Sidelobe Contamination in Bistatic Radars

Transcription

1 1313 Sidelobe Contamination in Bistatic Radars RAMÓN DEELíA ANDISZTAR ZAWADZKI Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada (Manuscript received 8 September 1999, in final form 24 November 1999) ABSTRACT The problem of sidelobe contamination in a bistatic network is explored. The McGill bistatic network consists of one S-band Doppler radar and two low-gain passive receivers at remote sites. Operational experience with the bistatic network indicated many cases in which sidelobe contamination seemed nonnegligible. To confirm these findings a sidelobe simulation model was constructed. Comparison between simulations and actual data showed a good reproduction of the observed effect, with differences explained by uncertainties in both transmitter and receiver antenna patterns. It is also shown that this effect may have damaging consequences in Doppler fields in both convective and stratiform precipitation events. An index of contamination is introduced to detect areas of low-quality data. 1. Introduction The concept of bistatic radar is as old as the concept of radar itself [for a review of the history of bistatic radar see Glaser (1986)]. It consists of a system capable of sending a pulse (transmitter) at a given site and a system capable of receiving an echo from a target at a different site (receiver). The more conventional monostatic radar delivers the pulse and receives the echo at the same site and with the same antenna. Several researchers have explored the use of bistatic radar systems for detecting weather echoes, among them Atlas et al. (1968), Doviak and Weil (1972), Crane (1974), Awaka and Oguchi (1982), and Dibbern (1987). In addition, some work has been done regarding the use of polarimetric parameters in a bistatic system by Shupyatsky (1974) and Aydin et al. (1998). But it was really after the pioneering work of Wurman et al. (1993) that the idea of bistatic radars in meteorology was reborn, especially due to its Doppler capability. A bistatic multiple-doppler network consists of one traditional transmitting Doppler radar and one or more passive, nontransmitting, nonscanning radar receivers at remote sites. Multiple bistatic receivers provide multiple-look angles at a volume of weather in the same manner as multiple Doppler radars do. The Doppler shifts of the radiation scattered obliquely by the raindrops toward the passive remote receiver can be measured. Then, with two or more Doppler measurements Corresponding author address: Ramón de Elía, Department of Atmospheric and Oceanic Sciences, McGill University, 805 Sherbrooke W., Montreal, PQ H3A 2K6, Canada. relia@zephyr.meteo.mcgill.ca from different viewpoints, several techniques can be used for determining the full wind field over a particular area (Wurman et al. 1993; Protat and Zawadzki 1999). The McGill University Bistatic Network has been implemented in collaboration with the University of Oklahoma and the National Center for Atmospheric Research. It became operational by the end of 1995 and has been operating almost continuously since then with a satisfactory stability. It consists of the McGill S-band scanning Doppler radar located 30 km west of downtown Montreal, and two bistatic receivers located south and northwest of the Island of Montreal (see configuration in Fig. 1). A bistatic radar system uses a single source of illumination; thus, observations of individual storm regions by the transmitter and the bistatic receivers are taken simultaneously. This is not the case of the monostatic multi-doppler radar system, unless a synchronized scanning is used. Radial velocities are not measured simultaneously but are separated in time up to the few minutes required for each radar to scan a given volume. In convective environments, significant storm feature evolution can occur between these measurements. There are some disadvantages in the bistatic radar approach as compared to the multiple-doppler measurements. The use of low-gain receiving antenna can cause the receiving sites to be less sensitive (near 15 db less) than the traditional high-gain radars at comparable range. In addition, the wide viewing angle of the antenna can cause the bistatic receivers to be more sensitive to multiple scattering contamination and sidelobe contamination. The success of the prototype system (Wurman 1994) suggested that the above limitations are often not serious. However, operational experience with 2000 American Meteorological Society

