Investigation of relationships between Ka-band radar reflectivity and ice and liquid water contents

The relationships between Ka-band (0.86 cm) equivalent radar reflectivity factor Z(e) (mm(6)/m(3)) and cirrus cloud ice content and ice crystal precipitation content IWC (mg/m(3)) are developed through regression analyses by utilizing a numerical scheme that combines the conjugate gradient and the fast Fourier transform method (CG-FFT), and the Rayleigh approximation, to calculate backscattering. The approach takes into account models based on several hexagonal ice crystal habits, but does not consider crystal aggregates. It is concluded that the Z-IWC relationships depend only slightly on the polarization state and zenith angle of the radar beam as a result of oriented particle scattering effects. For vertically pointing operations, we find IWC=7.49Z(e)(0.78) for aircraft-measured cirrus cloud compositions, and IWC=21.8Z(e)(0.79) for precipitating ice crystals measured in polar regions. In addition, the regression equation linking the radar reflectivity factor Z to liquid water content LWC (g/m(3)) is calculated from the results of simulations from an adiabatic cloud model, yielding Z=3.6/N-d LWC1.8, where N-d is the concentration of cloud droplets. The dependence of Z on N-d results from water vapor/droplet competition effects, which restricts the sizes of the largest (and most strongly Rayleigh scattering) droplets in the population. Comparison with empirically-based relationships for cumulus and stratocumulus clouds shows the best agreement for N-d of about 100 cm(-3).