c© 2009 Ethan Schofield Miller
RADIO AND OPTICAL TECHNIQUES FOR LOCATING
EQUATORIAL PLASMA IRREGULARITIES
BY
ETHAN SCHOFIELD MILLER
B.S., Ohio Northern University, 2003
M.S., University of Minnesota, 2005
DISSERTATION
Submitted in partial fulfillment of the requirements
for the degree of Doctor of Philosophy in Electrical and Computer Engineering
in the Graduate College of the
University of Illinois at Urbana-Champaign, 2009
Urbana, Illinois
Doctoral Committee:
Assistant Professor Jonathan J. Makela, Chair
Professor Erhan Kudeki
Professor Steven J. Franke
Professor Andreas C. Cangellaris
ABSTRACT
Plasma density depletions occur in the post-sunset F region ionosphere almost nightly during certain
seasons at equatorial latitudes. These depletions contain density irregularities of scales ranging from
a few centimeters to thousands of kilometers. Spread-F , the disruption of ionospheric measurements
with ionosondes and incoherent scatter radar, and scintillation (fading) of trans-ionospheric radio
communication and navigation signals are well-known symptoms of depletions. This dissertation
describes new techniques to combine optical and radio ionospheric remote sensing data in common
formats to leverage observational strengths and mitigate weaknesses, leading to new or improved
physical interpretations. Principally, a technique for locating scintillation-causing irregularities in
the Earth’s equatorial regions using radio occultation and airglow imaging is presented. A similar
technique is employed to study the relationship between Bragg-scale radar backscatter and depletions
observed with the airglow imager. A climatology of airglow and radar data from the central Pacific
that uncovers regularly occurring post-midnight depletions is also presented. Combined airglow and
radar data from these events suggest that polarization electric fields within mesoscale traveling iono-
spheric disturbances (MSTIDs) seed post-midnight equatorial plasma depletions during geomagnetic
quiet periods at solar minimum.
ii
Nos esse quasi nanos, gigantium humeris insidentes, ut possimus plura eis et remotiora videre, non
utique proprii visus acumine, aut eminentia corporis, sed quia in altum subvenimur et extollimur
magnitudine gigantea.
—Bernard of Chartres
iii
ACKNOWLEDGMENTS
My wife Sarah often remarks that she had no idea what she was getting into when she married a
Ph.D. student. Despite that, she has loved, supported, admonished, and encouraged me in ways
that no one else can. For that, I am very grateful. My parents Mic and Leah Miller not only instilled
in me the curiosity of a scientist and the practicality of a technician, but they have enthusiastically
encouraged my education and research.
Jonathan Makela gave me the opportunity to tinker with equipment and ideas, travel widely,
and meet interesting people. His support and patience as an advisor have been invaluable. I have
enjoyed both classroom and personal interactions with the other members of my committee, Erhan
Kudeki, Steve Franke, and Andreas Cangellaris. They have left their mark on me and my work. I
am also grateful to Farzad Kamalabadi and Gary Swenson for insightful conversations on remote
sensing and engineering education.
The operational linchpin in the Remote Sensing and Space Science group is Paula O’Connor. She
navigated the world of university business, international travel, and a rag-tag collection of vendors,
keeping us on the move and doing research. Dan Jordan provided logistical support. Scott McDonald
and Marc Stevens were invaluable resources in the machine shop and at the Urbana Atmospheric
Observatory facility. Mary Schlembach and Bill Mischo kept me stocked with books and journals.
I shared a spacious office with Chad Carlson, Scott Anderson, and Tony Mangognia. We have
spent hours talking about remote sensing, education, physics, engineering, and life in general. Marco
Milla and Pablo Reyes provided intimate details of the Jicamarca radar. Joe Comberiate, Romina
Nikoukar, and Daniel Yao lent their considerable signal processing experience on occasion. I have
also enjoyed working closely with Shaun Armstrong, Dwayne Hagerman, Peter Hedlund, Yiyi Huang,
Shawn Adderly, Sameeraj Rao, Dan Fisher, and many others as a part of the Airglow and Irregu-
larities group.
The wider CEDAR community has been extraordinarily supportive: Koki Chau (JRO) and Dave
Hysell (Cornell) have provided data, insight, and criticism. Mike Kelley (Cornell) sent me to Maui to
work on the imagers and GPS receiver. Rebecca Bishop (Aerospace), Roland Tsunoda (SRI), Keith
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Groves (AFRL), Sunanda Basu (BC/NRL), and Warner Ecklund (CXI) have provided access to
valuable data. Stig Syndergaard (UCAR) got me started doing radio occulation analysis. Countless
others have shared valuable feedback to presentations, posters, and papers.
Jake Burger (Boeing/Maui), Gale Brehmer (CTIO/Chile), Jorge Brillones (CTIO/Chile), Ron
Mahabir (UWI/Trinidad), and Alan Gross (Bonaire) have been resilient and diligent maintainers
of our instrumentation in the field. We would not be able to collect the volume or quality of data
without them.
The work presented in this dissertation was supported by a variety of sources, including a start-up
grant from the University of Illinois at Urbana-Champaign to Jonathan Makela, National Science
Foundation grant ATM-0517641, Naval Research Laboratory contract N00173-05-1-G904, and a
National Science Foundation CAREER award.
v
TABLE OF CONTENTS
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
LIST OF ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi
LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii
CHAPTER 1 THE EQUATORIAL IONOSPHERE . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Quiescent Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Irregularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Irregularity Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.6 Questions and Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.6.1 Four problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.6.2 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.7 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
CHAPTER 2 IONOSPHERIC OBSERVATIONS AND REMOTE SENSING . . . . . . . . 19
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Radio Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.1 Ionosondes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.2 Backscatter radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.3 Satellite beacons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.4 Irregularity imaging with occultation . . . . . . . . . . . . . . . . . . . . . . . 34
2.3 Optical Imaging Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.3.1 Airglow chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.3.2 Intensity interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3.3 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3.4 Flat field calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.3.5 Spatial calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.3.6 Post-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.3.7 Keogram representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
CHAPTER 3 ELECTRIC FIELD MAPPING AND THE FIELD-ALIGNED AIRGLOW
IMAGING TECHNIQUE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2 Electric Field Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2.1 Physical derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2.2 Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2.3 Model ionosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
vi
3.2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.3 Interpretation of Airglow Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.3.1 Equatorial plasma depletions . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.4 Field-Aligned Imaging Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
CHAPTER 4 LOCALIZATION OF SCINTILLATION-CAUSING REGIONS . . . . . . . . 69
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2 Instrumentation and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
CHAPTER 5 RELATIONSHIP BETWEEN COHERENT BACKSCATTER AND
AIRGLOW DEPLETIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2 Instrumentation and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.4.1 Depletions and backscatter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.4.2 Airglow layer altitude estimation . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.4.3 Decaying backscatter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.4.4 Climatology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
