QuantilePredictions Ktl 5.3.1At-Site Flood Quantile Predictions: Gauged Carcfuncnrs Xfl 5.3.2 At-SiteFlood Quantile Prediction s:Ungaugcd Catchments. '10 5,4 Summary
6 ConclusionsandRecommendat ions References
AppendixA:At-site 1100d quantilepredictionslorgauged sites Append ix B:At-site110<"x! quantile predictions(or ung.mgcLsites
AppendixC; Flowdata used
""
107List of Figure s
I.I Locatio n ofAcch Pro vince ,Indonesia 1.2 Acch province principal rivers and WRDA' s 2.1 Locations ofbasins andstreamflo wgaugesused
4.1 Theoretical L-momcn trelationship s fo rassumed distri butions (Hosking , 1986)
4.2 L-momcnt diagramscomparingthesample at-siteestimates and theo reti calrelations hipsbetwee nL-ku rtosis andt-skewnessfor nine Acch river basins
4.J L-momcntdiagramscomparingthe sampleregional weighted averagefor the Acch region with theoret ical relatio nships for Lk..rtosis and L-skcwn ess
10
".1
45
45 5.1 Theregionalplotand finedcurveforAcch region (applying
Dalrymp le'smethod) 64
5.2 Thereg ionalplotand fittedcu rve forAcchregion (applyingNERC method )65 5.3 The regionalplot and fitted curv e forAceh region(ba sed onstatio nyear
app roac h)
5.4 Co mpariso n of estimated XTat vario usreturn periods basedonfiveinde x floodapproaches
67
69 5.5 TheAC Fof theresidualsforthe two predic to r equationof theMAF 82 5.5 The norm alprobability plotofthe resid ual sforthetwo predictor
equationof the MAF
5.7 Plotof residuals ve rsus predictedvetoes (inlllg)10idenlify
bomoscedasticityof residualsof the lWOpredictorequation furtill' MAF :U 5.8 Comparisonof at-sitefloodquantileestimates of gaugedsite for nrc
Jambu AyeRiverat lhokNibong
5.9 Comparisonofat-sitefloodquanti leestimatesofungaugcd sitefortill"
TripaRiver at GunungKong
vii
List of Tabl es
::!.l Meaand populationofWRDAs in AcehProvince
2.2 Tho: drainagebasinscharacteristicsand reco rded no w duration II -\.1 Length of recordof annualmaximum floods usedforfrequency analysis )3 -1.2 Summarystatist icslortheAcehprovi ncefloodnowdata sets 38 -1•.1 Standarderrors of variousdistribut ion,'; used -II -u At-sile estimatedflood quantilemagnitudesin the Aceh riversbasedon
best tit distribut iona\ eachsite
-\.S Result ofregional weightedaverageL-moment ratiosandtheregional shapefactorkofthe GEVdistrib ution
-1.6 Catchment char acteristics ofgaugedcatchmentsin Aceh Provi nce 51 -1.7 Catch ment characteristicsofunga uged catchmentsinAcehProvince 51 5.1 Floodflow ratios at certainreturnperiods.medianand mean flood flow
muos (applying Dalrymple's method)
5.2 MeanIlow ratiosat each 0.5 class interval y variate(applyingNERC method)
5..' Regionalaverage PWMs(ii\ O)'regionalparametersa,m (applyingthe PWMs method)
5A Regionalweighted average L-moment ratios(I and~),regional
viii
65
66
parametersa.m(applying Lrnorncntmethod)
5.5 Compa rison of estimatedXl'atvarious return periods based <In fivem<k \ flood procedures
5.6 Growthfactorssummarized from MudybyIOH(I'lHJ)forJawa;\1\\1
Sumatra 'I)
5.7 Growthfactorsfortheninc gaugedcatchmentsin theAcchregion 71 5.8 Growthfac torsforthelive ungaugcd catchments intheAcchregil1n 71 5.9 Corr elation matrixfor logs ofMAFandcatchmentchuractcns ucsofthe
Arch river basins
'"
5.10 StepwiseregressionfortheAcchprovincedata of cstinuuingMAl' 79 5.11 Results ofhypothesistesting ofregre ssion coefficients (at n
=
O.O.'i)for estimatingMA F
5.12 Thelogarithm ofobservedMAF,catch mentcharacteristics, estimated MAFandthe residualerrors(E1J
5.13 Coefficientsofregressionderived for estimat ingMAFand each Qrfur theAceh riverbasins
5.14 TheobservedMAF .catchmentcharacteristics,estimatedMAF andn:sitilial errors(E.:!JwiththeMAF and residual errors afteradjusting constant coefficient
5.15 Finalcoefficients of regression derived afleradjusting constant coefficientforestimating theexpectedMAFand eachOrfortheArch riverbasins
XI)
X4
X5
5.16 Comparison of at-siteflood quanutcs(Or)for gauged site of the Jambu AyeRive: atLhokNibong
5.17 Comparison of at-siteflood qoantiles (Qr)forungaugedsite of the Tr-ipaRiverat Gunung Kong
Abbreviations
ACP Auto Correlat ionFunction
AIJU AechDesign Unit
EVI,EV2 , EV3 Extreme ValueTypeI,2,3 (distribution) GEV GeneralExtremeValue (distribution) (iL GeneralizedLogistic(distribution) GI'A GeneralizedPareto (distribution) IOH InstituteofHydrology, Wallingford.U.K . I.I.G Log-logistic (distribution) LN2 Two parameterLognormal (distribution) LNJ Three parameter Lognormal (distribution)
l.~ least Squares
P-IAF MeanAnnualFlood
MA R MeanAnnua l Runoff
MML Methodof Maximum Likelihood
89
91
MOM NERC P3
PM W SIMS TcE V USWRC WMO
Method ofMome nts
NaturalEnvironmen tRe~trchCouncil.U.K.
PearsonType3 (distribution) ProbabilityWeig hledMome nt ChannelSlope
Two-componentExtremeValue(distr ibution) United Stateswa ter Resources Counci l WorldMeteorological Organizatiou
,;
Chapter 1 Introduction
1.1. GeneralDescription
The special district of Aceh is a province ofIndo nesia and one of the eight provincesIIllSumatra, as shown in Figure1.1.In 1983.theDirecto rate of Planning and Programming,a branchof theDirectorate GeneralofWater Resources Development, established theAceh Design Unu(ADD) withtechnicalassistancefromthe British Govcrumcm (BinnieandPartners, Consultants). Thepri me taskof the ADUwas to compileall inventory ofwaterresourcesandtoproduce awaterresourcesdevelopment plan.Theplan.presentedboth forshort and longterm development,was followedby implementation andcoverednol only irrigation.but alsoaquaculture,swampreclamation and drainage.ri....erimprove mentand 1100dcontrol,munic ipaland industrialwater usc, and hydro-electric/m ulti- purposeprojects. Under this plan 15 Water Resources DevelopmentAreas (WR DA's)were set up,each of whichconsists of one or more adjacen t river basins. as show nin Figure1.2,
In eeinterest ofprotectingmesedevelopmentareasfrom1l00ddan1Jt~·.hnltlf the major riversin Acehwithfloodproblemsbave their(1\\:n specialpmj~'\1,These arc theAcehRiver UrgentFloodControlProject.andtheArasundo-lam bu A)-c•Ir ril; ;tli\ltl andFlood ControlProject.both startedin 1981. F1u•.1dingisalsc a pwh1cmf\' r1Ilt'~t of the other rivers in Acch.TheRiver whosecontourlies withinthe~5I\\cm:altitude andareasaroundthe rivermouthforexample,arcof signiflcancc interms{IftlllUtirisk and erosionbecausemesearedense lypopu lat~areas.
