Growth of Rosette Ice Crystals and Impact on Cirrus Development

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Clouds are the most important atmospheric constituent for determining the earth's albedo. Many clouds are composed of ice crystals. The life of such clouds and their effect on solar and terrestrial radiation depend on the sizes, shapes, and concentration of the ice crystals, and their growth and evaporation. This project is a theoretical study of certain microphysical properties of rosette-shaped ice crystals, which are a common constituent of cirrus clouds. In particular, the work focuses on developing an accurate formulation of the growth and evaporation of rosette crystals by the condensation-diffusion process. The rate of growth of an ice crystal in a given environment is determined by the size and shape of the crystal and the excess vapor pressure over the equilibrium value for ice. The conventional theory that describes these effects makes use of an analogy between the equation for the diffusion of water vapor in air and the equation in electrostatics that describes the distribution of potential around a charged conductor. Using this analogy, the shape is described in terms of the electrical capacitance of a conductor having the same shape as the ice crystal. This provides a great simplification in the theory of crystal growth. A single parameter, the capacitance, is used instead of solving for the rate of vapor deposition point-by-point over the complex surface of the crystal. Values of the capacitance are known for simple crystal forms such as plates, columns, and needles, but not for rosettes, which are the predominant form at temperatures colder than about -40C. In the first part of this study, mathematical approximations will be formulated to describe the shapes of rosette crystals of various thickness, lengths, and numbers of branches. For those that closely approximate the crystals that have been observed in cirrus clouds, the capacitance will be computed using finite element numerical techniques. In the second part of the study, the capacitance values will be employed in an existing numerical model of cirrus clouds to establish accurate parameterizations of rosette growth rates. Simulated clouds including crystals of various forms will then be employed with existing radiative transfer codes to determine the effects of cirrus clouds through their life cycles on solar and terrestrial radiation. Sensitivity studies will produce useful information for the broad scientific community to access the influence of cirrus clouds on the global climate process.