Developing and evaluating ice cloud parameterizations for forward modeling of radar moments using in situ aircraft observations

Observing ice clouds using zenith pointing millimeter cloud radars is challenging because the transfer functions relating the observables to meteorological quantities are not uniquely defined. Here, the authors use a spectral radar simulator to develop a consistent dataset containing particle mass, area, and size distribution as functions of size. This is an essential prerequisite for radar sensitivity studies and retrieval development. The data are obtained from aircraft in situ and ground-based radar observations during the Indirect and Semi-Direct Aerosol Campaign (ISDAC) campaign in Alaska. The two main results of this study are as follows: 1) An improved method to estimate the particle mass-size relation as a function of temperature is developed and successfully evaluated by combining aircraft in situ and radar observations. The method relies on a functional relation between reflectivity and Doppler velocity. 2) The impact on the Doppler spectrum by replacing measurements of particle area and size distribution by recent analytical expressions is investigated. For this, higher-order moments such as skewness and kurtosis as well as the slopes of the Doppler spectrum are also used as a proxy for the Doppler spectrum. For the area-size relation, it is found that a power law is not sufficient to describe particle area and small deviations from a power law are essential for obtaining consistent higher moments. For particle size distributions, the normalization approach for the gamma distribution of Testud et al., adapted to maximum diameter as size descriptor, is preferred.