78137277 Lesson 3 Unit Hydro Graph Method Theory

LESSON 3LESSON 3LESSON 3LESSON 3Unit Hydrograph MethodUnit Hydrograph MethodUnit Hydrograph Method Unit Hydrograph Method

and Theoryand Theoryand Theoryand Theory

Monthly Rainfall DistributionMonthly Rainfall Distribution

Average AnnualAverage Annual PrecipitationPrecipitation

Basin Recharge and RunoffBasin Recharge and RunoffBasin Recharge and RunoffBasin Recharge and Runoff InterceptionInterception –– water so retained as some portion ofwater so retained as some portion ofInterception Interception –– water so retained as some portion of water so retained as some portion of

precipitation are intercepted by leaves and precipitation are intercepted by leaves and vegetation stemsvegetation stemsgg

Depression storage Depression storage –– includes water retained as includes water retained as puddles in surface depressionpuddles in surface depressionp pp p

Soil moisture Soil moisture –– held as capillary water in smaller held as capillary water in smaller pore spaces of the soil or as hygroscopic water pore spaces of the soil or as hygroscopic water po e spaces o t e so o as yg oscop c atepo e spaces o t e so o as yg oscop c ateadsorbed on the surface of soil particlesadsorbed on the surface of soil particles

Basin recharge Basin recharge –– portion of precipitation that does not portion of precipitation that does not gg p p pp p pcontribute to contribute to streamflowstreamflow or groundwater or groundwater

(i.e., interception, depression storage & basin recharge)(i.e., interception, depression storage & basin recharge)

Basin Recharge and RunoffBasin Recharge and RunoffBasin Recharge and RunoffBasin Recharge and Runoff

Rainwater or Snow Melt

Overland Flow VerticalOverland Flow(Surface Runoff)

Interflow Vertical Percolation

Path of rainwater or snowmelt to a streamPath of rainwater or snowmelt to a stream((exclusive of water withheld as basin rechargeexclusive of water withheld as basin recharge)%)%

Basin Recharge and RunoffBasin Recharge and RunoffBasin Recharge and RunoffBasin Recharge and Runoff Direct Runoff (DRO)Direct Runoff (DRO) –– overland flow and interflowoverland flow and interflowDirect Runoff (DRO) Direct Runoff (DRO) –– overland flow and interflowoverland flow and interflow BaseflowBaseflow –– water flowing in a stream that is derived from water flowing in a stream that is derived from

groundwatergroundwatergroundwatergroundwater Effluent Streams Effluent Streams –– stream channels that have perennial stream channels that have perennial

flow; below groundwater tableflow; below groundwater tableflow; below groundwater tableflow; below groundwater table


Basin Recharge and RunoffBasin Recharge and RunoffBasin Recharge and RunoffBasin Recharge and Runoff Direct Runoff (DRO)Direct Runoff (DRO) –– overland flow and interflowoverland flow and interflowDirect Runoff (DRO) Direct Runoff (DRO) –– overland flow and interflowoverland flow and interflow BaseflowBaseflow –– water flowing in a stream that is derived from water flowing in a stream that is derived from

groundwatergroundwatergroundwatergroundwater Effluent Streams Effluent Streams –– stream channels that have perennial stream channels that have perennial

flow; below groundwater tableflow; below groundwater tableflow; below groundwater tableflow; below groundwater table Influent Streams Influent Streams –– stream channels which go dry if stream channels which go dry if

much time elapses between rainsmuch time elapses between rains i ei e intermittentintermittentmuch time elapses between rains, much time elapses between rains, i.e.,i.e., intermittent intermittent streamsstreams


The HyetographThe HyetographThe HyetographThe Hyetograph Graph of Rainfall Rate (Graph of Rainfall Rate (in/hr or mm/hr) in/hr or mm/hr) vsvs Time Time

(hr) at a single gage location(hr) at a single gage location(hr) at a single gage location(hr) at a single gage location

Usually plotted as a bar chart of gross RFUsually plotted as a bar chart of gross RF

Net Rainfall is found by subtracting infiltrationNet Rainfall is found by subtracting infiltration

Integration of Net Rainfall over time = Integration of Net Rainfall over time =

Direct Direct Runoff Volume Runoff Volume (DRO) ((DRO) (in or mm) in or mm) over a over a

