Thermal Structure of the Topside Ionosphere
at Low Latitudes:
New Observational Opportunities
Pei Chen Lai and William J. Burke
Boston College/Institute for Scientific Research
19 March 2014
Abstract
Knowledge about the range of states that the topside ionosphere can assume and the conditions
that give rise to them is essential for improving existing models used in a host of practical and
research applications. Still, the topside is at best a partially explored region. Electron density
profiles (EDPs) acquired during COSMIC-GPS radio occultation events offer promise for fuller
views of the topside. However, their reliance on Abel inversions has given users pause.
This presentation proceeds in three stages: First, we review the physics and mathematical
techniques underlying EDP extractions during occultation intervals as well as the measurement
capabilities of other relevant in situ sensors. Second, recognizing that reliance on Abel inversions
constitutes the technique’s Achilles heel, we performed a limited comparison of COSMIC EDPs
with electron densities measured by sensors on the Communications/Navigation Outage Forecast
System (C/NOFS) satellite during conjunction intervals. Results show that COSMIC EDPs were
in closer agreement with ion densities measured by the C/NOFS than were those predicted by
widely used models. Third, we outline a new technique that combines the capabilities of sensors
on the COSMIC, C/NOFS and DMSP satellites to infer altitude profiles of electron and ion
temperatures (Te, Ti), mean ion masses <mi> and ionospheric scale heights H at altitudes between
the F-layer peak and 850 km. Data acquired during eight COSMIC-C/NOFS-DMSP conjunctions
on 24 – 25 October 2011 are used to demonstrate the proposed method’s feasibility then outline
our plan to apply it to large databases. Our ultimate goal is to specify topside EDP taxonomies
that occur at low latitudes as well as the temperature and mass distributions required to support
them.
Outline and Objective
• This presentation addresses five questions:
(1)
(2)
(3)
(4)
(5)
Where is GPS and how does it operate?
What is COSMIC and what does it measure?
How do COSMIC receptions of GPS signals get turned into EDPs?
Can we trust COSMIC EDPs and learn something new from them?
What value added do data from RPAs on C/NOFs and DMSP bring?
• Our objective is to introduce this audience to GPS-COSMIC capabilities
for providing useful information about the thermal structure and dynamics
of the low-latitude ionosphere in the altitude range 200 to 800 km.
Global Position System
• GPS consists of 24 operational satellites flying
in 55o inclined, circular orbits at an approximate
altitude of 22,000 km.
- 6 orbital planes with 4 satellites per plane
- Dual frequency transmitters
f1 = 1.57542 GHz
f2 = 1.2276 GHz
• GPS receivers identify incoming code with a
precision of better than 1 ns (30 cm) by receiver
clock from the carrier waves “precise ranging
code” (10.23 Mb/s).
• The accuracies of clocks between COSMIC and
GPS are 10 to 15 m and < 1μs.
Constellation Observing System for
Meteorology Ionosphere and Climate
• COSMIC is a joint Taiwan - US mission
that was launched into 72o inclined orbits
from Vandenberg AFB on 14 April 2006.
• It consists of 6 identical 3-axis stabilized
satellites
• Initial altitude: 500 km.
• Sequentially raised to ~ 800 km.
• Orbital nodes separated by ~ 2 hours
in local time.
COSMIC Payload
GOX Occultation Antenna
GOX Occultation Antenna
COSMIC-GPS Radio Occultations
Schematics of COSMIC-GPS
radio occultation events
Cosmic may rise above
or
sink below GPS horizon
Altitude
EDP
Temperature
Schreiner et al. (1999), Radio Sci.,
34, 949–966.
GPS-to-COSMIC Propagation:
• The well-known dispersion relation for EM waves propagating in the
2
2
2
2
ionosphere with  >> pe >> ce >> en is: k  (   pe ) / c ,
2
3
where  pe  q ne /  0 me  2 f pe and f pe (kHz )  8.98 ne (cm )
• The phase v and group vg speeds of the waves are:
v 
c
2
 pe
1 2

