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

<p>Ice particle mass- and projected area-dimension (<em>m</em>-<em>D</em>&nbsp;and&nbsp;<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&nbsp;<em>m</em>-<em>D</em>&nbsp;or&nbsp;<em>A</em>-<em>D</em>&nbsp;power law is often not valid over all ice particle sizes, few studies have addressed this fact. This study develops self-consistent&nbsp;<em>m</em>-<em>D</em>&nbsp;and&nbsp;<em>A</em>-<em>D</em>&nbsp;expressions that are not power laws but can easily be reduced to power laws for the ice particle size (maximum dimension or&nbsp;<em>D</em>) range of interest, and they are valid over a much larger&nbsp;<em>D</em>&nbsp;range than power laws. This was done by combining ground measurements of individual ice particle&nbsp;<em>m</em>&nbsp;and&nbsp;<em>D</em>&nbsp;formed at temperature&nbsp;<em>T</em> &thinsp;&lt;&thinsp; &minus;20 &deg;C during a cloud seeding field campaign with 2-D stereo (2D-S) and cloud particle imager (CPI) probe measurements of&nbsp;<em>D</em>&nbsp;and&nbsp;<em>A</em>, and estimates of&nbsp;<em>m</em>, in synoptic and anvil ice clouds at similar temperatures. The resulting&nbsp;<em>m</em>-<em>D</em>&nbsp;and&nbsp;<em>A</em>-<em>D</em>&nbsp;expressions are functions of temperature and cloud type (synoptic vs. anvil), and are in good agreement with&nbsp;<em>m</em>-<em>D</em>&nbsp;power laws developed from recent field studies considering the same temperature range (&minus;60 &deg;C &thinsp;&lt;&thinsp; <em>T</em> &thinsp;&lt;&thinsp; &minus;20 &deg;C).</p>