sedimentation.

The first endmember is subject to a similar catalog of unconstrained assumptions as required by the treatment of Carlson et al. (1988), the most notable among them being the great uncertainty in the supersaturation driving droplet condensation. Also, the model physics underlying this quiescent atmosphere seems to be self-contradictory, on the one hand explicitly assuming that there is too little convection to regulate the maximum size of the droplets, yet on the other hand implicitly assuming that there is enough convection to supply the vapor necessary to drive condensational growth.

However, the second case of Marley et al. (1999) requires significantly fewer assumptions, and is also appropriate to tropospheric condensation clouds. This second case serves as a starting point for the calculation of the cloud particle sizes in our model.

The Present Model
=================

We model all condensation clouds as horizontally homogeneous (globally averaged) structures whose vertical extent is governed by a balance between the upward turbulent mixing of condensate and vapor ($q_{\rm t} = q_{\rm c} + q_{\rm v}$) and the downward transport of condensate due to sedimentation: $$\begin{aligned}
\label{K_pde}
-K \frac{ \partial q_{\rm t}}{\partial z} - f_{\rm rain} w_* q_{\rm c} = 0\end{aligned}$$ where $K$ is the 