2
 pe
 c  (1 
)
2 2
2
2
 pe
 pe
vg  c  1  2  c  (1 
)

2 2
• Group delays and phase advances depend only on electron
densities ne encountered along propagation path lengths s:
q2
t  
2c 0 me f 2 (2 ) 2
COSMIC

GPS
ne ds  
40.3
STEC
2
cf
GPS-to-COSMIC Propagation: Applications
Define the excess phase parameter S as the difference between signals
propagating in vacuum over distance |rCOSMIC – rGPS| and along S0 the
actual ray path through the ionosphere.
COSMIC
S0 

ds
GPS
S = S0 - |rCOSMIC – rGPS|
where   1- fpe2 / 2 f 2 is the index of refraction.
GPS-to-COSMIC Propagation: Applications
Schreiner et al. (1999) showed that
bending angles for L1 and L2 signals
are very small:
• 1.118 10-4  for ne = 1010 m-3
• 2.07 10-3  for ne = 1013 m-3
Hence, we assume that GPS signals
propagate along very similar paths.
Thus STEC can be calculated with
either f 1 or f 2 or both frequencies.
Bottom Line: Approximate GPS-COSMIC propagation paths as straight lines.
GPS-to-COSMIC Propagation: Applications
S1 f1
S2 f 2
(S1  S2 ) f1 f 2
STEC  


40.3
40.3 40.3( f12  f 22 )
• Using both frequencies any clock-based errors exactly cancel.
• Occultation intervals last about 12 minutes
• Since STEC measurements are recorded at rate of ~1 per second,
about 700 are accumulated to form each EDP.
• Inverse Abel transformations are then used to calculate ne along
vertical tangent lines.
ne (r )  
1

r0  rCOSMIC

r0  r
dSTEC (r0 ) / dr0
r r
2
0
2
dr
GPS-to-COSMIC Propagation: Applications
• r0 = distance from center of Earth to a specific altitude
• r = distance from center of Earth to height of tangent point
• ne profiles can then be integrated to obtain vertical TEC
800 km
VTEC 

