The meaning and significance of the definition of ice crystal maximum dimension: impacts on calculated cloud properties from two-dimensional particle images

Many algorithms that analyze two-dimensional particle images acquired by in-situ imaging probes use different definitions of particle maximum dimension (Dmax) for deriving number distribution functions, N(Dmax). Common definitions include maximum length in the horizontal or photodiode array direction (D_P), maximum length in vertical or time direction (D_T), and their combinations, such as ½(D_P+D_T) and √(D_P²+D_T² ). The diameter of the minimum circle enclosing the particle has also been used. The concentrations of particles in different size ranges can vary by up to an order of magnitude in some size ranges when using different definitions of Dmax. Substantial differences in the N0, μ and λ values used to characterize N(Dmax) as gamma functions are also seen.

The use of different definitions of Dmax also affects the calculation of bulk cloud and optical properties from the imaging probe data. For example, ice water content, extinction, and effective radius calculated by mass- and area-dimensional relations can vary by 2-3 times. Further, the mass-weighted terminal velocity can differ by 60%, and precipitation rate by one order of magnitude due to different definitions, leading to differences of microphysical process rates used in numerical models. These differences occur because fundamental relationships used to derive the bulk properties, such as relations for particle velocity and mass with particle dimension, are identically applied regardless of the Dmax definition. The uncertainties in derived size distributions using different definitions can propagate to these calculated bulk properties through the same model. These differences show the need to use consistent definitions of Dmax for defining N(Dmax) and the functional dependence of particle microphysical properties on Dmax. Implications for numerical modeling studies and remote sensing retrievals are discussed.