The Imperfect Phase Pattern of Real Parabolic Radar Antenna and Data Quality
1. Introduction
Radar antennas play an important role in the quality of radar measurements and characterizing them is hence required. Generally, the classic power pattern of the radar antenna is readily available for most radars and has been used to evaluate data quality. Antenna differential phase patterns have been measured and simulated particularly for analyzing the quality of dual-polarization measurements (Chandrasekar and Keeler 1993; Mudukutore et al. 1995; Hubbert et al. 2010; Moisseev et al. 2010; Myagkov et al. 2015). However, absolute antenna phase patterns of operating weather radars are seldom discussed because there are challenges to directly measure it in the far field, and there is no obvious motivation to do so.
To understand why antennas have phase and power patterns requires reflecting on how antennas function in principle. The energy source from the feed horn illuminates a parabolic reflector that focuses the energy into a narrow conical beam because of the constructive and destructive interference of the reflecting waves. The geometry of the parabolic antenna as a reflector makes waves as plane waves within the main lobe in the far field from the radar, where the phase surfaces are theoretically constant at a given range from the center of the reflector; then, there is a pronounced one-way π phase shift between the main beam and the first sidelobe as contributions to the beam pattern from the sides of the rotating antenna become in phase and dominate those from the center of the antenna. In real physical antennas though, phases shift differently than for perfect antennas.
This exploration of the absolute antenna phase pattern originally began as part of an effort to measure the phase returned from fixed ground targets that are used for retrieving the near-surface refractivity of air. Temporal phase variations of a stationary ground target occur as a result of changes in the refractivity along the radar beam path (Fabry et al. 1997). One problem of this technique is the aliasing of temporal phase change, resulting in biases of refractivity estimations. To overcome this problem, Besson and Parent du Châtelet (2013) suggested collecting returned phases at more than one elevation in order to increase the temporal resolution and to mitigate the phase aliasing problem. But, we were uncertain whether the phase measured from a target (less than) 1° away from the beam center is the same as that measured at the center of the beam. In other words, information on the antenna phase pattern is required to describe the phase added by the antenna to targets located away from the antenna axis. This need prompted us to study the rarely investigated absolute phase pattern of weather radar antenna.
Measuring the antenna phase pattern in the far field is challenging, as it requires an external emission source of superb phase stability. Thus, the far-field radiation pattern is usually obtained by the Fourier transform of the aperture field distribution. In the absence of detailed information on the aperture field distribution, we were forced to measure the phase pattern of our radar indirectly.
2. The phase pattern of the McGill parabolic radar antenna
a. Revealed by scanning a pointlike target
The antenna power pattern can be obtained by multiple ways; one of the ways involves scanning a pointlike ground target (Rinehart and Tuttle 1981), such as an isolated stationary tower whose echo does not scintillate and has a relatively small angular extent compared with the main lobe. When the antenna points directly at the ground target, the peak return power is observed. Away from the antenna center axis, received power decreases in the main lobe of the antenna as a function of azimuth and elevation following a generally Gaussian function in linear units: the result is a convolution of a point target with the original antenna gain pattern. The same process can be used to study the antenna phase pattern.
In this experiment, the McGill S-band radar scanned an isolated communication tower and collected high-resolution pulse-by-pulse in-phase (I) and quadrature (Q) data of successive plan position indictors (PPIs) scans at elevation angles from 0.3° to 2° with 0.1° intervals from 2015 to 2105 UTC 25 January 2012. The characteristics of the McGill radar are shown in Table 1. This selected isolated communication tower is located at 27.5 km and about 10 m below the radar antenna level. The vertical angular extent of this target is about 0.04°, approximately 5% of the 0.8° antenna beamwidth at horizontal polarization. Since isolated ground targets are relatively small compared with the radar beamwidth and the range resolution, they can be treated as pointlike targets.
Characteristics of the McGill radar.
