Towards determining the parameters of layer with scattering irregularities that cause coherent echo, based on the Irkutsk Incoherent Scatter radar data

0.22 MB·English

by  K. V. Grkovich

Towards determining the parameters of layer with s
attering irregularities
that
ause
oherent e
ho, based on the Irkutsk In
oherent S
atter radar
data.
Grkovi
h K.V.,Berngardt O.I.
February 2, 2008
Institute of Solar-Terrestrialphysi
s SB RAS, Irkutsk, Russia
8
0
0
E-mail: berngiszf.irk.ru
2

n
a
Abstra
t
J
3 Inthepaperwehavepresentedate
hniqueofdeterminingthes
atteringirregularities(that
ause
oherente
ho)layer
parametersusingtheIrkutskISradardata. Itisshownthatourte
hniquehasne
essarya

ura
y(forheightandthi
kness

] - about 2.5 km, for aspe
t sensitivity - 5dB/degree). Pro
essing of the experiments 25-26.12.1998 and 15-16.07.2000 has
h
shown a good agreement of data
al
ulated with the data obtained by other investigators: an average layer height is
p
110-120km, average layer thi
kness 5km, average aspe
t sensitivity - 15dB/degree. The investigation of the experiments
-
o withhightemporalresolutionallowedustoobservetemporalvariationsoftheirregularitieslayerparameters. Theaverage
e thi
kness and height of the layer does not
ontradi
t the data obtained by other investigators. The investigation of
g the experiments with high temporal resolution allowed to dete
t time variations of the layer parameters. The temporal
s. variations of theaspe
t sensitivity are observedbyus for the(cid:28)rst timeand requires additional investigations.
c
i
s
y1 Introdu
tion.
h
pOne of the most important e(cid:27)e
ts that a(cid:27)e
ts to the ionospheri
and transionospheri
radiowavepropagationis a s
attering
[
on the inhomogeneities of di(cid:27)erent s
ales. That is why, when studying the ionosphere they pay valuable attention to

1the diagnosti
s of the ionospheri
inhomogeneities. At middle latitudes, the least observed but the most a(cid:27)e
ting to the
vradiosignalspropagationarethe irregularitieselongatedwith the Earth magneti
(cid:28)eld. S
atteringby theseirregularitieshas
5
high aspe
t sensitivity, that
auses a strong dependen
e of s
attered signal amplitude on transmitted and re
eived waves
8
orientation. One of the physi
al me
hanisms of
reation of su
h inhomogeneities, elongated with the Earth magneti
(cid:28)eld,
4
0in the ionospheri
E-layer is the growth of two-stream and gradient-drift irregularities. The ne
essary
onditions for the
.growth of these irregularities are powerful ele
tri
(cid:28)eld, high ele
tron-to-ion velo
ity and high ele
tron density gradients
1
existen
e [Farley, 1963, Buneman, 1963℄. Su
h inhomogeneities are observed at high and equatorial latitudes and
ould
0
8a(cid:27)e
t to the re
eived signal from 8MHz to 1GHz [Haldoupis, 1989℄. The
onditions for arising these inhomogeneities at
0mid-latitudes most frequently are satis(cid:28)ed during strong geomagneti
disturban
es. At polar and equatorial latitudes these
:requirements are satis(cid:28)ed in less disturbed
onditions [Haldoupis, 1989, St.-Mauri
e et al., 1989℄. Radiosignals s
attered at
v
ithese inhomogeneities are known as radioaurora, or
oherent e
ho (CE).The CE signals have been observed at the Irkutsk
X
IS radarsin
e1998. During the lasttime at the IrkutskIS radaranumber of stronggeomagneti
disturban
es a

ompanied
rwith CE observations have been observed [Zolotukhina et al.,2007℄.
a
The experiment geometry is shown at (cid:28)g.1. Irkutsk IS radar is a monostati
tool and transmits a periodi
al sequen
e
of radiopulses. It re
eives s
attered signal after ea
h transmitted pulse and averages s
attered power from pulse to pulse.
Wide antennapatterallowsus toanalyzethe signals
attered fromabigrangeofradarrangesalmostat thesametimewith
a good time and spatial resolution (1-2 minutes and 15 km.
orrespondingly). More detailed the experiment geometry and
the radar
hara
teristi
s was des
ribed at [Potekhin et al., 1999℄.
1
Fig 1. The geometryof the experiment
DuetotheIrkutskISradarlo
ationand
onstru
tionpe
uliarities[Zherbtsov et al., 2002℄thes
atteredCEsignalusually
has two peaks in the power pro(cid:28)le - at ranges 550 and 1100 km
orrespondingly, at these ranges the line-of-sight is most

