• During the past decade we have learned how to “forward-model” the altitude variations of F-
region incoherent scatter signals (power, correlations, spectra) collected with multi-beam radar 
configurations including polarization and spatial diversity:
• Experience gained in differential-phase (Feng et al.), MST-ISR (A. Akgiray M.S. Thesis) 
experiments, and also beam-scanned ALTAIR results... 
• Advances in ISR theory close to perp-to-B:  Sulzer and González (1999), Woodman (2004), 
Kudeki and Milla (2005), M. Milla PhD Thesis work...
• Faster computing, availability of clusters, reliable magnetic field model (IGRF)...
Perp-to-B incoherent scatter 
measurements of F-region drifts, 
density, and temperatures at JRO 
Erhan Kudeki1,  Marco Milla1,  Pablo Reyes1,  Jorge Chau2,  and  Otto Castillo2
(1) University of Illinois               (2) Jicamarca Radio Observatory
• As a consequence we are reaching the point of being able to conduct difficult experiments 
at JRO such as measuring F-region densities and temperatures simultaneous with 
high-quality perp-to-B drifts:
• We describe here one such experiment conducted in June 2008 and show 
preliminary results.
0 2 4 60
100
200
300
400
500
600
700
800
900
Densities [1011 m−3]
He
igh
t [
km
]
1 1.5 20
100
200
300
400
500
600
700
800
900
Te/Ti
He
igh
t [
km
]
Basic idea used in the experiment:    In an ionosphere with Ne and Te/Ti 
profiles shown on the left, a north-south beam scan would produce a total backscatter 
power map shown on the right, with the sharp enhancement (“dagger”) in the direction 
where the radar beam is perpendicular to B:
                                    away from perp to B, otherwise                ,    
A scan like this cannot be done at JRO having fixed beams, but the effect has been observed 
and fully modeled at ALTAIR to estimate Ne and Te/Ti parameters from power scan data. 
η =Ps ∝ Ne1 + Te/Ti Ps ∝ Neη
12 14 16 18 20
100
200
300
400
500
600
700
Power (dB)
He
igh
t (
km
)
Principal Polarization
Date: 20−Sep−2004 12:22 PM
50.36°
79.43°
80.47°
81.50°
89.44°
12 14 16 18 20
100
200
300
400
500
600
700
Power (dB)
He
igh
t (
km
)
Orthogonal Polarization
Date: 20−Sep−2004 12:22 PM
50.36°
79.43°
80.47°
81.50°
89.44°
At ALTAIR, operating at
422 MHz, magneto-ionic 
effects are negligible, so 
that total power can be 
collected using a single 
polarization (circular).
