1. Introduction

The simultaneous transmission and reception of horizontally (H) and vertically (V) polarized waves (SHV) has become a very popular way to achieve dual-polarization measurements for weather radar. Previously, radars achieved dual-polarization measurements by either employing a fast, high-powered waveguide switch or by using two separate transmitters (Brunkow et al. 2000; Keeler et al. 2000). Both technologies incur significant costs to the operation and maintenance of the radar. The premise of the SHV technique is that as the transmitted wave propagates, no cross coupling occurs between the H and V electric field components. Mathematically, this requires that the propagation matrix be diagonal (Vivekanandan et al. 1991). An advantage of the SHV technique is that the expense of either a fast waveguide switch or two transmitters is avoided. There are other advantages of SHV mode (see Doviak et al. 2000 for details). Disadvantages of SHV mode are that 1) the linear depolarization ratio (LDR) is not measured, and, 2) if there is cross coupling of the H and V waves, there can be measurement biases. Thus, the viability of the SHV dual-polarization technique is based on having 1) a zero mean canting angle of the propagation medium and 2) negligible antenna polarization errors. If either condition is not met, cross coupling occurs between the H and V channels, which can cause measurement biases.

Measurement biases in the SHV mode have been investigated (Sachidananda and Zrnić 1985). Doviak et al. (2000) evaluated cross-coupling errors of SHV mode and concluded that since the mean canting angle of rain is close to zero, the biases were acceptable. More recently, Wang and Chandrasekar (2006) and Wang et al. (2006) investigated the biases in SHV polarization measurements resulting from cross-coupling errors caused by the radar system polarization errors as a function of ϕ_dp (differential propagation phase). They concluded that system isolation between the H and V channels must be greater than 44 dB in order to ensure that the Z_dr bias is within 0.2 dB for worst-case errors.

Ryzhkov and Zrnić (2007) examined the effects of nonzero mean canting angle of the propagation medium on SHV mode measurements. Data gathered in SHV mode with KOUN, the National Severe Storms Laboratory’s (NSSL’s) S-band dual-polarization Doppler radar, displayed Z_dr radial bias “stripes” after the radar waves passed through the ice phase of either convective cells or stratiform precipitation. They propose that the nonzero mean canting angle of the propagation medium produces coupling between the H and V polarized waves that causes the anomalous Z_dr signatures.

All reflector-type antennas will introduce polarization errors to the desired H and V transmitted polarization states, causing cross coupling between the H and V channels. This will bias polarization measurements of precipitation unless the antenna interchannel isolation is extremely low. This paper investigates and quantifies the expected magnitude and phase of antenna polarization errors via an analysis of solar measurements and a known typical LDR system limit. Importantly, the antenna polarization errors are interpreted in terms of their tilt and ellipticity angles, which has not been done before. Such an analysis provides insight as to the nature of the antenna polarization errors. Specifically, we show that the antenna polarization errors are dominated by the ellipticity angle errors, at least for the National Center for Atmospheric Research (NCAR) dual-polarization Doppler radar (S-Pol). The radar model that is introduced by Hubbert and Bringi (2003) is modified to accommodate arbitrary transmitting polarization states, which also has not been shown before. The transmit differential phase, as defined in this paper, is distinctly different and independent from the phases of the antenna polarization errors. Thus, the model allows for the separate parameterization of both transmit differential phase and antenna-induced polarization errors, and for an analysis of their impact on SHV mode Z_dr and ϕ_dp biases. For example, the effect of cross coupling caused by the propagation medium is demonstrated with the model, and it is shown that small changes in ϕ_dp with range can cause significant bias in Z_dr. It is shown that the Z_dr bias is a strong function of differential transmit phase.

