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where c1, a1 and b1 refer to return period T1 and c2, a2 and b2 are applicable for return period T2, etc. Generally, it will be observed that the coefficients a and b are approximately the same for all the return periods and only c is different for different return periods. In such a case one general equation may be developed for all the return periods as given by:
(3)
where T is the return period in years and K and d are the regression coefficients for a given location. If a and b are not same for all the return periods, then an individual equation for each return period may be used.
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Since annual maximum series consider only the maximum value each year, it may happen that the annual maximum in a year is less than the second or even third largest independent maximum in another year. Hence, the values at the lower end of the annual exceedance series will be higher than those of the annual maximum series. Consequently, the return period derived for a particular I(D) based on annual maximum series will be larger than one would have obtained from annual exceedances. The following relation exists between the return period based on annual maximum and annual exceedance series (Chow, 1964):
(4)
where:
TE = return period for annual exceedance series
T = return period for annual maximum series
Figure Definition of partial duration series
The ratio TE /T is shown in the next figure. It is observed that the ratio approaches 1 for large T. Generally, when T < 20 years T has to be adjusted to TE for design purposes. Particularly for urban drainage design, where low return periods are used, this correction is of importance.
Figure: Relation between return periods annual maximum (T) and annual exceedance series (TE).
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