1. Introduction

In addition to military applications for target recognition and tracking (Brookner 2008), phased-array radar (PAR) technology has recently been successfully introduced to the weather community. The nation’s first phased-array weather radar, the National Weather Radar Testbed (NWRT) operating at a wavelength of 9.38 cm, was developed in Norman, Oklahoma, through a joint effort of a government–university–industry team (Zrnić et al. 2007). The NWRT demonstrated that its pulse-to-pulse electronic beam-steering capability enables meteorological measurements that are as accurate in shorter storm surveillance times as those achieved with a conventional dish antenna with a mechanically steered beam. The shorter surveillance times result in faster data updates and offer the capability to observe detailed evolutions of severe storm phenomena (Yu et al. 2007; Heinselman et al. 2008). The NWRT also has a hybrid capability to both mechanically and electronically steer the beam. This capability has allowed multipattern measurements of the same meteorological volume to successfully mitigate both stationary and moving clutter (Zhang et al. 2011). Furthermore, the NWRT uses an antenna from the AN/SPY1-A monopulse radar of the Aegis system (Sherman 1988), which has sum and difference channels; these can be combined to implement a spaced-antenna interferometry (SAI) technique for crossbeam wind measurement (Zhang and Doviak 2007) and subvolume inhomogeneity/object detection (Zhang and Doviak 2008). It has been also theorized that the AN/SPY1-A auxiliary channels could support the implementation of adaptive clutter cancellation techniques (Le et al. 2009).

While PAR technology has recently received widespread attention in the weather community, weather radar polarimetry has matured to a point that it is being implemented on the national network of Weather Surveillance Radar-1988 Doppler (WSR-88D) radars (Doviak et al. 2000) using its conventional dish antenna. Polarimetric radar provides multiparameter measurements that reveal detailed microphysics of storms in addition to hydrometeor classification, accurate precipitation estimation, and improved weather nowcasts. Therefore, the weather community and the nation expect that the future multifunction phased-array radar (MPAR) will retain all of the capabilities of the polarimetric WSR-88D (Smith et al. 2008). It is the polarimetric capability that the second MPAR symposium (online at http://www.ofcm.noaa.gov/mpar-symposium) identified as the most challenging technical issue that the community is facing.

The challenge comes from the fact that highly accurate polarimetric radar measurements are required to provide meaningful information. However, biases inherent to planar polarimetric phased-array radar (PPPAR) exist and can be larger than the intrinsic values if the beam is directed away from the planar array’s broadside. For example, the intrinsic Z_DR values range only from about 0.1 dB for drizzle and dry snow to 3–4 dB for heavy rain and large drops. Thus, it is desirable that the measurement error for Z_DR be of the order of 0.1 dB (Zhang et al. 2001; Brandes et al. 2003). However, the Z_DR bias for a PPPAR can be a few decibels (Zhang et al. 2009a). Hence, it is crucial for the success of the MPAR project that the system configuration for a PPPAR is selected correctly and designed optimally.

Currently, the possible antenna array configurations include linear array, planar array, circular/cylindrical array, and spherical array. The linear array needs one mechanic rotation for weather surveillance like the rapid Doppler on Wheels (rapid DOW; see Wurman 2003) and the proposed design for the Center for Collaborative Adaptive Sensing of the Atmosphere (CASA) instrument (Hopf et al. 2009). For the planar array, multiple faces (normally four) are needed (e.g., the SPY-1A), but the planar array has sensitivity loss and polarization bias if the beam points away from the broadside (Zhang et al. 2009a). A circular or cylindrical configuration has been used for direction finding and communications (Royer 1966; Raffaelli and Johansson 2003). For satellite communication applications, the spherical array is optimal and flexible in its use of the antenna aperture size and in its symmetry (Tomasic et al. 2002). For weather applications, however, the spherical array cannot provide the high cross-polar isolation required to accurately measure precipitation.

