Towards better copolar correlations: Correlate what, correlate how?

The correlation between horizontally and vertically polarized signals is probably the most valuable piece of information provided by dual-polarization radars. Though its quantitative estimation does not provide any specific insight, it has proved extremely useful almost exclusively for target type identification (TID). At its root, the complex copolar correlation coefficient ρ_co provides a combined measure of the uniformity of Z_dr and of (Φ_dp + δ) of targets within the illuminated volume. Its value rests in its property to be high for uniformly-shaped Rayleigh targets in well-behaved weather situations, and become low when targets with varied shapes and beyond the Rayleigh regime become dominant. Yet its proper estimation is not without problems: it can become biased in the presence of significant noise as well as in the presence of gradients of Φ_dp within the beam, rendering its use for TID difficult under these situations. While many approaches to deal with noise have been proposed, we have not found one that performs satisfactorily without introducing SNR-dependent biases.

Since correlation is used almost exclusively for TID, we chose to study the problem of its determination from an unusual angle: can we design and/or better estimate a correlation-like quantity that is less sensitive to biases from noise of different sources and from gradients of ödp within the beam while preserving or enhancing its usefulness for TID? Two parallel efforts were undertaken. To specifically solve the low-SNR evaluation problem, we have explored more complete equations of the respective contributions of noise and signal at different lags to obtain smaller biases. To attack the bias caused by gradients of Φ_dp, we experimented with the real copolar correlation of signal amplitude instead of the complex copolar correlation of signal to counter the dependence on radar illumination.