THE NEAR-SURFACE LAYER OF THE OCEAN
the coherence between the velocity and integrated acceleration, as shown in
Figure 3-7c. The velocity contamination at frequencies less than 1 Hz is
associated with the ship’s motion and is outside of the band used for
turbulence estimates. Above 8 Hz, there are varying degrees of
contamination, with high coherence at 18, 25, 50 and 110 Hz. Removal of
this vibration contamination by extrapolating the spectrum through known
motion peaks or using a notch filter turns out to be relatively ineffective here
because the resonant properties of the bow frame and ship depend on the
position of the air-water interface with respect to the frame, which changes
during the pitching period. Instead, we use the coherent noise cancellation
technique, based on the Wiener filter, developed by Schoeberlein and Baker
(1996) and tested with the TOGA COARE bow data in Soloviev et al.
(1999).
One important aspect of implementing the Wiener filter is to insure that
the reference correlation matrix is not singular and thus can be inverted. This
can be a problem when using data that contains a strong low-frequency
component, such as the ship’s motion and the surface wave velocities at
frequencies less than 1 Hz. To avoid this problem, the data are pre-whitened
by numerical differentiation. To restore the velocity spectrum after the
coherent noise cancellation, the signal is integrated.
Figure 3-7b shows the velocity spectrum after applying the coherent
noise cancellation techniques using the Wiener filter with 60 weights; Figure
3-7d presents the residual coherence. Note that the 95% confidence intervals
of the coherence encloses zero. This means that no statistically significant
coherent contamination is left in the filtered signal. The effectiveness of the
Wiener filter in the time domain is demonstrated in Figure 3-8.
In Figure 3-9, the spectrum of the velocity signal processed with the
Wiener filter as described above is compared to the sensor electronics noise
spectrum. The corresponding 95% confidence intervals are shown with thin
lines. The confidence intervals for the spectral estimates calculated from 10min velocity segments are very small because the number of degrees of
measured in a laboratory tank with motionless seawater during the postcruise calibration. The RMS noise for the u channel over the frequency
range 2-200 Hz was 0.8 mm s
-1 .
Since the electronic noise and the measured velocity signal are not
correlated, the noise spectrum can be subtracted from the u velocity
spectrum. However, if the experimental spectrum is close to its noise level,
this procedure may result in unrealistic negative spectral components at
some frequencies. (Note that in Figure 3-10 we subtract the noise spectrum
from the velocity spectrum only for demonstration purposes.)
166
freedom is large (234). The noise spectrum shown in Figure 6a was
the coherence between the velocity and integrated acceleration, as shown in
Figure 3-7c. The velocity contamination at frequencies less than 1 Hz is
associated with the ship’s motion and is outside of the band used for
turbulence estimates. Above 8 Hz, there are varying degrees of
contamination, with high coherence at 18, 25, 50 and 110 Hz. Removal of
this vibration contamination by extrapolating the spectrum through known
motion peaks or using a notch filter turns out to be relatively ineffective here
because the resonant properties of the bow frame and ship depend on the
position of the air-water interface with respect to the frame, which changes
during the pitching period. Instead, we use the coherent noise cancellation
technique, based on the Wiener filter, developed by Schoeberlein and Baker
(1996) and tested with the TOGA COARE bow data in Soloviev et al.
(1999).
One important aspect of implementing the Wiener filter is to insure that
the reference correlation matrix is not singular and thus can be inverted. This
can be a problem when using data that contains a strong low-frequency
component, such as the ship’s motion and the surface wave velocities at
frequencies less than 1 Hz. To avoid this problem, the data are pre-whitened
by numerical differentiation. To restore the velocity spectrum after the
coherent noise cancellation, the signal is integrated.
Figure 3-7b shows the velocity spectrum after applying the coherent
noise cancellation techniques using the Wiener filter with 60 weights; Figure
3-7d presents the residual coherence. Note that the 95% confidence intervals
of the coherence encloses zero. This means that no statistically significant
coherent contamination is left in the filtered signal. The effectiveness of the
Wiener filter in the time domain is demonstrated in Figure 3-8.
In Figure 3-9, the spectrum of the velocity signal processed with the
Wiener filter as described above is compared to the sensor electronics noise
spectrum. The corresponding 95% confidence intervals are shown with thin
lines. The confidence intervals for the spectral estimates calculated from 10min velocity segments are very small because the number of degrees of
measured in a laboratory tank with motionless seawater during the postcruise calibration. The RMS noise for the u channel over the frequency
range 2-200 Hz was 0.8 mm s
-1 .
Since the electronic noise and the measured velocity signal are not
correlated, the noise spectrum can be subtracted from the u velocity
spectrum. However, if the experimental spectrum is close to its noise level,
this procedure may result in unrealistic negative spectral components at
some frequencies. (Note that in Figure 3-10 we subtract the noise spectrum
from the velocity spectrum only for demonstration purposes.)
166
freedom is large (234). The noise spectrum shown in Figure 6a was