In this study, we examine cylindrical polarimetric phased-array radar (CPPAR) for practically scan-invariant weather measurements. The CPPAR has azimuth scan-invariant properties and has very minor dependence on elevation at low elevation angles. Because the WSR-88D scan strategy has coarser elevation sampling at higher elevation angles, and because the CPPAR’s angular resolution coarsens as beam elevation angle increases (thus filling angular gaps created by coarser sampling), the gradual decrease in elevation resolution is a beneficial feature. In section 2 the meteorological measurements with a PPPAR are simulated and the PPPAR’s deficiencies are revealed. In section 3, a cylindrical array configuration is described and the CPPAR performance is quantified through a theoretical analysis and simulation. An example design and simulation results are given in section 4. Summary and discussions are provided in the last section.

2. Issues with a PPPAR

For a PPPAR, three or four faces are normally used to cover the 360° in azimuth. Because the antenna faces and their broadside directions are fixed, the beam and polarization characteristics change depending on the electronic beam direction. To obtain an intuitive impression, we show KOUN (a prototype dual-polarized WSR-88D) measurements of reflectivity and differential reflectivity in Fig. 1. Also shown are the simulated measurements that would be made by a four-face PPPAR comprising an array of crossed dipoles, and those if each face had the same size aperture as KOUN. Crossed Hertzian dipoles are used for sake of simplicity without having to specify the design and size of the array elements. Although other types of antenna elements (e.g., a patch) can be simulated in a similar way, detection performance would be worse because these elements have increased directive gain and thus have a larger scanning loss. Furthermore, Z_DR bias would still exist, but it is correctable (Zhang et al. 2009a).

It can be seen that the reflectivity and differential reflectivity measurements are the same as those of KOUN at the four broadside directions. However, the measurements are considerably different at beam positions away from the broadsides: (i) Z_H sensitivity is lost and (ii) Z_DR has significant bias. There is a 7.5-dB sensitivity loss for the horizontally polarized beam if it is 45° from the broadside (it would be a 15-dB loss if the three-face PPPAR were used and the beam was 60° from the broadside). This is due to the combined effect of the decreased gain of the horizontal dipole radiation pattern and the decreased gain of the array caused by the smaller projected aperture in directions away from broadside. In addition to the 7.5-dB sensitivity loss for horizontally polarized waves, vertically polarized waves also have some loss (i.e., 1.5 dB) for beams steered to 45° from broadside. Although the biases in the reflectivity factor and differential reflectivity seen in Figs. 1c,d are correctable, sensitivity loss can only be compensated by increased power or aperture size.

The scan-variant measurements are unacceptable to meteorologists unless the data are calibrated to remove the radar system effects (Zhang et al. 2009a). Although the Z_DR bias can be compensated, the sensitivity lost and worsening angular resolution is costly to recover. One might think to use the vertical polarization for the prime reflectivity measurements, but there will still be loss due to the projected area being diminished, and the azimuthal resolution will be worse by . Furthermore, the lost sensitivity and angular resolution for other polarimetric measurements (Z_DR, ρ_hv, and ϕ_DP) is also costly to recover because the antenna size and/or transmitter power both need to be increased.

For meteorological applications, the four-face PPPAR’s gain and beamwidth changes are most significant for beams that are electronically steered in azimuth. To compensate for the 7.5-dB loss (i.e., for horizontally transmitted waves at the azimuth limits of ±45°), without increasing transmitted power, the antenna aperture would need to be increased by a factor of 5.66 in the horizontal direction; this is clearly a prohibitively expensive solution. Alternatively, to ensure that the beamwidth at ±45° is practically equal to the beamwidth in elevation, and is no worse than the beamwidth of the WSR-88D, the antenna size in the horizontal direction must be increased by a factor of ; however, in this case the transmitter power would need to be increased by a factor of 4 to not lose detection capability. Thus, the aperture size of the planar PPAR needs to be 8.54/cos(10°) m in the vertical plane, and 12.08 m in the horizontal, which is significantly larger than the WSR-88D reflector diameter. The dimension in the vertical plane assumes that the array face is tilted 10° from the vertical to provide a vertical beamwidth at zero degrees of elevation to match the WSR-88D’s beamwidth. Clearly there is motivation to decrease the array size while matching the WSR-88D capabilities, and with this in mind the cylindrical array is examined.

