##### 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)

Page 239

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)

Page 239

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