WatershedWatershedWatershedWatershed

Mass Curves & RainfallMass Curves & RainfallMass Curves & Rainfall Mass Curves & Rainfall HyetographsHyetographsy g py g p

Instantaneous HydrographInstantaneous HydrographInstantaneous HydrographInstantaneous Hydrograph

• Rainfall falls over the basin• Intensity I reaches the outlet -Ii y

response based on travel time• Produces a total storm; responseS ll B iS ll B i Produces a total storm; response

hydrograph as shownLittl d l d t

Small BasinSmall Basin

• Little delay and no storage • The above only occurs in small QQi i = I= Iii AA

urban basins or parking lots

Unit Hydrograph (UH) MethodUnit Hydrograph (UH) MethodUnit Hydrograph (UH) MethodUnit Hydrograph (UH) Method

• Linear transform method• Converts complex rainfall to Pi pstreamflow at outlet

• Produces a total storm

i

Uj

• Produces a total storm hydrograph from given UHU d i l t h d• Used in complex watersheds

• Each subarea is uniqueQ

• Storage effects consideredT

Qn = Pn U1 + Pn-1 U2 + Pn-2 U3 + … +P1 Uj

TimeTime AreaAreaTimeTime--Area Area MethodMethodMethodMethod

• Watershed travel times

• Time Area Graph

• Rainfall Intensities• Rainfall Intensities

• Add and Lag Method

• Resulting Hydrograph

Time Area HydrographTime Area HydrographPeak Flow at QPeak Flow at Q22

Time Area HydrographTime Area Hydrograph

• Q1 = P1 * A1

• Q2 = P2*A1 + P1*A2

• Q =P *A + P *A• Q3 =P3*A1 + P2*A2

+ P1*A3

• And So Forth

At time step 2, PAt time step 2, P22 over Aover A11 and Pand P11 over Aover A22arrive at the same time arrive at the same time --

Similar for time step 3 with 3 contributorsSimilar for time step 3 with 3 contributors

Time Area HydrographTime Area HydrographTime Area HydrographTime Area Hydrograph

Example. Example. Develop the hydrograph for the watershed area Develop the hydrograph for the watershed area given below for a rainfall intensity of 0.5 in/hr falling given below for a rainfall intensity of 0.5 in/hr falling uniformly for 4 hoursuniformly for 4 hoursuniformly for 4 hours.uniformly for 4 hours.



Time

(hr)

Hyetograph Ordinate

R1:Rn

Basin No. Time to Gage Basin Area A1:An

(ac)( ) (ac)01 0.5 A 1 1002 0.5 B 2 2003 0.5 C 3 3004 0 5 D 4 1004 0.5 D 4 1005 0.566789

The HydrographThe HydrographThe HydrographThe Hydrograph

Graph of discharge vs. time at a single locationGraph of discharge vs. time at a single location

Rising Limb, Crest Segment, Falling LimbRising Limb, Crest Segment, Falling Limb, and , and

R iR iRecession Recession

Base Flow is usually subtracted to yield DROBase Flow is usually subtracted to yield DROBase Flow is usually subtracted to yield DROBase Flow is usually subtracted to yield DRO

Peak gives the maximum flow rate for the eventPeak gives the maximum flow rate for the eventgg

Area under curve yields volume of runoff (Area under curve yields volume of runoff (in or in or

mmmm))

Hydrograph Hydrograph -- Watershed Flow Watershed Flow y g py g pResponse to RainfallResponse to Rainfall

Peak Flow and time to peak relate to area/shape

Peak Flow

Lag or time to peak

of watershed Area under curve is the

Hydrograph

low

Peak Flow

RFRFArea under curve is the volume of DRO Time Base is the time that

Volume of RunoffDRO

Out

fl

Time Base is the time that flow exceeds baseflow Time to peak or Lag is

Time Base

Time to peak or Lag is measured from center of mass of rainfall pattern

Time

mass of rainfall pattern

Rainfall and Runoff ResponseRainfall and Runoff ResponseRainfall and Runoff ResponseRainfall and Runoff ResponseFl M d

2000 0.60

Flow Measuredfrom USGS Gage 403Inside Harris Gully

1400

1600

1800

s ) 0.40

0.50

800

1000

1200

Outfl

ow (c

fs

0.30 Rain

fall (in

)