The paper is organized as follows. Section 2 describes the radar model of Hubbert and Bringi (2003) and how antenna polarization errors are accounted for. The model is then modified to permit arbitrary transmit polarizations, and model results are given. Section 3 shows how antenna polarization errors can be estimated from experimental data. The summary and conclusions are given in section 4. In Hubbert et al. (2009, hereafter Part II), experimental data from the NCAR S-Pol and from NSSL’s S-band research radar, KOUN, illustrate the theory established herein, in Part I.

2. The model

The radar scattering model is described in Hubbert and Bringi (2003), but is briefly reviewed here for convenience and clarity. The model is then expanded to accommodate arbitrary transmit polarization states (refer to Fig. 1). The particles in the backscatter volume and the coherent propagation medium are independently modeled. The “steady” propagation medium is modeled via a 2 × 2 matrix that includes absolute attenuation (A_h), differential attenuation (A_dp), differential propagation phase (ϕ_dp), and mean canting angle (θ) as parameters. The resolution volume (or backscatter medium) is modeled as an ensemble of precipitation particles with gamma drop size distribution (DSD) and various spatial orientation distributions via the T-matrix method (Vivekanandan et al. 1991; Waterman 1969). Antenna polarization errors are modeled similar to McCormick (1981) and Bringi and Chandrasekar (2001) and are beam integrated so that a pair of complex numbers characterizes the H and V antenna polarization errors. Our modeling of antenna errors is very similar to Wang and Chandrasekar (2006). The transmit polarization state is defined at the reference plane as shown in Fig. 1. The antenna system refers to the microwave path from the reference plane through the antenna dish.

The scattering geometry used is the backscatter alignment (BSA) convention (Bringi and Chandrasekar 2001). Canting angles are measured counterclockwise from the positive horizontal axis in the plane of polarization (i.e., the plane containing the H and V axis perpendicular to the propagation direction). Further details of the radar model are given in appendix A.

a. Modeling antenna polarization errors

The radar antenna and surrounding microwave circuitry introduce microwave cross coupling that gives rise to polarization errors so that pure H or V polarization are not transmitted. Polarization errors have been covered in detail (McCormick 1981; Metcalf and Ussails 1984; Bringi and Chandrasekar 2001; Hubbert and Bringi 2003; Wang and Chandrasekar 2006). Some of the sources of polarization error are nonideal feedhorn, nonideal parabolic reflector, antenna support struts, and edge effects. These polarization errors are distributed across the radar antenna patterns and thus can vary across the beam, especially where the cross-polarized lobes exist (Ussailis and Metcalf 1983; Bringi and Chandrasekar 2001). For distributed precipitation media, the resulting error is an integrated effect and we model these distributed errors with a 2 × 2 polarization error matrix. The assumption is that the scattering medium is homogenous across the antenna pattern.

The polarization errors are included in the model by pre- and postmultiplication of 𝗦, where 𝗦 is the scattering matrix in Eq. (A4), by the error matrix ϒ,

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where

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with constraints i_h² + |ξ_h|² = i_υ² + |ξ_υ|² = 1, where i_h and i_υ are real. The polarization errors of the H and V channels are represented by the complex numbers ξ_h and ξ_υ, respectively. The polarization errors can also be equivalently represented in the following several ways: 1) the polarization ratio χ [see Eq. (A6)], 2) the geometric parameters of tilt angle α and ellipticity angle ε, and 3) the phasor descriptors γ and ζ. For H errors

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and for V errors

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because the definition of χ used here is the ratio of the V to H electric field components. Referring to the polarization ellipse of Fig. 2, the polarization error terms ξ_h and ξ_υ can also be related to the geometric polarization ellipse parameters α and ε, and the phasor descriptors, where γ = tan⁻¹(|E_υ|/|E_h|) and arg(E_υ/E_h) = ζ = ζ_υ − ζ_h. The tilt angle α is measured from the positive horizontal axis to the major axis of the polarization ellipse and ε is defined as tanε = (minor axis)/(major axis).

