Scattering Along the Specular Direction from the Sea Modeled as a Fractal Surface

Models linking the electromagnetic field scattered from the sea surface along the specular direction to the speed of the wind blowing over the surface are of fundamental importance for wind speed retrieval via Global Navigation Satellite System Reflectometry (GNSS-R). In this work, by modelling the sea surface as a fractional Brownian motion (fBm) random process and using the Kirchhoff approximation (KA), we express the sea bistatic normalized radar cross section (NRCS) at specular direction directly in terms of sea surface spectrum parameters, and hence of wind speed. This avoids the need of intermediately computing the large-scale sea surface slope variance, which in turn would require the definition of a somewhat arbitrary cut-off surface wavenumber. We show that the obtained theoretical relationship between wind speed and σ0 is in reasonable agreement with the empirical ones available in literature.