Introduction

Most dual-polarization meteorological radars transmit and receive in the same polarization basis. For example, radars that operate in an H-V basis typically transmit separate pulses of horizontally (H) and vertically (V) polarized radiation and receive the backscattered returns in the same polarization as transmitted (the co-polar return), and sometimes in the orthogonal polarization (the cross-polar return). Radars that operate in a circular polarization basis transmit a given circular polarization (LHC or RHC) and receive the backscattered signals in parallel L and R channels to obtain the dual-polarization measurements. Alternate pulses of LHC and RHC radiation can also be transmitted, but it is not necessary to do so. In this paper we describe measurements obtained when the transmitted and received signals are in different polarization bases. The received signals in this case are both copolar-like.

H and V measurements can be used to determine important parameters of the scatterers and of the propagation medium. These include the differential reflectivity $Z_{\rm DR}$, the differential propagation phase $\phi_{dp}$, and the H-V correlation coefficient $\rho _{HV}$. The quantities are usually obtained by transmitting alternate pulses of H and V radiation and receiving the backscattered returns in the same polarization as transmitted. $Z_{\rm DR}$ is determined from the ratio of the co-polar backscattered powers of the H and V transmissions. Differential phase is obtained by coherently correlating the H and V returns from successive pairs of transmitted pulses. The phase differences of the pulses are dominated by the Doppler shift during the interpulse intervals and are secondarily affected by the desired differential phase effects. The Doppler contribution is canceled out by correlating interlaced sets of pulse pairs, $R_a = \langle H^*V \rangle$ and $R_b = \langle V^*H \rangle$, and by differencing the arguments of the two quantitites. The random nature of the Doppler phase shift from one pulse to the next increases the uncertainty of the $\phi_{dp}$ estimate, however, adding noise to an already weak effect. Similar difficulties beset $\rho _{HV}$ measurements. The normalized magnitudes of R_a and R_b give $\rho_{{HV}}(T)$, where T is the interpulse interval. $\rho_{{HV}}(T)$ is reduced from the correlation $\rho_{{HV}}(0)$ at zero time lag by the Doppler effects, which decorrelate the signal with time. An estimator of $\rho_{{HV}}(0)$ is obtained by assuming that the Doppler spectrum is gaussian, but the uncertainty of the estimate is increased both by the random nature of the Doppler signal and possibly by the gaussian spectral assumption. The various processing algorithms and estimator variances are well summarized by Doviak and Zrnic (1993).

The alternating pulse technique determines the polarization parameters using a single receiver channel but requires a high-power polarization switch to generate the H and V transmissions. By using a second receiver to measure the cross-polar return, one can also determine the linear depolarization ratio LDR.

In this paper we describe results in which simultaneous H and Vtransmissions are used to determine the polarization variables. The returns are measured in parallel H and V receiving channels. This approach has the advantage that $\phi_{dp}$ and $\rho _{HV}$ are determined directly from simultaneous measurements and are not contaminated by the Doppler effects. Also, a polarization switch is not needed. Dwell time is reduced because the two polarizations are transmitted together rather than on successive pulses, and because less averaging is needed in the absence of the Doppler effects.

The simultaneous transmission approach was first suggested by Sachidananda and Zrnic (1985) as a way of making fast scan differential reflectivity measurements. Its greater value is in improved $\phi_{dp}$ and $\rho _{HV}$measurements (e.g., Jameson and Davé, 1988; Balakrishnan and Zrnic, 1990a, Kostinski, 1994). In recent years the CSU-CHILL radar was modified to transmit H and V signals simultaneously (as well as individually) by operating two transmitters and two receivers in parallel. This eliminated the need for a polarization switch and allowed results from the alternating and simultaneous approaches to be compared (Brunkow et al., 1997).

The results reported in this paper are from the 3-cm New Mexico Tech (NMT) dual-polarization radar, which utilized a power divider to obtain the simultaneous transmissions. Nearly equal H and V powers were transmitted and the relative phases of the two components were adjusted to produce circular polarization. The CSU-CHILL radar transmits slant ${45^\circ}$ linear polarization. The two types of transmissions differ only in their relative phase; as part of this paper we discuss the relative advantages of the two polarizations.