ANNUAL FLOOD PEAKS—RIVER GANGA
15.4 ANNUAL FLOOD PEAKS—RIVER GANGA
(i) Gumbel’s method Eq. (15.6):
Q T = Q + Kσ Q = 6635.63 cumec, σ = 3130.8 cumec
From Table 15.5 for n = 87, y n = 0.55815, σ n = 1.1987
F T I y − T-yr y X = log log n
Q = Q +K HG σ
KJ T σ
Y = –0.834 – 2.3 X T
2.79 15365 (ii) Stochastic Method Eq. (15.17):
Q min = 2341 cumec; Q = 6635.63 cumec; n f = 77
Q T =Q min + 2.3 ( Q –Q min ) log
. HG T
KJ
F = 2341 + 2.3 (6635.63 – 2341) log 77 .T I HG 87 KJ
∴ Q T = 2341 + 9890 log (0.885 T) ...(15.27) T-yr
0.885 T
log (0.885 T)
9890 log (0.885 T) Q T cumec
18601 (iii) Log-Pearson Type III distribution. For the grouped data of annual floods in Table
15.7, computations are made in Table 15.5 to obtain the statistical parameters of the Log- Pearson Type-III distribution [see Eqs. (14.27 a, b, c)].
Σ f (log ) x
Σ f 87 Σf (log x − log ) x 2 . 3 3315
Std. dev:
σ log x =
n − 1 87 − 1
C-9\N-HYDRO\HYD15-2.PM5 FLOOD FREQUENCY—PROBABILITY AND ST Table 15.7 . Log-Pearson Type-III distribution for the annual floods of river Ganga (1885-1971) (Example 15.1)
CI Mid-pt. of CI
Frequency
f(log x f(log x cumec)
(log x
(log x
0.2130 0.0570 OCHASTIC METHODS 12-14
Σf. log (x) = 67.3856
Σ f . log ( ) x
For grouped data: log x =
Σ f 87
HYDROLOGY
nf Σ (log x − log ) x 3 (. 87 0 5165 )
Putting variate x = flood peak Q(1000 cumec), the distribution Eq. (14.28) becomes
...(15.28) and Q T for any desired T can be computed by knowing the value of K for g = 0.81 and desired
log Q T = log Q + Kσ log Q
T from Table 14.2. K = f(g, T)
Q T T-yr
K .σ log Q
log Q T
from Table
( σ log Q = 0.1962)
= log Q +K σ log Q
(1000 cumec)
14.2 ( log Q = 0.7750)
Probability P% of > Q –
þ ý Once in any year for annual floods 3 to 5 times in any year for partial floods
Semi-log paper
floods
ual R. Ganga at Haridwar (n. India): flood frequency data)
ann
40 87 years annual flood peaks (1885-1971)
1 2 3 curves
175 partial floods > 4333 cumec (1885-1971) 4 5 ý K (g þ
Q T = 2341
Log–P Q
cumec) 2 n+ 1
Log
ual floods (1000
y– 0.56 ) Gumbel: peak 20
Observed 87-yr
Par flood = 19136 cumec tial
floods
20 Q T Flood = 6635 3 4 T) – l nn { (2.01 l 15 T)}] model
15 Plotting
10 [ (2.01 n+1 l n
cumec : Stochastic
T= position
Q= T 4333 + 4.05 floods = 175, >4333
10 (175 partial floods)
Recurrence interval (T-yr)
Fig. 15.5 Flood-frequency curves of River Ganga at Hardwar (1885-1971)
FLOOD FREQUENCY—PROBABILITY AND STOCHASTIC METHODS
The frequency curve Q T vs. T is drawn on log-log paper (Fig. 15.6) and also compared with other well known distributions in Fig. 15.5. Chow (1951) has shown that most frequency distributions can be generalised as
...(15.29) where K is the frequency factor.
Log-log paper
Observed (88-yr)
flood - 19136 cumec
(1000 , 8 Log-Pearson Type- III Q T 6 frequency curve
Recurrence interval (T-yr)
Fig. 15.6 Log-Pearson Type-III distribution, Ganga floods (1885-1971)
The flood frequency curves by the above four methods have been plotted on semi-log paper, (Fig. 15.5). It can be seen that the highest annual flood peak of 19136 cumec during a
F period of 87 years + T = 87 1 = 88 − yr I has exceeded the 100-yr flood given by Gumbel’s method
HG 1 KJ
and that computed by the new stochastic model based on the partial duration series. However, in this case, the stochastic method using annual flood data and Log-Pearson Type-III distribu- tion give safe design values.