Meteor radar response function: Application to the interpretation of meteor backscatter at medium frequency

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109,, doi: /2004ja010450, 2004 Meteor radar response function: Application to the interpretation of meteor backscatter at medium frequency M. A. Cervera 1,2 Intelligence Surveillance and Reconnaissance Division, Defence Science and Technology Organisation, Edinburgh, South Australia, Australia D. A. Holdsworth 2 and I. M. Reid 2 Atmospheric Radar Systems Pty. Ltd., Thebarton, South Australia, Australia M. Tsutsumi National Institute of Polar Research, Tokyo, Japan Received 26 February 2004; revised 8 June 2004; accepted 26 August 2004; published 16 November [1] Recently, Cervera and Elford (2004) extended earlier work on the development of the meteor radar response function (Elford, 1964; Thomas et al., 1988) to include a nonuniform meteor ionization profile. This approach has the advantage that the height distribution of meteors expected to be observed by a radar meteor system is able to be accurately modeled and insights into the meteoroid chemistry to be gained. The meteor radar response function is also an important tool with regard to the interpretation of meteor backscatter in other areas, e.g., modeling the expected diurnal variation of sporadic meteors, investigating the expected echo distribution over the sky, and the calculation of the expected rate curves of meteor showers. We exemplify each of these techniques from the analysis of meteor data collected by the Buckland Park 2 MHz system during October In addition, we show that the response function may be used to quantify the echo rate of a given shower relative to the sporadic background and thus determine if that shower is able to be detected by the radar. INDEX TERMS: 6245 Planetology: Solar System Objects: Meteors; 6952 Radio Science: Radar atmospheric physics; 6949 Radio Science: Radar astronomy; 6999 Radio Science: General or miscellaneous; KEYWORDS: meteors, meteor radar, response function Citation: Cervera, M. A., D. A. Holdsworth, I. M. Reid, and M. Tsutsumi (2004), Meteor radar response function: Application to the interpretation of meteor backscatter at medium frequency, J. Geophys. Res., 109,, doi: /2004ja Introduction [2] It has previously been shown that for a given radar system the theoretical echo rate of meteors originating from a particular point source radiant may be determined and performing this analysis for all radiants over the sky yields the response of the radar to meteor backscatter [Elford, 1964; Thomas et al., 1988; Ceplecha et al., 1998]. This analysis, the result of which is termed the meteor response function, employed a uniform meteor ionization profile. Recently Cervera and Elford [2004] described modifications to the meteor radar response function analysis which used a more realistic nonuniform meteor ionization profile. The main advantage of their approach was that they were 1 Also at Atmospheric Radar Systems Pty. Ltd., Thebarton, South Australia, Australia. 2 Also at Department of Physics and Mathematical Physics, University of Adelaide, Adelaide, South Australia, Australia. Copyright 2004 by the American Geophysical Union /04/2004JA able to accurately model the height distribution of meteor echoes expected to be observed by a radar system. Once developed, they employed their modified meteor response function to investigate meteor backscatter observed by narrow beam MST radars. In particular, Cervera and Elford [2004] examined the effects of the beam zenith angle on the expected echo rates and angles of arrival and how the meteor echo rates and height distribution varied with the carrier frequency of the radar, the meteoroid composition and preablation speed. [3] Cervera and Elford [2004] showed, as expected, that for beams oriented closer to zenith the overall echo rates were lower while the sidelobe response increased. The effect of the radar carrier frequency on the meteor echo rates and their height distribution was also expected with lower-frequency radars able to observe meteors at much greater altitudes. They noted that the effect of the preablation meteoroid speed on the expected rates and height distribution of meteor echoes were higher echo rates and a greater altitude of ablation with larger meteoroid speeds. This has important implications for the measurement of the 1of10

