Refinements to ice particle mass dimensional and terminal velocity relationships for ice clouds: Part I: Temperature dependence

This two-part study attempts to find appropriate mass dimension and terminal velocity relationships that, when considered together with particle size distributions (PSD), agree with coincident measurements of ice water content (IWC), and with variables related to higher moments such as the mean mass-weighted fall speed. Reliable relationships are required for improving microphysical parameterizations for weather forecast models and developing methods for evaluating them, subjects addressed in detail in Part II of this study.

Here, a range of values from 1.5 to 2.3 is assumed for the exponent b in the mass dimension relationship, m = aD b, where D is the maximum particle dimension, to bound its likely value for sizes above about 100 μm. Measured IWC and size spectra are used to find appropriate values for the coefficient a. It is demonstrated that all values of the exponent b, with appropriate a coefficients, can fit the IWC measurements.