Document Text Contents
Page 238
C-9\N-HYDRO\HYD8-1.PM5 225
FLOODS-ESTIMATION AND CONTROL 225
When the flood items are tabulated in terms of mean flood, Cv = �. If the annual flood is
x and the mean flood is x , then the annual flood in terms of mean flood is x/x . The coefficient
of variation for annual precipitation data is equal to the standard deviation of the indices of
wetness.
While a small value of Cv indicates that all the floods are nearly of the same magnitude,
a large Cv indicates a range in the magnitude of floods. In other word Cv represents the slope
of the probability curve, and the curve is horizontal if Cv = 0. The actual length of records
available has a very little effect on the value of Cv, i.e., Cv for a 20-yr record varies very little
from that for a 100-yr record.
The coefficient of skew, Cs is seriously affected by the length of record and will be too
small for a short period; Cs is then modified to allow for the period of record (n) by multiplying
by a factor (1 + k/n) where the constant K = 6 to 8.5. If even this adjusted Cs does not give a
curve to fit actual observed data, an arbitrary value of Cs will have to be assumed to fit the
curve for the given annual flood data. From this theoretical curve can then be read off the
probability or the percentage of time, of a flood of any given magnitude occurring, usually,
Cs 2 Cv ...(8.21)
The coefficient of flood indicates the general magnitude of the floods in the particular
stream; hence, it fixes the height of the curve above the base. Using Cf, the mean flood of a
stream, for which no flood data are available, can be got, as
Mean flood = Cf ×
A0.8
2 14.
...(8.22)
The exponent 0.8 is the slope of the line obtained by plotting the mean annual flood
against water-shed area for a number of streams. Almost all observed data till to-date confirm
this value originally obtained by Fuller.
8.5 ENCOUNTER PROBABILITY
Even if a flood of a long recurrence interval is chosen, there is always a possibility that the
flood can be exceeded more then once during the interval. The probability of ‘r’ events occur-
ring in ‘N’ possible events is given by
P(N, r) =
N
r N r
!
! ( ) !�
Pr (1 – P)N–r ...(8.23)
where P = probability of a single event.
If r = 0, the flood will not be exceeded during the ‘N’ years, the useful life of the struc-
ture. Then Eq. (8.23) becomes
Probability of non-exceedance, P(N, 0) = (1 – P)
N ...(8.23 a)
So, the probability that the design flood (T-year flood, annual probability of occurrence
P = 1/T) will be exceeded one or more times during N year (useful life of the structure) is given
by
Probability of exceedance, PEx = 1 – (1 – P)
N ...(8.23 b)
and the percentage risk = PEx × 100 (8.23 c)
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C-9\N-HYDRO\HYD8-1.PM5 226
226 HYDROLOGY
Thus, the probability of a 100-year flood will not be exceeded in the next 50 years is
P(N, 0) = 1
1
100
50
�FHG
I
KJ = 0.6 or 60%
or 6 chances in 10; and the probability that the 100-year flood will be exceeded once or more
during the next 50 years is
PEx = 1 – 0.6 = 0.4 or 40%
or 4 chances in 10
As another example, to determine the recurrence interval of a design flood having a
63% risk of being exceeded during a 100-year period
PEx = 1 – (1 – P)
N
0.63 = 1 – (1 – P)100
from which P = 0.01. Hence, T =
1 1
0 01P
=
.
= 100 years.
The percentage probabilities of floods (or rainfall) of different recurrence intervals (T)
to occur in particular periods (N) are given in Table 8.4.
Table 8.4 Probability (%) of T-yr flood to occur in a period of N-years
Period (N-years) Average recurrence interval of flood (T-yr)
5 10 50 100 200
1 20 10 2 1 0.5
5 67 41 10 5 2
10 89 65 18 10 5
25 99.6 93 40 22 12
50 — 99.5 64 40 22
100 — — 87 63 39
200 — — 98 87 63
500 — — — 99.3 92
Partial duration curve method Partial duration curves are plotted showing the flood
discharges against their probable frequency of occurrence in 100 years and not against per-
centage of time as in the annual flood series.
Probable frequency =
m
y
× 100 ...(8.24)
where m = order number or rank of the particular flood in the series of items selected and
arranged in the descending order of magnitude
y = total length of record in years
The number of flood items selected need not be greater than the number of years in
record to simplify the procedure. Gumbel paper should not be used for partial series, which
usually plot better on semi-log paper.
