Ann. Geophys., 26, 2217–2228, 2008
www.ann-geophys.net/26/2217/2008/
© European Geosciences Union 2008
Annales
Geophysicae
Determination of meteoroid physical properties from tristatic radar
observations
J. Kero1 , C. Szasz1 , A. Pellinen-Wannberg1,2 , G. Wannberg1 , A. Westman3 , and D. D. Meisel4
1 Swedish
Institute of Space Physics, Kiruna, Sweden
University, Kiruna, Sweden
3 EISCAT Scientific Association, Kiruna, Sweden
4 SUNY Geneseo, Geneseo, NY, USA
2 Umeå
Received: 3 January 2008 – Revised: 19 March 2008 – Accepted: 8 April 2008 – Published: 5 August 2008
Abstract. In this work we give a review of the meteor
head echo observations carried out with the tristatic 930 MHz
EISCAT UHF radar system during four 24 h runs between
2002 and 2005 and compare these with earlier observations.
A total number of 410 tristatic meteors were observed. We
describe a method to determine the position of a compact
radar target in the common volume monitored by the three
receivers and demonstrate its applicability for meteor studies. The inferred positions of the meteor targets have been
utilized to estimate their velocities, decelerations and directions of arrival as well as their radar cross sections with unprecedented accuracy. The velocity distribution of the meteoroids is bimodal with peaks at 35–40 km/s and 55–60 km/s,
and ranges from 19–70 km/s. The estimated masses are between 10−9 –10−5.5 kg. There are very few detections below
30 km/s. The observations are clearly biased to high-velocity
meteoroids, but not so biased against slow meteoroids as has
been presumed from previous tristatic measurements. Finally, we discuss how the radial deceleration observed with
a monostatic radar depends on the meteoroid velocity and
the angle between the trajectory and the beam. The finite
beamwidth leads to underestimated meteoroid masses if radial velocity and deceleration of meteoroids approaching the
radar are used as estimates of the true quantities in a momentum equation of motion.
Keywords. Interplanetary physics (Interplanetary dust; Instruments and techniques) – Radio science (Instruments and
techniques)
1
Introduction
Meteor head echoes are radio wave reflections from the
plasma generated by the interaction of meteoroids with the
atmosphere at about 70–140 km altitude. The echoes are
characterized by being transient and Doppler shifted. The
received power is confined in range, as from a point source,
and the target moves with the line-of-sight velocity of the
meteoroid.
The first meteor investigations 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. Some of the measurements were optimized to provide specular trail reflections (Evans, 1965) whereas others
were optimized for detecting head echoes of shower meteoroids travelling down-the-beam (Evans, 1966). To study
head echoes with a monostatic radar requires that the geometry of the detections be carefully taken into consideration, as
only the radial component of the velocity is observed. Evans
(1966) pointed the radar beam at shower radiants when these
were visible at very low elevations to get as big a crossbeam
detection volume as possible and applied strict restrictions to
ensure that the detections originated from meteoroids confined in a small angle from boresight. Sporadic meteors do
not come from compact radiants and therefore cannot be assumed to be down-the-beam or perpendicular to it.
There was then a 30-year pause in the use of narrow
beam HPLA radars for meteor observations, and when they
resumed, the improved signal processing techniques and
large data handling capacities proved them suitable for studies of sporadic meteor head echoes (Pellinen-Wannberg and
Wannberg, 1994; Mathews et al., 1997).
The tristatic capability of the EISCAT UHF system makes
it a unique tool in determining meteoroid physical properties
and investigations of the head echo scattering process. We
present the methods used for meteor head echo observations
carried out during four 24 h runs between 2002 and 2005 as
well as a summary of the determined physical characteristics
of the observed meteoroids.
Correspondence to: J. Kero
([email protected])
Published by Copernicus Publications on behalf of the European Geosciences Union.
2218
J. Kero et al.: Tristatic radar observations of meteors
Table 1. Season, year, start/stop dates and times, number of detected tristatic meteors, interpulse period (IPP), pulse repetition frequency
(PRF) with two pulses per IPP, pulse length (Tpulse ), and receiver sampling period (Tsampling ) for the meteor campaigns with EISCAT UHF.
2
Season
Year
Start–Stop (UT)
Vernal equinox
2002
19–20 Mar, 12:00–12:00
No of meteors
IPP (µs)
PRF (Hz)
Tpulse (µs)
Tsampling (µs)
50
4334
461
32×2.0=64.0
0.6
101
3312
604
32×2.4=76.8
0.6
Summer solstice
2005
2005
21–22 Jun, 14:00–10:00
23 Jun,
10:00–14:00
Autumnal equinox
2005
21–22 Sep, 07:00–07:00
194
3312
604
32×2.4=76.8
0.6
Winter solstice
2004
21–22 Dec, 08:00–08:00
65
4334
461
32×2.4=76.8
0.6
Experiment overview
The data presented in this study has been collected during
four campaigns carried out with the EISCAT UHF radar system as summarized in Table 1. These campaigns were scheduled at vernal/autumnal equinox and summer/winter solstice.
A total number of 410 tristatic meteor head echoes contain
enough data points for time-of-flight velocity calculations to
be compared to the Doppler velocity measurements.
The EISCAT UHF system operates at around 930 MHz
and comprises three 32 m parabolic dish antennae with
Cassegrain feeds and 0.6◦ one-way half-power beamwidths.
One transmitter/receiver is located near Tromsø, Norway,
and two remote receivers are located in Kiruna, Sweden, and
Sodankylä, Finland. The common volume monitored by all
three receivers was during all campaigns situated at an altitude of 96 km, about 161 km in range from Kiruna, 279 km
from Sodankylä and 164 km from Tromsø, as illustrated in
Fig. 1. The angle between the Kiruna antenna pointing direction and the Tromsø beam was 75.6◦ during the campaigns. The corresponding figure for Sodankylä and Tromsø
was 122.2◦ .
The Doppler frequency measured at a remote receiver is
proportional to the sum of the line-of-sight projections of the
meteoroid velocity (v) onto the transmitter beam (vT ) and
the receiver beam (vR ) as sketched in Fig. 2. Its magnitude is
proportional to the projection of the meteoroid velocity onto
the plane spanned by the two beams. The velocity component measured in a bistatic geometry is usually defined
as being along the bisector of the transmitter and receiver
beams. The meteoroid velocity component along the bisector is calculated by dividing the measured velocity (vT +vR )
with 2× cos γ , where γ is the bisector angle and equal to the
half-angle between the transmitter and the receiver beams.
A 32-bit binary phase shift keyed (BPSK) coded pulse
sequence with a bit length of 2.4 µs was used in three of
the four campaigns (Table 1), giving total pulse lengths of
76.8 µs (Wannberg et al., 2008). The transmitted waves are
left- and the received waves are right-hand circularly polarized.
Ann. Geophys., 26, 2217–2228, 2008
Three frequencies were used with two pairs of pulse sequences transmitted in each radar cycle, every pair separated by half an interpulse period (IPP). Narrow bandpass
filters are used in Sodankylä around 930 MHz to prevent interference from nearby GSM base stations. For this reason, the first pulse sequence in each pair was transmitted at
929.6 MHz in order to be receivable at Sodankylä. To avoid
reception of echoes from previously transmitted pulse sequences still within the ionospheric F-layer with the Tromsø
transmitter/receiver, the second pulse sequence alternated between 927.5 and 928.7 MHz. The whole IPP was 4334 µs
during the vernal equinox and winter solstice campaigns,
which means a separation time of 2167 µs between consecutive transmissions/receptions. This enables parameters
such as meteoroid line-of-sight velocity and echo power to
be monitored with a frequency of 461 Hz. The received signals were oversampled by a factor of four at all sites with
a 0.6 µs sampling period. The detection of tristatic pulsating events in the winter solstice data triggered us to shorten
the IPP of the later campaigns to 3312 µs, the lowest achievable IPP with the utilized pulse scheme by reason of beam
duty cycle regulations. This gives a monitoring frequency of
604 Hz. The Kiruna reception scheme was also modified to
receive both pulses in each pulse pair instead of only one.
The two pulses in each pulse pair are separated by 90 µs.
When decoding the received BPSK coded echo sequences
of a meteor echo, the Doppler shift corresponding to the lineof-sight velocity of the meteoroid has to be taken into account. Wannberg et al. (2008) have developed an inverse algorithm in which optimum pulse compression at each individual radar pulse sequence is found by optimizing the Doppler frequency and assumed position of the first meteor echo
sample in the dump. In this way, we get two independent
measurements of the line-of-sight velocity: a direct estimate
of the Doppler velocity, and a very precise estimate of the
range rate when comparing the location of meteor echo samples in consecutive dumps.
