Microphysical consequences of the spatial distribution of ice nucleation in mixed-phase stratiform clouds

Mixed-phase stratiform clouds can persist even with steady ice precipitation fluxes, and the origin and microphysical properties of the ice crystals are of interest. Vapor deposition growth and sedimentation of ice particles along with a uniform volume source of ice nucleation lead to a power law relation between ice water content w_i and ice number concentration n_i with exponent 2.5. The result is independent of assumptions about the vertical velocity structure of the cloud and is therefore more general than the related expression of Yang et al. (Geophys. Res. Lett. doi:10.1002/grl.50700, 2013). The sensitivity of the w_i-n_i relationship to the spatial distribution of ice nucleation is confirmed by Lagrangian tracking and ice growth with cloud volume, cloud top, and cloud base sources of ice particles through a time-dependent cloud field (Yang et al., Geophys. Res. Lett. doi:10.1002/2014GL060657, 2014). Based on observed w_i and n_i from Indirect and Semi-Direct Aerosol Campaign, a lower bound of 0.006 m^-3 s^-1 is obtained for the ice crystal formation rate.