Figure1,1LocationofAcch Province,Indonesia.
fhc i\DUwasrequired10esti matefloodflowsineach ofthe Vv"RDA"s. To
omam
theseestimates,theADU used aflooddesign manual for Javaand Sumatra /puhli'ihcdin1983by theInstituteof Hydrology (I0 H)Wallingford.UK:andthe In '>1ilulc llfHydraulicEngineeri ngIDPMA). lndonesia).tngenerat.thismanual provides c~till\all.~of mean annual1100d(MAf)basedon differenttypesof dataandanaverage Iloodfrequcncjgrowth curve based on theGumbeldistribution. Thefloodestimation procedureis simpleto apply; theMAF is estimated .andthe result is then multipliedby a growthfactorrelated tothe requiredreturnperiod. The resultingvalue:istheflood quantitcmagnitude.Themanual however. usedthe Gumbeldistributio n forallriverbasinswithin Iawa and Sumatra.and includesonlylivesites within Aceh Province. Ofthose. only one watershedhada recordlengthof live or more years. Thesefive sites were Aceh RiveratKampungDarang,PeusanganRiverat Beukah,JambuAyeRiver at Rampahand at LhokNibong.andSusoh Riverat Kola Tinggi. Theilrecordlen gths werefour.three.
four .eight .andthreeyears durationrespecuvely.
SincetRepublicationoftheabovementioned manual.thedata base offloodflows has increased. AIpresentthenumberof watershedswithfive or moreyears of recorded flowhasincreased from onetonine. ln addition to the streamflowdata. more informationon landuse,topography.and other physiographiccharact eristicsofthe watersheds hasbeenassembled.
weh~lan~SBbenQ Q
Figure1.2 Aceh provinceprincipalriversandWRDA's
Engineerspreparingdesig ns forthe WROl\' srecognize thelimitations of the flood design manual ,andareint erested inamoreaccurate floodestimation procedure c\pcciallyforungaugedtwins.Theyareoftenrequiredto estimatethemagnitudeand fn.'qucocy of flocxl eventsfrom relatively short records ofte n containingnon- representativedata.Also,thereareoccasionallynoavailablerecord s.The atturacy of theestimationprocedureisimportantbecause itaffectsbothcostsand safety standards ofthe engineeringdesigns.
An alternativemethod of estimatingfloodsat an ungaugedsiteor asitewitha very shortrec ordis to useobserveddata atsites withinahomo geneoushydrologic region.Thismethod of analysisiscalledregionalfloodfreq uencyanalysis.
1.2. Objectiveor theThesis
Theobjectiveof this research is to usefloodnowdata from thenine representativebasinswithinthe15 WRDA' s,aswellasphysiographicand climatic data, In develop a methodof regionalfloodfrequency analysisfor theprovince.
Twoprincipalregional analysismethods offloodfrequencyare consideredinthis thesis:
Indexfloodmethod s: thesemethods providea regionalfloodfrequency curve or tabtewhich isUSUallynor malized bytheMAF.Five estimation approacheswertused:Dalrym ple 's method,NaturalEnvironmentResearch Council (NERC.197 5)method. theProbabilityweightedMome nts(PWMs) method.the stationyear approach,andtheLcmomentsmethod.
2) Multipleregional regression: this methodisbasedon at-sitefloodqU;Ull l !c :\
(eachQT)and/or the MAF ateach gauged stream asurcdependent variable.
and catchment characteristicsupstream of eachcorrespondingI:augedstream as the independent variables.
Thesetwo regionalapproachesof Ilu.dfrequencyalongwithat-site 1l11llll frequency analysis and thepreviousstudy(I0 H,1983)are compared.
1.3 ThesisOutline
Thischapterprovidesanintroduction to the floodingproblemfor the Acch provincerivers. A description of thestudy area isgiveninthenextchapter, Chaptcr 3sum marizes thecurrentbody of literaturerelevant to regional!loodFrequency developmentfor thepresentstudy.The preliminaryprocedures forat-sill.'and regional floodfrequency analyses are discussedin Chapter4.Chapter5contains the development and applicationof the regionalestimationtechniques.Conclusions and recommendations are presented in Chapter 6.Appendicesare provided immediatelyafterthe References.
Chapter 2
Description of the Study Area
2.1. GeneralDescr iption
Thebasinareaconsideredinthis stud yis loce«..'dinAcehProvince,Indonesia, The regio n lies at thenorthernend of Sumatra.The climateis tropical.Thetotalland areaof55,852krn! includes Weh IslandintheNorth.and SimeulueIslandand the Bnnyakgroupor islandsonthe SOUlhwestcoast.The regionismountainous.particularly theBarisanmountainrange.Thehighestpeakis about3000mto3400m abovemean
sea leve l. Bycontrast,theelevatio nsofthe rivers at thegaugedlocationsliewithin a range cf5mID430 m above meansealev el. The areaandpopulationdistribution, l.J<lscdon1980data(Binnic andPart ners,19 88), is sho wninTable2.1. The location of thebasinswithin theWRDAis showninFigure1.2.Onaverage , thepopulationdensity oftheregionis about 48.3 people persquarekilometre,and populationgrowthrate is about1.8%perannum.
Table1.1Areaand pop ula tion
or
WRDAs inAcchProv iuc cWRDA Ar'" Rural Urba n To l.al IJl.lpula ti oll Iknsity (km1) population populat ion populatio n \~rSlln/kl1l.') 1 :!.574 161.183 141.8 18 .' 04.00 1 12.l.\l
2 2.208 70.713 70.71.\ .12.0
3 3,321 49.169 49.169 14.S
4 2,447 41.235 4l.2 35 1(1.9
5 3,846 103.718 14,847 118.565 .'11.1\
6 4,025 40,934 40.934 Hl..'!
7 2,145 152,796 4,34 1 157,137 7.U
8 4,060 61,695 61.695 1~.2
9 7,557 187,111 4 ..134 191,445 2~..\
10 2.781 361,755 5,950 367.705 lJ2.2
11 5,465 549 ,842 42 ,358 592.200 lORA
12 5.150 132,718 132.718 25.H
13 2,664 138.021 138,021 5l.H
I' 5,630 226,621 19.351 245.972 ·0.7
15 1,979 39,2 16 39.216 19.11
Total 55,852 2,316,7 17 233,999 2.550,726
LanduseinAceh Provincecan begroupedintosix mainclasses:villages (1.5%1. ricefields(4,5% ),estatecrops(4,7%),mixedgardencrops (2.5%),forc.~ t(7R.1%J. and openareasuch as bush.lakes.swamps andwasteland (8,7 %). Presently.indications are that thelevelofemploymentin agriculturewillremain fairlysta ble, but mayhe somewhatoffsetbyan annual decreaseinnumbers,aspeoplebecomeinte restedin occupationsotherthan farming,Sincethepublicatio n ofthe originalprovincialplan,the
local governmenthasviewedthedevelopment planin termsofan indu strialzone.detin ed asthe morepopulousdistrictalongthenorthand east coasts.andanagricul tural zone, including the remainingareasinthemiddle,westernandsouthern reg ions of the provin ce.
2.2 Locationand DrainageBasins Used
Thedrainagebasinsusedintheanalysisliewithin theWRDAplan.Itshouldbe norcothateachWRDAconsistsof oneormoreriverbasins. Theinclusio nofagiven basin within the WRDAwas based00the availability offloodflow information andother physiographic characteristics. Nine river basinswhich have 5ormoreyear s floodnow data arc:
AcehRiver at KampungDarang(KD), LambeusoiRiveratSango(SO), SeuneganRiverat UjungSlan g(UB), KluctRiver at GuoungPudung (GP), LaweAlasRiveratSukarimbun (S R), BamRiverat Klibeut(KL).
PcusanganRiveratBeukah (BK), JambuAyeRiveratLhok Nibong(LN),and TamiangRiverat Kuala Simpang(KS).
The locations ofthedrainage basinsand thestreamflow gaugesusedare shown ir-Figu re2.1 .and thebasincharacteris ticsand lengths ofrec ordare shownin Table2.2.
C'D~eUoCla..t.(;'1\
""••~l,."
~&o"'n .''''''.<J
~'-'
..
". ..
_ WRo.o &_ .,y
$,. ...