Frequency method may be used for drainage basins of any size. The reliability of the
frequency estimates depends on the length of the observed record rather than the method of
probability analysis. Thus, if a 50-year record is available, a 10-yr flood may be predicted with
Page 476
C-9\N-HYDRO/IND.PM5
462 HYDROLOGY
Stage-discharge rating curve, 176, 178, 184
adjustment of, 181
extension of, 181
Statistics, elements, 327
mean, median, 43, 44, 327, 328, 331
mode, 328, 331
skew distribution, 328
skewness, 329
coefficient of, 330
variance, 329
Station-year method, 24
Storage capacity, reservoir, 281, 383, 488
Storage coefficient, aquifer, 194
basin, 375, 399
Storm characteristics, correlation of,
depth-duration, 11, 45
intensity-duration, 46
intensity-duration-frequency (IDF), 38, 41, 114
design, 49, 217
track, 9
maximum probable (MPS), 10
Storm maximisation, 10
by moisture charge, 10, 217
by unit hydrograph method, 221
Streams, classification of, 103
effluent, 103
ephemeral, 103
influent, 103
intermittent, 104
perennial, 104
Stream flow components, 96
separation of, 120
Stream flow computation, 171, 185
contracted area method, 172, 186
salt concentration method, 172
slope-area method, 171, 187
Stream gauging, methods of 171
area-velocity method, 172, 176, 179
by current meter, 174, 176
selection of site, 183
Supra-rain technique, 83
curve, 85
Synthetic stream flow, 379
Synthetic unit hydrograph, Snyder’s, 149
Tank irrigation, 109
length of weir, 111
yield for, 109
Tapti basin, 6
hydrological study, 5-12, 36
Thiessen polygon method, 27, 28
Time-area diagram (TAD), 378, 398, 400
Time of concentration, 109, 398
runoff from, 109, 398
Transpiration, 67
ratio, 67
Transmissibility, 196, 199
Trap efficiency, 301-303
Unit hydrograph, 113, 124, 379
application of, 157, 158, 160
alteration of duration, 136
assumptions of, 113
average, 136
derivation of, 124, 129
from complex storms, 130, 132
dimensionless, 156
elements of, 126
instantaneous (IUH), 149, 379, 393, 401
limitations of, 127
matrix method, 135
propositions of, 127
runoff estimation from, 113
SCS method, 157
synthetic (SUH), Snyder’s 149
transposing of, 154
Unit storm, 127
Unsaturated flow, 66
Valley storage, 97, 106
Variance, 327
Velocity measurements, 172
Velocity rods, 172
Water balance, 87, 445
of Krishna river basin, 87
Water bearing formations, 192
Water losses, 60
Watershed leakage, 87
Page 477
C-9\N-HYDRO/IND.PM5
INDEX 463
Water resources, World’s, 1
of India, 1
Well hydraulics, 196
Cavity wells, 200
Dupuitt’s equations, 196-198
Jacob’s equations, 433-438
Open (dug) wells, 202
Thies equations, 432-438
Well interference, 207
Wells spacing, 207
W-index, 82
Yield (see runoff estimation), 106, 429
for tank, 109
rational method for, 106, 108
C-9\N-HYDRO\HYD8-1.PM5 225
FLOODS-ESTIMATION AND CONTROL 225
When the flood items are tabulated in terms of mean flood, Cv = �. If the annual flood is
x and the mean flood is x , then the annual flood in terms of mean flood is x/x . The coefficient
of variation for annual precipitation data is equal to the standard deviation of the indices of
wetness.
While a small value of Cv indicates that all the floods are nearly of the same magnitude,
a large Cv indicates a range in the magnitude of floods. In other word Cv represents the slope
of the probability curve, and the curve is horizontal if Cv = 0. The actual length of records
available has a very little effect on the value of Cv, i.e., Cv for a 20-yr record varies very little
from that for a 100-yr record.
The coefficient of skew, Cs is seriously affected by the length of record and will be too
small for a short period; Cs is then modified to allow for the period of record (n) by multiplying
by a factor (1 + k/n) where the constant K = 6 to 8.5. If even this adjusted Cs does not give a
curve to fit actual observed data, an arbitrary value of Cs will have to be assumed to fit the
curve for the given annual flood data. From this theoretical curve can then be read off the
probability or the percentage of time, of a flood of any given magnitude occurring, usually,
Cs 2 Cv ...(8.21)
The coefficient of flood indicates the general magnitude of the floods in the particular
stream; hence, it fixes the height of the curve above the base. Using Cf, the mean flood of a
stream, for which no flood data are available, can be got, as
Mean flood = Cf ×
A0.8
2 14.
...(8.22)
The exponent 0.8 is the slope of the line obtained by plotting the mean annual flood
against water-shed area for a number of streams. Almost all observed data till to-date confirm
this value originally obtained by Fuller.
8.5 ENCOUNTER PROBABILITY
Even if a flood of a long recurrence interval is chosen, there is always a possibility that the
flood can be exceeded more then once during the interval. The probability of ‘r’ events occur-
ring in ‘N’ possible events is given by
P(N, r) =
N
r N r
!
! ( ) !�
Pr (1 – P)N–r ...(8.23)
where P = probability of a single event.
