Abstract
In the atmosphere, there are condensation nuclei of various sizes, and the large hygroscopic nuclei do not need the supersaturation of vapour for condensation which occur on them. Therefore the supersaturation would be very small, if the rate of condensation is where R1 is the gas constant of dry air of 1 gram, x the mixing ratio of the air below the condensation level. The formulas (1) and (4) were solved numerically under the conditions (3') and (5), and the following initial conditions: r=r0, T=Tw=T0 at h=h0. (6)
As an example, four cases in table 1 were calculated. The numbers 105 and 106 of n in Table 1 correspond to 107 and 1070 cloud particles in 1cm3 at the cloud base. In all the cases, h0=1000m, r0_??_0, T0=20°C.
The result in the case II is given in Fig. 2. In this figure, abscissa is the height h, and the temperature Tw, T, the lapse rate of air temperature-dT/dh, the supersaturation C-Cs/Cs (Cs is the saturated vapour concentration at the temperature of air), and the radii of cloud particles are represented by full line curves.
The results of all cases I-IV are given in Fig. 3. There are the curves of air temperature, supersaturation and radii of cloud particles. It is seen from the figures that the supersaturation is tabulated in Table 2. They should be in order of 3% in extreme cases, but may be less than 1% usually.
