Deepwater wave conditions used as input to the models were determined from 

 Waverider measurements made on 13 September 1978. Input wave conditions for 

 both models are a period of 7.3 seconds, a wave height of 4.2 feet (1.3 meters), 

 and a direction (from which waves are propagating) of 17° counterclockwise from 

 the pier facing seaward. 



An example of output from the wave ray program is shown in Figure 2. In- 

 formation of this type is provided along each ray from its initial to final 

 point. A discussion of these output parameters and other details of the pro- 

 gram are contained in the program documentation available at CERC. Results 

 from one of the plotting options of the program are illustrated in Figure 3 

 by a diagram of wave rays showing the convergence and divergence of rays as 

 they proceed from their initial point offshore toward the shore. Since it is 

 assumed that wave energy is conserved between rays, the energy as the rays 

 converge is confined to smaller areas and results in higher waves. Unrealis- 

 tically high waves may be predicted in some instances due to the limitations 

 of the theory. No specific criterion is currently available to define such 

 cases; the results must be Interpreted carefully in areas of ray convergence. 

 An aid in Interpretation is the beta or ray separation factor 3. When this 

 factor approaches zero, calculated wave heights are not valid. How far from 

 zero beta has to be for valid results is a question under investigation. At 

 present, the results obtained in the range -0.5 < 3 < 0.5 are questionable. 



An example of the output from the spectral model is shown in Figure 4. In 

 comparison to the wave ray model in Figure 3, both models are shown to predict 

 similar patterns of ray convergence and divergence. It is difficult to deter- 

 mine if the ray patterns shown in Figures 3 and 4 accurately depict the actual 

 pattern of waves at the pier for the given angle of approach. A qualitative 

 judgment can be made by comparing a photo of the CERC radar scope (Fig. 5) to 

 the ray diagrams. The continuous white segment across the bottom of the photo 

 is the radar reflection from the shoreline. The line at the center of this 

 segment and perpendicular to it is the pier. The white spot in the center of 

 the photo is the end of the pier where the radar is situated. The other white 

 line segments are reflections from wave crests. A line traced perpendicular 

 to these crests is a wave ray. The pattern of wave crests in Figure 5 shows 

 that there will be a convergence of wave rays to the right of the pier and a 

 divergence to the left. This is also apparent in the ray patterns in Figures 

 3 and 4 which indicate the model results are qualitatively correct. A com- 

 parison of the wave height measured along the pier and that calculated with 

 the two models is shown in Figure 6. 



Wave heights are available at each grid point from the spectral model and 

 are plotted from the grid line parallel and closest to the pier. Wave heights 

 from the ray model are available along each ray at points indicated by a (+) 

 in Figure 3. The interpolation program used to obtain evenly spaced bathym- 

 etry was also used to obtain wave heights at the grid points of the spectral 

 model using the unevenly spaced wave heights from the ray program. The plotted 

 wave heights for the ray model are thus interpolated values which lie along 

 the same grid line as chosen for the spectral model. Little variation in wave 

 height is indicated from the spectral model. Larger variations are shown for 

 the ray model but that at grid point 25 is suspect since the beta factor is 

 less than 0.5 at that point along the ray and such a difference in significant 

 wave height over one grid distance is unreasonable. 