loseto the perpendi
ular to the magneti
(cid:28)eld. As preliminaryanalysishasshownthe peaksshape and lo
ationdepend on
the
hara
teristi
s of s
attering irregularities. The aim of this paper is to determine s
attering irregularities
hara
teristi
s
within the therm of a standard model. The task is not a new one. Su
h experiments have been made at some radars with
narrow (or steerable) antenna pattern [St.-Mauri
e et al., 1989, Foster et al., 1992℄. This allow to determine
hara
teristi
s
of s
attering irregularities in terms of layer of irregularities - height of the layer is approximately 110km, layer thi
kness is
about 10km, sometimes a number of thin layers has been observed at the same time [St.-Mauri
e et al., 1989℄. The aspe
t
sensitivityhasbeeninvestigatedatthesefrequen
iesbyotherinvestigatorsandgivesaverageestimatesofabout15dB/degree
[Foster et al., 1992℄. Due to the Irkutsk IS radar antenna pattern pe
uliarities the te
hniques used at other radars do not
work - antenna pattern at lower side lobes (used to re
eive CE signals) is
lose to an isotropi
one. That is why the aim of
the paper is to obtain a stable algorithm for determining the
hara
teristi
s of the layer with irregularities - the height, the
thi
kness and the aspe
t sensitivity of irregularities from the power pro(cid:28)le dependen
e on range.
2 The model of the s
attered signal.
For solving the de
lared aim the numeri
al modelling has been made to obtain a dependen
e of CE power pro(cid:28)le on radar
range and s
attering layer
hara
teristi
s. The observed power pro(cid:28)le is produ
ed by s
attering on irregularities generated
during strong geomagneti
disturban
es in ionospheri
E-layer and elongated with the Earth magneti
(cid:28)eld.
P(R)
Themodel(1)usedtodes
ribeaveragepowerofthes
atteredsignalonradarrange(powerpro(cid:28)le )in
ludesaspe
t
sensitivity of s
attered signal in exponential form [Foster et al., 1992℄ (with a

ura
y of an arbitrary multiplier):
P(R)=f(E) |u(2R−r)|2|g(−→r )|2exp(−(h−h0)2)exp(−(arccos(−→rrB−→B))2)d−→r
c r (△h)2 △ϕ r2 (1)
Z
f(E)
u(2R-−rd)ependen
e on the ele
tri
(cid:28)eld;
−→r c -sounding signal pulse shape;
g( )
r -antenna pattern;
h
- height at the s
attering point;
h0 △h △ϕ
−→- layer height, -layerthi
kness, - aspe
t sensitivity;
B
−→r- ve
tor of magneti
(cid:28)eld;
- ve
tor from the observation point to the s
attering point.
The
al
ulation has been made is based on the interna−→trional referen
e model for magneti
(cid:28)eld (IGRF) and the Irkutsk
g( )
IS radar antenna pattern model (
urrently used by us) r . As a model of s
attering irregularities a Gaussian layer with
h0 △h
irregularities has been
hosen,
hara
terized by its height and thi
kness . Spe
tral density of the irregularities, whi
h
de(cid:28)nes the aspe
t sensitivity of the s
attered signal power from the magneti
(cid:28)eld was
hosen in exponen−→tial form. This
△ϕ B
dependen
eisde(cid:28)nedbytheaspe
tsensitivity andbytheanglebetweenline-of-sightandmagneti
(cid:28)eld . Theele
tri
E f(E) u(t)
(cid:28)eld e(cid:27)e
ts in the s
attered power is in
luded−→as some multiplier . The shape of the transmitted pulse was also
r =0
taken into
onsideration. The
oordinate
enter
orresponds to the antenna
enter.
h0,△h,△ϕ
At (cid:28)g.1 power pro(cid:28)les, whi
h were obtained by the des
ribed model for di(cid:27)erent parameters , are shown.
The red-
olor line
orresponds to the averageparameters of irregularities. From this (cid:28)gure one
an see that pro(cid:28)les for the
di(cid:27)erent parameters
an
hange drasti
ally.
2
1
105 km, 20 km, 25 dB/deg
110 km, 10 km, 15 dB/deg
0,8 115 km, 2.5 km, 25 dB/deg
120 km, 20 km, 10 dB/deg
0,6
)
m
r
o
n
(
r
e
w
o
P 0,4
0,2
0
500 750 1000
R, km
Fig.2 Model power pro(cid:28)les for thedi(cid:27)erent model values
h0,△h,△ϕ
The sear
hof unknown parameters overthe experimentally measured powerpro(cid:28)leswasmade by the sear
h
mod exp
ofthe
orrelation
oe(cid:30)
ientoverthenumberofpreliminary
al
ulatedmodelpro(cid:28)les(2). Theindexes and forpower
pro(cid:28)les
orresponds to the power pro(cid:28)les
al
ulated from the model and for experimental power pro(cid:28)les
orrespondingly.
Σ
The a

