Constraining mass-diameter relations from hydrometeor images and cloud radar reflectivities in tropical continental and oceanic convective anvils

In this study the density of ice hydrometeors in tropical clouds is derived from a combined analysis of particle images from 2-D-array probes and associated reflectivities measured with a Doppler cloud radar on the same research aircraft. Usually, the mass-diameter m(D) relationship is formulated as a power law with two unknown coefficients (pre-factor, exponent) that need to be constrained from complementary information on hydrometeors, where absolute ice density measurement methods do not apply. Here, at first an extended theoretical study of numerous hydrometeor shapes simulated in 3-D and arbitrarily projected on a 2-D plan allowed to constrain the exponent beta of the m(D) relationship from the exponent sigma of the surface-diameter S(D) relationship, which is likewise written as a power law. Since S(D) always can be determined for real data from 2-D optical array probes or other particle imagers, the evolution of the m(D) exponent can be calculated. After that, the pre-factor alpha of m(D) is constrained from theoretical simulations of the radar reflectivities matching the measured reflectivities along the aircraft trajectory. The study was performed as part of the Megha-Tropiques satellite project, where two types of mesoscale convective systems (MCS) were investigated: (i) above the African continent and (ii) above the Indian Ocean. For the two data sets, two parameterizations are derived to calculate the vertical variability of m(D) coefficients alpha and beta as a function of the temperature. Originally calculated (with T-matrix) and also subsequently parameterized m(D) relationships from this study are compared to other methods (from literature) of calculating m(D) in tropical convection. The significant benefit of using variable m(D) relations instead of a single m(D) relationship is demonstrated from the impact of all these m(D) relations on Z-CWC (Condensed Water Content) and Z-CWC-T-fitted parameterizations.