A multiple-Doppler radar network can be constructed using only one, traditional, transmitting pencil-beam radar and one or more passive, low gain, non-transmitting receivers at remote sites. Radiation scattered from the pencil beam of the transmitting radar as it penetrates weather targets can be detected at the receive-only sites as well as at the active transmitter. The Doppler shifts of the radiation received at all the sites can be used to construct two- and three-dimensional windfields in a manner similar to that used with traditional Doppler radar networks.
There are unique scientific advantages to a bistatic multiple-Doppler network: 1. All radial velocity measurements from individual resolution volumes are collected simultaneously since there is only one source of radiation. 2. The intensity of the obliquely scattered radiation can be compared to Rayleigh scattering predictions and used for hail detection. 3. Rapid-scanning of localized weather phenomena can be aided by elimination of the need to scan with multiple radars.
This type of multiple-Doppler radar network also has significant economic advantages. Passive sites contain no high voltage transmitting equipment or large rotating antennas. They require no operators and much less maintenance. We estimate initial investment costs and subsequent operational and maintenance costs are less than 1/30 that of conventional radars.
There are shortcomings particular to these types of networks: 1. Passive, low gain, receiving sites are more sensitive to contamination from transmitter side-lobes and to secondary scattering from weather echoes. 2. Low gain receiving sites are less sensitive to weak weather echoes. 3. Cartesian (u,v,w) windfields derived from bistatic network data exhibit about twice the expected error as those constructed from data from traditional monostatic networks containing equal numbers of radars. Multiple scattering and side-lobe contamination levels are acceptable in most situations and can be reduced with the use of higher gain receiving antennas. The low sensitivity and higher errors of the bistatic networks can be ameliorated with the use of multiple passive sites, a practical solution due to their very low cost.
Several investigators have explored the use of bistatic radar systems for detecting weather echoes. Doviak and Weil (1972) used a very long baseline, high gain system and measured the scattering intensity from a precipitation melting layer. They obtained signal strengths that were consistent with the light precipitation that was occurring at the time. Crane (1973) succeeded in measuring Doppler shifts in near-forward-scattering from rain with a similar long baseline system. Changes in the Doppler shifts of the received signals were attributed to local windfield variations. Others, including Atlas et al. (1968), have calculated the bistatic scattering intensity from clear air targets.
where p is the angle enclosed by the transmitter-particle and transmitter-receiver vectors, D is the distance between the transmitter and the receiver, and a and e are the azimuth and elevation angles of the particle relative to the transmitting radar. This formulation is illustrated schematically in Figure 3, for the two-dimensional case (y=0). In this simplified case the angle p is equal to the elevation angle of the transmitter.
In bistatic systems the length of effective radar resolution volumes [roughly proportional to d(range along the transmitted beams)/d(delay time)] are not constant. This can be seen easily by contrasting the arrival time of radiation scattered from transmitted beams directed toward and away from the bistatic receiver along the transmitter-receiver baseline. All radiation scattered forward towards the receiver arrives at the receiver simultaneously, regardless of the scatterers' locations along the beam (all path lengths are identical). In contrast, radiation backscattered towards the receiver is delayed by one microsecond for each 150 meters change in scatterer placement along the baseline. In this case, the effective length of resolution volumes is the same as that for a traditional monostatic weather radar. The same result occurs if the scatterers are off the baseline but are extremely distant from the bistatic network. At most transmission angles, near the bistatic couplet, but away from its baseline, the resolution volume length is expanded by factors ranging from 1 to 4. This is illustrated in Figure 4.
Resolution volumes are also expanded if the bistatic receivers employ low gain, wide angle receiving antennas. In a typical monostatic weather radar, the high gain transmitting and receiving antenna reduces the intensity of both transmitted and received signals at the beam edge. However, in the low gain bistatic case there is little signal rejection at receipt. Effective resolution volume dimensions are expanded. The expansion is dependent on the transmitter-scatterer-receiver geometry which changes the shape of these volumes ( Doviak and Weil, 1972, Doviak and Zrnic, 1993 ). Care must be taken to accurately define these resolution volumes which are not simply the intersection of the transmitter and receiver beam patterns as suggested erroneously by Atlas, et al. (1968).
A complication caused by the bistatic geometry is that the distances particles must travel to cause given path length and phase changes vary with location relative to the transmitter and receiver. Near the baseline between the two sites, this distance is large, thus there is an effective increase in the unambiguous velocity and a decrease in the precision of velocity estimates. The unambiguous velocity is proportional to del(t), where t is the time required for radiation to travel from the transmitter to a scatterer's location and then to the bistatic receiver, and is shown in Figure 6, normalized by the value calculated for a monostatic radar.
