Runoff - Hydrology and Irrigation Engineering

Hydrology And Irrigation Engineering

1. Runoff, Hydrograph

2. Module-III
•Runoff:Definition,conceptof
catchment,factorsaffecting
runoff,rainfall–runoff
relationshipusingregression
analysis.
•Hydrographs: Definition,
componentsofhydrograph,base
flowseparation,unithydrograph,
assumption,applicationand
limitations,derivationfrom
simplestormhydrographs,S
curveanditscomputations,
ConversionofUHofdifferent
durations

3. catchment

4. 4

5. factors affecting runoff hydrograph

6. Rainfall –Runoff relationship using regression analysis

7. 7
Hydrograph
Hydrographsaregraphicalrepresentationsof“flowparameters
againsttime”.Whenastormfallsinacatchment,afterinitial
lossesandlossdueinfiltration,rainfallexcesseventuallyflowsto
themainstream.
“Ifthedischarge‘Q’,averagevelocity’V’anddepthorstage‘Y’at
outletpointofthestreamismeasuredfrombeginningofthe
stormtotheendofstorminthecatchmentandiftheyareplotted
againsttime,theymaybecalledHydrograph”.
i)If‘Q’isplottedagainsttime‘t’,itiscalledflowor“flood
Hydrograph”
ii)If‘V’isplottedagainst‘t’,itisknownas“Velocity
Hydrograph”
iii)Ifdepth‘Y’orstage‘H’isplottedagainsttime‘t’,itiscalled
depthor“StageHydrograph”.
“ButmostcommonlyinHydrology,Hydrographmeansthe
graphofflowrate‘Q’againsttime‘t’”
HYDROGRAPH ANALYSIS

8. 8
HydrographofSingleandComplexStorms(Picture-I)
HYDROGRAPH ANALYSIS

9. 9
HydrographofSingleandComplexStorms(Picture-II)
HYDROGRAPH ANALYSIS

10. 10
Components of Hydrograph of Isolated Storm
i.ABisapproachsegment
ii.BCisrisinglimporconcentrationcurve
iii.CPDiscrestsegmentorpeaklimb
iv.DEisfallinglimb
v.LowerportionDEiscalled“GroundWaterDepletion”curve
vi.Pisthepointofcrestorpeak
vii.t
Bistimeofrise
viii.T
pisthetimeofpeak
ix.AreaunderABEisthevolumeofbaseflow(shownbyshaded
line).Thisvolumeisassumedtohavenocontributionofstorm.
x.AreabetweenBPEandBEisthevolumeofdirectsurfacerunoff
(DSR)shownbydots.
xi.OAisthevalueofdischargeatinitialtimet=0andthisOAmay
beassumedtobethebaseflow.
xii.‘C’isthefirstpointofinflexionand‘D’isthesecondpointof
inflexion.
xiii.OE
1isthebaseperiod‘T’ofthehydrograph
HYDROGRAPH ANALYSIS

11. 11
HydrographSegment
HYDROGRAPH ANALYSIS

12. 12
Segments of Hydrograph of an Isolated Storm
Hydrographisbroadlydividedintofollowingthreesegments;
RisingLimb/Segment
Intheinitialtimeofrainfall,lossescausethedischargetorise
slowly.Buildingupofstorageisevidentlygradual.
However,ifthestormiscontinuous,aaccumulativedischarge
fromupstreamreachestheoutlet(asinfiltrationandabsorption
lossdecreaseswithtime).“Ofcourse,shapeofbasinandstorm
characteristicsaffecttherisinglimp”.
PeakLimb/CrestSegment
ItisthemostimportantpartofHydrograph.Peakoutflowis
essentialfordesignofHydraulicStructures.Whenrunoffsfrom
allsourcesreachtheoutlet,peakflowoccurs.
Inlargecatchment,peakflowmayevenoccurafterthestorm.
“Estimationofpeakflowanditstimeofoccurrencearevery
importantinHydrology”.
HYDROGRAPH ANALYSIS

