Secondary ice production by fragmentation of freezing drops: Formulation and theory

A numerical formulation is provided for secondary ice production during fragmentation of freezing raindrops or drizzle. This is obtained by pooling laboratory observations from published studies and considering the physics of collisions. There are two modes of the scheme: fragmentation during spherical drop freezing (mode 1) and during collisions of supercooled raindrops with more massive ice (mode 2). The empirical scheme is for atmospheric models. Microphysical simulations with a parcel model of fast ascent (8 m s^-1) between -10° and -20°C are validated against aircraft observations of tropical maritime deep convection. Ice enhancement by an order of magnitude is predicted from inclusion of raindrop-freezing fragmentation, as observed. The Hallett-Mossop (HM) process was active too. Both secondary ice mechanisms (HM and raindrop freezing) are accelerated by a positive feedback involving collisional raindrop freezing. An energy-based theory is proposed explaining the laboratory observations of mode 1, both of approximate proportionality between drop size and fragment numbers and of their thermal peak. To illustrate the behavior of the scheme in both modes, the glaciation of idealized monodisperse populations of drops is elucidated with an analytical zero-dimensional (0D) theory treating the freezing in drop-ice collisions by a positive feedback of fragmentation. When drops are too few or too small (≪1 mm), especially at temperatures far from -15°C (mode 1), there is little raindrop-freezing fragmentation on realistic time scales of natural clouds, but otherwise, high ice enhancement (IE) ratios of up to 100-1000 are possible. Theoretical formulas for the glaciation time of such drop populations, and their maximum and initial growth rates of IE ratio, are proposed.