Studies of the polarimetric covariance matrix. Part II: Modeling and polarization errors

A polarimetric radar covariance matrix model is described to study the behavior of the co-to-cross covariances in precipitation. The 2x2 propagation matrix with attenuation, differential attenuation, and differential phase is coupled to the backscatter matrix leading to a propagation-modified covariance matrix model. System polarization errors are included in this model as well. This model is used to study the behavior of the magnitude and phase of the co-to-cross covariances and the linear depolarization ratio (LDR) in rainfall. It is shown that the model predictions are consistent with data collected with the Colorado State University (CSU)-University of Chicago-Illinois State Water Survey (CHILL) radar in intense rainfall. A method is also given for estimating the system polarization errors from covariance matrix data collected in intense rainfall.