" -g_..,,
••"'''''''11o.'. ngI«DI Son fOISGl
UJ "..... IUll &_" '1&«1 O" _ "III OI'II._ ''' . _ ll HI S" .,,'_URI O:W.',S"'U"lII O:SI
Figure2.J Lccauonsofbasinsandnreamno wgaugesused
10
Table2.2 Thedrai nage basins characteristic sandrec o rdedflow duration
WRDA Riverbasinin WRDAI Area Mean Main Site Recor ded stream channel elevation tlood Stationlocation (km1) length slo pe (m) (year)
(km) (m/ m)
I Aceh atKp.Da ran g 1078.0 66.04 0.0 175 22 II
2 LambeusoiatSango 580,4 33.20 0.06 14 12 12
3 Teunom atT.Kareung 2236.0 112.00 0.0154 25 2
4 Woylaat Mangi Tukut 2327.0 105.00 0.0150 21 4
5 Scuneg anatU.Slang 352.0 50.80 0.0375 93 7
6 TripaatGunung Kong 2707.0 157.00 0.01l2 26 3
7 Susoh erKutatinggi 193.8 24.00 0.0406 48 4
8 KluctatG.Pudung 460.0 100.80 0.0146 22 6
9 L. Alas al Suka rimbun 1384.0 96.52 0.0 160 430 8
10 Bareat Kibeut 270.0 35.60 0.02 76 19 II
II Pcusangan at Beukah 2214.0 137.80 0.0169 15 13
12 JambuayeatL.Nibong 4420,0 231.2 0 0.0084 5 16
IJ PeurelakatG.Jane ng 1050.0 91.50 0.0 107 25 0
14 Tamiang at K.Simpang4598.0 177.80 0.0140 17 7
2.3 Sources
or
DataDa taconcerningthefloodflow,topographic,demo graphicand phys iogra p hic characte risticswereprovidedby th efollow ing sources:
a) Floodflow data wereco llectedfromtheAceh-we rerReso urce sDevelopment Services (Ac e h· WRDS).in BandaAce h. Recent data wereprovidedbythe InstituteofHydraulic Engineeringin Bandung.
b)The topographicmaps were obtai ned{ro m theAceh· WRDSin BandaAceh.
II
Daraon demographicandphysiographiccharacteristics(e.g.•population,land use, forest,basin slope,soiland isohyctalrainfallmapsjwereprovidedhy the AcehRegionalPlanning Boardin BandaAcch.Thedataweretakendircccly from themaps, andwerecomparedwith correspondinginform;uimlav.nlablc from the IOH (1983) or ADUreports.
c) Someclimateinformationwas providedbythe Instituteo(MCh..'tJrlllngy ;nul Geophysicsin Jakarta.
2.4 Reg ionalHydrology andClimate
Aceh Provinceis situatedinthe tropicalzone. Characteristicsof Ihisreginnarc significantly influencedbytropical hydrologyandclimate.Rainfallc.Ii slr i hu' i (~nin this region is controlledbythreemain factors: the IOOl\500n systemsuf South-East Asia;11111 Australia,equatorialdoublerainy seasons,andlocal topographic influences (Wildaud Hall , 1982) .
The eastand westmonsoons arc cha racterizedbydistinctseasonaleha llge.~in winddirection. Thewest monsoonapproac hesduringNovember,asthehounrlary between the decliningandthe progressingair masses moves slowlybUIlrconststcmty southwards. ByDecember, the ...est monso onisnormally establishedandremains do minant throughJanuary and February.Moisture drawn upover theSouthChinaSea produces heavyrainfall over Peninsular Malaysia but onlymoderaterainfall overAcch Province.MarchtoMayisaninter-monsoontransitionperiod.This isfollowedby tile eastmonsoon which lastsfromJune toAugust.Itcarriesdryairproduceddur ingthe
12
winterInhigh-pressurezone soverAustralia.Somemoisturepickedup fro m the Indian Ocean(ailsmainly onthesouth-west slopesoftheBarisanmountain range andthe ...«/
~"tJa~talplain.Asecondtrans itionperiodfollo wsunnlthewescmonsoon isreestablished
byDecember.
Theequatori a l doublerainy seasonsarecausedbyregio nsofaboveaverage temperature whichisfollowedbya shanlagdue to the annualvariationofthesun's decline.Inthisregion, the sun reachesitszenithinapproaimatelylate Marchandmid September. Tworainfallpatternsexist withtheheaviest period fromOctobe rto Novcrnncr,The periodfromMarchtoMay is also wet, Thedriestperiod occursin February (especiallyon the eastcoast)andinJune andJuly thro ughouttheprovince.
Thelocaltopographyclearlyinfluencestherainfall distribution. This isbecause of meinteractionofthepredo minant monsoonand theBarisanmo untainrange. Annual rainfalldecreasestowa rdsthe north coast,reducinginsomeareastoaslittle as1200 nun.Byco mparison.thewest coastisconsiderablywetter,with typical ly3500mmof rainfallannually.risi ng to4500 mmand 5000rnminthenearbymountai ns(Binnieand Partners1988).
Mean monthly temperatureatBanda Aceh forexample. variesby only 7.341 duringthe year.havingamaximum of 27"' '' CinJune::mda minimumof25..."Cin Dece mber.Meanannualtemperaturevaries withelevation, decreasingfro m about26~
Cat seale velbyro ughly0.52 "Cpet100 metre rise inelevatio n(BinnieandPart ners.
!IJSH).
Meanannual relativehumidityfallstypical lyin therange of 80% to90%,There
lJ
isno evidenceof any correlationbetween relativehumidity andelevation frontwakw l.
The variationofthemonthlymeansisnearly5%and diurnalrangeisfrom hl.l%III 100%.
Sunshineduration is highlyvariablebeth spilliallyandseasonally. AltilUtk Is expected10influencesunshine durationmarkedly,withregitlnsofpersistentdllutll'uwr occurring infoothillsofthewestcoastandinthevalleysides in thecentral inter- mountain basins.Sunshine durationistraditionallymeasured from0800hour1\11N.)t) hourlocaltime,Meanannualsunshinedurationisabout44%ofmaximumlklssihl~, whilemeanmonthly sunshinevariesbyupto about15%fromthe meanannualvalue.
Win dvelocitiesaregenerallylightthroughtheye arwith little seasonalvariation.
In BandaAceh,windspeedat2 m abovegroundvariesfrom 5.0 to6.6kmrhnur.MC;\Il annualwindspeedoverthe wholeprovince variesfrom1.8to5.6 km/hollr.
Potentialevapotranspiration for the provinceis approximalely the!o;llllC;IS.in NonhSumatra(asindicated by Wild andHall,1982). Potential evapotran!ipir.tliI11l fm a shangreencrop(anindexalbedo25)varies fromar'klnJ 1250mmlyc.ar1111Ihe..:a.\I coastal plain10around1430mrnlyearon theWI.'S1coastal plain. Annual puIcntial evapotranspiration reducesby roughly 100 mmfortach500 mrise inctcvutioe.
2.5 Physiogr aph y andTopography
Aceh province ismountainous,particularly in ibcBarisanmountainrall!:C, in whichthe highestpeak isabout 3000 to3400 m. The regionconsists of upper Palaeozoic andMesozoic sedimentaryrockswithgraniticintrusio nsminnie anu t'an ncrs.
14
l'Jij~) . There arcthreevolcanoeswhichhaveshownsignsof recentactivity.These volcanoes lie onafault ....nich is particularlyvisiblein theAceh Rivervalley, inthe upper catchmentsof Tcunom andMeurebcRivers, and inthe valley ofLaweAlas aroundKutacane.
Coastalplains arc~enerallywiderlocallyat Ihemouthsof rivers. butarenarrow 1< 4km,toward thenonh andeast coasts. Tidal swamps occurat themouths ofthe principal riversonthe cast coast.On thewest coast.the coastalplai nis generallywider (up1020m},andshowsactive aggradation ofsediments fromcoastaland riversources.
Someplaces on the west coasthaveno coastalplain.
