Behaviour of Cloud Models As Seen from Theory of Dynamical Systems and Asymptotic Analysis

Cloud parameterisations are usually based on a formulation of ordinary differential equations (ODEs); however; in contrast to other fields in atmospheric physics, in cloud physics we cannot start on a basis system of equations, based on first principles (not as, e. g., Navier-Stokes equations in hydrodynamics). Thus, the formulation of cloud processes could be quite different in terms of non-linear terms. In the spirit of the theory of dynamical systems, thus it is a priori not clear if the long term behaviour of different cloud models is at least similar.

We formulate and investigate a generalized model for warm clouds. Cloud models incorporated in operational weather prediction models are obtained by a specific choice of the parameters in the general model. We determine steady states and pursue a stability analysis. Furthermore, we carry out numerical simulations and detect bifurcations, i. e. a fixed point destabilizes and a periodic orbit occurs. Additionally, we apply an asymptotic expansion approach and identify leading order equations, time scales at which cloud microphysics takes place, and the dominant microphysical cloud processes for the respective cloud models. First results show that the models behave quantitatively different, thus clouds as represented in these models might have divergent properties.