Chapter 3 Hydrograph Analysis

Hydrograph Analysis

Components of Runoff

Hydrograph Characteristics

Unit Hydrograph Theory

Synthetic Unit Hydrographs

q (m3/s)

t (hr)

The major characteristics of streamflow are:

its volume for a certain duration (month or year)

different uses & storage

its extreme values

drought & flood

Hydrograph Analysis

i (mm/hr) q (m3/s)

t (hr)

input

(Rainfall) system

(Basin)

t (hr)

output

(Runoff)

Components of Runoff

Channel Precipitation

Surface Runoff

Interflow

Groundwater Flow

Interception, depression

storage, soil moisture are

LOSSES for streamflow.

The other portions of

precipitation reach streams

sooner or later.

In a rainfall block interception Loss for streamflow

storage

(mm/hr)

depression moisture i

soil ater

groundwinterflow

streamflow infiltration

surface runoff

channel precipitation

COMPONENTS OF RUNOFF

In a rainfall block

In the channel channel precipitation surface flow

interflow

groundwater flow

groundwater table GW flow

interception

Loss for streamflow

streamflow surface runoff

channel precipitation i (m

m/h

r)

Hydrograph Hydrograph discharge vs time

(m3/s, lt/s) (min, hr, day, month, yr)

Sometimes plotted as stage vs time.

The comparison of hydrographs with the corresponding

rainfall hyetographs provides a lot of information about the

rainfall-runoff relation of the basin.

Q (m3/s, lt/s)

HYDROGRAPH

t (min, hr, day, week, month, year)

Shape of the rising limb = f(rainfall intensity & basin

characteristics s.a. infiltration

capacity, shape, slope, etc.)

Shape of falling limb = f(basin characteristics s.a. depression,

surface & subsurface storages)

Characteristics of the rainfall do not impact the falling limb

since recession starts after the end of the rainfall.

tL r

Hydrograph peak rate

crest

inflection

points

The crest of the hydrograph

is governed by the duration

of rainfall.

rising limb

(concentration

curve) surface runoff

(direct runoff)

falling limb (recession curve)

(depletion curve)

A GW recession

base flow

tp t (hr)

tb

q (

m3/s

)

Hydrograph shapes for different

conditions

The shape of the

hydrograph varies with the orientation of the storm in

surface flow

channel precipitation

interflow

i

f

F

: rainfall rate

: infiltration rate

: total amount of infiltrated water

SMD : soil moisture deficiency

Case 2 i<f F>SMD

t1 t2 t (hr)

t1 t2 t (hr)

Case 4 i>f F>SMD

t1 t2 t (hr)

no rain

t (hr)

groundwater

flow

groundwater

GW table

flow

Case 3 i>f F<SMD

q (

m3/s

)

q (

m3/s

) q (

m3/s

)

q (

m3/s

) q (

m3/s

)

Case 1 i<f F<SMD

t1

t2

t (hr)

q (m3/s)

B

A

Basin A Basin B t (hr)

Hydrograph Separation Techniques

Separation line between surface runoff & baseflow is not

definite & varies widely depending on the existing

conditions.

Inaccuracies in separation are not very important for many

storms, since the max. rate of discharge is only slightly

affected by the base flow.

Methods for seperation: Simple Method

Approximate Method

Barnes (Semi-log) Method

Seperation Methods

1. Barnes (Semi-log) Method

1 Total flow (SF+SSF+BF)

q q0 e α1t

4 Base flow (BF)

2 (SF+SSF) (1) – (4)

q q 0 e

α2t

5 Subsurface flow (SSF)

3 Surface flow (SF) (2) – (5)

Q 1 9

(m3/s) 8

7

6

5

4

3

2

1 3

1 9

8

7

6

5

4

4

2 3

5 2

1 E (linear)

t (hr)

q

(m3/s)

q

(m3/s) q

(m3/s)

q

(m3/s)

Master depletion curve (representative depletion curve)

Slope is related to storage coefficient

of the basin

q = q0e-αt

log q = log q0 - t α log e

y a b x

y = a + bx (straight line on semi-log paper)

log q (m3/s)

master depletion line

t (hr)

Unit Hydrograph (UH) Theory

Hydrograph of surface runoff (direct runoff) resulting from

1 cm of excess rainfall which is uniformly distributed over

basin area at a uniform rate during a specified period of time.

Depth = 1 mm for arid or semi-arid regions or if basin is small.

Given by Sherman in 1932.

It is assumed that the UH is representative for the runoff

process of a basin.

Baseflow should be separated from total flow to find direct

runoff, and all the losses should be subtracted from total

precipitation before any analysis.