The power returned from a ground target as a function of antenna pointing angle generally follows the square of the one-way antenna power pattern because the same antenna is used on both transmission and reception, and reciprocity applies. Figure 1 illustrates the high-resolution two-way power pattern scanning the ground target, which is at 113.58° azimuth and −0.13° elevation. The signal-to-noise ratio (SNR) of the maximum power return is about 83.5 dB, and the power around the main beam axis shows the saturation of the receiver due to the strong return of the ground target. When the antenna points away from the target, the returned power gradually decreases. On our radar antenna, the sidelobes are asymmetric both in azimuth and elevation; there are clear power minima between the main lobe and the first sidelobe above and on the right-hand side. However, only the lower portion of the antenna pattern is obtained due to the limitation of our 1967 vintage radar antenna system that is incapable of pointing at low elevations.
Two-way patterns of (top) the relative power (
Citation: Journal of Atmospheric and Oceanic Technology 33, 12; 10.1175/JTECH-D-16-0143.1
The two-way phase pattern from a ground target is related to the power pattern and is also asymmetric in azimuth (Fig. 1). Note that the phase shown here is relative to the phase measurements of the peak echo power at the lowest 0.3° elevation—that is, 
b. Confirmed by receiving signals from a distant microwave source
To confirm measurements from ground targets, we conducted another antenna pattern measurement experiment using a microwave emission source in the far field. The details of this measurement process are discussed in the appendix. Though the process of obtaining a phase pattern proved more difficult than we hoped, the results confirm that the two-way antenna phase patterns obtained from the corrected emission point source (Fig. 2) and from the communication tower (Fig. 1) are qualitatively similar; both two-way phases are constant near the axis of the main beam, change gradually with the power gradient as the antenna points away from the beam center, and particularly show the notable change at the power minimum between the main lobe and the first sidelobe. The phase differences are about 270° between the main lobe and the first sidelobe on the right side and above, but they are smaller on the left side (Fig. 2). The two-dimensional spatial correlation of these power patterns is above 0.9. The size of the ground target is larger than the point emission source, and the width of the power pattern of the main beam from the ground target is a little bit broader than that of the emission source. Even though there might be some concerns of using a possibly complicated ground target to obtain the antenna power and phase patterns, we gained confidence that isolated towers can be treated as pointlike targets because the power and phase patterns obtained by the two approaches proved similar enough. The setups of these two experiments are not as ideal as measurements for a formal antenna test range; nevertheless, we still observed the qualitative characteristics of the phase pattern of the radar antenna.
Patterns of two-way (top) relative power (
Citation: Journal of Atmospheric and Oceanic Technology 33, 12; 10.1175/JTECH-D-16-0143.1
The measured phase pattern revealed from these experiments are slightly different from the theoretical phase pattern of the parabolic antenna mentioned in section 1. The observed two-way phase pattern shows gradual variation along with the power gradient on the edge of the main beam near the null, which is in contrast to the theoretical sharp phase change. The two-way phase difference between the main lobe and the first sidelobe is less than the expected 360°. These anomalies in phase and in power patterns might be explained by the imperfect geometry of antennas: the inaccurate positioning of the phase center of the feed horn and the focal point of the parabolic reflector, the presence of struts, and irregularities in the shape of the reflector (Doviak and Zrnić 1993; Mudukutore et al. 1995). Some small fluctuations of measured phase within the main beam may also be due to atmospheric scintillation.
3. Antenna phase pattern and data quality
Based on the characteristics of the observed antenna phase pattern, we investigated its impact on radar data quality.
a. Radar refractivity retrieval
The quality of the phase change of reliable fixed ground targets is key to retrieve accurate refractivity of the air. The profiles of power and phase show the clear signature of the variation of the antenna pattern in elevation (Fig. 3). Changes in the phase returned from ground targets located close to the main beam axis are primarily caused by air refractivity change and are not significantly affected by the antenna phase pattern, even when the electromagnetic wave propagation condition alters diurnally. If the observed ground targets are located close to an antenna null—that is, with higher scanning elevations or for close-range targets—then the phase added by the antenna changes significantly with wave propagation conditions, introducing biases in refractivity retrievals.
