Rainfall-Runoff modelingRainfall-Runoff modeling

• Forecasting and predictingForecasting and predicting– Flood peaksFlood peaks– Runoff volumesRunoff volumesDue to Large rain and snowmelt eventsDue to Large rain and snowmelt events

***especially important when we have no prior recorded ***especially important when we have no prior recorded experience.experience.

1.1.extreme flood producing rainsextreme flood producing rains2.2.Major land-use changesMajor land-use changes3.3.Altered climatic regimesAltered climatic regimes

• Physical and empirical based modelsPhysical and empirical based models

Approach (empirical)• Output-hydrographsOutput-hydrographs

– Inputs: hyetographsInputs: hyetographs– Produces an identifiable resultProduces an identifiable result

• Important pts.Important pts.1.1. Hyetograph represents only a portion of the total input in the Hyetograph represents only a portion of the total input in the

associated response of the hydrographassociated response of the hydrograph2.2. Hydrograph represents only the identifiable response to the Hydrograph represents only the identifiable response to the

current hyetograph.current hyetograph.• Does not include baseflow (earlier events)Does not include baseflow (earlier events)• Or portion of the streamflow after the event response.Or portion of the streamflow after the event response.

3.3. Determination of event-flow volume based on hydrograph Determination of event-flow volume based on hydrograph separation.separation.

4.4. Volume of effective water inputs=volume of event flowVolume of effective water inputs=volume of event flow5.5. Based on reasonable assumptions rather than hydrologic Based on reasonable assumptions rather than hydrologic

processes.processes.

implicit assumption

• Water that appears as output in the same water that is identified from the hyethograph.– In reality-substantial portion of the water

appearing is “old water”. Water that has entered the watershed from a previous event

Effective water input

• Weff=W-”losses” DSETlosses c

Design Floods v. Floods

• Models are used to generate design floods from actual storms.

– Design of culverts, bridges, flood retention basins, levees, dam spillways, or floodplain management.

1. Forecast flooding from in-progress storms.

2. Calibrate models.

3 models for design flows

1. Rational method• Urban areas

2. SCS method• Sub-urban and rural areas

3. Unit hydrograph• Generate design flows for large watersheds

Rational Method

SCS Method

• Most widely used method for design purposes.

Unit Hydrograph

• Most widely used transfer function for systems modeling.

• Definition: basin outflow resulting from 1”(1 cm) of runoff generated uniformly over the drainage area at a uniform rate.

Unit Hydrograph TheoryUnit Hydrograph Theory

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Unit Hydrograph “Lingo”Unit Hydrograph “Lingo”

• Duration• Lag Time• Time of Concentration• Rising Limb• Recession Limb (falling limb)• Peak Flow• Time to Peak (rise time)• Separation• Base flow

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Graphical RepresentationGraphical Representation

Lag time

Time of concentration

Duration of excess precipitation.

Base flow

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Methods of Developing UHG’sMethods of Developing UHG’s

• From Streamflow Data

• Synthetically-ungaged streams– Snyder– SCS– Time-Area (Clark, 1945)

• “Fitted” Distributions

• Geomorphologic

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Unit HydrographUnit Hydrograph

• The hydrograph that results from 1-inch of excess precipitation (or runoff) spread uniformly in space and time over a watershed for a given duration.

• The key points :1-inch of EXCESS precipitationSpread uniformly over space - evenly over the watershedUniformly in time - the excess rate is constant over the

time intervalThere is a given duration

UHG’sUHG’s

• 2 key assumptions for the development.2 key assumptions for the development.

1.1. Linearity-Linearity-Given a UHG, a hydrograph for a Given a UHG, a hydrograph for a runoff depth other than unity can be obtained runoff depth other than unity can be obtained by multiplying the UHG ordinates by the by multiplying the UHG ordinates by the indicated runoff depth. Therefore, the time indicated runoff depth. Therefore, the time base of the hydrograph is the same as the time base of the hydrograph is the same as the time base of the UHG.base of the UHG.

2.2. Superposition- Superposition- summation of corresponding summation of corresponding hydrograph or UHG ordinateshydrograph or UHG ordinates

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Derived Unit HydrographDerived Unit Hydrograph

0.0000

100.0000

200.0000

300.0000

400.0000

500.0000

600.0000

700.0000

0.00

00

0.16

00

0.32

00

0.48

00

0.64

00

0.80

00

0.96

00

1.12

00

1.28

00

1.44

00

1.60

00

1.76

00

1.92

00

2.08

00

2.24

00

2.40

00

2.56

00

2.72

00

2.88

00

3.04

00

3.20

00

3.36

00

3.52

00

3.68

00

Baseflow

Surface Response

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Derived Unit HydrographDerived Unit Hydrograph

0.0000

100.0000

200.0000

300.0000

400.0000

500.0000

600.0000

700.0000

0.0000 0.5000 1.0000 1.5000 2.0000 2.5000 3.0000 3.5000 4.0000

Total Hydrograph

Surface Response

Baseflow

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Derived Unit HydrographDerived Unit Hydrograph

Rules of Thumb :… the storm should be fairly uniform in nature and the excess precipitation should be equally as uniform throughout the basin. This may require the initial conditions throughout the basin to be spatially similar. … Second, the storm should be relatively constant in time, meaning that there should be no breaks or periods of no precipitation. … Finally, the storm should produce at least an inch of excess precipitation (the area under the hydrograph after

correcting for baseflow).