3. Configuration and formulation for CPPAR

Realizing the deficiencies of a PPPAR for weather measurements, we propose a CPPAR (see Zhang et al. 2009b).

As sketched in Fig. 2, there are M × N dual-polarized radiating elements arranged azimuthally (M) and axially (N) on the surface of a cylinder. Multiple simultaneous beams are formed with each beam generated from a sector of the cylindrical surface with the broadside direction along the bisector of the illuminated sector. Using CPPAR, polarization orthogonality is preserved in all directions.

To study the radiation characteristics of a CPPAR, we choose a coordinate system with its z direction along the cylinder’s axis (Fig. 3). An array element (mn: mth row, nth column), comprised of crossed h and v dipoles is located at ϕ_n, z_m on the cylindrical surface at r_mn = a_xR cosϕ_n + a_yR sinϕ_n + a_zz_m, where R is the cylinder’s radius, the row height z_m ranges from −D/2 to +D/2, where D is the axial length of the cylindrical array (equal to the diameter D of the WSR-88D), and the bold unit vectors represent the Cartesian coordinates (a_x, a_y, a_z) (Fig. 3). Azimuth location ϕ_n is measured relative to the x axis and is ϕ_n = nΔϕ, n = 1, 2, 3, …. The electric field at r = a_xr sinθ cosϕ + a_yr sinθsinϕ + a_zr cosθ, transmitted by the mnth q (i.e., q = h or v) dipole, is (Ishimaru 1997, section 2.4)

View Expanded

where k = 2π/λ, λ is the radar wavelength, ɛ is the permittivity for an assumed uniform precipitation-free atmosphere,

View Expanded

where is the moment of dipole q at location mn, and a_r is the unit vector along r.

Using the far-field approximation, we have the electric field at r radiated by the mnth q dipole

View Expanded

where

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In this paper superscripts (h) and (v) are used to identify the horizontal and vertical dipoles, repsectively. Following the procedure of Zhang et al. (2009a), we can express the electric fields in the plane of polarization (Doviak and Zrnić 2006, their Fig. 8.15) at r as

View Expanded

View Expanded

where and are the fields respectively transmitted by the h and v dipoles along the normal to the plane of the dipoles (i.e., the crossed dipole’s broadside direction) located at ϕ_n, z_m. Thus,

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with a like expression for and e_n^(h) is

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a form analogous to Eq. (5a) of Zhang et al. (2009a), but one that accounts for the ϕ_n angular rotation about z of the coordinate x, y axes to x′, y′ for the mnth element. Here, e^(v) is

View Expanded

which is identical to that given by Eq. (5b) of Zhang et al. (2009a). Note that e_n^(h) is a function of dipole location but e^(v) is not and, as pointed out by Zhang et al. (2009a), e_n^(h) is not orthogonal to e^(v).

To form a beam pointing in the (θ₀, ϕ₀) direction, a phase shift

View Expanded

is applied to each of the mn elements that are used to form the beam. The phase shifts given by (4) produce a beam in the (θ₀, ϕ₀) direction.

