Wave Spectra

In general, the transfer functions gain between signals from the video images and in-situ measurement show quantitative variation. Examination of the component of the transfer function identified that three frequency ranges may have different characteristic. Transfer function gain showed decrease in frequency lower than 0.05 Hz. At frequency 0.05 – 0.40 Hz, the transfer functions gain showed constant mean value, and start to decrease in frequency higher than 0.40 Hz. The result for transfer function analysis suggests a close relationship between the video image signal and in-situ measurement within the frequency range of 0.05 – 0.40 Hz.

According to the coherence function analysis, the result suggests that the relationship condition between two signals is non-linear, thus, the fundamental assumption for the estimation of linear transfer function gain may be violated in this analysis. The nonlinearities of the transfer function can be introduced by several ways. The varying of the sun light condition throughout the day will introduce a nonlinear transfer function from the video image spectrum. Wave breakings or residual foams are other nonlinearity phenomena in shallow water areas that also give influence in the transfer function. Furthermore, the distortion of the video images due to increasing distance away from video camera can lead an error in spectral estimation.

Although it is difficult to make a quantitative comparison between the signals of pixel brightness on video image data and the wave gauges, the similarity in the shape of wave spectra can be seen in the auto spectral analysis, which indicated that the peak frequencies estimated from time series of pixel brightness on video image sequences show a reasonably good correspondence with the wave gauge data. It seems that time series of pixel brightness on video images contain the energy distribution information of the wave field that can be used to estimate wave spectra.

The time series of 512 points sampled at intervals of 1.0 second were first standardized using zero mean and subdivided into 128-points segment with 50%

overlap for spectral estimation. This process of analysis resulted in 7 segments of data with spectral resolution of 0.0078 Hz. Fast Fourier Transform was implemented with each Hanning-window segment and averaged to calculate wave spectrum.

Video images recorded on 18 August 2006 were used in the spectral analysis. On this day, the observed significant wave height based on NOWPHAS database was below 1.0 m and the wave direction was approached from NE direction. The results of the wave spectrum of pixel brightness on video image are shown in Figure 4.13.

Figure 4.13 Examples of raw spectrum (top) and smoothed spectrum (bottom) from pixel brightness on video images

Figure 4.14 Comparison of wave spectrum from video images and in-situ sensor recorded on 18 August 2006 at 09.00 h.

Comparison of wave spectrum between the time series of pixel brightness on video images and in-situ measurement is shown in Figure. 4.14. It can be seen that the normalized wave spectra are similar in shape. The figure shows a narrow band spectrum with major sharp peak at frequency 0.117 Hz, which corresponds to peak period of 8.5 seconds. This peak frequency corresponds with peak period from offshore measurement (T_1/3 = 8.2 seconds). Meanwhile multiple weaker peaks appear at higher frequency from 0.2 Hz to 0.4 Hz. These multiple weaker peaks are present due to nonlinear wave components, which is a typical characteristic of the shallow water spectrum. Also, the spectrum shape from wave gauge is smoother because the frequency resolution is less than of the pixel brightness on video images. Below 0.05 Hz and above 0.4 Hz, the white noise decreases due to band-pass filter with a high pass filter and a low pass filter.

Figure 4.15 Time series of wave spectra estimated from video images and in-situ sensor on 18 August 2006.

Figure 4.16 Time series of single peak frequency, fp from video images and in-situ sensor on 18 August 2006.

Figure 4.15 shows another example of comparison between the wave spectra from the video images and in-situ measurement on 18 August 2006. In the figures, the peak frequency was very close in both wave spectra. While in some cases, for example at 11.00 h and 15.00 h, the video images and in-situ spectra presented different peak frequency. It is important to remark that the time series of pixel brightness on video images depend on not only wave slope but also other phenomena such as sea ripples, wave breaking, sun glitter, etc. On the other hand, the wave gauge data represent as true water surface elevations.

However, in general, it can be concluded that the video images and in-situ spectra show similar form with the frequency peaks positioned very close to each other as indicated in Figure. 4.16. The figure shows the single peak frequency observed from the video images and in-situ measurement varied between 0.09 Hz and 0.13 Hz. The average of peak frequency from the video images and in-situ are 0.09 Hz and 0.10 Hz, respectively. The average of peak frequencies agreed well with a difference of only 0.01 Hz between video images and in-situ spectra.

Another example of comparison between the wave spectra from the video images and in-situ measurement on moderate condition (9 October 2006) is shown in Figure 4.17 and 4.18, respectively.

Figure 4.17 Time series of wave frequency spectra estimated from video images and in-situ sensor on 9 October 2006

Figure 4.18 Time series of single peak frequency, f_p from video images and in-situ sensor on 9 October 2006