13. 13
Segments of Hydrograph of an Isolated Storm
RecessionLimb/DepletionCurve
Therecessionlimbrepresentsthe“withdrawalofwaterfrom
storageafterallinflowstothechannelhaveceased.“Therefore,it
istimeindependentofrainfallorinfiltrationandisessentially
dependentonchannelfeaturesalone”.
HYDROGRAPH ANALYSIS

14. Effective Rainfall (ER)

15. Base flow Separation
Forthederivationofunithydrograph,thebaseflowhastobeseparatedfromthetotal
runoffhydrograph
Baseflowistheinitialflowofthestreambeforetheraincomes.“Itisthesustained
ordryweatherflowofthestreamresultingfromtheoutflowofperennialoralmost
permanentgroundwaterflowthatreachesthechannel”.Thisbaseflowofsuch
channelismoreorlessassumedtobeconstant.

16. Base flow Separation Procedure
1.Bysimplydrawingaline‘AC’tangentialtoboththelimbsat
theirlowerportion.Thismethodisverysimplebutis
approximateandcanbeusedonlyforpreliminaryestimates.
2.Extendingtherecessioncurveexistingpriortotheoccurrenceof
thestormuptothepoint‘D’directlyunderthepeakofthe
hydrographandthendrawingastraightlineDE.WhereEisa
pointonhydrograph‘N’daysafterthepeak&N(indays)is
givenby
N= 0.84A
0.2
3.SimplybydrawingastraightlineAE,fromthepointofriseto
thepointEonthehydrograph,‘N’daysafterthepeak.

17. 17
ComputationofDirectSurfaceRunoff(DSR)fromaStorm
Enclosedfigureshowsthefloodhydrographofastormwithflood
ordinatesatdifferenttimeintervalΔ
t.“Fromthefloodhydrograph,
separatethebaseflowbyanyoneofthemethodsdescribedearlier”.
Letthe“BaseFlow”isseparatedbysimplestraightlinemethodand
DirectSurfaceRunoff(DSR)Hydrographisdrawn(figureenclosed).
LetQ
1,Q
2,Q
3,Q
4,….,Q
n-2,Q
n-1,Q
naretheordinatesofDirectSurface
Runoff(DSR)HydrographatdifferenttimeintervalΔ
t.
Findtheareaunderthe(DSR)Hydrograph,whichwillrepresentthe
volumeof(DSR);
AreaunderthecurveAPB=VolumeofDSR
=A
1+A
2+A
3+A
4+…..+A
n-2+A
n-1+A
n
=1Q
1Δ
t+[Q
1+Q
2]Δ
t+[Q
2+Q
3]Δ
t+[Q
3+Q
4]Δ
t+…+[Q
n+2+Q
n+1]Δ
t
2 2 2 2 2
+[Q
n-1+Q
n]Δ
t+1Δ
t
2 2
HYDROGRAPH ANALYSIS

18. 18
=[1QΔ
t+Q
1Δ
t]+[Q
2Δ
t+Q
2Δ
t]+[Q
3Δ
t]+[Q
4Δ
t+Q
4Δ
t]+…+[Q
n-2Δ
t+Q
n-2Δ
t]
2 2 2 2 2 22 2 2
+[Q
n-1Δ
t+Q
1Δ
t]+[Q
nΔ
t+Q
nΔ
t]
22 2 2
=[(Q
1+Q
2+Q
3+Q
4+….Q
n-2+Q
n-1+Q
n)]Δ
t
=∑QΔ
t
Q=TotalvolumeofDirectSurfaceRunoff.If‘Q’inm
3
/sec,&Δ
tinhr.
VolumeofDSR=∑QΔ
tm
3
x(60x60)sec
sec
=∑QΔ
tm
3
x(60x60)m
3
If‘A’istheareaofthecatchmentinkm
2
,A=Ax10
6
m
3
DSRincm={[(60x60)∑QΔ
t]x100}cm
Ax10
6
DSR=0.36∑Qxt(cms)
A
Thus,DSRvolume(depthincm)=Rainfallexcessornetrainfall
HYDROGRAPH ANALYSIS