At JRO, operating at 50 
MHz, MI-effects are 
important, and thus both 
“co-pol” and “x-pol” 
components of the 
scattered power need to 
be collected and 
processed to make Ne 
and Te/Ti estimation using 
a similar approach.
ALTAIR power scan: Simulated total power 
and JRO beams used in 
June 08 experiment:
WEST
SOUTH
EAST
2
1 5
4
3 6
UP-POL DN-POL
TX
RX
RX1=WEST BOWTIE
RX2=WEST QUARTER
RX5=SOUTH CO-POL
EQUAL
POWER
IN ALL
BEAMS
RX3=EAST BOWTIE
RX4=EAST QUARTER
RX6=SOUTH X-POL
MAGNETIC
NORTH
RX1.RX2*=NS INTERF. RX3.RX4*=NS INTERF. 
June 08 experiment:  A multi-beam and 
dual-polarization mode taking advantage of 
the modularity of the JRO antenna:
Co-pol X-pol
• A multi-slab magneto-ionic propagation model based on IGRF (see next slide):
• “Rotates” the polarization vectors of tx’ed x-pol (dn) and y-pol (up) signals 
in proportion to electron density and magnetic aspect angles:
• Faraday rotation at large aspect angles
• Cotton-Mouton effect at small aspect angles
• Two-way antenna beam pattern (see slide 7) calculations based on FFT’s of 
phasing distributions on antenna modules of both polarizations:
• Includes complex valued two-way cross-beam patterns for “rotated” signal 
components --- e.g., east beam (dn) couples to west beam (up) via common 
sidelobes
• Receiver gains included as model unknowns in addition to Ne and Te/Ti
• Ionosonde virtual heights can be used as additional constraints
• Updated collisional IS theory (see slide 14) used to relate the backscatter RCS 
to ionospheric state parameters
Forward model details
XY
Z
Qx
Qy
1
B
θ
kˆθˆ
φˆ
Iterate after modifying ∆n, n¯, a, θˆ, φˆ due to slow varing density and #B
vx ∝ pˆx · (Eθ θˆ + Eφφˆ) vy ∝ pˆy · (Eθ θˆ + Eφφˆ)
∆n =
nO − nX
2
n¯ =
nO + nX
2
a =
FO
YL
n
2
O,X = 1−
X
1− FO,X
YL = Y cos θ, YT = Y sin θ, Y =
Ω
ω
, X =
ω2p
ω2
A magneto-ionic propagation problem through a multi-slab ionosphere model: 
pˆx
FO = F1 − F2, FX = F1 + F2, F1 =
Y 2
T
/2
1−X
, F 22 = F
2
1 + Y
2
L
pˆx =
kˆ × kˆ × xˆ
|kˆ × kˆ × xˆ| ≡ Exoxˆ+ Eyoyˆ + Ezozˆ ≡ Eθoθˆ + Eφoφˆ
Polarization
unit vector: 
bˆ
φˆ =
bˆ× kˆ
|bˆ× kˆ|
θˆ = φˆ× kˆ
21
5
4
3
6
DN-POL
RX1=WEST BOWTIE
RX2=WEST QUARTER
RX5=SOUTH CO-POL
RX3=EAST BOWTIE
RX4=EAST QUARTER
RX6=SOUTH X-POL
UP-POL
MAGNETIC
NORTH
RX1.RX2*=NS INTERF. RX3.RX4*=NS INTERF. 
MAGNETIC
NORTH
!x’ (rad)
! y
’ (
ra
d)
South beam (One quarter)
D2W = 73.73 dB
ABS = 4375.94
 