2 1314 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 FIG. 1. McGill Doppler bistatic network. the bistatic network at McGill University suggested sidelobe contamination (SICO) should be given serious consideration. When wind field reconstructions are performed with Doppler data from a bistatic network, some of the wind components may be overspecified. The 3D wind retrieval algorithm should objectively indicate which measurement is going to be the most trustworthy. This work is centered on the study of the sidelobe contamination problem. It begins with a detailed explanation of the phenomena in section 2. Section 4 describes the Sidelobe Simulation (SISI) model that simulates bistatic reflectivity data and is used as a tool to discriminate clean data from contaminated data. Section 5 presents the results of four simulations, two for a convective and two for stratiform precipitation cases. Results are discussed in section Sidelobe contamination (SICO) a. Monostatic case The electromagnetic pulse emitted by a radar with a parabolic antenna is usually thought of as a narrow conical volume traveling in a direction dependent on the position of the antenna. This simplified version is normally adequate to understand most of the phenomena related to monostatic and bistatic radars. However, a more complete description of the procedure is needed for a careful analysis of the SICO. In practice, the electromagnetic pulse is emitted in all directions at the same time, but the power depends strongly on the direction. The largest amount of power is sent in the direction in which the antenna is pointing, and smaller amounts of energy are sent in other directions. For a monostatic radar the surface of constant phase is a sphere of radius r. Thus, at a given time, the main beam receives a backscattered power P m from a range r. At the same time, the sidelobes sample a ring at the same distance r with varied intensity. The total received power is P t P m P s, where P s is the total power received by the sidelobes. Generally, the range is given by the time delay in the signal, and the angular position is given by the orientation of the antenna center. Therefore, the total received power P t (instead of P m ) is assigned to the volume defined by the main beam. This approximation is good enough when P s can be considered negligible in comparison with P m. In order to have a small P s, antennas are required to have very low secondary lobes. Standard parabolic antennas usually have acceptably low secondary lobes for monostatic applications. Certain antennas such as the one from the Next Generation radar (NEXRAD) have been built with specific limits for the sidelobes. Figure 2 shows a reflectivity pattern from the McGill radar at a range of 27 km at different elevations and azimuths. The observed targets are mainly ground clutter, the most conspicuous being the Mont-Royal, a hill of 200 m above its surroundings, located close to downtown Montreal. Most of the echos at higher elevations come as a result of secondary lobes detecting the Mont- Royal and others come from lesser targets. As shown by Rinehart and Tuttle (1981), this may contain valuable information regarding the antenna pattern. In the case of a monostatic radar, both the transmitted and received pulse go through the same antenna. A signal sent through a weak sidelobe is received by the same weak sidelobe further reducing the power of the undesired signal. Mathematically, it is possible to write this relation as P r (r,, ) G 2 (, )Z(r,, ), (1) where P r (r,, ) is the received power at range r in the direction given by the azimuth, and the elevation angle, both angles measured from the center of the antenna. The one-way antenna pattern gain is G, and Z(r,, ) is the reflectivity field. Figure 4 shows the McGill radar one-way antenna pattern as a function of azimuth at a 0.5 elevation angle. b. Bistatic case Figure 3 illustrates the case of a storm core being illuminated by a sidelobe while the main beam probes a region with stratiform precipitation. Both signals reach the receiver at the same time if they come from the surface of constant phase, which for a bistatic system is an ellipsoid with the transmitter and receiver as foci (See appendix A). This contaminates the region at which the main lobe is pointing with information exported from the region of higher reflectivities. For a bistatic receiver, the power received at a given angle may be written as

3 1315 FIG. 2. Reflectivity pattern at 27 km from J. S. Marshall Observatory, at different azimuths and elevations. This field was obtained during a clear day. The main target is the Mont-Royal, a hill of around 200 m above its surrounding. Effects of secondary lobes can be seen as the echo is present at different heights. P r (r 2,, b ) G t (, )G r (, b )Z B (r 1,, ), (2) where angles,,, and b, as well as ranges r 1 and r 2 are defined in appendix B and Z B is the bistatic reflectivity. Now the antenna gains G t (transmitter) and G r (receiver) are allowed to be different. As discussed in the introduction, the gain of the remote receiver G r (, b ) is lower than G t (, ). In the case of a receiver antenna with broad azimuthal pattern, the main lobe of G r can be considered to be isotropic for a large region. Therefore, the product of both gains, will be proportional to the one-way main antenna pattern. Hence, we have P r (r 2,, b ) G t (, )Z B (r 1,, ). (3) From (1) and (3) it can be seen that while in the monostatic system the sidelobe contamination is determined by the two-way antenna gain, however, in a bistatic radar system with a broad azimuthal pattern it is well approximated by the one-way gain and, consequently, has sidelobes twice as intense (in db). 3. Antenna patterns a. Transmitter The transmitter antenna pattern is the principal element responsible for the SICO in the bistatic system as outlined in the previous section. Thus, it is important

4 1316 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 FIG. 3. Simplified diagram of the effect of sidelobe contamination in a bistatic radar. Since echos are assigned to the area where the antenna is pointing, sidelobes create a fictitious target when pointing toward a high reflectivity zone. Since the time of arrival of the signal corresponds to a given ellipse, a ghost echo is created in this ellipse in the direction the radar is pointing. to have prior knowledge of the distribution of power as a function of angle. The original antenna pattern of Mc- Gill s monostatic radar provided by the manufacturers (circa 1966) was suspect due to the age. The antenna pattern depicted in Fig. 4 was taken during August 1998 (a period of major improvements in which the radar was necessarily offline). Since the Mc- Gill radar is polarized vertically, the pattern for this polarization is shown. Given the circumstances of these measurements, only an azimuthal description at 0.5 is available. The measurement was performed as follows. A transmitter was installed on the roof of a building 3 km from the radar site with a simple horn as an antenna. In this location there was a clear view of the radar tower. The scanning radar was operated as a receiver only and turned the full circle giving a resolution of 33 points per degree. It is noteworthy that the new measurements were extremely similar to the ones performed over 30 years ago. In order to recreate a three-dimensional structure it is supposed that the pattern is axisymmetric. Although this is not exactly so, it can give a good first approximation to the problem. The main feature in this pattern is the peak at the center of the antenna (0 ) and a slow decay in power until a minimum at around 50 is found. Another two maxima are found before the back of the antenna is reached (180 ). One or both may be due to the energy spill over the dish. A similar description can be applied to the other half rotation. It is possible that values below 50 db were never attained due to the low power of the remote transmitter that sets a high level of noise. A closer view of the pattern around the main peak FIG. 4. One-way antenna pattern of the McGill monostatic radar for the vertical polarization and the lowest elevation angle (0.5 ). The two lower panels are close-ups of the upper panel. reveals the existence of many sidelobes above 30 db. In particular, the maxima at 10 and 10 appear very conspicuous. These probably originated due to the struts in the antenna that fix the feed in the center. If this is the case, this maxima may not exist in any other axis than in the vertical and horizontal, and hence, an axisymmetric generation of a three-dimensional pattern may overestimate the magnitude of the sidelobes. As seen before, Fig. 2 can also be interpreted as proxy for the antenna pattern. It shows that some unexpected maxima are also found in diagonal axes, although they seem to have lower intensity in comparison with the vertical axis.