19. 19
FloodHydrographofaSingleStorm
HYDROGRAPH ANALYSIS

20. 20
CalculationofDirectSurfaceRunoff(DSR)Hydrograph
(Depth)
HYDROGRAPH ANALYSIS

21. 21
Example:-
CalculateDirectSurfaceRun-offforRainfallexcessfromaStorm
Hydrographfromthefollowingdata.AssumeAreaofCatchmentas
30km
2
HYDROGRAPH ANALYSIS
Date and TimeOrdinate of Hydrograph
Total Q (Cumecs)
Base Flow
(Cumecs)
Direct Runoff
(Cms)
1 2 3 4
14.08.2012
0500 14 14 0
0800 25 12 13
1100 51 11 40
1400 65 10 55
1700 54 11 43
2000 28 13 15
2300 14 14 0
∑Q = 166

22. 22
HYDROGRAPH ANALYSIS
Solution
Findthe“ordinatesofstormHydrograph”,representingtotal
dischargeQatagiventimeinterval,say‘t’hours.
Separatethe“BaseFlow”byanyofthemethods.Findthe
ordinatesofthebaseflowatthesametimeinterval.
Findtheordinatesof“DirectRun-off”bysubtractingthe
ordinatesofbaseflowfromtotaldischargeordinates.
TheDirectSurfaceRun-off(depthincm)isfoundfromthe
expression.

23. 23
HYDROGRAPH ANALYSIS

24. UnitHydrograph
UnitHydrograph(UH)is“definedastheHydrographofsurfacerunoffofa
catchmentarearesultingfromunitdepth (usually1cm)ofrainfall
excessornetrainfalloccurringuniformlyoverthebasinandatuniformrate
foraspecifiedduration”.
EffectiveRainfall:alsoknownasexcessrainfallisthatpartoftherainfallthatbecomes
directrunoffattheoutletofthewatershed.Itisthusthetotalrainfallinagivenduration
fromwhichabstractionssuchasinfiltrationandinitiallossesaresubtracted.
UnitHydrographisalinearmodelofthecatchmentwhichisusedtofindout
thevolumeofDSRdueto1cmofdirectsurfacerunoffor1cmofrainfall
excess.Thisisalwaysconstantforthecatchmentsinceareaofthe
catchmentisconstant.
Ifrainfallcomestothecatchmentproducing2cmofrainfallexcess,“the
ordinatesoftheDSRwillbetwiceasgreatoftheUnitHydrograph(UH)
ordinatesandvolumeofDSRwillbetwotimethevolumeofDSRofunit
hydrograph”.
HYDROGRAPH ANALYSIS

25. AssumptionsinDerivationofUHTheory
i.Therainfallisof“uniformintensity”withinitsspecifiedduration.
ii.Theeffectiverainfallis“uniformlydistributed”throughoutthe
wholeareaofdrainagebasin.
iii.“ThebaseoftimedurationofHydrographofdirectrunoffdueto
effectiverainfallsofunitdurationisconstant”.Baseperiodof
Hydrographofdifferentrainfallintensitiesremainapproximately
same.Asrepresentedinenclosedfigure.
iv.TheordinatesofDSRHydrograph“duetonetrainsofdifferent
intensitiesbutsamedurationareproportional”.
v.AUnitHydrographreflectsallthecombinedphysical
characteristicsofthebasin.
HYDROGRAPH ANALYSIS

26. Limitations
•Forunithydrographanalysisstormsofshortduration
shouldbeselectedsinceuniformintensityoverlong
durationislesslikelytooccur.
•UH’scanbeeffectivelyappliedtodrainagebasinswith
smallarea,sinceuniformarealdistributionofrainfallover
largeareasislesslikelytooccur.
•Basinswithoddshapesparticularlythosewhicharelong
andnarrowwillcommonlyhaveunevenrainfalldistribution
andhenceunithydrographarenotwelladoptedtosuch
basins.
•Theunithydrographmethodcanbeappliedwhenthe
majorportionoftheprecipitationisintheformofsnow

