Square ocean waves in france12/30/2023 ![]() ![]() The triangles denote the MSS, integrated up to 0.1 mm from (14). The MSS corresponding to equilibrium spectrum of background gravity waves is not included here. Figure 1a is for upwind the component and Fig. Figures 1a,b give the MSS components, calculated from (14) and (15), for six different wavenumbers. Here Φ w ( k, ϕ) is the spectrum of gravity–capillary waves, given by (12) and (13) k p, the lower limit of integration, is the wavenumber at spectral peak of fully developed gravity waves. (1997) had considered both specular reflection and Bragg resonance in the calculation of the RBCS, Liu and Yan (1995) did not consider the contribution from specular reflection. (1997), as an improvement to the original values of Liu and Yan (1995). They are obtained from the study of Liu et al. These values were determined through the comparison of RBCS calculated from radar backscatter theory with the ERS-1/-2 scatterometer empirically based models CMOD3 and CMOD4. Other parameters are m = 1/320, h = 1.3, δ = 5 cm s −1, α 2 = 0.000 05, α 1 = 0.0002 for the leeward side of background waves α 1 = 0.001 for the windward side of background waves. 6(b): field data, U 10 = 4.0–6.0 m s −1), and the laser slope gauge laboratory measurement of Jäå and Riemer (1990, see their Fig. 3: fetch = 28.9 m, U 10 = 2–10 m s −1), the filed measurement ( Klinke and Jäå 1995, see their Fig. Here, D e = exp, where the coefficient α e is determined to be 0.0011 (cm rad −1) 2.5 (cm s −1) 0.75, based on the image slope gauge laboratory measurement ( Klinke and Jäå 1992, see their Fig. In (12), D e is called the eddy viscosity and generated by turbulence at wind&ndash$ift layer. Where m is a constant, u∗ is the wind friction velocity, δ is the threshold wind friction velocity, c is the wave phase speed, and α 1 and α 2 are the dissipation coefficients due to wave–drift interaction. The involved physics and arguments are given in section 7. How to obtain a reasonable estimate for the MSS in a wider range of wavenumber is the main subject from section 2 through section 6. An optical sensor can detect water wave slopes generated by arbitrarily short water waves up to the wavelength of reflected light, while microwave radar can only measure a part of the surface slopes up to the radar wavelength. Their derived values are much higher than the observations of Cox and Munk (1954a, b), and much higher than the values required in (8). The MSS has also been derived from the ocean surface spectra ( Donelan and Pierson 1987 Apel 1994). (1992) is equal to our MSS for k up to 100 rad m −1. ![]() The comparison shows (not included in this paper) that the derived MSS by Jackson (1991) and Jackson et al. In their papers, the MSS contributed by the shorter waves is regarded as small structure and their effect on radar backscatter is included in the effective reflection coefficient, due to their special mathematical approach. (1992) used their derived MSS to determine the Phillips constant in the equilibrium range. (1992) is the part contributed by gravity waves. The eddy viscosity is due to turbulence at the wind-drift layer, which suppresses the spectrum of high-frequency waves with wavelengths on the order of millimeters. The parasitic capillary wave dissipation due to molecular viscosity can be balanced by the energy supply from the underlying waves, hence it is removed from the model. It is suggested that the k p/ k dependence observed in the range of gravity waves should not be extended to the region of short waves. This effect can be denoted by c 2/ U 2 10 or c 2/ c 2 p dependence of short-wave spectrum. The short-wave dissipation due to wave–drift interactions has the effect of suppressing the spectral density at high wind condition, which further influences the directional spreading rate. The physics included in this model on gravity–capillary wave spectrum is also illustrated. Also, the RBCS, calculated using the C-band filtered MSS, is in keeping with the ERS-1/-2 scatterometer empirically based algorithms CMOD3 and CMOD4. ![]() The radar backscatter cross section (RBCS), calculated from specular reflection theory using the Ku-band filtered MSS, is in keeping with the empirically based Ku-band models by Brown for the GEOS-3 13.9-GHz altimeter, and by Witter and Chelton for the Geosat 13.5-GHz altimeter. The MSS integrated from the above two spectra over high-frequency dissipation length (1 mm) fits the optical observations very well. The mean-square slope (MSS) of the sea surface for upwind and crosswind is derived, based on Phillips’ equilibrium spectrum and the model herein on gravity–capillary wave spectrum.
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