CHAPTER 6 EVIDENCE OF A MID-LATITUDE SEED FOR EQUATORIAL PLASMA
DEPLETIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.2 Instrumentation and Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
CHAPTER 7 CONCLUSION AND FUTURE DIRECTIONS . . . . . . . . . . . . . . . . . 103
7.1 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.1.1 Data presentation and analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.1.2 Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.2 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.2.1 Seeding of depletions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
7.2.2 Inverse scattering and radio occultation . . . . . . . . . . . . . . . . . . . . . 105
APPENDIX A DATA MANAGEMENT WORKFLOW . . . . . . . . . . . . . . . . . . . . 108
A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
A.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
APPENDIX B A CASE STUDY IN FIELDING INSTRUMENTATION . . . . . . . . . . . 110
B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
B.2 Site Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
B.3 Equipment Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
B.4 Transportation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
B.5 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
B.5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
B.5.2 Specific details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
B.6 After the Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
vii
APPENDIX C GEOMAGNETIC FIELD MODELS . . . . . . . . . . . . . . . . . . . . . . 120
C.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
C.2 Step Size Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
C.3 IGRF vs AACGM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
AUTHOR’S BIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
viii
LIST OF TABLES
2.1 Reaction Rate Coefficients for the 630.0-nm Emission . . . . . . . . . . . . . . . . . 38
B.1 List of Tools and General Consumables Required for PICASSO/GPS Installation . . 115
ix
LIST OF FIGURES
1.1 Empirical models of the electron and neutral density profiles in the ionosphere-
thermosphere system. The electron density is from the International Reference Iono-
sphere, IRI 2007 [Bilitza and Reinisch, 2008], and the neutral densities come from
NRLMSISE-00 [Picone et al., 2002]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Typical low-latitude conductivity profiles for solar maximum conditions up to 900 km
at local (a) noon and (b) midnight. Note that the Pedersen and Hall conductivities
are scaled by 106. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Illustration of the equatorial ionosphere at the sunset terminator. This example is
taken from the central Pacific region (geo: 2◦ N, 203.5◦ E) in late August 2005. The
equatorial F -region density plotted in the vertical (time-altitude) plane and the off-
equator E region density plotted in the horizontal (time-latitude) plane were modeled
using the International Reference Ionosphere (IRI) 2007. The thermospheric neutral
wind vectors are from the Horizontal Wind Model (HWM07). The electrodynamic
quantities are labeled according to Farley et al. [1986] . . . . . . . . . . . . . . . . . 5
1.4 Equatorial anomaly crests over the central Pacific observed through the 135.6-nm
nightglow emission by the GUVI instrument. Each strip of airglow image represents
one orbit of the TIMED spacecraft. The time of the geomagnetic equator crossing is
given in UT at the top. Data courtesy of JHU/APL. . . . . . . . . . . . . . . . . . . 6
1.5 Ionograms from Jicamarca, Peru´, on the night of 22 October 2006 under (a) normal
(at about 1930 LT) and (b) spread (2030 LT) conditions. Frame (c) is the coherent
backscatter map from the Jicamarca radar for the same time period. The highlighted
vertical lines refer to the times of the ionograms in subfigures (a) and (b). Data
courtesy of Jicamarca Radio Observatory. . . . . . . . . . . . . . . . . . . . . . . . . 8
1.6 Cartoon of the gravitational Rayleigh-Taylor instability operating in the equatorial
ionosphere. The geomagnetic field, B, is directed into the page. Region 1 has much
higher plasma density than Region 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.7 Evolution of equatorial plasma depletion during growth. Lines of magnetic latitude
extend from lower left to upper right. The center (dotted) line is the geomagnetic
equator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.8 Modulation of density and location of the northern equatorial arc observed from space
by the IMAGE spacecraft. The southern arc was reflected across the geomagnetic
equator. After [Immel et al., 2006]. (Reproduced with permission of the American
Geophysical Union.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.9 Geometry of the space-to-ground radio wave scintillation problem. A slab of irregu-
larities with thickness L exists at a distance z from the receiver. The transmitter is
much farther from the irregularities than the receiver (Fresnel approximation). . . . 14
1.10 SCINDA S4 plots from Anco´n, Peru´, in September and October 2006. Notice that
scintillation occurs almost on a nightly basis. After [Miller and Makela, 2008]. (Re-
produced with permission of the American Geophysical Union.) . . . . . . . . . . . . 15
2.1 Range-time-intensity (RTI) plot of backscatter SNR for the Christmas Island 50-MHz
radar on the night of 4 August 2003. . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
x
2.2 A cartoon illustration of the slit camera problem in backscatter radar. The ten panels
across the top represent snapshots of an irregularity process that moves left-to-right
and evolves with time. The bottom panel is the aggregate of strips from the center
of each of the ten panels. It is clear that changes in velocity smear the slit panel
image. Irregularities also enter the left side of of the beam fully formed or continue
developing once they exit the right side. . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Radar images of plasma bubble formation from Jicamarca, Peru´. The images are ap-
proximately 9 minutes apart. The first three frames show “bottom side” irregularities
at 350 km and the last two show irregularities forming up to about 500 km. (Figures
courtesy of Jicamarca Radio Observatory.) . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4 Illustration of the time-of-arrival principle applied to GPS. Three transmitters labeled
{A,B,C} produce synchronized pulses that are received at Z. By computing the
transit times of the pulses, the location of Z can be fixed. . . . . . . . . . . . . . . . 28
2.5 Cartoon of immersion occultation geometry. The bending angle is exaggerated for
effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.6 Abel transform geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.7 Occultation inversion during the mid-day time period. The left plot shows the cali-
brated TEC as a function of the ray tangent altitude. The center plot is the inverted
electron density profile. The right plot is the SNR on the GPS L1 frequency. Data
provided courtesy of the UCAR COSMIC Project Office. . . . . . . . . . . . . . . . . 33
2.8 Nighttime occultation inversion in the presence of irregularities at many scales. The
left plot shows the calibrated TEC as a function of the ray tangent altitude. The
center plot is the inverted electron density profile. Notice that the inverted profile is
negative up to 225 km. This is an artifact of the spherical symmetry assumption in
an atmosphere that is not spherically symmetric. The right plot is the 1-Hz SNR on
the GPS L1 frequency. Large, rapid fluctuations occur over most of the occultation.
This suggests that small-scale irregularities (which may be associated with equato-
rial plasma depletions) are present. Data provided courtesy of the UCAR COSMIC
Project Office. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.9 Forward (top) and inverse (bottom) models of diffraction due to irregularities at
x = 100. The forward field was sampled at x = 200. In the inverse model, the
reconstructed field exhibits a focusing effect at x = 100. This indicates the position
of the irregularities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.10 Geometry of the two-dimensional diffraction tomography (“back propagation”) prob-
lem. The receiver is in low-Earth orbit over the eastern Caribbean. The GPS satellite
is far below the figure. The 2-D solution is computed in the plane drawn tangent to
Earth’s surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.11 Simplified OI transition diagram showing commonly observed equatorial airglow emis-
sions. This figure is a considerably simplified version of Figure 1 in Tinsley et al.