27. DerivationofUHfromasimpleFloodHydrograph–
(IsolatedStorm)
Step1FromthegivenfloodHydrograph,“separatethebaseflow”by
anyoneofthemethods.Mostcommonlyusedmethodto
drawastraightlinewithoutmucherrorforsimplicity(Figure
enclosed)
Step2DeterminethevolumeofDSRHydrographbytheformula;
“VolumeofDSR=∑QΔ
t
”
Step3Dividethisvolumeby“knownAreaofCatchment”togetDSR
volume(depthincm)i.e.,“netrainfallorrainfallexcess”.
Step4DividetheordinatesofDSRbythedepthofDSRHydrograph
toobtainordinatesofUH.
Step 5 Plot the ordinates of UH of the catchment as per enclosed
figure.
HYDROGRAPH ANALYSIS

28. UnitHydrographDerivation
HYDROGRAPH ANALYSIS

29. Example-I
HYDROGRAPH ANALYSIS
CalculateandDrawa“UnitHydrograph”fromaStormHydrograph,resulting
fromaCatchmentAreaof25km
2
.Thedataisshowninthefollowingtable:

30. HYDROGRAPH ANALYSIS
DirectRunoff=0.36(∑Qxt)=0.36x822x2=23.7cm
A 25

31. HYDROGRAPH ANALYSIS
UnitHydrographfromaSingleFloodHydrograph

32. Example-II:-(UH)fromaSingleFloodHydrograph(Isolated)
HYDROGRAPH ANALYSIS

33. LimitationsandUsesofUHTheory
Limitations
i.Similarrainfalldistributionfromstormoveralargeareaisrare.
HenceUHtheoryissuitedtocatchmentareaunderabout500km
3
(=2000sq.miles)
ii.Oddshapedbasinsparticularlythosewhicharelongandnarrow,
commonlyhaveveryunevenrainfalldistributionandhenceUH
theoryforsuchbasinsisnotmuchsuitable.
iii.Inmountainousregions,subjecttoorographicrainfall,aerial
distributionisveryuneven,butthepatterntendstoremainthe
samefromstormtostorm,andUHtheorymaynotbe
successfullyapplied.
iv.Theunithydrographmethodcannotbeappliedwhenan
appreciableportionofthestormprecipitationfallsassnow.
v.Thecatchmenthavinglargestoragelikereservoir,lake,lowareas,
etc.affectthelinearrelationshipandhencetheorycannotbe
applied.
vi.Ifthevariationofbaseperiodandpeakflowvarymorethan+/-
10%,theoryappliedisnotgenerallyaccepted.
HYDROGRAPH ANALYSIS

34. LimitationsandUsesofUHTheory
Uses
i.AstheUHisa“linearmodelofthecatchment”,itisusedto
determinerunoffHydrographoftheCatchmentevenfor
extrememagnitudefor“thecalculationofpeakdischargeto
designtheHydraulicStructures”.
ii.Itcanalsobeusedforfloodforecastingandwarning.
iii.Basedonrainfallrecords,“itisusedforextensionofflood
records”.
HYDROGRAPH ANALYSIS

35. CALCULATION OF STORM
HYDROGRAPH
FROM
THE GIVEN UNIT HYDROGRAPHS
OF VARIOUS RAINFALL
INTENSITIES
HYDROGRAPH ANALYSIS

36. Applicationofthe(UH)Theoryforthe“ConstructionofaFlood
HydrographResultingfromRainfallofSingleDuration”
TheUnitHydrographcanbeusedtoconstructa“FloodHydrograph“
resultingfromrainfallofthe“sameunitdurationforwhichtheUnit
Hydrographisavailable”.
ThenumberofUnitHydrographsforagivendrainagebasinis
theoreticallyinfinitesincetheremaybeoneforeverypossible
durationofrainfallandeverypossibledistributionpatterninabasin.
PracticallyonlyalimitednumberofUnitHydrographscanbeused
foragivenbasin.“TheUnitHydrographselectedforcomputingthe
floodHydrographshouldbecorrespondingtothestormoflike
durationandpattern”.
However,atoleranceofasmuchas25%oftheUnitHydrograph
durationcanordinarilybeacceptedwithoutmuchseriouserror.Thus
a6-hoursUnitHydrographmustbeappliedforstormsof4.5to7.5
hoursduration.
Alternatively,UnitHydrographhavingasimilarrangeindurationmay
beaveragedtoobtainanaverageUnitHydrograph.
HYDROGRAPH ANALYSIS
Case-I