ne (h)dh
200 km
Critical assumptions for valid Abel inversions:
(1) Propagation paths are nearly straight lines
(2) GPS and COSMIC orbits are nearly circular
(3) Electron density profiles are spherically symmetric,
i.e. horizontal gradients along ray paths are weak.
Cosmic Data Products and Availability
• COSMIC is administered by the
National Space Organization (NSPO)
and
the University Corporation for
Atmospheric Research (UCAR)
• EDP data are available in tabular
format via the internet from the
\Taiwan Analysis Center for COSMIC
(TACC): http://tacc.cwb.gov.tw/
and
UCAR: http://www.cosmic.ucar.edu/.
• The example to the right shows an EDP
and useful ephemeris information
derived from downloaded data files.
Complementary Data Sources:
SSIES on DMSP & CINDI on C/NOFS
RPA Measurements:
RPA Schematic
i+
e-
i+
Vsat
negative bias
swept voltage
negative bias
(1) 3 components of ion drift
velocities (Vi)
(2) Ni tot, Ni O+, and Ni light
(3) Ion temperatures Ti
collector plate
photo & secondary
to electronics
electrons
Current – Voltage Sweeps
Log I
Intercept  Ni
Slope  -1/Ti
(4) Mean ion mass < mi >
• SSIES has a boom-mounted
spherical Langmuir probe to
measure electron densities Ne
and temperatures Te.
• Infer topside scale heights
-6
-4
-2 0 2 4
Applied Voltage
6
8
10
H = kB(Te +Ti) / < mi> g
Two COSMIC Case Studies:
Solar Min and Max Storms
• To help understand COSMIC measurements we undertook two case studies
• The first case focused on VTEC measurements acquired during an 80-day period
in late 2007 in which ejecta from a coronal hole swept by Earth three times.
• During the first and third encounters the corotating interaction region (CIR)
at the leading edge of the high-speed stream evoked weak responses in
the dayside ionosphere.
• Strong responses seen during the second encounter demonstrated effects of
penetrating electric fields generated by complex interplanetary sources that
included the near simultaneous arrival of an ICME.
• The second case study sought to determine whether COSMIC EDPs are
trustworthy. Their differences from predictions of the NeQuick model led
previous investigators to conclude that horizontal electron density gradients
degrade COSMIC EDPs to unacceptable levels. We present empirical
tests of this dire conclusion.
Case Study 1: November 2007 Storm
EIT image from SOHO on
18 November 2007 showing
a large coronal hole near the
Sun’s central meridian
Schematic representation of a corotating
region at the leading edge of a high speed
stream in the solar wind approaching Earth.
Within streams nSW is very low.
Magnetic flux emanating from coronal holes are unipolar, with radial
components that point either toward or away from the Sun.
Case Study 1: November 2007 Storm
80-day period centered on
the November 2007 storm:
(A) F10.7: daily and 81-day running
averages
(B) NSW (red) and VSW (blue)
(C) IMF BX (blue) and BY (red)
(D) Magnetospheric electric field
(E) Dst index
Vertical dash, marking the arrivals of high speed streams in the vicinity
Earth, are separated by 27-day solar rotation periods.
Case Study 1: November 2007 Storm
Days 322 – 327, 2007
(A) Solar wind density (red) and speed
