Abstract
Aerosol-cloud interactions are one of the key uncertainties in understanding future climate change. A commonly used method for constraining these interactions is using ship tracks. Aerosol-containing plumes from ships can develop into linearly shaped clouds identifiable in satellite images, isolating the aerosol impact on clouds. Previous studies have shown that ship tracks form more commonly in clean conditions, but even accounting for this, many ships that might be expected to form ship tracks do not. This leads to uncertainties in aerosol-cloud interactions and their climate impact.  Ship track formation depends on the aerosol-containing plumes from the ship being sufficiently concentrated upon reaching the cloud. The cloud must also be sensitive to aerosol. In focus are updraft-limited clouds: smaller updrafts promote slower cooling as a cloud parcel rises, higher critical supersaturation values and lower aerosol activation fractions. It is not clear which of these are more important, but it is vital to understand them if we are using ship tracks to retrieve cloud sensitivity to aerosol.    We develop a plume-parcel model to address these issues to estimate cloud droplet enhancements in ship tracks. Ship aerosol concentrations at the cloud height were modelled as plumes, simulating the shorter timescales of injection. Droplet number concentration enhancements were estimated using Köhler theory for over one hundred thousand ships off the coast of California.  Using a constant updraft, the model was able to achieve reasonable enhancements (r2 ranging between (0.32, 0.4)). These enhancements were shown to be significantly sensitive to the choice of the updraft. In order to examine the hypothetical updraft values required for activation, an optimisation algorithm was developed to fit updrafts to cloud enhancement observations; a 1-1 correlation was achieved between observed and parameterised enhancements. Updrafts consistent with Köhler theory are considerably smaller than cloud-top radiative cooling-based estimates, suggesting that these clouds are less sensitive to aerosol than current estimates suggest. 
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