The nonlinear open system cloud is analyzed in this basic study in the context of the theory of self-organization. Emphasis is placed on the microphysical processes of riming, accretion, and sedimentation in a supercooled cloud containing several types of precipitation particles. These processes are mathematically described using a parameterization scheme of the Kessler type.
This model of the competition of precipitation particle types for cloud water is analogous to the famous predator-prey model in population dynamics. The models differ, however, in the role of the exponents in the transformation rates, which can be interpreted as control parameters for the cloud physics model.
The number as well as the type of attractors depend on a set of parameters including, for example, the attributes of the chosen type of precipitation particles and the prescribed external source rates. If only spherically shaped precipitation particles are considered, the system is characterized by a single point attractor. If flat precipitation particles are allowed, self-organization in time, in the form of a periodic attractor and multistability, may occur depending on the strength of the external forcing, and the dynamics permits different long-term evolution patterns. In the case of multistability, the initial conditions decide which one of the attractors will be reached. Over a wide range of external source rates, one of the precipitation species will dominate in the long term. As an example, suppression of rain in the presence of supercooled cloud water and precipitation ice particles is reproduced. With a vanishing precipitation source rate only a single precipitation species finally remains in the system (selection or hyperselection). Characteristic timescales depend on the chosen parameter values; in the examples presented they are of the order of an hour or less.
This study elucidates how special assumptions in the parameterization scheme influence the long-term behavior of the system “cloud” and gives an example of a structurally unstable system.