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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