The incident horizontal and so-called “vertical” (i.e., the vertical field lies in the vertical plane, but is only vertical at the 90° zenith angle) fields E_ihmn and E_ivmn in the plane of polarization are given by (Zhang et al. 2009a)

View Expanded

where , and

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is a matrix that projects the elements’ broadside electric field to the plane of polarization at r, and accounts for h dipole orientation at ϕ_n. In this analysis we assume that each dipole radiates only into the outward hemisphere with an equator in the plane of the crossed dipole element. Magnitude signs are placed around the dipole moment to emphasize that the dipole phase is incorporated into . Although the subscript index m does not appear in the matrix, it is attached to 𝗣_mn to emphasize that the projection applies to the mnth h and v dipoles. The subscript h and v on E_ihmn and E_ivmn denotes these are the horizontal and vertical fields transmitted by the mnth dipoles and incident on the scatterer; note that E_ivmn has contributions from both the h and v dipole moments, whereas E_ihmn depends only on the h dipole’s moment.

Radiation patterns with specified sidelobe levels and beamwidths can be achieved with a proper weight applied to each element. Hence, the total incident field at r is the weighted contributions from all of the active elements used to form the beam at (θ₀, ϕ₀). This field can be expressed as

View Expanded

where the weighting matrix 𝗪_mn is applied to each element, and the angular dependence of the broadside field generated by the mnth h and v dipole moments is incorporated into 𝗪_mn; that is, all dipoles have M^(h) = M^(v), which is taken to be the dipole’s source excitation modulated by 𝗪_mn. Here, E_ih is the total horizontal field generated by all the h and v dipoles that are used to form the beam. Because the h dipoles change orientation depending on their azimuth ϕ_n, the weighting vector can be expressed as

View Expanded

where the upper-left matrix element 1/cos(ϕ₀ − ϕ_n) compensates for the projection loss of the H dipole–radiated field onto the horizontal polarization direction along the beam’s boresight. The boresight always lies in the plane containing the bisector of the angle encompassing the azimuth sector containing the elements forming the beam; in effect, the boresight of the CPPAR is always in the broadside direction. Alternatively,

View Expanded

is the location of the active dipoles in an angular sector (e.g., 120° for a three-beam CPPAR) centered on ϕ₀ with (2N_a + 1) active array elements in the azimuthal span of (n₀ − N_a, n₀ + N_a).

Likewise, the lower-right matrix element 1/sinθ₀ compensates for the projection loss of the V dipole–radiated field onto the vertical direction; this correction is normally close to unity because the elevation angle (π/2 − θ₀) for weather measurements is typically small.

The scalar weight is for isotropic radiators; these weights are selected to control the sidelobe levels. The WSR-88D antenna pattern is mimicked by selecting

View Expanded

The term in the parenthesis is equivalent to the WSR-88D illumination taper but applied to those mnth dipoles whose projection onto the vertical plane bisecting the cylinder lies within the πD²/4 area, where D is the diameter of the WSR-88D dish antenna (dipoles outside this circular area, but lying within the angular sector of elements forming the beam, have zero weight); the cos(ϕ − ϕ₀) term accounts for the change of the density of the array elements projected onto the vertical plane and the term b = 0.16 accounts for edge illumination of the WSR-88D reflector (Doviak et al. 1998). Although mimics the illumination taper on the WSR-88D antenna for the boresight direction, the analogy no longer exists for azimuths in off-boresight directions. This is because the active elements on the cylinder have a density that lacks the symmetry of the dish antenna about the vertical bisector of the circular area.

On the beam’s boresight (i.e., θ = θ₀, ϕ = ϕ₀), the radiated fields from all the elements are in phase so the phase term in (6) disappears and the incident wave field becomes

View Expanded

Because the active elements and the weighting factor are symmetric about ϕ₀ and z_m = 0, there is no on-axis cross-polar radiation. That is, the vertically polarized wave field caused by the horizontal dipole at ϕ₀ − n′Δϕ cancels that field from the dipole at the opposite azimuth ϕ₀ + n′Δϕ. This cross-polar null on the axis is important for accurate polarimetric radar measurement of precipitation (Wang and Chandrasekar 2006; Zrnic et al. 2010). This is one of the main reasons for using a CPPAR commutating scan in which the beam direction changes in azimuth by shifting a column of active elements and maintaining the weight’s symmetry about the beam center. This way, the beam characteristics of the CPPAR are scan invariant; this is not so for the PPPAR.

