An effect of turbulent clustering on scattering of microwave radiation by small particles in the atmosphere

A coherent scattering of electromagnetic waves by clusters of inertial Rayleigh particles in atmospheric turbulence is considered. A preliminary estimate based on the Maxwell-Garnett theory and the Rayleigh approximation for single clusters demonstrates an importance of the coherent scattering contribution. It is confirmed by a general solution in a combination with theoretical estimates for the two-point probability density function for low-inertia spherical particles in isotropic turbulence. An approximate analytical expression for the coefficient characterizing effect of coherent scattering by the particle clusters is derived. The calculations for small Stokes numbers typical of water droplets in cumulus clouds yield an estimate of the coherent scattering effect on the microwave radar reflection. The model suggested allows solving the inverse problem to determine the pair correlation function for cloud particles. It is expected to be important for the investigations on particle-turbulence interaction in the atmosphere. The theoretical model developed is true not only in the limit of low-inertia particles and can be potentially used at arbitrary Stokes numbers in other applications.