Ehsan Erfani 

Ice clouds pose crucial challenges in climate model simulations and remote sensing retrievals due to complicated mechanisms of ice cloud formation that span from micro scale to planetary wave scale. Despite numerous attempts to parameterize these processes, many questions remain unanswered. This technical note provides a summary of the most common and recent studies on ice clouds and compiles important equations in a simple yet applicable manner to relate key microphysical properties of cirrus and ice clouds such as ice particle effective diameter, ice water path, cloud optical depth, particle number concentration, fall velocity, and particle size distribution. Additionally, it introduces relationships between ice particle mass (m) and dimension (D), as well as ice particle projected area (A) and D, which are essential for parameterizing the diverse shapes of ice particles in ice clouds. The equations provided in this technical note are valuable for the accurate representation of cirrus and ice clouds in remote sensing and climate modeling.