umulation i should be made overthe radar range dis
reets Pi =P(Ri,h0,△h,△ϕ).
Σ
(Pexp∗(Pmod+C))
i i i
K(h0,△h,△ϕ)=
(2)
Σ Σ
(Pexp)∗ (Pmod+C)2
i i i i
s
C
The sear
hofthe
onstant whi
hde(cid:28)nesthe noiselevel(ionospheri
and ele
troni
alnoise) wasmadea

ordingto the
C
fun
tional (2) maximum
ondition in form (3). It
ould be rewritten in form of the linear equation for (4):
dK
=0
dC (3)
Σ Σ Σ Σ
Pexp∗ (Pmod)2− (Pexp∗Pmod)∗ Pmod
i i i i i i i i i
C =
n∗ Σ (Pexp∗Pmod)− Σ Pmod∗ Σ Pexp (4)
i i i i i i i
The range of layer height values was
hosen from 100 to 125 km, layer thi
kness - from 2.5 to 20 km, aspe
t sensitivity
- from10 t0 25dB/grad. With the step of 2.5 km for height and thi
kness, and 2.5dB/grad for aspe
t sensitivity the model
powerpro(cid:28)leshavebeen
al
ulatedandsummarizedasamatrix. To
he
kthestabilityofthesolution,in
ludingthepresen
e
of the noise, a number of tests has been made to test its stability at all model parameters
ombinations. The testing has
been made by adding noises whi
h
orrespond both to the ionospheri
noise and statisti
al noise whi
h arise due to limited
number of samples used for averaging. During the testing 3 variants of the noise have been used. Averaginghas been made
over 500 single soundings:
1. The noise with
onstant averageamplitude that
orrespondsto the ionospheri
noise. In this
ase the noiseamplitude
was 2% from the power pro(cid:28)le maximum.
2. The noise with amplitude that is proportional to the power signal at given radar range, it
orresponds to the stati
al
noises. The amplitude of the noise was 4% from the
urrent power pro(cid:28)le value (at given height).
3
3. Low-frequen
ynoise,
orrespondingto the re
eivingte
hnique
auses. Noise amplitude was2% from the powerpro(cid:28)le
maximum, frequen
y was within a
tual (cid:28)lters bandwidth used for experiments.
The error distributions for testing results are shown at (cid:28)g.3. Green
olor
orresponds to the low-frequen
y noise, blue
olor

orresponds to the ionospheri
-like noise, magenta
olor
orresponds to the statisti
al noise. At the left top of the (cid:28)gure -
the resultsfor the layerheight, at the righttop- forthelayerthi
kness,at the bottom- forthe aspe
tsensitivity. From this
(cid:28)gure it is
learthat aspe
t sensitivity is less stable parameterto
al
ulate, the most stable parameters arelayerheight and
thi
kness. When
al
ulating aspe
t sensitivity, the algorithm provides less stable results, but inspite of this it gives a good
pre
ision, and errors with amplitudes more than model dis
reet 2.5dB/degree do not ex
eed 2% of all the tested samples.
The algorithm provides less stability for low-frequen
y noises.
1 1
0.1 0.1
0.01
0.01
0.001
0.001
0.0001
0.0001
1e-05
1e-05
-4 -3 -2 -1 0 1 2 3 4 5 6
-4 -3 -2 -1 0 1 2 3 4 5 6
dThick (km)
dH (km)
1
ionospheric noise
0.1
statistical noise
low freq. noise
0.01
0.001
0.0001
1e-05
-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16
dAsp.sens (dB/degr)
Fig.3 Errors distribution of invertingof noised model data.
In addition to testing the model inversiona

