Regionalization of Watersheds: An Approach Based on Cluster Analysis

247 Pages·2008·9.934 MB·English

by  A. Ramachandra Rao, V.V. Srinivas (auth.)

Regionalization of Watersheds
Water Science and Technology Library
VOLUME58
Editor-in-Chief
V.P.Singh,TexasA&MUniversity,CollegeStation,U.S.A.
EditorialAdvisoryBoard
M.Anderson,Bristol,U.K.
L.Bengtsson,Lund,Sweden
J.F.Cruise,Huntsville,U.S.A.
U.C.Kothyari,Roorkee,India
S.E.Serrano,Philadelphia,U.S.A.
D.Stephenson,Johannesburg,SouthAfrica
W.G.Strupczewski,Warsaw,Poland
Thetitlespublishedinthisseriesarelistedattheendofthisvolume.
Regionalization of Watersheds
An Approach Based
on Cluster Analysis
A. Ramachandra Rao
SchoolofCivilEngineering,PurdueUniversity,WestLafayette,IN,USA
and
V.V. Srinivas
DepartmentofCivilEngineering,IndianInstituteofScience(IISc),Bangalore,
India
A.RamachandraRao
PurdueUniversity
WestLafayette,IN,USA
V.V.Srinivas
IndianInstituteofScience
Bangalore,India
ISBN:978-1-4020-6851-5 e-ISBN:978-1-4020-6852-2
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Dedication
Thisbookisrespectfullydedicatedto
theuniqueyoginiofthetwentiethcentury
MaathaJayalakshmi
andtohersonthegreatSiddha Purusha
SriSriSriGanapathiSachchidanandaSwamiji
of
AvadhoothaDattaPeetham
ShriGanapathi Sachchidananda Ashrama,
Mysore570025,India
with namaskarams
Preface
Design of water control structures,reservoir management, economic evaluation of
flood protection projects, land use planning and management, flood insurance as-
sessment, all rely on knowledge of the magnitude and frequency of floods. Often,
estimationofthisinformationisnoteasybecauseofpaucityoffloodrecordsatthe
targetsites.Regional flood frequency analysis(RFFA) entailsestimatingtheflood
frequencydistributionatatargetsitebyutilizingfloodrecordspooledfromseveral
otherwatersheds,whicharesimilartothewatershedofthesiteinfloodproducing
mechanisms. The process of identifying similar watersheds for pooling peak flow
information is known as regionalization. Research in this area is active over past
fourdecadeswithnewandintriguingfindingsconstantlybeingreported.
Clustering techniques are useful to identify groups of watersheds which have
similarfloodproducingmechanisms.Thisbookdealswithregionalizationofwater-
sheds.Itprovidesadetailedaccountofseveralrecentlydevelopedclusteringtech-
niques,includingthosebasedonfuzzysettheoryandartificialneuralnetworks.It
alsodocumentsresearchfindingsonapplicationofclusteringtechniquestoRFFA.
Anattemptismadetomakethetechnicallevelofexplanationsimpleandcompre-
hensiveforthebenefitofpractitioners.
Inregionalfrequencyanalysis,theoptimalnumberofregionsisbasedoncluster
validation measures and visual interpretation. The potential of various cluster va-
liditymeasuresinidentifyingoptimalsetofregionsisinvestigated.TheL-moment
basedhomogeneitytestsformthebasistochecktheregionsforhomogeneity.The
regions formed by any regionalization method are, in general, heterogeneous and
theyneedadjustmentstomakethemhomogeneous.Itisdemonstratedthatthesub-
jectivity involved and the effort needed to identify homogeneous groups of water-
shedswithconventionalapproachesaregreatlyreducedbyusingefficientclustering
techniques.Toachievebetterresults,somemodificationsaresuggestedtoconven-
tional fuzzy clustering approach to regionalization in Chapter 3. Further, a novel
two-level self-organizing feature map based clustering approach is developed in
Chapter4.Thetheoreticalbackgroundoftheproposedapproachesisprovidedand
theirperformanceinpracticalsituationisassessed.
InRFFA,adistributionsuchaslog-PearsontypeIIIorGeneralizedextremevalue
is recommended as default choice to fit peak flows in different parts of the world.
