Unit Hydrograph - Advanced Hydrology - Lecture Slides, Slides of Aeronautical Engineering

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Lecture 4: Introduction to unit hydrograph

Module 3

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Unit hydrograph (UH)

• The unit hydrograph is the unit pulse response function of a linear hydrologic system.
• First proposed by Sherman (1932), the unit hydrograph (originally named unit-graph) of a watershed is defined as a direct runoff hydrograph (DRH) resulting from 1 in (usually taken as 1 cm in SI units) of excess rainfall generated uniformly over the drainage area at a constant rate for an effective duration.
• Sherman originally used the word “unit” to denote a unit of time. But since that time it has often been interpreted as a unit depth of excess rainfall.
• Sherman classified runoff into surface runoff and groundwater runoff and defined the unit hydrograph for use only with surface runoff.

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Terminologies

1. Duration of effective rainfall : the time from start to finish of effective rainfall 2. Lag time (L or t (^) p ): the time from the center of mass of rainfall excess to the peak of the hydrograph 3. Time of rise (T (^) R ): the time from the start of rainfall excess to the peak of the hydrograph 4. Time base (Tb ): the total duration of the DRO hydrograph Base flow

Direct runoff

Inflection point

T (^) R^ t^ p

Effective rainfall/excess rainfall

Q (cfs)

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Derivation of UH : Gauged watershed

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1. Storms should be selected with a simple structure with relatively uniform spatial and temporal distributions
2. Watershed sizes should generally fall between 1.0 and 100 mi2 in modern watershed analysis
3. Direct runoff should range 0.5 to 2 in.
4. Duration of rainfall excess D should be approximately 25% to 30% of lag time tp
5. A number of storms of similar duration should be analyzed to obtain an average UH for that duration
6. Step 5 should be repeated for several rainfall of different durations

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Unit hydrograph

Rules to be observed in developing UH from gaged watersheds

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Obtain a Unit Hydrograph for a basin of 315 km 2 of area using the rainfall and stream flow data tabulated below.

Time (hr) Observed hydrograph(m^3 /s) 0 100 1 100 2 300 3 700 4 1000 5 800 6 600 7 400 8 300 9 200 10 100 11 100

Time (hr)

Gross PPT (GRH) (cm/h) 0-1 0. 1-2 2. 2-3 2. 3-4 0.

Stream flow data (^) Rainfall data

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Unit hydrograph

Example Problem

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• Empirical unit hydrograph derivation separates the base flow from the observed stream flow hydrograph in order to obtain the direct runoff hydrograph (DRH). For this example, use the horizontal line method to separate the base flow. From observation of the hydrograph data, the stream flow at the start of the rising limb of the hydrograph is 100 m 3 /s
• Compute the volume of direct runoff. This volume must be equal to the volume of the effective rainfall hyetograph (ERH)

VDRH = (200+600+900+700+500+300+200+100) m 3 /s (3600) s = 12'600,000 m 3

• Express VDRH in equivalent units of depth:

VDRH in equivalent units of depth = V (^) DRH /Abasin = 12'600,000 m 3 /( m 2 ) = 0.04 m = 4 cm

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Unit hydrograph

Example Problem Contd…

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Module 3

Unit hydrograph

Example Problem Contd…

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0 2 4 6 8 10 12

Q (m

3 /s)

Time (hr)

Observed hydrograph

Unit hydrograph

DRH

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• Determine the duration D of the ERH associated with the UH obtained in 4. In order to do this: 1. Determine the volume of losses, VLosses which is equal to the difference between the volume of gross rainfall, VGRH , and the volume of the direct runoff hydrograph, VDRH. VLosses = VGRH - V (^) DRH = (0.5 + 2.5 + 2.5 +0.5) cm/h 1 h - 4 cm = 2 cm 2. Compute the f -index equal to the ratio of the volume of losses to the rainfall duration, t (^) r. Thus, ø -index = VLosses /t (^) r = 2 cm / 4 h = 0.5 cm/h 3. Determine the ERH by subtracting the infiltration ( e.g. , ø -index) from the GRH:

Module 3

Unit hydrograph

Example Problem Contd…

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