2 Table 1. Experimental Parameters Used for Meteor Observations With the BPMF Radar Parameter Value Peak transmit power, kw 50 Transmit half-power full width, deg 10 Transmit beam zenith, deg 24 Transmit beam azimuths, deg 0, 90, 180, 270 Transmit polarization linear PRF, Hz 16 Coherent integrations 4 Effective sampling time, s 0.25 Number of samples 380 Record length, s 95 Sampling height resolution, km 2 Number of heights 40 Start height, km 70 Number of receivers 5 meteoroid speed distribution as traditional VHF meteor radars are biased against the detection of high-velocity meteoroids ablating at high altitudes (the so-called meteor echo height ceiling effect). [4] The investigation of meteor backscatter observed by MST radars by Cervera and Elford [2004] was performed using hypothetical radars. In this paper we turn our attention to a real radar system, the Buckland Park 2 MHz system, and employ the meteor radar response function to model the expected height distribution, diurnal variation and the distribution of meteor echoes over the sky during 22 October These expected results are then compared with observations from this period. The response function will also be used to investigate the expected flux of the Orionids meteor shower relative to the background sporadic meteors. We show that useful insights relating to expected shower echo rates and hence which showers are able to be observed by particular radar systems are realized through an analysis of the response function. 2. Experimental Setup and Meteor Detection [5] The Buckland Park medium frequency (BPMF) radar [e.g., Briggs et al., 1969] is located 35 km north of Adelaide ( S, E). The radar operates at a frequency of 1.98 MHz. The main antenna array consists of 89 crossed half-wave dipoles arranged in a square grid with spacing 91.4 m, forming a filled circle of diameter 914 m. The radar has recently been overhauled [Reid et al., 1995], involving the complete replacement of the antenna array and the transmitting and receiving system. The main array can now also be used for transmission, enabling the radar to operate as a true Doppler radar [Vandepeer and Reid, 1995]. [6] The observations described in this paper were conducted between 0040 and 0546 LT on 22 October 1997 [Tsutsumi et al., 1999]. The radar operating parameters are shown in Table 1. Transmission was performed using the north-south aligned antennas, resulting in a linearly polarized transmitted signal with half-power full width of about 10. The transmit beam direction was steered every two minutes between four directions with azimuth angles of 0, 90, 180 and 270 and zenith angle 24. A PRF of 16 Hz was used to avoid range aliasing from multihop F region returns. Reception was performed on five east-west aligned dipoles forming an interferometer with baselines of 91.4 m (0.6l) and 457 m (3l) for angle of arrival (AOA) determination. As the shortest baseline exceeds 0.5l, AOAs cannot necessarily be determined without ambiguities. Echoes at a zenith angle of larger than 56.4 contaminate the first lobe of the interferometer. However, considering that more than 90% of underdense meteor echoes occur at heights above 80 km [Nakamura et al., 1991], ambiguities can be avoided by limiting the maximum sampling range. If the lowest height a meteor can be detected is assumed to be 80 km, echoes which return at the zenith angles larger than 56.4 are never sampled at ranges below 145 km. We therefore set the radar sampling range to be between 70 to 148 km in the present study. In reality, some ambiguities can exist because echoes can be detected below 80 km. However, echoes at the lower altitudes can be easily identified due to their long (>20 s) decay times. These echoes were removed for the subsequent analysis. [7] Meteor echoes were detected and processed as follows Detection [8] Meteor echo candidates were detected by requiring the power series of receiver 1 to exceed a meteor echo model. The model used was an exponential with peak power 6 db above the noise level and a decay time of 1.5 s. Echoes with a peak signal-to-noise ratio (SNR) greater than 10 db and a duration longer than 1.5 s were selected for further analysis. The relatively long pulse width (30 msec) used resulted in oversampling, with meteor echoes sometimes appearing in several adjacent range bins. To avoid using the same echo twice only the range bin with the strongest echo power was selected. In order to avoid contamination from E-layer scatter with meteor-like characteristics, only meteor echoes detected at ranges above 110 km are used in this study AOA Determination [9] AOAs of the detected candidates were estimated using the phase differences between the five receivers. The phase differences were calculated using the zero-lag cross-correlation phases of the time series ±1 s either side of the meteor echo. Calibration of the phase delays were carried out according to Holdsworth et al. [2004]. Phase differences estimated from the smallest baseline were first used to estimate rough arrival directions, and more accurate directions were determined by using the largest baseline Receiver Combining [10] The five complex series were coherently averaged after removing the phase differences. This theoretically increases the signal-to-noise ratio by 7 db. This is essentially equivalent to postset beam steering, and suppresses signals from locations other than the AOA Underdense Echo Selection [11] Underdense echoes were selected by searching the combined receiver power series. Power series showing a sharp (<1 s) increase and then an exponential decrease with time were identified as underdense echoes and used in the following analyses. All echoes were manually examined before being accepted Diffusion Coefficient Estimation [12] Ambipolar diffusion coefficient of each underdense echo was evaluated by least squares fitting an exponential 2of10