ura
yin presen
eofthe noise, atesting ofthe experimentaldatawasmade
in presen
e of the same noises. The obtained results di(cid:27)er from the results obtained when inverting the model pro(cid:28)les in
presen
e of the noise. The most stable parameters are still layer height and thi
kness. The less stable is aspe
t sensitivity,
thatwas
al
ulatedwith unsu

essfula

ura
y. Asopposedto thetestingofthemodeldata,thetestingoftheexperimental
data provides non-symmetri
al error distributions, and in number of
ases does not provide the ne
essary a

ura
y. This
e(cid:27)e
t
ouldbeexplainedbythefa
tthatanumberof
aseswe
ouldnotde(cid:28)neas'
oherente
ho'. Inspiteofthisthenumber
of parameters erroneously de(cid:28)ned (that are out of model a

ura
y) is pretty small, and this allows us to suggest the model
as adequate to the experiment data.
4
1 1
0.1 0.1
0.01 0.01
0.001 0.001
0.0001 0.0001
1e-05 1e-05
-10 -5 0 5 10 15 -20 -15 -10 -5 0 5
dHeight, km dThickness, km
1
statistical noise
0.1 ionospheric noise
low freq. noise
0.01
0.001
0.0001
1e-05
-15 -10 -5 0 5 10 15 20
dAspectSens, dB/deg
Fig.4a Errors distribution of invertingnoised experimental data (25-26.09.1998 experiment)
1 1
statistical noise
ionospheric noise
0.1 0.1
low freq. noise
0.01 0.01
0.001 0.001
0.0001 0.0001
1e-05 1e-05
-10 -5 0 5 10 15 20 25 -20 -15 -10 -5 0 5
dHeight, km dThickness, km
1
0.1
0.01
0.001
0.0001
1e-05
-15 -10 -5 0 5 10 15
dAspectSens, dB/deg
Fig 4b. Errors distribution of inverting noised experimentaldata ( 16.07.2000 experiment)
5
3 Dis
ussion.
During the work the data obtained at Irkutsk IS radar was pro
essed for strong geomagneti
storms on 25-26.09.1998 and
15-16.07.2000. The data pro
essing has shown a su

essful agreement between the model and the experimental data (more
thanahalfoftheexperimentalpro(cid:28)lesagreeswiththeexperimentaldata,withthe
orrelation
oe(cid:30)
ient0.98,andin90%of

oherente
hoobservation
asesthe
orrelation
oe(cid:30)
ientisnolessthan0.94). At(cid:28)g.5a-bthedependen
eoftheparameters
(invertedwiththedes
ribedte
hnique)ontimeisshown. Fromthe(cid:28)g.5a-bone
anseethattimedependen
eofirregularities
layer parameters (espe
ially its height and thi
kness) usually has smooth time variations. So we
an explain power pro(cid:28)le
time dependen
e by variationsofthese parameters. Thisallowsus to supposethe
orre
tnessof themodel fordes
ription of
the experimental data.
125
)
m
k
(
ht 120
g
ei
h
r 115
e
y
a
L
110
)
m 10
k
(
s
s
e
n
k 5
c
hi
r t
e
ay 0
L
30
)
r
g
e 25
d
B/
d
( 20
s
n
e
p.s 15
s
A
10
)
m
k
0
0
5
= 1000
r
(
r
e
w
o
P 17 18 19 20 21 22 23 24
Time (LT,hours)
Fig 5a Experimentaldata pro
essing results for 25-26.09.1998 experiment.
6
) 130
m
k
(
ht 125
g
ei
h 120
r
e
y
a
L 115
)
m 20
k
(
s 15
s
e
n
k 10
c
hi
r t 5
e
y
a 0
L
30
)
r
g
de 25
B/
d
( 20
s
n
e
S 15
p.
s
A
10
m) 1e+05
k
0
0
5
=
r
r( 10000
e
w
o
P
6 7 8 9
Time (LT,hours)
Fig 5b Experimental data pro
essing results for 15-16.07.2000 experiment.
The fast variations observed espe
ially in aspe
t sensitivity time variations
ould be
aused by the following:
1. Non-optimal time resolution of the experimental data (for now ~ 4 minutes)
2. Latitudinal
hangesofthemodel parameters,notin
luded into
onsideration. It isthe ele
tron-iondrift velo
ity, that