Mathematically, these variables are related by (Azzam and Bashara 1989)

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and

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As can be seen from Eqs. (3) through (7), if the ξ_h(ξ_υ) is real then ε is zero and if ξ_h(ξ_υ) is imaginary then α is zero. If the errors are orthogonal,

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then ϒ is unitary and (1) represents an orthogonal change of polarization basis. Expressing the polarization errors using the geometric descriptors gives a convenient and intuitive way to analyze polarization errors.

Given the tilt and ellipticity angles of the polarization state (or ellipse), the corresponding phasor parameters are easily found using the relations in Eqs. (7). Then, the antenna error matrix terms ξ_h and i_h are found as

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and finally

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Similarly, the vertical polarization error ξ_υ is found from α_υ and ε_υ (remembering that the polarization ratio is defined as χ = i_υ/ξ_υ) as

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and finally

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It is also useful to express the polarization ratio in terms of its real and imaginary parts as (Tragl 1990)

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b. Modeling simultaneous H and V transmission

The model thus far was constructed so that the transmit and receiving polarization states are the same according to radar polarimetry theory. The covariance matrix of Eq. (A5) is a convenient form for covariance analysis and for polarization basis transformations; however, it is not a transmission matrix. It does not express a transfer relationship between an arbitrary input polarization and the resultant output covariances, as does the Mueller matrix (Azzam and Bashara 1989). To model the H and V receiving covariances that result from arbitrary transmitting polarizations, a 4 × 4 covariance matrix is formed using the feature vector

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Taking the outer product of the feature vector yields the 4 × 4 covariance matrix in the H–V basis as

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where 〈·〉 denotes ensemble (spatial) or temporal averages (which are equivalent because of the assumption of ergodicity). Note that the covariance matrix is Hermitian. It can be shown that the matrix of Eq. (17) may be transformed to the Mueller matrix (Azzam and Bashara 1989), and thus the covariance matrix of Eq. (17) can also be used as a transfer function matrix

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where 𝗝_i and 𝗝_o are 4 × 1 input and output coherency matrices. In terms of the desired polarization characteristics of the incident polarization, namely, tilt angle (α) and ellipticity angle (ε), 𝗝_i becomes

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If linear, a slant of 45° transmitting polarization is desired (i.e., SHV mode), and then α = 45° and ε = 0°. SHV variables of interest can then be calculated, for example, as

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where the superscript “shv” denotes SHV variables. In this way, the radar model is modified to allow for arbitrary transmitting polarizations (but still receiving H and V) by putting the covariances of Eq. (A5) into the matrix form of Eq. (17). The input vector is then controlled by Eq. (19) via the tilt and ellipticity angles of the desired transmitting polarization state.

The advantages of the presented radar model are that 1) no approximations are made in terms of the relative significance of the various error terms and 2) transmit, propagation, backscatter, and antenna model parameters are all independently set so that the effect of varying each parameter on the polarization variables of Z_dr, ϕ_dp, etc., can be investigated.

3. Estimating antenna polarization errors

The estimation of the complex error terms ξ_h and ξ_υ for antennas is difficult, and they are not typically supplied by antenna manufacturers. There are ways, however, to estimate the magnitude of the error terms and to generally qualify their character. Two generally available and measurable quantities are LDR and passive solar scan measurements.

For well-designed radars with parabolic, center-fed antennas, the dominant cross-coupling factor is the antenna (Bringi and Chandrasekar 2001). The radar system lower limit of LDR can be estimated by measurement in drizzle where raindrops are considered circular so that the backscatter (and propagation) medium cause no cross coupling, and thus intrinsic LDR is −inf dB. Theoretically, LDR can be expressed as a function of the polarization errors ξ_h and ξ_υ (Bringi and Chandrasekar 2001). It can be shown (see appendix C) that LDR measurements in drizzle are approximately

