wD 
~ 
3.0 Go Ibs) 10,0 0 
n > a 
Ss 20 2 ho = re C 
— wo ~— 
Cc 
a uw E> al). 
= = 
® 10 Ops ® 
Cc > Cc 
uJ rs) w oO! 
Cc 
wo 
0.0 Ss 0.0 oe 00 
0.0 0.5 10 @ 001 0.1 1.0 0.01 0.1 1.0 
Frequency (Hz) re Frequency (Hz) Frequency (Hz) 
1Q0 0 3.0 
a 100 a 
Se = 2.0 E 
= 1/0 a 
® ® 1.0 
Cc 
OM Ww 
00 0.0 
0.0 0.5 1.0 0.0 10.0 20.0 30.0 
Frequency (Hz) Period (s) 
Figure 4. Five formats frequently used in displaying wave energy spectra. The 
actual spectrum is identical in all five graphs. The frequency band- 
width, (Af)3, is constant for all j so that energy values and energy 
density values differ by a constant factor (see eq. 2). The plots 
would look the same if energy were replaced by energy density, but 
the vertical scale would change (from Harris, 1972). 
3. Natural Variability. 
Wave energy spectra are naturally variable simply because they are based on 
a finite length record of a wave field which varies in time and space. Spectra 
computed for successive records of a relatively stationary wave field are never 
identical and often differ noticeably. The magnitude of spectral variation in 
time is illustrated by spectra derived at 2-hour intervals from two pressure 
gages along the southern California coast (Fig. 5). The significant wave height 
is nearly constant in the figure. 
Spatial variation of the spectrum over short alongshore distances in shallow 
water is also shown in Figure 5. Each spectrum in the top row of the figure can 
be compared to the spectrum immediately below it to see variations between spec- 
tra from two gages 80 feet (24 meters) apart. In this figure, spatial variations 
are smaller than temporal variations. Spatial variations would be expected to 
be greater if the gages were farther apart or the water depth varied between 
measurement points. Variations between spectra from gages situated along a line 
perpendicular to shore are shown in Figure 6. The spatial variations are more 
prominent in this figure than in Figure 5. 
