Unit Hydrographs (Streamflow Estimation)gn.dronacharya.info/.../Unit-2/hydrograph2.pdf · Changing the Duration of UH Very often, it will be necessary to change the duration of the

Unit Hydrographs

(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 Hydrograph 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 Components

Time Base

Methods 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 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 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

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 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

Using 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)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30

Time

Flo

w

Changing 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-Curve

0.00

10000.00

20000.00

30000.00

40000.00

50000.00

60000.00

0 6

12

18

24

30

36

42

48

54

60

66

72

78

84

90

96

102

108

114

120

Time (hrs.)

Flo

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 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 UHG

0.00

2000.00

4000.00

6000.00

8000.00

10000.00

12000.00

14000.00

Time (hrs.)

Un

it H

yd

rog

rap

h F

low

(cfs

/in

ch

)

0.00

10000.00

20000.00

30000.00

40000.00

50000.00

60000.00

Flo

w (

cfs

)

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 of 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 UHs

Snyder (this is good

enough for course)

SCS

Time-area

Snyder

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 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

0

100

200

300

400

500

0 5 10 15 20 25 30 35

Time

Flo

w

Time (hr) Precipitation

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

0

100

200

300

400

500

0 5 10 15 20 25 30 35

Time

Flo

w

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