37. Procedure
ThecalculationsforthestormHydrographcorrespondingto‘n’cmof
rainfall-excessaredoneinthetabularformasperenclosedtable;
Directrunoffordinates=(ordinatesofUnitHydrograph)x‘n’cm
Step-I:Writedownthe“givenhourlyordinates”(Discharge)of
UnitHydrograph.
Step-II:MultiplytheordinatesofUnitHydrographwith‘n’cmof
Rainfall.
Step-III:Listoutthegivenhourly“baseflow(m
3
/sec)”
Step-IV:Findoutthetotalstormordinatesi.e.=Step-II+Step-III
Theaboveprocedureiselaboratedbytheenclosedtable.Throughan
example(CalculationofStormHydrographResultingfrom8cm
Rainfall.
HYDROGRAPH ANALYSIS

38. HYDROGRAPH ANALYSIS
4 5
Example:-CalculateStormHydrographof8cmRainfall

39. Case-II
ApplicationofUnitHydrographTheory“fortheConstructionofa
FloodHydrographResultingfromtwoormorePeriodsof
Rainfall(MultiDurationRainfall)”fromaSingleUH
AUnitHydrographofsomespecificunitdurationcanalsobe
utilizedforconstructionoffloodHydrographresultingfromthe
“rainfalllastingforalongerduration”.
Theessentialcondition,however,isthatthestormpatternshould
bethesameasthatfortheUnitHydrograph.
Asanexample,leta3-hoursUnitHydrographisavailable,andit
isrequired“tocomputethefloodHydrographresultingfroma
rainfalllastingfor9-hourswithvariableintensitiesofrainfall”.
Theintensityrateshaving“n1cm/3-hours”forthefirstperiodof
3-hours,“n2cm/3-hours”forthesecond3-hours,andthatof
“n3cm/3-hours”forthelast3-hours.
HYDROGRAPH ANALYSIS

40. Step-I
Thestormisdividedinto3parts,andthefloodHydrographof
eachpartiscomputedseparatelyandadded.
Step-II
TheHydrographsforthesecondpartofthestormstarts3hours
laterthanthatforthefirstpart.
Step-III
Similarly,theHydrographforthethirdpartofthestormstarts6
hourslaterthanthatforthefirst,or3hourslaterthanthatforthe
secondpart.
Theaboveprocedureisillustratedthroughtheenclosedexample.
HYDROGRAPH ANALYSIS
Procedure

41. Example:-
Findtheordinatesofa“stormHydrographresultingfroma3hours
stormwithrainfallof2.0,6.75and3.75cmsduringsubsequent3
hoursintervals”.TheordinatesofUnitHydrographaregiveninthe
followingtable.Assumeaninitiallossof5mm,infiltrationindexof
2.5mm/hourandbaseflowof10cumecs.
HYDROGRAPH ANALYSIS
Ordinates of given Unit Hydrograph
Hours03060912151821240306091215182124
Ordinate of
UH
011036550039031025023517513095654022100

42. Solution:-
i)Rainfallexcessduringthefirstthreehours
=20–(2.5x3)–5=7.5mm=0.75cm
ii)Rainfallexcessduringthesecondthreehours
=67.5–(3x2.5)=60mm=6cm.
iii)Rainfallexcessduringthelastthreehours.
=37.5–(3x2.5)=30mm=3cm
TheRainfallexcessasratiooftheunitRainfallof1cmduringthe
subsequent3hoursintervalsare0.75,6and3.
ThecomputationsofRunoffdueto0.75cmrainfallexcesswill
startfrom03hours.Thecomputationsofrunoffdueto6cm
rainfallexcesswillstartfrom6hours.Lastly,thecomputationsof
runoffdueto3cmrainfallexcesswillstartfrom9hours.
“Theaboveprocedureisillustratedintheenclosedtable”.
HYDROGRAPH ANALYSIS

43. Table:-
HYDROGRAPH ANALYSIS

44. FloodHydrographResultingfromaStormofLongerDuration
HYDROGRAPH ANALYSIS

45. Example:-
CalculationofStormHydrographResultingfromSingle
UnitHydrographofVariousRainfallIntensities
HYDROGRAPH ANALYSIS
Contd…..