5 1317 b. Receiver 1) CALIBRATION OF BISTATIC RECEIVERS The power received by the bistatic radars must be interpreted to allow for different kinds of studies. The most common of these interpretations states that after correcting for geometry, and antenna pattern, this value can be considered to be proportional to the bistatic reflectivity Z B. Since the correction for side scattering is, in this case, straightforward as shown in appendix C, the measurement can also be thought of as a bistatic estimation of the monostatic reflectivity Z, and be written as r2 cos ( /2) Z b(r 1,, ) kp r(r 1,, ), (4) 2 GG(, ) cos t r b where P r is the received bistatic power; r 1,, and are the monostatic range, azimuth, and elevation angle, respectively; k the bistatic calibration constant; cos 2 the factor that accounts for side scattering (see appendix C); G t and G r the transmitter and bistatic antenna gain, respectively; r 2 the bistatic range; and the bistatic angle (see appendix B for a definition of,, and b ). Although the power is received in the remote site, it is written in the monostatic spherical coordinate system. Correction of received power with an approximated antenna pattern will produce unrealistic features. In addition, received power that has been heavily contaminated by sidelobes will overestimate the real value also producing unrealistic features. Since it is impossible to differentiate one from the other, it has been decided to present the bistatic reflectivity field without the correction for the receiver antenna pattern. For this purpose we will define the normalized power N as the product between the reflectivity and the receiver antenna pattern. Then, N(r 1,, ) Z b(r 1,, )G r(, b) r2 cos ( /2) kp r(r 1,, ). (5) 2 G cos In this work we have chosen to use two different approaches for calibrating the bistatic normalized power. R For isolated cells. Since the angular extent is small, the receiver antenna pattern can be considered uniform, and hence bistatic values can be forced to match the monostatic values. In order to minimize the bias caused by sidelobe contamination, the matching is performed using the highest values in the storm (e.g., Fig. 9). R For large area coverage of precipitation. Since the receiver antenna pattern is not accounted for, normalized power fields N display a structure that resembles the antenna pattern. In this case, bistatic values in the regions of higher gain in the bistatic receiver are matched with monostatic values. With this defi- t nition bistatic values underestimate the monostatic ones in the regions of lower gain in the bistatic receiver (e.g., Fig. 5). For comparison, Fig. 7 depicts the raw power field as measured by the passive receiver. Calibrated data are shown in Fig. 6. 2) ANTENNA PATTERN STRUCTURE The receiver antenna has been described in some detail in Wurman et al. (1993). It consists of a low-gain antenna made out of a slotted waveguide and a corner reflector. The waveguide is installed vertically, having enough slots to create a beam 12 wide in the vertical. The reflector consist of two metal sheets forming a corner of 60. This reflector helps to increase the gain in the horizontal but still keeps a wide enough beam (of around 50 ). Although never measured, the antenna pattern was expected to have a beam with a maximum in the principal axis (J. Wurman 1998, personal communication); however, this has not been the case for bistatic receiver 1. Figure 5 depicts horizontal cross sections for a 2-h average of stratiform precipitation for the period UTC 31 May The reflectivity measured by the monostatic radar shows a rather uniform field, while the normalized power measured by bistatic receiver 1 exhibits a pattern with two maxima, with a local minimum in the region where the antenna is pointing (north). Topographic maps of the area and visual inspection suggested that no blocking, due to natural nor human origin, was present. In order to confirm that the observed pattern originated from the antenna itself and not by blockage or mismanagement of the data, a clockwise rotation of the antenna pattern of approximately 20 was performed. Figure 6 depicts a horizontal cross section of the normalized power field seen by bistatic receiver 1, at an altitude of 2 km for a 1-h average of stratiform precipitation for the period UTC 11 July Comparison between the normalized power fields before and after the rotation of the receiver antenna (see Fig. 7) suggests that the characteristic two maxima pattern is intrinsic to the antenna and not due to blocking or data mismanagement. The difference with respect to the original design is not fully understood, although it is probably due to a waveguide shift while handling. 3) ESTIMATION OF RECEIVER ANTENNA PATTERN The power P r measured by the bistatic receiver can be thought of as the convolution of the reflectivity and both antenna patterns in the illuminated ellipsoid. It may be written as P r G t G r * kz B, (6) where * stands for convolution in the ellipsoid, G t