 
−0.1 −0.05 0 0.05 0.1
−0.1
−0.05
0
0.05
0.1
−40
−35
−30
−25
−20
−15
−10
−5
0
!x’ (rad)
! y
’ (
ra
d)
West beam (Bow−tie)
D2W = 78.30 dB
ABS = 4716.19
 
 
−0.1 −0.05 0 0.05 0.1
−0.1
−0.05
0
0.05
0.1
−40
−35
−30
−25
−20
−15
−10
−5
0
!x’ (rad)
! y
’ (
ra
d)
West beam (One quarter)
D2W = 74.88 dB
ABS = 3111.32
 
 
−0.1 −0.05 0 0.05 0.1
−0.1
−0.05
0
0.05
0.1
−40
−35
−30
−25
−20
−15
−10
−5
0
!x’ (rad)
! y
’ (
ra
d)
East beam (Bow−tie)
D2W = 78.04 dB
ABS = 4363.89
 
 
−0.1 −0.05 0 0.05 0.1
−0.1
−0.05
0
0.05
0.1
−40
−35
−30
−25
−20
−15
−10
−5
0
!x’ (rad)
! y
’ (
ra
d)
East beam (One quarter)
D2W = 74.54 dB
ABS = 2888.92
 
 
−0.1 −0.05 0 0.05 0.1
−0.1
−0.05
0
0.05
0.1
−40
−35
−30
−25
−20
−15
−10
−5
0
3-Tx, 6-Rx
3-Beam directions
1 polarization diversity (south)
2 spatial diversities (west and east) 
WEST
SOUTH
EAST
2
1 5
4
3 6
UP-POL DN-POL
TX
RX
RX1=WEST BOWTIE
RX2=WEST QUARTER
RX5=SOUTH CO-POL
EQUAL
POWER
IN ALL
BEAMS
RX3=EAST BOWTIE
RX4=EAST QUARTER
RX6=SOUTH X-POL
MAGNETIC
NORTH
RX1.RX2*=NS INTERF. RX3.RX4*=NS INTERF. 
Time [Hour]
Ra
ng
e 
[km
]
DEWD 3Bb − South Beam (Up−pol) − Date: 24−Jun−2008
 
 
6 8 10 12 14 16 18 20100
200
300
400
500
600
700
SN
R 
+ 
1 
[d
B]
0
1
2
3
4
5
Time [Hour]
Ra
ng
e 
[km
]
DEWD 3Bb − South Beam (Dn−pol) − Date: 24−Jun−2008
 
 
6 8 10 12 14 16 18 20100
200
300
400
500
600
700
SN
R 
+ 
1 
[d
B]
0
1
2
3
4
5
Time [Hour]
Ra
ng
e 
[km
]
DEWD 3Bb − East Beam (Dn−pol) − Date: 24−Jun−2008
 
 
6 8 10 12 14 16 18 20100
200
300
400
500
600
700
SN
R 
+ 
1 
[d
B]
0
1
2
3
4
5
Time [Hour]
Ra
ng
e 
[km
]
DEWD 3Bb − East Beam (Dn−pol) − Date: 24−Jun−2008
 
 
6 8 10 12 14 16 18 20100
200
300
400
500
600
700
SN
R 
+ 
1 
[d
B]
0
1
2
3
4
5
Time [Hour]
Ra
ng
e 
[km
]
DEWD 3Bb − West Beam (Up−pol) − Date: 24−Jun−2008
 
 
6 8 10 12 14 16 18 20100
200
300
400
500
600
700
SN
R 
+ 
1 
[d
B]
0
1
2
3
4
5
Time [Hour]
Ra
ng
e 
[km
]
DEWD 3Bb − West Beam (Up−pol) − Date: 24−Jun−2008
 
 
6 8 10 12 14 16 18 20100
200
300
400
500
600
700
SN
R 
+ 
1 
[d
B]
0
1
2
3
4
5
21
5
4
3
6
DN-POL
RX1=WEST BOWTIE
RX2=WEST QUARTER
RX5=SOUTH CO-POL
RX3=EAST BOWTIE
RX4=EAST QUARTER
RX6=SOUTH X-POL
UP-POL
MAGNETIC
NORTH
RX1.RX2*=NS INTERF. RX3.RX4*=NS INTERF. 
MAGNETIC
NORTH
0 2 4 6
x 104
100
200
300
400
500
600
700
800
900
Power
Ra
ng
e 
[km
]
 
 
[1] West 1
[2] West 2
[3] East 1
[4] East 2
[5] South (Up)
[6] South (Dn)
0 2 4
x 104
100
200
300
400
500
600
700
800
900
Correlation
 
 
[1,2] West
[3,4] East
[5,6] South
−100 0 100
100
200
300
400
500
600
700
800
900
Phase [deg]
 
 
[1,2] West
[3,4] East
[5,6] South
“Beam weighted” simulations of power and
cross-correlation profiles for the six receivers:
0 2 4 60
100
200
300
400
500
600
700
800
900
Densities [1011 m−3]
He
igh
t [
km
]
1 1.5 20
100
200
300
400
500
600
700
800
900
Te/Ti
He
igh
t [
km
]
Hypothetical ionosphere:
Simulated co-pol and x-pol
power distributions:
6
8
10
12
14
16
18
20
250
300
350
400
450
500
550
600
1
1.5
2
 
Time [Hours]
DEWD 3Bb − Temperature ratio (Te/Ti) − Date: 24−Jun−2008
Height [km] 
Te
/T
i
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
6 8
10 12
14 16
18 20
300
400
500
600
0
1
2
3
4
x 1011
 
