frequency of 21.5 and 17.) respectively.(Figure 6). The percentages of 
frequencies derived by hindcasting were as follows: North 17.5%, East 16.5%, 
South 15.0%, Southwest 16.3%. Relative to the directions Northwest, North, 
and Northeast, the discrepancy between the observed and hindcast wave 
frequencies may be accounted for by the fact that there are a series of 
shoals averaging 35 feet in depth and having minimum depths of 20 feet located 
some 0 miles from the Lightship in these directions. Waves having periods 
in excess of 3 seconds would refract in passing over these shoals and would 
not necessarily approach the Lightship from the original deep water directions; 
and in some cases (depending on period) would never reach the Lightship. 
Thus without making numerous wave refraction diagrams covering these directions 
and all periods in excess of 3 seconds, it is impossible to make a good 
wave direction comparison between observed and hindcast data. 
A comparison of observed and hindcast wave heights and periods (Figure 7) 
showed very good similarity of phase pattern; for the most part observed 
peaks and hindcast peaks occurred simultaneously with some individual linear 
difference in height and period. The average wave height difference (hind- 
cast greater than observed) was 0.06 foot and the average wave period 
difference was 1.9 seconds over the three week period under observation, 
where the observed wave heights averaged about 35 feet (ranging from 1 to 
11 feet) and the observed period averaged about seconds (ranging from 2 
to 12 seconds). The fact that the hindcast values are consistently greater 
than the observed may be attributed in part at least to the difference 
between the significant wave hindcast and the somewhat lower "average" wave 
observed. 
About 50 percent of all swell waves considered had a deviation (hind- 
cast height minus observed height) of plus or minus 1 foot or less, and 
73 percent had a deviation of plus or minus 2 feet or less (Figure 8). 
As shown in Figure 8a there was a small percentage of waves wherein 
the differential between hindcast and observed heights was greater than 
2 feet up to a maximum of 9 feet; the explanation of this large discrepancy 
is not immediately apparent as the majority of these waves came from the 
south and southeast and consequently would not be affected by refraction. 
No refractive effects have been considered in this comparison of hindcast 
and observed data; however the use of refraction diagrams would probably 
result in only a negligible difference in the height deviation already 
given as, excluding those waves crossing Nantucket whoals, only those waves 
with periods of 8 seconds or more would be affected by refraction, as the 
lightship is moored in 180 feet of water. 
Figure 8b shows a histogram of wave period deviation (hindcast minus 
observed). About 36 percent of all waves had a deviation of plus or minus 
1 second or less and 57 percent had a deviation of plus or minus 2 seconds 
or less. 