6 1318 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 FIG. 5. Two-hour average fields for the period UTC 31 May Four different fields at an altitude of 2 km: the upper-left panel depicts the monostatic reflectivity, the upper right the Ste-Clotilde bistatic normalized power, the lower left the Beaubriand bistatic normalized power, and the lower right the monostatic Doppler. Both bistatic normalized power can be thought as a proxy for receiver antenna patterns. corresponds to the transmitter antenna, G r the receiver antenna, and k includes the geometrical and calibration factors. Assuming that the transmitter pattern G t can be written as the sum of the main beam and the sidelobes as G t G M G S, (6) becomes P r G M G r * kz B G S G r * kz B. (7) Since the main beam is a sharp peak, it can be thought of as a Dirac delta and therefore the received power becomes P r kg M G r Z B G S G r * kz B. (8) The first term on the right-hand side is no longer a convolution. This means that the received power can be thought of as two parts, one due to the power of an individual volume illuminated by the main lobe and the other due to the convolution of sidelobes with all the scatterers in the ellipsoid. For a quasi-uniform reflectivity field in a region where the receiver antenna gain G r is high, the second term becomes negligible and hence (8) can be expressed as P r kg M G r Z B. (9) As shown in appendix C the bistatic reflectivity Z B in the Rayleigh range can be approximated as Z B Z cos 2, (10) where Z is the monostatic reflectivity, and the angle subtended by the polarization vector of the scattered signal and the receiver. It is worth noting that when both transmitter and receivers are polarized vertically (as is McGill s bistatic network), cos 2 is very close to 1 for

7 1319 FIG. 6. One-hour average of bistatic receiver 1 normalized power field for the period UTC 11 Jul This field can be thought as a proxy for the receiver antenna pattern. Note the change in orientation of the two main lobes (see Fig. 5). low-elevation angles (see appendix C). This makes the correction negligible in most of the domain. Then, the receiver antenna pattern can be written as P r G r 2. (11) kg Z cos M This expression allows us to estimate the antenna pattern by using the received bistatic power P r and the monostatic reflectivity Z. This approximation fails when the main beam illuminates a region where the receiver gain is low enough so that the second term of (8) becomes dominant. Therefore, the estimated antenna pattern loses accuracy as the receiver gain is farther from its maxima. Figure 8 depicts the antenna pattern of receiver 1, obtained by using (11) expressed in dbz. Data from the monostatic and bistatic receivers were taken from a ring at about 10 km from the receiver for the same case as shown in Fig. 6. The two maxima already mentioned are clearly present and centered at 8 of elevation. The minimum below the left-hand maxima does not seem to be part of the antenna pattern. Inspection of the monostatic reflectivity suggests strong ground clutter contamination. In order to obtain a receiver antenna pattern to use in the SISI model, the previous pattern was fit with Gaussian functions and the following approximation was found: FIG. 7. One-hour average of bistatic receiver 1 power field for the period UTC 11 Jul Figure 6 shows the same field after calibration. ] [ ] ( 8 ) ( 22 ) [ ] ( 8 ) ( 47 ) [ ( 8 ) ( 22 ) G r (, ) exp exp exp, (12) FIG. 8. Antenna pattern G r of receiver 1 obtained by using Eq. (11) expressed in dbz. Data from the monostatic and bistatic receiver were taken from a ring at about 10 km from the receiver for the same case as shown in Fig. 6. The two maxima already mentioned are clearly present and centered at 8 of elevation.

8 1320 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 where is the azimuth and the elevation angle. The zero in the azimuthal angle is defined in the direction where the antenna points (north). 4. The sidelobe contamination simulation model (SISI model) This section is devoted to the simulation of the sidelobe contamination. In order to quantify and to better understand this effect, a numerical model has been constructed. The model can simulate both the bistatic reflectivity and Doppler velocity if appropriate data are available. a. Simulation of the reflectivity Given the monostatic reflectivity field, that is assumed to be error free, the power P m that reaches the bistatic receiver coming from an echo generated by the main lobe can be expressed as GG(, t r b) 2 P m(r 1,, ) k VmZ(r 1,, ) cos, (13) rr 1 2 where r 1,, and are the monostatic range, azimuth, and elevation angle, respectively; k the bistatic calibration constant; V m the sampled volume; Z the monostatic reflectivity; cos 2 the factor that accounts for side scattering (see appendix C); G t and G r the transmitter and bistatic antenna gain, respectively; and r 2 bistatic range (see appendixes D and B for a definition of V m,, and b ). Although the power is received in the remote site, it is written in the same monostatic spherical coordinate system. In order to obtain the total power P t that reaches the receiver, it is necessary to integrate the power scattered by all targets located on the ellipsoid of constant phase. The integration is performed in the volume bounded by two ellipsoids, the external being the head and the internal the tail of the pulse. The signal coming from each scatterer inside this illuminated volume arrives simultaneously to the receiver. Explicitly, it may be written as 1 c cos( ) 2 P t(r 1,, ) k Z(r,, ) G t(, )G r(, ) b cos d d, (14) 2 r cos ( /2) 2 where and are the integration variables that sweep the entire ellipsoid. Other primed variables are functions of and as defined in appendix B. The volume in the shell has been written in polar coordinates (the natural coordinates for the monostatic data) and in terms of the pulse length c. Since the shell is much thinner than the distance to the transmitter, the radial integration becomes trivial. Therefore, the triple integral is reduced to a double one (this is not strictly valid near the baseline where pulses reach lengths comparable to the distance between the transmitter and receiver). Since the radar data are available in a discrete polar grid, the previous expression can be discretized to obtain c i j k m l P (r,, ) k Z(r,, ) t l m m j l k 2 G t(, )G r(, ) b cos cos, (15) r 2 cos ( /2) i where range r 1 is available each kilometer, and azimuth and elevation angles j and k, each degree. Once this integral is performed for each grid point using the reflectivity Z given by the monostatic dataset, a simulation of the power that reaches the bistatic receiver is obtained. More useful than the received power is the measured reflectivity by the bistatic receiver. This can be obtained by using the radar equation for the bistatic system. Then, the reflectivity measured by the bistatic receiver becomes r2 cos ( /2) Z b(r 1,, ) P t(r 1,, ). (16) c 2 k GG t r(, b) cos 2 Here, as in the monostatic radar, it is assumed that the received power is originated in a volume defined by the main lobe of the transmitter antenna pattern. It is worth noting that Z b is the simulated reflectivity observed by the bistatic receiver once all the corrections (antenna patterns, geometry, side scattering) are performed. SIDELOBE CONTAMINATION INDEX (SICO INDEX) As shown in section 2, the total power P t can be thought of as being the sum of two sources of power, P m originated in the targets illuminated by the main lobe, and P s originated in the targets illuminated by the sidelobes. It is useful to define an index that compares the intensity of these two sources of power, and this may be done by defining a sidelobe contamination index as I 100, (17) SICO P t that can be estimated as P s

