A physically-based algorithm for estimating the relationship between aerosol mass and cloud droplet number

In this study, we present a relationship between total accumulation mode aerosol mass concentrations and cloud droplet number concentrations (N-d). The fundamental aim with the present method is to arrive at a physically-based conversion algorithm in which each step in the conversion is based on real physical processes that occur and can be observed in the atmosphere, and in which all of the fields involved can be observed or modeled. In the last conversion (the critical part in the algorithm), we use measurements of the size distributions of cloud droplet residual particles for different pollution conditions. This conversion assumes that the size of the residual particles can be described with a lognormal distribution function and uses the Hatch-Choate relationship to convert between residual volume and number. The relatively sparse data set with which we have developed the present algorithm results in a course classification of the aerosol mass field. Consequently, uncertainties need to be recognized when using the algorithm in its present form in model calculations. The algorithm has been used on data from 15 days and the agreement between calculated and observed N-d values is, with one exception, within a factor of 2 and for many of these cases also much better than a factor of 2. In addition to the results of the algorithm itself, we also present a least-squares fit to the predicted N-d values. To improve the algorithm in the longer-term requires more data of scavenging fractions, particle chemical composition and density, and residual particle size distributions as a function of aerosol mass loading and cloud type.