Previous tristatic EISCAT meteor experiments and results
are described by Janches et al. (2002).
www.ann-geophys.net/26/2217/2008/
J. Kero et al.: Tristatic radar observations of meteors
J. Kero et al.: Tristatic radar observations of meteors
Zenith
Zenith
East
68.88ºN, 21.88ºE
km
164
South
161 km
km
132 k
Sodankylä
(Finland)
67.36ºN, 26.63ºE
Kiruna
(Sweden)
67.86ºN, 20.44ºE
Ground projection
of common volume
m
Ground projection
of common volume
391 km
m
161 km
South
Tromsø
km
(Norway)
1
69.59ºN, 19.23ºE 99
km
km
96 km
279
96 km
Tromsø
(Norway)
1
69.59ºN, 19.23ºE 99
East
68.88ºN, 21.88ºE
132 k
164
2219
3
J. Kero et al.: Tristatic radar observations of meteors
Kiruna
(Sweden)
67.86ºN, 20.44ºE
◦
Fig.1.1.Sketch
Sketchofofthe
thetetrahedron
tetrahedrongeometry
geometryused
used in
in the
the meteor
meteor studies.
studies. The
The full
Fig.
full beamwidths
beamwidths are
are plotted
plottedas
as11◦ and
andare
aredrawn
drawntotoscale.
scale.
Fig. 1. Sketch of the tetrahedron geometry used in the meteor studies. The full b
Meteor analysis
vT
Bisector
The EISCAT radar systemγ is designed
for studying beamγ
vR
filling, ionospheric plasmas giving rise to incoherent
scatter
vT target αposition determination has
echoes. Hence, compact
cos γ To be able to compare the meanot been realized before.
sured
signal-to-noise ratio (SNR) of avhead echo streak
with
Receiver
Transmitter
the beam pattern, we need
vT + vRto know the amount of transmitv × cos α =
ted power as well as the
antenna
receiving sensitivity in the
2 × cos
γ
particular direction that a meteor echo arrives from. We have
trajectory
therefore used an ideal radiation patternMeteoroid
(Nygrén,
1996) with
a primary reflector size of 30 m, which best matches the measured beamwidth, and a secondary reflector size of 4.48 m to
estimate the antenna vgain
as a function of an angular disR
γ
placement from the cos
boresight
axis. The maximum gain at
boresight is 48 dB. The
support
structure of the secondary revT + vR
flector induces azimuthal
sidelobe
gain variations, which we
cos γ
have not tried to take into account. Therefore we restrict ourselves to the RCS measurements of meteors detected within
the
−32.dBThe
beamwidth.
Fig.
Doppler frequency at a remote receiver is proportional
vT +
vR . The
velocity component
the bisector
Thereto are
several
advantages
of knowingalong
the position
of isa
(vT + vtarget
× cosprecisely.
γ) .
R ) / (2very
meteor
It is not only vital for studying the RCS, but also to get the best possible velocity determination of the targets. When a meteoroid passes through
3 beam,
Meteor
the
or Analysis
rather through the common volume, the angles
between the velocity vector and the transmitter and receiver
The EISCAT
radar
system of
is time.
designed
studying
beam5.2
beams
change as
functions
Wefor
show
in Sect.
filling,
ionospheric
plasmas
giving
rise
to
incoherent
scatter
that this geometric effect can not be neglected. In order to
echoes. Hence, compact target position determination has
estimate the mass and the atmospheric entry velocity of a
not been realized before. To be able to compare the meameteoroid, its deceleration must be determined as precisely
sured signal-to-noise ratio (SNR) of a head echo streak with
as possible. This can only be done if the position of the target
www.ann-geophys.net/26/2217/2008/
the beam pattern, we need to know the amount of transmitted power as well as the antenna receiving sensitivity in the
vT
particular direction that a meteor
echo arrives from. We have
therefore used an ideal radiation pattern (Nygrén, 1996) with
γ
γ
a primary reflector size of 30
m, which
best matches
the meavR
sured beamwidth, and av secondary reflector size of 4.48 m to
T
α
estimate the antenna cos
gain
γ as a function of an angular displacement from the boresight axis. The maximum gain at
v
Receiver
Transmitteris 48 dB. The support structure of the secondary
boresight
vT + vR sidelobe gain variations, which
reflector induces
azimuthal
v × cos α =
× cos into
γ
we have not tried to 2take
account. Therefore we restrict ourselves to the RCS measurements of meteors detecMeteoroid trajectory
ted within the –3 dB beamwidth.
Bisector
3
the be
ted po
particu
therefo
a prim
sured
estima
placem
boresi
reflect
we ha
strict o
ted wi
vR
There are several advantages
of knowing the position of a
cos γ
meteor target very precisely. It is not only vital for studyvT + to
vR get the best possible velocity deing the RCS, but also
cos
γ
termination of the targets. When a meteoroid passes through
the beam, or rather through the common volume, the angles
between the velocity vector and the transmitter and receiver
Fig. 2.
2. The
The Doppler
Doppler frequency
frequency atat aa remote
remote receiver
proporFig.
isis proporbeams
change
as functions
of time. We
showreceiver
in Section
5.2
tional to
to vvTT+v
+RvR. .The
Thevelocity
velocitycomponent
componentalong
alongthe
thebisector
bisectorisis
tional
that this geometric effect can not be neglected. In order to
(vTT+v
+Rv)R/)(2×
/ (2 cos
× cos
γ ).γ) .
(v
estimate
the mass and the atmospheric entry velocity of a
meteoroid, its deceleration must be determined as precisely
as possible. This can only be done if the position of the target
3 Meteor
Analysis
inside
the
inside
the common
common volume
volume isis known.
known. The
Thedeceleration
decelerationofofa a
meteoroid
during
the
one-tenth
of
a
second
ititisismonitored
meteoroid
during
thesystem
one-tenth
of a second
monitored
EISCAT
radar
is designed
isThe
usually
comparable
to, or smaller
than,for
the studying
change inbeamraisfilling,
usually
comparable
to,
or
smaller
than,
the
change
in raionospheric
plasmas
giving
rise moving
to incoherent
dial velocity
of a constant
velocity
target
throughscatter
the
dial
velocity
of a constant
velocity
target moving through the
echoes.
compact
target
has
beam
withHence,
the evolving
angles
not position
taken intodetermination
account.
beam
with
the
evolving
angles
not
takentointo
account.
not been realized before. To be able
compare
the measured signal-to-noise ratio (SNR) of a head echo streak with
Ann. Geophys., 26, 2217–2228, 2008
The
meteo
ing th
termin
the be
betwe
beams
that th
estima
meteo
as pos
inside
meteo
is usu
dial ve
beam
2220
J. Kero et al.: Tristatic radar observations of meteors
VKIR = 12.84km/s
slope =12.89km/s
320
315
1150 1160 1170
Pulse compression
-1
30
324
20
10
323
0
1150 1160 1170 1180
1150 1160 1170 1180
VTRO = -20.78km/s
560
550
Pulse compression
SNR (dB)
(km/s)
Range gate
-20
0.2
1150 1160 1170 1180 1150
1160
1170
64.4
1180
199.1°
0.5
199.0°
0
1150 1160 1170 1180 1150
1160
1170
1180
1
30
-20.5
64.6
20
10
-19.5
0
1150 1160 1170 1180
1150 1160 1170 1180
IPP
1150 1160 1170 1180
IPP
IPP
0.8
84.2°
0.6
0.4
0.2
84.1°
1150 1160 1170 1180 1150
IPP
1160
1170
Zenith distance
TRO
1150 1160 1170 1180
570
-21
0.4
slope = -20.81km/s
-22
-21.5
64.8
1
40
SNR (dB)
Range gate
-2
1150 1160 1170 1180
0.6
Azimuth
(km/s)
0
325
-1.5
10
65
slope = -1.76km/s
-3
-2.5
20
1150 1160 1170 1180
VSOD = -1.78km/s
Pulse compression
Range gate
(km/s)
KIR
V
12.5
325
0.8
V (km/s)
13
SNR (dB)
330
12
V
65.2
30
13.5
SOD
1
335
14
V
J. Kero et al.: Tristatic radar observations of meteors
5
1180
IPP
Fig. 3.
3. Doppler
Doppler velocity (column 1), range gate (column 2), SNR (column 3), and pulse compression (column
Fig.
(column 4)
4) versus
versus IPP
IPP as
as seen
seen from
from
Kiruna (row
(row 1), Sodankylä (row 2), and Tromsø (row 3). The rightmost column shows meteoroid velocity
Kiruna
velocity (top)
(top) azimuth
azimuth (middle)
(middle) and
and zenith
zenith
distance (bottom)
(bottom) on the ordinates and IPP on the abscissae. The solid lines present the values found when
distance
when combining
combining the
the least-squares
least-squares fitted
fitted
values of
of Doppler
Doppler velocity and range from all receivers. The dashed lines indicate the values found when
values
when assuming
assuming aa straight
straight trajectory.
trajectory. The
The
values given
given in the subplot headers are the weighted arithmetic mean of the Doppler velocities (column 1)
values
1) and
and the
the slopes
slopes of
of the
the linear
linear curves
curves
fitted to
to the
the range data (column 2).
fitted
for samples
high SNR. Assuming that there is only one
3.1
Meteorwith
detection
target in the illuminated volume, the range can be found to
an even3higher
by making
a weighted
Figure
showsprecision
an example
of the primary
radarleast-squares
parameters
fit
to
the
data
points.
We
thus
estimate
the
range
to the
deduced for an observed meteor. The top row of the
fourtarget
first
from
all
three
antennae
at
all
interpulse
periods
and
calcucolumns contains data from Kiruna, the middle row from
Solate the position
therow
meteoroid
from theAll
three
rangesare
as
dankylä,
and the of
third
from Tromsø.
abscissae
described
in
Section
3.2.