Profiles of two-way (left) power and (right) phase calculated from 1° azimuth average centered on the azimuth of the ground target at 113.58° in Fig. 1. Thirty-two pulses are averaged for each beam.
Citation: Journal of Atmospheric and Oceanic Technology 33, 12; 10.1175/JTECH-D-16-0143.1
To properly use the phase at multiple elevations to increase the temporal resolution of radar refractivity retrieval as suggested by Besson and Parent du Châtelet (2013), we must be aware that the phase changes significantly with the antenna power gradient. Figure 4 presents a daily average phase difference between 0.3° and 0.5° elevations, illustrating the systematic bias of phase change for radar refractivity retrieval due to the antenna phase pattern. The phase differences in the areas of ground clutters (higher relative power values under a condition of clear weather; Fig. 4, left panel) are mostly close to zero at far ranges, since targets are illuminated in the main lobe. The greater value of the phase at higher elevation than at the lower elevation implies that the target is located near the bottom edge of the main lobe. A ring of negative values shown within a 5-km radius of the radar coverage results from targets far below the main beam axis, probably in the first sidelobe. For most surveillance weather radars, the difference between the first two scanning elevation angles is usually more than the 0.2° shown here. Therefore, the phase pattern of the parabolic antenna must be taken into account when combining multiple elevation angels to increase the temporal resolution of refractivity retrievals.
(left) Daily average two-way relative power at 0.3° elevation PPI on 21 Jul 2012 under a clear-weather condition, highlighting the location and strength of ground echo targets. McGill radar is at the center of the figure. Ground clutters are shown in reddish colors. (right) Daily average phase difference between 0.3° and 0.5° elevation scans for echoes with an average relative power is greater than −40 dB. Rings of negative phase difference (2–3-km range) and positive phase difference (5–10-km range) can be observed; these occur because targets at these ranges are close to the antenna null, where a small difference of 0.2° in elevation leads to a large difference in the phase added by the antenna.
Citation: Journal of Atmospheric and Oceanic Technology 33, 12; 10.1175/JTECH-D-16-0143.1
b. Ground clutter mitigation and radial velocity biases
The phase returned from pointlike targets located in regions illuminated away from the antenna beam center changes notably in azimuth (Figs. 5a,b). Thus, the width of Doppler velocity spectrum broadens with increasing azimuth and elevation away from the center of the main beam, and for the McGill antenna the Doppler spectrum becomes asymmetric with a nonzero mean velocity (Figs. 5c–e). The velocity of the adjacent beam 1° azimuth away from the stationary target is about 1 m s−1 for the McGill S-band radar. Note that the magnitude of the radial velocity bias on the edge of targets caused by the antenna phase pattern is larger than the effect of the antenna rotation speed (Rinehart 1991): for the McGill radar, the bias of the radial velocity at the adjacent beam 1° from the target axis introduced by the antenna rotation effect (given six rpm and a 5.45-m distance between the axis of rotation and the feed horn) is about 0.06 m s−1. The change of the Doppler spectrum and the radial velocity at these adjacent beams with respect to a stationary ground target (the center of the main beam axis) can be explained by the varying phase added by the antenna phase pattern.
(a) Amplitude and (b) phase of the echo from a dominant ground target as a function of azimuth at three elevations, 0.3°, 0.6°, and 0.9°. Note the receiver saturation at 0.3° scan. Relative Doppler spectra (dB) calculated from the given 1° azimuth intervals [shown by different markers in (b)] are displayed in (c)–(e). All relative Doppler spectra are normalized to their maximum power to ease comparisons.
