between the definitions of wave parameters obtained by the zero up- and down-crossing methods for

description of irregular sea states.

(c) Both methods usually yield statistically similar mean values of wave parameters. There seems to

be some preference for the zero-downcrossing method (IAHR 1986). The downcrossing method may be

preferred due to the definition of wave height used in this method (the vertical distance from a wave trough

to the following crest). It has been suggested that this definition of wave height may be better suited for

extreme waves (IAHR 1986).

(d) Using these definitions of wave parameters for an irregular sea state, it is seen in Figures II-1-26 and

II-1-27 that, unlike the regular (monochromatic) sinusoidal waves, the periods and heights of irregular waves

are not constant with time, changing from wave to wave. Wave-by-wave analysis determines wave properties

by finding average statistical quantities (i.e., heights and periods) of the individual wave components present

in the wave record. Wave records must be of sufficient length to contain several hundred waves for the

calculated statistics to be reliable.

(e) Wave train analysis is essentially a manual process of identifying the heights and periods of the

individual wave components followed by a simple counting of zero-crossings and wave crests in the wave

record. The process begins by dissecting the entire record into a series of subsets for which individual wave

heights and periods are then noted for every zero down-crossing or up-crossing, depending on the method

selected. In the interest of reducing manual effort, it is customary to define wave height as the vertical

distance between the highest and lowest points, while wave period is defined as the horizontal distance

between two successive zero-crossing points (Figures II-1-26 and II-1-27). In this analysis, all local maxima

and minima not crossing the zero-line have to be discarded. From this information, several wave statistical

parameters are subsequently calculated. Computer programs are available to do this (IAHR 1986).

(3) Definition of wave parameters.

(a) Determination of wave statistics involves the actual processing of wave information using the

principles of statistical theory. A highly desirable goal is to produce some statistical estimates from the

analyzed time-series data to describe an irregular sea state in a simple parametric form. For engineering, it

is necessary to have a few simple parameters that in some sense tell us how severe the sea state is and a way

to estimate or predict what the statistical characteristics of a wave record might be had it been measured and

saved. Fortunately, millions of wave records have been observed and a theoretical/empirical basis has

evolved to describe the behavior of the statistics of individual records.

(b) For parameterization, there are many short-term candidate parameters which may be used to define

statistics of irregular sea states. Two of the most important parameters necessary for adequately quantifying

a given sea state are characteristic height *H *and characteristic period *T*. Other parameters related to the

combined characteristics of *H *and *T*, may also be used in the parametric representation of irregular seas.

(c) Characteristic wave height for an irregular sea state may be defined in several ways. These include

the *mean height*, the *root-mean-square height*, and the mean height of the highest one-third of all waves

known as the *significant height*. Among these, the most commonly used is the significant height, denoted

as *H*s or *H*1/3. Significant wave height has been found to be very similar to the estimated visual height by an

experienced observer (Kinsman 1965). The characteristic period could be the *mean period*, or *average zero-*

(d) Other statistical quantities are commonly ascribed to sea states in the related literature and practice.

For example, the mean of all the measured wave heights in the entire record analyzed is called the *mean wave*

II-1-66

Water Wave Mechanics

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