IPP. Each IPP is 3312 µs long and the whole detection thus
lasts for about 0.11 s. The leftmost column shows the DoppThe direction of the meteoroid trajectory is estimated by
ler velocity values corresponding to the best frequency found
combining the three measured Doppler velocities (leftmost
in the decoding process for each receiver. Positive direction
column in Figure 3) at the simultaneously derived target posis here defined as away from the radar. The second column
itions. The solid lines in the azimuth and zenith distance panshows the range gate of the target, the third one displays
els of Figure 3 (rightmost column) show how these quantities
the SNR, and the fourth one presents the pulse compression.
vary when linear least-squares fits of the measured Doppler
The pulse compression can reach a maximum value of 88%
velocities are combined and fed into a velocity vector cal(Wannberg et al., 2008).
culation routine together with the positions determined using
received
signal fits
is oversampled
by aThe
factor
of four.
theThe
linear
least-squares
of the range data.
direction
of
Hence,
each
bit
in
the
transmitted
code
is
represented
by
arrival changes as a function of IPP due to the limited goodfour
in this
the example,
received the
datadeviation
stream. isThis
is utilized
in
ness points
of fit. In
extremely
small.
Ann. Geophys., 26, 2217–2228, 2008
A
of a few tenths
a degree
is quite
thecurvature
fitting procedure
to findofthe
position
of thecommon.
peak of the
decoded
power
within
a
fraction
of
a
range
gate
with
The dashed lines in the rightmost column of Figurea 3centre
repof gravity
routine.
The Sodankylä
datathree
(rowre2,
resent
the search
direction
of arrival
calculated range
from all
column at
2)the
demonstrates
of containing
this method.
the
ceivers
central IPPthe
of accuracy
the data set
theAsleast
meteoroid
trajectory
aligned
almost
perpendicularly
to the
number
of data
points,is in
this case
Tromsø.
Owing to Earth’s
Tromsø-Sodankylä
target path.
moves However,
only through
gravity,
a meteoroidbisector,
follows the
a curved
the
two rangefrom
gateslinearity
during during
the observation.
Integer of
values
of
deviation
the few kilometers
its trarange are
marked
by dottedvolume
horizontal
lines.compared
The estimated
jectory
within
the common
is small
to the
target positionuncertainties.
data points are
to slightly
differ
the
measurement
Weseen
therefore
assume
thatfrom
the deweighted direction
least-squares
rate (solid
line) in
termined
is thefitted
mostrange
accurate
estimation
of the
the centratral partfor
of the
the whole
panel. duration
There isofa the
gapevent.
at IPP 1163, where the
jectory
range value jumps from 323.63 to 323.35. The gap occurs
Meteoroid
velocity
are of
calculated
each inwhen
the range
to the estimates
leading edge
the echo,from
expressed
as
dividual
Doppler
velocity
data
point.
The
velocity
componan integer value, has shifted by one range gate and is probaent
measured
are divided
by the
bly values
best described
byata each
valuereceiver
of aboutsite
323.5.
The center-ofcosine
of
the
angle
from
the
derived
meteoroid
trajectory
to
gravity search routine seems to be able to find the true target
the direction of the velocity component. Since the angles
position to an accuracy of at least a third of a range gate, or
change with significant amounts when the meteoroid propag30 m. The solid line has a value of 323.55 at the step and a
ates through the measurement volume, they are recalculated
www.ann-geophys.net/26/2217/2008/
3.2
Position determination
The position of a compact target observed by the three
EISCAT UHF receivers can be visualized as situated at the
intersection point of three geometrical shapes: a sphere centered around the Tromsø antenna and two prolate spheroidal
surfaces, both with Tromsø in one focal point and one of the
remote antennae in the other. A prolate spheroidal surface
is defined by x 2 /a 2 +(y 2 +z2 )/b2 =1, where a is the semimajor axis and b is the semi-minor axis. The total range from
Tromsø via the target (by definition situated on the surface)
to a remote receiver is equal to 2a and can be derived from
the measurements. The value of the semi-minor axis b of
each spheroid can be readily determined from the identity
b2 =a 2 −c2 , where 2c is the distance between the transmitter
and the receiver in the focal points of the spheroid.
The radius of the sphere centred around Tromsø is equal
to the monostatic range, rTRO . The position of a target is
determined by finding the spatial coordinates x, y, and z
that simultaneously solve the spheroidal equations of both re2 ,
mote receivers and the spherical equation, x 2 +y 2 +z2 =rTRO
with all quantities expressed in a common coordinate system.
This has to be performed numerically with an optimization
routine as measurement uncertainties are involved.
As it turns out, the measured ranges do not generally provide an accurate position of a target. One first has to determine and correct for some small offsets that are probably
caused by group delay in the transmission lines, remote station clock offset, and the small but cumulative errors in the
antenna-pointing directions. The last two sources of errors
can vary between campaigns even if the experimental setup
is identical, but are constant during one measuring occasion.
The total offsets were less than 4 µs for all experiments,
except for an offset of 6.6 µs at the 2005 autumnal equinox
when the Kiruna GPS receiver had been replaced. The offsets were determined by starting with the assumption that
the pointing directions of the antennae were correct. Then
we altered the arrival times of the received echoes by small
amounts until the set of all trajectories in each experiment
came to be grouped around the centre of the common volume. Finally, we plotted the projections of all echoes onto
planes perpendicular to each receiver beam to manually
check how well the calibration succeeded. In Fig. 4, the
pointing direction of the Tromsø beam has been adjusted by
www.ann-geophys.net/26/2217/2008/
1.0
65.8
0.9
65.6
2
0.8
65.4
1
0.7
0
0.5
−1
0.4
0.3
−2
−3
−4
−3
−2
−1
0
1
2
Distance from boresight (km)
65.2
V (km/s)
0.6
Normalized SNR
slope corresponding to −1.76 km/s. The slope is very close
to the arithmetic mean of the Doppler velocity (–1.79 km/s)
and the solid line is estimated to represent the true range of
the target to an order of accuracy of one-tenth of a range gate,
or 9 m.
The rightmost column in Fig. 3 shows estimated meteoroid
velocity (top), as well as the direction of arrival expressed as
azimuth (middle) and zenith distance (bottom). The calculations of these quantities are further described in Sect. 3.3.
2221
6
Distance from boresight (km)
J. Kero et al.: Tristatic radar observations of meteors
65.0
64.8
64.6
0.2
64.4
0.1
64.2
3
Fig. 4.
194194
meteoroid
trajectories
observed
at autumnal
equiFig.
4. The
The
meteoroid
trajectories
observed
at autumnal
nox projected
ontoonto
a plane
perpendicular
to thetoTromsø
beam.beam.
The
equinox
projected
a plane
perpendicular
the Tromsø
maximum
SNRSNR
of each
headhead
echoecho
streakstreak
is normalized
to one.
The
maximum
of each
is normalized
to The
one.
white
circlecircle
marks
the –3
(0.6◦(0.6
). ◦ ).
The
white
marks
thedB
−3beamwidth
dB beamwidth
using the of
derived
target
at every IPP.
The resulting
one-tenth
a degree
so position
that its boresight
coincides
with the
meteoroid
velocity
estimates
are
plotted
in
Figure
5. An
error
concentration point of the head echo streaks. The
same
is
in
the
derived
direction
of
the
trajectory
would
reveal
itself
done for Kiruna and Sodankylä independently.
as The
a systematic
difference
between
calculated
procedure
described
above the
enables
us to meteoroid
study the
velocity
estimates
from
each
site.
The
length
of every
the vertical
temporal development of the RCS of each and
event
bars
plotted
for theway
Kiruna
Tromsø
data
in Figure 5for
show
in
a very
efficient
nowand
that
we can
compensate
the
the estimated
datalittle
uncertainbeam
pattern. uncertainties.
The measured The
RCSSodankylä
changes very
during
ties are
of the orderasofin ±3
km/s andprovided
are not shown
in The
the
many
observations,
the example
in Fig. 3.
graph
as
they
exceed
the
displayed
velocity
range.
outcome of the position determination algorithm can thereThe
a meteoroid
velocity
data point
esfore
be uncertainty
verified by of
comparing
the SNR
of these
eventsiswith
timated
as
inversely
proportional
to
the
pulse
compression
the beam pattern traced out along the trajectory.
squared, divided by the cosine of the angle between the measuredTristatic
velocity velocity
component
and the determined trajectory. The
3.3
determination
uncertainty in the Tromsø velocity data for this event is in
casedetermine
of high pulse
compression
estimated towe±0.08
To
the velocity
of a meteoroid,
makekm/s
one
(solid bars). and
Theone
uncertainty
in the
data that
fromthe
Kiruna
is esassumption
assumption
only:
meteoroid
timatedalong
to ±0.2
km/s (dashed
bars), our
larger
than the uncermoves
a straight
line through
measurement
voltainty The
in theaccuracy
Tromsø of
data
to the
from30the
ume.
thedue
range
datagreater
pointsangle
is about
m
Kiruna
bisector
the trajectory
than from
velocity
for
samples
withtohigh
SNR. Assuming
thatthe
there
is onlycomone
ponentinmeasured
in Tromsø.