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Deriving a UHG from a StormDeriving a UHG from a Stormsample watershed = 450 mi2sample watershed = 450 mi2

0

5000

10000

15000

20000

25000

Time (hrs.)

Flo

w (

cfs)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Pre

cip

itat

ion

(in

ches

)

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Separation of BaseflowSeparation of Baseflow

... generally accepted that the inflection point on the recession limb of a hydrograph is the result of a change in the controlling physical processes of the excess precipitation flowing to the basin outlet.

In this example, baseflow is considered to be a straight line connecting that point at which the hydrograph begins to rise rapidly and the inflection point on the recession side of the hydrograph.

the inflection point may be found by plotting the hydrograph in semi-log fashion with flow being plotted on the log scale and noting the time at which the recession side fits a straight line.

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Hydrograph & BaseflowHydrograph & Baseflow

0

5000

10000

15000

20000

25000

0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105

112

119

126

133

Time (hrs.)

Flo

w (

cfs)

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Separate BaseflowSeparate Baseflow

0

5000

10000

15000

20000

25000

Time (hrs.)

Flo

w (

cfs)

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Sample CalculationsSample Calculations

• In the present example (hourly time step), the flows are summed and then multiplied by 3600 seconds to determine the volume of runoff in cubic feet. If desired, this value may then be converted to acre-feet by dividing by 43,560 square feet per acre.

• The depth of direct runoff in feet is found by dividing the total volume of excess precipitation (now in acre-feet) by the watershed area (450 mi2 converted to 288,000 acres).

• In this example, the volume of excess precipitation or direct runoff for storm #1 was determined to be 39,692 acre-feet.

• The depth of direct runoff is found to be 0.1378 feet after dividing by the watershed area of 288,000 acres.

• Finally, the depth of direct runoff in inches is 0.1378 x 12 = 1.65 inches.

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Obtain UHG OrdinatesObtain UHG Ordinates

• The ordinates of the unit hydrograph are obtained by dividing each flow in the direct runoff hydrograph by the depth of excess precipitation (Weff).

• In this example, the units of the unit hydrograph would be cfs/inch (of excess precipitation).

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Final UHGFinal UHG

0

5000

10000

15000

20000

25000

0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105

112

119

126

133

Time (hrs.)

Flo

w (

cfs)

Storm #1 hydrograph

Storm#1 direct runoff hydrograph

Storm # 1 unit hydrograph

Storm #1 baseflow

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Determine Duration of UHGDetermine Duration of UHG

• The duration of the derived unit hydrograph is found by examining the precipitation for the event and determining that precipitation which is in excess.

• This is generally accomplished by plotting the precipitation in hyetograph form and drawing a horizontal line such that the precipitation above this line is equal to the depth of excess precipitation as previously determined.

• This horizontal line is generally referred to as the -index and is based on the assumption of a constant or uniform infiltration rate.

• The uniform infiltration necessary to cause 1.65 inches of excess precipitation was determined to be approximately 0.2 inches per hour.

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Estimating Excess Precip.Estimating Excess Precip.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Time (hrs.)

Pre

cip

itat

ion

(in

ches

)

Uniform loss rate of 0.2 inches per hour.

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Excess PrecipitationExcess Precipitation

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Time (hrs.)

Exc

ess

Pre

c. (

inch

es)

Small amounts of excess precipitation at beginning and end may

be omitted.

Derived unit hydrograph is the result of approximately 6 hours

of excess precipitation.

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Changing the DurationChanging the Duration

• Very often, it will be necessary to change the duration of the unit hydrograph.

• If unit hydrographs are to be averaged, then they must be of the same duration.

• The most common method of altering the duration of a unit hydrograph is by the S-curve method.

• The S-curve method involves continually lagging a unit hydrograph by its duration and adding the ordinates.

• For the present example, the 6-hour unit hydrograph is continually lagged by 6 hours and the ordinates are added.

Convolution methodConvolution method

• Based on principles of both linearity and Based on principles of both linearity and superposition.superposition.

• Procedure for deriving a storm hydrograph from a multiperiod rainfall event. – Changes duration w/o precip. event equal to

duration of the UHG.