Developing and bounding ice particle mass-and area-dimension expressions for use in atmospheric models and remote sensing

Ice particle mass- and projected area-dimension (<em>m</em>-<em>D</em> and <em>A</em>-<em>D</em>) power laws are commonly used in the treatment of ice cloud microphysical and optical properties and the remote sensing of ice cloud properties. Although there has long been evidence that a single <em>m</em>-<em>D</em> or <em>A</em>-<em>D</em> power law is often not valid over all ice particle sizes, few studies have addressed this fact. This study develops self-consistent <em>m</em>-<em>D</em> and <em>A</em>-<em>D</em> expressions that are not power laws but can easily be reduced to power laws for the ice particle size (maximum dimension or <em>D</em>) range of interest, and they are valid over a much larger <em>D</em> range than power laws. This was done by combining ground measurements of individual ice particle <em>m</em> and <em>D</em> formed at temperature <em>T</em> &lt; −20 °C during a cloud seeding field campaign with 2-D stereo (2D-S) and cloud particle imager (CPI) probe measurements of <em>D</em> and <em>A</em>, and estimates of <em>m</em>, in synoptic and anvil ice clouds at similar temperatures. The resulting <em>m</em>-<em>D</em> and <em>A</em>-<em>D</em> expressions are functions of temperature and cloud type (synoptic vs. anvil), and are in good agreement with <em>m</em>-<em>D</em> power laws developed from recent field studies considering the same temperature range (−60 °C &lt; <em>T</em> &lt; −20 °C).冰粒子质量-最大尺度（m-D）与投影面积-最大尺度（A-D）幂律关系（power laws）常被广泛应用于冰云微物理与光学特性的研究，以及冰云特性的遥感反演领域。尽管长期以来已有研究证实，单一的m-D或A-D幂律关系往往无法覆盖全部冰粒子尺度范围，但鲜有研究针对这一局限性展开系统性探讨。本研究构建了自洽的m-D与A-D表达式，此类表达式并非严格的幂律形式，但可针对目标冰粒子尺度（最大尺度，即D）范围简化为幂律关系，且其适用的D尺度范围远宽于传统幂律关系。本研究通过将云播撒外场试验中，于温度T < -20℃条件下生成的单个冰粒子的m与D的地面测量数据，与二维立体成像（2D-S）探头、云粒子成像仪（CPI）探头获取的D、A测量数据，以及相同温度下天气云（synoptic clouds）与砧状冰云（anvil ice clouds）中的m估算值相结合，完成了上述表达式的构建。最终得到的m-D与A-D表达式为温度与云型（天气云与砧状云）的函数，且与近期针对相同温度范围（-60℃ < T < -20℃）开展的外场研究中所构建的m-D幂律关系具有良好的一致性。