9 1321 Pt Pm I 100. (18) SICO When I SICO 0 sidelobe contamination is nil, and I SICO 100 indicates pure contamination. b. Simulation of the Doppler velocity Contamination in the Doppler measurements depends on the estimator used. This model is based on the pulsepair processor (Doviak and Zrnić 1993) since it is the one used in the McGill bistatic network. In Doviak and Zrnić (1993) it is shown that the autocovariance function of the received signal can be written as P t 1/2T s s 1/2T s R(T ) S( f ) exp( j2 T f) df, (19) s where R(T s ) the covariance of the received signal at lag T s, the pulse repetition time, S( f) the spectrum of velocities inside the sampled volume, where f 2 /, being the velocity and the radar wavelength, and j the imaginary unit. Assuming a symmetrical velocity distribution with respect to f d, the previous equation can be rewritten as 1/2T s s s d S( f ) exp[ j2 T s( f f d)] df, 1/2T s (20) R(T ) exp( j2 T f) where now the integral is a real number. Under this assumption, the mean frequency, that is the mean velocity, can be obtained from the argument of the autocovariance R(T s ). This formulation can be discretized as N s i s i i R(T ) P exp( j2 T f), (21) where P i is the individual power of each of the integrated echos. In this approximation it is assumed that the spectrum width is mainly generated by the accumulation of power coming from different sidelobes, and that the spectrum width inside each of the data points is negligible. Considering that the individual source of power lay on the bistatic ellipsoid, this formula can be rewritten as (15) but with inclusion of the complex phase. Then, i j k R(T s)(r 1,, ) s c m l 1 2 l m k exp( j2 T f )Z(r,, ) G (, )G (, ) cos m j l k 2 t r b cos. (22) r cos ( /2) 2 The apparent velocity a is obtained as a ( /4 T s ) argr(t s ). (23) It is very important to notice that there is a dramatic difference between the reflectivity and the Doppler data. The reflectivity is a scalar field and hence can be observed from different locations giving the same value (at least in theory). On the other hand, the velocity is a vector field, and thus, projection changes with view point. Therefore, the contaminated bistatic Doppler field cannot in general be simulated since the noncontaminated bistatic Doppler field is not available. In the reflectivity case the monostatic field was taken as the noncontaminated bistatic field. The previous development shows that the velocity originated in each sidelobe is weighted by the reflectivity and both antenna patterns. That is, a velocity coming from a region of high reflectivity and well illuminated by both antennas will predominate. Regions with reflectivity contamination are going to have Doppler contamination as well. However, since the real Doppler field is unknown, it is not possible to evaluate from the observations the extent of the contamination. It may be the case that the velocity has been contaminated from a parcel that has the same velocity. In this case, although the contamination in reflectivity is high, the Doppler velocity stays unaffected. 5. Results In order to assess the quality of the SISI model several comparisons with real data have been performed. In this work four cases are shown, two convective and two widespread stratiform precipitation events. a. Convective cases 1) 7 MAY 1998 Figure 9 depicts reflectivity fields at an altitude of 2.0 km for the monostatic (upper left) and two bistatic receivers (1 in the upper right, 2 in the lower left), as well as Doppler field (lower right) from the bistatic receiver 1. On 7 May 1998 two small convective systems remained in the bistatic domain for nearly 20 min. The depicted time is 2250 UTC. Doppler measurements represent a different component of the displacement of a target for each instrument and hence no comparisons are possible. Reflectivity, on the other hand, being a scalar field allows for equivalent measurements in any direction. Once the effects of the geometry and polarization are removed, differences between the fields are due to the nature of the instruments as well as antenna patterns. In the present case, due to the small size of the system under study, the receiver antenna pattern does not affect the measurements much. A comparison between the monostatic and bistatic receiver 1 reflectivity fields shows a dramatic difference: in the latter, both convective centers form extended elliptic arcs. The same can be seen in the Doppler field,