Inter msof riversystems, all rivers (exceptthe LaweAlas River in the central riftvalley) follow a normal course tothe sea on eitherside ofthe centralmountains of the HarisanMountai nrange. Mostriversarecharacte rizedbysteepboulder-strewn upper catchmentswifhdenseprimaryforest cover,whichflauenintobraided channels , thenmeanderin theirlower reaches as theyemerge fromthefoothills ontothe coastal plains.
IS
Chapter 3
Flood Frequency Analysis
Floodfrequencyanalyseshave been widely used toobtain estimatesofflood quantile magnitudes,QT.so as 10 providea reliable decision-making tool for hydraulic works orfloodalleviation programmes.Many procedures havebeendevelopedfor 1l00d frequencyanalysispurposes. Using these procedures.thefloodquantile ala particular site in a river can be estimated from data that arcspecific to thesite and procedure.
The method used forestimating the magnitudeof flood qu....ntilesdepends onthe availabilityof data,and on the formof thedistributionandtheestimatio n procedure used.Three methodsoffloodfrequency analysiscan be distinguishedaccording to the amountand type of data used.Thefirst method, based on singlestation analysis.USes onlyat-site data, and is applicableifthe gauged catchmentshave long periods of recorded streamflow.The second methodisbased onaco mbinationof at-site data and neighbouring gauged catchmentsand can be used in a regional context. The third method is based ona regression approach;it uses onlyregional data andcanbeapplied in a regionalcontextto developflow characteristics which aretransferredfrom gauged
16
catchments toungaugedcatchments. The lattertwomethods are applicableto hydrologicallyhomogeneous regions.Forbolh ofthese methods,there aretypicallyfive stages involvedin
ure
frequencyanalysis.Theseare:datacollec tion and analysis, singlestation analysis,
choiceofa regionalfrequencydistribution.
delineationofhomogeneousregions.and estimationofregionalflood quantiles.
3.1. DataCollectionand Analysis
Estimatingthe magnitude offloodquantilesis dependent uponthe availabili ty of data.Therequired data foraregionincludeflood flows andcatchment Characteri stics withinthe region. Theflood data maybeevaluated bythetypeofflooddataandthe sample properties.Fora givenregion,the catchment characteristics aremainly divided intotwo group! thephysiographiccharacteristicsspecific tothecatchmentandthe climaticcbaracreristicsover Ihe catchment.Thesecharacteristics areevaluated foreach catchment.
3.1.1Types of FloodData
AssummarizedbyBeable andMcKerchar (1982),thereare threetypes offlood samples: annual series,peaksoverthresholdseries,and histo rical series. The most common type istheannual series,which contains thefloodpeakfor eachyar of record.
17
Thistype ofsampling.providesdatapoints fromseparateflood events.Adii;.ld\';llll;l~~' of thistypeofsampleisthatitmayemphasize! small floodpeaksandnegjcctlarl,w r1"1"'~.
An alternativetypeof sampleis mepartial durationseries. which;lppc;.USIII overcomethedisadvantageof the annual series.This kindof sampleconsistsofalt tlo...llI peaksabove achosen base level. Samplepoints neee 10becheckedmoreOnCRlilrtheir serial correlationthanan annual series.sincelargelloods oftencontain morethanone peak aboveme baselevel. Accordingto Chow (1960$.pp. 8-23),the partial duration seriesonly hasan advantage overthe annualserieswhen predictionsofflood Ilow nrc requiredforreturnperiodsof less than10 years.
Additio nalhistorical informationon waterlevelsduring1100deventsis frc1lucally available.WhenIhisinformatio nis reliable. it shouldbeusedincombinationwithIhc dausample taken fro mthecontinuousstreamflow record. Theinclusionofadditional historical informationoftensignificantly increasesthelengthof a sample.Thereforeil is more likelythat theflood frequencyanalysiswillbeimproved.Theinfo rmationmay also aidinestablishingtheupper threshold of the frequency curve.
In thisthesis.theprimarydata sampleswere annualseries. which werethe maximum flood flowsforeach year ofrecord foreachstation.Itwasnotnecessary tn constructa partial durationseries for thisstudy becausethe maininterestisinfloods with return periods greater than 10year s.
3.1.2SampleProperties
Thedata sampleshouldhave thefollowingpropertiesifthe analysisisintended
18
for generalizationoverthe populationdistribution(Beable andMcKerchar . 1982):
sufficientlength,completeness,degree of homogeneity,randomness and reliability,and representativeness,
Sam pleLengt h: Dalrymple (1960) indicatedthat afloodflow shouldhave a recordthatisfive ormore yearslong,although itis commontyacceptedthat quantiles shouldnot be deterrtc.ed forreco rds shorter than 10 years. AccordingtoBeableand McKerchar(1982),10 annualfloodpeakitems maybeused,sincedata samplesof about 10 yearsin length are oftenthe only ones available.However IOH (1983), usingreliable dataof 4 or moreyearsinlength was ableto estimatemean annualfloodand then to use thatmeasure to derivefloodfrequencygrowth factorsfor Jawa andSumatra.
Comp lete ness: The data sampleused shouldbe taken froma continuous streamflow record.Gaps in the dailyrecord are not Importan t,aslo ng as the maximum flood peak is notmissing. However,thetimeunits which include the gaps should comprise onlya small portionof thetotal samplelength,
Homeneeeuy: Data samples shouldbe consideredin terms of theirdegree of homogeneity. Thismeans thatthe data samples have occurred under the same conditions. Factorsaffecting the homogeneityofa sampleinclude:human activity,faulty records, and changesinthe gaugingcontrolconditions.
Randomn ess and Reliability: When dataare assumed to be independent and random.thereshould beno serialcorrelationbetweenthe consecutivefloodpeakitems, Therefore. thesamples shouldalsobetaken from reliable measuring instruments.
Repr esent ativen ess: Data shouldalso bereprese ntativeof the population
19
distributio nof data points.This may be diili culttodeterminebecausethe population is unknown. Howe ver .ifthereisa long-term stream flowrecordfor asimilar catc hment nearby.therepre sentativenesscan be testedsta tistica lly (McGuinness and Brakcnxick '964).
3.1.3Catchment Char acter istics
Thecatchment characteri sticscanbe dividedintotwogroups;thosedescrihing the physical catchment,andthose depictingthe climateoverthecatchment. The physical characte risticsincludethesizeandshape ofthecatchment,thestreamchannel.
andthe hydraulicproperties of the soilandthe vegetation.Climaticinfo rmationincludes meanannua lrainfall,and rainfallintensity of one dayrainfall at agiven return period.
Thecatchment characteristics whichmayinfluencethe mean annualfloodsor floodquantiles foragivenreturnperiodhave been described byNERC(197~ )andllseO byBeableandMck erche r (1982),and IOH(1983 ). Therelevant characteri stics..rc:
ca tchment area, mainchannellength, mainchannelslope, meancatchment elevation,
stream frequency,
percen tage ofthe catchment that is forested, mean annual rainfall over catchment , and therainfallintensity of a given returnperiod,
20
In terms of rainfall intensity,Beable and McKerchar (1982) usedtheone day rainfall with a return period oftwo years,while IOH(983)used the mean annual maximum one day rainfall.
For the purposesof this thesis, the procedurefor estimatingthe physicaland climatic characteristicscombined Beable and McKerchar'sapproachwith that 0:IOH, with certainnecessary adjustments. This procedure is summarized and presented in Chapter4.
3.2 SingleStationAnalysis
Singlestation analysis is requiredtoprovide data fordeveloping regional equations (suitablefor ungauged sites)as well as for providing estimates for gauged rivers. The annual series offlood flows for each station are assumedtorepresent a random sample froma populationofflood values whose distribution canbedefinedby a probabilitydensityfunctionwhich is dependentona few paramete•.i. Frequency distributions havingtwo or three parameters areusuallyused in theanalysis.These parametersarerelatedtothe location (mean), scale (standarddeviation)and shape (skewnesscoefficient) of the distribution.The methods forestimating the parametersare further discussed inthe nextsection.
3.2.1 PlottingPosition
Frequency analysis requires theidentificationof the probability or the return period of each sample point. Various formulaeare available for estimating these
21
probabilities,calledplotting positionsbecausethey are used toprepareprobabilitypiou.
