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0 100 200 300 400 500

0 100 200 300 400 500

Fig. 11.15 (a) Frequency of annual maxima of different magnitude plotted as a histogram. (b) Continuous probability distribution of annual maximum flood peaks.

Fig. 11.15 (a) Frequency of annual maxima of different magnitude plotted as a histogram. (b) Continuous probability distribution of annual maximum flood peaks.

The probability that an annual maximum, Q, lies between two values, a and b, is given by:

fbp(Q)dQ

For any given magnitude, X, the probability that an annual maximum equals or exceeds X, i.e. that Q > X is:

r TO

which is the area shaded under the probability curve (Fig. 11.15b). If F(X) is the probability of Q < X :

and clearly:

P(X) is the probability of an annual maximum equalling or exceeding X in any given year, since it is the relative proportion of the total number of annual maxima that have equalled or exceeded X. If X is equalled or exceeded r times in N years (N large), then P(X) ^ r/N. The return period for X is, however, T(X) = N/r. Thus:

0 0

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