Even if a frequency or frequency-direction spectrum has been accurately deter- 

 mined, these methods have a number of shortcomings when used to predict the kine- 

 matics of irregular waves. Shortcomings include the inaccuracies inherent in linear 

 wave theory, particularly in shallow water and with large waves. 



An additional difficulty arises from the superposition of many waves. This problem 

 is known as high frequency contamination of the crest kinematics (Forristall 1985; Lo 

 and Dean 1986; Bishop and Donelan 1987). Fundamentally, the difficulties arise 

 from the approximations made by linear wave theory in the free surface boundary 

 conditions. In linear theory the free surface boundary conditions are applied at the 

 mean water level, and thus predictions made above that level are strictly out of 

 the solution domain. If the full free surface boundary conditions are not satisfied, 

 the resulting predictions will be inaccurate, particularly near the free surface. In 

 particular, the hyperbolic function quotients that define the vertical variation of the 

 kinematics become very large in the region above the MWL for the high frequency 

 (and high wave number) components. This results in substantial high frequency 

 fluctuations in the predicted kinematics near the crest. 



In an attempt to reduce the inaccuracies in linear superposition's predictions of the 

 near surface kinematics, empirical modifications to Airy theory have been adopted 

 (Wheeler 1969; Lo and Dean 1986). This method, known as Wheeler stretching, 

 locally adjusts the vertical dimension to prevent the evaluation of the hyperbolic 

 quotients from being evaluated above the MWL. The result is a hybrid global-local 

 method in that the frequency, wave numbers, and amplitude of each wave are deter- 

 mined globally, but the coordinate system is defined locally, varying with time. 



The stretching method produces predictions of crest kinematics that seem to 

 match measured data better than simple linear superposition, but it no longer satis- 

 fies either the Laplace equation (mass conservation), or the full free surface boundary 

 conditions. 



Another attempt to improve on the accuracy of determining the kinematics from 

 directional spectra is the recent work by Prislin et al. (1997), and Prislin and Zhang 

 (1997). This method seeks to reconstruct wave kinematics from a directional spec- 

 trum using a second order Stokes-type interacting wave theory. The spectrum is 