Given the field incident on a hydrometer, the scattered wave field can be expressed as [Doviak and Zrnić 2006, section 8.5.2.1]

View Expanded

where 𝗦′ is the backscatter matrix of a hydrometeor and includes propagation effects (Zhang et al. 2009a).

Although (10) can give the H, V electric fields at any receiving array element, we need to determine the fields parallel to the respective dipole axis. The fields parallel to the dipole axes are obtained by projecting E_{s mn} onto the respective dipole directions, and with the proper weighting and phase shifts. In this case the total received wave field is expressed as

View Expanded

4. Sample design to mimic the WSR-88D

The operational WSR-88D radar has high performance for meteorological observations: it has a dish antenna with a diameter of 8.54 m, a beamwidth of about 1°, and the first sidelobe below −26 dB. It is desirable for the MPAR to have either similar or better performance. Figure 4 shows a table of the specifics of sample designs for a CPPAR with two, three, or four beams; each mimics the NEXRAD beamwidth at the largest electronic scan angle, and element separations used are 1.0, 0.75, and 0.5 wavelength. Considering the trade-off for maximizing the effective aperture and the number of beams, it is efficient to use either three or four simultaneous beams for a CPPAR, consistent with what is recommended by Josefsson and Persson (2006, chapter 3). It is relatively easy to control sidelobes with the four beams and short distance for element separations. For comparison, a PPPAR of three and four faces, with a beamwidth at its largest scanning azimuth angle (60°/45°) that matches the WSR-88D, is also shown in the table. The number of elements for a PPPAR is calculated based on elements occupying only the area inside the ellipse filled with array elements.

In the case of three beams, a 120° sector of a CPPAR is used to form a beam. This would require a cylinder of 8.54/sin(60°) = 9.88-m diameter and 8.54-m height. This is significantly smaller than the 17.1 m (i.e., 8.54 × 2) major axis of the elliptical array for a three-face PPPAR that matches, at the extremes of electronic steering of 60°, the WSR-88D resolution; furthermore, there is no need to increase the total power by a factor of 16 (12 dB) to compensate for the loss of detection capability in these directions. For the four simultaneous beams, a 90° sector is used to form a beam. A cylinder of 12.1 m (∼8.54 × ) diameter is needed. The cylinder’s diameter is the same as the major axis of the elliptical array of the four-face PPPAR, and the total number of elements for the CPPAR is the same as for the PPPAR. However, the elements at the corners of the CPPAR can be used for sidelobe blanking and pattern synthesis, whereas the PPPAR would have to have extra elements for such functions. Additionally, the total power of the CPPAR does not need to be increased by a factor of 4 (6 dB). Assuming the element spacing to be the wavelength of 10 cm, there would be 380 array columns and a total of 32 680 elements covering the cylinder. Commutating one column, the CPPAR beam moves 0.95° about the beamwidth. If element spacing is reduced to one-half a wavelength (i.e., 5 cm), 760 array columns would be needed to cover the cylinder; this significantly increases the number of total elements to 130 720. Nevertheless, this will allow for oversampling at a 0.474° angular spacing and lower sidelobes. Such fine angular sampling can also be achieved with the one-wavelength spacing of elements, but then the phase of each column would need to be shifted by half the angular increment between the array elements.

Calculated CPPAR one-way-radiated power density patterns for the above-mentioned four-beam case and their comparisons with theoretical WSR-88D pattern are in Figs. 5 –8. Figure 5 shows 3D copolar and cross-polar patterns for the CPPAR with tapering and polarization compensation. The cross-polar radiation is everywhere at least 45 dB below the copolar peak, indicating that the CPPAR has high performance for preserving polarization purity. In Figs. 6 –8 the copolar patterns are on the two planes through the boresight: the patterns on the horizontal plane are shown in the upper panels, and those on the vertical plane are in lower panels.

