Near‐nadir radar backscatter from a well‐developed sea

Abstract

Recent advances in understanding dynamics and statistical geometry of wind-generated gravity waves necessitate a re-examination of the radar return as a function of external factors. The Kirchhoff approximation for the case of well-developed seas is analyzed. In this peculiar case, the equilibrium range in the wave number spectrum (approximated by ak -(4-2•) where/x > 0 can be interpreted as a fractal codimension of the surface) corresponds to a cascade pattern in the surface geometry. Its high wave number cutoff (the internal scale h), determined by the dissipation of energy due to wave breaking, is shown to be a major factor of the radar backscatter] This intrinsic scale is evaluated (h --• 0.4 m), and both the geometrical and the physical optics terms are related to major parameters of wind-wave dynamics. The range of validity of the Kirchhoff approximation and the relative importance of the diffraction correction are analyzed. Finally, the radar cross section tr ø of well-developed seas is compared with that of poorly developed seas (when /x = 0). The great qualitative difference shown in the wind speed dependence of tr ø for these two regimes is pointed out as a source of a considerable error trend recently discovered in satellite altimeter wind measurements. GLAZMAN: RADAR BACKSCATTER FROM SEA 1213 Transl., 18(10), 821-827, 1982b. Zakharov, V. E., and M. M. Zaslavskii, Shape of the spectrum of energy carrying components of a water surface in the weak-turbulence theory of wind waves, lzv. Atmos. Oceanic Phys., Engl. Transl., 19(3), 207-212, 1983a. Zakharov, V. E., and M. M. Zaslavskii, Dependence of wave parameters on the wind velocity, duration and its action and fetch in the weak-turbulence theory of wind waves, lzv. Atmos. Oceanic Phys., Engl. Transl. , 19(4), 300-306, 1983b.

Fractals and the small perturbation scattering model

“…We call "physical" fBm surfaces [Jaggard, 1990] those satisfying (1) only in a limited range of scales. For such surfaces, use of the continuity conditions of tangential fields is possible if at the smallest scales the surface is regular [Agnon and Stiassnie, 1991; Glazman, 1990]. Finally, we recall that increments of an fBm process over a fixed distance are stationary, but the fBm process itself is not stationary [Falconer, 1990;Flandrin, 1989].…”

Remote sensing of the roughness of a fractal sea surface

“…Barrick and Lipa [1985] addressed this issue early on, suggesting a cutoff proportional to )•. Using the full wave Glazman [1990] gives a qualitative analysis of the dependence of the spectral power law dependence on a nondimensional fetch parameter, i.e., the degree of development of the sea. He models the spectral density by a power law and introduces an exponential high-wavenumber decay at an intrinsic microscale of 0.4 m which corresponds to kd=2.5 m -1 and a rapid low-wavenumber cutoff.…”

“…Stiassnie et al, [1991]). See Glazman [1990] for a discussion of the curvature criterion. The 'fractal' model of the sea surface is limited to a finite range of scales.…”

Satellite altimeter measurements of surface wind

“…Actual wave dynamics and surface roughness regimes are highly diverse and are much more complex than those implied in our preceding theoretical analyses [Glazman and Weichman, 1989;Glazman, 1990;Glazman and Srokosz, 1991]. However, the success of the present experimental effort indicates that the idealized notion of the degree of sea development (quantified by the pseudo wave age) is a viable concept which remains practically useful under realistic conditions.…”

“…The notion of the wave age is not free of some controversy [Pierson, 1991]. Theoretical background on this topic along with implications of the theory and its use in the context of ocean remote sensing are provided by Glazman and Weichman, [1989], Glazman [ 1990, and Glazman and Srokosz [1991]. As before [Glazman and Pilorz, 1990], we shall estimate the wave age based on the buoy-supplied wind speed UB and significant wave height HB.…”