Thethe
scatter
thebe
Sodankylä
target
the illuminated
volume,
rangeofcan
found to
data
is caused
its bisector
and theatrajectory
almost
an
even
higher by
precision
by making
weighted being
least-squares
perpendicular.
fit
to the data points. We thus estimate the range to the target
Weights
usedantennae
for determining
least-squares
fits and
to the
vefrom
all three
at all interpulse
periods
calculocity
are chosen
inversely proportional
to the
estimlate
thedata
position
of theasmeteoroid
from the three
ranges
as
ated uncertainties.
Hence, both the pulse compressions and
described
in Sect. 3.2.
theThe
geometry
of the
trajectory
are used
to calculate
them. by
direction
of the
meteoroid
trajectory
is estimated
The accuracy
of the
meteoroid
velocity
determination
is
combining
the three
measured
Doppler
velocities
(leftmost
better when
using
comparedderived
to combining
the
column
in Fig.
3) atthis
themethod
simultaneously
target posisimultaneously
velocity
components
all three
tions.
The solid estimated
lines in the
azimuth
and zenith from
distance
panreceivers
both
speed show
and direction
at quantities
each IPP.
els
of Fig.to3 calculate
(rightmost
column)
how these
Therewhen
is another
advantage
severalDoppler
events
vary
linearimportant
least-squares
fits of as
thewell:
measured
have low SNR
and provide
fewadata
pointsvector
from one
velocities
are combined
andonly
fed ainto
velocity
calor two ofroutine
the receivers,
SNR anddetermined
a long series
of
culation
together but
withgood
the positions
using
Ann. Geophys., 26, 2217–2228, 2008
64.0
115
Fig. 5.
sine of th
certainti
Sodanky
exceed t
measure
receiver
If at lea
data, th
The u
the effe
measure
calculat
The s
squares
general
nomial
ablation
spheric
The
ure 5 an
Kiruna,
clearly
locity a
effect o
and is fu
a movin
ent.
3.4
M
A stand
use its d
equatio
sphere,
atmosph
2222
65.8
1.0
0.9
65.6
0.8
65.4
0.7
0.4
0.3
65.0
64.8
64.6
0.2
64.4
0.1
64.2
nal equiam. The
one. The
esulting
An error
al itself
eteoroid
vertical
5 show
certainn in the
nt is espression
he meary. The
nt is in
8 km/s
a is esuncerrom the
ty comdankylä
almost
the vee estimons and
em.
ation is
ing the
all three
ch IPP.
l events
om one
eries of
Kiruna
Sodankylä
Tromsø
65.2
V (km/s)
0.5
Normalized SNR
0.6
J. Kero et al.: Tristatic radar observations of meteors
J. Kero et al.: Tristatic radar observations of meteors
64.0
1150
1155
1160
1165
1170
1175
1180
IPP
Fig.
divided
byby
thethe
cosine
Fig. 5.
5. Velocity
Velocityestimates
estimatesfrom
fromeach
eachreceiver
receiver
divided
cosine
the angle
to derived
the derived
meteoroid
trajectory.
Estimated
unof
theofangle
to the
meteoroid
trajectory.
Estimated
uncercertainties
Kiruna
Tromsø
shown
as vertical
tainties
for for
Kiruna
andand
Tromsø
are are
shown
as vertical
bars.bars.
TheThe
SoSodankylä
uncertainties
are km/s
±3 km/s
andnot
areplotted
not plotted
they
dankylä
uncertainties
are ±3
and are
as theyas
exceed
exceed
the displayed
the
displayed
velocityvelocity
range. range.
measurements
from thefits
other/-s.
few data.
data points
from each
the
linear least-squares
of the A
range
The direction
of
receiver
are
enough
for
an
accurate
direction
determination.
arrival changes as a function of IPP due to the limited goodIf at of
least
of the
receivers
provides aislong
sequence
of
ness
fit. one
In this
example,
the deviation
extremely
small.
data,
the
deceleration
can
also
be
deduced.
A curvature of a few tenths of a degree is quite common.
The use of the position of the target at each IPP cancels
The dashed lines in the rightmost column of Fig. 3 reprethe effect of the changing angle as the meteoroid traverses the
sent the direction of arrival calculated from all three receivers
measurement volume. This is important for accurate velocity
at the central IPP of the data set containing the least number
calculation and thus crucial for deceleration determination.
of data points, in this case Tromsø. Owing to Earth’s gravThe slanted solid line in Figure 5 is a weighted linear leastity, a meteoroid follows a curved path. However, the deviasquares fit to the calculated meteoroid velocity estimates. In
tion from linearity during the few kilometers of its trajectory
general, we do not try to describe the velocity with a polywithin the common volume is small compared to the meanomial or exponential function, but fit the data directly to an
surement uncertainties. We therefore assume that the deterablation model to estimate the meteoroid mass and the atmomined direction is the most accurate estimation of the trajecspheric entry velocity (Szasz et al., 2007).
tory for the whole duration of the event.
The ratios between the meteoroid deceleration in Figestimates are calculated evident
from each
inureMeteoroid
5 and thevelocity
radial acceleration/deceleration
in the
dividual
Doppler velocity
data data
point.
The velocity
Kiruna, Sodankylä
and Tromsø
(Figure
3, columncompo1) are
nent
values
measured
each
receiver
site the
are meteoroid
divided by vethe
clearly
different
from atthe
ratios
between
cosine
of
the
angle
from
the
derived
meteoroid
trajectory
to
locity and the radial velocities. This behaviour is due to the
the
direction
of
the
velocity
component.
Since
the
angles
effect of finite beamwidth on radial velocity measurements
change
with significant
amounts
the meteoroid
propaand is further
discussed in
Sectionwhen
5.2. The
radial velocity
of
gates
through
the
measurement
volume,
they
are
recalculated
a moving target is biased by its transversal velocity componusing
ent. the derived target position at every IPP. The resulting
meteoroid velocity estimates are plotted in Fig. 5. An error
in
derived direction
of the trajectory would reveal itself
3.4theMeteoroid
mass estimation
as a systematic difference between the calculated meteoroid
velocity
estimates
each site.
The length
of the vertical
A standard
way offrom
estimating
the mass
of a meteoroid
is to
bars
plotted
for thevelocity
Kiruna and
and deceleration
Tromsø datainina Fig.
5 show
use its
determined
momentum
the
estimated
uncertainties.
Sodankylä
data uncertainequation
(Bronshten,
1983). The
Travelling
through
the atmoties
are of
the order decelerates
of ±3 km/s due
and to
arecollisions
not shown
in the
the
sphere,
a meteoroid
with
graph
as they constituents.
exceed the displayed
range.
atmospheric
To alsovelocity
take into
account that
Ann. Geophys., 26, 2217–2228, 2008
The uncertainty of a meteoroid velocity data point is estimated as inversely proportional to the pulse compression
squared, divided by the cosine of the angle between the
measured velocity component and the determined trajectory.
The uncertainty in the Tromsø velocity data for this event is
in case of high pulse compression estimated to ±0.08 km/s
(solid bars). The uncertainty in the data from Kiruna is estimated to ±0.2 km/s (dashed bars), larger than the uncertainty
in the Tromsø data due to the greater angle from the Kiruna
bisector to the trajectory than from the velocity component
measured in Tromsø. The scatter of the Sodankylä data is
caused by its bisector and the trajectory being almost perpendicular.
Weights used for determining least-squares fits to the velocity data are chosen as inversely proportional to the estimated uncertainties. Hence, both the pulse compressions and
the geometry of the trajectory are used to calculate them.
The accuracy of the meteoroid velocity determination is
better when using this method compared to combining the
simultaneously estimated velocity components from all three
receivers to calculate both speed and direction at each IPP.
There is another important advantage as well: several events
have low SNR and provide only a few data points from one
or two of the receivers, but good SNR and a long series of
measurements from the other/-s. A few data points from each
receiver are enough for an accurate direction determination.
If at least one of the receivers provides a long sequence of
data, the deceleration can also be deduced.
The use of the position of the target at each IPP cancels
the effect of the changing angle as the meteoroid traverses the
measurement volume. This is important for accurate velocity
calculation and thus crucial for deceleration determination.
The slanted solid line in Fig. 5 is a weighted linear leastsquares fit to the calculated meteoroid velocity estimates. In
general, we do not try to describe the velocity with a polynomial or exponential function, but fit the data directly to an
ablation model to estimate the meteoroid mass and the atmospheric entry velocity (Szasz et al., 2007).
The ratios between the meteoroid deceleration in Fig. 5
and the radial acceleration/deceleration evident in the
Kiruna, Sodankylä and Tromsø data (Fig. 3, column 1) are
clearly different from the ratios between the meteoroid velocity and the radial velocities. This behaviour is due to the
effect of finite beamwidth on radial velocity measurements
and is further discussed in Sect. 5.2. The radial velocity of
a moving target is biased by its transversal velocity component.