10 1322 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 FIG. 9. Horizontal cross section of two convective cells at 2250 UTC 7 May Upper-left panel shows monostatic reflectivity at 2.0 km, upper right shows bistatic receiver 1 reflectivity at 2.0 km, lower left shows bistatic receiver 2 reflectivity at 2.0 km, and lower right shows bistatic receiver 1 reflectivity at 6.5 km. Sidelobe contamination is clearly seen by comparison. where movement is measured in a precipitation-free area according to the monostatic radar. The bistatic measurements tend to expand the original field in the direction of the bistatic ellipsoid. However, the most conspicuous features are unchanged. Bistatic receiver 2 does not show a clear contamination arc, although some traces are visible. This is due to the fact that the echo originated from the sidelobes is lower than the noise level of the instrument. Figure 10 shows the simulation of the SICO for the case of bistatic receiver 1. A comparison between this figure and the previous one indicates a successful qualitative simulation of the contamination. However, the simulation gives a wider sector and generally less intense contamination. This can be due to the fact that the antenna pattern is not completely accurate, due to the effect of the discretization, and also because the monostatic data that feeds the model are not the real data but an approximation. In addition, an underestimation of the threshold for the signal-to-noise ratio may create high reflectivity values from noise after the range correction is applied. The upper-right panel of Fig. 10 depicts the index I SICO using the sidelobe power P s and the main beam power P m estimated with SISI. As expected, the index has very low values in the area where the strongest echos of reflectivity are present. The same happens on the east side of the storm. This can be explained by noticing that the echo is quite uniform along the bistatic ellipse and hence contamination is less noticeable. On the other hand, the surroundings of the storm core along the ellipses are heavily contaminated reaching values above 90. As expected, areas with weak echos are heavily contaminated by nearby strong echos. This

11 1323 FIG. 10. Sidelobe contamination simulation for bistatic receiver 1 for the case shown in Fig. 9. Upper-left panel show reflectivity at an altitude of 2.0 km, and lower-left panel depicts reflectivity at 6.5 km. Panels on the right show the I SICO contamination index for the same heights. problem is expected to be serious at the edge of most storms, a zone intimately linked with the storm dynamics. The last panel shows that the contamination is also important in the upper part of the storm, above the core, for the the same reasons as discussed above. 2) 2 AUGUST 1997 On 2 August 1997 a convective system passed through the domain covered by the bistatic network. This case has been extensively studied by Protat and Zawadzki (1999), who performed a three-dimensional wind field retrieval over an area of 20 km 20 km with 7 km in the vertical. In order to ensure the quality of the Doppler bistatic data, the authors performed several tests. When three receivers are available (monostatic two bistatic), low-level horizontal wind fields can be reconstructed using different pairs of receivers. Wind retrievals obtained using the different sources showed no relevant differences for this case, suggesting that good Doppler data are predominant in both receivers. Figure 11 (upper panel) shows the contamination index I SICO obtained by the simulation for an altitude of 2.0 km in the same area investigated by Protat and Zawadzki (1999). In general, low values predominate, but contamination increases as expected when the edge of the storm is reached (lower panel). This result agrees with the one obtained by Protat and Zawadzki (1999) discussed above, and suggests that the quality of the data can be highly case dependent. Storms with conspicuous cores will be more affected, since large differences in reflectivity make the contamination more dramatic.

12 1324 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 FIG. 12. Measured (upper panel) and simulated (lower panel) bistatic normalized power horizontal cross section for bistatic receiver 1 at an altitude of 3.5 km on 1517 UTC 31 May FIG. 11. Horizontal cross sections at 2.8 km of contamination index I SICO (upper panel) and monostatic reflectivity (lower panel) for 2231 UTC 2 Aug The box indicates where wind field has been retrieved by Protat and Zawadzki (1999). b. Stratiform cases Two main characteristics make stratiform cases ideal for an in-depth analysis: (i) large area coverage and (ii) uniform wind field with vertical shear so that Doppler contamination can be observed. In addition, it is necessary to have measurements of bistatic power fields (initiated only in May 1998). Since no single stratiform case in our archives has the desired characteristic for a complete analysis, two case studies are presented here. In the first one, a comparison between measured and simulated normalized power N is presented, in the second one, a detailed analysis of the contamination problem is discussed. 1) 31 MAY 1998 On 31 May 1998 an intense stratiform precipitating system covered the Montreal region, the most intense period extending from 1400 to 1600 UTC. As in the convective case, the SISI model has been used to simulate the expected normalized power field for the bistatic receiver. Figure 12 (upper panel) depicts the measured bistatic normalized power field at an altitude of 3.5 km from bistatic receiver 1 at 1517 UTC. The lower panel shows the simulation at the same height and time. The general structure of the field is well recovered. The minimum in the axis located north of the receiver (at BRcv1) is reproduced, and the axis with the two maxima are well located. Even the gradients of reflectivity near the bistatic receiver are very well captured. Differences may be mostly due to the lack of an accurate bistatic receiver antenna pattern. 2) 13 AUGUST 1997 On 13 August 1997 a widespread stratiform precipitation event with a remarkable vertical shear (Fig. 15,

