Water supersaturation in convective clouds

The microphysics-dynamics interaction of clouds was theoretically studied in the zone after maximum supersaturation (S-1)(mc) where the droplet number concentration remains nearly constant. The analytic solution obtained, employing the Maxwellian droplet growth theory, describes (S-1)(mc)=Iw(u)(3/4)n(-1/2), where I is the proportionality constant, w(u) the updraft velocity and n the number concentration of the droplets. This solution agrees well with previous studies. Factor 1 increases with altitude in the adiabatic atmosphere, decreases with temperature under constant pressure and increases with pressure under constant temperature. For the zone sufficiently after (S-1)(mc), an approximate relationship (S-1)proportional to r(-1) proportional to t(-1/3) is shown to hold, where (S-1) is the supersaturation, r the average droplet radius and t the time. Using the diffusion-kinetic theory of droplet growth, which includes the effects of thermal accommodation and condensation coefficients, numerically soluble relationships are derived for (S-1), r and t. Application of this theory is shown to increase (S-1)(mc) considerably. The Maxwellian analytic solution that is obtained, the variation of Factor I under different atmospheric conditions and the effect of condensation and thermal accommodation coefficients through the use of the diffusion-kinetic droplet growth theory suggest that maximum supersaturation may reach as high as 10% and beyond in convective clouds.