148
STATISTICAL DESCRIPTIONS OF OFFSHORE WAVES
Wave Height Distributions
Examinations of offshore wave data hâve shown that the surface wave heights
H follow the Rayleigh (1880) probability density function, p(H). The following
exposition involving this probability follows that of Goda (1985) and Young
(1999), originally proposed by Barber (1950) and Putz (1954). The particularly
useful form of the Rayleigh probability density function is
=
(«)
ma
in which Hrma is the root-mean-square (rms) wave height of a given record. The
square of this latter quantity is defined as
fOO
H^ms=H^=l H2p(H)dH
Jo
(67)
As the notation V H‘ implies, Hrms is formed by squaring the height of each
wave in a given record, taking the arithmetic average of these quantities, and
then taking the square root of the resuit. The mean or average wave height is
defined by
Ho =
Hp(H)dH
(6-8)
Based on the Rayleigh distribution, the average wave height, Hq, the significant wave height, H„, and the 1/10 highest wave height, H1(/10, are deduced
as
Ho = 0.87Hrm<;
H„ = 1.42ffrms;
H1/10 = 1.80Hrms
(6-9)
These three wave heights are depicted in Figure 6.2, which is a plot of the
Rayleigh distribution given by équation (6.6). Also shown is the height of the
most probable wave, which is at the peak of the curve.
Further, the most probable maximum wave height, Hmax, dépends on the
duration of the storm or length of the wave record. The following relationship
is often used to approximate this maximum wave height:
Hmex ~ 0.707H, ln N
(6-10)
Here A is the number of waves in the record. When N is not known, a reasonable
approximation to this maximum wave height is
Hmax = 1.77H,
(6-11)
For very severe storm waves or for waves in very shallow water near the breaking
point, équations (6.10) and (6.11) should be used with caution.