13 1325 FIG. 13. Left panels depict horizontal cross section of monostatic reflectivity. The upper-left panel shows the 2.0 km, and the lower left the 5.8-km altitudes. Panels on the right depict Doppler velocities at 2.0 km, with the monostatic in the upper one and the bistatic in the lower one. lower panel), covered the Montreal region. Figure 13 shows on the left-hand side the monostatic reflectivity at an altitude of 2.0 km (upper panel), and at 5.8 km (lower panel). Both fields are rather uniform, the first FIG. 14. Schematic of the methodology used to compare monostatic and bistatic Doppler data. Plane A contains the monostatic Doppler measurement and plane B contains the bistatic Doppler measurement. When plane B is half-way between the transmitter and receiver, the measured components are parallel to those in plane A. In case of a uniform wind field both instruments measure the same wind component. well below the bright band (located at 3.5 km) and the latter above. Differences in values between rain and snow are around 12 dbz. The right-hand side depicts the monostatic Doppler at an altitude of 2.0 km (upper panel), and the bistatic Doppler velocity from receiver 1 at the same height. The monostatic Doppler field suggests a rather uniform wind structure that, in addition, rotates with height (not shown). The bistatic Doppler field extends over a shorter range due to the low-gain antenna at the receiver. Uniformity in the wind field gives the possibility of comparing Doppler velocities in the following way: bistatic velocities are perpendicular to the ellipsoid of constant phase (see Fig. 14). Therefore, at half the distance between transmitter and receiver, the measured component is perpendicular to the baseline. A cross section of the bistatic Doppler in the plane (B) contains, hence, the wind component parallel to the plane. A parallel plane (A) but centered at the monostatic radar contains, like any other plane centered at the radar, the wind component parallel to the plane. In an ideal horizontally uniform wind field (and reflectivity too, to account for drop fall velocities) velocity measurements in both planes should be the same. Figure 15 depicts the monostatic reflectivity at line

14 1326 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 FIG. 16. Cross section along line B of the contamination index I SICO (upper panel) and bistatic Doppler velocity (lower panel). Both fields were obtained with the SISI model for the case depicted in Fig. 13. FIG. 15. Cross section of monostatic reflectivity along line B (upper panel), bistatic Doppler velocity along line B (middle panel), and monostatic Doppler velocity along line A (lower panel). Lines A and B are defined in Fig. 13. B (upper panel), the bistatic Doppler velocity at line B (middle panel), and the monostatic Doppler velocity at line A. The reflectivity shows a clear bright band, an area of lower reflectivity above (snow), and higher reflectivities below (rain). The monostatic Doppler velocity illustrates well the shear at different levels but also shows that wind field is not perfectly uniform (parallel isolines expected). The bistatic Doppler velocity differs notably from the monostatic Doppler. The most striking difference appears above the bright band in the first 20 km. In addition, the lowest level at any distance also shows differences. On the other hand, values around the bright band look similar almost everywhere, and measurements in the snow region improve farther away from the baseline. In order to reproduce this effect with the model, an uncontaminated bistatic Doppler field is needed. As a proxy for this we use a Velocity Azimuth Display analysis performed on the monostatic Doppler data. Then, the bistatic Doppler measurement of this field is created. Figure 16 shows results from the simulation in the cross section of line B. The index of contamination I SICO obtained is depicted in the upper panel, while the simulated contaminated bistatic Doppler is shown in the lower part. A comparison between the simulated bistatic Doppler and the measurements in Fig. 15 reveals that most of the features were well simulated principally, the values in the region above the bright band and within the first 20 km from the baseline, and the values in the lowest levels. The contamination index I SICO exhibits a wide range of values. The lowest are found in the region of the bright band and away from the radar, and accordingly, a good wind measurement is obtained. A zone of very high values is found in the snow region in the first 20 km from the baseline. This corresponds to the strong contamination in the Doppler values found in both the simulation and the real data. This is probably due to an exportation of values from the bright band to the sector of much lower reflectivity above it. High contamination is also found in the lower levels, probably due to the low gain of the passive antenna in this region. In order to understand the decrease of contamination with distance, recall that in (8) the second term on the right-hand side is an integral over an ellipsoid. This ellipsoid grows in size with distance, and may grow so much that some of its area is even beyond the troposphere. Since targets cover a fixed volume of the atmosphere, increasing the size of the ellipsoid reduces the relative contamination area. On the other hand, ellipsoids very close to the radar are fully covered by rain, maximizing the contamination term. 6. Discussion Contamination by secondary lobes in a bistatic radar was studied by means of a numerical algorithm. The

