EM 1110-2-1100 (Part II)
30 Apr 02
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 Hs or H1/3. 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-
crossing period, etc.
(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
height H. The largest wave height in the record is the maximum wave height Hmax. The root-mean-square of
Water Wave Mechanics