all the measured wave heights is the *rms wave height H*rms. The average height of the largest *1/n *of all waves

in the record is the *H*1/n where n = 10, 11, 12, 13,..., 99, 100 are common values. For instance, *H*1/10 is the

mean height of the highest one-tenth waves. In coastal projects, engineers are faced with designing for the

maximum expected, the highest possible waves, or some other equivalent wave height. From one wave record

measured at a point, these heights may be estimated by ordering waves from the largest to the smallest and

assigning to them a number from *1 *to *N*. The significant wave height *H*1/3 or *H*s will be the average of the first

(highest) *N/3 *waves.

(e) The probability that a wave height is greater (less) than or equal to a design wave height *H*d may be

found from

(II-1-114)

where *m *is the number of waves higher than *H*d. For an individual observed wave record the probability

distribution *P(H > H*d) can be formulated in tabular form and possibly fitted by some well-known distribution.

The root-mean-square wave height *H*rms may be computed as

j *H*j

1

2

(II-1-115)

in which *H*j denote the ordered individual wave heights in the record.

(f) Probability distributions discussed in the irregular wave section of the CEM refer to short term wave

statistics. This subject concerns the probability that a wave of a given height will occur given that we know

the statistics of the sea surface over a 16- to 60-min period. A short-term wave statistics question might be,

for example, "If we have measured the waves for 15 min and found that Hs is 2m, what is the chance that a

wave of 4 m may occur?" This must be contrasted to long-term wave statistics. To obtain long-term wave

statistics, a 15-min record may have been recorded (and statistics of each record computed) every 3 hr for 10

years (about 29,000 records) and the statistics of the set of 29,000 significant wave heights compiled. A long-

term wave statistics question might be, "If the mean significant wave height may be 2m with a standard

deviation of 0.75m, what is the chance that once in 10 years the significant wave height will exceed 4 m?"

These are two entirely different statistical questions and must be treated differently.

(g) A similar approach can be used for the wave period. The mean zero-crossing period is called the

period *T*c. Therefore, in the time domain wave record analysis, the average wave period may also be obtained

from the total length of *record length T*r either using *T*z or *T*c (Tucker 1963). These periods are related to *T*r

by

(II-1-116)

Water Wave Mechanics

II-1-67

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