QQ RFRF

Rainfall Measuredfrom USGS Gage 400

400

600

0.10

0.20

from USGS Gage 400at Harris Gully Outlet

0

200

6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00Time

0.00

i i i ii i i iFebruary 12, 1997 on Harris Gully

Net Rainfall * Area = integration of direct runoff hydrographNet Rainfall * Area = integration of direct runoff hydrograph

VolVol under blue bars * Area = Volume under red line (hydrograph)under blue bars * Area = Volume under red line (hydrograph)

Hydrograph Hydrograph Flood RoutingFlood Routingf P i t 1 t P i t 2f P i t 1 t P i t 2from Point 1 to Point 2from Point 1 to Point 2

O l d fl i tOnce overland flow arrives at a stream - becomes channel flow

Channel flow begins as low flow and increases with accumulation

Flood wave moves downstream at a predictable velocityat a predictable velocity

Subarea flows contribute to theSubarea flows contribute to the flood wave along the stream

Wave maximum near outlet**

Hydrograph Hydrograph Flood RoutingFlood Routingfffrom from Pt 1 to Pt 4 in the Stream Pt 1 to Pt 4 in the Stream

G and F to Pt 1G and F to Pt 1

211

G and F to Pt 1G and F to Pt 1Pt Pt 1 to Pt 1 to Pt 22D to Pt 2D to Pt 2 2D to Pt 2D to Pt 2Pt Pt 2 to Pt 32 to Pt 3EE, C, and B to Pt3, C, and B to Pt3

33

, ,, ,Pt Pt 3 to Pt 43 to Pt 4A A to Pt 4to Pt 4

4ComputeCompute

4Final hydrographFinal hydrograph

Hydrograph Flood Routing to Hydrograph Flood Routing to N t D t L tiN t D t L tiNext Downstream LocationNext Downstream Location

Crest

RisingFalling Limb

1

Recession

RisingLimb

Limb2

Time Base of Hydrograph

Flood wave is Flood wave is laggedlagged and and attenuatedattenuated as it moves downstreamas it moves downstream

Brays BayouBrays BayouBrays Bayou Brays Bayou High FlowHigh Flow

Kissimee RiverKissimee River -- The EvergladesThe EvergladesKissimee River Kissimee River The EvergladesThe Everglades

II--45 over Clear Creek45 over Clear Creek -- 19791979II 45 over Clear Creek 45 over Clear Creek 19791979

California California -- TemeculaTemecula

Hurricane Katrina Hurricane Katrina -- Most Most Damaging Storm in U S HistoryDamaging Storm in U S HistoryDamaging Storm in U.S. HistoryDamaging Storm in U.S. History

MississippiMississippiMississippiMississippi

New OrleansNew Orleans

$100 billion loss$100 billion loss

Surface Flow DistributionSurface Flow DistributionSurface Flow DistributionSurface Flow Distribution

Horton’s Infiltration ConceptHorton’s Infiltration Conceptppf(t) = Rate of water loss into soilf(t) = Rate of water loss into soilf = fc + (fo - fc) exp (-kt)

fc = final rate value

fo = initial rate value

K d tK = decay rate

Can integrate to getCan integrate to get

F(t) = Vol of infiltrationF(t) Vol of infiltration

Horton’sHorton’s EquationEquationHorton s Horton s EquationEquation

index Methodindex Method index Methodindex Method• Assumes constant• Assumes constant rate over time of rainfall

• Volume above line is DRO

• Volume below line isVolume below line is F(t)C t d b t i l• Computed by trial and error

Example ofExample of IndexIndexExample of Example of IndexIndex

DRODRO

VOL Infiltration F(t)( )

Example ofExample of IndexIndexExample of Example of IndexIndexA 4 9 i f DRO f 560 B iAssume 4.9 in of DRO from a 560 acre BasinSet up a general Eqn for indexindex

2(1.4 - +3(0.7-

Find by trial and error by assuming a value and solvingTry = 1.5 in/hr; And it only accounts for 0.8 x 3 = 2.4 in

fof DRO0.5 in/hr yields 9.0 in of DRO - too much DRO 1.0 in/hr or 2(.4) +3(1.3)+2(.1) = 4.9 inches

M fi ld DM fi ld D L k T iL k T iMansfield Dam Mansfield Dam -- Lake TravisLake TravisUnit HydrographsUnit HydrographsS Curve Method Synthetic UHSynthetic UHMulti-period stormsUH Applications Kinematic Wave

Hydrograph computed at outlet of Hydrograph computed at outlet of each subareaeach subarea

