Estimation of the Spectral Division Parameter in a Two-Scale Model for the Case of GNSS Ocean Reflectometry

In the seminal paper (G. S. Brown, “Backscattering from a Gaussian Distributed, Perfectly Conducting Rough Surface,” IEEE Trans. Antennas Propag., vol. 26, pp. 472–482, 1978) the spectral division parameter
$k_{d}$
, was introduced in the two-scale (or composite) model for calculating backscatter from wind-driven ocean surface waves at near-nadir incidence. In this model, the geometric optics is used to describe scattering related to the long-wave portion of the surface height spectrum
$(k\leq k_{d})$
while first-order perturbation theory is used to describe the scattering generated by the short-wave portion of the spectrum
$(k > k_{d})$
. In the above paper, it was suggested that a specific numerical value of the spectral division parameter should satisfy the relation
$4k_{0}^{2}\overline{\zeta_{s}^{2}} < < 1$
, where
$k_{0}=2_{7}r/\lambda$
, and
$\lambda$
is an EM wavelength;
$\overline{\zeta_{s}^{2}}$
is the mean-square height of the short-wave component of the surface roughness. tt has been established that for the roughness spectrum of the
$k^{-4}$
type the value of
$k_{d}$
can take on the values
$\approx k_{0}/d$
, where
$d=3$
. This model is widely used for many years, for example, in ocean radar altimetric applications.