3.4
Meteoroid mass estimation
A standard way of estimating the mass of a meteoroid is to
use its determined velocity and deceleration in a momentum
equation (Bronshten, 1983). Travelling through the atmosphere, a meteoroid decelerates due to collisions with the
atmospheric constituents. To also take into account that
www.ann-geophys.net/26/2217/2008/
s repord higher
f an obution is
. From
n) have
ated the
stogram
eceleratimated
values.
ion imis trend
of their
de of the
ajectorbserved.
onfused
70
70
60
60
50
50
40
40
30
30
20
20
10
10
35
No of meteors
No of meteors
30
25
20
15
10
5
0
0
20
30
40
50
60
−90
−80
−70
−60
−50
−40
Deceleration
70
−30
−20
−10
0
0
(km/s2)
Velocity at 96 km (km/s)
Fig. 7. Distribution of observed deceleration and a scatter plot of
the velocity versus deceleration.
Fig. 6.
6. Distribution
Distribution of observed velocities.
Fig.
70
70
No of meteors
the mass
of a meteoroid changes due to ablation during
an
60
60
observation, we have implemented the standard meteoroid50
atmosphere
interaction processes (Öpik, 1958) in a 50numerical single-object
ablation model to compare with our
ob40
40
servations. Ablation is the collective term for several kinds
30 loss including vaporization, sublimation, fusion
30 and
of mass
loss of molten droplets. The model is implemented in a way
20
20
similar to that of Rogers et al. (2005) and references therein,
originally
based on Öpik (1958), Bronshten (1983) and
10
10 Love
and Brownlee (1991), with the addition of a sputtering model
0
0
−90 −80
−70 −60
−40 −30
−20 −10
0
as described
by Tielens
et al.−50(1994).
The input
meteoroid
paDeceleration (km/s)
rameters to the model are above-atmosphere velocity, mass,
density and zenith distance. MSIS-E-90 (Hedin, 1991) is
used
atmospheric
densities.
The measured
RCSplot
is asFig. 7.forDistribution
of observed
deceleration
and a scatter
of
sumed
to
be
proportional
to
the
meteoroid
mass
loss
via
an
the velocity versus deceleration.
overdense scattering mechanism (Close et al., 2002; Westman et al., 2004). The model is further described by Szasz
et al.
(2007)
in detailofbythe
Kero
The
RCS and
distribution
265(2008).
tristatic meteors that appear
the –3
width
of the
Tromsø
beamisiscompared
provided
Theinside
velocity
anddBRCS
data
of each
meteor
in Figure
8 as
histogram
and abyscatter
plot the
of observed
and
fitted to
thea ablation
model
adjusting
input pavelocity propagated
versus RCS.down
Kerothrough
et al. (2008b)
have shown
rameters
the atmosphere
to ourthat
obthe RCSs altitude
measured
simultaneously
the three receivers
are
servation
using
a fifth orderatRunge-Kutta
numerical
equivalent technique
and that the
targets
have similar
at asintegration
with
a variable
step sizeproperties
(Danby, 1988).
pect angles
all on
thethe
way
out toradar
130◦measurement
from the direction
of
Here
we focus
tristatic
technique
propagation
meteoroid.
Thiscould
suggests
that the head
echo
and
suffice itof
toasay
that the data
be employed
together
targetany
is essentially
spherical
in the
forward the
direction,
conwith
kind of physical
model
describing
atmosphere
sistent withprocesses,
the polarization
by described
Close et al.
interaction
e.g., themeasurements
ablation model
by
(2002) and the plasma
and electromagnetic
simulations
of
Campbell-Brown
and Koschny
(2004), the analytical
scattermeteor
head
by Dyrud
al. (2007).simulaing
model
byechoes
Close performed
et al. (2004),
or theetnumerical
A by
histogram
meteoroid masses estimated at the
tions
Dyrud etofal.the
(2007).
starting altitude of each observation and a scatter plot of velocity versus mass is displayed in Figure 9. The masses range
10−9.5 to 10−6 kg. The distribution of the data in the
4from
Results
scatter plot agrees with the general notion that slow, lowmassvelocity
meteoroids
escape detection
with HPLA
radars
(Close
The
distribution
of the detected
meteors
is reported
et
al.,
2007),
but
we
cannot
draw
any
firm
observational
in Fig. 6. None of the meteoroids has a speed higher conthan
www.ann-geophys.net/26/2217/2008/
Velocity at 96 km (km/s)
mpared
ut paraour obmerical
, 1988).
chnique
ogether
osphere
ibed by
scattersimula-
2223
7
Velocity at 96 km (km/s)
uring an
teoroidnumerour obal kinds
ion and
n a way
therein,
nd Love
g model
meteorvelocity,
n, 1991)
S is ass via an
2; Westy Szasz
J. Kero et al.: Tristatic radar observations of meteors
72 km/s, which is the highest geocentric speed of an object
on a bound orbit in the solar system. The distribution is bimodal with peaks at 35–40 km/s and 55–60 km/s. From the
measurements, Szasz et al. (2008) have estimated the atmospheric entry velocities and calculated the heliocentric orbits
of the meteoroids.
The deceleration distribution is presented as a histogram as
well as a scatter plot showing velocity versus deceleration in
Fig. 7. The displayed decelerations are estimated linearly to
enable a comparison with other reported values. It is evident
from the scatter plot that high deceleration implies high velocity, but not necessarily vice versa. This trend is probably
due to faster meteoroids being at the end of their trajectories
and losing mass more rapidly at the altitude of the common
volume than slow meteoroids on similar trajectories. Only a
few km of each meteoroid trajectory is observed. The measured deceleration must therefore not be confused with the
total deceleration.
The RCS distribution of the 265 tristatic meteors that appear inside the −3 dB width of the Tromsø beam is provided
in Fig. 8 as a histogram and a scatter plot of observed velocity
versus RCS. Kero et al. (2008b) have shown that the RCSs
measured simultaneously at the three receivers are equivalent and that the targets have similar properties at aspect angles all the way out to 130◦ from the direction of propagation of a meteoroid. This suggests that the head echo target
is essentially spherical in the forward direction, consistent
with the polarization measurements by Close et al. (2002)
and the plasma and electromagnetic simulations of meteor
head echoes performed by Dyrud et al. (2007).
A histogram of the meteoroid masses estimated at the
starting altitude of each observation and a scatter plot of velocity versus mass is displayed in Fig. 9. The masses range
from 10−9.5 to 10−6 kg. The distribution of the data in the
scatter plot agrees with the general notion that slow, lowmass meteoroids escape detection with HPLA radars (Close
Ann. Geophys., 26, 2217–2228, 2008
J. Kero et al.: Tristatic radar observations of meteors
J. Kero et al.: Tristatic radar
radar observations
observationsof
ofmeteors
meteors
J. Kero et al.: Tristatic radar observations of meteors
70
70
70
60 60
60
60
60
60
50 50
50
50
50
50
40 40
40
40
40
40
30 30
30
30
30
30
20 20
20
10 10
20
20
20
10
10
NoNo
ofof
meteors
meteors
No of meteors
Velocity
at
km
(km/s)
Velocity
Velocity
at 96
at
9696
kmkm
(km/s)
(km/s)
70 70
70
10
10
0 0
−60
−60
0
−60
−50
−50
−50
−40
−40
RCS(dBsm)
(dBsm)
−40
RCS
−30
−30
−30
−20
−20
−20
00
0
RCS (dBsm)
Fig.8.8.Distribution
Distributionofofthe
themonostatic
monostaticRCS
RCSmeasured
measured inin Tromsø
Tromsø
Fig.
Fig.
8. Distribution of
the monostatic
RCS measured
for
the
265
meteors
appearing
inside
the
–3
dB
beamwidth
and a
Fig.
8.
Distribution
of
the
monostatic
RCS
measured
in
Tromsø
for the
the 265
265 meteors
meteors appearing
appearing inside
inside the
the −3
–3 dB beamwidth and
for
a
scatter
plot
of
the
velocity
versus
RCS.
The
RCS
is
expressed
dB
for
the
265
meteors
appearing
inside
the
–3
dB
beamwidth
and
a
scatterplot
plot of
of the
the velocity
velocity versus
versus RCS.
RCS. The
The RCS
RCS is
is expressed asasdB
scatter
relative
toof
a square
meteor
(dBsm).
scatter
plot
the velocity
versus
RCS. The RCS is expressed as dB
relative
to
a
square
meteor
(dBsm).
relative to a square metre (dBsm).
relative to a square meteor (dBsm).
70
70
70
60
60
60
50
50
50
40
40
40
30
30
30
20
20
20
10
10
10
0
−6 0
−6
0
−6
NoNo
of of
meteors
meteors
No of meteors
Velocity
atat
96at
km
(km/s)
Velocity
Velocity
96
96
km
km
(km/s)
(km/s)
70
70
70
60
60
60
50
50
50
40
40
40
30
30
30
20
20
20
10
10
10
0
0−9.5
−9.5
0
−9.5
−9
−9
−9
−
−8.5
−8
−7.5
−7
−6.5
Mass at−8first detection
(log10 kg)
−
−8.5
−7.5
−7
−6.5
−
−8.5 at first
−8 detection
−7.5
−7 10 kg)
−6.5
Mass
(log
Mass at first detection (log10 kg)
Fig. 9. Distribution of estimated meteoroid masses at detection and
Fig.
9. Distribution
of estimated
masses at detection and
a scatter
plot of velocity
versus meteoroid
mass.
Fig.