The WeibuU formulaiscommonly usedbecauseof its simplicity. Inacomprehensive review of plotting positions,however.Cunnane(1978) noted that the Wcibullformula providesbiased plottingpositions,whichon averagelead 10anoverestimationof'1001.1 quantilesforhigh rerum periods.
Cunnane(1978) alsoconcluded thatthe selectionofa plotting positionformula for a sample depends onthe assumed distributionto fitthe sample. For example,for samplesfittingtheTypeIextremevalue (EVil distribution,theGringortcn formula provides unbiasedplottingpositions. Forunbiasedplotting positionswherea single simple formula is required for usc withall distributions,Cunnane'sformula providesa good compromise.Thisformula is given as:
F _ (1 - 2/5 )
J.- (..0+ 1/5 ) (J.1)
where F,is the probabilityplotting position for the ;'" smallestofnobservations.
This plottingpositionformulaisused inthe package program , Consolidated FrequencyAnalysisversion3 (CFA3,1991)bytheHydrology Divisionof thewater Resources Branch of EnvironmentCanada.
3.2.2Estimationof Parameters
Many methods have been developedto obtain anestimate ofdistribution parameters, Kite(1988),describedfour parameterestimationtechniques .These may be listed inascending orderof efficiencyas: graphical,LeastSquares(LS), MethodOf
22
Moments (MOM) and the Method ofMaximumLikelihood(MML). The MMLis somewhat more difficultto apply in practice becauseit oflen requires a computerto perform iterative calculation.
WMO(1989), listedfivemethodsof parameter estimation.Theseinclude MOM, MML,LS,ProbabilityWeightedMoments (PWM)(Greenwoodet.al., 1979) , and Sextiles (Je nkinson, 1969). WMO concludedthatwhile theMOMis easyto apply,it isnotasefficientastheMML,especially in three parameterdistributions .The PWM method hasgoodstatistical propertes for distributionthat canbe explicitly expressed in inverse form.
Bebee et.al .•(1993)compared five methods of parameterestimations.These are:
the MML,the MOM,themethod of mixedmomentsorgeneralizedmethodof moments, thePWM method.and theLrnc rnents method. They concluded thai the MMLis optimallyunbiased and displaysminimumvariance,but mightresult in bad estimatesin small samples.TheMOMiswidelyused because of itssimplicity.as it is basedon the mean, variance and skewness coefficient. ThePWM method, which is based on linear co mbinations of orderstatistics,has gained wide popularity and has been usedin many recent studies. The Lmcmenr method whichisa linear combination of PWMs as suggested byHosking (1990)providesgreaterclarity in astatisticalinterpretation than the PWMs.
3.3 Choice ofa Frequency Distribution
Many theoreticaldistributions have been developedfor frequencyanalysis
"
purposes. Kite(1988),described some ofthefrequency analysis techniquesfor estimatingfloods and drought. Kitesuggestedsomecommonly useddistributions in hydrology e.g.,normal,twoparameterlognormal(LN2).threeparameter101:00011011 (LN3),Type1extremevalue (Gumbel). Pearson Type III(P3). log-PeanonTypo:111 (l P3) and Type III extreme value (EV3).
WMO (1989)hassuggestedfourteen candidatedistributionsforusewithannual maxima.These include:lognonn al, P3,Gumbel,Type II extremevalue,EV3,Gamma, LP3,General ExtremeValue (GEV),Weibull,Wakeby,Boughton,TwoCo mponent Extreme Value (TCEV),Log-logistic (llG) andGeneralLogistic(Gl ). WMO (1984, 1989).however ,reportsthatthe selection of distributionsis often notchoseninany Objectivemanner,bUIpickingone fromdistributions that arc widelyaccepted.
A studybyHalctanir (1992),comparedvariousflood frequencydistributions in Anatcl ia,Turkey. Hakt.anir appliedtheLN2.lN3.smemax, two-step-power.log- Boughton.Gumbel.PJ,LPJ, LLG and Wakebydistributionsto annualseriesofflood flows(~JO observations),of 45unregulatedrivers inAnalOlia. Hefoundthat the LN3,lN2,and Gumbel distributionspredicted extreme right-taileventsbetterthan the other distributions.
A recentstudy by Vogel et.al. (1993),uses L-momentdiagramsforevaluating data at61sites acrossAustralia.Theyshowedthatthe Generalized Pareto(GPA), LP3, LN3,GEV andWakebydistributions arealladequateapproximar-cnstothe distribution ofannualfloodFlows inAustralia.
The abovediscussionshowsthat hydrologistshave reacheddifferentconclusions
24
concerningthebestmethodfor parameterestimationandthebest probabilitydistrib ution to representfloodflows.The most frequently usedmethodsfor estimatingparameters, ho wever, aretheMOM, the MML,andthe methodofPWMs.The LN2,LN3,GEV, Gumbel,P3 andLP3 arethedistrib utionswhich havebeen most widelyusedin many 11001.1 freq uencystudiesthroughout theworld.
For this study,the methods of parameterestimation that wereused were the MOM and theMMLforat-sitefloodfrequencyanalysis. Thesewere chosenbecause they arereadily available in package programs. Five distributions weretried tomodel theannual maximumfloodsof thenineriversin theprovince . Thesedistributions were:
LN2,LN3,Gumbel,GEVand LP3. Toassist inthe selectionofthe appropriate frequency distribu tion, theLcmomenrdiagram developed byHosking(l986)that comparessample estimatesof theLmomernratioswith their populationratioswas also used forevaluatingthesuitabilityofthe various alternativedistributionsfor modelling flood flowsin theregion.
3.4 Delineationof Homogeneous Regions
tnregional frequency analysis.many studies havebeencarriedout toidentify homogeneou sregions. Therearethreeprincipal methods commonly usedtodelineate a studyregion intohomogeneous regions. Thefirstis basedon geogra phical or administratively defined regions such as provincial, national , rivers, valley, latitude/longitudeboundaries .The secondisbasedonthe similarityof physiographi cand climate characte risticssuch as geology, land use,drainage characteristics and
25
rainfall/runoff similarit y. The third isbased onfloodcharacteristicssuchas she homogeneitytestof Dalrymple(1960),similarity of the coefficient ofvariation (C.)test within the region (Cunnane, 1987)or a heterogeneity measure based onI.-moments (Hosking, 1993).In practice,theremaybeconsiderable overlap among method s,and boundaries maychange as more information becomesavailable.
Aceh Provinceis a relativelysmall areain which totryto delineatethe river basins into varioushomogeneous regions.Geographically ,the basinswithintheprovince have similar characteristics and show similar physiographicand climaticfeatures ,with theexceptionof one of thebasinson the westcoastoftheregion whichhasa relatively highrainfall magnitude,asmallcatchmentarea and a steepchannel slope. Aswell, identification oftheregion based onfloodstatistics maynot givea clear answe rdue to thelackof longperiods offlow recordswhicharcrequired toperformhOlllogenei ty lesls offlood statistics. Therefore,for practicalreasons,itisassumedthattncregionis homogeneousinterms offlood and physiographiccharacteristics, Asadditional!luod flowinformation becomeavailablein future,perhapsthisquestion can he more clearly answered.
3.5 Estimation of RegionalFlood Quantilcs
Theregional method of flood quantileestimationusesa combinationof at-site dataanddata from neighbouringgauged catchments. The conceptbehind aregiun:IJ floodfrequency analysis isthat the regionsarc reasonablyhomogeneousin terms of climate, topography and physiographiccharacteristics,andthevariouscatchmentsdi.~p!;IY
26
flood freq uencyproperties. The regional method usuallyproduces a regionalflood frequency curve ortable .Tht curve isassumedto begenerally applicable10catchments in theregionandmaybeapplied toboth gaugedand ungauged catchmen ts.Becausethe regional frequencycurveis based onpooling recordsfrom the region, it provides amore reliable wayof estimatingfioodquantile thanasinglefrequency curvefinedto a relativelyshortrec ord at a site.
Many procedures have been suggested(or estimatingregionalfloodquaruiles.
