A novel approach for characterizing the variability in mass-dimension relationships: results from MC3E

Mass-dimension (m-D) relationships determining bulk microphysical properties such as total water content (TWC) and radar reflectivity factor (Z) from particle size distributions are used in both numerical models and remote sensing retrievals. The a and b coefficients representing m = aD(b) relationships, however, can vary significantly depending on meteorological conditions, particle habits, the definition of particle maximum dimension, the probes used to obtain the data, techniques used to process the cloud probe data, and other unknown reasons. Thus, considering a range of a;b coefficients may be more applicable for use in numerical models and remote sensing retrievals. Microphysical data collected by two-dimensional optical array probes (OAPs) installed on the University of North Dakota (UND) Citation aircraft during the Mid-latitude Continental Convective Clouds Experiment (MC3E) were used in conjunction with TWC data from a Nevzorov probe and ground-based S-band radar data to determine a and b using a technique that minimizes the chi-square difference between the TWC and Z derived from the OAPs and those directly measured by a TWC probe and radar. All a and b values within a specified tolerance were regarded as equally plausible solutions. Of the 16 near-constant-temperature flight legs analyzed during the 25 April, 20 May, and 23 May 2011 events, the derived surfaces of solutions on the first 2 days where the aircraft-sampled stratiform cloud had a larger range in a and b for lower temperature environments that correspond to less variability in N(D), TWC, and Z for a flight leg. Because different regions of the storm were sampled on 23 May, differences in the variability in N(D), TWC, and Z influenced the distribution of chi-square values in the (a, b) phase space and the specified tolerance in a way that yielded 2.8 times fewer plausible solutions compared to the flight legs on the other dates. These findings show the importance of representing the variability in a;b coefficients for numerical modeling and remote sensing studies, rather than assuming fixed values, as well as the need to further explore how these surfaces depend on environmental conditions in clouds containing ice hydrometeors.