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 = a D 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 χ 2 that minimizes the difference between observed and retrieved radar reflectivity. Robust dependences of a and b on 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 constant m–D relationship overestimates the mass of large aggregates when D mm is between 3–6 mm and temperatures are between −15–0 °C. Multiple m–D relations 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.