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24. Bragg scattering

Bragg formula As the incidence angle of the ERS SAR is oblique (23) to the local mean angle of the ocean surface, there is almost no direct specular reflection except at very high sea states.

It is therefore assumed that at first approximation Bragg resonance is the primary mechanism for backscattering radar pulses.

The Bragg equation defines the ocean wavelengths for Bragg scattering as a function of radar wavelength and incidence angle:

The short Bragg-scale waves are formed in response to wind stress. If the sea surface is rippled by a light breeze with no long waves present, the radar backscatter is due to the component of the wave spectrum which resonates with the radar wavelength.

The threshold windspeed value for the C-band waves is estimated to be at about 3.25 m/s at 10 meters above the surface. The Bragg resonant wave has its crest nominally at right angles to the range direction.

For surface waves with crests at an angle ϕ to the radar line-of-sight (see the figure on the left) the Bragg scattering criterion is

where: λ's is the wavelength of the surface waves propagating at angle ϕ to the radar line- of sight.

The SAR directly images the spatial distribution of the Bragg-scale waves. The spatial distribution may be effected by longer gravity waves, through tilt modulation, hydrodynamic modulation and velocity bunching.

Moreover, variable wind speed, changes in stratification in the atmospheric boundary layer, and variable currents associated with upper ocean circulation features such as fronts, eddies, internal waves and bottom topography effect the Bragg waves.