Time [Hours]
DEWD 3Bb − Electron Density (Ne) − Date: 24−Jun−2008
Height [km]
 
Ne
 [m
−3
]
0.5
1
1.5
2
2.5
3
3.5
4
x 1011
0 2 4 6
x 104
100
200
300
400
500
600
700
800
900
Power
Ra
ng
e 
[km
]
 
 
[1] West 1
[2] West 2
[3] East 1
[4] East 2
[5] South (Up)
[6] South (Dn)
0 2 4
x 104
100
200
300
400
500
600
700
800
900
Correlation
 
 
[1,2] West
[3,4] East
[5,6] South
−100 0 100
100
200
300
400
500
600
700
800
900
Phase [deg]
 
 
[1,2] West
[3,4] East
[5,6] South
Time [Hour]
Ra
ng
e 
[km
]
DEWD 3Bb − South Beam (Up−pol) − Date: 24−Jun−2008
 
 
6 8 10 12 14 16 18 20100
200
300
400
500
600
700
SN
R 
+ 
1 
[d
B]
0
1
2
3
4
5
Time [Hour]
Ra
ng
e 
[km
]
DEWD 3Bb − South Beam (Dn−pol) − Date: 24−Jun−2008
 
 
6 8 10 12 14 16 18 20100
200
300
400
500
600
700
SN
R 
+ 
1 
[d
B]
0
1
2
3
4
5
Time [Hour]
Ra
ng
e 
[km
]
DEWD 3Bb − East Beam (Dn−pol) − Date: 24−Jun−2008
 
 
6 8 10 12 14 16 18 20100
200
300
400
500
600
700
SN
R 
+ 
1 
[d
B]
0
1
2
3
4
5
Time [Hour]
Ra
ng
e 
[km
]
DEWD 3Bb − East Beam (Dn−pol) − Date: 24−Jun−2008
 
 
6 8 10 12 14 16 18 20100
200
300
400
500
600
700
SN
R 
+ 
1 
[d
B]
0
1
2
3
4
5
Time [Hour]
Ra
ng
e 
[km
]
DEWD 3Bb − West Beam (Up−pol) − Date: 24−Jun−2008
 
 
6 8 10 12 14 16 18 20100
200
300
400
500
600
700
SN
R 
+ 
1 
[d
B]
0
1
2
3
4
5
Time [Hour]
Ra
ng
e 
[km
]
DEWD 3Bb − West Beam (Up−pol) − Date: 24−Jun−2008
 
 
6 8 10 12 14 16 18 20100
200
300
400
500
600
700
SN
R 
+ 
1 
[d
B]
0
1
2
3
4
5
Least-squares fit beam-
weighted power and cross-
correlation profiles obtained
from the six receivers to 
estimate the Ne and Te/Ti 
profiles at 5 min integration 
intervals:
Time [Hours]
He
igh
t [
km
]
DEWD 3Bb − Temperature ratio (Te/Ti) − Date: 24−Jun−2008
 
 
6 8 10 12 14 16 18 20
250
300
350
400
450
500
550
600
Te
/T
i
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
Time [Hours]
He
igh
t [
km
]
DEWD 3Bb − Temperature ratio (Te/Ti) − Date: 23−Jun−2008
 
 
6 8 10 12 14 16 18 20
250
300
350
400
450
500
550
600
Te
/T
i
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
Time [Hours]
He
igh
t [
km
]
DEWD 3Bb − Electron Density (Ne) − Date: 23−Jun−2008
 
 
6 8 10 12 14 16 18 20
250
300
350
400
450
500
550
600
Ne
 [m
−3
]
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10
11
Time [Hours]
He
igh
t [
km
]
DEWD 3Bb − Electron Density (Ne) − Date: 24−Jun−2008
 
 
6 8 10 12 14 16 18 20
250
300
350
400
450
500
550
600
Ne
 [m
−3
]
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10
11
June 23-24, 2008 Experiments: Ne and Te/Ti estimates:

−200 −150 −100 −50 0 50 100 150 20073.5
74
74.5
75
75.5
76
76.5
77
77.5
78
78.5
Velocity [m/s]
Po
we
r s
pe
ctr
um
 [d
B]
West beam (Bow−tie)
Date: 23−Jun−2008 13:25:00
 
 
282.15 km
297.00 km
311.85 km
326.70 km
Spectral fitting and Te plans
Velocity [m/s]
Ra
ng
e 
[km
]
West beam (One quarter)
Date: 23−Jun−2008 13:25:00
 
 
−200 −150 −100 −50 0 50 100 150 200
0
100
200
300
400
500
600
700
800
900
70
71
72
73
74
75
76
77
78
79
80
Velocity [m/s]
Ra
ng
e 
[km
]
West beam (Bow−tie)
Date: 23−Jun−2008 13:25:00
 
 
−200 −150 −100 −50 0 50 100 150 200
0
100
200
300
400
500
600
700
800
900
70
71
72
73
74
75
76
77
78
79
80
Velocity [m/s]
Ra
ng
e 
[km
]
East beam (One quarter)
Date: 23−Jun−2008 13:25:00
 
 
−200 −150 −100 −50 0 50 100 150 200
0
100
200
300
400
500
600
700
800
900
70
71
72
73
74
75
76
77
78
Velocity [m/s]
Ra
ng
e 
[km
]
East beam (Bow−tie)
Date: 23−Jun−2008 13:25:00
 
 
−200 −150 −100 −50 0 50 100 150 200
0
100
200
300
400
500
600
700
800
900
70
71
72
73
74
75
76
77
78The spectrum Doppler shift is a 
direct measurement of the drift.
The spectrum width will tell us what 
the temperatures are.
Once the densities and Te/Ti are known, we can analyze our spectrum 
measurements and estimate the remaining parameter (Te) from the 
width of the spectrum. For this purpose an Incoherent Scatter theory 
valid for all magnetic aspect angles is needed.
Jicamarca antenna beam 
illuminates this range of 
magnetic aspect angles
Collisional IS spectrum model
Frequency (Hz)
As
pe
ct 
an
gle
 (d
eg
)
Electron Gordeyev integral (Ne=1E12m!3, Te=1000K, !B=3m)
 
 
!1500 !1000 !500 0 500 1000 15000
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Re
{Je
(f)}
 (d
B)
!20
!10
0
10
20
30
40
Based on the Fokker-Planck 
collision model, we have developed 
a Monte-Carlo procedure to 
compute the electron Gordeyev 
integral for all magnetic aspect 
angles (including the perpendicular 
to B direction).
Using this collisional IS spectrum theory and including 
magnetoioinic propagation effects we can model the beam-
weighted spectrum measured at Jicamarca. Using this model, 
we can fit the data and obtain Te. Of course, we can use these 
estimates to improve our estimates of Ne and Te/Ti.
Conclusions, Future Work
• We have learned how to model and fit multi-beam/multi-polarization power and 
correlation data to estimate electron density and Te/Ti profiles in addition to F-
region vertical and EW drifts under quiet (non-turbulent) ionospheric conditions. 
• We still need to streamline the process for routine operational use.
• Spectral fitting for Te estimation should now be possible given the Te/Ti profiles and 
the development of collisional ISR spectral model.
• This is the fulfillment of objectives set about a decade ago, when spectral Te 
estimations were first tried (Bhattacharyya, 1998) and the inadequacy of ISR theory 
close to perp-to-B was first realized. 
• June 08 data set will be used in our renewed attempt to estimate Te.
• The forward models developed should also be useful in model verification/assimilation: 
e.g., in LISN project, we can examine to what extent the LISN model ionosphere (Ne, Te, 
Ti) fits the Jicamarca multi-beam/multi-polarization correlation and spectrum profiles --- 
a first step towards assimilation of JRO data in LISN.