Unit Hydrograph (UH) Theory

UH assumptions:

1. Excess rainfall is uniformly distributed within a specified period of time.

2. Excess rainfall is uniformly distributed over the basin area.

3. Base time of direct runoff is constant for a specified duration of rainfall.

4. Ordinates of direct runoff hydrograph are directly proportional to the total amount (depth) of direct runoff ( = depth of excess rainfall) for the same duration rainfalls.

5. Unit hdrograph is unique for a basin.

1. Linearity assumption

(Principle of superposition,

Principle of proportionality)

2. Principle of time-invariance

When basin characteristics change UH changes

i (mm/hr)

i ni

t (hr) tr

q (m3/s)

nq i

hydrograph for ni mm/hr rain

qi

hydrograph for i mm/hr rain

t (hr)

tb (same base time)

Unit Hydrograph

The unit hydrograph is denoted as dUHt ( d in cm, t in hr)

The depth of flow for a hydrograph the area under the hydrograph.

q

(m3/s)

a q3 3

q 4

a q2

1 1

t t

2

a q qn

a n+1

t t t (hr)

...

V = q*t

Figure 7.18 Determination of volume of runoff

d = V

A

= A

q dt q * Δt

A

∑q = sum of ordinates of the

hydrograph (m3/s)

dt = time interval (s)

A = basin area (m2)

d = depth (m)

Unit Hydrographs of Different Durations

There are 2 methods to obtain UHs of different durations

for a basin when a UH of certain duration is known The lagging method

S-curve method

The Lagging Method

A UH of certain duration can easily be obtained by using

the lagging method if a UH of different duration is known

for the basin.

The only condition is that the durations be multiples of

each other.

HYDROGRAPH ANALYSIS – lagging method

i

(mm/hr) 1 cm 1 cm

t (hr)

tr tr

q

(m3/s)

UHtr [UH2]

tr hour lagged UHtr [UH2]

t (hr)

tb tr

i

(mm/hr) 1 cm

tr

q (m3/s)

t (hr)

UHtr [UH2]

t (hr)

tb

1 cm

i

(mm/hr) 1 cm tr t (hr)

tr

q

(m3/s)

addition of two hydrographs

= 2UH2tr [2UH4]

tb

UHtr [UH2] tr hour lagged UHtr

[UH2]

t (hr)

tr

UH2 + (2 hr lagged) UH2 = 2UH4

i

(mm/hr) 1 cm 1 cm

t (hr)

tr tr

q

(m3/s) addition of two hydrographs = 2UH2tr [2UH4]

UH2tr [UH4]

UHtr [UH2]

tr hour lagged UHtr [UH2]

t (hr)

tb tr

HYDROGRAPH ANALYSIS – lagging method

qp es

As tr es tp

tb

es

es

i

(mm/hr) 1 cm 1 cm 1 cm

t (hr)

tr tr tr q

(m3/s)

tb

UHtr

tr hour lagged UHtr

2 tr hour lagged UHtr

t (hr)

tr tr

i

(mm/hr) 1 cm 1 cm

t (hr)

tr tr q

(m3/s)

UHtr

tr hour lagged UHtr

t (hr)

tb tr

i (mm/hr)

1 cm

tr

t (hr)

q

(m3/s)

UHtr

t (hr)

tb

UHt + (t hr. lag) UHt + (2t hr.lag) UHt =3UH3t

i

(mm/hr) 1 cm

tr

1 cm 1 cm

tr tr t (hr)

q (m3/s)

addition of 3 hydrographs = 3UH3tr

UH3tr

UHtr

tr hour lagged UHtr

2 tr hour lagged UHtr

t (hr)

tb tr tr

The S-Curve Method

It is used to obtain UHs of different durations that are

not multiples of each other.

S-curve is the hydrograph that would result from an

infinite series of UHs of tr durations, each delayed tr hours

wrt the preceding one.

In other words, it is the hydrograph of the runoff of

continuous rainfall with an intensity of 1/tr.

S-curve has the form of a mass curve, the discharge of the

basin becoming constant after the time of concentration.

Thus each S-curve is unique for a specified UH duration, in

a particular drainage basin.