46. HYDROGRAPH ANALYSIS

47. Case-III
S-Hydrograph(S-Curve)
S-HydrographorS-CurveisaHydrographwhichisproducedbya
“continuouseffectiverainfallataconstantrateforindefinite
period”.
Itisa“continuousrisingcurve”,intheformofletter‘S’,till
equilibriumisreached.Atthetimeofequilibrium,“itwill
representaconstantrateofcontinuouseffectiverainfall,sayR
o
cmperhour”.
Atthetimeofequilibrium,“theS-Curvewillrepresentarunoff
dischargeasunder”;
Q
o=(Ax100x100)R
o
100x3600
=AR
ocumec
36
(WhereAisthecatchmentareainhectares)
HYDROGRAPH ANALYSIS
Contd…

48. Ifthecatchmentarea‘A’isin“squarekilometers”,thedischarge
representedbyS-Curve,atthetimeofequilibriumisgivenby;
Q
o=(Ax1000x1000)R
o
100x3600
=(AR
0)x100(cms)
36
=2.778AR
o(cms)
(‘A’=Areaofcatchmentinkm2andR
o=Constantrateof
continueseffectiveRainfall.)
TheS-HydrographorS-Curveisconstructedby“addingtogether
numberofUnitHydrographsofunittimeduration(T
0)spacedata
unittimeduration(T
0)(i.e.,durationofeffectiverainfall).
“ThisisillustratedintheenclosedexamplewereinS-Curvehas
beendrawnfor6hoursUnitHydrograph.Areaofbasinis311
km
2
”.
HYDROGRAPH ANALYSIS

49. HYDROGRAPH ANALYSIS
ComputationofS-HydrographfromSuccessiveUnitHydrograph
Contd…

50. HYDROGRAPH ANALYSIS
Thisdischargeof144cumecswillbeachievedintheabovetableat36
hours(whichisequaltobaseperiod–T
0hours.)

51. HYDROGRAPH ANALYSIS
DerivationofS-HydrographfromSeriesofUnitHydrograph

52. CALCULATION OF UNIT
HYDROGRAPH
FROM
THE GIVEN UNIT HYDROGRAPHS
OF VARIOUS INTENSITIES
HYDROGRAPH ANALYSIS

53. ConstructionofUnitHydrographofDifferentUnitDuration
fromtheaUnitHydrographofgivenUnitDuration
UnitHydrographmaybeofdifferentduration‘D’.Ifaunit
hydrographof2hrs.durationavailable,unithydrographof4hrs.
duration,6hrs.duration,8hrs.duration,etc.maybeobtainedi.e.,
theunithydrographtobederivedisanintegralmultiple.Insuch
cases,durationsfrom2hrs.to4hrs.,6hrs.etc.canbedoneby
methodofsuperposition.
However,iftheDurationofUnitHydrographtobederivedisless
thandurationofknownUnitHydrograph,“thismethodof
superpositionwillnotholdgood”.Thus,UnitHydrographof
differentdurationmaybederivedbythefollowingtwomethods.
i)MethodofsuperpositionwhendurationofUHtobederivedis
2times,3timesor4timesofthedurationofknownUH.
ii)S-Curvemethod(Summationhydrographmethod)when
durationofUHtobederivedislessthanthedurationofthe
knownUH.
HYDROGRAPH ANALYSIS
Case-I