Thestipulationthataparticularfloodfrequencydistributioncanbepreferredtofit
vii
viii Preface
peakflowdatainalltheregionsisinvestigatedinChapter5.Furtherthevalidityof
simplescalingmethodsthathavebeendevelopedinRFFAistestedinpracticalsitu-
ation.Itisdemonstratedthatbetterfloodestimateswithsmallerconfidenceintervals
areobtainedbyanalysisofdatafromhomogeneouswatersheds.Theimportanceof
regionalizationinfloodfrequencyanalysisisdemonstrated.
ItissuggestedthatChapter1bereadbeforeproceedingtootherchapters.There
aresomerepetitionsforthesakeofcompleteness.Thewords:site,watershed,and
catchmentareusedinterchangeably.Featurevectorsthatareformedusingsitechar-
acteristics are referred to by the words object, data point, and site at several loca-
tions.Similarly,thewords:model,method,procedure,algorithmandtechniqueare
usedinterchangeablytorefertoclusteringalgorithm.
Professor Rao would like to thank the members of his family, Smt. Mamatha
Raohiswife,Dr.MaliniRaoPrasadhisdaughter,Dr.SathyaPrasadhisson-in-law,
Karthik A. Rao and Siddhartha S. Rao his sons and especially Kum. Shambhavi
N. Prasad, his delightful grand daughter for their support. Dr. Srinivas would like
to acknowledge Sri. Sharma and Smt. Katyayani his parents, Smt. Srivatsala his
wife,andfamiliesofhissistersSmt.RadhikaandSmt.Sudhafortheircontinuous
encouragement and affection. He would like to express his gratitude to Prof. Rao
S Govindaraju and his student Mr. Shivam Tripathi, School of Civil Engineering
PurdueUniversity,forusefuldiscussionsandinputtoChapter4.
Some of the material in the first four chapters of this book is reprinted from
three papers published by the authors in Journal of Hydrology (Rao and Srinivas
(2006a),RaoandSrinivas(2006b),andSrinivasetal.(2008)),withpermissionfrom
Elsevier.AuthorsexpresstheirspecialthankstoElsevierSciencesforgrantingthe
permission.
Wewouldliketothankanumberofpeopleforbothdirectandindirectsupport
during the period that we worked on this book project. We would like to thank
Dr. V.P. Singh for his support. We thank the Publishing Editorial and Production
staff at Springer Publishers (Dordrecht, The Netherlands) who helped in bringing
this book project to a successful conclusion. Our special thanks are due to Petra
D.vanSteenbergen(PublishingEditor).Wealsothankauthorswhoseworkiscited
inthisvolume,fortheircontributionstothisresearch.
WestLafayette,IN A.RamachandraRao
Bangalore V.V.Srinivas
September,2007
Contents
1 Introduction................................................... 1
1.1 RegionalizationforFloodFrequencyAnalysis................... 1
1.2 ApproachestoRegionalization................................ 2
1.3 ClusterAnalysisinRegionalization............................ 4
1.3.1 AttributesUsedinRegionalization ...................... 4
1.3.2 ClassificationofClusteringAlgorithms .................. 6
1.3.3 StepsinRegionalizationbyClusterAnalysis ............. 7
1.3.4 IssuesinClusterAnalysis ............................. 9
1.4 TestingRegionalHomogeneity ............................... 10
1.4.1 AdjustingtheRegions ................................ 11
1.4.2 DiscordancyMeasure................................. 12
1.5 DataUsedinExamples...................................... 13
1.6 OrganizationoftheText ..................................... 15
2 RegionalizationbyHybridClusterAnalysis ....................... 17
2.1 IntroductiontoHybridClusterAnalysis ........................ 17
2.2 ClassificationofHardClusteringAlgorithms.................... 17
2.2.1 HierarchicalClusteringMethods........................ 18
2.2.2 PartitionalClusteringMethods ......................... 21
2.2.3 HybridClustering .................................... 22
2.3 ClusteringAlgorithmsandPerformanceAssessment ............. 23
2.3.1 HybridAlgorithm .................................... 23
2.3.2 SingleLinkageandCompleteLinkageAlgorithms ........ 24
2.3.3 Ward’sAlgorithm .................................... 25
2.3.4 HardClusterValidityMeasures......................... 28
2.4 ApplicationofHybridClusteringAlgorithmstoRegionalization ... 32
2.4.1 FeatureExtraction.................................... 32
2.4.2 ResultsfromClusteringAlgorithms ..................... 35
2.4.3 ValidationoftheResults .............................. 38
2.4.4 TestingtheRegionsforRobustness ..................... 48
