Backscattering by turbulent irregularities: A new analytical description

A general theoretical description of backscattering by turbulent irregularities is given. It is done so within the context of single scattering, which corresponds to the weak microwave reflections observed in atmospheric sounding. The traditional description for such effects is the cross-section approximation, which relates the backscattered power directly to the spectrum of turbulent irregularities evaluated at the Bragg wave-number K = 4π/λ. This analysis avoids most of the assumptions implicit in the former method, and shows that the scattering is not confined to the resonance condition for many situations of interest. The turbulence is assumed to be isotropic but not homogenous. The spectrum method is exploited, so that the backscattered power is expressed as the weighted integral of the wavenumber spectrum of turbulent irregularities, and a specific model need not be assumed until the last step. It is found that the spectral weighting function describing backscattering can be expressed as an infinite sum of the product of two terms. The first is determined solely by the sounder's aerial pattern. The second is fixed by the signal waveform and/or the distance variation of the intensity of inhomogenous turbulent fluctuations. In this way, the propagation features of the problem can be resolved before a turbulent model is introduced. The method is illustrated for omnidirectional, dipole, and narrow-beam aerials. Possibilities for extensions of this analysis are discussed last.