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).