Growth of Rosette Ice Crystals and Impact on Cirrus Development

云是决定地球反照率的最重要的大气成分。许多云都是由冰晶组成的。这种云的寿命及其对太阳和地面辐射的影响取决于冰晶的大小、形状和浓度，以及它们的生长和蒸发。这个项目是对玫瑰花状冰晶的某些微观物理性质的理论研究，玫瑰花状冰晶是卷云的常见组成部分。特别是，这项工作的重点是开发一个准确的公式，通过凝聚-扩散过程的玫瑰花结晶体的生长和蒸发。冰晶在特定环境中的生长速度取决于晶体的大小和形状，以及超过冰平衡值的超额蒸汽压。描述这些效应的传统理论利用了水蒸气在空气中扩散的方程与描述带电导体周围电势分布的静电学方程之间的类比。利用这个类比，用与冰晶形状相同的导体的电容来描述形状。这大大简化了晶体生长理论。使用单个参数，即电容，而不是逐点求解晶体复杂表面上的气相沉积速率。对于简单的晶体形式，如板状、柱状和针状，电容值是已知的，但对于玫瑰花环则不是，玫瑰花环是温度低于-40摄氏度的主要形式。在这项研究的第一部分，将用数学近似来描述不同厚度、长度和支数的玫瑰花结晶体的形状。对于那些与在卷云中观察到的晶体非常接近的那些，将使用有限元数值技术来计算电容。在研究的第二部分，电容值将被用于现有的卷云数值模式，以建立玫瑰花丛生长速度的精确参数。然后，包括各种形式的晶体的模拟云将与现有的辐射传输代码一起使用，以确定卷云在其生命周期中对太阳和地面辐射的影响。敏感性研究将为广大科学界提供有用的信息，以了解卷云对全球气候过程的影响。

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.