[1973]. There are a number of high-energy states with transitions that populate the
1D and 5P states that are not shown here. . . . . . . . . . . . . . . . . . . . . . . . . 37
2.12 630.0-nm emission profile compared to ne and [O2] profiles. Peak emission/density
altitudes are indicated by the horizontal line and marker (◦). In the oxygen profile,
the electron density peak altitude and scale-height are indicated. . . . . . . . . . . . 39
2.13 KEO architecture all-sky airglow imager fitted with a CCD camera (back). PICASSO
architecture all-sky airglow imager (front). . . . . . . . . . . . . . . . . . . . . . . . . 41
2.14 (a) Geographic view of the PICASSO narrow-field imager at Cerro Tololo, Chile
(CTIO). The field of view assumes a 250-km emission altitude for the airglow. (b)
This figure shows the meridional cross-section, highlighting that the lines of sight are
nearly parallel to the geomagnetic field. . . . . . . . . . . . . . . . . . . . . . . . . . 42
xi
2.15 (a) Geographic view of several instruments in the central Pacific. The CASI curve is
the field of view for CASI at 250 km altitude and 15◦ elevation. The CNFI curve is
the CNFI field of view at 250 km. The dashed curves in between −150◦ and −155◦
are beams of the CXI radar mapped along the geomagnetic field into the off-equator
ionosphere at 250 km. (b) Meridional-cut view of the CNFI-CASI-CXI geometry. The
approximately parallel family of curves are the geomagnetic field. The CXI beams
are oriented ⊥ B just north of the geomagnetic equator. CNFI (oblique) and CASI
(zenith) fields of view are indicated. Notice that the CNFI lines of sight are nearly
parallel to the geomagnetic field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.16 Illustration of the rotational and translational parameters for orienting an imaging
system. North is indicated by N , zenith by Z, and the optical axis of the imager
by AX. The optical axis is defined by the geographic location of the imager and its
azimuth (ξ) and elevation (ε). The orientation of the CCD with respect to the optical
axis is defined by a rotation γ and a translational offset (δx, δy). . . . . . . . . . . . 45
2.17 Example calibration iteration from the imaging system near Sangre Grande, Trinidad
(similar to the Bonaire system discussed in Appendix B). The triangles are locations
of stars from BSC5 given the proposed orientation of the imager. The circles are stars
found in the image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.18 (a) Illustration of the differential angle α in the two-dimensional plane containing the
intersection vector OX and the imager location vector OA. Re is the Earth radius, h
is the layer altitude, & is the elevation, and α is the differential angle. (b) Derivation
of the actual latitude of a pixel. XA appears to have a constant latitude only as
a matter of illustrative convenience. In practice, XA may be any great circle that
connects X and A. (c) Derivation of the actual longitude of a pixel. δλ represents the
differential longitude added to the site longitude for a given azimuth and elevation
(via differential angle α). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.19 Airglow image from Cerro Tololo, Chile, from 15 September 2006 mapped to geo-
graphic coordinates at 250-km altitude. Note the dark irregularity bands stretching
approximately from north to south. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.20 Airglow images from Cerro Tololo, Chile, from 16 September 2006 in CCD pixel
coordinates showing (a) no denoising, (b) dark frame, (c) subtraction of dark frame,
(d) star removal, (e) Daubechies wavelet denosing, and (f) histogram equalization.
Each image processing step (c)–(f) is performed on the results of the previous step. . 52
2.21 Airglow image from Cerro Tololo, Chile, from 15 September 2006 in CCD pixel co-
ordinates. This image has had the dark noise removed and has been processed with
the denoising algorithm presented by Atkinson et al. [2006]. . . . . . . . . . . . . . . 53
2.22 Example keogram of 630.0-nm airglow data collected at Haleakala, Hawaii, on 11
September 2002. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.1 The (a) polar, (b) middle latitude, and (c) equatorial geometries. . . . . . . . . . . . 56
3.2 (a) Reduction of field strength reduction at 300 km for different wavenumbers. (b)
Original result of Farley, 1959. (Reproduced with permission of the American Geo-
physical Union.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.3 (a) Relative strength at 250 km in the Northern hemisphere for field sources of differ-
ent scale sizes at different heights in the Southern hemisphere. (b) Geometry of the
field line with log10 ne in the background (units of m−3). . . . . . . . . . . . . . . . . 61
3.4 Electric field strength mapped from geomagnetic equator (apex) to nominal 630.0-nm
airglow emission altitude (250 km) in the CNFI field of view for field structure scales
of {2,4,8,16,32,64} km. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
xii
3.5 Circuit model of two magnetic field lines showing the specific (series) and Pedersen
(shunt) conductivities. This model is inaccurate in the sense that the flux tube might
be better modeled with dependent sources mixed among the resistors to represent
other current sources. The c0∂φ/∂z′ term in Equation (3.8) belies this condition. This
model is conceptual only and does not accurately model all aspects of the ionosphere
circuit. See text. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.6 (a) A field-aligned 630.0-nm airglow image from Cerro Tololo, Chile, projected onto
the assumed emission layer at 250 km. (b) The same image as (a) with the airglow
depletions extruded along the geomagnetic field to produce a three-dimensional map
of the irregularities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.7 Field-aligned imaging geometry from Haleakala, Maui, Hawaii. . . . . . . . . . . . . 66
3.8 Relative spatial blurring across the field-of-view of the PICASSO2 narrow-field im-
ager operating at Cerro Tololo, Chile. In theory, the contours refer to the smallest
resolvable feature dimension. In practice, it is best to interpret them as a relative
measure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.9 Relative spatial blurring across the field-of-view of the Cornell Narrow-Field Imager
operating at Haleakala, Hawaii. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.1 Illustration of the three-step extrusion procedure used in this work. (a) The airglow
image is projected onto the assumed airglow layer height of 250 km. The locations
of the ionospheric pierce points (x) of two look directions of the SCINDA station
at Anco´n, Peru´, and the imager (o) at Cerro Tololo, Chile, are marked. (b) The
field lines corresponding to depletions in the airglow are selected to create a three-
dimensional map of the field-aligned depletion. (c) Occultation ray paths connect-
ing a GPS satellite and a COSMIC/FORMOSAT-3 satellite have been added. The
COSMIC/FORMOSAT-3 satellite is orbiting over the western coast of South America
and over Panama. The ray paths in red correspond to σ > 0.10, indicating some ir-
regularities are present along the ray path. Note that these ray paths are also crossing
the geomagnetic field lines associated with the depletion. . . . . . . . . . . . . . . . . 72
4.2 Three-dimensional view illustrating the problem geometry. The cyan curves represent
the depletion region as estimated by extruding the airglow image. The black curve
above the LEO (COSMIC/FORMOSAT-3) orbit on the top (left) ends of the ray
paths is a relative measure of SNR variance. Only every 10th ray path is shown for
clarity. The ray paths highlighted in red have increased SNR variance, suggesting
that they host irregularities. Only the portions of the ray paths that are below the
orbit of the LEO are shown. Blue dots are placed at the tangent point for each ray
path. This illustrates the distance (∼ 500 km) between the bubble intersection and
the tangent point. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.3 The top panel shows an example of an airglow image mapped along the geomagnetic
field onto the surface swept out by the occultation ray paths. This extrusion allows
the altitude of the irregularities to be read off the plot directly. COSMIC GPS L1
SNR is shown in the bottom panel. The dashed and solid lines correspond to the
beginning and end of irregularities inferred from the COSMIC occultation SNR data,
respectively. Corresponding lines are drawn on the projected airglow image in the top
panel. Markers indicate the position of depletions in the airglow image. The mean
altitude of the intersection of the ray path and airglow depletions is recorded as the
irregularity altitude for that ray path. Thus, irregularities are inferred to occur over
a range of 210–350 km. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
xiii
4.4 The temporal distribution of selected occultation events and the availability of airglow
imagery data. Individual occultation events are marked with a blue dot. By default,
the imager collects data between sunset and moonrise or between moonset and sunrise,
as the case may be. The relative lack of coincident airglow and occultation data for
days 260–289 is mostly a function of data availability, not a lack of bubble activity.
The Kp index is plotted along the bottom. . . . . . . . . . . . . . . . . . . . . . . . . 75
4.5 Distribution of intersection points with altitude and σ in the pre-midnight (UT < 4)
time frame. Due to the availability of coincident data, this corresponds to data taken
during days 254–270. The “All” statistics show all intersections between identified
depleted flux tubes and occultation ray paths, regardless of σ. The “Irregularity”
statistics show the distribution of intersections between depleted flux tubes and oc-
cultation ray paths that exhibit σ > 0.10. . . . . . . . . . . . . . . . . . . . . . . . . 76
4.6 Similar to Figure 4.5. Due to the availability of coincident data, this corresponds to
data taken during days 280–300. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.7 VHF scintillation recorded by the SCINDA station at Anco´n, Peru´. The heavy ver-
tical dashed lines correspond to the times of occultations used in this study. Each
occultation corresponds to scintillation on one or both of the VHF links; see text for
discussion. Note that several of the occultations are nearly coincident in time and are
not distinguishable on these plots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.8 L-band scintillation recorded by a GPS scintillation monitor at Cerro Tololo, Chile.