This angle-dependent scattering intensity strongly impacts the usefulness of bistatic radars and the choice of appropriate transmitting sources and receiver sites. If horizontally polarized radiation is transmitted, then there is a circular region at ground level from which there is very little scattering toward a particular receiver. This region is the locus of all points from which the E-vector of transmitted beams point at the receiver. Using typical monostatic weather radar parameters, [those of the NCAR CP-2 radar which was used in our prototype bistatic system: transmitted power = 1.2x10^6 W, antenna gain = 33,900 (45.3 dB), beamwidth = 0.0163 rad, wavelength = .1068 m, and pulse length = 300 m], a bistatic receiving antenna gain of 32 (15 dB), a minimum detectable signal strength of -110 dBmW, and a typical transmitter-receiver baseline of about 20 km ( transmitter and receiver at same elevation), Figures 7a and 7b show the equivalent reflectivity factor of the minimum detectable signal at the ground and at an elevation of 2 km above the radar sites. Note that at moderate transmitter beam elevation angles, the transmitted E-vector always points well away from the receiver and the low-sensitivity region is therefore much less pronounced than at the ground. Unfortunately, the low-sensitivity notch at the ground is co-located with the region in which dual-Doppler wind synthesis is best, as can be seen by comparing Figure 7a with Figure 14. Many Doppler weather radars, including the WSR-88D, are only capable of transmitting horizontally polarized radiation. The worst portions of the low-sensitivity notch are very narrow. Nevertheless, if directly measured ground level winds are desired, horizontally polarized transmissions should be avoided, if possible. Ground level winds could still be obtained through the use of multiple, closely spaced, bistatic receivers resulting in high observation angles and small ranges at most locations, narrower notches and, most importantly, multiple-Doppler coverage from other bistatic couplets in the notches. Of course velocity information can be retrieved at signal levels significantly below the displayed SNR=1 levels of Figure 7.
The use of vertical polarization moves the low-sensitivity notch from the ground to a vertical plane over the transmitter-receiver baseline. Figures 8a and 8b show the minimum detectable equivalent reflectivity factor when using vertically polarized transmitted radiation. Bistatic systems that employ circular polarization would have no low-sensitivity notch. While not nearly as sensitive as a traditional monostatic weather radar, the displayed bistatic configuration, using vertically polarized transmissions, provides a minimum sensitivity of 0-10 dBZ within the useful multiple-Doppler lobes and below -5 dBZ within 4 km of the receiving site. This is adequate for most purposes, but applications that require extreme sensitivity need to use higher gain receiving antennas, say 25 dB, shorter transmitter-receiver baselines, or multiple receiver configurations to achieve sensitivities below -15 dBZ. Again, it is important to note that velocity information can be retrieved at signal levels significantly below the display SNR=1 levels of Figure 8.
It has been assumed, in these calculations, that the scattering particles are perfect Rayleigh scatterers. If large hail is present, then Mie scattering formulations must be used and the expected power and location of low sensitivity notches will be altered. Large hail may be indicated in regions where the received power deviates from that predicted by Rayleigh approximation formulations.
where VRi are the radial velocities measured by the n radars, ai and ei are the azimuth and elevation angles of the n radars, and u,v,wp are the Cartesian components of the particle velocity field. In dual-Doppler analyses the vertical air parcel velocity, wa, is obtained through the integration of mass continuity. If measurements are available from more than three radars (or more than two, in the case of dual-Doppler analyses where mass continuity is used), and a reflectivity-terminal velocity relationship is assumed, the system of equations is overdetermined and can be solved by minimizing error.
where VRi are the particle velocities perpendicular to the ellipsoidal constant phase surfaces calculated from the Doppler shifted radiation at the n bistatic sites, ai and ei are the azimuth and elevation angles of the illuminated volume relative to the n passive receiving sites, VRt is the radial velocity calculated at the transmitting radar, and at and et are the pointing angles of the transmitting antenna. Equation (3) for a three receiver network can be solved for (u,v,wp) as follows:
The overdetermined cases can be solved similarly, by minimizing error.
Typical standard deviations in bistatic networks are twice that of monostatic networks consisting of comparable numbers of radars. Figure 9 shows the standard deviations in overdetermined dual-Doppler horizontal and the triple-Doppler vertical particle velocity syntheses using one monostatic transmitter, two bistatic receiver radar network compared with a three monostatic transmitter radar network.
