Wave steepness is presented as an extension and a valuable add-on to the conventional set of sea state parameters retrieved from satellite altimetry data. Following physical model based on recent advances of weak turbulence theory wave steepness is estimated from directly measured spatial gradient of wave height. In this way the method works with altimetry trajectories rather than with point-wise data. Moreover, in contrast to widely used parametric models this approach provides us with instantaneous values of wave steepness and period. Relevance of single-track estimates of wave steepness period is shown for wave climate studies and confirmed by a simple probabilistic model. The approach is verified via comparison against buoy and satellite data including crossover points for standard 1 second data of Ku-band altimeters. High quality of the physical model and robustness of the parametric ones are examined in terms of global wave statistics. Prospects and relevance of both approaches in the ocean wave climate studies are discussed.
Wave turbulence, satellite altimetry, wave steepness, parametric and physical models of wave period
1. Abdalla, S., Cavaleri, L. Effects of wind variability and variable air density on wave modeling, // J. Geophys. Res., 2002. - v. 107 - no. C7 - p. 17-1.
2. Babanin, A. V., Soloviev, Y. P. Field investigation of transformation of the wind wave frequency spectrum with fetch and the stage of development, // J. Phys. Oceanogr., 1998. - v. 28 - p. 563.
3. Badulin, S. I. A physical model of sea wave period from altimeter data, // J. Geophys. Res. Oceans, 2014. - v. 119 - p. 856.
4. Badulin, S. I., Babanin, A. V., Resio, D., Zakharov, V. Weakly turbulent laws of wind-wave growth, // J. Fluid Mech., 2007. - v. 591 - p. 339.
5. Badulin, S. I., Babanin, A. V., Resio, D., Zakharov, V. Numerical verification of weakly turbulent law of wind wave growth // Proceedings of the IUTAM Symposium held in Moscow, 25-30 August, 2006. Vol. 6 of IUTAM Bookseries. Eds. Borisov, A. V., Kozlov, V. V., Mamaev, I. S., Sokolovskiy, M. A. - Berlin: Springer., 2008. - p. 175.
6. Badulin, S. I., Pushkarev, A. N., Resio, D., et al. Self-similarity of wind-driven seas, // Nonl. Proc. Geophys., 2005. - v. 12 - p. 891.
7. Badulin, S. I., Zakharov, V. E. Ocean swell within the kinetic equation for water waves, // Nonl. Proc. Geophys., 2017. - v. 24 - p. 237.
8. Barrick, D., Lipa, B. Analysis and interpretation of altimeter sea echo, // Advances in Geophysics, 1985. - v. 27 - p. 60.
9. Brown, G. The average impulse response of a rough surface and its applications, // IEEE Trans. Antennas Propagat., 1977. - v. 25 1 - p. 67.
10. Cavaleri, L., Alves, J.-H. G.-M., Ardhuin, F., et al. Wave modelling - the state of the art, // Progr. Ocean., 2007. - v. 75 - p. 603.
11. Chen, K. S., Chapron, B., Ezraty, R. A global view of swell and wind sea climate in the ocean by satellite altimeter and scatterometer, // J. Atmos. Ocean. Technol., 2002. - v. 19 - no. 11 - p. 1849.
12. Donelan, M. A., Pierson. W. J. Jr. Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry, // J. Geophys. Res., 1987. - v. 92 C5 - p. 4971.
13. Donelan, M., Skafel, M., Graber, H., Liu, P., et al. On the growth rate of wind-generated waves, // Atmosphere Ocean, 1992. - v. 30 - no. 3 - p. 457.
14. Dumont, J. P., Rosmorduc, V., Picot, N., Bronner, E., Desai, S., Bonekamp, H., Figa, J., Lillibridge, J., Scharroo, R. OSTM/Jason-2 Products Handbook, iss. 1 rev. 8 - JPL, NOAA/NESDIS: CNES, EUMETSAT., 2011. - 63 pp.
15. Gagnaire-Renou, E., Benoit, M., Badulin, S. I. On weakly turbulent scaling of wind sea in simulations of fetch-limited growth, // J. Fluid Mech., 2011. - v. 669 - p. 178.
16. Gavrikov, A. V., Krinitsky, M. A., Grigorieva, V. G. Modification of satellite altimetry database globwave for diagnosis of sea wave fields, // Oceanology, 2016. - v. 56 - no. 2 - p. 301.
17. Glazman, R. Effects of sea maturity on satellite altimeter measurements, // J. Geophys. Res., 1990. - v. 95 - no. C3 - p. 2857.
