Hydraulic Structures: Fourth Edition

and

^2 s

N

1

1



N

i 1

[ln(Hs) μs]^2.

Before attempting to estimate the design wave height for a return period,
we must first ensure that the collected data are closely approximated by
the chosen probability distribution. The following steps may be adopted.

1. The values of Hsfor each of the record are arranged in the ascending
   order of magnitude. Let the number of HsbeN.


2. A plotting formula is used to relate P(Hs) with Hsand to plot this on
   the probability paper is

P(Hs).

3. The data points (Hs,P(Hs)) are plotted on a probability paper corre-
   sponding to the chosen probability distribution. The data points will
   collapse on a straight line if they follow the chosen distribution (see
   Worked example).


4. The straight line is extrapolated to determine the design wave height
   for the chosen return period TR. If the time interval of the records is
   , then

TR/P(Hs)

in which is expressed in units of years. For example, if 3 h, it is

equivalent to 1/2920 year.

If the log-normal distribution does not fit the data, the data may be
approximated by the Weibull distribution:

P(Hs)exp (^) 
k 1
. (14.60)
Hcis the minimum wave height at the site; it is found by examining the
long-term records by trial and error in the search for the best fit to the
Weibull distribution. The parameters H 0 andk 1 are obtained after arriving
at the best fit. Note that the Weibull distribution uses three parameters, as
against two in the log-normal distribution.
Extreme value distributions may be used for estimating the design
wave height for a specified return period. They deal with the largest value
of the wave height in each year over a period of years. Extreme value sta-
tistics require data for a considerable number of years. If they are not
Hs Hc

H 0
number of waves exceeding Hs

N 1

WAVE STATISTICS 601