Since the cost of bistatic receiving sites are very low, less than 1/30 of that of conventional transmitters, it is practical to deploy many of them in a typical network. In this fashion, accurate windfields can be retrieved at a much lower cost than with traditional systems. Figure 10 shows the same fields as Figure 9, but comparing a one monostatic ten bistatic radar network with a four monostatic radar network in an airport or regional surveillance application. The ten bistatic radar network provides extremely accurate windfield synthesis. The vertical particle velocities are determined accurately down to elevations below 2 km allowing mid- and low- level boundary conditions to be applied to the downward integration of mass continuity as described in Wurman (1991), thus avoiding common problems associated with the establishment of ground level boundary conditions. The cost of such a network is less than that of a two transmitter monostatic radar network and less than 1/3 that of the compared four monostatic transmitter network.
Volume update rates are limited by the most slowly scanning radar. Consequently, rapid-scanning and other exotic and expensive techniques cannot escape this difficulty unless all radars in a network employ new methods and/or new technology. Bistatic networks employ only one source of illumination from the single transmitter. Therefore, all data from individual resolution volumes are taken simultaneously. If a single rapidly-scanning transmitter is used, then short-interval multiple-Doppler analyses can be performed.
Bistatic networks, in contrast, are much less expensive. One high cost monostatic transmitting radar must be acquired, if an existing one is not available. The addition of several passive receiving sites is relatively inexpensive. These receivers, containing no moving parts or transmitting hardware, require an investment of less than $50,000, generally less than 1/30 that required for an additional transmitter. The bistatic sites can function unattended, thus saving significantly on operational expenses. Consequently, a network containing ten or more receivers can be purchased and operated for less than the cost of a single additional transmitter. The accuracy of retrieved windfields from such a network is roughly equivalent to that of a four monostatic transmitter system, even if storm evolution errors are neglected. Universities or other organizations who currently have single transmitters could easily achieve multiple-Doppler capabilities and enhance their capability to study a wide range of atmospheric phenomenon on a continual basis. Airports or other sites could upgrade NEXRAD installations into full bistatic multiple-Doppler networks which could explicitly resolve the full vector winds of severe weather events and aircraft wake vortices. Mesoscale and other models could be initialized with the winds retrieved by these networks.
Much of this scattered radiation passes completely through intense weather to be detected by the receivers or wasted into space or the ground. A portion, however, is scattered again within the storm or by another storm. Some of this multiply scattered radiation reaches the receiver as illustrated schematically in Figure 11. In systems using 0.1 m transmissions, the probability of a scattered photon being scattered again is usually small, ( only 1/2200 per 300 meters even in a 60 dBZ environment ). At 0.05 m, and especially at 0.03 m, the probability is much higher.
Since all radiation arriving at the receiver at any particular delayed time period from transmission is assigned to the same location according to the ranging equations, the integrated intensity of the radiation arriving from all multiple scattering paths must be compared to the intensity from the single scattering path in order to determine the level of contamination. With a high gain receiving antenna, only multiple scattering paths that re-enter the narrow beam must be considered since the antenna rejects signals entering from other angles. One of the rare situations in which this is significant is the flare echo, described in Zrnic (1987) and Wilson and Reum (1988). With wide angle bistatic antennas, however, many possible re-entry paths into the receiver need to be considered.
The results of a simple Monte-Carlo simulation of l = 0.1 m photons scattering illustrate this result more quantitatively (Figure 12). In the model, photons were scattered from an assumed narrow beam of radiation that penetrated an intense weather echo. The number of photons impacting on the bistatic receiver as a function of time was summed. In this simple model, scattering was assumed to be isotropic. The relative intensity of multiply and singly scattered radiation is shown as an equivalent reflectivity. This is defined as the monostatic reflectivity factor that would have resulted in the same number of photons being received at the bistatic site as a result of primary scattering. This idealized case shows how very sharp reflectivity gradients will be unresolvable in low gain bistatic systems. The presented simulation represents a pathological worst case where the 60 dBZ reflectivity region covers 1/2 of the sky visible from the receiver.
The limitations of multiple scattering and its 1/l4 dependence may require that bistatic Doppler networks use the longest practical transmitted wavelengths, preferably 0.1 m or even longer. It is possible that sophisticated signal processing techniques may be able to distinguish between single scattering and multiple scattering signals, perhaps by comparing with data from other receivers in the network. The use of higher gain receiving antennas reduces this problem at the cost of reducing the atmospheric volume visible to each receiver.