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The LDR system limit values for S-band radars with well-designed, center-fed parabolic reflector antennas are typically reported to be in the −30- to −35-dB range (Keeler et al. 2000; Brunkow et al. 2000). To gauge the expected magnitude of the antenna polarization errors, we assume that ξ_h = ξ_υ and that ξ_h and ξ_υ are either completely real or imaginary. Then, let the system limit LDR = 10 log₁₀(2ξ_h)² = −30 dB [using Eq. (23)]. Solving gives |ξ_h| = |ξ_υ| = 0.0158. If the LDR limit is −35 dB, then |ξ_h| = |ξ_υ| = 0.00889. Equivalently, these errors correspond to tilt and ellipticity angles of the polarization state (polarization ellipse) of the antenna. The angles are 0.91° and 0.51° for LDR limits of −30 and −35 dB, respectively. If the ξ_h and ξ_υ are real, the angles are tilt angles, and if the ξ_h and ξ_υ are imaginary, the angles are ellipticity angles. Of course, in general the antenna errors will be complex. This calculation indicates the magnitude of the antenna errors that can be expected in terms of the geometric polarization ellipse parameters, which are used later in the model.

a. Solar scan measurements

Solar data can also be used to quantify antenna polarization errors. S-Pol collects solar data by performing a “box scan” of the sun in the passive mode. The sun here is considered to be an unpolarized radio frequency (RF) source subtending a solid angle of about 0.53° (Jursa 1985; Tapping 2001). The dimension of the box scan is approximately 3° high (elevation angle) by 7° wide (in azimuth), and the radar scan elevation steps are 0.2°. The scanning rate is 1° s⁻¹ so that one complete solar box scan requires about 2 min. Noise samples are collected while the radar is pointing away from the sun so that the thermal background noise can be estimated and used to correct the measured sun data. S-Pol’s sensitivity is −113 dBm and the sun’s measured power is about −100 dBm when the main antenna beam is centered on the sun. The data are interpolated to a square 2° × 2° grid in 0.1° intervals. The data are first corrected for sun movement and for distortion caused by scanning in elevation and azimuth angle rather than in a rectangular grid.

Shown in Fig. 3 in the top panels are the H and V “pseudo”-antenna patterns, respectively, obtained from S-Pol data gathered on 19 May 2008 during the Terrain-Influenced Monsoon Rainfall Experiment (TiMREX) in southern Taiwan. The powers are uncalibrated. These are termed pseudo–antenna patterns because the sun is not a point source and thus the given antenna patterns are a convolution of the antenna beam pattern of S-Pol with the solar disk. The complex H and V time series data can be used to create a cross-channel correlation antenna pattern. The simultaneously received voltage time series from a single dwell angle, V_h(i) and V_υ(i) for the horizontal and vertical channels, respectively, are correlated in usual fashion as

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Thus, ω gives the pointwise (spatial) correlation from temporal averages. This correlation data from all dwell angles is interpolated to a grid. The resulting magnitude and phase of the correlation product of Eq. (24) are given in Fig. 3 in the bottom two panels. If solar radiation is unpolarized, then the correlation of data between any two orthogonal receiving polarization channels is zero by definition. The correlation magnitude in Fig. 3 (bottom left) shows two principal “lobes” in the lower two quadrants where the correlation increases to about 0.07. These large areas of increased correlation coefficient are manifestations of the antenna polarization errors. The antenna errors are obviously a function of azimuth and elevation angle and are not constant across the 2° × 2° antenna patterns shown. The areas of maximum correlation do, however, fall outside the 3-dB beamwidth of the antenna [which is about 0.9° (Keeler et al. 2000)], which helps reduce the magnitude of the cross coupling. Figure 3d shows the complex behavior of the phase of the correlation product, with the phases being fairly constant in the regions of the highest correlation. For the lower-left quadrant, this phase is −100°, while the lower right quadrant phase is about +60°. These antenna pattern correlations can be integrated to obtain a single complex correlation coefficient and this is discussed later in the text.

