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Successful simulation of cloud-aerosol interactions (indirect aerosol effects) in climate models requires relating grid-scale aerosol, dynamic, and thermodynamic fields to small-scale processes like aerosol activation. A turbulence and cloud parameterization, based on multi-variate probability density functions of sub-grid vertical velocity, temperature, and moisture, has been extended to treat aerosol activation. Multi-variate probability density functions with dynamics (MVD PDFs) offer  a solution to the problem of the gap between the resolution of climate models and the scales relevant for aerosol activation and a means to overcome the limitations of diagnostic estimates of cloud droplet number concentration based only on aerosol concentration. <br><br> Incorporated into the single-column version of GFDL AM3, the MVD PDFs successfully simulate cloud properties including precipitation for cumulus, stratocumulus, and cumulus-under-stratocumulus. The extension to treat aerosol activation predicts droplet number concentrations in good agreement with large eddy simulations (LES). The droplet number concentrations  from the MVD PDFs  match LES results more closely than diagnostic relationships between aerosol concentration and droplet concentration. <br><br> In the single-column model simulations, as  aerosol concentration increases, droplet concentration increases, precipitation decreases, but liquid water path can increase or decrease

Multi-variate probability density functions with dynamics for cloud droplet activation in large-scale models: single column tests