Dependence of Mass–Dimensional Relationships on Median Mass Diameter

Saisai Ding, Greg Michael McFarquhar, Stephen W. Nesbitt, Randy J. Chase, Michael R. Poellot, Hongqing Wang

Research output: Contribution to journalArticlepeer-review


Retrievals of ice cloud properties require accurate estimates of ice particle mass. Empirical mass-dimensional (m-D) 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 a and b coefficients in m-D relationships on median mass diameter (Dmm) is studied. Using combined cloud microphysical data collected during the Olympic Mountains Experiment and coincident observations from Airborne Precipitation Radar Third Generation, Dmm-dependent (a, b) 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 a and b on Dmm are shown with both parameters significantly decreasing with Dmm, leading to smaller effective densities for larger Dmm ranges. A universally applied constant m-D relationship overestimates the mass of large aggregates when Dmm is between 3-6 mm and temperatures are between-15-0 °C. Multiple m-D relations should be applied for different Dmm 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.

Original languageEnglish (US)
Article number756
Issue number7
StatePublished - Jul 17 2020


  • Equally plausible surface
  • Mass-dimensional relationship
  • Median mass diameter
  • Radar reflectivity

ASJC Scopus subject areas

  • Environmental Science (miscellaneous)


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