(blue)
(B) IMF BX (blue) and BY (red):
Note: crossing of heliospheric current
sheet (HCS).
(C) IMF BY (red) and BZ (blue)
(D) Magnetospheric E field (~ 1 mV/m)
(E) Sym-H index minimum (~ -70 nT)
Note: relative UTs of ICME, CIR,
HSS and HCS
UT
Case Study 1: November 2007 Storm
COSMIC VTEC versus Local Time
• VTEC Distribution sampled by
COSMIC plotted as functions
of local time in 9 latitude bins
in northern (left) and southern
(right) hemispheres.
• From this perspective VTEC
increased during the storm’s
main phase and soon relaxed.
• Apparently, no surprises!
Case Study 1: November 2007 Storm
COSMIC VTEC versus Universal Time
• Distribution of VTEC sampled by
COSMIC: days 322 – 327, 2007
plotted as functions of universal time
in 9 latitude bins in northern (left)
and southern (right) hemispheres.
• Sym-H index and VS in bottom plots
• Viewed from this perspective we
see that VTEC increased on during
day of the storm’s main phase then
relaxed.
• Decreased during first half of say 325!
•
Why?  Penetration electric field
and deviation from photochemical equilibrium.
COSMIC EDPs: Study 2
COSMIC – C/NOFS – DMSP
Conjunctions
C
24 and 25 October 2011
V
④ ⑥
②
①
COSMIC EDP: Study 2
Interplanetary and Storm Dynamics
Top Panel Traces:
20
400
10
200
0
30
0
20
SW
-3
(cm )
P
SW
600
VSW (km/s)
30
N
800
B B B (nT)
(nPa)
40
Interplanetary Drivers and
Geomagnetic Responses
• NSW
density (red)
• VSW
speed (black)
• PSW
dynamic pressure (blue)
Middle Panel Traces
Z
10
Y
0
X
• IMF BX (black)
-10
•
-20
• IMF BZ (blue)
• IMF BY (red)
-30
100
SSC Main
Phase
Sym H (nT)
50
0
1-minute averages
GSM coordinates
Bottom Panel Trace:
Recovery
Phase
• Sym H index (black)
-50
• Red dots indicate UT of EDP acquisitions.
-100
-150
-200
297:00
297:12
298:00
298:12
299:00
• Vertical dashed lines mark beginnings
of main & recovery phases
COSMIC EDP: Study 2
C/NOFS and Model Comparisons
Midnight
Dawn
Dusk
Noon
(B-P)
(C-P)
(D-P)
(A-M)
(B-M)
(C-M)
(D-M)
Pre-Storm
(A-P)
(B-R)
(C-R)
(D-R)
Recovery
(A-R)
Main Phase
Z
COSMIC EDP Study
Statistical Comparisons with C/NOFS
7
10
N = 0.612 * N
10
5
10
4
e
10
6
10
5
10
4
0.698
N = 6.31 * N
e
10
4
10
5
6
10
10
7
6
10
5
10
4
R = 0.774
-3
10
0.848
i
e
e
1000
1000
7
R = 0.799
i
-3
6
10
N = 37.88 * N
NeQuick: N [cm ]
10
7
R = 0.858
i
e
-3
COSMIC: N [cm ]
e
1.03
PBMod: N [cm ]
10
1000
1000
-3
C/NOFS: N [cm ]
i
10
4
10
5
6
10
-3
C/NOFS: N [cm ]
i
10
7
1000
1000
10
4
10
5
6
10
10
7
-3
C/NOFS: N [cm ]
i
Electron densities from EDPs:
• COSMIC (left)
• NeQuick (middle)
• PBMod (right)
Log – Log Plots
Power - Law Regression Analyses
Plotted as functions of Ni measured at C/NOF altitudes on days 297 ( ) and 298 ( ).
Dotted lines are guides indicating results if inferred Ne from EDPs = Ni from CNOFS
COSMIC Electron Density Profiles
Topside Scale Heights
COSMIC-CNOFS-DMSP Conjunctions
Top:
• Orange, black and purple
lines mark EDPs from
PBMod, COSMIC & NeQuick
• Red/blue dots show Ni
from C/NOFS / DMSP
14
Bottom:
-3
Ln Ne (cm )
13
• Linear regressions Ln (Ne)
versus altitude for h > 700 km
12
11
10
650
700
750
800
850
Altitude (km)
900
950 650
700
750
800
850
900
950
Altitude (km)
 dLn( Ne )  kB (Te  Ti )
H  1/ 