S - Curve

i

(mm/hr) tr

q

(m3/s)

tr tr tr

t (hr)

S - curve Qe

UHt r

tr tb tr

t (hr)

tr tb

i

(mm/hr) t (hr)

t tr tr r

q

(m3/s)

t (hr)

tr tr tb

i

(mm/hr) t (hr)

t tr r

q

(m3/s)

t (hr)

tr

i

(mm/hr) t (hr)

tr

q (m3/s)

t (hr)

tb

n = tb/tr

Qe = i * A (mm/hr * km2)

Qe = d/tr * A = 1/tr * A

(d= 1 cm)

Qe = constant outflow (m3/s) A = area of basin (km2)

tr = duratio of UH (hr)

Q 2.78 A

e

t r

S - Curve

There may be fluctuations around the constant flow Qe

due to a number of reasons.

One of them may be the duration of effective

precipitation, tr.

It may be shorter or longer than the actual effective

precipitation duration with uniform intensity.

Another one may be the uneven distribution of rainfall in

the basin or nonlinearities in the system.

Obtaining UH using S-curve (t2 < t1)

i (mm/hr)

t (hr) t1 t1

q (m3/s)

t1

St1

t (hr)

i

(mm/hr)

q

(m3/s)

t1 t1

t2

t (hr) t1

St1

(t2 hr. lag) St1

t2

t

(hr)

i

(mm/hr) t (hr)

q

(m3/s)

t1

t2

t1 t1

St1

(t2 hr. lag) St1

UHt 2 =

t1 Diff. t2

Diff. = t2 UH

t1 t 2

t2 tb

t

(hr)

i

(mm/hr) t (hr)

q

(m3/s)

t1

t2

t1 t1

St1

(t2 hr. lag) St1

Diff. = t2

UH t1 t 2

t2 tb

t

(hr)

UH t1 [s

t 2 t t1 (t 2 hr. lag) s

t1 ]

2

Diff. = St1 - (t2 h.l.) St1

Diff. = (t2 . 1/t1) UHt2= t2/t1 UHt2

7. Determine the representative UH for the basin by

averaging the peak flows,

times to peak, and

time bases of the UHs.

The average UH is then sketched following the shapes of

the individual hydrographs.

8. Adjust the area under the curve to unit depth.

q

(m3/s)

qp2

qp3

qp1

. average peak

( p1 p2 p3

q + q + q , t p1 + t + t

3 p2 p3 ) 3

average unit

hydrograph

average base time

tb1 + tb2 + tb3 )

tp3 tp2 tp1

( tb2

tb3

3

tb1 t (hr)

Example UH1 of a basin is given.

Determine UH2 , UH3 and area of this basin by lagging method

Time (hr)

UH1

m3/s

1 hr.lag UH1

2UH2

UH2

2 hr.lag UH1

3UH3

UH3

0 0 0 0 0 0

1 12 12 6

0 12 4 2 36 48 24

3 24 12 60 30 0 48 16

4 18 36 42 21 12 72 24

5 12 30 15 24 3

6 78 26

6 6 18 9 18 2

4 54 18

7 0 6 3

8 12 0 0 18 36 12

9 6 12 18 6

0 6 6 2

0 0 0

q 108 108 108 Σq* Δt Σq* Δt

UH1 + (1 hr. lag) UH1 = 2 UH2 d A A d

UH1 + (1 hr. lag) UH1 + (2 hr. lag) UH1 = 3 UH3

A 108*1*3600

0.01 38.88*106 m2

38.88 km2

1 Example UH of a basin is given.

Determine UH2 and UH3 of this basin by S-curve method

UH

1

[S

(2 hr.lag) S ]

UH

1 [S

(3 hr.lag) S ] N = tb / tr = 7/1

= 7

2 2

1 1 3 3

1 1

UH t 2 [s

t1

t t1 (t hr. lag) s ] 2 t1

2

t (hr) UH1 1 h.l UH1

2 h.l UH1

3 h.l UH1

4 h.l UH1

5 h.l UH1

6 h.l UH1

S1

2 h.l S1

dif

f

UH2

3 h.l S1

dif

f

UH3

0 0 0 0 0 0 0

1 12 0 12 12 6 12 4

2 36 12 0 48 0 48 24 48 16

3 24 3

6

12 0 72 12 60 30 0 72 24

4 18 2

4

36 12 0 90 48 42 21 12 78 26

5 12 18 24 36 12 0 102 72 30 15 48 54 18

6 6 12 18 24 36 12 0 108 90 18 9 72 36 12

7 0 6 12 18 24 36 12 108 102 6 3 90 18 6

8 0 6 12 18 24 36 108 108 0 0 10

2

6 2

9 0 6 12 18 24 108 108 10

8

0 0

Synthetic Unit Hydrograph

Snyder Method

SCS Method

(developed by Soil Conservation Services, 1957)

Espey Method

Mockus Method

DSİ Synthetic Unit Hydrograph Method

Time Area Method