Citation: Journal of Atmospheric and Oceanic Technology 33, 12; 10.1175/JTECH-D-16-0143.1
The characteristics of the antenna phase pattern revealed from a pointlike ground target might be helpful to improve clutter filtering techniques, which generally assume a symmetric fixed-shaped (Gaussian width) clutter spectrum. Some new sophisticated method might be developed based on the antenna phase pattern, particularly for ground targets close to the edge of the main beam or near the null with nonzero velocities. For example, since the spectrum of the clutter is wider when scanned by the edge of the beam, it suggests that clutter filtering at higher elevation should use broader filters than at very low elevation. Besides, the complicated returned signal from multiple targets within a sampled volume or from adjacent beams can be also examined by integrating the individual power and phase patterns of targets at given positions. Dual-polarization data affected by ground targets (Friedrich et al. 2009) can be further quantitatively studied.
We also investigated the effects of the antenna phase pattern on the radial velocity estimation of a cloud/precipitation system and can make some general comments. The 2D convolution results of the antenna pattern and a stationary cloud/precipitation system with a simple Gaussian-shaped power pattern in azimuth are examined. The observed bias of radial velocity is less than 1 m s−1 for typical cloud and precipitation systems that are larger than the beamwidth of the antenna, but it is stronger at the edges of ground targets or small convective cells at far range whose azimuthal width is of the order of a beamwidth. Thus, unless there are strong reflectivity gradients where the large phase shifts associated with the main beam edges might dominate the measured velocity, the antenna phase pattern does not introduce a significant bias in the radial velocity measurement.
4. Summary
This paper presents the measurement of the phase pattern of parabolic radar antennas and evaluates its impact on the radar data quality that is seldom discussed in the meteorological radar community. The phase patterns obtained by two observation approaches, active scanning of an isolated fixed communication tower and passive reception of a point emission source, both lead to a consistent pattern of phase within the main beam and large changes as we approach antenna nulls. In high-reflectivity gradients typical of clutter environments, the antenna pattern adds some artifacts to the radar data measurements and hence should be considered in ground target selection for radar refractivity retrieval and other measurement techniques for data quality issues that are specifically dependent on target phases.
Acknowledgments
The authors thank Dr. Véronique Meunier, Alamelu Kilasmbi, and Raman Krishnamoorthy of the J. S. Marshall Radar Observatory of McGill University for their help in the antenna measurement. We also thank the three anonymous reviewers, whose contribution considerably improved the original manuscript. This work was made possible thanks to the support from Environment and Climate Change Canada and the Natural Sciences and Engineering Research Council of Canada.
APPENDIX
Characterization of the Antenna Phase Pattern Using a Far-Field Microwave Source
An experiment using a point emission source was designed to confirm the antenna phase pattern obtained from ground targets. The radar passively received the signal from this source deployed 10.92 km away at an azimuth of 318.5° and about 50 m above the antenna level. The 
The resulting one-way relative power pattern (Fig. A1a) obtained from the emission source shows an azimuthally asymmetric pattern similar to that from the isolated ground target (Fig. 1). Even though the phases still vary with the power gradient at each given elevation (
The phase measurements made with RHIs sample multiple elevations in a short time and can be used as a reference to correct the phase of PPI scans. But before using the RHI data, we needed to deal with the slow response of our elevation angle readback for RHI scans (Figs. A1c,d), which complicated the proper estimation of elevation angles. Based on the fact that the power returns from the RHI scan should be the same as the measurements from the PPI scans at a given position, the power profile of the RHI scans is shifted in elevation to match the power of PPI scans (Fig. A1c). After the elevation reading biases are estimated, we can displace the phase of the RHI scans to the corrected position [
The relative phase of PPI scans with respect to that of the RHI scan is calculated at each elevation (i.e.,
The phases of PPI scans are corrected by forcing the relative phase profile measured at 317.5° azimuth to match the corrected phase of RHI at 317.5° azimuth (i.e.,
Six-panel plot illustrating the process used to correct the phase drift between the source and receiver, as well as the antenna’s slow elevation response. (a),(b) Measurements of the one-way relative power (dB, normalized to the peak power at 0.3° elevation whose SNR is 60 dB) and phase (degrees) from PPI scans at successive elevations. (c) Original relative power measurements with delayed elevation response on the RHI (gray line) and power shifted in elevation to the corrected position (black lines) based on the returned power of the PPI scan (red triangles) as a reference. (d) Derived elevation correction permitting us to use the phase from the RHI (gray line for the original data, black line for the elevation-shifted one) to determine which phase should have been read by successive PPIs (red line) at the azimuth of the RHI. (e) Relative phase pattern with respect to the azimuth of the RHI, 317.5°, derived from the original data shown in (b). (f) Corrected one-way relative phase pattern derived by adding the phase correction of the RHI scan in (d) to the relative phase field in (e) and then shifting these corrected phases for the phase of the peak power equal to 0°.