Twoprincipalmethodsaretheindexfloodmethodsandtheregressionmethod.Both methods canbeusedfor estimatingfloodquantilesatgaugedand ungauged sites.
3.5.1IndexFlood Approaches
Theearliestmethod ofregionalfrequencyanalysisis theindexfloodmethod.
Thismethodis popular in many parts of the worldbecauseitis easy to understand and to applyand hasgivengood results.Theregional procedureestimatesthedistribution of a dimensionle ssfloodvariateXl'whereXl=QlIQ. Qis called theindexflood and is usually takenasthemeanannualfloodat each at-sitesampleestimate. Assuming that theresultingvari ateXlhasthe sameform of distributionatevery site, the parametersofthe distrib utionofXlare obtained fro mthe combined regional data sets.
Manyprocedures havebeendeveloped to obtain the parameters oftheXT distribution.Six main regionalindexfloodproceduresarediscussedinthis section: the original methodof Dalrymple (1960),regional dimensionless momentsmethod(Nashand Shaw,(965 or USWRC , 1976, 1?77,(981),NERC method(1975), retunalPWMs
27
method (Wallis, 1980),station year approach,andLmomcntsmethod (Hoskingand Wallis, 1992 and 1993).
The first appro achwas initiatedby the US Geology Survey (Dalry mple. 1960).
Theapproach is basedon a dimensionless regional averaging of equallcngjh records from unregulatedrivers withi na given area which have beenpreviously tested for homogeneityatthe level of alen yearreturn period.The homogeneity test is based on the assumption thatthe EVIdistributionunderliesthe llood population.althoughthere is no assurance that annual seriesofflood flows areEV1distributed.A regional Hood frequency curve is obtained by plottingmemedian ormeanpeaknow ratios at given return periods againstfrequencies on EVI probabilitypaper.
Nash and Shaw(1965)introduced regionalaveragi ngof dimension lessmoments.
The regional average values ofthe coefficient of variation and thecocfficicnlofskewness arc used. They canbeused10estimateparametersofanytwo or three parameter distributionfor Xl=QIQ.A variationof this approachis(Qestimate themoments and skewness ofthe logarithm s of the at-site data and adopt aregionalaveragevalue of the skewness or a weightedvalue oftheregional andat-siteestimateof the skewness (USWRC,1976,1977 , 1981).The USWRCmethodassumes thatallfloodseries inthe region are distrib utedas anLP3distributio nand quantileestimationis obtained by moment estimationinthe log-domain.However,there is also no guaranteethatannual maximum floods areLP3 distributed.Theuse ofLP3 is actuallybased onsuggestions forinstitutional uniformityrecommended by US Federa lagenci es(Benson,196Kj.
2B
The index flood method was also used by NERC (1975)forBritish andIrish conditionsandlaterwas implementedinNewZealand(Beable and McKerchar,1982).
TheNERC method modifies Dalrymple's(1960) methodby usingregionallyaveraged standardisedorderstatisticsin a graphical procedure to estimatetheXTdistribution.This averagingisinte ndedtoreduce the effectof outliers ontheregio nalcurve fittingmethod dueto thepossibilitvof sampling variation of eachindividualstreamflowrecord fora regio n.
Wallis(1980)suggested an objective numerical method,based on regionally avera gedstandardised PWMs (ProbabilityWeightedMoments).Thismethod has been found\0beeasyto applyand isefficient forestimat ingflood quantiles. The PWM proce dureswe re introd uced by Greenwood et.al.(1979)and furtheranalyzed by Hosking(1986).PWMscanbeusedwith all distributionsthat canbedefined in inverse formsuchastheuniform,exponential,EVI,Logistic, Normal,Raleigh,GPA, GEV, GL,Lognormal,Gamma, GeneralizedLambda and Wakeby distributio ns(seealso Hosking,1986 andWMO,1989). Thus.thismethod rules out data are distributed as LP3,
Cunnane(1987,1988)included the stationyear method inhis reviewofstatistical floodquantile analysis. The methodisbased onpoolingallstandardiseddata values within~.regionand treating them as a singlesamplefroma populatio nfor parameter estimationpurposes. Thisapproach isreferred to as a regionalpooling of data. In contrast.thc othermethods involvearegional averagingof data or statistics of those data.
29
Recentresearch on regional frequency analysisbyHosking andWallis(I~2.
1993) describesanindex flood procedure based onl-moments.Then'k:thod is1;l;lSl,.'d(\11
the linearcombinationsof thePWMsbUI possesses greaterctariryfor snuistical interpretation (Hosking.1986).Theregional analysisbasedontheL-IIl Il Illl.'111llk."Ihl>l.t includes identifying unusualsitesin a region.assessinga homogeneous region,;lI\d assessinga candidate distributionof adequatefit to the data. TheseanalysesC;1Il efficientlyuset.-momenrstatisticsoftheat-site data(Hosking.!990).
Inadditionto the indexfloodapproach,othermore complicated andless pl.ljlular approachesinclude the Two ComponentExtreme Value (TCEV) andB.1yc.~iall approaches(Cunnane,1987).
3.5.2Logarithmic Regressionfor EachQTApproach
Thisapproachhasbeen usedin manyfloodfrequencystudiesin United Stales (Rcskie.1978.citedbyTaskerand Moss,1979; Tasker, 1987),and h:lsnlsnhce nused by theNewfoundland waterResourcesDivision (Beersing,1990). This appro.1ch is based on estimating Qyseparately ateach site inthe regionfromagiven distribution fur a selectionof Tvalues such as 2,5, 10, 20,50 and 100 years. The logarithmic regressionretaucn is established betweenOrforeachvalueof T andth~catchmcm characteristics. Thefloodquantlles atgaugedandungauged catchmentscan Ihenbe estimatedusingtheseregression equationswiththerelevantcatchmentcharacteristics.
3.
3.6 StudyApproach
Inthisthesis.two principalregionalFloodfrequencyestimationapproaches were adopted, the indexfloodapproachandthelogarithmic regression for eachQr approach. Thesetwo approaches were chosenbecause theyare the mostpopularprocedureused in 1ll,IIlycountries,and theshortrecords availabledid notjustify the use of more complicatedtechniques.Fiveindexfloodprocedureswere used inthis study, including Dalrymple (1960),NERC{I975),PWMs,the stationyears and thcL-moments, and the resultswerecompared.Inaddition 10the comparisonstudy, the methodofmultiple regression(based on1e.1Stsquaresparameter estimation) was used 10derivethe logarithmicregression'--illationCoreachQron catchmentcharacteristics.A methodfor tnascorrection due10logarithmic transformation,developedbyMiller, er.al (l984) was used10provide unbiased regression equations.
31
Chapter 4
Preliminary At-Site and Regional Analyses
4.1 Introduction
Thischapter discussesthepreliminaryoverview of at-site and regional l1tlO\l frequencyanalysesfor the Acehprovince rivers.As mentionedin the previouschapter.
a prerequisiteof theregionalapproach isthe identification of regions or data.~C! SthaI have homogeneous flood frequencybehaviour. AcchProvince,which is a relativ,:Jy small area,was assumed\0be a physicallyhomogeneousregionin termstil'1l00dnow distribution.Asdiscussed in the previous chapter with regard to regionalanalysis.the following steps are requiredbeforeundertakingthe estimationofregional frequency distribution.These are: (I)screening of the data, (2) providing at-sitefloodfrequency magnitudes.(3)selecting a regionalfrequencydistributio n,and (4)obtainingcatchment characteristics. The years for whichannualmaximumstrcamnowswereused fortht:
9 riverbasinsare listed in Table 4.1.
32
:::
Table~.I: Lengthof rec-irdof annualmaximum floodsused for frequencyanalysis
Sire Stationname Years
72 73 74 75 76 71 78 79 SO 81 82 83 84 85 86 87 88
,.
I Acehat KampungDarang (KD)
-- -_ ...