The radar model presented above represents the antenna polarization errors as a single complex number for the H and V polarizations, that is, the polarization errors are integrated. Even though antenna errors are distributed, this is a useful approximation that simplifies analysis and permits a realistic numerical evaluation and simulation of polarization errors. The assumption is that there is a homogeneous distribution of scatterers across the antenna beam.

It can be shown that for small polarization errors (see appendix B)

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where Ω is the pattern-integrated correlation coefficient.

b. General observations

Solving Eqs. (23) and (25) simultaneously yields

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where LDR_ℓ is LDR in linear units. The real parts are not solvable, but obviously ℜ(ξ_h + ξ_υ) = ℜ(ξ*_h + ξ_υ).

Starting with Eqs. (23) and (25) several interesting observations are possible. The theoretical conditions for making LDR minus infinity and Ω zero are ξ_υ = −ξ_h, and ξ_υ = −ξ*_h, respectively. In terms of the geometric polarization quantities, the system LDR limit minima condition is

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and the minimum condition for Ω is

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Again, for low solar cross correlation, the errors must be near orthogonal. This is consistent with the observation that the cross correlation of passive solar measurements from two orthogonal polarization states is, by definition, zero if the solar radiation is unpolarized, as is assumed. It is interesting to note that for minimum LDR, the H and V tilt angles are orthogonal while the ellipticity angles are not. This is a direct artifact of radar polarimetry theory and the radar voltage equation (Kennaugh 1949–1954; Hubbert 1994; Hubbert and Bringi 1996). Because the polarization basis of the radar is transformed from linear H and V polarizations to the circular polarization basis by increasing ε from 0° to 45°, the depolarization ratio from a circular scatterer (e.g., a circular raindrop) goes from −inf to +inf dB [e.g., see Fig. 7 from Hubbert (1994) or Fig. 3.10 of Bringi and Chandrasekar (2001)]. Thus, for increasing orthogonal ellipticity errors, the LDR system limit will increase while Ω is unaffected. Also, note that the orthogonal tilt angle errors will not increase the LDR system limit (as determined from measurements in drizzle) nor will they increase Ω. Therefore, neither LDR drizzle measurements nor solar correlation measurements will detect orthogonal tilt antenna errors. For example, these measurements would not reveal whether a radar was unleveled, that is, whether the desired H polarization state of the antenna was not parallel to the earth. Equivalently, it can be shown that if the H and V errors are orthogonal, this implies the phase relationship ζ_υ = π + ζ_h, where ζ_h = arg(ξ_h/i_h) and ζ_υ = arg(i_υ/ξ_υ). If the antenna errors meet the LDR minimum criteria, that is, ξ_υ = −ξ_h, then ζ_υ = π − ζ_h.

Thus, the cross-correlation Ω can be either zero or very low, indicating that the receive polarization states are orthogonal or nearly orthogonal, but this does not necessarily mean that the LDR system limit is low. Conversely, the LDR system limit can be low, indicating that the H and V tilt errors are nearly orthogonal and that the ellipticity errors are nearly equal, but Ω could be relatively high.

From the S-Pol solar data of Fig. 3, the integrated solar correlation coefficient is calculated to be Ω = 0.0038 + j0.00088. There is very likely system phase offset included in this number, such as the differential phase from the reference plane to the I and Q time series samples (see Fig. 1), so that the phase of Ω is not an accurate estimate of the phase of ξ_h + ξ*_υ. However, the magnitude of Ω should be an accurate estimate of the magnitude of ξ_h + ξ*_υ. The magnitude of Ω is about 0.0039, and from the measurements in drizzle S-Pol’s LDR limit is about −31 dB. Using Eqs. (23) and (25), we can write