3 Figure 1. Geometry of the echo plane for the condition of specular backscatter. decay to the combined receiver power series between the peak of the meteor echo and the position where the echo falls to the noise floor. The peak of the echo was the largest power in echo time series while the noise floor was determined using the mean power at times outside meteor echo Radial Velocity Estimation [13] The radial wind velocity was estimated by least squares fitting a linear model to the combined receiver phase series between the peak of the meteor echo and the position where the echo falls to the noise floor. 3. Interpretation of MF Meteor Backscatter [14] Before we use the meteor radar response function to interpret the meteor backscatter observed by the BPMF radar we give a brief summary of its derivation. A full account is given by Cervera and Elford [2004]. [15] The maximum electron line density, q M, of a meteor produced from a meteoroid with a given preablation speed, v 1, is related to its zenith angle, c, and the preablation mass of the meteoroid, m 1, by q M / (m 1 ) a (cos c) b. If the heat capacity of the meteoroid and the energy lost by radiation are not included in the ablation theory, and that ablation is assumed to occur in an isothermal atmosphere then a = b = 1 [see, e.g., McKinley, 1961]. Cervera and Elford [2004] show from a comprehensive theory of ablation, which includes the above effects, that a = (V/40) and b = (V/40) 3.5, where V is the meteoroid speed in km/s. In their analysis they assumed a =1asadiffers from unity by less than 5% and we follow the convention. The response function analysis is carried out in terms of the maximum zenithal line density q z, i.e., the maximum value of the electron line density that would be produced if the meteoroid was incident vertically: q z = q M /(cos c) b. [16] The flux of meteoroids above an initial mass m 1 from a unit area of sky is assumed to be given by a simple power law m c 1, where c is the interplanetary mass index. Thus the flux of meteoroids with initial speeds v 1 that produce trails with maximum zenithal electron line densities greater than q z,is h i c: Nq ð z Þ ¼ Kq c z ¼ K q M ðseccþ b ð1þ The value of c varies inversely with meteoroid mass, but for those meteoroids that give rise to underdense meteor trails, radar measurements indicate that c = 1.0 ± However, for shower meteors c can vary from 1.8 to 0.4, and the assumption of an inverse power law distribution is not valid. The value of the constant K has been calculated by Thomas et al. [1988] based on meteor observations with the Jindalee radar (minimum detectable q z of m 1 ) and has the value of 1040 m 2 s 1 ster 1 (at least for this radar). If one is only interested in relative rate responses then the actual value of K is not needed as K is only a multiplicative factor and the response may be normalized to 1.0. [17] The condition of specular backscatter defines the geometry of the echo plane (see Figure 1). Analysis of all meteor reflection points P within the echo plane together with equation (1) yields the response function: Z nðq r ; f r Þ ¼ R E K N v ðv 1 v 1 Z h2 q c M h¼h 1 Þðcosec q r 1 þ h R E bc Z p=2 Þ ðbcþ F¼ p=2 ð Þ fdhdf dv 1 ; ð2þ where f ðf; hþ ¼ 1 þ h " 1 sin q sin 2 q þ 2h # 1=2 R E R E and h 1 and h 2 are the end and beginning heights of the meteor ionization profiles, R E is the radius of the Earth, N v (v 1 ) is the meteoroid velocity distribution, F is the azimuth angle of the meteor in the echo plane, and q r and f r are the radiant elevation and azimuth. ð3þ 3of10

4 meteors is N pulses above a threshold then a d is [Ceplecha et al., 1998] a d ¼ t 1 e T=t ; ð5þ T where T is the interpulse period and t is t ¼ l2 16p 2 D ; ð6þ Figure 2. Response of the BPMF radar to meteor backscatter for an east pointing beam 24 off zenith. The maximum response is to meteor radiants at an elevation and azimuth of (25.5, 278 ). The response function has been normalized to the peak response. [18] In order to carry out the response function calculation the value of q M that can just be detected at each position P in the echo plane is required as a function of v 1 and c. This requires suitable meteor ionization profiles at each v 1 and c and the minimum detectable electron line density q min of the radar system at each point P. For a given v 1 and c, ablating meteoroids produce unique ionization profiles (with maximum values q M ) which depend on their initial mass m 1. The specification of a particular value of q (viz. q min ) and a height h (from P) identifies a unique ionization profile and its associated q M (and m 1 ) for each v 1 and c. This value is used in equation (2). [19] Look up tables of q as a function of h for a range of values of v 1 and c