Occultations are marked with dashed vertical lines. Notice that Cerro Tololo’s po-
sition below the equatorial arcs affords greater opportunity to observe scintillations
due to increased background electron density. See text. . . . . . . . . . . . . . . . . . 78
5.1 Composite keogram (top for each day), RTI gram (middle), and airglow velocigram
(bottom) for 19 and 20 August 2004. See text for discussion. . . . . . . . . . . . . . 84
5.2 Composite data for each day 24–29 August 2005. The format of the plot is the same
as Figure 5.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.3 Climatological reductions of the CNFI airglow image (top), CXI radar backscatter
(center two), and solar flux and Kp index (bottom) data sets for 2002–2009. The
colors represent 20-day sliding percentages of days when irregularities were observed. 87
5.4 (a) RTI gram time series cuts from 19 August 2004 corresponding to apex altitudes of
300, 450, and 600 km. The solid (blue) line corresponds to the airglow intensity. The
dashed (red) line corresponds to radar backscatter. These quantities are normalized
over ranges of [1000,7000] counts and [-20,20] dB, respectively, to create the [0,1] scale.
Although it is difficult to make out some of the structure on the low-altitude plot, the
higher altitude plots show that the backscatter coincides with the depleted regions.
(b) RTI gram time series cuts from 12 August 2005. In this case, there appears to be
some “phase shift” between the airglow images and the radar backscatter, e.g., 600
km between 1100 and 1300 UT. See text for discussion. . . . . . . . . . . . . . . . . 89
5.5 Series of cartoons that illustrate two example irregularity location scenarios. The top
row illustrates a block of irregularities located in the depleted region (left), convolved
with a radar beam (center), to produce a backscatter map (left). The bottom row of
figures is analogous, with the exception of the differing irregularity structure. This
suggests that the irregularities are either located along one wall or in the center.
These plots are for one range gate, just as the plots in Figures 5.4a and 5.4b. . . . . 90
5.6 Series of RTI grams from 12 August 2005 produced with the assumed airglow emission
altitude varied from 220 to 400 km. The height of the airglow layer does change as
a function of time. At different times, different altitudes may match better. See text
for detailed discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.7 Automatically determined airglow peak emission altitude (in 20-km bins) compared
with MSIS/IRI modeled emission altitude for 12 August 2005 and 19 August 2004,
left to right, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
xiv
6.1 Data summary “RTI-gram” from 23 November (327) 2005. Headers show Kp index
for ±5 days. The three panels contain (top) a keogram of the airglow, (middle) RTI-
gram of the airglow and radar backscatter, and the plasma drift velocity estimated
from features in the local airglow layer (bottom). See text for discussion. . . . . . . 97
6.2 Supplemental RTI-gram plot similar to Figure 6.1 with Doppler velocities and widths
from the Christmas Island radar. The light and dark bands of the MSTID structure
correspond directly to downward and upward Doppler velocities, suggesting that the
structure is electrified and driving E × B drifts. Broader widths imply more recent
development of the irregularities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.3 Selected airglow images from CNFI and CASI on 23 November (327) 2005. Images
are projected to the airglow layer at (nominally) 250 km altitude. The north and
east beams of the Christmas Island radar are also overlaid by mapping along the
geomagnetic field. Dots appear on the beams when the received SNR is > −10 dB
indicating FAI. Arrows coarsely indicate the motion of the structures. . . . . . . . . 99
6.4 Data summary from 2 September (246) 2008. Same format as Figure 6.1 except there
are no drifts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.5 A schematic of polarization electric fields (Ep) within a mid-latitude structure driving
a perturbation (via Vp) at the equator. . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.1 Flow-chart showing the interaction between potential seeding mechanisms for equa-
torial plasma depletions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.2 Three electron density profiles retrieved from C/NOFS Occultation Receiver for Iono-
spheric Sensing and Specification (CORISS) from the central Pacific on 29 November
(334) 2008. These profiles were produced from the sub-orbital TEC assuming spheri-
cal symmetry. See text for discussion. Figures were provided by Rebecca Bishop and
Paul Straus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
A.1 Workflow developed to manage the data presented in this dissertation. . . . . . . . . 109
B.1 Composite satellite photograph of Bonaire showing the proposed instrument locations.
The site marked “Alan and Jane” was the final location for installation. . . . . . . . 112
B.2 Schematic of the complete instrument package installed in Bonaire. . . . . . . . . . . 113
B.3 Photograph of the inside of the equipment housing. . . . . . . . . . . . . . . . . . . . 114
B.4 Cross-sectional view of the Unistrut pylon arrangement. . . . . . . . . . . . . . . . . 118
C.1 Comparison of the error with respect to 100-m step size for steps of 500 m, 1 km, 5
km, 10 km, and 50 km, when mapping CXI north beam range gates to 250 km. . . . 121
C.2 Comparison of the error with respect to IGRF tracing with 100-m step size to
AACGM, when mapping CXI east (solid curve) and north (dashed curve) beam range
gates to 250 km. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
xv
LIST OF ABBREVIATIONS
AACGM Altitude-adjusted, corrected geomagnetic, coordinate system
AFRL U. S. Air Force Research Laboratory
ALTAIR ARPA Long-Range Tracking and Instrumentation Radar
BPSK Binary phase-shift keying
C/A GPS coarse acquisition code
CASI Cornell All-Sky Imager (located on Mt. Haleakala in Hawaii)
CEDAR Coupled Energetics and Dynamics of Atmospheric Regions (NSF research program)
CHAMP Challenging Microsat Project, carries an occultation receiver
CNFI Cornell Narrow-Field Imager (located on Mt. Haleakala in Hawaii)
C/NOFS Communication/Navigation Outage Forecast System
CORISS C/NOFS Occultation Receiver for Ionospheric Sensing and Specification
COSMIC Constellation Observing System for Meteorology, Ionosphere, and Climate, occul-
tation experiment
CTIO Cerro Tololo Inter-American Observatory, La Serena, Chile
CXI Christmas Island 50-MHz radar
EAR Equatorial Atmosphere Radar, Kototabang, Indonesia
ECEF Earth-centered, Earth-fixed, coordinate system
ECI Earth-centered, inertial, coordinate system
EEJ Equatorial electrojet
EPB Equatorial plasma bubble
ESF Equatorial spread-F
GPS Global Positioning System
GPS/MET GPS/Meteorology occultation experiment
GUVI Global Ultra-Violet Imager (on TIMED satellite)
HWM Horizontal Wind Model
IGRF International Geomagnetic Reference Field model
IOX Ionospheric Occultation Experiment, occultation experiment
xvi
IRI International Reference Ionosphere model
JHU/APL Johns Hopkins University Applied Physics Laboratory
JRO Jicamarca Radio Observatory, Jicamarca, Peru´
L1 Primary GPS L-band frequency (1.57542 GHz)
L2 Secondary GPS L-band frequency (1.22670 GHz)
MSTID Medium-scale traveling ionospheric disturbance
NASA U. S. National Aeronautics and Space Administration
NRL U. S. Naval Research Laboratory
