Relationships between IWC and polarimetric radar measurands at 94 and 220 GHz for hexagonal columns and plates

Ice crystal models of a hexagonal column and hexagonal plate are used for deriving power-law relationships between ice water content (IWC) and various radar measurands, including Z_h, K_DP, A_h, and Z_DR (which are used together with Z_h, or K_DP,) at 94- and 220-GHz frequencies. The scattering computations are performed with the finite-difference time-domain method. The IWC and radar measurands are simulated based on gamma model size distributions characteristic of cirrus clouds. All the relationships involving the polarimetric measurands K_DP and Z_DR have less than 15% standard error (in the IWC estimate) when applied to the simulated size distributions. The standard errors for the IWC-Z_h and IWC-A_h relationships reach 40%. These should be considered as lower limits to the errors resulting from the relationships. The biases increase with variations in the model ice crystal aspect ratio, density, and canting angle. The least affected relationships are those involving Z_h, and A_h, alone. Combining Z_DR with Z_h, increases the biases compared to using only Z_h. The largest biases from all of these relationships arise as a result of applying those for columns to plates and vice versa. This indicates the need for differentiating ice crystal types. The clustering of hexagonal columns and plates in different regions of the Z_h,-Z_DR and Z_h-K_DP planes are suggested as a possible means of identifying them at side incidence, in addition to their depolarization signatures.