Observations with monostatic radars show that the intensity of contamination from this effect is about 60 dB below the average intensity of radar echoes covering large portions of the sky, effectively limiting the useful dynamic range of monostatic radars. This level of contamination results after two-way reduction of the antenna side-lobes, both at transmission and at receipt. Bistatic receivers may employ non-rotating antennas that range from quasi-omnidirectional to relatively high gain. Using the 60 dB two-way signal rejection value from above, truly omnidirectional receivers are limited to approximately 30 dB of effective dynamic range. A more typical receiver, employing a 15 dB horn, receiving signals from a dual-Doppler lobe with dimensions of roughly 60 x 20 degrees, would have 45 dB of dynamic range. Receivers customized for boundary-layer work or wake-vortex detection in limited regions could use antennas with much higher gains resulting in much greater effective dynamic ranges. Higher gain antennas employed for aircraft wake vortex detection or other purposes can have values of 55 dB or more.
There are several approaches to meeting this timing requirement, falling into two main categories. In the first, extremely accurate time is kept at both the transmitter and receiver sites and the pulse transmission time is sent, possibly by telephone line, to the receiver sites. The information will arrive well after scattered radiation, but if the pulse repetition frequency changes only rarely, the time of previous pulse transmissions can be used to calculate those in the future. In the second method, the transmitted pulse is detected directly at the receiving sites. This direct radiation, from the existing side-lobes or through radiation beamed intentionally at the remote receiving antennas, will always arrive before any scattered radiation and can be used to start a ranging clock.
Atomic clocks can provide extreme timing accuracy but drift relative to each other. Even though accurate within 1 part in 1012, they will tend to drift apart by roughly 100 ns per day. Therefore these clocks have to be re-calibrated frequently. Either as a method of re-calibration or as an independent timing method, the arrival time of direct path radiation from the side-lobes of the transmitter antenna could be measured. This radiation may be difficult to detect in sheltered locations, thus complicating the accurate calculation of its arrival time. The preferred method of achieving both timing and frequency coherence is to link both sites to an external standard. Both Loran and Global Positioning Satellite (GPS) signals can provide the needed information, but only the GPS signals include time-of-day information so that the timing coherence can always be maintained without re-calibration. Both signals can be used to achieve frequency coherence to well within one part in 1010 ( 0.3 Hz at l = 0.1 m ) if disciplined oscillators with high short-term stability are used.
Some very early and encouraging pre-deployment results in a light precipitation event are presented in Figure 15. This data was taken while the receiver was still in the laboratory only 10 km from CP-2 and as a result the region of expected low error in the bistatic dual-Doppler analysis is correspondingly smaller than that of the configuration in Figure 14. Horizontal windfield vectors illustrate a fairly constant NNE flow at about 10 m/s in both the monostatically and bistatically calculated fields. There is close agreement, within 1-2 m/s, between the two fields throughout much of the intersection region of the bistatic and monostatic dual-Doppler low expected error lobes in the center of the plotted region. The differences in the two fields probably arise from several factors, including the lack of clutter rejection in the bistatically retrieved velocities and the spread of the Mile High Radar beam through strong vertical windshear in the monostatically retrieved velocities.
In addition, preliminary frequency and timing coherence testing using the Mile High Radar, which has had no frequency generation hardware modifications, has been conducted. Early results indicate that bistatic receivers may successfully be used with unmodified NEXRAD-type radars ( with the sensitivity limitations associated with horizontally polarized transmissions noted in Section 4 ). A more complete description of these tests and resulting data will also be presented in a subsequent paper.
The prototype network contains just one passive bistatic receiving site. A block diagram schematic of the prototype bistatic network is shown in Figure 16. Frequency and timing coherence are achieved through the use of GPS signals. The CP-2 generating hardware has been replaced with a GPS-locked system. Pulse transmission timing and transmitter pointing angles as well as other information are being sent via telephone line to the receiving site.
A major objective of this prototyping is the construction of an inexpensive and portable bistatic receiver. The receiver antenna is a standard 15 dB horn ( entire assembly less than 0.03 m3 and 10 kg ) pointing into one of the dual-Doppler lobes. Standard mixing and filtering elements are being used. Frequency and timing coherence are achieved by using commercially available, personal computer-based GPS frequency locking hardware. It has been found that frequency and timing coherence can also be maintained for several hours after being manually set by zeroing the Doppler shift of direct path signals from CP-2. Data acquisition and signal processing occur on cards which also fit inside the personal computer. Specialized frequency multiplying and synthesizing equipment provides both S-Band and IF signals to the transmitter and the receiver. The complete receiving unit has a volume of less than 1 m3, a mass of less than 40 kg, plugs into a standard AC electrical outlet, and can be placed on a desk or in an automobile. Based on the costs of this prototype, is anticipated that future receiving units can be assembled for less than $50,000.
