| Summary: | Retrievals of ice cloud properties require accurate estimates of ice particle mass. Empirical mass–dimensional (<i>m</i>–<i>D</i>) relationships in the form m=aDb are widely used and usually universally applied across the complete range of particle sizes. For the first time, the dependence of <i>a</i> and <i>b</i> coefficients in <i>m</i><i>–</i><i>D</i> relationships on median mass diameter (<i>D</i><sub>m</sub><sub>m</sub>) is studied. Using combined cloud microphysical data collected during the Olympic Mountains Experiment and coincident observations from Airborne Precipitation Radar Third Generation, <i>D</i><sub>mm</sub>-dependent (<i>a</i>, <i>b</i>) coefficients are derived and represented as surfaces of equally plausible solutions determined by some tolerance in the chi-squared difference χ2 that minimizes the difference between observed and retrieved radar reflectivity. Robust dependences of <i>a</i> and <i>b</i> on <i>D</i><sub>mm</sub> are shown with both parameters significantly decreasing with <i>D</i><sub>mm</sub>, leading to smaller effective densities for larger <i>D</i><sub>mm</sub> ranges. A universally applied constant <i>m</i><i>–</i><i>D</i> relationship overestimates the mass of large aggregates when <i>D</i><sub>mm</sub> is between 3–6 mm and temperatures are between −15–0 °C. Multiple <i>m</i><i>–</i><i>D</i> relations should be applied for different <i>D</i><sub>mm</sub> 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.
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