On the meteoric head echo radar cross section angular dependence



[1] We present radar cross section (RCS) measurements of meteor head echoes observed with the tristatic 930 MHz EISCAT UHF radar system. The three receivers offer a unique possibility to accurately compare the monostatic RCS of a meteor target with two simultaneously probed bistatic RCSs at different aspect angles. Meteoroids from all possible directions entering the common volume monitored by the three receivers are detected, out to an aspect angle of 130° from the meteoroid trajectories. The RCS of individual meteors as observed by the three receivers are equal within the accuracy of the measurements. This is consistent with an essentially isotropic scattering process as has previously been inferred from polarization measurements by S. Close et al. (2002). There is a very weak trend present in our data suggesting that the RCS may decrease at a rate of 0.2 dB per 10° with increasing aspect angle.

1. Introduction

[2] The first meteor head echo investigations carried out with what today is termed a high power large aperture (HPLA) radar were conducted by Evans [1965, 1966] with the 440 MHz Millstone Hill radar. The transient and strongly Doppler-shifted characteristics of the echoes supported the assumption already suggested by McKinley and Millman [1949] that head echo targets are compact regions of plasma, co-moving with the meteoroids and relatively independent of aspect. The much smaller radar cross section (RCS) as compared to that of meteor head echoes observed at longer wavelengths [McIntosh, 1963], however, lead Evans to the conclusion that what he observed was something different from previously reported head echoes. Yet the difference is more likely an indication of strong head echo RCS wavelength dependence [Close et al., 2002].

[3] Jones and Webster [1991] have analyzed meteor head echoes observed with the 33 MHz radar at the Springhill Meteor Observatory. The azimuthal symmetry of the detected meteors encouraged the assumption of an isotropic reflection process. The same conclusion was drawn by Close et al. [2002], who have investigated the polarization ratio of the head echoes at 160 MHz and 422 MHz with ALTAIR (Advanced Research Projects Agency Long-Range Tracking and Instrumentation Radar). The received polarization ratio was high regardless of detection altitude, RCS, or aspect angle, a result consistent with spherical targets.

[4] The head echo scattering process is still an open issue, but a comprehensive understanding of it is crucial to fully make use of the vast volume of observational data, e.g., for global mass influx estimations [Janches et al., 2006]. An example of an analytical model of the head echo is given by Close et al. [2004], and numerical simulations have been performed by Dyrud et al. [2007a].

[5] We present tristatic observations of meteor head echoes conducted with the 930 MHz EISCAT (European Incoherent SCATter facility) UHF radar system located in northern Scandinavia. The geographical configuration of the three receivers has been exploited such that the common volume of the antenna beams was simultaneously viewed from disparate angles, enabling a comparison of the monostatic RCS with two bistatic RCSs.

2. Experiment Overview

[6] The data used in this study have been recorded during a series of campaigns carried out with the 930 MHz EISCAT UHF system from 2002 to 2005 [Szasz et al., 2007]. The radar system comprises three Cassegrain antennae with 32 m primary reflectors and 4.48 m secondary reflectors. The transmitter (which is also used as a monostatic receiver) is located near Tromsø, Norway (69.59°N, 19.23°E) and the two remote receivers are located in Kiruna, Sweden (67.86°N, 20.44°E) and Sodankylä, Finland (67.36°N, 26.63°E). The azimuth, elevation and range from the three antennae to the common volume were kept constant during the campaigns collecting the presented data and are summarized in Table 1. The angle between the Kiruna antenna pointing direction and the Tromsø beam was 75.6°. The corresponding figure for Sodankylä and Tromsø was 122.2°.

Table 1. Azimuth, Elevation, and Range From the Three Antennae to the Common Volume
Range160.4 km278.5 km163.6 km

[7] A 32-bit coded pulse sequence with binary phase shift keying (BPSK) and a bit length of 2.4 μs were used in all experiments, giving total pulse lengths of 76.8 μs (G. Wannberg et al., The EISCAT meteor code, submitted to Annales Geophysicae, 2008). The transmitted waves are left- and the received waves are right-hand circular in Tromsø. The signals at the remote receivers are elliptically polarized due to the oblique tristatic geometry and the electron scattering cross-section being angular dependent.

[8] For optimal decoding of the received echo sequences from a moving meteor target, the Doppler-shift has to be taken into account. We use an inverse algorithm to optimize the pulse compression by finding (1) the sequence of recorded complex voltage samples that constitute a meteor echo in each received radar pulse sequence and (2) the Doppler-shift of each echo.

[9] The received signals were oversampled by a factor of four at all sites with a 0.6 μs sampling period. The experiment pulse repetition frequency was 604 Hz, which typically provides more than 30 independent measurements of the RCS at each receiver during the passage of a meteoroid through the common volume.

