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Empirical relationships that link cloud droplet number (CDN) to aerosol numberor mass are commonly used to calculate global fields of CDN for climate forcingassessments.  In this work we use a sectional global model of sulfate and sea-saltaerosol coupled to a mechanistic aerosol activation scheme  to explore thelimitations of this approach.  We find that a given aerosol number concentrationproduces a wide range of CDN concentrations due to variations in the shape of theaerosol size distribution. On a global scale, the dependence of CDN on the sizedistribution results in regional biases in predicted CDN (for a given aerosolnumber).  Empirical relationships between aerosol number and CDN are oftenderived from regional data but applied to the entire globe.  In an analogousprocess, we derive regional "correlation-relations" between aerosol numberand CDN and apply these regional relations to calculations of CDN on the globalscale.  The global mean percentage error in CDN caused by using regionallyderived CDN-aerosol relations is 20 to 26%, which is about half the globalmean 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 regionsof persistent stratocumulus when an aerosol-CDN correlation relation from theNorth Atlantic is used. These regions produce much higher CDN concentrations(for a given aerosol number) than predicted by the globally uniform empiricalrelations. CDN-aerosol number relations from different regions also show verydifferent sensitivity to changing aerosol. The magnitude of the rate of changeof CDN with particle number, a measure of the aerosol efficacy, varies by afactor 4. CDN in cloud processed regions of persistent stratocumulus isparticularly sensitive to changing aerosol number. It is therefore likelythat the indirect effect will be underestimated in these important regions

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