15 1327 degree of contamination depends mainly on the monostatic antenna characteristics. In our case, results show that contamination by sidelobes is not a minor problem and should be addressed carefully. In the convective case, it is seen that the area of strong gradient in reflectivity around the core of the storm is heavily contaminated. In the stratiform case, the region above the bright band was affected by contamination coming from strong echos in the region of melting and liquid precipitation. These two particular cases suggest that bistatic radars may be affected by sidelobe contamination in both types of precipitation, although experience shows that there may be great variability from case to case. Since some of the regions are corrupted due to sidelobe contamination, retrieval algorithms should take this information into account and reject data if necessary. However, full and reliable antenna patterns of both receiver and transmitter are needed for an accurate estimate of contamination. Overestimation or underestimation of sidelobes may cause rejection of valuable data or acceptance of contaminated ones. The contamination index I SICO has already been adapted and implemented in the wind retrieval algorithm presented by Protat and Zawadzki (1999). It is used as a weight in the cost function so that Doppler values in regions of high contamination have a small impact on the retrieved wind field. This and other developments will be reported in future papers. More receivers may be needed if the rejected data are an important percentage of the total. It is clear that receivers at different locations are going to create different contamination ellipsoids and hence the contaminated region will not be the same. However, the use of many receivers only partially solves this problem since contaminated regions from different receivers may overlap in large areas. The clearest overlapping occurs at the base and top of the reflectivity core (Fig. 10 lowerright panel). In this case, the vertical extension of the transmitter antenna pattern is the most important source of contamination and hence no receiver located at ground level will successfully probe these regions. It is interesting to note that the defined contamination index I SICO can also be used with the original reflectivity data instead of the simulated ones. This would be of great advantage since simulations may take a long computation time. However, noise in the data and the lack of a reliable receiver antenna pattern precludes straightforward estimations. Results regarding this approach to the problem will be reported on soon. This may be of particular interest in an operational setting. The model developed here can be also a useful tool for designing an optimal network, helping to define the location as well as the number of receivers needed. In addition, since the model includes the possibility of working with the desired polarizations, work in this area can also be addressed. For example, studying the effect of changing the polarization from vertical to diagonal or analyzing the effect of sidelobe contamination in the hypothesis of Ayden et al. (1998), which suggests that the bistatic radar has the potential to discriminate hail from rain. Some of the work done or proposed here may be improved if measurements with the transmitter and receiver, located at the same site, were performed. This would give the opportunity of a thorough analysis of the secondary lobe problem since a ground truth would be available. It has been suggested by Sachinadanda et al. (1984) that contamination by sidelobes in a monostatic radar can be reduced by varying the antenna pattern from pulse to pulse. This study was carried out theoretically on a phased array system. This is a possibility that may have to be taken into account for further developments in the bistatic system. Acknowledgments. We are very grateful to the people in the McGill Radar Group who provided help in many ways through a stimulating intellectual environment. In addition, Frédéric Fabry and Christian Pagé were extremely helpful in both academic and practical tasks. We would also like to thank Jeff Keeler for his cooperation during his visit at McGill University. Finally, we are very grateful to Marco Carrera for his thorough work in the final correction of this work. APPENDIX A Ellipsoids of Constant Phase In the monostatic radar targets located on surfaces of equal range give returns with the same phase. Surfaces of equal phase are spheres centered at the radar. When the transmitter and the receiver are not collocated, this concept is more complicated. Now the trip is done along two different paths: from the transmitter to the target and from the target to the receiver. Then, the total distance traveled by the pulse changes from L m 2r 1 in the monostatic radar to L r 1 r 2 in the bistatic. Surfaces of equal distance now are described by ellipsoids with foci in both the transmitter and the receiver as show in Fig. A1 and described by the equation 2 x y z 1. (A1) 2 L L B L B 4 APPENDIX B Elements of Bistatic Geometry This appendix describes the simple but fundamental elements of the bistatic geometry. Figure B1 contains the elements to build the geometrical relations needed. Generally, the range from the monostatic radar r 1, the azimuthal angle, the angular position of the receiver, the distance between transmitter and receiver B, and the elevation angle are known:

16 1328 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 FIG. B1. Main geometrical definitions in the bistatic geometry. FIG. A1. Isolines of equal distance r 1 r 2 traveled by a pulse are described by ellipses with the transmitter T and the receiver R as foci. The perpendicular to the ellipse bisects the bistatic angle. 2 r2 r1 B 2r1Bcos cos r r B cos 2r 1 r r 1 r 2 (B1) (B2) sin sin (B3) b r1 cos sin sin r2 cos b (B4) 2 r1 cos r2 cos b B cos. 2r1 r2 cos cos b (B5) APPENDIX C Polarization When scatterers are much smaller than the radar wavelength it can be assumed that the reemitted echo follows the Rayleigh approximation. Figure C1 shows the case of both receiver and transmitter vertically polarized, where E g is the scattered electric field, and E the projection of the scattered electric field in the direction of the polarization of the receiver. Under this definition, it can be shown that the bistatic scattering cross section can be written as b cos 2, (C1) where is the backscattering cross section and b is the bistatic scattering cross section and can be obtained from cos cos cos b sin sin b cos. (C2) This relation shows that the cross section is nil when the angle n, nbeing an integer. Thus, when the scattered electric field is perpendicular to the direction of polarization of the bistatic receiver, no signal is received. This relation also shows that the bistatic cross section is always equal or smaller than the monostatic or backscattering cross section. Expression (C1) can also be written in terms of reflectivity as Z B Z cos 2, (C3) where Z B is the bistatic reflectivity and Z the monostatic reflectivity. Since the McGill transmitter is polarized vertically and radar scanning is quasihorizontal, side scattering correction is almost negligible. APPENDIX D Resolution Volume in the Bistatic Radar The diagram in Fig. D1 is used to estimate a quantitative relation between the pulse length in the monostatic radar and the one in the bistatic. In the enlarged FIG. C1. This diagram illustrates the geometrical relations between the polarization of the scattered electric field E g, and the projection of the scattered electric field in direction of the polarization of the receiver E.