If r = 0, the flood will not be exceeded during the ‘N’ years, the useful life of the struc-
ture. Then Eq. (8.23) becomes
Probability of non-exceedance, P(N, 0) = (1 – P)
N ...(8.23 a)
So, the probability that the design flood (T-year flood, annual probability of occurrence
P = 1/T) will be exceeded one or more times during N year (useful life of the structure) is given
by
Probability of exceedance, PEx = 1 – (1 – P)
N ...(8.23 b)
and the percentage risk = PEx × 100 (8.23 c)
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C-9\N-HYDRO\HYD8-1.PM5 226
226 HYDROLOGY
Thus, the probability of a 100-year flood will not be exceeded in the next 50 years is
P(N, 0) = 1
1
100
50
�FHG
I
KJ = 0.6 or 60%
or 6 chances in 10; and the probability that the 100-year flood will be exceeded once or more
during the next 50 years is
PEx = 1 – 0.6 = 0.4 or 40%
or 4 chances in 10
As another example, to determine the recurrence interval of a design flood having a
63% risk of being exceeded during a 100-year period
PEx = 1 – (1 – P)
N
0.63 = 1 – (1 – P)100
from which P = 0.01. Hence, T =
1 1
0 01P
=
.
= 100 years.
The percentage probabilities of floods (or rainfall) of different recurrence intervals (T)
to occur in particular periods (N) are given in Table 8.4.
Table 8.4 Probability (%) of T-yr flood to occur in a period of N-years
Period (N-years) Average recurrence interval of flood (T-yr)
5 10 50 100 200
1 20 10 2 1 0.5
5 67 41 10 5 2
10 89 65 18 10 5
25 99.6 93 40 22 12
50 — 99.5 64 40 22
100 — — 87 63 39
200 — — 98 87 63
500 — — — 99.3 92
Partial duration curve method Partial duration curves are plotted showing the flood
discharges against their probable frequency of occurrence in 100 years and not against per-
centage of time as in the annual flood series.
Probable frequency =
m
y
× 100 ...(8.24)
where m = order number or rank of the particular flood in the series of items selected and
arranged in the descending order of magnitude
y = total length of record in years
The number of flood items selected need not be greater than the number of years in
record to simplify the procedure. Gumbel paper should not be used for partial series, which
usually plot better on semi-log paper.
Frequency method may be used for drainage basins of any size. The reliability of the
frequency estimates depends on the length of the observed record rather than the method of
probability analysis. Thus, if a 50-year record is available, a 10-yr flood may be predicted with
Page 476
C-9\N-HYDRO/IND.PM5
462 HYDROLOGY
Stage-discharge rating curve, 176, 178, 184
adjustment of, 181
extension of, 181
Statistics, elements, 327
mean, median, 43, 44, 327, 328, 331
mode, 328, 331
skew distribution, 328
skewness, 329
coefficient of, 330
variance, 329
Station-year method, 24
Storage capacity, reservoir, 281, 383, 488
Storage coefficient, aquifer, 194
basin, 375, 399
Storm characteristics, correlation of,
depth-duration, 11, 45
intensity-duration, 46
intensity-duration-frequency (IDF), 38, 41, 114
design, 49, 217
track, 9
maximum probable (MPS), 10
Storm maximisation, 10
by moisture charge, 10, 217
by unit hydrograph method, 221
Streams, classification of, 103
effluent, 103
ephemeral, 103
influent, 103
intermittent, 104
perennial, 104
Stream flow components, 96
separation of, 120
Stream flow computation, 171, 185
contracted area method, 172, 186
salt concentration method, 172
slope-area method, 171, 187
Stream gauging, methods of 171
area-velocity method, 172, 176, 179
by current meter, 174, 176
selection of site, 183
Supra-rain technique, 83
curve, 85
Synthetic stream flow, 379
Synthetic unit hydrograph, Snyder’s, 149
Tank irrigation, 109
length of weir, 111
yield for, 109
Tapti basin, 6
hydrological study, 5-12, 36
Thiessen polygon method, 27, 28
Time-area diagram (TAD), 378, 398, 400
Time of concentration, 109, 398
runoff from, 109, 398
Transpiration, 67
ratio, 67
Transmissibility, 196, 199
Trap efficiency, 301-303
Unit hydrograph, 113, 124, 379
application of, 157, 158, 160
alteration of duration, 136
assumptions of, 113
average, 136
derivation of, 124, 129
from complex storms, 130, 132
dimensionless, 156
elements of, 126
instantaneous (IUH), 149, 379, 393, 401
limitations of, 127
matrix method, 135
propositions of, 127
runoff estimation from, 113
SCS method, 157
synthetic (SUH), Snyder’s 149
transposing of, 154
Unit storm, 127
Unsaturated flow, 66
Valley storage, 97, 106
Variance, 327
Velocity measurements, 172
Velocity rods, 172
Water balance, 87, 445
of Krishna river basin, 87
Water bearing formations, 192
Water losses, 60
Watershed leakage, 87
Page 477
C-9\N-HYDRO/IND.PM5
INDEX 463
Water resources, World’s, 1
of India, 1
Well hydraulics, 196
Cavity wells, 200
Dupuitt’s equations, 196-198
Jacob’s equations, 433-438
Open (dug) wells, 202
Thies equations, 432-438
Well interference, 207
Wells spacing, 207
W-index, 82
Yield (see runoff estimation), 106, 429
for tank, 109
rational method for, 106, 108
