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RESEARCH PRODUCT

Subvisible cirrus clouds – a dynamical system approach

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Abstract. Ice clouds, so-called cirrus clouds, occur very frequently in the tropopause region. A special class are subvisible cirrus clouds with an optical depth lower than 0.03. Obviously, the ice crystal number concentration of these clouds is very low. The dominant pathway for these clouds is not known well. It is often assumed that heterogeneous nucleation at solid aerosol particles is the preferred mechanism although homogeneous freezing of aqueous solution droplets might be possible. For investigating subvisible cirrus clouds as formed by homogeneous freezing we develop a simple analytical cloud model from first principles; the model consists of a three dimensional set of ordinary differential equations, including the relevant processes as ice nucleation, diffusional growth and sedimentation, respectively. The model is integrated numerically and is investigated using theory of dynamical systems. We found two different states for the long-term behaviour of subvisible cirrus clouds, i.e. an attractor case and a limit cycle scenario. The transition between the states constitutes a Hopf bifurcation and is determined by environmental conditions as vertical updraughts and temperature. In both cases, the microphysical properties of the simulated clouds agree reasonably well with simulations using a complex model, with former analytical studies and with observations of subvisible cirrus. In addition, the model can also be used for explaining complex model simulations close to the bifurcation qualitatively. Finally, the results indicate that homogeneous nucleation might be a possible formation pathway for subvisible cirrus clouds.