TABLE OF CONTENTS Kinsman (1965, p. 386) is careful to point out that a valid specification of real ocean waves must integrate the following three concepts: 1) Fourier and spectral analyses of random processes, 2) probability theories applied to stochastic processes, and 3) hydrodynamics. Techniques from the first two concepts that do not depend on the physics of the hydrodynamic processes are available for analyzing real ocean waves. However, only those techniques from concepts that may be related rigorously to the physics of the hydrodynamics of real ocean waves are reviewed.
The theoretical techniques reviewed are applicable to stationary ergodic processes and are limited strictly to short term statics. Isaacson and MacKenzie (1981) give an excellent review of long term statistical and probabilistic techniques applied to real ocean waves. The significance of the stationary ergodic hypothesis is that the ensemble average E[ x( t 1)] at the same time t 1 shown in Fig. 9.1 of an infinite number of finite length time series x 1( t 1), x 2( t 1), x 3( t 1), , x ?( t 1) is equivalent to the temporal average over all times shown in Fig. 9.2 of an infinitely long single time series x 1( t 1), x 1( t 2), x 1( t 3), , x 1( t ?); i.e.,
