Analytical estimation of droplet concentration at cloud base

• Published in: Journal of Geophysical Research: Atmospheres Vol. 117; no. D18
• Main Authors: Pinsky, M., Khain, A., Mazin, I., Korolev, A.
• Format: Journal Article
• Language: English
• Published: Washington, DC Blackwell Publishing Ltd 27.09.2012; American Geophysical Union
• Subjects: Atmospheric sciences; Chemistry; Clouds; droplet concentration; Earth sciences; Earth, ocean, space; Exact sciences and technology; Geophysics; Meteorology; nucleation of droplets; numerical modeling; Physics; Supersaturation; supersaturation maximum; Theoretical physics; Water mixing; Vertical speed; models; droplets; accuracy; Supersaturation; concentration; Dimension spectrum; Exact solution; parametrization; Cloud base; new methods; temperature; Mixing ratio; size distribution; Comparative study
• ISSN: 0148-0227; 2169-897X; 2156-2202; 2169-8996
• DOI: 10.1029/2012JD017753

In the present study a new method of calculating droplet concentration near cloud base is proposed. The ratio of maximum supersaturation Smax 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 Smax depends on vertical velocity as Smax ∝ w3/4 and on droplet concentration as Smax ∝ 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 Smax and related quantities are analyzed. Key Points A new analytical method of calculation of supersaturation maximum is proposed Universal dependence of supersaturation maximum on W and drop concentration The method allows calculation of drop concentration at any CCN distribution