  The representation of cloud processes in weather and climate models is
crucial for their feedback on atmospheric flows. Since there is no general
macroscopic theory of clouds, the parameterization of clouds in corresponding
simulation software depends crucially on the underlying modeling assumptions.
In this study we present a new model of inter-mediate complexity (a
one-and-a-half moment scheme) for warm clouds, which is derived from physical
principles. Our model consists of a system of differential-algebraic equations
which allows for supersaturation and comprises intrinsic automated droplet
activation due to a coupling of the droplet mass- and number concentrations
tailored to this problem. For the numerical solution of this system we
recommend a semi-implicit integration scheme, with efficient solvers for the
implicit parts. The new model shows encouraging numerical results when compared
with alternative cloud parameterizations, and it is well suited to investigate
model uncertainties and to quantify predictability of weather events in moist
atmospheric regimes.