were generated for the procedure detailed above. We used the ablation theory described by Cervera and Elford [2004] which considers the energy and momentum budgets of the ablating meteoroid and employs the Langmuir and Clausius-Clapeyron equations to describe the ablation of the meteoroid. [20] The minimum detectable electron line density is dependent on the parameters of the radar system. For underdense meteors q min is given by: the echo decay time constant for underdense meteors. [21] Figure 2 displays the response function for the BPMF radar for the main beam directed 24 off zenith eastward. Note the peak response occurs at an elevation of 25.5, 1.5 greater than expected from a simple argument based on the antenna pattern. This is due to the lower sensitivity of radars to meteor echoes with radiants originating from low elevations and is a result of the lowelevation meteoroids traversing a larger volume of the atmosphere. For these meteors the ionization is spread over a larger distance lowering the resultant electron line density of the trail. [22] The response from the east pointing main beam is sensitive to meteor radiants from the west. In addition, the effect of the sidelobes of the antenna pattern on the response function is clearly visible with high response to meteor radiants from the east. The effect is stronger than one might expect given that the sidelobes are down by 10 db on the main beam. However, one must also take into account the large transmitting volume of the sidelobes Height Distribution [23] The expected height distribution of meteor echoes is readily determined during the response function calculation by replacing the integration over height with an integration over all radiant positions on the sky [Cervera and Elford, 2004]: q min ¼ 6: R 3=2 P 1=2 R ðp T G T ðq; fþg R ðq; fþa r a v a d Þ 1 ; l ð4þ where R is range, P R is the minimum detectable power by the system, P T is the transmitted power, G T and G R are the transmit and receive gains, l is wavelength, and a r and a v are attenuation factors due to the initial radius of the trail and the finite velocity effect. We will not discuss these attenuation factors here; however, see Ceplecha et al. [1998] and Cervera and Elford [2004]. The quantity a d is an echo selection factor due the diffusion of the trail once formed and is dependent on the meteor echo detection criteria. If the detection criterion for underdense Figure 3. Comparison of the observed height distribution (solid line) with that calculated from the meteor radar response function (dashed line). 4of10

5 Z ZZ nh ðþ¼r E K N v v 1 sky gðb; l l Þðcosec q r Þ ðbcþ Z p=2 q c M 1 þ h ðbcþ fdfdwdv 1 ; ð7þ F¼ p=2 R E where g(b, l l ) is an appropriate meteor radiant distribution (in our case the sporadic meteor radiant distribution), b and l are the ecliptic latitude and ecliptic longitude of the meteor radiant, and l is ecliptic longitude of the Sun. It is convenient to use Sun-centered longitude as the position of the broad sources of the sporadic meteor radiant distribution (see the following section) are invariant over the year in this frame. To carry out the integration the (b, l l ) coordinate frame is required to be transformed to the (q r, f r ) coordinate frame. For our purposes we found that the form of g had a negligible effect on the height distribution and could be set to 1 for all (b, l). This had the advantage of simplifying the above integral. [24] This calculation has been performed for the BPMF radar during October, and the results appear in Figure 3 together with the observed height distribution. Atmospheric temperature and pressure are required as a function of height and we employ those values provided by the CIRA86 model atmosphere. The modeled height distribution has been normalized to the total number of echoes observed. A suitable meteoroid velocity distribution is required for the calculation and we use that measured by Cervera et al. [1997]. [25] The agreement between the modeled and observed height distribution is quite good. However, the observed height distribution is more sharply peaked and the maximum response occurs at a lower altitude. This is could be due to the atmospheric parameters, upon which the ablatory characteristics of meteoroids are highly dependent [Elford, 1980], that were input to the response calculation. These were monthly average values rather than actual values for the night in question. We would expect better agreement for observations averaged over several nights. It may be possible to gain insight into this sensitivity through the modification of the atmospheric conditions. [26] We note that the height distribution, both modeled and observed, has a much lower contribution from very high altitude meteors than observed by Steel and Elford [1991] and finishes at a lower altitude of 125 km as opposed to 140 km. This is due to the range cutoff of 148 km in radar data acquisition system and the echo detection requirement of underdense echoes with an echo duration >1.5 