Contents preface (VII) introduction 1—37

Table 2.4. Values of the constants a, b, c and d for Eqs. (2.32) and (2.33)

Region	a	b	c	d
Mahi and Sabarmati	1.161	– 0.635	0.433	0.704
Lower Narmada and Tapi	1.920	– 0.780	0.523	0.323
Mahanandi	1.121	– 0.660	1.970	0.240
Godavari	1.968	– 0.842	0.253	0.450

2.8.1.3. Unit Hydrograph Method
One can use already known or derived unit hydrograph for a catchment basin to predict the peak flood hydrograph in response to an extreme rainfall i.e., the design storm in the catchment as discussed in Art. 2.7.
2.8.1.4. Flood Frequency Method
The data of annual maximum flood in a given catchment area for a large number of successive years (i.e., data series of the largest flood in each successive year) are arranged in decreasing order of magnitude. The probability P of each flood being equalled or exceeded, also known as the plotting position, is given as

P =	m	(2.34)
N + 1

where, m is the order number of the relevant flood in the table of annual floods arranged in decreasing order and N is the total number of annual floods in the data. Return period (or recurrence interval) T_r is the reciprocal of the probability, P. Thus,

T =

1

(2.35)

r _P
Frequency of flood (or any other hydrologic event) of a given magnitude is the average number of times a flood of given (or higher) magnitude is likely to occur.Thus, the 100-year flood is a flood which has a probability of being equalled or exceeded once in every 100 years. That is, P = 1/100 and T_r = 100 years.
One can draw a graph between the flood magnitude and its return period (or plotting position) on the basis of the data series of annual floods and fit a curve to obtain probability (or empirical) distribution. This graph may be extrapolated to get the design flood for any other return period. Such plots are used to estimate the floods with shorter return periods. For longer return periods, however, one should fit a theoretical distribution to the flood data. Some of the commonly used theoretical frequency distribution functions for estimating the extreme flood magnitudes are as follows:
(a) Gumbel’s extreme value distribution
(b) The log-Pearson Type III distribution, and (c) The log normal distribution.

Flood frequency analysis is a viable method of flood-flow estimation in most situations. But, it requires data for a minimum of 30 years for meaningful predictions. Such analysis gives reliable predictions in regions of relatively uniform climatic conditions from year to year.

HYDROLOGY

89

2.8.2. Design Flood
Design flood is the flood adopted for the design of a hydraulic structure. It would be, obviously, very costly affair to design any hydraulic structure so as to make it safe against the maximum flood possible in the catchment. Smaller structures such as culverts, storm drainage systems can be designed for relatively small floods (i.e., more frequent floods) as the consequences of a higher than design flood may only cause temporary inconvenience and some repair works without any loss of life and property. However, failure of structures such as spillway would cause huge loss of life and property and, therefore, such structures should be designed for relatively more severe floods having relatively larger return period. Table 2.5 provides guidelines for selecting design floods (14). The terms PMF and SPF in the Table 2.5 have the following meaning :
PMF, i.e., probable maximum flood is the extreme large flood that is physically possible in a region as a result of severemost (including rare ones) combination of meteorological and hydrological factors. SPF is the standard project flood that would result from a severe combination of meteorological and hydrological factors. Usually, SPF is about 40 to 60% of
PMF.