The size parameter , complex refractive index and particle shape determine scattering strength and direction. In the small-sphere Rayleigh scattering regime, scattering cross-section scales as ; the Mie scattering regime is needed when particle size approaches the wavelength. Particle number density and particle size distribution, aerosol hygroscopicity and the angular fraction returned to space control an ensemble's radiative effect. High scattering does not imply strong cooling if most light is scattered forward or the particle also absorbs strongly; single-scattering albedo distinguishes scattering from absorption.
Past exam of the mathematics course of the University of Cambridge 2022 iii Paper 315 1 a Solution 2026-09-28
For the plane-parallel radiative transfer equationangular integration gives the zeroth radiation-field moment equationThe net radiative heating per unit volume is thereforeRadiative equilibrium requires it to vanish, equivalently that the frequency-integrated radiative flux be independent of depth:In local thermodynamic equilibrium with coherent isotropic scattering,where is the single-scattering albedo. Since , the condition becomesConservative scattering redistributes directions but contributes no net material heating.