54. UnitHydrographofDifferentDurations
Phase-A:-
ConstructionofLongerperiodUnitHydrographfromagiven
UnitHydrographofShorterUnitPeriod/Duration.
MethodofSuperposition
i)Asshown(figureenclosed)D-hrUHisplotted(Curve-1)
ii)AlsoplottheUHlaggedbyDhrs.(Curve-2)
iii)AddthetwoUnitHydrographsandplotit(Curve-3)
iv)DivideCurve-III,i.e.DSRHydrographby2Ddurationtoget
thecurveshownbydottedline,i.e.(Curve-4)
Itisnotedthatbaseperiodof2-D-hrUHshownbydottedline
increasesbyD-hrsfromthegivenUHofThrsbaseperiod.
Therefore,thepeakof2-D-hrsUHwilldecreaseasthebase
periodisincreasedfromTto(T+Dhrs)
HYDROGRAPH ANALYSIS

55. Example–UnitHydrographofDifferentDurations
A4-hrUHofdifferentdurationsisshowninthefollowingtable.Derive
the8hrUnitHydrograph.
HYDROGRAPH ANALYSIS
Column(5)givestheordinatesof8-hrunitHydrographderivedfrom
column(4)andunitUHincolumn(2).Thepeakofthe8-hrUHis
reducedto16m
3
/secfrom20m
3
/secasthebaseperiodisincreased
from20to24hrs.

56. MethodofSuperposition
HYDROGRAPH ANALYSIS

57. Example-II:-MethodofSuperposition
HYDROGRAPH ANALYSIS

58. Case-II
UnitHydrographofDifferentDurations-S-CurveMethod
S-Curve(SummationCurve),alsoknownasS-Hydrographisa
Hydrographproducedbya“continuouseffectiverainfallofunit
depthataconstantrateforindefiniteperiod”.Itisacurve
obtainedbysummationofaninfiniteseriesofUnitHydrographs
eachlaggedbyD-hrswithrespecttoprecedingone.
ItisshownthatwhenaUHof‘n’‘D’durationisrequiredwhere‘n’
iswholenumberlike2,3,4etc.,methodofsuperpositionserves
thepurpose.If‘n’isin-fraction,thenS-Curvemethodisrequired.
Asanexample,fromUHof4hrs.duration,todevelopUHof2hrs.
durationcannotbedevelopedbytheperviousmethodof
superposition.Insuchsituation,“S-Hydrographisconstructed.
WhichisusedtofindtheUHofdesiredduration”.
Asshown(figureenclosed),S-Hydrographiscontinuouslya
risingcurvewhichultimatelyattainsaconstantvaluewhen
equilibriumdischargeisreached.
HYDROGRAPH ANALYSIS

59. UnitHydrographofDifferentDurations
UnitHydrographcanbederivedasunder;
Step1“ConstructtheS-Curve”fromthegivenUnitHydrographof
knowntimedurationD-hrs.
Step2“Thenadvanceoroffset”thepositionofalltheordinatesof
“S-Hydrograph”foraperiodequaltothedesireddurationof
D
0hrs.ofunknownUH.“NamethisS-Hydrographasoffset
Hydrograph”.
Step3Findthe“Difference”oftheordinatesofOriginalS-Curveand
“OffsetHydrograph”.
Step4“Dividethiseachdifference”by(D
0/D)togettheordinatesof
newUHofD
0hrs.duration.
HYDROGRAPH ANALYSIS

60. S-HydrographorS-Curve
HYDROGRAPH ANALYSIS

61. HYDROGRAPH ANALYSIS
Letitberequiredtoobtaina“UnitHydrograph”ofunitperiodt
0froma
givenUnitHydrographofunitperiod.T
0,“wheret
0canbeeithergreater
orsmallerthanT
0”.Forthis,theS-Hydrographmethodwillbeused.
FromthegivenUnitHydrographofunitperiodT
0,“S-Curveisderived”.
ThisS-CurvewillrepresentaconstanteffectiverainfallofR
0=1/T
0
cm/hour.
“Anoffsetcurveisthendrawnbyadvancingoroffsettingthepositionof
originalS-Curve”foraperiodequaltothedesiredunitperiodtohours.
“ThedifferencebetweentheordinatesoforiginalS-Curveandtheoffset
S-CurvedividebytheR
0t
0“willgivetheordinateofthedesiredUnit
Hydrograph.
Thus,foranytimeperiodt,ifthedifferenceordinatesofthetwoS-
CurvesisΔy,thentheordinateofthedesiredUnitHydrographoft
0unit
period.
Δy=Δy =Δy.T
0
R
0t
0(1/T
0)t
0 t
0
Phase-B:
ConstructionofShorterorLongerPeriodUnitHydrograph
fromagivenUnitHydrograph

