Ocean microwave backscatter distributions

A probability density function, p(a), for the instantaneous amplitude of the backscattered field at moderate incidence angles is proposed. The key step is in writing the (slowly varying) backscatter cross section, σ0, as an exponential function to second order in the long wave slope component, sx, along the scatterometer look direction; that is, σ0 ∼ exp (a1sx + a2sx2). The function p(σ0) is then computed by a straightforward transformation of the normally distributed slope component, while p(a) follows from Bayes' theorem assuming p(a|σ0) to be Rayleigh distributed. The proposed probability density function was compared to Ku band dual-polarized data taken at 20° and 45° incidence during the Synthetic Aperture and X Band Ocean Nonlinearities experiments at the Chesapeake Light Tower and at Forschungsplatform Nordsee. The function p(a) was found to follow a Weibull distribution with slope parameter v ≅ 1.9 for small amplitudes. At large amplitudes the distribution lengthens but appears to be neither Weibull nor K distributed as has been reported for neargrazing incidence data.