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where 0.028 = 10^(−31dB/20). The real parts of the arguments of the absolute values in Eqs. (32) and (33) are equal, and therefore there must be significant canceling of the imaginary parts of ξ_h and ξ*_υ in Eq. (32) to account for the large magnitude difference between 10^(LDR/20) and |Ω|. Interpreting these measurements in conjunction with Eqs. (3)–(7) gives some insight as to the nature of the S-Pol antenna errors. Orthogonal tilt angle errors (with no ellipticity angle errors) require that α_υ = α_h + 90°, ℜ(ξ_h) = −ℜ(ξ_υ), and ℑ(ξ_h) = ℑ(ξ_υ) = 0. Under this condition both LDR_ℓ and Ω are both zero, so obviously orthogonal tilt angle errors cannot produce the observed measurement. Additionally, nonorthogonal tilt angle errors will increase both LDR_ℓ and Ω and therefore they cannot account for LDR_ℓ ≫ |Ω|². For orthogonal ellipticity errors (with no tilt angle errors), ℜ(ξ_h) = ℜ(ξ_υ) = 0 and ℑ(ξ_h) = ℑ(ξ_υ). Therefore, for increasing orthogonal ellipticity errors, LDR_ℓ increases while Ω is not affected. It follows that S-Pol antenna errors are likely dominated by ellipticity errors and the H and V ellipticity errors are such that

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Orthogonal tilt errors are detected by neither the system limit LDR nor the Ω measurements, and they could be significant. We assume, however, that physically the feed horn is well aligned (leveled) and this then would make these errors negligible. Under these conditions, ℜ(ξ_h) = ℜ(ξ_υ) ≈ 0, and then

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Using Eqs. (3), (4), and (6), the H and V ellipticity angles are found to be ε_h = −0.91° and ε_υ = 0.69°. These antenna error values are used in the model in Part II. Summarizing, if LDR is significantly >10 log₁₀(|Ω|²), then the H and V ellipticity errors must be closer to orthogonal, that is, ε_υ ≈ −ε_h, rather than close to equal, that is, ε_υ ≈ ε_h.

The functional relationship between the antenna errors and SHV Z_dr is found by calculating SHV mode Z_dr in drizzle (see appendix C) as

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where β is the differential transmit phase arg(E_υ^t/E_h^t). Equation (37) shows that the first-order H and V antenna error terms appear in the form ξ_h + ξ_υ, as they do in the LDR system limit in Eq. (23). This shows that the sum of the antenna errors appears both in SHV Z_dr and LDR, and antenna errors that increase LDR will also, in general, increase SHV Z_dr bias. However, as shown in appendix C, Z_dr is a strong function of differential transmit phase and differential propagation phase. The conclusion is that the LDR system limit of a radar is a good indicator of the expected SHV Z_dr bias. Later, we present curves that relate the LDR system limit to the SHV Z_dr bias.

4. Model results

Next, the model is used to examine biases in the SHV mode for the 1) transmit errors, 2) nonzero mean propagation canting angle, and 3) antenna polarization errors. Again, the radar variables are plotted as a function of principal plane . Because is the independent variable and K_dp is of more meteorological interest than ϕ_dp, the normalized SHV mode K_dp is expressed as

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where is normalized SHV K_dp, is SHV K_dp, and is the principal plane K_dp [see Eq. (A2) and surrounding text for clarification of principal plane]. For the relatively small antenna polarization errors examined here, and therefore the errors in are small.

The backscatter medium is modeled as rain with a zero mean canting angle, a standard deviation of canting angles of 5°, Z_dr = 2.8 dB, and LDR = −35 dB. For this study, the characteristics of the backscatter medium are relatively unimportant in terms of characterizing antenna polarization errors and the effect of nonzero mean canting angle of the propagation medium on Z_dr. Thus, the mean canting angle of the backscatter medium is always 0°. For the propagation medium, typical S-band values of absolute attenuation A_h = 0.0165 dB °⁻¹ (of ) and differential attenuation A_dp = 0.0035 dB °⁻¹ (Bringi and Chandrasekar 2001) are used unless otherwise stated.