3. RCS Calculations

[10] The RCS of the meteor head echoes at each receiver is estimated by a suitable version of the radar equation [Skolnik, 1962]:

equation image



= radar cross section,


= received power,


= receiver range,


= transmitter range,


= receiver antenna gain,


= angular distance from receiver boresight axis,


= transmitter antenna gain,


= angular distance from transmitter boresight axis,


= radar wavelength,


= receiver polarization factor, and


= transmitted power.

The received power is given by

equation image

where Tmet is the equivalent signal temperature of the echo, kB is the Stefan-Boltzmann constant, and bw is the receiver bandwidth. The equivalent signal temperature, Tmet, is calculated by multiplying the signal-to-noise ratio with the equivalent system temperature, Tsys, which is estimated by calibration noise injection and continuously monitored during experiments. The noise levels of the calibration sources at all receivers have been independently verified with measurements of the off-ecliptic sky noise and supernova remnant Cassiopeia-A. The receiver polarization factor, Ψr, compensates for the geometry dependent reduction of the scattered power towards the remote receivers.

[11] The EISCAT UHF antennae are identical and have a maximum gain of G(0) = 48 dB and a full one-way −3 dB beam width of nearly 0.7° [EISCAT Scientific Association, 1978]. The measured beam width is best described by a primary reflector size of 30 m. We have adopted this value to estimate the antenna gain, G(θ), as a function of an angular displacement, θ, from the bore axis, utilizing an ideal radiation pattern [Nygrén, 1996]. The secondary reflector support structure induces azimuthal sidelobe gain variations, which we have not tried to take into account. We therefore restrict ourselves to only use the RCS measurements of meteors detected within the −3 dB beam width. The position of a meteor target is determined to an accuracy better than 100 m from the ranges measured at the three receivers (J. Kero et al., Determination of meteoroid physical properties from tristatic radar observations, submitted to Annales Geophysicae, 2008). It is situated in the intersection point of three geometrical shapes: a sphere centered on the Tromsø antenna and two prolate spheroidal surfaces, both with Tromsø in one focal point and one of the remote antennae in the other one.

4. RCS Observations

[12] The tristatic EISCAT UHF system offers a unique possibility to observe the same meteor from three directions simultaneously when the meteoroid travels through the common volume. A meteor head echo is characterized by being transient and usually highly Doppler-shifted. The target is always confined within a range bin (90 m) and the range rate is equal to the Doppler-shift of the echo to a very high precision (Wannberg et al., submitted manuscript, 2008). The received power is compared to the beam pattern traced out along the trajectory of a meteoroid during its passage through the common volume. About 40% of the events have time profiles of the received power that resemble the beam pattern. The rest deviate significantly. Differences may be caused by ionization bursts due to, e.g., quasi-continuous disintegration, gross fragmentation, interference from a few distinct and simultaneously illuminated fragments [Kero et al., 2008], or plasma effects. An example of the latter is given by Dyrud et al. [2007b], whose simulations show that the RCS may undulate if the peak plasma frequency of the head-echo target is close to the radar frequency.

[13] The velocity components of the meteoroids measured at the three receivers are utilized to calculate their direction of arrival in the common volume, presented as azimuth and zenith distance in Figure 1. It is evident from the figure that there are no blind regions of arrival from which meteors are undetectable. The monostatic RCS measured in Tromsø (RCST) is displayed in color for the 265 meteors that appear within the −3 dB width of the antenna beam. There are more meteoroids arriving from the south-west region, the direction of the Earth apex during the forenoon. A full review of the astronomical aspects of the detected meteoroids will be given by C. Szasz et al. (Orbit characteristics of the tristatic EISCAT UHF meteors, submitted to Monthly Notices of the Royal Astronomical Society, 2008). The collection of detections from this region is an effect of the strengths and locations of the sporadic meteor sources [Jones and Brown, 1993] during the measurements and not a selection effect caused by the scattering geometry.

Figure 1.

Azimuth and zenith distance of the direction of arrival for 410 tristatic meteors (triangles). The frame circles correspond to zenith distances 15°, 30°, 45°, 60°, and 90°. The monostatic radar cross section (RCS) measured in Tromsø (RCST) is displayed in color for the 265 events inside the −3 dB width of the Tromsø antenna beam.

[14] We assume that a meteor target is rotationally symmetric around the meteoroid trajectory. Hence we define the Tromsø aspect angle, ɛT, as the smallest angle from a meteoroid's direction of propagation to the line-of-sight direction of the Tromsø receiver. Bistatic aspect angles, ɛKT and ɛST, are defined similarly but measured from the direction of propagation to the two interior bisectors of the angles between the transmitter beam and each remote receiver beam. Figure 2 reports the aspect angle distributions of the detected meteors, as well as an explanatory sketch where the aspect angles are defined. Meteors are observed at virtually all possible aspect angles, limited by the antenna pointing directions.

Figure 2.

Distribution of the number of tristatic meteors as a function of aspect angle with respect to the Kiruna-Tromsø bisector (ɛKT), the Sodankyl-Tromsø bisector (ɛST), and the Tromsø beam (ɛT). The aspect angles are illustrated in a sketch.