Hydrographs routed to the outlet Hydrographs routed to the outlet of the watershedof the watershed

Hydrographs routed thru one reach of Hydrographs routed thru one reach of the watershedthe watershed

I – Q = dS/dt

Di t ib ti f R i f llDi t ib ti f R i f llDistribution of RainfallDistribution of Rainfall

•• InfiltrationInfiltration

•• Detention StorageDetention Storage

•• Depression StorageDepression Storage

•• DirectDirect RunoffRunoff•• Direct Direct RunoffRunoff

H d h R l tiH d h R l tiHydrograph RelationsHydrograph RelationsNet RainfallNet Rainfall

Rising LimbRising LimbRising LimbRising Limb

CrestCrest

Falling LimbFalling Limb

RecessionRecession

Base FlowBase FlowBase FlowBase Flow

Direct Runoff DRODirect Runoff DRO

Base Flow MethodsBase Flow MethodsBase Flow MethodsBase Flow Methods•• Straight LineStraight Line

ABC ti thABC ti th•• ABC continue the ABC continue the recession recession -- concave concave

•• Empirical methodEmpirical method

I filt ti L CI filt ti L CInfiltration Loss CurvesInfiltration Loss Curves

11 H t M th dH t M th d1.1. Horton MethodHorton Method

MethodMethod

3.3. Initial and Initial and Constant LossConstant LossConstant LossConstant Loss

Typical Rainfall andTypical Rainfall andTypical Rainfall and Typical Rainfall and Hydrograph ResponseHydrograph ResponseHydrograph ResponseHydrograph Response

TimeTime AreaAreaTimeTime--Area Area MethodMethodMethodMethod

•• Watershed Watershed IsochroneIsochrone

•• HyetographsHyetographs

•• Time Area HistogramsTime Area Histograms•• Time Area HistogramsTime Area Histograms

•• Add and Lag MethodAdd and Lag Method

•• Resulting HydrographResulting Hydrograph


P1 * A1P1 * A1•• P1 * A1P1 * A1

•• P2*A2 + P1*A2P2*A2 + P1*A2•• P3*A1 + P2*A2 P3*A1 + P2*A2

++ P1*A3P1*A3+ + P1*A3P1*A3

Unit HydrographUnit HydrographUnit HydrographUnit HydrographLinear Methods

Tested in numerous WSTested in numerous WS

Stood the test of time

Regional calibration

Still most used approachStill most used approach

Basin response Basin response with a volume of 1 in (25 mm) of Direct with a volume of 1 in (25 mm) of Direct Runoff resulting from a rainstorm of specified duration Runoff resulting from a rainstorm of specified duration and areal patternand areal pattern

Measured Hydrograph

Adjusted for Net RF

Adjusted forAdjusted for2 inches2 inches Adjusted forAdjusted forNet RainfallNet RainfallOf 1 InchOf 1 InchOf 1 InchOf 1 Inch

Base Flow and InfiltrationBase Flow and InfiltrationBase Flow and InfiltrationBase Flow and Infiltration•• Subtract BFSubtract BFNet rainfallNet rainfall •• Subtract BFSubtract BF

•• Subtract InfiltrationSubtract InfiltrationInfiltrationInfiltration

Net rainfallNet rainfall

•• Determine Net RainDetermine Net Rain

•• Integrate hydrographIntegrate hydrographPeak FlowPeak Flow Integrate hydrographIntegrate hydrograph

•• Adjust hydrograph Adjust hydrograph Peak FlowPeak Flow

ordinates to match net ordinates to match net

rainfall Volrainfall Vol

•• Determine UHDetermine UH

D = 2D = 2--Hr Unit HydrographHr Unit HydrographD = 2D = 2--Hr Unit HydrographHr Unit Hydrograph

Adjusted Net Rainfall Adjusted Net Rainfall one inch over basinone inch over basin

QQppQQpp

Change UH DurationChange UH DurationChange UH DurationChange UH Duration

Consider Consider 1 hr1 hr UHUH

Add and Lag two UH Add and Lag two UH

by one hourby one hourby one hourby one hour

Sum and divide by 2Sum and divide by 2

R lt iR lt i 2 h2 h UHUHResults in Results in 2 hr2 hr UHUH

3 hr Unit Hydrograph3 hr Unit Hydrograph3 hr. Unit Hydrograph 3 hr. Unit Hydrograph from a 2 hr UH (D/D’)from a 2 hr UH (D/D’)from a 2 hr. UH (D/D )from a 2 hr. UH (D/D )