NRLMSIS NRL Mass-Spectrometer Incoherent Scatter atmosphere model
NSF National Science Foundation
PICASSO Portable Ionospheric Camera and Small-Scale Observatory
RTI Range-time-intensity (alt. Rayleigh-Taylor instability)
RTV Range-time-velocity
SBAS Satellite-Based Augmentation System
SCINDA AFRL Scintillation Network Decision Aid, network of scintillation receivers
SCINTMON Cornell University GPS Scintillation Monitor
SNR Signal-to-noise ratio
SRI Formerly Stanford Research Institute, now SRI International
TEC Total electron content
TECU TEC unit, 1016 e−/m2
TIMED Thermosphere Ionosphere Mesosphere Energetics and Dynamics satellite mission
TOA Time-of-arrival
UCAR University Corporation for Atmospheric Research
WAAS Wide-Area Augmentation System
xvii
LIST OF SYMBOLS
A Azimuth, Einstein efficiency
B Magnetic field vector
c0 Speed of light in a vacuum
c Wave speed
E Electric field scalar
E Electric field vector
F Force vector
f Radio frequency (angular units)
fp Plasma frequency (angular units)
h Altitude
hmF2 Height of the peak electron density in the F2 layer
I Received SNR
J Current (density) vector
k Wavenumber, reaction rate coefficient
k Wavevector
Kp Planetary K index, a measure of geomagnetic activity
me Electron mass
mi Ion mass
ne Electron density
ni Ion density
nmF2 Peak electron density in the F2 layer
nn Neutral density
qe Fundamental electronic charge
re Classical electron radius
Re Earth radius
S4 Short-time normalized variance of received SNR
xviii
T Neutral temperature
Tn Neutral temperature
Te Electron temperature
Ti Ion temperature
u Scalar electric field, also zonal neutral wind
U Neutral wind vector
v Zonal neutral wind
V Plasma drift
z Coordinate axis in the direction of wave propagation, altitude
α Right ascension
β Wavenumber, Einstein efficiency
δ Latitude
& Horizon elevation
&0 Permittivity of free space
η Photochemical volume emission rate
λ Longitude, radio wavelength, Debye length
νei Electron-ion collision frequency
νen Electron-neutral collision frequency
νin Ion-neutral collision frequency
ξ Azimuth
σ¯ Conductivity tensor
σ Conductivity, also a generalized representation of S4 that does not imply 50-Hz sample
rate
σ0 Specific conductivity
σH Hall conductivity
σP Pedersen conductivity
τ Group delay
ΥFF Flat-field matrix
φ Electric potential
ω Radio frequency (angular units)
ωp Plasma frequency (angular units)
Ωi Ion gyrofrequencies
Ωe Electron gyrofrequencies
xix
CHAPTER 1
THE EQUATORIAL IONOSPHERE
1.1 Introduction
The ionosphere and thermosphere envelop Earth in the altitude range of approximately 70–1000
km. The defining characteristic of the ionosphere is its composition of partially ionized gas plasma.
Because both neutral (thermosphere) and ionized (ionosphere) species are present at these heights
and they exist in the presence of Earth’s geomagnetic field, the ionosphere is host to a number
of interesting phenomena such as spectacular auroral displays and otherwise “invisible” waves and
turbulence that affect radio waves passing through the region. Figure 1.1 shows empirical models
of the ionospheric electron and thermospheric neutral densities at a typical low-latitude site near
Hawaii. The neutrals dominate density until well above the ionosphere. Molecular oxygen and
nitrogen are dominant in the lower atmosphere, but lighter species such as atomic helium and
hydrogen dominate at high altitudes.
The day-to-day behavior of the ionosphere/thermosphere system is driven by the sun. The
ionosphere forms as neutral species in the thermosphere absorb EUV and X-ray radiation from the
sun. Ions and electrons produced at lower altitudes drift upward due to diffusion and the effects of
the geomagnetic field. Thermospheric winds arising from solar convection drive dynamo currents in
the presence of the geomagnetic field. These three effects—production (and loss), particle drift, and
dynamos—will guide most of our discussions about the ionosphere.
The ionosphere is divided into three regions labeled D, E, and F . The regions are differentiated
mostly through their compositions, which in turn affect collision rates between species, which in turn
affects the plasma conductivity, which is anisotropic due to the geomagnetic field. The D region
occupies the lower portion of the ionosphere, at an altitude of about 70–90 km. It is characterized
by high neutral density, and therefore, a high frequency of both electron-neutral and ion-neutral
collisions. Although the D region is not of particular interest to this work, the high collision
frequencies make it the major contributor to daytime ionospheric absorption of low-frequency (< 30
MHz) radio waves. In the E region, 90–120 km, ion-neutral collisions remain important; however,
1
0100
200
300
400
500
600
700
800
900
1000
Density [m−3]
Al
titu
de
 [k
m
]
ne and Neutrals − 13 September (258) 2005
10−5 10 0 10 5 10 10 10 15 10 20 10 25
 
 
[e−]
Σ [x]
ON
Ar
He
H
2N
2O
Figure 1.1: Empirical models of the electron and neutral density profiles in the ionosphere-
thermosphere system. The electron density is from the International Reference Ionosphere, IRI
2007 [Bilitza and Reinisch, 2008], and the neutral densities come from NRLMSISE-00 [Picone et al.,
2002].
electron-neutral collisions are less important. The E region contains many ions, both from solar
production and metallic ions from meteor ablation. In the low-latitude ionosphere, as discussed in
the next section, the E region hosts the equatorial electrojet (EEJ) and the E-region dynamo, which
are dominant features of that region. The F region, loosely the remaining ionosphere from 120 to
1000 km, is predominately electrons and light ions. As a consequence of this, collisions are not
dominant. The size of the F region and its constituency of mobile electrons make it very important
in the propagation of radio waves. A defining metric of the plasma density is the plasma frequency,
which is the resonant frequency of a parcel of plasma. As such, it varies with time and position.
Below the plasma frequency, radio waves are reflected by the plasma. Above the plasma frequency,
increasing electron density corresponds to decreased refractive index at a given radio frequency.
Irregularities in the plasma density, especially dynamic, turbulent irregularities, may have pro-
found effects on radio waves passing through the ionosphere. A class of these equatorial F -region
irregularities is the subject of this dissertation. This dissertation is primarily concerned with the
behavior of the equatorial ionosphere and irregularities therein that degrade satellite radio com-
munication and navigation systems. The remainder of this chapter is devoted to the equatorial
ionosphere, its day-to-day behavior, and the irregularities that are produced there. Some of the
outstanding problems will be identified, especially those addressed in this dissertation. An outline
of the dissertation concludes the chapter.
2
10−2 100 102 104
0
100
200
300
400
500
600
700
800
900
Conductivity [S/m]
Al
tit
ud
e 
[km
]
Cerro Tololo conductivities [local noon, solar max]
 
 
specific
Pedersen × 106
Hall × 106
10−2 100 102 104
0
100
200
300
400
500
600
700
800
900
Conductivity [S/m]
Al
tit
ud
e 
[km
]
Cerro Tololo conductivities [local midnight, solar max]
 
 
specific
Pedersen × 106
Hall × 106
(a) (b)
Figure 1.2: Typical low-latitude conductivity profiles for solar maximum conditions up to 900 km
at local (a) noon and (b) midnight. Note that the Pedersen and Hall conductivities are scaled by
106.
