Generalization of Atmospheric Nonspherical Particle Size: Interconversions of Size Distributions and Optical Equivalence

Atmospheric particles exhibit various sizes and nonspherical shapes, which are factors that primarily determine the physical-optical properties of particles. The "sizes" of nonspherical particles can be specified based on various size descriptors, such as those defined with respect to a volume-equivalent spherical radius, projected-area-equivalent spherical radius, geometric radius, or effective radius. Microphysical and radiative transfer simulations as well as remote sensing implementations often require the conversions of particle size distributions (PSDs) in terms of the number concentration, projected area, and volume. The various size descriptors cause ambiguity in the PSD interconversion, and thereby result in potentially misleading quantification of the physical-optical properties of atmospheric nonspherical particles. The present study aims to provide a generalized formula for interconversions of PSDs in terms of physical variables and size descriptors for arbitrary nonspherical particles with lognormal and gamma distributions. In contrast to previous studies, no empirical parameters are included, allowing intrinsic understanding of the nonspherical particle effects on the PSD interconversion. In addition, we investigate the impact of different size descriptors on the single-scattering properties of nonspherical particles. Consistent single-scattering properties among different nonspherical particles with the same size parameter are found when the size descriptor is the effective radius, whereby their mechanisms are suggested based on a modified anomalous diffraction theory. The overarching goal of this work is to eliminate the ambiguity associated with a choice of the size descriptor of nonspherical particles for Earth-atmosphere system models, cloud-aerosol remote sensing, and analyses of in situ measured atmospheric particles. Significance StatementAtmospheric dust and ice crystals have various sizes and mostly nonspherical shapes. Different definitions of these particle sizes and shapes cause uncertainties and even result in misleading solutions in the numerical modeling and remote sensing of atmospheric properties. We derived generalized analytical formulas to rigorously treat the sizes and shapes of particles in the atmosphere, and also investigated the importance of the treatment of particle sizes on the particle properties essential to the Earth-atmospheric climate system. This study aims to eliminate the ambiguity associated with particle sizes and shapes in atmospheric research.