Asymptotic Behavior of Lidar Scattering Properties of Absorbing Dust Aerosols Across Rayleigh and Geometrical-Optics Regimes: Theory and Implications

Abstract. Lidar ratio (S), linear depolarization ratio (δ), and single-scattering albedo (ω) are central quantities for dust typing and property retrieval in lidar remote sensing. We investigate their dependence on size parameter (x) and iron oxide fraction of mineral dust using TAMUdust2020 and triaxial-ellipsoid calculations. Results show a consistent asymptotic structure that is weakly sensitive to particle shape in both limits of scattering theory. In the Rayleigh limit (x≪1), S ∝ x⁻³ and ω ∝x³, while δ remains small. In the geometrical-optics limit (x≫1), δ decreases toward low values and ω →1/2, whereas S increases because backscatter is reduced relative to extinction by strong absorption and diffraction-dominated scattering. These asymptotic constraints provide a unified physical interpretation of multiwavelength dust-lidar behavior and help explain observed spectral variability of dust depolarization and lidar ratio. A key implication is that large, strongly absorbing dust can produce optical signatures that overlap with weakly depolarizing aerosol classes, which may bias standard classification and inversion schemes toward underestimation of coarse and super-coarse dust contributions.