-- "" - - -- -- -=
=- -=-""2 Lambeusoi atSango(SG) ... -== ==== - - -_...=...=== ===-
--
3 Seuneganat Ujung Blang(UB) ..._ .... . - =-====
- -
,
KluelarGunungPudung(GP) ====== = = = = = =5 Lawe Alasat Sukarimbun (SR) .. "" -- -_ ...-= =====- 6 Bam atKlibeut(Kl) ====
=- -_ .... == ==
====-=-=7 Peusar-ganatBeukah(OK) _... ====""""- - - --=""=
=-
=<=-- - -8 JambuAyeallook Nibong(LN)== ==
=_ __ _ _ _
m==== =""=_ ...
===== ==--
9 Tamiang al Kuala Simpang(KS) -- - - -- ==""=... .. .
4.2 Screeningof theFloodFlow Data
The first stage of data screeningis the inspection of the sample properties Ill' the data.In this analysis,the records for eachof the nine sites wereassumed1\1h<L\'C sufficient length, to be homogeneous,and to be random. Thenext stage is the identiticationof unusualsitesin which at-site samples may cxhihit rhffcrcm characteristics fromthose found at othersites.The procedure suggestedbyHtl.~kingand Wallis (1993) which measuresthe discordancy (D,) of the site was used in thisanalysis.
The procedure provides anindicationof unusualsamplesin a region asawholehased on the sample L-momentsat each site. Themathematicaldefinitionsofthe Lmomcms presentedbelow were used inboth this screening and also inthe method01" parameter estimationofthe regional indexflood by the P"".'Mandt-mo menrmethods.
4.2.1PWMsand L-Moments
The L-moments definedby Hosking(1986,1990)arc linearcombinationsIII"lhe PWMs (Greenwood et.al.,1979).ThePWMs ofa random variable X with CUllIU1011ivc distributionfunction F(X) aregiven as:
(4.1)
wherer
=
0,1,2,3, ..TheL-moments are linear combinationsof the cquauon above and are defined byHosking (1986,1990)as the following quantities:34
(4.2)
u.c
Lonomcnts ratios arc given by:(4 .3)
The Alisitmeasureoflocationrthemean ofthe distribution),Alis a measure ofscale, AIisa measure ofske wness. AJ is ameasure of kurtosisandtheL-CY (1) isthe analogue of thecoe ffic ient of variation.1\istheL-skewness.and 14is thet-kurtosis.
Inpractice,Landwehrct.al (1979)showed thatPWMsfrom a samplecanbe estimatedusingtheunbiased estimator{1,according to the following equation,and the sampleisarranged in order of"I~x!~Xl...:os;X••
br=n-1E (j-l) ( j- 2 ) . , .(j-r) :lC
j (4.4)
J-1 ttl-I )(n -:il)•• •(.a-r) Thesample unbiased estimatorsoftheA.are givenby:
(4.5)
The sample valuesoft,ofthe1,andtof1are asymptoticallyunbiasedforlarge n,and
35
can be obtained usingthefollowingequations:
(-l.ti )
Fromthe above equations.the followingsteps lassLl~gcstcdby Hosking.uul Wallis.[993)were used to performthescreening of thenine sampling sitesin/\\' 1.'11 Province.
I) Foreachsite . theflood flows werestandardizedbythe meanannual 1100d.Q.Thesestandardized values wereused to definethet.-mcmcut ratiossuch as L-CV(t).Lskcwoess(I,)and Lkunosis(I,)using the equationsabove.
2) Foreach sitei,ulis a vector of I. IIandI~values.and is calculatedusing the following equation. Theunwcightcd group averageIiisobtained immediately after the initial definitionofII;:
('\.7)
(4.8)
3) The sample covariance matrix isdefinedusing the following equation:
»
S" (N_1.)-l
I't
(u 1-ii)(u 1-ii) Z' (4.9 )4) For sitei,the measureof discordancyis defined using the equation:
36
(4 . 1 0)
(5) Fromthe above computation,ifthe D, value for siteiislar ge ,itis an indication thatthis site isdiscordant from the group as awhole and itmay indicate the presenceof errorsinthe data.
4.2.2 Result'!
From the floodflo w data intheAceh region,thesummarystatistics were calcula ted,andpresentedin Table 4,2 , Itshowsthe discordancy measure ,Djwhichis anind icatorof unusual11000 flow ateach sitein theregion. andthe vario us L-moment ratios.
Choosing a singlevalue of D, thatcanbe used asa criterion fordeciding whether asiteis unusual is not easy.Hoskingand Wallis(1993) suggested 0,~3 asacriterion for decla ring a site to beunusual. Aswell, the data forsites with the largest values shouldbere-examined. [t eanbe seenfromTable 4.2 thatall0iare:s:3.indicatingthat then: arc nounusual sitesidentified,
37
Table .l..:!:Summary statisticsfo r theAccn province 11\,11,'0.1t1..1WJ;\t;\ sets
SiteRiverBasin n Mean I I, I, D,
I Krueng Aceh It 286 0.2019 0.12~2 0..'296 I Ahl.,lS
,
Lambeusci"
549 O. 2::!89 0.08 79 0.t)9 76 0.90 2X3 Seune gan 7 183 0.0640 0.0550 0.06 25 0.7.1:-:5
4 Kluet 6 460 0.1772 0.1.,'::\ 0.1207 0.2hh7
5 LaweAlas 8 274 0.0 860 O.07 S7 O.069X O.2I.Jl'ln
6 Bare It 79 0.1619 0.156 6 0.\173 OAhll'l
7 Peusangan 13 460 0.151 2 0.0126 -O.\J.lJ 8 I.J755 8 ambuAye
"
761 0.0900 D.17S5 0.0222 104054
9 amiang 7 1184 0.0757 0.1069 O.22M 1.0 2 15
4.3 At-Site Flood Freque ncyAna lysis
Itisneces saryto deter minethe at-site 1100J trequcncy magnitudesat cach site for fourreasons.First.these magnitude sarc requiredwhen apply ingDa lrymple ·s merhod.
Second,meceflnaly~t'<.arc requiredtoderive regressionequatio ns betweentheseIl..KJl!
magnitude satagiven returnperiodandca tchme ntcha racteristics. Third. thesc at-sitc analysesarc required foridentifying the bestflooddistributionft,r Acehprovincerive rs . Finally. theseat-siteanalysesare req ui red for co mparisonwithregional frequenc y analyses .
A generalfreque ncymodel calibratedfromat-site samplefo r the estimation ,,1 floodquan tile QT canbe expressedas(Cu nnane,1987):
(4.11)
where
Or
istheeventmagnitude ata givenreturnperiod,T.~lo~1•~l an:~aJJ1pl...38
e,Uln iLtc'ofrocauon . scare and shapeparametersof a selected distributmna]form flq;IJI.y. fOI)is a standar dised variatevalue of return period Tfrom thefl.l distrtburion.
The dim ibutions considered inthis studyare the Gumbel(EVI).lN2.LNJ.
(jl:V.andlIJJdl~ri bution s.The method ofmomentswas used tofilalltwo parameter di'o1 ritmt ionswhilelhemethodofmaxnnumlikelihoodwasused10iiiallthree parameter di\l.ributions.
ThecomputerprogramCFA).1991deve lopedbytheHyd rologyDiv isionof Water Resour cesBranc h of Environ mentCanada was used todeterminetheexpecte d flood tt o ws ofvariousreturn periodsat eachofthe ninegauging stationsforthe three parameter di.,tribulions. Thisprogr a m allowsfor the fittingoffourdistributio ns:the GEV. LNJ.LP)distributions.and thewakeby (a5parameterdistrib ution).Forthetwo p..ara mc tcrdistri b utions.the computer prog ramspro vided byKite(19 88 )were used in this 'ludy.
tcsurnarcs oflloodquantileswith2.5.10.20.SO. 100.and 200 yearreturn period swere derived based onthe five theoretical distributionsandonemp iricallit.
Fillingforeach distribut ionandthecalculation ofthe so-ca.Iled standard errorthrough the lcasl squaresmethodwasused10dete rm inethe bestfittin g distribution.
