v ≅ (2V )
1/ 2
for V small
(12)
v ≅ [2(1 - R )]
1/ 2
for R l arg e
4. STATISTICAL RESULTS
Monthly statistical calculations were done for each of the months that had wave direction
measurements from 1990-1999. The overall vector mean wave direction parameter was used in these
calculations both for the WIS information and the measurement information. Statistics are presented for
waves 1.0 m and higher. The measurement height was used for imposing the 1-m limit. Directions of low
wave heights can diverge and contaminate the directional difference distribution and the 1- m limit
produced consistent results for the various locations.
Figure 2 shows the wave direction statistics for NDBC 42007 and WIS for 1997 excluding August,
which had less than 20 coincident direction pairs. Figure 2 also excludes January through March
because there were no measurements. The monthly mean directional difference is shown by a circle.
Note that most months except April, May, and December (months 4, 5, and 12) show positive mean
directional differences indicating that the buoy wave direction (in polar coordinates using vector direction-
waves going toward this direction) is more clockwise than the WIS direction. The maximum mean
directional difference, 16 deg, occurs in September, 1997. The concentration statistic is shown by a
triangle in Figure 2. Recall that concentrations below 5.0 indicate more dispersion in the distributions.
The May (month 5) results fall in this category. Correlations for all months fall between 0.75 and 0.90
indicating reasonable correlation between the measured and hindcasted wave directions. Another very
important factor in the statistics is the number of coincident observations. May has only 49 observations
so this may not be a good sample of the whole month. Figure 3 shows a plot of the 118 directional
differences for November. The plot shows a definite bias to positive directional differences. An event
right after November 20 shows some obvious disagreement between 42007 and WIS. Figure 4 gives a
picture of the actual comparison by showing measured mean wave directions at 42007 plotted with
coincident WIS mean wave directions for November 1997. Note that wave directions in Figure 4 are in
meteorological convention. July has a small directional difference, concentration above 5.0, and 0.966
correlation (see Figure 2). Figure 5 shows the measured and WIS information that produced these
statistics. Note that all these plots show that the concentration statistic and circular correlation provide an
excellent description of the monthly directional comparison. Table 2 lists all the statistical values for the
comparisons of mean wave direction for NDBC 42007 and WIS for 1997. Column 3 lists the monthly
mean directional difference in degrees; columns 4 and 5 give the upper and lower 95% confidence limits
^
on the monthly mean directional difference; k is the concentration statistic. The number of paired values
for the month is shown in the next column; cor is the linear correlation; circor is the circular correlation.
The last 3 columns give the resultant, variance and standard deviation of the directional difference
distribution. A researcher could take this statistical information into account and verify differences in
results from using WIS directional hindcast information at this time and location.
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