Analytical estimation of droplet concentration at cloud base

In the present study a new method of calculating droplet concentration near cloud base is proposed. The ratio of maximum supersaturation S-max to the liquid water mixing ratio when Smax is reached near cloud base is found to be universal, and it does not depend on the vertical velocity w and droplet number concentration N. It is found that S-max depends on vertical velocity as S-max proportional to w(3/4) and on droplet concentration as S-max proportional to N (-1/2). The droplet concentration calculated using the simple approach agrees well with exact solutions obtained numerically using high precision parcel models. Comparison with the results of other parameterizations is presented. It is demonstrated that the approach proposed in the study can be applied to an arbitrary form of activation spectra or any CCN size distribution given either analytically or by tables. Moreover, it can be applied for the cases when the CCN size spectrum changes with time. Temperature dependencies of S-max and related quantities are analyzed.