5. Summary and conclusions

Biases in simultaneous H and V transmit (SHV) radar data were investigated via a radar-scattering model. The model includes the transmit errors, antenna polarization errors, propagation medium, and backscatter medium. The validity of the SHV technique is based on the following two assumptions: 1) a zero mean canting angle of the propagation precipitation medium and 2) negligible antenna polarization errors. Violation of either condition will cause cross coupling of the H and V electric field components, which in turn biases polarimetric variables. Differential reflectivity (Z_dr) is particularly sensitive to the cross coupling. How the cross-coupled signal combines (constructively versus destructively) with the primary copolar field component depends upon their relative phase, and thus the biases are strong functions of differential propagation phase ϕ_dp and differential transmit phase.

The zero mean canting angle is a good approximation for rain but not for ice particles. The Z_dr bias resulting from oriented ice crystals has been reported before (Ryzhkov and Zrnić 2007), and the results reported here support that work. Demonstrated here for the first time was the impact of differential transmit phase on SHV Z_dr. It was also shown that the phase difference between the H and V transmit signals at the plane of reference (see Fig. 1) will significantly shape the Z_dr errors as a function of principal plane ϕ_dp. For example, consider the ice phase of storms where ice crystals can be aligned by electric fields so that their mean canting can be significantly away from 0°. If the transmit polarization state is circular, only 2° or 3° of need accumulate, which in turn will cause several tenths of a decibel bias in SHV Z_dr. This bias will be difficult to correct and can have deleterious effects on particle classification schemes that rely on accurate Z_dr estimates.

Antenna error–induced cross coupling was also investigated. The model indicates that antenna errors of the magnitude to be expected from well-designed, center-fed parabolic reflectors will cause significant SHV Z_dr bias in rain after sufficient ϕ_dp accumulation. The model shows that if Z_dr bias is to be kept below 0.2 dB, the LDR system limit must be reduced to about −40 dB. This is largely in agreement with Wang and Chandrasekar (2006) who quote a similar requirement of a −44-dB LDR system limit for worst-case antenna errors.

SHV Z_dr bias in rain will also affect Z_dr measurements in the ice phase of storms. Any SHV Z_dr bias acquired in the rain will be carried forward into the subsequent ice phase along that radar radial; that is, if 0.3 dB of Z_dr bias were accumulated in rain before the radar signal reached the ice phase, then the Z_dr measurements in the ice phase would also manifest the 0.3-dB bias.

Estimates of the magnitude and type (tilt versus ellipticity angle) of antenna polarization errors for well-designed, center-fed parabolic reflector antennas, such as NCAR’s S-Pol, were estimated. Describing antenna errors with the geometric polarization ellipse parameters of tilt and ellipticity angles help provide insight as to the nature the antenna errors. If a radar has an LDR measurement limit of −30 dB (determined from measurements in drizzle), the corresponding magnitude of either tilt or ellipticity angle polarization error is about 1°. If the cross correlation of H and V solar measurements are also considered, then the relative values of the tilt and ellipticity angle error can be better estimated. For S-Pol it was shown that the H and V antenna errors are characterized by nearly orthogonal ellipticity angles. The ellipticity angles were estimated based on knowledge of the S-Pol LDR system limit and solar scan measurements. These antenna error estimates were used in the model and were found to predict the experimentally observed S-Pol SHV Z_dr bias and the behavior of LDR measurements through a rain medium. This is further addressed in Part II.

Achieving an LDR limit figure of −40 dB is very difficult and the authors are not aware of any S-band weather radars that are capable of this, except for the new Colorado State University–University of Chicago–Illinois State Water Survey (CSU–CHILL) dual-offset-fed antenna. It may not be cost effective to design a radar with a center-feed parabolic antenna that achieves such a level of cross-polar isolation, and this cost must be considered against the above-mentioned benefits of implementing the SHV mode dual-polarization radar systems.