62. HYDROGRAPH ANALYSIS
Example-I
DerivationofUnitHydrographoft
0(=3hours)unitdurationfromthe
givenUnitHydrographofdurationT
0(=6hours)

63. HYDROGRAPH ANALYSIS
ConstructionofShorterorLongerPeriodofUnitHydrograph
fromagivenUnitHydrograph

64. Example-II:-ofS-CurveMethod
Givenbelowaretheordinatesof4hrsUHofabasin.
Derive2hrsUHfromitusingS-CurveMethod.
HYDROGRAPH ANALYSIS

65. HYDROGRAPH ANALYSIS

66. HYDROGRAPH ANALYSIS

67. Case-III
DerivationofUHfromComplexStorm
Practically,“itisnotalwayspossible“tohavesuchisolated
storms”.StormshavingdifferentrainfallexcesslikeR
1,R
2andR
3
mayoccur.“Suchstormsofdifferentrainfallexcessarecalled
complexstorm”.
Assume3stormswhichcanproducerainfallexcessR
1,R
2and
R
3.TheHydrographofthese3storms(afterdeductingbaseflow)
isshowninfigureenclosed.
LetQ
1,Q
2,Q
3,…..Q
naretheknownordinatesofcomplexstormas
perfigureenclosedandU
1,U
2,U
3,…..U
nareordinatesofUnit
Hydrographwhicharetobedetermined.R
1,R
2andR
3areknown
rainfallexcessesduetocomplexstorm,whicharealsoknown.
Then;
HYDROGRAPH ANALYSIS

68. DerivationofUHfromComplexStorm
Q
n=R
nU
1+R
n-1U
2+R
n-2U
3+….,
When
n=1,Q
1=R
1U
1
(i.e.Q
1andR
1areknown,U
1isdetermined)
n=2,Q
2=R
2U
1+R
1U
2
(i.e.Q
2,R
2,U
1,R
1areknown,U
2isdetermined)
n=3, Q
3=R
3U
1+R
2U
2+R
1U
3
(i.e.Q
3,R
3,U
1,U
2,R
1,R
2areknown,U
3isdetermined)
n=4,Q
4=R
4U
1+R
3U
2+R
2U
3+R
1U
4,
R
4U
1iszero,sinceno4
th
rainfallisconsidered
SinceQ
4,R
3,R
2,R
1,U
2,U
3areknown,U
4canbedetermined
Thus,allordinateofUnitHydrographU
1,U
2,U
3,U
4,……U
ncanbe
determinedandresultingUnitHydrograph(UH)canbeobtained.
HYDROGRAPH ANALYSIS

69. DerivationofUHfromComplexStorm
HYDROGRAPH ANALYSIS

70. Derivation(UH)fromComplexStorm
Example
DrawtheUnitHydrographfromthecomplexstormhavingthedata
givenbelow;
HYDROGRAPH ANALYSIS
Solution
NetRainfallareDSRindepth1
st
hr=4–5ΦIndex=4–2x1=2cm
2
nd
hr=3–2x1=1cm
3
rd
hr=2.5–2x1=0.5cm
Time (Hrs) 012345678910111213
UH Ordinates
m3/sec
0 5811096532614 8 5 4 31.51 0
ComputethestormHydrographresultingfromthreehourstormrainfall
asunder:-
Time 1
st
hr 2
nd
hr 3
rd
hr
Rainfall depth (cm)4 3 2.5
TakeΦ-indexas2cm/hrandassumeabaseflowof2m3/sec.

71. ExampleofDerivation(UH)fromComplexStorm
HYDROGRAPH ANALYSIS