Ice clouds microphysical retrieval using 94-GHz Doppler radar observations: Basic relations within the retrieval framework

[1] High quality measurements of ice cloud properties from ground- and space-based sensors are key for improving our understanding of processes that affect ice cloud radiative effects and lifetime. Doppler cloud radars provide two independent measurements (reflectivity and Doppler velocity) to constrain the ice clouds microphysical retrievals. However, the retrievals are highly sensitive to the choice of the scattering forward model for non-spherical particles at millimeter-wavelengths and the selection of parameters in the mass- and velocity-size relationships, as well as to the representation of the particle size distribution (PSD). In this paper (part 1), the development of the basic relations used in the retrieval is presented. A novel approach for reducing the number of free parameters required to describe the microphysical properties of ice particles is described. The new proposed form of the mass-size relationship significantly reduces the sensitivity of the quantities of interest to the power law mass exponent, leaving only one parameter controlling mass dimensional relationship. A similar approach is adopted in the velocity calculation. In order to reduce the retrieval's dependence on the size distribution, the PSD defined for liquid-equivalent diameter is described using the concept of double moment normalization. The two normalizing quantities, mean mass-weighted diameter (D_m) and ice water content (IWC) are controlled mainly by the PSD size interval that is also an important contributor to the two Doppler observables. Both D_m and IWC are generally not very sensitive to the PSD segments of the smallest and largest particles that are considered as very uncertain.