2.4.5 FinalResults ........................................ 48
2.5 ConcludingComments ...................................... 51
ix
x Contents
3 RegionalizationbyFuzzyClusterAnalysis ........................ 57
3.1 Introduction ............................................... 57
3.2 ClassificationofFuzzyClusteringAlgorithms................... 57
3.3 TheFuzzyC-MeansAlgorithm ............................... 59
3.3.1 DescriptionoftheAlgorithm........................... 59
3.3.2 AssignmentofNewSitestoFuzzyClusters .............. 63
3.4 FuzzyClusterValidityMeasures .............................. 63
3.5 ExampleofUsingFuzzyC-MeansAlgorithmforRegionalization .. 68
3.5.1 FeatureExtraction.................................... 68
3.5.2 ResultsfromFuzzyC-meansAlgorithm ................. 68
3.5.3 TestingtheRegionsforRobustness ..................... 98
3.6 ConcludingComments ......................................102
4 RegionalizationbyArtificialNeuralNetworks.....................113
4.1 Introduction ...............................................113
4.2 KohonenSelf-OrganizingFeatureMaps(SOFMs) ...............113
4.2.1 AlgorithmofKohonenSelf-OrganizingFeatureMap.......114
4.3 ExampleofUsingSOFMsforRegionalization ..................117
4.3.1 FeaturesUsed .......................................117
4.3.2 ResultsfromSOFM ..................................118
4.3.3 TestingtheRegionsforRobustness .....................136
4.4 RegionalizationbyTwo-StageClusteringofSOFM ..............141
4.4.1 Introduction.........................................141
4.4.2 AlgorithmforFuzzyClusteringofKohonenSOFM........141
4.4.3 ExampleofUsingTwo-LevelFuzzySOFM ..............145
4.5 ConcludingComments ......................................153
5 EffectofRegionalizationonFloodFrequencyAnalysis .............155
En-ChingHsu,A.RamachandraRao,V.V.Srinivas
5.1 Introduction ...............................................155
5.2 RegionalIndexFloodMethodBasedonL-Moments .............156
5.2.1 Introduction.........................................156
5.2.2 RegionalL-MomentMethod ...........................157
5.2.3 At-SiteandRegionalParameterEstimation...............158
5.3 RegionalRegressionAnalysis ................................167
5.3.1 Introduction.........................................167
5.3.2 GLSRegionalRegressionResults.......................168
5.4 CombinationofGLSRegionalRegressionandL-MomentMethod .174
5.5 ComparativeAnalysis .......................................184
5.5.1 SplitSampleTestfortheFirstMethod...................184
5.5.2 SplitSampleTestfortheSecondMethod ................188
5.5.3 SplitSampleTestfortheThirdMethod ..................189
5.5.4 ComparisonoftheThreeMethods ......................192
5.6 SimpleScalinginRegionalizedWatersheds.....................196
Contents xi
5.7 Probability Distributions for Flood Frequency Analysis
inRegionalizedWatersheds.................................. 199
5.7.1 ParameterEstimation .................................200
5.7.2 QuantileEstimation ..................................201
5.7.3 ProbabilityDistributions ..............................201
5.7.4 DataAnalysis .......................................202
5.7.5 DimensionlessandStandardizedQuantileMeasures .......208
5.8 ConcludingComments ......................................211
6 ConcludingRemarks ...........................................213
6.1 General Remarks on Clustering Approach to Regional Flood
FrequencyAnalysis......................................... 213
6.2 RecentDevelopments .......................................216
6.2.1 TestsofRegionalHomogeneity.........................216
6.2.2 MethodsforCharacterizingRegionalFrequency
Distribution ........................................ 217
6.2.3 MethodsforRegionalFrequencyAnalysis ...............217
6.2.4 Goodness-of-fitMeasuresforRegionalFrequencyAnalysis .217
6.2.5 Non-StationaryFloodFrequencyAnalysis ...............218
6.2.6 FloodFrequencyAnalysisinClimateChangeScenarios....219
6.2.7 SimulationofFloodsUsingOutputfromGCMs...........220
References.........................................................223
IndexofNotation...................................................233
Abbreviations......................................................237
Index .............................................................239