1.2 Conductivity
In a collisionless plasma, charged particles in the presence of the geomagnetic field gyrate in the
plane perpendicular to the magnetic field. Although the particles are free to move parallel to the
magnetic field, they do not readily move in the perpendicular direction. Ions and electrons may
move perpendicular to the magnetic field under electrodynamic influences, such as the E×B drift,
or interactions (collisions) with other particles. This situation yields anisotropic conductivity. In
a coordinate system (aˆx,aˆy,aˆz)1 with aˆx perpendicular to the geomagnetic field in the (magnetic
meridional) plane swept out by the geomagnetic field and aˆz parallel to the geomagnetic field, aˆy is
the remaining Cartesian coordinate perpendicular to both aˆx and aˆz. The conductivity tensor for
this geometry is written
σ¯ =

σP −σH 0
σH σP 0
0 0 σ0
 , (1.1)
where σP , σH , and σ0, are the Pedersen, Hall, and specific conductivities, respectively. The Pedersen
conductivity is in the direction perpendicular to B and parallel to the E field; that is, it is due to
currents driven by F = qeE. The Hall conductivity is in the direction of the E × B drift. The
conductivities are finite due to collisions between species. The specific conductivity is about 105
larger than either the Pedersen or Hall conductivities. Figure 1.2 shows a typical set of conductivity
profiles for an equatorial location up to 900 km.
1This is sometimes written (aˆφ,aˆθ,aˆp).
3
1.3 Quiescent Behavior
Principal among the large-scale quiescent processes of the equatorial ionosphere are the E- and
F -region dynamos. Fundamentally, the dynamos operate due to the wind-driven currents and the
conservation expression requiring divergence-free current (Kirchhoff’s current law), which can be
expressed in the steady state as
∇ · J = 0. (1.2)
Due to the relatively high density of neutrals in the E region, the ion-neutral collision frequency is
high there. This facilitates the E-region dynamo as thermospheric neutral winds drag ions across
field lines in the part of the E region where σH is the dominant conductivity [e.g., Heelis, 2004].
Since the net flow of charge constitutes a current, Equation (1.2) must be satisfied by drawing cur-
rent into the circuit along the geomagnetic field lines. At night, the E (and D) region(s) recombine
quickly, reducing the Hall and Pedersen conductivities there. The F -region dynamo, which is dom-
inated by the effects of the Pedersen conductivity, then takes over [Heelis, 2004; Rishbeth, 1997].
The thermospheric zonal wind drives a current that is predominantly in the magnetic meridional
direction, that is, a Pedersen current:
J = σ¯ · (U×B) . (1.3)
Because the conductivity of the ionosphere is inhomogeneous, polarization electric fields form as
charges build up at the terminator separating the day and night sides of the Earth. In order to
satisfy the electromagnetic form of Kirchhoff’s voltage law,
∮
E · d0 ≈ 0, (1.4)
this charge separation creates an eastward electric field on the day side of the Earth and a west-
ward electric field on the night side. This zonal electric field is designated Eφ in Figure 1.3, which
illustrates the sunset terminator and some associated electrodynamic and neutral properties. The
plasma densities and neutral winds shown in Figure 1.3 are from IRI2007 and HWM07, respec-
tively [Bilitza and Reinisch, 2008; Drob et al., 2008], for a representative day, 22 August 2005, at
a point (geographic 2◦ N, 203.5◦ E) in the central Pacific. At the geomagnetic equator where the
B is northward and approximately parallel to Earth’s surface, the plasma drifts upward during the
4
    
 w
es
t (
da
y)
ea
st
 (n
ig
ht
)
2
4
6
8
10
12
14
0
5
10
15
20
0
20
0
40
0
60
0
80
0
10
00
UT
 [h
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5
day and downward at night under the influence of the zonal electric field Eφ at a velocity
Vdrift =
E×B
|B|2 . (1.5)
As the plasma drifts upward into lower density regions, partial pressure gradient forces and
gravity push the plasma back down the highly conductive field lines. This plasma forms two crests of
increased density, one on either side of the geomagnetic equator. The regions of increased ionization
are known by various names; however, for the purpose of this work we refer to them as the equatorial
anomaly crests.2 The equatorial anomaly crests are a prominent feature that is observable from
the ground and space using optical airglow emissions, as well as electron density measurements.
Figure 1.4 illustrates the crests of the equatorial anomaly as observed optically at 135.6 nm by
the Global Ultraviolet Imager (GUVI) instrument on the Thermosphere, Ionosphere, Mesosphere,
Energetics and Dynamics (TIMED) spacecraft [Christensen et al., 2003].
053807151030
150 180 210 240
Geo. Lon
-40
-20
  0
 20
 40
Ge
o.
 L
at
.
0.0
50.0
R
0853
Figure 1.4: Equatorial anomaly crests over the central Pacific observed through the 135.6-nm night-
glow emission by the GUVI instrument. Each strip of airglow image represents one orbit of the
TIMED spacecraft. The time of the geomagnetic equator crossing is given in UT at the top. Data
courtesy of JHU/APL.
Following sunset, the zonal electric field reverses (to the West) in order to satisfy the KVL
relationship above. The description given here follows Farley et al. [1986], but there are several
competing theories [e.g., Rishbeth, 1971; Haerendel and Eccles, 1992; Eccles, 1998]. Before the field
reverses, it frequently increases rapidly, increasing the E×B drift and raising the ionosphere [Wood-
2It has been reasoned that they are no longer anomalous since the theory of their formation is well established,
but the name remained.
6
man, 1970; Fejer et al., 1979; Farley et al., 1986]. This effect is known as the prereversal enhancement
(PRE) or post-sunset rise (PSSR). The prereversal enhancement is an important feature of the equa-
torial ionosphere. Vertical drift velocities are on the order of 40 m/s. The PRE is a seasonal feature,
although it also appears to be strongly affected by the solar cycle [Fejer et al., 1979; Kelley , 1989].
At Jicamarca, the largest PREs are observed at solar maximum during the equinoxes and summer.
One of the most important features of the PRE is its association with the growth of equatorial
plasma irregularities.
1.4 Irregularities
A number of ionospheric irregularity types occur at equatorial and low latitudes. For instance, the
electrojet is subject to turbulence and irregularities that disrupt radar measurements of ionospheric
profiles [e.g., Berkner and Wells, 1937; Bowles et al., 1960]. Otherwise, for practical purposes, these
irregularities are apparently benign. However, in the F region, large plumes of irregularities grow
after sunset on a nearly daily basis in some geographic areas and seasons. These irregularities have a
profound effect on trans-ionspheric radio communication and navigation signals, causing everything
from minor fading to complete loss of signal lock. Since their initial discovery in the 1930s, post-
sunset equatorial irregularities have been a subject of intense scientific and practical interest [Booker
and Wells, 1938].
Booker and Wells discovered irregularities using an ionosonde. Ionosondes were the earliest iono-
spheric radio remote sensing instruments [Breit and Tuve, 1925]. They are small, swept-frequency
(1–20 MHz or so) radars with vertical beams that are used to measure the altitudes of scattering lay-
ers. Under normal circumstances, the upward-traveling wave continues until it reaches the altitude
where the plasma frequency equals the radio frequency and the wave is reflected. The group delay
of reflected pulses is measured to determine the virtual height of reflection, which can be used to
determine the altitude of the peak plasma density. A normal ionogram showing a relatively smooth,
thin curve for virtual height is shown in Fig. 1.5a. Multiple traces indicate that the pulse has been
reflected one or more times by the ground and again off the ionosphere. When the ionosphere is
no longer smooth, scattering occurs at many altitudes, spreading the virtual height curve, as shown
in Fig. 1.5b. This is the phenomenon known as equatorial spread-F . Study of 50-MHz coherent
backscatter from irregularities associated with spread-F began in the 1960s and 1970s at Jicamarca,
Peru´ [Farley et al., 1970; Woodman and Hoz , 1976]. Figure 1.5c shows the 50-MHz backscatter SNR
7
(a) (b) (c)
Figure 1.5: Ionograms from Jicamarca, Peru´, on the night of 22 October 2006 under (a) normal (at
about 1930 LT) and (b) spread (2030 LT) conditions. Frame (c) is the coherent backscatter map
from the Jicamarca radar for the same time period. The highlighted vertical lines refer to the times
of the ionograms in subfigures (a) and (b). Data courtesy of Jicamarca Radio Observatory.
observed as the irregularities drifted across the Jicamarca radar beam. Notice the correspondence
between spread-F on the ionogram in Figure 1.5b and strong F -region backscatter observed by the
radar in Figure 1.5c at the same (2030 LT) time. Earlier at 1900 LT, no spreading was observed
in the ionogram (Figure 1.5a) and no F -region backscatter was observed by the radar. The heavy
layer of echoes in the 100–120 km altitude range is due to electrojet instabilities mentioned briefly
at the beginning of this section.
