A hierarchy of nonlinear multiparametric models of cloud dynamics and microphysics

Three one-dimensional models of pure water (warm) cloud, represented by systems of three, four and five nonlinear ordinary differential equations, respectively, are formulated. They are treated as nonlinear dynamical systems. In all of them, the microphysics is parameterized by Kesslerʹs scheme; the vertical dynamics is modeled by means of the equation of convective motion inside the cloud. The steady solutions for all models are sketched in Appendix A. The evolution of the systemsʹ behaviour of the simplest model is studied. Depending on the parametersʹ values, the attractor is a fixed point or a limit cycle, or the system is structurally unstable. For some specific combinations of parameters, the system demonstrates chaotic behaviour and the transition to chaos is realized through period-doubling bifurcation. The detailed study of the more complex models, proposed here, is a future task.