The relationship between aerosol and cloud drop number concentrations in a global aerosol microphysics model

Empirical relationships that link cloud droplet number (CDN) to aerosol number or mass are commonly used to calculate global fields of CDN for climate forcing assessments. In this work we use a sectional global model of sulfate and sea-salt aerosol coupled to a mechanistic aerosol activation scheme to explore the limitations of this approach. We find that a given aerosol number concentration produces a wide range of CDN concentrations due to variations in the shape of the aerosol size distribution. On a global scale, the dependence of CDN on the size distribution results in regional biases in predicted CDN (for a given aerosol number). Empirical relationships between aerosol number and CDN are often derived from regional data but applied to the entire globe. In an analogous process, we derive regional 'correlation-relations' between aerosol number and CDN and apply these regional relations to calculations of CDN on the global scale. The global mean percentage error in CDN caused by using regionally derived CDN-aerosol relations is 20 to 26%, which is about half the global mean percentage change in CDN caused by doubling the updraft velocity. However, the error is as much as 25-75% in the Southern Ocean, the Arctic and regions of persistent stratocumulus when an aerosol-CDN correlation relation from the North Atlantic is used. These regions produce much higher CDN concentrations (for a given aerosol number) than predicted by the globally uniform empirical relations. CDN-aerosol number relations from different regions also show very different sensitivity to changing aerosol. The magnitude of the rate of change of CDN with particle number, a measure of the aerosol efficacy, varies by a factor 4. CDN in cloud processed regions of persistent stratocumulus is particularly sensitive to changing aerosol number. It is therefore likely that the indirect effect will be underestimated in these important regions.