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 ae rosol mass concentrations and cloud droplet number concentrations (N-d). Th e fundamental aim with the present method is to arrive at a physically-base d conversion algorithm in which each step in the conversion is based on rea l 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 th e size distributions of cloud droplet residual particles for different poll ution conditions. This conversion assumes that the size of the residual par ticles can be described with a lognormal distribution function and uses the Hatch-Choate relationship to convert between residual volume and number. T he relatively sparse data set with which we have developed the present algo rithm results in a course classification of the aerosol mass field. Consequ ently, uncertainties need to be recognized when using the algorithm in its present form in model calculations. The algorithm has been used on data fro m 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 m uch 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.