Dependence of Mass-Dimensional Relationships on Median Mass Diameter

Retrievals of ice cloud properties require accurate estimates of ice particle mass. Empirical mass-dimensional (m-D) relationships in the form m = aD(b) are widely used and usually universally applied across the complete range of particle sizes. For the first time, the dependence of a and b coefficients in m-D relationships on median mass diameter (D-mm) is studied. Using combined cloud microphysical data collected during the Olympic Mountains Experiment and coincident observations from Airborne Precipitation Radar Third Generation, D-mm-dependent (a,b) coefficients are derived and represented as surfaces of equally plausible solutions determined by some tolerance in the chi-squared difference chi(2) that minimizes the difference between observed and retrieved radar reflectivity. Robust dependences ofaandbon D-mm are shown with both parameters significantly decreasing with D-mm, leading to smaller effective densities for larger D-mm ranges. A universally applied constantm-Drelationship overestimates the mass of large aggregates when D-mm is between 3-6 mm and temperatures are between -15-0 degrees C. Multiplem-Drelations should be applied for different D-mm ranges in retrievals and simulations to account for the variability of particle sizes that are responsible for the mass and thus for the variability of particle shapes and densities.