ould
ause the most signi(cid:30)
ant
hanges of any parameter.
3. Errors in the Irkutsk IS radar antenna pattern model (
urrent model has not been
alibrated at lower sidelobes,
a(cid:27)e
ting to the power pro(cid:28)le shape)
4. Not in
luding into
onsideration an azimuthal aspe
t sensitivity of the irregularities (the model of s
attered signal
is isotropi
in the plane perpendi
ular to the magneti
(cid:28)eld, due to the fa
t that we do not know ele
tri
(cid:28)eld dire
tion
exa
tly).
4 Con
lusion
In the paper we have presented a te
hnique of determining the s
attering irregularities (that
ause
oherent e
ho) layer
parametersusingtheIrkutskISradardata. Itisshownthatourte
hniquehasne
essarya

ura
y(forheightandthi
kness-
about2.5km,foraspe
tsensitivity-5dB/degree). Pro
essingoftheexperiments25-26.12.1998and15-16.07.2000hasshown
a good agreement of data
al
ulated with the data obtained by other investigators: an average layer height is 110-120km,
averagelayer thi
kness 5km, averageaspe
t sensitivity - 15dB/degree [Foster et al., 1992℄.
The investigation of the experiments with high temporal resolution allowed us to observe temporal variations of the
irregularities layer parameters. The average thi
kness and height of the layer does not
ontradi
t the data obtained by
otherinvestigators[Haldoupis, 1989,Foster et al., 1992℄. Theinvestigationoftheexperimentswithhightemporalresolution
allowed to dete
t time variations of the layer parameters. The temporal variations of the aspe
t sensitivity are observed by
us for the (cid:28)rst time and requires additional investigations.
The work was done under support of RFBR grant #07-05-01084-a.
Referen
es
[Zherbtsov et al., 2002℄ ZherebtsovG.A.,ZavorinA.V., MedvedevA.V., NosovV.E., PotekhinA.P., Shpinev B.G.Irkutsk
In
oherent S
atter radar// Radio te
hniques and ele
troni
s.- 2002.- V.47, No 11. p.1-7.
[Zolotukhina et al.,2007℄ N.A. Zolotukhina, O.I. Berngardt, B.G. Shpinev. Studying magnetospheri
disturban
es a

om-
panied by midlatitude
oherent e
ho signals//Geomagnetism and aeronomy 47. #3. pp. 343-350.
2007
7
[Buneman, 1963℄ Buneman O., Exitation of (cid:28)eld-alligned sound waves by ele
tron streams, Phys.Rev.Lett., 10,285-
287, 1963.
[Farley, 1963℄ Farley D.T., A plasma instability resulting in (cid:28)eld-alligned irregularities in the ionosphere, JGR,
68, 6083-6097,1963.
[Foster et al., 1992℄ J.C.Foster,D.Tetenbaum,C.F.delPozo,J.-P.St-Mauri
e,D.R.Moor
roft.Aspe
tanglevariations
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ity,andaltitudeforhigh-latitude34-
mE-regionirregularities,J.Geophys.
Res. 97, 8601-8617,1992.
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irregularities// Ann. Geo-
phys. V. 7. #3. P.239-258.1989.
[Potekhin et al., 1999℄ PotekhinA.P., BerngardtO.I., KurkinV.I.,ShpynevB.G., ZherebtsovG.A.Observationofabnor-
mallypowerfuls
atteringwithISTPISradar,Pro
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Symposium on Atmosphere and O
ean Opti
s, 1999.
[St.-Mauri
e et al., 1989℄ St.-Mauri
e J.-P., J.C. Foster, J.M. Holt, and C. del Pozo. First results on the observation of
440-MHzhigh-latitude
oherente
hoesfromtheE-regionwiththeMilstoneHillradar,J.Geophys.
Res. 94, 6771-6798,1989.
8