9.
of
meteoroid
Fig.
9. Distribution
Distribution
of estimated
estimated
meteoroid masses
masses at detection and
a scatter
plot of velocity
versus mass.
aa scatter
scatter plot
plot of
of velocity
velocity versus
versus mass.
mass.
clusion on the correlation between velocity and mass as the
clusion
theaffected
correlation
betweenmodel
velocity
and mass as
massesonare
by ablation
assumptions.
In the
the
et
al., 2007),
butcorrelation
we cannot
draw any
firmassumptions.
observational
clusion
on the
between
velocity
and mass In
asconthe
masses
are
affected
byofablation
model
the
momentum
equation
the ablation
model, the velocity
(v)
clusion
on
correlation
velocity
and mass
as
masses
arethe
affected
by
model
assumptions.
In the
momentum
equation
of ablation
thebetween
model,
velocity
(v)a
to deceleration
(v̇) ratio
isablation
proportional
to the
mass
(m) via
momentum
equation
the
ablation
model,
the 3velocity
(v)
masses
are affected
byofablation
model
assumptions.
In the
6
topower
deceleration
(v̇) ratio
is proportional
tovmass
law (Bronshten,
1983),
where m ∝
/v̇ . (m) via a
to
deceleration
(
v̇)
ratio
is
proportional
to
mass
(m)
via
a
momentum
equation
of
the
ablation
model,
the
velocity
(v)
power
law (Bronshten,
1983),
where mof∝the
v 66 /modelled
v̇ 33 .
Figure
10 presents the
distribution
atmopower
law
(Bronshten,
1983),
where
m
∝
v
/
v̇
.
to
deceleration
(
v̇)
ratio
is
proportional
to
mass
(m)
via
a
Figure entry
10 presents
distribution
of the
modelled
spheric
masses,the
which
is very similar
massatmodistri6 /to
3the
Figure
10
presents which
the
distribution
of the
atmo1983),
where
m∝v
v̇modelled
. massdetected
power
law
(Bronshten,
spheric
very similar
the
distributionentry
foundmasses,
by Close et al.is(2007)
for thetometeors
spheric
entry
masses,
which
is(2007)
very similar
the mass
distriFigure
10 presents
of
theto
modelled
atmobution
found
by (Advanced
Closethe
et distribution
al.Research
for
the
meteors
detected
with
ALTAIR
Projects
Agency
Longbution
found
by
Close
et
al.
(2007)
for
the
meteors
detected
spheric
entry
masses,
which
is
very
similar
to
the
mass
distriwith
ALTAIR
(Advanced
Research Projects
LongRange
Tracking
and Instrumentation
Radar).Agency
Since we
use
with
ALTAIR
Projects
Agency
LongClose
et model,
al.Research
(2007)
the meteors
bution
found
by(Advanced
a single-body
ablation
the for
estimated
masses
are
not
Range
Tracking
and Instrumentation
Radar).
Sincedetected
we
use
Range
Tracking
and for
Instrumentation
Radar).masses
Since
we
use
with
ALTAIR
(Advanced
Research
Projects
Agency
Longrepresentative
fragmenting
meteoroids.
Fragmentaa truly
single-body
ablation
model,
the estimated
are
not
atruly
single-body
ablation
model,
the estimated
are use
not
Range
Tracking
and
Instrumentation
Radar).
Since
we
tion
will
always
increase
the deceleration,
butmasses
often
increase
representative
for
fragmenting
meteoroids.
Fragmentarepresentative
for
fragmenting
meteoroids.
Fragmentaatruly
single-body
ablation
model,
the
estimated
masses
are
not
thewill
RCSalways
as well.
These the
twodeceleration,
effects in combination
are simtion
increase
but often increase
tion
will
always
the
deceleration,
often
increase
truly
representative
for
fragmenting
meteoroids.
Fragmentailar
in the
model
toeffects
the choice
of but
a lower
meteoroid
the
RCS
as ablation
well.increase
These
two
in combination
are
simthe
RCS
asablation
well.
These
effects
in combination
are simtion
will
increase
the
deceleration,
oftenmeteoroid
increase
density.
This
results
in two
atolarger
particle
area
ilar
in
thealways
model
the
choice
ofcross-sectional
abut
lower
ilar
in the
ablation
model
toenhanced
the
choice
ofcross-sectional
a loss
lower
the
RCS
as
well.
These
effects
inmass
combination
are
over
mass
ratio,
gives
anlarger
formeteoroid
the simsame
density.
This
results
in atwo
particle
area
density.
results
in an
a to
larger
particle
area
ilar
theThis
ablation
model
the choice
ofcross-sectional
aloss
lower
overinmass
ratio,
gives
enhanced
mass
formeteoroid
the same
over mass ratio, gives an enhanced mass loss for the same
Ann. Geophys., 26, 2217–2228, 2008
NoNo
ofof
meteors
meteors
No
of
meteors
2224
88
8
40
40
40
35
35
35
30
30
30
25
25
25
20
20
20
15
15
15
10
10
10
55
5
00
−9
−9
0
−9
−8.5
−8.5
−8.5
−8
−8
−8
−7.5
−7.5
−7
−7
−6.5
−6.5
Entry
(log
−7.5mass
−6.5
Entry
mass −7
(log1010kg)
kg)
Entry mass (log10 kg)
−6
−6
−6
−5.5
−5.5
−5.5
Fig. 10.
10. Distribution
Distribution of
of estimated
Fig.
estimated
atmosphericentry
entrymasses
massesfor
forthe
the
Fig.
10.
Distribution
estimated atmospheric
atmospheric
entry
masses
for
the
detected
meteoroids.
Fig.
10.
Distribution
of
estimated
atmospheric
entry
masses
for
the
detected
meteoroids.
detected meteoroids.
detected meteoroids.
meteoroid
mass
and increases
the RCS
and the deceldensity.
This
results
in a largerboth
particle
cross-sectional
area
meteoroid
mass
and
increases
both
the RCS
and the deceleration
as compared
to
a particle
with
a higher
density.
The
meteoroid
mass
and
increases
both
the
RCS
and
the
decelover
mass
ratio,
gives
an
enhanced
mass
loss
for
the
same
eration as compared to a particle with a higher density. The
mass determined
for aincreases
fragmenting
meteoroid
isand
therefore
an
eration
as compared
a particle
with
higher
The
meteoroid
mass and
both
thea RCS
the decelmass determined
for ato
fragmenting
meteoroid
isdensity.
therefore
an
underestimation
of
the
total
mass of
theafragments.
mass
determined
for
a
fragmenting
meteoroid
is
therefore
an
eration
as
compared
to
a
particle
with
higher
density.
The
underestimation of the total mass of the fragments.
Szasz
et al. (2007)
have
modelled
luminosity
of the
underestimation
of
the
total mass
ofmeteoroid
thethefragments.
mass
determined
for
a
fragmenting
is
therefore
an
Szasz et al. (2007) have modelled the luminosity of the
detected
meteors
and
estimate
them
to
befragments.
inluminosity
the range of +9
Szasz
et
al.
(2007)
have
modelled
the
the
underestimation
of
the
total
mass
of
the
detected meteors and estimate them to be in the range of +9
to +5 absolute
visual
detected
meteors
and magnitude.
estimate
them to the
be in
the range of
of the
+9
et al. visual
(2007)
have modelled
luminosity
to Szasz
+5 absolute
magnitude.
to +5 absolute
visual
detected
meteors
and magnitude.
estimate them to be in the range of +9
to +5 absolute visual magnitude.
5 Discussion
5 Discussion
5 Discussion
5.1 Comparisons with previous results
55.1 Discussion
Comparisons with previous results
5.1 Comparisons with previous results
The velocity distribution displayed in Figure 6 differs from
5.1
Comparisons
with previous
results
The
velocity
distribution
displayed
in Figure
differs
previous
EISCAT
measurements.
out6
of ten from
obThe
velocity
distribution
displayed inEight
Figure
6 differs
previous
EISCAT
measurements.
Eight
out
of Janches
tenfrom
observed
tristatic
EISCAT
UHF
meteors
analyzed
by
previous
EISCAT
measurements.
Eight
of
ten
ob6 differs
from
The
velocity
distribution
displayed
in
Fig.out
served
tristatic
EISCAT
UHF
meteors
analyzed
by
Janches
et al. (2002)
were
determined
to
have Eight
velocities
higher
than
served
tristatic
EISCAT
UHF
meteors
analyzed
by
Janches
previous
EISCAT
measurements.
out
of
ten
obet
(2002)
were determined
to have
higher
than
60al.
km/s,
the fastest
one estimated
to 86 velocities
km/s. It has
therefore
et
al.
(2002)
were
determined
to
have
velocities
higher
than
served
tristatic
EISCAT
UHF
meteors
analyzed
by
Janches
60
km/s,
the fastest
to 86 km/s.
It has therefore
been
presumed
thatone
theestimated
radar detections
are heavily
biased
60
km/s,
the fastest
one
estimated
to 86velocities
km/s.
Itheavily
has
therefore
et
al.
(2002)
were
determined
to
have
higher
than
been
presumed
that
the
radar
detections
are
biased
to high-velocity meteoroids. The RCS distribution
of
the
been
presumed
that
the
radar
detections
are
heavily
biased
60
km/s,
the
fastest
one
estimated
to
86
km/s.