s. Removal of these echo selection effects should enable the detection of the short-lived echoes from the high-altitude meteors. It is expected that for meteoroids to ablate at these high altitudes, their chemistry must be different than that of the usual stony meteoroids [Lebedinets, 1991; Elford et al., 1997; Cervera and Elford, 2004]. Indeed, they are likely to be organic or tarry in nature. New ionization profile tables are required to be generated for these meteoroids and this would impact upon the response function calculation and hence the expected height distribution. A response function analysis of these high-altitude meteors should enable us to investigate the proportion of meteoroids being composed of organic materials. This, however, is beyond the scope of this paper. A preliminary analysis is presented by Cervera and Elford [2004] Sporadic Meteor Echo Rate Diurnal Variation [27] The distribution of sporadic meteor radiants over the celestial sphere is not isotropic, but rather consists of several broad sources [Elford et al., 1964; Jones and Brown, 1993; Brown and Jones, 1995]. Convolving the response function with the sporadic radiant distribution yields the total expected meteor echo rate [Elford and Hawkins, 1964; Thomas et al., 1988]. An appropriate transformation of coordinates must be performed to convert the response function from the elevation-azimuth frame to the celestial coordinate frame. As this depends on the local solar time on a particular day, the total expected meteor echo rate as a function of time is obtained on the day in question. The expected diurnal variation of the sporadic meteor echo rate is ZZ nt ðþ¼ nðq; fþgðb; l l ÞdW; ð8þ sky where g(b, l l ) is the sporadic meteor radiant distribution. [28] There are 6 sources which contribute to the sporadic radiant distribution and these are the Helion (H), Anti- Helion (AH), North- and South-Apex (NA, SA), and Northand South-Toroidal (NT, ST) sources. The H and AH sources are due to meteoroids in high-eccentricity, lowinclination orbits crossing the Earth s orbit toward the Sun (AH) and away from the Sun (H). The NA and SA sources originate from the apex of the Earth s way and are meteoroids swept up by the Earth s orbital motion. Finally the toroidal sources are due to meteoroids with highly inclined orbits (typically ±60 ). Jones and Brown [1993] and Brown and Jones [1995] have summarized various meteor survey programs and have produced a model of the sporadic meteor radiant distribution based on representations of the 6 sources with the following probability distribution: lnðþ1 2 cos g Pðg g 0 Þ ¼ exp ð ð ÞÞ ; ð9þ 1 cosðg 0 Þ where g is the angular distance from the center of the source and g 0 is the mean radius of the source. They summarize the parameters which describe these sources. Figure 4 displays this model normalized to 4p over the sky. While the Brown and Jones [1995] model is smooth both spatially and temporally (it does not model any dayto-day variability) it does represent the structure of the broad sources very well. [29] Figure 5 displays the expected diurnal variation of meteor sporadic echoes on 22 October 1997 for the east beam. Unfortunately due to the ionospheric returns at MF/ HF during daylight hours, we are restricted to collecting meteor data presunrise. Thus we cannot make a comparison of the observed and expect diurnal variations over the entire day. Figure 6 displays the comparison for the four beams combined during our data collection period. We observe that the general trend of the two curves agree. 5of10

6 Figure 4. Sporadic meteor radiant distribution based on the model of Brown and Jones [1995] Response to Meteor Showers [30] The expected time of passage of meteor showers may be determined from the response function in a manner similar to the calculation of the diurnal variation of sporadic meteor echoes. An appropriate shower radiant distribution must be used. However, upon consideration of the narrow distribution of typical showers we may, without loss of generality, employ a delta function with the appropriate radiant coordinates. [31] Elford et al. [1994] and Cervera et al. [1997] show that the radiant coordinates of meteor showers may be accurately determined using a single station narrow beam radar operated in a mode where the beam direction is alternately switched east and west each minute. The response function is an integral component of this technique. Measurement of the time difference between the detection of the shower in each beam yields the radiant declination while the measurement of the time of passage (in either beam) yields the radiant right ascension. We are unable to make use of this technique with the BPMF radar due to the relatively wide response of the main beam and the high response of the sidelobes at azimuths opposed to the main beam. [32] The Orionid meteoroid stream is active from 2 October to 7 November with peak rates on 21 October [Cook, 1973; McBeath, 1993]. Figure 7 shows the expected echo rate