The simultaneity of the sampling of individual resolution volumes reduces errors associated with storm evolution. It remains true that evolution will occur during the time associated with a complete volume scan by the transmitter, and in a rapidly evolving convective situation, this could be significant. But, bistatic networks are uniquely suited to take advantage of new rapid-scanning techniques and phased array transmitters. In a bistatic network, only one exotic and expensive radar transmitter need be purchased and operated in order to achieve rapid updates of full three-dimensional vector winds in complete volumes.
The extremely low cost of passive bistatic receiving sites makes bistatic networks very attractive when compared to traditional monostatic networks. For the equivalent expense of much less than two monostatic radar transmitters, weather sensitive sites such as airports can be provided with full three-dimensional vector winds from a one transmitter, ten receiver system. This affordability makes them practical for a wider and more frequent range of scientific studies. They could be used on an operational basis to initialize numerical models with full three-dimensional velocities rather than merely radial winds. Aircraft wake vortices of arbitrary orientation could be detected through the use of the combination of upwardly looking bistatic receivers and monostatic transmitter/receivers.
The limitations of low gain systems, namely low sensitivity ( ~ 5 dBZ at 10 km range as compared to -25 dBZ for monostatic, high antenna gain, radars ), reduced dynamic range, and sensitivity to multiple scattering must be considered. Either they must be tolerated as acceptable to applications, or they must be minimized. Many applications can accept the 5 dBZ sensitivity limitation since most severe weather over much of North America occurs at much higher reflectivities. The limitations of multiple and side-lobe scattering are usually not important. The use of higher gain receiving antennas, say 20-25 dB, would significantly improve both sensitivity and resistance to side-lobe contamination. Multiple antennas at each passive site ( or many nearby sites ) would have to be used to cover the same volume and would require additional processing power. Still, the cost of a complete receiving network could be kept below that of a single additional transmitting monostatic radar.
Figure 16. double column width 6.5 inches Wurman, et al. Paper HK-128
Atlas, D.,K. Naito, and R.E. Carbone, 1968: Bistatic microwave probing of a refractively perturbed clear atmosphere. Journal of the Atmospheric Sciences, 25, 257-268.
Battan, L.J., 1959, Radar Observation of the Atmosphere, revised edition, University of Chicago Press, Chicago, IL, 324 pp.
Crane, R.K., 1973: Analysis of Data from the Avon-to-Westford Experiment, Technical Report 498, Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, MA, 45 pp.
Doviak, R.J., and D.S. Zrnic, 1993, Doppler Radar and Weather Observations, second edition, Academic Press, San Diego, CA, 562 pp.
Doviak, R.J., J. Goldhirsh, and A.R. Miller, 1972: Bistatic-radar detection of high-altitude clear-air atmospheric targets. Radio Science, 7, 993-1003.
Doviak, R.J., and C.M. Weil, 1972: Bistatic radar detection of the melting layer. J. Appl. Meteor., 11, 1012-1016.
Lhermitte, R.M., 1968: New developments in Doppler radar methods. Proceedings, 13th Radar Meteorology Conference, Montreal, Canada, American Meteorological Society, Boston, MA, 14-17.
Lhermitte, R.M., and M. Gilet, 1976: Acquisition and processing of tri-Doppler data. Proceedings, 17th Radar Meteorology Conference, Seattle, WA, American Meteorological Society, Boston, MA, 1-6.
Pratte, J.F., and R.J. Keeler, 1986: Sensitivities of operational weather radars. Preprints, 23rd Conference on Radar Meteorology and Conference on Cloud Physics, Snowmass, CO, American Meteorological Society, Boston, MA, JP333-336.
Ray, P.S., C.L. Ziegler, and R.J. Serafin, 1980: Single- and multiple-Doppler radar observations of tornadic storms. Monthly Weather Review, 108, 1607-1625.
Rogers, P., and P. Eccles, 1971: The bistatic radar equation for randomly distributed targets. Proceedings of the IEEE, 59, 1019-1021.
Wilson, J.W., and D. Reum, 1988: The flare echo: reflectivity and velocity signature. J. Atmos. Ocean. Technol., 5, 197-205.
Wurman, J., 1991: Forcing mechanisms of thunderstorm downdrafts. Preprints, 25th International Conference on Radar Meteorology, Paris, France, American Meteorological Society, Boston, MA, J63-66.
Zrnic, D.S., 1987: Three-body scattering produces precipitation signature of special diagnostic value. Radio Science, 22, 76-86.
