Hydraulic Structures: Fourth Edition

From equation (14.49), for the Pierson–Moskowitz spectrum,

Hs0.447g
1/2/π^2 f^2 m. (14.55)

Numerical integration of the JONSWAP spectrum carried out by Carter

(1982) leads to an expression for Hsas

Hs0.552g
1/2/π^2 f^2 m. (14.56)

The estimate of a design wave on the basis of recorded data may also be

made using the long-term wave statistics. Hsis often selected with a certain

return period TR, i.e. the design (significant) wave height is expected to be

exceeded in one year over TRyears. Thus

TR1/P(Hs). (14.57)

It is common practice to use a 50- or 100-year return period as a level of

protection for most coastal structures. Alternatively the design may be

based on the encounter probability E. It is the probability that the design

wave is equalled or exceeded during the life of Lyears of the structure. The

encounter probability Eis

E 1 (1 1/TR)L (14.58)

For example, E0.33 for TR50 and L20 or for E0.1 and L20,

TR190.

Choice of larger return period for the design of a structure means

smaller probability Ethat the design wave will be exceeded during the life

of the structure.

Several probability distributions have been proposed to describe the

long-term statistics. Among them is the log-normal distribution commonly

used in coastal engineering. It is a normal or Gaussian distribution for the

variate ln(Hs) instead of Hs. The probability P(Hs) for the log-normal dis-

tribution is

P(Hs) 1 

Hs

0

exp 

1

2



2

dHs (14.59)

wherezsln(Hs). The two parameters μsandsare the mean and stan-

dard deviation of the variate ln(Hs). For a sample of Nvalues of Hs, they

are defined as

μs

N

1



N

i 1

ln(Hs)

zs μs



s

1



sHs

1



(2π)1/2

600 WAVES AND OFFSHORE ENGINEERING