3. A comparison of the Rayleigh pdf model with a large set of observa- 

 tions is described in the Shore Protection Manual (SPM) (1984). That com- 

 parison indicates that if both the number of waves and the RMS wave height 

 from a sea surface elevation record are modified to minimize differences 

 between model and data, a discrepancy of 10 to 15 percent remains in the low- 

 probability but high-wave tails of the distributions. These tails are 

 important for estimating extreme wave conditions, so it is important that they 

 be modeled correctly. The above result suggests that either the model or the 

 data (or both) are not representative of real ocean conditions to within the 

 stated percentages. 



4. On the other hand, Longuet-Higgins (1980) cites favorable com- 

 parisions of the Rayleigh pdf with data reported by Earle (1975) and 

 Forristall (1978). To achieve a favorable comparison, Longuet-Higgins 

 renormalized Forristall 's data with a spectrally based characteristic wave 

 height modified for effects of finite bandwidth. His argument was justified 

 in that the RMS wave height is the controlling parameter in a Rayleigh 

 distribution and the relationship between RMS wave height and spectrum-based 

 wave height can be altered when a narrow-band process is perturbed by low- 

 level energy at frequencies away from the peak frequency, as occurs often in 

 nature . 



5. Thornton and Guza (1983) extended tests of the Rayleigh pdf to 

 include highly nonlinear, actively breaking wave conditions in very shallow 

 water. They used data from a number of sensors in water depths as shallow as 

 1 m in the breaker zone at Torrey Pines Beach, California. The Rayleigh pdf 

 provided very good estimates of wave height statistics in comparison with 

 their observations. There was, however, a very slight overprediction of the 

 wave population in the high-wave tail of the pdf, somewhat like the result 

 given in the SPM (1984). 



6. None of the above tests specifically address the problem of height 

 distributions under conditions where an energy spectrum is distinctly multi- 

 modal. A simple example of such a condition occurs where two narrow-band 

 processes coexist but at well-separated frequencies. In nature, such a 

 condition can arise where a local, wind-driven sea is generated in the 

 presence of low-frequency swell. In general, one would not expect wave 

 heights from this scenario necessarily to be Rayleigh distributed because the 

 requirement of a unimodal , narrow-band process has been violated. In light of 