18. Gommenginger, C. P., Srokosz, M. A., Challenor, P. G., Cotton, P. D. Measuring ocean wave period with satellite altimeters: A simple empirical model, // Geophys. Res. Lett., 2003. - v. 30 - no. 22 - p. 2857.
19. Grigorieva, V. G., Badulin, S. I. Wind wave characteristics based on visual observations and satellite altimetry, // Oceanology, 2016. - v. 56 - no. 1 - p. 19.
20. Grigorieva, V., Gulev, S. Extreme waves in visual wave observations by VOS // Proceedings of the Rogue Waves 2008 Workshop, Eds. Olagnon, M., Prevosto, M. - Brest: Editions IFREMER., 2008. - p. 41.
21. Gulev, S., Grigorieva, V., Sterl, A., Woolf, D. Assessment of the reliability of wave observations from voluntary observing ships: Insights from the validation of a global wind wave climatology based on voluntary observing ship data, // J. Geophys. Res., 2003. - v. 108 C7 - p. 41.
22. Gulev, S. K., Grigorieva, V. G. Variability of the winter wind waves and swell in the North Atlantic and North Pacific as revealed by the voluntary observing ship data, // Journal of Climate, 2006. - v. 19 - p. 5667.
23. Hasselmann, K. On the nonlinear energy transfer in a gravity wave spectrum. Part 1. General theory, // J. Fluid Mech., 1962. - v. 12 - p. 481.
24. Hasselmann, K., Ross, D. B., Müller, P., Sell, W. A parametric wave prediction model, // J. Phys. Oceanogr., 1976. - v. 6 - p. 200.
25. Hsiao, S. V., Shemdin, O. H. Measurements of wind velocity and pressure with a wave follower during MARSEN, // J. Geophys. Res., 1983. - v. 88 C14 - p. 9841.
26. Hwang, P. A., Teague, W. J., Jacobs, G. A., et al. A statistical comparison of wind speed, wave height and wave period derived from satellite altimeters and ocean buoys in the Gulf of Mexico region, // J. Geophys. Res., 1998. - v. 103 - no. 10 - p. 10451.
27. Hwang, P. A., Wang, D. W. Field measurements of duration-limited growth of wind-generated ocean surface waves at young stage of development, // J. Phys. Oceanogr., 2004. - v. 34 - p. 2316.
28. Kitaigorodskii, S. A. Applications of the theory of similarity to the analysis of wind-generated wave motion as a stochastic process, // Bull. Acad. Sci. USSR, 1962. - v. Geophys. Ser., Engl. Transl. - p. 105.
29. Mackay, E. B. L., Retzler, C. H., Challenor, P. G., Gommenginger, C. P. A parametric model for ocean wave period from Ku-band altimeter data, // J. Geophys. Res., 2008. - v. 113 - p. 105.
30. Pierson, W. J., Moskowitz, L. A. A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitaigorodsii, // J. Geophys. Res., 1964. - v. 69 - p. 5181.
31. Snodgrass, F. E, Groves, G. W., Hasselmann, K. F., Miller, G. R., Munk, W. H., Powers, W. H. Propagation of ocean swell across the Pacific, // Phil. Trans. Roy. Soc. London, 1966. - v. 259 1103 - p. 431.
32. Toba, Y. Local balance in the air-sea boundary processes. Part I. On the growth process of wind waves, // J. Oceanogr. Soc. Japan, 1972. - v. 28 - p. 109.
33. Vignudelli, S., Kostianoy, A. G., Cipollini, P., et al. Coastal Altimetry - Berlin, Heidelberg: Springer-Verlag., 2011. - 588 pp.
34. Voronovich, A. G. Propagation of internal and surface gravity waves in the approximation of geometrical optics, // Izv. Atmos. Ocean. Phys., 1976. - v. 12 - p. 850.
35. Young, I. R., Zieger, S., Babanin, A. V. Global trends in wind speed and wave height, // Science, 2011. - v. 332 - p. 451.
36. Zakharov, V. E. Energy balance in a wind-driven sea, // Phys. Scr., 2010. - v. T142 - p. 1.
37. Zakharov, V. E., Badulin, S. I. On energy balance in wind-driven seas, // Doklady Earth Sciences, 2011. - v. 440 Part 2 - p. 1440.
38. Zakharov, V. E., Lvov, V. S., Falkovich, G. Kolmogorov spectra of turbulence. Part I - Berlin: Springer., 1992. - 263 pp.
39. Zakharov, V. E., Zaslavsky, M. M. Dependence of wave parameters on the wind velocity, duration of its action and fetch in the weak-turbulence theory of water waves, // Izv. Atmos. Ocean. Phys., 1983. - v. 19 - no. 4 - p. 300.
