Nucleation-droplet growth interactions and microphysical property development in convective clouds

In the microphysics-dynamics interaction above the convective cloud base, the analytic solutions with the Maxwellian droplet growth system obtained by Squires (1958) and Fukuta (1993), without including the relationship of the cloud condensation nucleus (CCN) activity spectrum, are shown to be partial or diagnostic solutions and that of Twomey (1959) as a complete or prognostic solution within its approximation. The diagnostic solutions of the diffusion-kinetic (DK) droplet growth system are numerically evaluated, and significant effects of accommodation coefficients to raise the supersaturation and droplet number concentration maxima are found. The relationship among the diagnostic solution, the prognostic solution, and the CCN activity spectrum is graphically explained, and a graphical method to obtain the DK prognostic solution is described. The prognostic solution with the Maxwellian system has been derived in a back-tracking manner and the solution is found to agree with that of Twomey in the functional relationship. The effect of parameters in the CCN activity spectrum on the maximum droplet number concentration has been assessed for the Maxwellian system. The prognostic solution of the DK system graphically obtained shows the droplet concentration increase from that of the Maxwellian typically by a factor between 1.5 and 2 with condensation coefficient of 0.03 and thermal accommodation coefficient of 1.0.