A Numerical Study of the Supersaturation Field around Growing Graupel

Abstract

Development of supersaturation around falling graupel in supercooled clouds was investigated numerically. The steady state temperature and vapor density profiles were obtained by solving the nonsteady state advective diffusion equations in air around a falling graupel, under a steady, incompressible and irrotational condition, first assuming the surface to be spherical and completely covered with freezing cloud droplets. From these special temperature and vapor density profiles, the corresponding steady state supersaturation field with respect to water was estimated, and the maximum supersaturation that a flow line experienced was obtained as a function of the air flow volume. Bigger graupel showed larger, sweeping air volume of lower maximum supersaturation. Then, to estimate the supersaturation around graupel of colder surface temperatures, a fraction, ?, of the surface covered by impinged and freezing droplets was introduced. Assuming a proportionality between the air volume and this ? and applying the data of the above special case, a way to estimate the maximum super saturation-air flow volume relationship of real graupel with arbitrary colder surface temperature was described. The wet growth or, ? = 1 was found to be more difficult with smaller graupel under lower liquid water contents and colder cloud temperatures.