It
has
therefore
to
high-velocity
meteoroids.
RCS
distribution
of are
the
present
observations
reported inThe
Figure
8 shows
that there
to
high-velocity
meteoroids.
The
RCS
distribution
of the
been
presumed
that
the radarindetections
are heavily
biased
present
observations
reported
Figure
8
shows
that
there
are
approximately as many large targets in the slower part of the
present
observations
reported
inThe
Figure
8the
shows
thatpart
there
are
to
high-velocity
RCS
distribution
of
the
approximately
as meteoroids.
many
large targets
slower
of
the
bimodal velocity
distribution
as thereinare
in
the faster
part.
approximately
as
many
large
targets
in
the
slower
part
of
the
present
observations
reported
in
Fig.
8
shows
that
there
are
bimodal
velocity
there are
in the faster
On the other
hand,distribution
the presentasvelocity
distribution
also part.
exbimodal
velocity
distribution
as
there
are
in
the
faster
part.
approximately
as
many
large
targets
in
the
slower
part
of
the
On
thea other
hand,
the present
velocitybelow
distribution
also
exhibits
drop in
the number
of detections
about 30
km/s
On
the other
the present
distribution
also
exbimodal
velocity
asvelocity
there are
in the
faster
part.
hibits
drop
inhand,
thedistribution
number
detections
below
about
30 km/s
and isastill
clearly
biased
toofhigh-velocity
meteoroids.
hibits
a
drop
in
the
number
of
detections
below
about
30
km/s
On
the
other
hand,
the
present
velocity
distribution
also
exand is still clearly biased to high-velocity meteoroids.
and
is
still
clearly
biased
to
high-velocity
meteoroids.
hibits
a
drop
in
the
number
of
detections
below
about
30
km/s
5.2 Radial Deceleration due to finite beamwidth
and
still clearly
biased todue
high-velocity
meteoroids.
5.2 isRadial
Deceleration
to finite beamwidth
5.2
Radialfronts
Deceleration
due to finite
The phase
in the far-field
regionbeamwidth
of a transmitter an5.2
Radial
deceleration
due to finite
tennaphase
are not
planer,
but far-field
spherical.
Thebeamwidth
Doppler
shift of the
The
fronts
in the
region
of a transmitter
anThe
phase
fronts
in the
region
of a transmitter
transmitted
wave
incident
on a compact
moving
tenna
are not
planer,
but far-field
spherical.
The target
Doppler
shift along
of anthe
tenna
are not
planer,
but far-field
spherical.
The
Doppler
shiftthereof
the
The
phase
fronts
inwith
the
region
of a depends
transmitter
ana straight
trajectory
an
angle
to
the beam
transmitted
wave
incident
on
a compact
target
moving
along
transmitted
wave
incident
on
a
compact
target
moving
along
tenna
are
not
planer,
but
spherical.
The
Doppler
shift
of
on where
in the
beam
the target
located.
A simple
afore
straight
trajectory
with
an angle
to theisbeam
depends
thereafore
straight
trajectory
with
an
angle
to
the
beam
depends
therethe
transmitted
wave
incident
on
a
compact
target
moving
sketch
provided
Figurethe11.target
Similarly,
the scattered,
on iswhere
in thein beam
is located.
A simple
fore
onaiswhere
in trajectory
the
the11.
target
is generates
located.
A simple
along
straight
with
an
angle
to the
beam
deor reflected,
wave
from
a compact
target
sketch
provided
in beam
Figure
Similarly,
the spherical
scattered,
sketch
is
provided
in
Figure
11.
Similarly,
the
scattered,
pends
therefore
on
where
in
the
beam
the
target
is
located.
A
or reflected, wave from a compact target generates spherical
or reflected, wave from a compact target generates spherical
www.ann-geophys.net/26/2217/2008/
J. Kero et al.: Tristatic radar observations of meteors
simple sketch is provided in Fig. 11. Similarly, the scattered,
or reflected, wave from a compact target generates spherical phase fronts at the receiver. Only the part of a spherical phase front for which the phase is inside one Fresnel
zone contributes to the signal at the antenna output. Wave
propagation satisfies reciprocity. The Doppler shift of the received signal at the antenna output is therefore proportional
to 2×v× cos α, where v is the target velocity and α is the angle between a ray from the center of the antenna to the target.
The effect of beamwidth is very obvious when a meteoroid is receding from the radar. The meteoroid in the example
displayed in Fig. 3 is crossing the Kiruna bisector from behind. Hence the angle between the trajectory and the bisector
decreases with time. The Kiruna Doppler velocity therefore
increases at +16.8 km/s2 (from '12 km/s to '13.5 km/s). At
the same time, the Sodankylä Doppler velocity is decreasing at −18.0 km/s2 , and the Tromsø velocity at −24.8 km/s2 .
The meteoroid is approaching both of these receivers. The
radial velocity gradients are almost an order of magnitude
larger than the true deceleration plotted in Fig. 5 and estimated to −3.8 km/s2 .
Figure 12 shows the radial deceleration as a function of
meteoroid velocity and aspect angle for a non-decelerating
meteoroid and a meteoroid decelerating at −20 km/s2 . In
both cases, the target is assumed to approach a monostatic
radar at a range of 100 km. We have calculated the radial deceleration by letting the beamwidth approach zero. The radial velocity changes non-linearly as a function of time during the passage through a wide beam. The values given in
Fig. 12 are equal to the straight line tangents at the boresight
axis.
It is evident from Fig. 12a that the radial deceleration of
a constant velocity meteoroid increases both as a function of
meteoroid velocity and aspect angle. The radial acceleration
of a receding meteoroid has the same magnitude as the radial
deceleration of a meteoroid approaching from the opposite
direction. If the aspect angle is closer than the beamwidth
to 90◦ , the Doppler velocity switches sign during the observation.
The radial deceleration dependence on velocity and aspect
angle of a decelerating meteoroid is not as intuitive as in
the constant velocity example. For a target decelerating at
−20 km/s2 , as displayed in Fig. 12b, the radial deceleration
decreases with aspect angle if the velocity is below about
30 km/s, but increases if it travels faster than that.
5.3
Comparisons with other high-latitude HPLA radars
Mathews et al. (2007) have compared measurements from
the 430 MHz Arecibo Observatory UHF radar (AO), the
1290 MHz Søndre Strømfjord Research Facility (SRF) and
the 449.3 MHz 32 panel Poker Flat Advanced Modular Incoherent Scatter Radar (PF AMISR-32). These radars have all
been used in monostatic mode with a vertical or almost vertical pointing direction. The radial decelerations can therefore
www.ann-geophys.net/26/2217/2008/
J. Kero et al.: Tristatic radar observations of meteors
2225
Meteoroid
α1
trajectory
α2
directio
to 90◦ ,
vation.
The r
angle o
the cons
–20 km
tion dec
30 km/s
5.3 Co
Transmitter/Receiver
Fig. 11.
11. Sketch
Sketch of
of aa meteoroid
meteoroid trajectory
Fig.
trajectory in
in the
the far-field
far-field of
of aa radar
radar
beam
(solid
lines),
where
the
phase
fronts
are
spherical
beam (solid lines), where the phase fronts are spherical (dashed
(dashed
lines). The
The Doppler
Doppler shift
shift varies
varies as
lines).
as cos
cos α
α along
along the
the trajectory.
trajectory. For
Foran
an
approaching meteoroid:
meteoroid: α
α1<α
< α.2 .
approaching
1
2
be
as much
as the
55 receiver.
km/s2 larger
theoftrue
decelerations,
phase
fronts at
Onlythan
the part
a spherical
phase
as
illustrated
in the
Fig.phase
12. is
This
is, however,
negligible
comfront
for which
inside
one Fresnel
zone contributes totothe
the antenna
output.
Wave propagation
pared
thesignal
largestat reported
values
of deceleration
that are
2 . Doppler
satisfiesthan
reciprocity.
The
shiftvalues
of theof
received
signal
greater
1000 km/s
The highest
decelerations
at
the
antenna
output
is
therefore
proportional
to
2×v×cos
α,
are observed with SRF and PF AMISR-32. Both these faciliwhere
v
is
the
target
velocity
and
α
is
the
angle
between
a
ray
ties are located near the Arctic Circle at latitudes comparable
fromthe
theEISCAT
center ofUHF
the antenna
with
system.to the target.
To
compare
the
facilities,
et al. (2007)
a qualThe effect of beamwidth Mathews
is very obvious
when use
a meteority
factor
given
by
transmitted
power,
P
,
the
effective
aperoid is receding from the radar. The meteoroid
in the example
T
ture,
A
,
and
the
system
temperature,
T
.
The
so-defined
displayed
sysbisector from beeff in Figure 3 is crossing the Kiruna
quality
factorthe
hasangle
a value
of about
hind. Hence
between
the trajectory and the bisector
decreases with time. The Kiruna2 Doppler velocity therefore
P
1.3 MW
2 800 m
T × Aeffat +16.8
increases
km/s×
(from ' '
129km/s
MW to
m2'
/K13.5 km/s).