The coherent echoes observed by the 50-MHz radar correspond to irregularities in plasma density
at the 3-meter scale. The same mechanism is responsible for the spreading of the virtual height curve
on the ionograms, except that the frequencies involved are much lower and the irregularity scales
correspondingly larger. Coherent backscatter occurs at the Bragg wavelength, which is one half the
radio wavelength.
The term “spread-F” commonly refers to an entire linked set of irregularities spanning scales from
centimeters to megameters, although the term itself stems from the specular echoes described above.
There are three spread-F irregularity scales that are easily observed from the ground. Structures
larger than about 10 km up to a 1000 km or more are observable with airglow imagers. The 100–
1000 m range irregularities are observed through forward-scatter radio scintillation measurements.
Finally, the smallest irregularities on the order of meters are observed via coherent radar backscatter.
In situ rocket density spectra and forward scatter radio observations suggest that it is probable that
at least two classes of irregularities exist when fully developed, one at large (! 100 m) and the other
at small scales [e.g., Kelley et al., 1982; Yeh and Liu, 1982]. As early as 1956, it was theorized that
a collisional interchange instability, specifically the gravitational Rayleigh-Taylor instability, might
be responsible for the growth of large-scale plasma irregularities associated with equatorial spread-
8
F [Dungey , 1956]. The small-scale irregularity mechanism remains the subject of some debate and
will be addressed in Chapter 5.
The Rayleigh-Taylor instability can occur when a dense fluid is supported above a less-dense
fluid, as depicted in Figure 1.6. In the case of the equatorial ionosphere, a steep plasma density
gradient forms on the bottom side of the F region when the ion-rich E region recombines after
sunset. Since the geomagnetic field, B, is nearly horizontal at the equator, the gravitational effect
on electrons and ions drives a current in the zonal direction,
J =
nimig ×B
|B|2 . (1.6)
Above the gradient, there is plenty of plasma density and the gravity-driven current (J) is large.
Below the gradient, the density (and hence, the current) is low. A small perturbation in the gradi-
ent causes polarization charges to build up, keeping the current divergence-free. These polarization
charges force a polarization electric field (δE) to form within the perturbation, driving the pertur-
bation even larger by the δE×B drift. Once this process begins, it evolves rapidly.
+ +
+ + - - -
---
B
δE x B
δE
J
δE
δE x B
g
1
2
Figure 1.6: Cartoon of the gravitational Rayleigh-Taylor instability operating in the equatorial
ionosphere. The geomagnetic field, B, is directed into the page. Region 1 has much higher plasma
density than Region 2.
Figure 1.7 illustrates a cartoon of irregularity formation and growth. A seed instability (the result
of a transient or another phenomenon) forces the gradient in the bottom side of the F region into a
rapidly evolving non-linear Rayleigh-Taylor instability. As the depleted regions grow in altitude, the
9
Se
ed
in
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N
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as
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Li
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10
large-scale polarization electric fields associated with them are mapped along the geomagnetic field,
displacing the plasma in a wedge-shaped region [e.g., Farley , 1960; Aarons et al., 1980; Tsunoda
et al., 1982; Mendillo and Tyler , 1983]. A differential in the eastward neutral wind and the plasma
drift velocity causes gradient-drift instabilities to form on the western walls of the depletions, some
of which erupt into bifurcations. This theory is widely accepted and supported by models [Ossakow ,
1981; Hysell , 2000]; however, the lack of a suitable explanation for the seeding of equatorial spread-F
has left scholarly debate open on the issue.
Gravity waves propagating up from below the ionosphere/thermosphere have long been suggested
as one possible seed [e.g., Kelley et al., 1981]. One difficulty with the gravity wave theory lies in
the ability to observe them at thermospheric altitudes. In order to conserve momentum as the
atmospheric background density decreases, gravity wave amplitudes grow as the wave propagates
upward. This means that waves that are large in the thermosphere are frequently vanishingly small
at lower altitudes, making them difficult to observe near their origin. Furthermore, winds in a
gravity wave are parallel to the isodensity phase fronts. In order to perturb the plasma in the F
region, where the Hall and Pedersen conductivities are very low, the wind must have a significant
component parallel to the geomagnetic field. This suggests that gravity waves may not directly
impact the motion of the plasma. However, neutral wind field perturbation may affect the growth
rate of irregularities through the theories expressed in the next paragraphs.
Another interesting possibility is that the Rayleigh-Taylor instability could be initiated by polar-
ization electric fields generated in the E region north or south of the geomagnetic equator that map
along the geomagnetic field to the bottom side F region at the equator [Tsunoda, 2006, 2007]. This
process is probably responsible for at least a fraction of depletions observed forming more than 2–3
hours after sunset or during seasons in which depletion formation is unlikely. Evidence supporting
this theory is presented in Chapter 6.
Recent work based on data from the Jicamarca radar in Peru´ has shown that electrodynamics
of the evening ionosphere can produce seed instabilities capable of triggering the Rayleigh-Taylor
instability under favorable conditions ([Kudeki and Bhattacharyya, 1999; Hysell et al., 2004; Kudeki
et al., 2007]). These irregularities, termed bottom-type layers in [Woodman and Hoz , 1976; Hysell
and Burcham, 1998], grow with wavelengths on the scale of 20–30 km. The structure of bottom-
type layers was revealed using radar imaging techniques [Hysell , 1996; Woodman, 1997]. Although
bottom-type layers appear to be a necessary precursor to larger post-sunset irregularities, their
presence is not alone sufficient to seed depletion formation.
11
The E region recombines rapidly after sunset as ion production ceases, reducing conductivity
there. Lacking the E region as a load, the F -region dynamo currents seek closure in order to
remain divergence-free. That is, the F -region dynamo behaves like an energized relay coil in steady
state [Rishbeth, 1997]. In this analogy, abruptly breaking the circuit (without proper mitigation
circuitry) causes the relay to chatter before settling again to steady state. Likewise, the ionosphere
responds to this transient through several phenomena, including the pre-reversal enhancement of
the zonal electric field and irregularities on the bottom side of the F region [Kudeki et al., 2007].
Perhaps one of the more compelling studies in understanding the initiation of equatorial spread-
F is that of conditions which are necessary but perhaps insufficient. The seasonality [Gentile et al.,
2006] of equatorial spread-F is thought to be modulated in large part by the alignment between the
solar terminator and the geomagnetic meridian [Tsunoda, 1985]. According to this theory, when
the terminator is aligned with the geomagnetic field, the northern and southern E regions will
recombine at approximately the same time (neglecting plasma transport and density asymmetry),
producing the sharpest transient. Both models [e.g., Sultan, 1996]) and observations [e.g., Basu
et al., 1996] suggest that strong E×B drifts are required for irregularity development. The spacing
between the crests of the equatorial anomaly can serve as a proxy for the E×B drift. Basu et al.