 dh   mi  g (h)
COSMIC Electron Density Profiles
Topside Scale Heights
At DMSP altitudes RPA data showed that O+ was the dominant ion
Event
Te (K)
Ti (K)
HDMSP (km)
HCOS (km)
HNeQ (km)
HPBM (km)
1
1697
1801
236.7
233.5
231.4
236.0
2
2997
2512
372.6
346.7
204.4
351.5
High degree of agreement achieved between scale heights calculated with mi, Te, Ti
from DMSP and those from COSMIC and PBMod EDP slopes.
COSMIC Electron Density Profiles
Fitting Procedure
Recently we developed a low-pass, Fourier fitting procedure that
is piecewise continuous at the altitude of the F layer peak h = hp
15
4
k 0
800  hp
4
ln N (h  hp )    ck Cos(k   )  d k Sin(k   ) 
*
e
14
13.5
13
UT:
297:10:00
GLat:
6.8
o
N
6
:
433 km
p
12
200
300
-3
1.47 10 cm
e max
h
| h  hp |
o
GLong: 104
LT:
17:00
12.5
k 0
 
Case 1
e
e COSMIC
| h  hp |
Ln (N
 
14.5
) Ln (N *)
ln N (h  hp )    ak Cos(k   )  bk Sin(k   ) 
*
e
400
500
600
700
800
900
h (km)
200  hp
15
Ln (N *) = 0.00016 + 0.9999 Ln (N
e
14.5
CINDI on CNOFS measures: <mi>, Ti and Vi
e COSMIC
)
R = 1
e
Ln (N *)
14
Since
kB (Te  Ti )  dLn( N e* ) 
H
 

