Characteristics of Whitecaps Estimated from Image Processing of The Ocean Surface
Yukun WANG (Kyushu University), Ryo OHNISHI (Kyushu University), Yuji SIGIHARA (Kyushu University), Yoshihiro NAKAMURA (Kyushu University), Osama ELJAMAL (Kyushu University)

Introduction
Whitecaps generated by wave breaking on the ocean surface play
an important role in the local interaction between the atmosphereand the ocean. Figure 1 shows image of whitecaps. Whitecap
coverage is defined by the area of whitecaps per the unit oceansurface.
It has been recognized as one of important physicalquantities for describing the ocean surface fluxes such as themomentum, heat and carbon dioxide, so that the quantitativeevaluation of whitecap coverage becomes significant fromviewpoints of environmental hydraulics and ocean engineering.
Figure 2 shows whitecap coverage extracted by different threshold.
In this study, in order to validate typical estimation methods forwhitecap coverage, the AWE algorithm proposed by Callaghan andWhite (2008) was compared with the threshold method adopted
Fig. 1 Image of whitecaps
usually in previous studies. The agreement between both wasexamined on the basis of the influence of solar radiation. Previousstudies have suggested that the depth of bubble penetration
generated by wave breaking may be proportional to the significant
wave height. Based on this assumption, we proposed a new index
for expressing characteristics of whitecaps, i.e., whitecap depth,indicating the product of whitecap coverage and the bubble
penetration depth. This quantity denotes the averaged depth of thebubbly layer per the unit ocean area, and can be expected to becomea more significant quantity than whitecap coverage. In addition, forthe data of whitecap coverage obtained from the AWE method, weinvestigated the relation of whitecap depth with 10-m wind speed orFig. 2 Comparison between original and binary images
the windsea Reynolds number.

Analysis method

Automatic whitecap extraction (AWE) is an algorithm proposed byCallaghan and White (2008) to automatically determine the coverage of𝑃 𝑖 − 𝑃 𝑖 + 0.01
PIP i =× 100 (1) whitecap, which does not need to determine a subjective threshold by
𝑃 𝑖researcher. By setting a suitable threshold for each sea image, we canprevent the error by detecting non-whitecap region, and can calculate the𝑑𝛷 𝑖
𝛷 𝑖 − 𝛷 𝑖 + 𝛥𝑖value of whitecap coverage more accurately. In order to determine the=(2)𝑑𝑖𝛥𝑖threshold for AWE, PIP (percentage increase in the number of pixels) andthe image structure must be used, where PIP is defined as Eq. (1). As anFig. 3 Change of PIP for each intensity thresholdexample of the analytical results, Fig. 3 shows the variation of PIP with
the intensity threshold on the ocean surface image. In this study, since thePIP fluctuated greatly as shown in Fig. 3, the results have been smoothedby the four-point moving average to make the derivatives of PIP. The
derivative equation is given by the Eq. (2). Φ denotes PIP and its first andsecond derivatives. After the first derivative of PIP was calculated, it wassmoothed again by the four-point moving average, and then Eq. (2) isused again for the second derivative. In addition, after smoothing in thesame way, the third-order differential is performed. An example of aseries of the processes is provided in Fig.4. The AWE algorithmincreases the threshold from the minimum luminance value to themaximum luminance one, and identifies a zero crossing point where thenegative value changes first to the positive one. In Fig. 3(b), it can be
confirmed that the threshold exists between 0.28 and 0.29. Thus, thethreshold of 0.28 is set as the lower threshold for subsequent processing.
Fig. 4 Analytical results based on AWE algorithm.

Results

Fig. 5 Relations of Wc _AWE, Wc _FT with 10-m wind speed U10

Fig. 7 Relationships between WD_AWE, WD_FT and U10

Fig. 6. Relation between ΔWc and GSR

Fig. 8 Relationships between Wc_AWE, WD_AWE and RB◆It is seen from Fig. 5 that when 10-m wind speed becomes 5m/s or higher, Wc _FT is in good agreement with theempirical relations of Monahan (1993) and Sugihara et al. (2007). The value of Wc_AWE is larger than theirrelations, but indicating high consistency with the relation of Stramaska and Petelski (2003).
◆In Fig. 6, ΔW as the difference between Wc _FT and Wc _AWE is compared with the amount of the solar
2radiation GSR. When GSR exceeds about 0.7 kW/m , the value of ΔW is increase considerably. It is seen that
due to the influence of solar radiation, it is usually difficult to calculate whitecap coverage under the condition ofstrong sunlight. Therefore, in order to investigate properly the behavior of whitecap coverage, we shouldexclude the data of whitecap coverage when the solar radiation exceeded 0.7 kW/m2 .
◆Thorpe (1986) and Yoshioka et al. (2003) used the reflection intensity of sound beams in the ocean surface
boundary layer to visualize the vertical distribution of bubbles underneath the ocean surface. Their observations
demonstrated that the depth of bubbles generated by wave breaking becomes about 4 to 5 times of the significant
wave height Hs. Based on the findings, the product of whitecap coverage Wc and the bubble penetration depth
will be useful for expressing three-dimensional characteristics of the bubbly region of whitecaps. In this study,
we propose a new characteristic quantity as whitecap depth WD . Figure 7 shows the relations of WD_AWE andWD_FT with U10, both of which show a strong linear correlation, suggesting that WD is recognized as a suitable
quantity that can evaluate whitecaps more accurately than whitecap coverage.
◆A typical outcome is the work of Toba and Koga (1986), and they proposed that a dimensionless parameter RB.
As shown in Fig.8, there is a linear relation between Wc_AWE and RB, with a correlation coefficient of 0.6 as thelinear regression, whereas the relation of WD_AWE with RB has a higher correlation coefficient as 0.81, whichshows that as the new physical quantity for evaluating ocean whitecaps WD is more persuasive and expectable
than whitecap coverage WC.

Conclusion

Acknowledgements✓ In this study, by comparing whitecap coverage calculated by AWE with that of fixed threshold method, the usefulness of AWE in long-term observation was examined.
✓ After selecting the effective data of whitecap coverage, it was shown that the correlation coefficient between Wc_AWE 1/3 and U10 was 0.76.
✓ Whitecap depth WD, and verified the relation between WD and the windsea Reynolds number RB. The present results demonstrated that WD is in good correlation with RB, and thussuggesting that whitecap depth is more suitable parameter than whitecap coverage, which is only two-dimensional information on whitecaps.

This work was partially supported by a Grant-in-Aid for
Scientific Research (B) (Coordinator: Y. Sugihara, JSPS
KAKENHI Grant Number JP19H02249)