calculated for the Orionids during our period of observation. We note that there are high levels of Orionid activity expected at around 0100 LT for all four transmission beams which rapidly decreases before rising again at 0700 LT. This behavior was not noted in the observed hourly echo rates which was in close agreement with the expected sporadic diurnal variation. Indeed, there is little evidence to suggest that the radar detected Orionid meteors at all. There are two possible explanations: (1) the Orionid shower was not active on the date of observation, and (2) the radar is not sensitive to the Orionid meteors. We shall see Figure 5. Expected diurnal variation (normalized to the peak rate) for the east beam on 22 October Figure 6. Comparison of the observed (solid line) and expected (dashed line) diurnal variation for the four combined beams on 22 October The expected curve has been normalized to the total number of echoes. 6of10

7 Figure 7. Normalized rate response of the radar to the Orionids meteor shower on 22 October 1997 for transmission on each of the four beams. from the following argument that the latter is probably the case. [33] Elford [1967] summarized the observations of several researchers and showed that the mass index, s, of showers decreases for fainter meteors. The mass index is the exponent in the differential mass law and it is related to the exponent, c, of the cumulative mass law by s = 1 c. However, the mass index for sporadics remains constant at 2 even for faint meteors; thus, at low limiting zenithal line densities the sporadic flux swamps that of the showers [see Elford, 1967, Figure 5]. We were unable to find the mass index of the Orionids from previous work. However, the mass index of the h-aquarids may be used as these two showers are causally linked by a common meteoroid stream, that being associated with Halley s comet. The mass index for these meteors fainter than electrons m 1 is 1.6 (c = 0.6) [Weiss, 1961]. In addition, the results of Weiss [1957], summarized by Elford [1967], show that the ratio of the flux of the Orionids to sporadic meteors above a zenithal line density of electrons m 1 is 23/35. Thus the shower meteors are swamped by the sporadics as the radar is able to detect meteors with line densities down to electrons m 1. [34] We may calculate the expected ratio of Orionid to sporadic meteors using the response function. From equation (1) the cumulative flux of Orionid meteors above a limiting zenithal line density relative to the cumulative sporadic flux is given by: ð Þ F r ¼ K r qz co cs ; ð10þ where c o applies to the Orionids, c s to the sporadics and K r = K(Orionids)/K(sporadics). Table 2 displays values of c o for various radar magnitudes, M R. These values were obtained from Weiss [1961] except for +3 < M R < +6 where we interpolate c o to be 0.5. Now, M R is related to q z by the following relation [McKinley, 1961]: M R ¼ 40 2:5log 10 q z : ð11þ Converting M R to q z and using equation (10) together with Table 2, and using Weiss s [1957] flux results above electrons m 1 as the starting point, we calculated K r in each q z regime. During the calculation of the echo rate for the Orionids we used K r in place of K. Dividing this by the calculated sporadic echo rate (with K set to 1) yields the echo rate of the Orionids relative to the sporadic meteors. We found that the peak shower activity was exceeded by the sporadic background by a factor of 6. [35] If the shower activity is weak relative to the sporadic background, as in this case, then in order to identify the shower meteors other techniques in addition to the examination of echo rates must be used. These include the determination of the meteoroid entry speeds [e.g., Cervera et al., 1997] and determination of individual meteor radiants. The former is most useful for high-speed showers as the sporadic rate drops at these speeds. The latter requires the use of a multistation radar system, a technique developed by Gill and Davies [1956] and Davies and Gill [1960] Table 2. Cumulative Mass Law Index for the Orionid Shower Meteors at Various Radar Magnitudes a M R < < M R < < M R < (interpolated) > a From Weiss [1961]. The assumption has been made that the mass index for the Orionids is identical to that of the h-aquarids due to their association with the same meteoroid stream (see text for details). c o 7of10