~.3.1Selectionof Best Fill ing Distribution
Theselection amongtherivedistributionswas basedon theleast squaresmethod ofSTan da rderrorof tilfo r eachdistribution.This standard erro r of fitisameasureof
39
analysisare definedbythe equation[Kite.\<}881.
[ t
(',-Pl'I '"
SE. -'"-' - -n-p
(.1,12)
where Y,isthe actualdatapoint.'i',is a data poinr as ':Stilll;ltcubyth... dbtrihuti"nat probabilitiescomputed (rom thesorted ranksof Y,•nis the numh...rofpointx,;mdI'r~
thenumber of parameters .
Itshould be notedthat thecomputatio n of thestandard errorufti ti~dqX'lldel1t onthe plottingposition. As described inChapterj ,the unhiased11 1 1l11 i n ~poxtnou suggestedbyCunnaneI !l}78).whichis basedon,Isingle simplecompromise formulaI'm usewith all distributions.wasused inthis study.
4.3.2Results
Thestandarderro rs oftitfor eachdistributionused forthe nine rivers inthe regionare presentedin Table4.3,amitheat-sitemagnitudesh:ISCd onthishe....t III distributionare given in Table 4.4.In general. the order ofbestlitdistributions\(Jthe ninesites in theprovince were the EVI,LN2,GEV.LN3 and1.1>]respectively.Itis not easytochoo se a singlefrequencydistributionbased on at-sueanalysisalone. because uf the differen tbest fittingdistributionderivedat eachsite in the region.The extreme value distributionwas selectedfor use intheregional analysis based onthe abovercsult~, and onaconside rationto the Lrnornentratios.asdiscussed in thefollowingsection.
40
Table~.3: Standard errors oivarious distributionsused Standard ErrorsISE J of various distributions
SiteRiverbasin EVI LN2 GEV LN3 LP3
I Krueng Aceh 22.758.. 25.040 25.203 30.967 33.093 2 Larnbeusoi 143.535 .. 156.436 153.783 152.090 158.459
.1 Scuncgan 5.729 3.646 .. 5.548 9.001 6.2-40
4 Ktuct 9.3119 .. 13.254 13.910 14.243 2·U 77
5 Lawc Alas 11.726 11.807 12.538 10.459.. 12.633
6 Bare 5.121 5.505 5.068.. 6.555 5.957
7 Pcusangan 29,487.. 36. 202 32.354 31.659 29.?14 8 Jambu Aye 28.63Q 27.368.. 34.016 43.241 43.366
9 Tamiang 34.924 24.924· 39.576 50.473 52.787
In Region 29 1.308 304. 182 321.996 348.688 366.592
(general) II) (2) (3) (4) (5)
"llhc best titat each site(theminimum standard errors).
Table4.4: At-siteestimatedfloodquantile magnitudesin the Acehriversbasedon best lit distribution at-each site.
T Y At-siteestimatedflood quantiles(Or)
earslvariatc River basins
(EVI)
SiteI Site2 Site 3 Site4 Site 5 Site 6 Site 7 Site 8 Site 9 2 0.367 269.8 515.4- (82.5 440.8 267.0 74.9 441.9 751.7 1174.3 5 1.500 374.4 730.5 199.5 587.1 306.0 °7.4 559.8 855.7 1306.1 10 2.250 443.7 872.9209.1 683.9 333.0 112.0 637.9 915.7 1380.8 20 2.970 510.2 1009.4217.3 776.8 360.0 126.0 712.7 968.4 1445.6 50 3.902 596.2 1186.2227.0897.0 397.0 144.0 809.7 1031.3 1522.3 lUO 4.600 660.7 13 i8.7 233.6 987. 1425.0 157.0 882.3 1075.5 1575.6 200 5.296 125.0 1450.7239.91076.9 454.0 170.0 954.7 11l7.5 1625.9
4.4 Selectionof RegionalFlood FrequencyDistrihution
Thissectio ndiscusses theprocedurethatWi\Susedinlht.·sclccrinnIll'a rt.'l,!i\',lal frequency distributionfor the:Acehregion.Inthis context. the Lmomcnt di;lgr.lTllW;\~
used 10 compare sample estimatesofthedimensionless ratiosr.t,;lndtslas dis\"usscilin Section~.2)withtheir populationcounterpartsfor a range ofilSSIlI11L'ddistributions.
Both at-site t-momentratiosand regional weighted averageLmcmcmratios\\WC
compared.
4.4.1Procedure
The procedure to obtain the L-momentratiosat each sitehas beendiscussed in Section4.2.The L-momentratios ofthe at-suestandardizedfloodfle ws . particularly Lkurtosis and Lskewncss.are compared tothe theoreticalrelationships hetween L- kurtosisand Lskewnessfor severaldistributions.Figure 4.1com pares these theoretical relationships for normal,uniform,Gumbel.GEV.LN3,gamma(1'3).GPA,andthe lowerboundary ofall distributions. These theoret icalrelationshipswereconstructed usingthe polynomial approximationsdevelopedbyHosking(1986).Itisapparentthat the tWOparameter distribut ions are definedby onlya single point in the Lkurtosis and Lskewness -etatlonshtps.whilethethreeparameterdistributionsare moreflexible.
In addition.the procedure was alsoused ina regionalcontext for the selectionof the bestfit distribution regionallybasedontheweightedaverageL-C V.L-kur1o.~is.mtJ Lskewness for the region.The followingeq uations suggestedbyHosking(1992) were usedtoderi ve theseregional sampleweightedaverageL-mo ment ratio s:
42
(4 .13 )
wherer""J.~.Iis regionalweighted averageL-CV,IIandI~areregionalweighted average Lskcwncss and Lkurtosis.respectively.andn, is the samplelengthat siteL These regionalL-kun osis andLskewnessvalueswereco mparedtothetheoretical rctanceships. andwerealso supportedbypreviousat-sitecomparisons thatwere made inorder to selecttheapproximate regionaldistribution.
~ J
:,
' "
_..
~- '..- . '
l-Skewness
Figure4.1: Theoretical L-momentrelationships forassumed distributions{Hosking,1986)
43
-tA.2Results
Figure~. 2shows the sample <It-siteestimatesonthesameplotns thethl'llfcti..:"l relationshipsbetweenLkurtosis and Lskewnesscorresponding10the GEV, GUlllbd, L:"gamma. GPA, andthelower boundary of all distributions. ThisfigureSh\II\"Sthat, from themooets tested.theGEV,LNandgamn:-distributions'lppt.';lrtoIll'mOSI consistent with the sampleLcskewnessand Lkurtcsisforthe sitesin theregion. In Figure 4.2,nearlyfiveuftheobservations arc close10 theGEV,LN.mtlgauuua distributions. Althoughthere is largevariability inthe Lmoment ratioestimates.tfw GEV distributionappears toprovide the best overall fit, followed bythe LNand~;llnma distributions. The overall sampleL-moment ratios estimateispoorl y approximatedhy theGPAdistribution ,
Figure4.3showsthe sample regionalweig hted average Lmomentrauo s plnttrtl on the L-momemratiodiagram togetherwith thetheoreticalt-kurros!sandl.-skcwncss relationshipsof assumeddistributions. This figureshowsthatthe sample regional1,- kurtosis andLskewness fallcloseto the theoreticalGEV curve . Althoughthe sample regio nal Lkurtosls and Lskewnessrelationships alsofallclosetothetheoretical LNand gammacurves, fro m Figure4.2andtheprevious at-siteanalysis (Section 4.3) showthat theLN and gamma distributions seemto providea poorerrepresentationof theIlood flows distributioncomparedto the GEVdistributionforthe region considered.The GEV distributionisther eforeusedforthesubsequentestimationoffloodquantilcs.
44
• •....,.••,m.1
At- ....L-I/G...-+-1l,P...
Figure4.~: Lmomentdiagramscomparingthe sample at-site estimates and theoret icalrelationshipsbetweenLckunosi sand L- skewnessfornineAcehriver basins
• L·Skewness
figure4.3: L-moment diagrams comparing the sample regional weightedaverageforthe Acehregionwith theoretical relationships for t-kurtoslsandt-skewness
45