Figure 6 shows the copolar patterns whereby the dipoles have no equivalent tapering of the WSR-88D illumination, density adjustment, and polarization compensation. Because the WSR-88D pattern is for the tapered illumination, CPPAR has higher sidelobes in Figs. 6a,c. This is also true for the near sidelobes as seen in the zoomed-in plots on the right in Figs. 6b,d. The pattern sidelobes for horizontal polarization are a little lower than for vertical polarization because of the natural tapering caused by changes in orientation of the horizontal dipoles as a function of ϕ_n.

Figure 7 shows the CPPAR pattern results if Eq. (8), without the cosine term, is applied to the dipoles within the angular sector forming the beam. The sidelobes are substantially reduced except near ±90° azimuth angles. This is due to the nonsymmetrical density of the active array elements seen from the off-broadside directions. Nevertheless, the level is 50 dB below the copolar peak and for two-way patterns that are of interest for meteorological applications, the sidelobe level is 100 dB below the copolar peak. This low sidelobe level is due to the applied tapering. It is also noted that the difference between the two polarizations is now very small because the main contribution to the radiation field comes from array elements near the broadside where there is not much difference between the H and V polarizations. If density adjustment [i.e., the cosine term in Eq. (8)] and polarization compensation are applied, the results become even better (Fig. 8). The main lobes are almost identical to the WSR-88D reference pattern, which is crucial for high-quality polarimetric radar measurements. Although sidelobes still exist, the farther sidelobes are mostly lower than those of WSR-88D. This is because of the natural tapering in CPPAR.

5. Summary and discussions

In this paper, we have compared the planar and cylinder array configuration of PPAR for weather measurements, and we formulated a theory for studying the CPPAR performance. Because our main objective is to draw attention to some of the unique properties of the cylindrical phased array for weather observations with polarimetric radar, and not to provide a detailed design for a specific CPPAR, we have assumed ideal array elements with given excitation. It is known that a PPPAR has issues of scan-dependent beam properties, including changes in beam and polarization characteristics, polarization coupling, sensitivity loss, and complications in calibration. To compensate for the sensitivity loss, the four-faced PPPAR antenna would have to have a diagonal dimension doubled the size of the WSR-88D and an increase of power by a factor of 4.

The CPPAR configuration can also make azimuth scan-invariant, high-accuracy weather measurements without changing the beam and polarization characteristics while maintaining a manageable antenna size. Compared with PPPAR, CPPAR has the following advantages:

• (i) Scan-invariant polarimetric radar measurements with the same beamwidth and polarization characteristics in all azimuth angles for each elevation allow for easier calibration and data interpretation.

• (ii) Polarization purity: dual-polarized (H and V) wave fields are orthogonal in all direction, and hence maintain high-quality polarimetric data. Compensation is only needed for horizontal and vertical polarizations separately, but cross-polarization isolation is maintained.

• (iii) High efficiency of utilizing radiation power: Only certain array elements are activated and properly weighted to achieve the desired beams. The elements on the broadside are mostly activated and weighted higher; hence, less scan loss results from the element radiation pattern.

• (iv) Efficient use of spectrum: For example, the side-by-side and back-to-back beams might use the same frequency because they are always 90° (120°) apart in the case of four (three) beams.

• (v) The antenna aperture for fast data update or for multifunctionality with simultaneous multibeams is used optimally.

• (vi) Flexibility to choose the number of beams (e.g., two, three, or four) and assign different task among beams: For example, if four beams are generated, two beams can be used for weather surveillance and the other two for aircraft tracking, making it a candidate for the future MAPR. This flexibility can be combined with multiple frequencies used in currently proposed PPPAR, that is, one band of frequencies for the weather function and another band for aircraft surveillance.

• (vii) There is no need for the face-to-face matching as is required for a PPPAR, where each face is an individual radar system that could have different characteristics that need to be matched.