[15] Figure 3 shows the RCS measured with each antenna (Kiruna: RCSK, Sodankylä: RCSS, Tromsø: RCST) versus the simultaneously measured RCS with both of the others for the meteors that are within the −3 dB width of all three antenna beams. The RCS is expressed in dB relative to one square meter (dBsm) and spans from about −58 to −24 dBsm (1.6 mm2 to 40 cm2). Thus the RCS for different meteors vary over several orders of magnitude. The RCS diversity is not correlated with the angle between the trajectory and any combination of transmitter and receiver beams, but may in a complex manner be attributed to the combination of radar and plasma parameters [Dyrud et al., 2007b], and primarily to the meteoroid mass and velocity distributions [Close et al., 2007].

Figure 3.

The monostatic RCS measured in Tromsø (RCST) versus the simultaneously measured bistatic RCS in (left) Kiruna (RCSK), (middle) Sodankylä (RCSS), and (right) RCSS versus RCSK.

[16] The linear least-squares with fit to (left) RCST versus RCSK, (middle) RCST versus RCSS, and (right) RCSS versus RCSK have slopes of 1.03, 0.99, and 0.97 respectively. The residuals of fits with a slope equal to unity are randomly scattered with standard deviations of 1.8 to 2.3 dBsm. This scatter is larger than accounted for by the uncertainty in the determined meteoroid positions in the antenna radiation pattern alone. Also other uncertainties may contribute to the scatter; a few examples follow: (1) the three independent decoding procedures may have converged slightly differently, (2) interference due to echoes produced by more than one simultaneously illuminated meteoric fragment will in general be aspect angle dependent [Kero et al., 2008], (3) increased amounts of ionization from sudden meteoroid break-up processes may give angular dependent bursts in the RCS, and (4) plasma effects [Dyrud et al., 2007a, 2007b].

5. RCS Aspect Angle Dependence

[17] The RCS of different meteors varies over several orders of magnitude and does not reveal any aspect angle dependence. To investigate this further we have compared the simultaneously detected RCS at the different receivers for each meteor one by one. Ratios of the measured RCS are plotted versus the differences in the aspect angles of the detections in Figure 4: (top) the ratio of RCSK to RCST versus the difference ɛKT−ɛT, (middle) the ratio of RCSS to RCST versus ɛST−ɛT, and (bottom) the ratio of RCSS to RCSK versus ɛST−ɛKT. There is a weak trend present in all three RCS ratios, most prominent in the ratio of RCSS to RCST. This hints that the RCS decreases with increasing aspect angle, although the scatter of the data is larger than the trend. A linear least-squares fit gives a slope of about −0.13 dB per 10° for the ratio of RCSK to RCST, −0.28 dB per 10° for the ratio of RCSK to RCSS, and −0.20 dB per 10° for the ratio of RCSS to RCSK. The weak angular dependence we find is consistent with the polarization measurements by Close et al. [2002] where no trend was found, possibly limited by their signal-to-noise ratio.

Figure 4.

The ratio of the detected RCS versus the difference in aspect angle (as defined in Figure 2) for the 173 tristatic meteors within the −3 dB beam widths of all three antennae.

[18] Dyrud et al. [2007a] have done numerical modeling of meteor head echoes with finite difference time domain electromagnetic simulations. The head echo characteristics are investigated by comparing the simulated impinging and reflected electric field from a meteor plasma using particle-in-cell ions. Dyrud et al. [2007b] find a RCS aspect sensitivity of −0.43 dB per 10° for monostatic scattering, a value comparable to our observations. It should be stressed that our presented RCS ratios are estimated by comparing a bistatic RCS to the monostatic RCS or another bistatic RCS while the reported simulations were carried out assuming monostatic scattering.

6. Conclusions

[19] The head echoes observed with the tristatic EISCAT UHF system are detected at virtually all possible aspect angles all the way out to 130° from the direction of meteoroid propagation, limited by the antenna pointing directions. The RCS of individual meteors measured simultaneously at the three receivers are consistent within the accuracy of the measurements. The ratios of the RCS measured at the different receivers show a slight trend with respect to aspect angle. Larger aspect angles give rise to smaller RCS values. The RCS is close to isotropic in the whole observable range, consistent with an essentially spherical target as first measured by Close et al. [2002].

[20] The results are in quite satisfactory agreement with the plasma and electromagnetic simulations of meteor head echoes performed by Dyrud et al. [2007a], in which a weak aspect angle dependence is present.


[21] We gratefully acknowledge the EISCAT staff for their assistance during the experiment. EISCAT is an international association supported by research organizations in China (CRIPR), Finland (SA), France (CNRS), Germany (DFG), Japan (NIPR and STEL), Norway (NFR), Sweden (VR), and the United Kingdom (STFC). Johan Kero and Csilla Szasz are supported by the Swedish National Graduate School of Space Technology.