On retrieving the microphysical properties of cirrus clouds using the moments of the millimeter-wavelength Doppler spectrum

[1] Techniques that use only measurements provided by millimeter-wavelength Doppler radar for retrieving the properties of clouds provide certain practical advantages over techniques that require measurements from multiple instruments. We concentrate on the capacity of the moments of the Doppler spectrum to provide information suitable for retrieving the microphysical properties of cirrus clouds. Specifically, we present an algorithm that uses the zeroth and first moments of the Doppler spectrum (radar reflectivity and mean Doppler velocity) to retrieve the cloud particle size distribution. We also discuss a methodology for evaluating the second moment of the Doppler spectrum for information related to the width of the particle size distribution. The properties of observed cirrus particle spectra are first examined to ascertain what degree of complexity is required of assumed functional representations of particle spectra in cirrus volumes. We find that although particle spectra with bimodal tendencies are common, single-mode functions are able to capture the essential characteristics of these spectra to within observational uncertainty for most cirrus. Furthermore, two-parameter functions such as the exponential function are shown to be adequate representations of cirrus particle spectra in situations where the radar reflectivity factor is less than about −5 dBZe and the temperatures are colder than about 253 K. A technique for separating air motion contributions from the Doppler velocity is examined, and an approach for similarly processing the Doppler spectral width is introduced. In comparison to aircraft data, we find uncertainty in the derived quiet air velocity and spectrum width to be on the order of 20% and 40%, respectively. Using recent parameterizations of ice crystal terminal velocity, mass, and backscatter cross section, we present a straightforward algorithm for retrieving cirrus cloud microphysical properties from observations of radar reflectivity and Doppler velocity. A simulation experiment with variable particle habits and realistic observational error shows that the retrieval uncertainties are on the order of 60% and 40% for ice water content and mass median particle size, respectively. These uncertainty magnitudes are supported by comparison to aircraft data.