(1)
'
K
syssame time, the115
At T
the
Sodankylä
Doppler velocity is decreas2
ing atthe
–18.0
km/s2 , and
the system
Tromsø velocity
at –24.8
km/s
for
EISCAT
UHF
while AO,
SRF
and.
The meteoroid is approaching
of these receivers.
PF
AMISR-32 have 1.5×103 , both
19, and
0.67 MWm2 /K,The
reradial velocity gradients are almost an order of magnitude
spectively (Mathews et al., 2007). Being so big, AO is in
larger than the true deceleration plotted in Figure 5 and esa class of its own. Yet
events with large decelerations are
timated to –3.8 km/s2 .
detected with SRF and PF AMISR-32 as well. Since the
FigureUHF
12 shows
the aradial
deceleration
as operating
a functionfreof
EISCAT
has both
quality
factor and an
meteoroid
andbetween
aspect angle
a non-decelerating
quency
(at velocity
930 MHz)
those for
of these
two2radars, it
meteoroid
a meteoroid
decelerating at –20 km/s . In both
should
alsoand
observe
these events.
cases,
the
target
is
assumed
to approach
a monostatic
at
The rate of events recorded
during morning
hours radar
(04:00–
a
range
of
100
km.
We
have
calculated
the
radial
deceleration
08:00 LT) at the end of July and beginning of August was
by letting
the for
beamwidth
zero.
radial velocity
about
34 h−1
SRF andapproach
55 h−1 for
PF The
AMISR-32
(Mathchanges
non-linearly
as
a
function
of
time
during
the passage
within
ews et al., 2007). The rate of monostatic detections
wide beam.
The during
values given
in Figure
athrough
similaraaltitude
interval
the same
time 12
of are
dayequal
with
to the straight line tangents at the boresight axis.
EISCAT Tromsø UHF was 30–40 h−1 at summer solstice and
−1 at autumnal
It ishevident
from Figure
12a that
the radial
deceleration
of
50–60
equinox.
These
rates are
comparable
a constant
velocity
increases both
as atristatic
functionmeof
to
those from
SRF meteoroid
and PF AMISR-32,
but the
meteoroid
velocity
andtoaspect
angle.ofThe
acceleration
teor
rates are
limited
the extent
theradial
common
volume
of all
a receding
meteoroid
the same
magnitude
as 96±2
the radial
of
three receivers,
anhas
altitude
interval
of about
km,
deceleration
of
a
meteoroid
approaching
from
the
opposite
−1
and are therefore much lower (10–20 h ). The deceleration
Ann. Geophys., 26, 2217–2228, 2008
Mathew
the 430
1290 M
the 449.
herent S
been us
tical po
fore be
tions, as
compare
are grea
tions are
facilitie
parable
To co
ity facto
ture, Ae
quality
PT × A
Tsys
for the
PF AMI
spective
a class
detected
EISCAT
quency
should a
The r
at the en
for SRF
2007).
altitude
Tromsø
60 hr−1
to those
teor rate
all three
and are
ation di
has a m
Mathew
2226
J. Kero et al.: Tristatic radar observations of meteors
−5
−5
−20
−20
−25
−30
−30
−40
−35
−50
(a)
−10
20
30
40
Velo
50
ci t y
60
(km
/s)
70
o
0
−40
0
−2
0
−3
0
−4
−15
−20
−20
o
o 75
o 60
45
o
m
30
bea
15o
le to
Ang
−25
−30
−30
−40
−35
−50
−20
−30
10
o
90
−40
−10
−60
−45
0
−5
Radial deceleration (km/s 2 )
−15
−50
−55
(b)
20
30
Velo 40
ci t y
50
(km 60
70
/s)
0
o
Radial deceleration (km/ s2 )
−10
−60
10
−10
−10
−10
Radial deceleration (km/s 2 )
Radial deceleration (km/s 2 )
0
0
−45
0
−4 −50
o
o 75
o 60
45
o
m
o 30
bea
15
le to
Ang
o
90
−50
−55
Fig. 12. Radial deceleration as a function of meteoroid velocity and angle from the trajectory to the beam (aspect angle) for (a) a nondecelerating meteoroid and (b) a meteoroid decelerating at −20 km/s2 in the far-field at a range of 100 km from a radar. The radial deceleration is estimated as a linear value by letting the beamwidth approach zero. The contours in the bottom of the charts are projected isolines of
radial deceleration.
distribution of the tristatic meteors given in Fig. 7 has a much
smaller spread than the distributions reported by Mathews
et al. (2007). The total number of detected meteors was 271
with SRF and 443 with PF AMISR-32. The events with high
deceleration are scattered over a large altitude interval, which
includes 96 km.
From the present analysis we conclude that the
EISCAT UHF data contain no meteoroids with very large
decelerations. If they are not artifacts of the data analysis
methods applied by Mathews et al. (2007), their absence in
our observations means we have to use a different approach:
to find large decelerations we may have to investigate the few
data points in the very end of each event more carefully. Alternatively, the initial quality control must be altered where
events are excluded if the time-of-flight velocity cannot be
compared with the Doppler velocity. It might be necessary
to accept a smaller number of Doppler velocity data points
and higher uncertainty than in the present method of analysis. This will be investigated in a future study. A meteoroid
of large enough mass to produce detectable ionization must
break into small dust grains to decelerate this fast since a very
high momentum transfer is required. The individual grains
of a disrupted meteoroid have high cross-section area over
mass ratio and can together provide a transient amount of detectable ionization. We do not expect to be able to detect any
ionization produced along the atmospheric trajectory of one
single micron-sized particle.
Ann. Geophys., 26, 2217–2228, 2008
5.4
Factors that may affect the determined velocity
McKinley and Millman (1949) were the first to suggest that
the meteor head echo targets are compact regions of plasma,
co-moving with the meteoroids, and virtually independent of
aspect. We find no reason to assume otherwise and use the
determined target velocities as representative for the meteoroids themselves. There are, however, a few implications
that may introduce differences between the observed velocity and the meteoroid velocity.
Some meteor observations contain regular pulsations in
the received power. Kero et al. (2008a) have shown that
these are sometimes caused by interference between echoes
from two or more distinct scattering centers simultaneously
present in the radar beam. The Doppler shift of the returned
signal from two simultaneously illuminated meteoric fragments is proportional to a weighted arithmetic mean of their
Doppler velocities, with weights equal to the square root of
their RCSs. The pulsation rates are often seen to increase,
a behaviour consistent with two fragments of unequal crosssectional area over mass ratio separating from each other due
to different decelerations along the trajectory of their parent
meteoroid. The pulsation rate at a remote receiver is proportional to the sum of the projections of their differential velocity onto the transmitter and receiver beams in analogy with
the Doppler shift of the transmitted frequency. The component of the differential velocity along the bisector is found by
dividing the detected pulsation rate with 2× cos γ (as defined
in Fig. 2).
www.ann-geophys.net/26/2217/2008/
J. Kero et al.: Tristatic radar observations of meteors
Close (2004) indicates another reason why there may be a
difference between the observed range rate of a meteor target and the meteoroid velocity. If the radar target associated with a meteoroid scales as the atmospheric mean-free
path, there may be a significant time delay between the passage of the meteoroid and the formation of the radar target
at high altitudes. Owing to the exponentially increasing atmospheric density and consequently shorter mean-free path
of ablated atoms, the time delay decreases as the meteoroid
penetrates deeper into the atmosphere. Close et al. (2004)
argues that this effect in practice could give an acceleration
term that must be subtracted from the observed velocity. This
would explain some anomalous ALTAIR observations where
the head echo targets seem to accelerate.
The tristatic measurements with the EISCAT UHF radar
extend over a rather limited altitude interval around 96 km
and do not contain any accelerating events.
6
Conclusions
The tristatic EISCAT UHF system has been used in a series
of measurement campaigns from 2002–2005 to study meteoric head echoes. 410 meteors were simultaneously detected
with all three receivers and contained enough data points for
time-of-flight velocity calculations to be compared with the
Doppler velocity measurements. We have presented the meteor analysis methods used and how velocity, deceleration,
RCS and meteoroid mass are estimated from the observations.
The velocities of the meteoroids giving rise to the head
echoes are scattered from 19 to 70 km/s in a bimodal distribution, but with very few detections below 30 km/s. The
estimated masses are in the range 10−9 –10−5.5 kg and distributed very similarly to the masses determined for the ALTAIR head echo detections by Close et al. (2007).
Many monostatic radar observations are conducted with a
vertically pointed beam. Meteoroids will always approach
the radar with this measurement geometry. We have demonstrated that the effect of finite beamwidth leads to a radial
deceleration that is larger than the true deceleration (v̇) for
an approaching meteoroid. The radial velocity is, however,
always smaller than the true velocity (v). The use of radial deceleration and radial velocity in a momentum equation where m∝v 6 /v̇ 3 (Bronshten, 1983) therefore gives an
underestimated meteoroid mass (m).
Acknowledgements. 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). Two of the authors (JK and CS) are supported by
the Swedish National Graduate School of Space Technology. We
thank M. Campbell-Brown for valuable comments which have improved this paper.
www.ann-geophys.net/26/2217/2008/
2227
Topical Editor K. Kauristie thanks M. Campbell-Brown and
L. Dyrud for their help in evaluating this paper.
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