over the North Sea, where $N$ = 100 cm$^{-3}$ (Nicholls, 1984), while in California stratocumulus it increased from 0.3 to 0.5 as $N$ decreased from 40 cm$^{-3}$ in clouds contaminated by ship exhaust, to 10 cm$^{-3}$ in clean ambient air (from Figure 3*b* of Ackerman et al. 2000b). We note that in clean marine stratocumulus, reduced rain is observed (e.g., Taylor and Ackerman 2000) and predicted (e.g., Ackerman, Toon, and Hobbs 1993; Stevens et al. 1998) to result in deeper cloud layers, which is consistent with our simple model. However, any changes in cloud cover associated with precipitation changes are not represented in our model.

We have also calculated profiles of $f_{\rm rain}$ for deeper convection, using large-eddy simulations of trade cumulus clouds (Ackerman et al. 2000a), which are twice as deep as stratocumulus clouds ($\sim$1000 m compared to $\sim$500 m). As in the stratocumulus clouds, we find that $f_{\rm rain} < 1$ in the stratiform anvils at cloud top. However, $f_{\rm rain}$ is significantly enhanced throughout the bulk of the trade cumulus clouds, where it ranges from $\sim$ 2 to 6. Vertical winds are more symmetrically distributed in stratocumulus, and hence the convective velocity scale is representative of the 