3 HR UH3 HR UH

D l t Eff t UHD l t Eff t UHDevelopment Effects on UHDevelopment Effects on UH

Natural Natural Partial Partial Fully Developed Fully Developed

Actual Brays Bayou UHActual Brays Bayou UHActual Brays Bayou UHActual Brays Bayou UHFaster response with Faster response with

DevelopmentDevelopmentUltimateUltimate

pp

Higher peak flow withHigher peak flow with

DevelopmentDevelopmentPresentPresent DevelopmentDevelopment

Need to provide downNeed to provide down--19591959

PresentPresent

Stream capacityStream capacity

Synthetic UHSynthetic UHSynthetic UHSynthetic UHDeveloped for basin Developed for basin

that were that were ungagedungagedUltimateUltimate

Based on data from Based on data from

similarsimilar gagedgaged basinsbasinsPresentPresent similar similar gagedgaged basinsbasins

Most methods are veryMost methods are very19591959

PresentPresent

similar in naturesimilar in nature

Revolutionized ability toRevolutionized ability to

predict hydro responsepredict hydro response

Synthetic UH MethodsSynthetic UH MethodsSynthetic UH MethodsSynthetic UH Methods

Methods to characterize Methods to characterize ungaged basinsungaged basinsungaged basins ungaged basins

Use data and relationships Use data and relationships ppdeveloped from gagesdeveloped from gages

Variety of approaches butVariety of approaches butVariety of approaches but Variety of approaches but most based on most based on TTpp and and QQpp

England and U.S. led the England and U.S. led the efforts to standardize UHefforts to standardize UH

Synthetic UH MethodsSynthetic UH MethodsSynthetic UH MethodsSynthetic UH Methods

•• Snyder’s Method (1938)Snyder’s Method (1938)

•• Clark Method (1945)Clark Method (1945)

•• Nash (1958)Nash (1958)•• Nash (1958)Nash (1958)

•• SCS (1964, 1975)SCS (1964, 1975)( )( )

•• EspeyEspey--Winslow (1968)Winslow (1968)

•• Kinematic Wave (1970s)Kinematic Wave (1970s)

Snyder’s MethodSnyder’s MethodSnyder s MethodSnyder s Method

5 to 7 points5 to 7 points5 to 7 points5 to 7 points

SCS MethodsSCS MethodsSCS MethodsSCS MethodsT i l UHT i l UHTriangular UHTriangular UH

Dimensionless UHDimensionless UH

SCS Triangular UH ExampleSCS Triangular UH ExampleSCS Triangular UH ExampleSCS Triangular UH Example1 inch of RF over 1 6 hr duration1 inch of RF over 1 6 hr duration1 inch of RF over 1.6 hr duration1 inch of RF over 1.6 hr duration

22--hr Duration UH Example hr Duration UH Example ppQQpp at 400 cfs at 10 hr with 24 hr at 400 cfs at 10 hr with 24 hr TTbb

f f f ll /hf f f ll /hSix Hours of Uniform Rainfall = 0.25 in/hrSix Hours of Uniform Rainfall = 0.25 in/hr

1.5 Inches Total Rain1.5 Inches Total Rain300300

400400

200200

300300

100100

2 4 6 8 10 12 14 16 18 20 22 24 26 302 4 6 8 10 12 14 16 18 20 22 24 26 30

Time in HoursTime in HoursTime in HoursTime in Hours

SCS RAINFALL RUNOFF CURVESSCS RAINFALL RUNOFF CURVES

Unit Hydrograph ApplicationsUnit Hydrograph Applicationsy g p ppy g p pp

d ill ld ill lLand Use will alter Land Use will alter UH Peak and TimingUH Peak and Timing

Land Use 1Land Use 1

dd

UH Peak and TimingUH Peak and Timing

Land Use 2Land Use 2

Unit Hydrograph ChangesUnit Hydrograph Changes

Kinematic WaveKinematic WaveKinematic WaveKinematic Wave

Overland Overland

Collector Collector ChannelsChannels

Main StreamMain Stream

Manning’s EqnManning’s Eqn

Kinematic WaveKinematic WaveKinematic WaveKinematic Wave

78137277 Lesson 3 Unit Hydro Graph Method Theory

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