A novel approach for characterizing the variability in mass–dimension relationships: results from MC3E
Abstract. Mass–dimension (m–D) relationships determining bulkmicrophysical properties such as total water content (TWC) and radarreflectivity factor (Z) from particle size distributions are used in bothnumerical models and remote sensing retrievals. The a and b coefficientsrepresenting m=aD b relationships, however, can vary significantlydepending on meteorological conditions, particle habits, the definition ofparticle maximum dimension, the probes used to obtain the data, techniquesused to process the cloud probe data, and other unknown reasons. Thus,considering a range of a,b coefficients may be more applicable for use innumerical models and remote sensing retrievals. Microphysical data collectedby two-dimensional optical array probes (OAPs) installed on the University ofNorth Dakota (UND) Citation aircraft during the Mid-latitude Continental ConvectiveClouds Experiment (MC3E) were used in conjunction with TWC data from aNevzorov probe and ground-based S-band radar data to determine a and busing a technique that minimizes the chi-square difference between the TWC andZ derived from the OAPs and those directly measured by a TWC probe andradar. All a and b values within a specified tolerance were regarded as equallyplausible solutions. Of the 16 near-constant-temperature flight legs analyzedduring the 25 April, 20 May, and 23 May 2011 events, the derived surfaces ofsolutions on the first 2 days where the aircraft-sampled stratiform cloudhad a larger range in a and b for lower temperature environments thatcorrespond 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 inthe variability in N(D), TWC, and Z influenced the distribution ofchi-square values in the (a,b) phase space and the specified tolerance in away that yielded 2.8 times fewer plausible solutions compared to the flightlegs on the other dates. These findings show the importance of representingthe variability in a,b coefficients for numerical modeling and remotesensing studies, rather than assuming fixed values, as well as the need tofurther explore how these surfaces depend on environmental conditions inclouds containing ice hydrometeors.