Ice Multiplication by Breakup in Ice–Ice Collisions. Part I: Theoretical Formulation

Abstract

Abstract For decades, enhancement of ice concentrations above those of active ice nucleus aerosols was observed in deep clouds with tops too warm for homogeneous freezing, indicating fragmentation of ice (multiplication). Several possible mechanisms of fragmentation have been suggested from laboratory studies, and one of these involves fragmentation in ice–ice collisions. In this two-part paper, the role of breakup in ice–ice collisions in a convective storm consisting of many cloud types is assessed with a modeling approach. The colliding ice particles can belong to any microphysical species, such as crystals, snow, graupel, hail, or freezing drops. In the present study (Part I), a full physical formulation of initiation of cloud ice by mechanical breakup in collisions involving snow, graupel, and/or hail is developed based on an energy conservation principle. Theoretically uncertain parameters are estimated by simulating laboratory and field experiments already published in the literature. Here, collision kinetic energy (CKE) is the fundamental governing variable of fragmentation in any collision, because it measures the energy available for breakage by work done to create the new surface of fragments. The developed formulation is general in the sense that it includes all the types of fragmentation observed in previous published studies and encompasses collisions of either snow or crystals with graupel/hail, collisions among only graupel/hail, and collisions among only snow/crystals. It explains the observed dependencies on CKE, size, temperature, and degree of prior riming.