Limitations of the Wegener–Bergeron–Findeisen Mechanism in the Evolution of Mixed-Phase Clouds

Phase transformation and precipitation formation in mixed-phase clouds are usually associated with the Wegener–Bergeron–Findeisen (WBF) process in which ice crystals grow at the expense of liquid droplets. The evolution of mixed-phase clouds, however, is closely related to local thermodynamical conditions, and the WBF process is just one of three possible scenarios. The other two scenarios involve simultaneous growth or evaporation of liquid droplets and ice particles. Particle evolution in the other two scenarios differs significantly from that associated with the WBF process. Thus, during simultaneous growth, liquid droplets compete for the water vapor with the ice particle, which slows down the depositional growth of ice particles instead of promoting their growth at the expense of the liquid as in the WBF process. It is shown that the WBF process is expected to occur under a limited range of conditions and that ice particles and liquid droplets in mixed-phase clouds are not always processed in accordance with the WBF mechanism. Mixed-phase clouds play an important role in the formation of precipitation, radiative transfer for cloudy atmospheres, Earth’s radiation budget, and climate. Mixed-phase clouds are thermodynamically unstable and the process of phase transformation in them is often referred to as the “ice crystal theory,” which originated in the works of Wegener (1911), Bergeron (1935), and Findeisen (1938). In 1911, Alfred Wegener proposed a theory of ice crystal growth based on the difference in saturated water vapor pressure between ice crystals and supercooled liquid water droplets. According to Wegener (1911, p. 81), “The vapour tension will adjust itself to a value in between the saturation values over ice and over water. The effect of this must then be, that condensation continuously will take place on the ice, whereas at the same time liquid water evaporates, and this process must go on until the liquid phase is entirely consumed.” Furthermore, he suggested that this effect might lead to the formation of ice crystals large enough to fall through cloud, melt at lower (warmer) levels, and finally turn into raindrops. In the 1930s, Swedish meteorologist Tor Bergeron and German meteorologist Walter Findeisen contributed further to the ice crystal theory, which became known as the Wegener–Bergeron–Findeisen (WBF) theory. The important point, which apparently Bergeron (1935) was the first to recognize, is the condition that the number density of ice particles must be much smaller than that of the liquid droplets. Findeisen (1938) provided experimental confirmation of enhanced growth of ice crystals in clouds containing both ice crystals and supercooled liquid droplets. Glickman (2000) gives the following explanation for the “Bergeron–Findeisen process”: The basis of this theory is in fact that the equilibrium water vapor pressure with respect to ice is less than that with respect to liquid at the same subfreezing temperature. Thus within an admixture of these (ice and liquid) particles, and provided that the total water Corresponding author address: Alexei Korolev, Environment Canada, 4905 Dufferin St., Toronto, ON M3H5T4, Canada. E-mail: [email protected] 1 Ice crystal theory (or the ice process of precipitation) has also been referred to as “Bergeron,” “Bergeron–Findeisen,” and “Bergeron–Findeisen–Wegener” process or theory. 3372 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 64 DOI: 10.1175/JAS4035.1 © 2007 American Meteorological Society