8 Figure 8. Polar plot of the observed distribution of meteor echoes over the sky. Symbols N, S, E, and W indicate echoes detected while the direction of the beam upon transmission was in the north, south, east, and west, respectively. The dashed circles delineate off-zenith angles of 25 and 50. and used by many other researchers [e.g., Nilsson, 1964a, 1964b; Gartrell and Elford, 1975; Baggaley et al., 1994]. An alternative approach for determining shower radiants is the imaging radiant technique developed by Elford [Weiss, 1955], Jones and Morton [1977], and Jones [1977] which requires an all-sky meteor radar. This technique has been successfully employed by Morton and Jones [1982], Poole and Roux [1989], and Hocking et al. [2001]. Cervera et al. [1997] were able to detect the q-ophiuchids from echo rates alone. This was due to the mass index of this shower having a value of 1.9 (c = 0.9) [Cervera, 1996] which is close to the sporadic value; thus, these meteors were not swamped by the sporadic background. It may be postulated that showers with few small meteoroids (i.e., low mass index for faint meteors) have had the smaller particles perturbed out of orbit and are thus older showers. Showers such as the q-ophiuchids are probably younger as this process has not had time to take effect Distribution of Meteor Echoes Over the Sky [36] Figure 8 displays the observed meteor echo distribution over the sky. It is interesting to note that there is little difference in the echo distribution for each beam direction. Regardless of the beam direction, most of the echoes are detected in the southwestern quadrant of the sky. The second point to note is that most of the echoes are detected Figure 9. directions. Expected distribution of meteors echoes observed over the sky for the four transmission beam 8of10

9 Figure 10. Expected distribution of meteors echoes observed over the sky for the east transmission beam at various times of the day. The distributions have been normalized to the peak rate at 1800 LST. at off-zenith angles greater than the beam tilt of 24. The second point is easily explained by the previous discussion on the greater sensitivity of radar to meteor echoes originating from high-elevation radiants. However, to understand the general sky distribution of echoes, an analysis using the response function is required. [37] We calculated the expected sky distribution of meteors echoes as follows. For a given reflection point on the sky we calculated all the radiant directions from which meteors are able to be detected; the criterion being the requirement of orthogonality between the trail and look direction. The radar response to these radiants are obtained directly from the response function. These responses are then multiplied by the sporadic meteor flux for these radiant directions (after a transformation to heliocentric ecliptic coordinates) and then integrated to yield the total number of echoes for the particular reflection point on the sky. This is repeated for all reflection points over the sky. We display the results of this calculation (integrated over our period of observations) for the four transmission beam directions in Figure 9 and we immediately see that the agreement with the observations is excellent with a preponderance of meteor echoes in the southwest. In addition there are only minor differences between the echo distributions for the four beams displayed by the observations. [38] The meteor echo distribution observed over the sky is governed mainly by the sporadic radiant distribution. This is exemplified by Figure 10 where we display the expected echo distribution for the east transmission beam at various times of the day. Note also the diurnal variation in the direction of the meteor echoes in addition to the variation in the echo rates. 4. Conclusion [39] The response function of the BPMF radar was calculated and subsequently employed to interpret meteor backscatter observed on 22 October The expected height distribution and sporadic meteor diurnal variation were in close agreement with the observations. No evidence of the Orionid meteor shower was observed and the response function was employed to explain this with the expected peak shower rate 17% that of the sporadic background. In order to identify these meteors measurement of the meteoroid speeds and/or their radiant coordinates would be required. [40] Distributions of the meteor echo reflection points over the sky were examined and were found to be invariant of the direction of the beam used for transmission. Analysis using the response function showed that this was expected and it was discovered that the observed 9of10

10 sky distribution of meteor echoes was mainly dictated by the form of the sporadic meteor radiant distribution. [41] Acknowledgments. This work was funded by Autralian Research Council grants A and A [42] Arthur Richmond thanks Scott Palo and another reviewer for their assistance in evaluating this paper. References Baggaley, W. J., R. G. T. Bennett, D. I. Steel, and A. D. Taylor (1994), The advanced meteor orbit radar facility: AMOR, Q. J. R. Astron. Soc., 35, Briggs, B. H., W. G. Elford, D. G. Felgate, M. G. Golley, D. E. Rossiter, and J. W. Smith (1969), Buckland Park aerial array, Nature, 223, Brown, P., and J. Jones (1995), A determination of the strengths of the sporadic radio-meteor sources, Earth Moon Planets, 68, Ceplecha, Z., J. Borovicka, W. G. Elford, D. O. Revelle, R. L. Hawkes, V. Porubcan, and M. Simek (1998), Scattering of radio wave from meteor trails: Meteor phenomena and bodies, Space Sci. Rev., 84, Cervera, M. A. 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