Unit HydrographsCh-7 (Streamflow Estimation)

Transforming the Runoff from Rainfall

Unit Hydrograph Theory

Moving water off of the watershed… A mathematical concept (based on linearity) Linear in nature

Some History behind Unit Some History behind Unit Hydrograph TheoryHydrograph Theory Sherman – 1932(first to propose the concept of ‘Unit

Hydrograph’) Horton - 1933 Wisler & Brater - 1949 - “the hydrograph of surface runoff

resulting from a relatively short, intense rain, called a unit storm.”

The runoff hydrograph may be “made up” of runoff that is generated as flow through the soil (Black, 1990).

Lag time

Time of concentration

Duration of excess precip.

Base flow

Duration Lag Time Time of Concentration Rising Limb Recession Limb (falling

limb) Peak Flow Time to Peak (rise time) Recession Curve Separation Base flow

Unit Hydrograph ComponentsUnit Hydrograph Components

Time Base

Methods of Developing UH’sMethods of Developing UH’s

From Streamflow Data Synthetically

Snyder (for CEE4420 – just know the formula for calculating lag and concentration times that are in the Gupta book

SCS Time-Area (Clark, 1945)

“Fitted” Distributions

Unit HydrographUnit Hydrograph

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

The key points : 1-inch of EXCESS precipitation Spread uniformly over space - evenly over the watershed Uniformly in time - the excess rate is constant over the

time interval There is a given duration pertaining to the storm – NOT

the duration of flow!

Derived Unit HydrographDerived Unit Hydrograph

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0.32

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3.68

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Baseflow

Surface Response

Note: The baseflow shown here (and separated in next slide) was identified using a different graphical method). For the course – keep the baseflow separation simple to ‘flat rate deduction’ or the N=Ad0.2 approach)

Derived Unit HydrographDerived Unit Hydrograph

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Total Hydrograph

Surface Response

Baseflow

Using a UHUsing a UH• Remember what we covered in class last time on how to predict direct

runoff from a storm of given duration and depth of excess precipitation provided you knew the UH for the same duration of the storm:

“The direct runoff from a 2 hour storm with 2 units of excess rainfall shall be twice as much as the direct runoff from a 2 hour storm with 1 unit of excess rainfall”

Storm Hydrograph (4 inches vs 2 inches)

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Time

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w

Changing the Duration of UHChanging the Duration of UH Very often, it will be necessary to change the duration of the unit

hydrograph. Storms occur in all shapes (rainfall amount) and sizes (durations)

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.

Develop S-CurveDevelop S-Curve

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w (

cfs)

Continuous 6-hour bursts

S-Curve: You get this by adding the ordinates of multiple 6 hr UHs below

Convert to 1-Hour DurationConvert to 1-Hour Duration

1. To arrive at a 1-hour UH from a given 6 hour UH, two S-curves are lagged by 1 hour from each other and the difference between the two lagged S-curve (ordinates) is calculated for every timestep.

2. However, because the S-curve was formulated from unit hydrographs having a 6 hour duration of uniformly distributed precipitation, the hydrograph resulting from the subtracting the two S-curves will be the result of 1/6 of an inch of precipitation.

3. Thus the ordinates of the newly created 1-hour DR hydrograph in step 1must be multiplied by 6 in order to be a true unit hydrograph to get the final 1 hr UH.

4. The 1-hour UH should have a higher peak which occurs earlier than the 6-hour unit hydrograph. Does this make sense ? You are having the same amount of excess rainfall but in a shorter period so the storm is more intense and hence creates runoff faster.

Final 1-hour UHGFinal 1-hour UHG

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it H

ydro

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)

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S-curves are lagged by 1 hour and the difference

is found.1-hour unit

hydrograph resulting from lagging S-

curves and multiplying the difference by 6.

Steps for Changing duration Steps for Changing duration of UHof UH

Suppose you are asked to change the duration of a given 2 hour UH to a 6 hour UH. Let tr=2hr (original duration) and trb=6hr (required duration).

1. First lag a minimum of tb/tr number of 2 hour UHs. So suppose, tb (time base of flow) is 12 hours, then in this case you should lag at least 12/2=6 2 hour UHs. Round off this number to the nearest higher integer.

2. Next, add all the ordinates as a function of time. You should get an S-type shape where the flow will reach a steady-state and saturated value. In exam, step#1 is very handy to save time. And the moment you get your highest flow value, that can be your S-curve peak value that you can maintain from thereafter.

3. Now lag two S-curves (derived in step#2) by duration trb (6 hour). And then subtract the ordinates.

4. Step #3 will give you a DRH for a trb duration storm. Multiply the ordinates by tr/trb to get your 6 hour UH from the given 2 hr UH.

Synthetic UHsSynthetic UHs

Snyder (this is good enough for course)

SCS Time-area

SnyderSnyder

Since peak flow and time of peak flow are two of the most important parameters characterizing a unit hydrograph, the Snyder method employs factors defining these parameters, which are then used in the synthesis of the unit graph (Snyder, 1938).

The parameters are Cp, the peak flow factor, and Ct, the lag factor.

The basic assumption in this method is that basins which have similar physiographic characteristics are located in the same area will have similar values of Ct and Cp.

Therefore, for ungaged basins, it is preferred that the basin be near or similar to gaged basins for which these coefficients can

be determined.

Basic RelationshipsBasic Relationships

3.0)(catLAG

LLCt

5.5LAG

duration

tt

)(25.0.. durationdurationaltLAGlagalt

tttt

83 LAG

base

tt

LAG

p

peak t

ACq

640

Significance of Unit Hydrograph

Watersheds response to a given amount of excess precipitation is just a multiplier of the unit hydrograph

Use unit hydrograph as a basis to determine the storm hydrograph from any given rainfall distribution

Example

Given the following rainfall distribution

The watershed will respond as follows

Time Precipitation

1 0.5

2 3

3 1.5

4 0.2

Example

Incremental Storm Hydrographs

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1 0.5

2 3

3 1.5

4 0.2

For hour 1: multiply your 1 hr UH by 0.5 and plot it starting at t=1hr

For hour 2: multiply your 1 hr UH by 3 and plot it starting at t=2hr…. And so on

You get four DRHs plotted for each hour as above

Example

Incremental + Final Storm Hydrograph

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Now add all your ordinates to get the final DRH – shown here by the tallest DRH.

This is the DRH you will get from the storm of 4 hours with variable intensity