 mi  g (h) 
dh

1
13.5
13
12.5
 mi (h)  g (h)  H (h)
Te (h) 
 Ti (h)
kB
12
12
12.5
13
13.5
Ln (N
14
e COSMIC
14.5
15
)
In all examples R > 0.999
0.01
GLat:
6.8
o
o
GLong: 104
LT:
17:00
10
200
Ln Ne PBM
Ln(Ne cosmic)
Ln Ni CNOFS
Ln Ni DMSP
300
400
N
h
-3
1.47 10 cm
433 km
p
500
600
COSMIC PBM
-0.005
6
:
e max
0
700
800
900
-0.01
200
300
400
600
700
800
d Ln Ne /dh (km ): COSMIC PBM
297:04:39
08:00
o
4.8
GLong:
50.2
Ne max:
hp:
1.49 10 cm
279 km
o
6
-1
0
400
500
600
h (km)
700
800
900
600
700
800
900
0.001
0
-0.001
2
e
-0.005
Ln (Ne*)
Ln Ne PBM
Ln (Ne CNOFS)
Ln (Ne DMSP)
500
0.002
0.005
-3
12
300
400
2
GLat:
13
11
300
h (km)
0.01
UT:
LT:
14
10
200
-0.005
200
900
d Ln N / dh (km-2) COSMIC PBM
15
Ln Ne: COSMIC PBM CNOFS DMSP
500
h (km)
h (km)
Case 2
0
-2
297:10:00
2
12
UT:
0.005
2
13
e
Ln N
d Ln Ne / dh (km -1): COSMIC
14
d Ln Ne/dh (km ):
CASE 1
11
0.005
PBM
15
i
Ln N Cosmic PBM CNOFS DMSP
COSMIC & PBMod EDPs
with 1st and 2nd Derivatives
during conjunctions with CNOFS & DMSP
-0.01
200
300
400
500
600
h (km)
700
800
900
-0.002
200
300
400
500
600
h (km)
700
800
900
COSMIC & PBMod EDPs
with 1st and 2nd Derivatives
during conjunctions with CNOFS & DMSP
0.02
297:19:00
08:00
GLat:
-5.8
GLomg:
N
:
154
3.77 10U cm-3
h:
300 km
e max
p
o
-1
13
o
12
0.01
0
Ln (Ne*)
Ln Ne PBM
Ln (Ne CNOFS)
Ln (Ne DMSP)
10
200
-0.02
-0.02
300
400
500
600
700
800
900
200
300
400
h (km)
500 600
h (km)
700
800
200
900
0.02
GLat:
-4.8
GLong:
145
N
2.7 10 cm
h:
12
:
e max
o
5
-3
270 km
0.01
0
Ln (Ne*)
Ln Ne PBM
Ln (Ne CNOFS)
Ln (Ne DMSP)
300
400
500
600
h (km)
700
800
900
700
800
900
0
2
10
9
200
-0.01
e
11
500 600
h (km)
2
-1
p
o
400
0.01
-2
297:19:15
04:55
300
e
13
UT:
LT:
d Ln N / dh (km ): COSMIC PBM
Case 4
d Ln N / dh (km ): COSMIC PBM
Ln Ne: COSMIC PBM CNOFS DMSP
14
0
-0.01
-0.01
11
0.01
-1
14
UT:
LT:
d Ln Ne /dh (km ): COSMIC PBM
0.02
CASE 3
d Ln Ne /dh (km ): COSMIC PBM
e
Ln N : COSMIC PBM CNOFS DMSP
15
-0.02
200
300
400
500
600
h (km)
700
800
900
-0.01
100
200 300 400 500 600 700
h (km)
800 900
GLat:
7.1
GLong:
59.4
N
:
e max
h:
13
o
o
6
-3
1.42 10 cm
342 km
p
0.005
0
e
12
0.01
10
200
300
400
500
600
700
800
900
-0.01
200
300
400
500
600
700
800
:
e max
hp:
10
200
300
400
1.66 10 cm
472 km
500
0
e
-3
600
h (km)
700
800
900
-0.02
200
500
600
700
800
900
700
800
900
0.005
-2
0.01
-0.01
6
400
0
2
N
76
o
o
300
2
298:12:55
18:00
GLong:
11
900
e
13
4.5
-0.01
200
d Ln N / dh (km ): COSMIC PBM
14
d Ln N /dh (km ) COSMIC PBM
Ln (Ne*)
Ln Ne PBM
Ln (Ne CNOFS)
Ln (Ne DMSP)
GLat
-0.005
h (km)
CASE 6
UT:
LT:
0
h (km)
0.02
-1
Ln Ne: COSMIC PBM CNOFS DMSP
h (km)
15
12
0.005
2
-0.005
Ln (Ne*)
Ln Ne PBM
Ln (Ne CNOFS)
Ln (Ne DMSP)
11
0.01
-2
297:04:39
18:37
2
14
UT:
LT:
e
CASE 5
d Ln N /dh (km-1): COSMIC PBM
Ln Ne: COSMIC PBM CNOFS DMSP
15
d Ln N / dh (km ): COSMIC PBM
COSMIC & PBMod EDPs
with 1st and 2nd Derivatives
during conjunctions with CNOFS & DMSP
300
400
500
600
h (km)
700
800
900
-0.005
200
300
400
500
600
h (km)
COSMIC & PBMod EDPs
with 1st and 2nd Derivatives
during conjunctions with CNOFS & DMSP
-6.3
GLong:
26.7
N
:
e max
o
5
-3
4.4 10 cm
h:
13
o
GLat:
277 km
0.005
-1
p
0.01
Ln (Ne*)
Ln Ne PBM
Ln (Ne CNOFS)
Ln (Ne DMSP)
10
200
300
400
500
e
-0.005
2
e
11
600
700
800
-0.01
200
900
300
400
500
600
700
800
-0.005
200
900
297:03:39
05:45
GLat:
-9.5
GLong:
34.1
238 km
p
0
e
12
0.01
-2
h:
13
-3
7.3 10 cm
10
200
300
400
500
600
h (km)
700
800
900
800
900
700
800
900
0
-0.01
2
Ln (Ne*)
Ln Ne PBM
Ln (Ne CNOFS)
Ln (Ne DMSP)
700
2
:
e max
o
600
e
N
o
5
500
0.001
d Ln N / dh (km ): COSMIC PBM
UT:
LT:
d Ln N /dh COSMIC PBM
14
400
h (km)
0.02
15
Case 8
300
h (km)
e
Ln N : COSMIC PBM CNOFS DMSP
h (km)
11
0
2
0
e
12
0.005
-2
14
298:03:15
05:12
d Ln N / dh (km ): COSMIC PBM
UT:
LT:
CASE 7
d Ln N / dh (km ): COSMIC PBM
Ln N : COSMIC PBM CNOFS DMSP
15
-0.02
200
300
400
500
600
h (km)
700
800
900
-0.001
200
300
400
500
600
h (km)
COSMIC Electron Density Profiles
Summary and Conclusions:
• Presented case studies were undertaken to establish a feasible methodology
for testing the reliability of COSMIC-based topside EDPs and VTEC estimates
• The November 2007 and October 2011 storms provided a variety of external
driving conditions.
• The PLP on CNOFS provided high resolution ion densities for comparison with
EDPs estimated from COSMIC STEC measurements and model predictions.
• EDPs from COSMIC acquired within  15  were in better agreement with CNOFS
Ni measurements than model predictions.
• Early comparisons indicate that further study and analysis is worthwhile, using
Ni , Ti and Te from DMSP and C/NOFS to estimate topside thermal distributions.
• We have taken first steps towards developing an AI approach to EDP evaluations.