Citation: Journal of Atmospheric and Oceanic Technology 33, 12; 10.1175/JTECH-D-16-0143.1
REFERENCES
Besson, L., and Parent du Châtelet J. , 2013: Solutions for improving the radar refractivity measurement by taking operational constraints into account. J. Atmos. Oceanic Technol., 30, 1730–1742, doi:10.1175/JTECH-D-12-00167.1.
Chandrasekar, V., and Keeler R. J. , 1993: Antenna pattern analysis and measurements for multiparameter radars. J. Atmos. Oceanic Technol., 10, 674–683, doi:10.1175/1520-0426(1993)010<0674:APAAMF>2.0.CO;2.
Doviak, R. J., and Zrnić D. S. , 1993: Doppler Radar and Weather Observations. 2nd ed. Dover Publications, 562 pp., doi:10.1016/B978-0-12-221422-6.50007-3.
Fabry, F., Frush C. , Zawadzki I. , and Kilambi A. , 1997: On the extraction of near-surface index of refraction using radar phase measurements from ground targets. J. Atmos. Oceanic Technol., 14, 978–987, doi:10.1175/1520-0426(1997)014<0978:OTEONS>2.0.CO;2.
Friedrich, K., Germann U. , and Tabary P. , 2009: Influence of ground clutter contamination on polarimetric radar parameters. J. Atmos. Oceanic Technol., 26, 251–269, doi:10.1175/2008JTECHA1092.1.
Hubbert, J. C., Ellis S. M. , Dixon M. , and Meymaris G. , 2010: Modeling, error analysis, and evaluation of dual-polarization variables obtained from simultaneous horizontal and vertical polarization transmit radar. Part I: Modeling and antenna errors. J. Atmos. Oceanic Technol., 27, 1583–1598, doi:10.1175/2010JTECHA1336.1.
Moisseev, D., Keränen R. , Puhakka P. , Salmivaara J. , and Leskinen M. , 2010: Analysis of dual-polarization antenna performance and its effect on QPE. Proc. Sixth European Conf. on Radar Meteorology and Hydrology (ERAD 2010), Sibiu, Romania, National Meteorological Administration, P2.5. [Available online at http://www.vaisala.com/Vaisala%20Documents/Scientific%20papers/05_ERAD2010_0247_extended.pdf.]
Mudukutore, A., Chandrasekar V. , and Mueller E. A. , 1995: The differential phase pattern of the CSU CHILL radar antenna. J. Atmos. Oceanic Technol., 12, 1120–1123, doi:10.1175/1520-0426(1995)012<1120:TDPPOT>2.0.CO;2.
Myagkov, A., Seifert P. , Wandinger U. , Bauer-Pfundstein M. , and Matrosov S. Y. , 2015: Effects of antenna patterns on cloud radar polarimetric measurements. J. Atmos. Oceanic Technol., 32, 1813–1828, doi:10.1175/JTECH-D-15-0045.1.
Rinehart, R. E., 1991: Spurious velocities in Doppler radar data caused by a moving antenna feedhorn. J. Atmos. Oceanic Technol., 8, 733–745, doi:10.1175/1520-0426(1991)008<0733:SVIDRD>2.0.CO;2.
Rinehart, R. E., and Tuttle J. D. , 1981: A technique for determining antenna beam patterns using a ground target. Preprints, 20th Conf. on Radar Meteorology, Boston, MA, Amer. Meteor. Soc., 672–675.