[2009] have presented observational and modeled examples of “collapsed” equatorial anomaly crests
which appear to inhibit the formation of F -region irregularities. In the SAMI3 [Huba et al., 2005]
model, collapses are generated in conjunction with local reversal of the equatorial electrojet from
east to west in the afternoon. This suggests that these counter-electrojet events can be inhibitors
of spread-F .
Figure 1.8 is an oft-shown illustration of a wave-4 structure in the equatorial arcs as observed from
the IMAGE instrument [Immel et al., 2006]. The locations of wider arc spacings are coincident with
tropical convection centers. England et al. [2006] explain this through the daytime modulation of the
equatorial plasma fountain through the E-region neutral wind. This is indeed interesting because
a study of AE-1 satellite data suggests that there is some correlation between tropical convection
and irregularity development [McClure et al., 1998]. This suggests an alternative, although as of yet
unverified, link between convection and irregularity development which may or may not depend on
gravity waves.
12
Figure 1.8: Modulation of density and location of the northern equatorial arc observed from space by
the IMAGE spacecraft. The southern arc was reflected across the geomagnetic equator. After [Immel
et al., 2006]. (Reproduced with permission of the American Geophysical Union.)
1.5 Irregularity Effects
The primary known impact of ionospheric irregularities is scintillation. Scintillation is an optical
diffraction effect that causes rapid fluctuations in the amplitude or phase of the received signal when
a radio wave propagates through a turbulent medium [e.g., Yeh and Liu, 1982]. Figure 1.9 illustrates
the geometry of the space-to-ground radio wave scintillation problem. A slab of irregularities with
thickness L exists at a distance z from the receiver. A transmitter illuminates the slab of irregularities
from −∞.
Irregularities have both a scale and a perturbation “depth” which affect the observed scintillation
on the ground. Commonly, amplitude fading occurs while the phase remains relatively constant.
This is the situation of “weak” scintillation. “Strong” scintillation entails phase scintillation in
addition to amplitude scintillation. Strong scintillation of this type is most common on VHF and
UHF trans-ionospheric radio links during solar maximum. Scintillation events are often classified
by their S4 index, which is a short-time normalized variance of the signal-to-noise ratio (SNR) of
the received signal,
S24 =
〈I2〉 − 〈I〉2
〈I〉2 , (1.7)
where I is the SNR and 〈·〉 represents the short-time average over a number of samples. The S4
index indicates the depth of the fade with respect to signal strength. That is, S4 = 1 indicates that
the fade is as large as the signal strength itself.
Irregularities that cause amplitude scintillation observed at a receiver are of the order of the
13
!"#
$#
L
z
! %
Figure 1.9: Geometry of the space-to-ground radio wave scintillation problem. A slab of irregularities
with thickness L exists at a distance z from the receiver. The transmitter is much farther from the
irregularities than the receiver (Fresnel approximation).
Fresnel scale, yielding a diffraction pattern that moves with respect to the receiver due to the motion
of the signal source, irregularities, and the receiver (in the case of the non-stationary receiver). An
estimate of the Fresnel scale based on the first Fresnel zone for a slab of random density is given by
dF =
√
λ(z − L/2), (1.8)
where z is the range to the far (with respect to the receiver) side of the slab and L is the slab
thickness [Yeh and Liu, 1982]. First-order estimates of the Fresnel scale for the irregularities as-
sociated with equatorial spread-F can be obtained by assuming that the slab is located at the F
peak. Scattering regions have been reported at altitudes higher than the F peak [Sokolovskiy et al.,
2002; Cerruti et al., 2006], although there is very little data on scattering altitude with which to
corroborate these results. Furthermore, the altitude of the F peak varies, yielding errors in the
Fresnel scale estimate without some independent measurement of this parameter [Batista and Abdu,
2004]. Estimation of the altitude distribution of scintillation-causing irregularities is the subject of
Chapter 4.
Irregularities can have a profound effect on satellite-based radio communication and navigation
systems. For navigation systems which rely on the propagation delay of signals from satellite-based
transmitters, depletions and gradients in electron density distort the accuracy of navigation solu-
14
!"" !"# !"$ !"% !"& !#'
'
'("
)
*+,-./,01,23.4
5
6
5789-:,!,:;<0;=,>34?
,
,
!&' !&) !&! !&@ !&6 !&"
'
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)
*+,-./,01,23.4
5
6
,
,
ABC,D3EF
ABC,G.EF
ABC,D3EF
ABC,G.EF
Figure 1.10: SCINDA S4 plots from Anco´n, Peru´, in September and October 2006. Notice that
scintillation occurs almost on a nightly basis. After [Miller and Makela, 2008]. (Reproduced with
permission of the American Geophysical Union.)
tions. If scintillation associated with these irregularities causes severe amplitude or phase fading,
the receivers may lose lock on the signal, rendering communication or navigation impossible for
periods of a few minutes or hours. Therefore, users of these systems are keenly interested in scin-
tillation detection, prediction, and mitigation systems. The U. S. Air Force operates a worldwide
system of VHF and L-band (1.6 GHz) receivers known as the Scintillation Network Decision Aid
(SCINDA) [Groves et al., 1997]. These receivers calculate 87-second S4 continuously as well as drift
velocities when irregularities are present to perform a cross-correlation. Figure 1.10 shows VHF
(240 MHz) SCINDA S4 data from Anco´n, Peru´, in September and October 2006. At this location,
scintillation is observed on a nearly nightly basis during these time periods.
The spectrum of irregularities observed by a scintillation receiver can be obtained through the
Fourier transform of the received signal. This technique has been utilized to study the scale dis-
tribution of irregularities [e.g., Yeh and Liu, 1982]. More recently, it has also been employed to
determine the altitude of irregularities [Bhattacharyya et al., 2001].
1.6 Questions and Contribution
1.6.1 Four problems
Generally speaking, there are four outstanding areas of research for equatorial F region irregularities:
Seeding of Equatorial Depletions / Spread-F
The first question pertains to the seeding and suppression of equatorial plasma depletions. Although
much work has been performed in this area, the complexity of proposed drivers and the variability of
15
the ionosphere-thermosphere system make it a challenging problem. Compelling evidence has been
provided to justify the claim that the initiation is a cascade or sequence of plasma instabilities. It
is theorized that the zonal [Kudeki et al., 2007] and meridional [Mendillo et al., 1992] neutral winds
play an important role in the initiation of irregularities. Therefore, it is conceivable that gravity
waves, which are a neutral perturbation phenomenon, may modify the background wind in a manner
conducive to irregularity development. Tsunoda [2007] has also shown that electric fields associated
with off-equator irregularities in the E or lower F region may be responsible for seeding of certain
kinds of irregularities.
Conjugacy of Depletions
The second outstanding area is in the conjugacy of depletion growth. Models and initial observations
suggest that below a certain scale, probably on the order of 10s of km, irregularities observed in the
northern geomagnetic hemisphere may not be well-correlated with those observed in the southern
geomagnetic hemisphere. Only a handful of temporally coincident conjugate airglow images have
ever been presented [Otsuka et al., 2002]. This has particular significance during geomagnetic storms,
when irregularities may be generated in the local ionosphere [Makela et al., 2006].
Distribution of Irregularity Scales
The third question is related to the second. That is the question of scales and irregularity location.
It is well-known that at large scales (many 10s of km), secondary irregularities tend to grow on
the western wall of the depletion under the influence of an eastward neutral wind [Tsunoda, 1983].
In the rare event of a westward neutral wind, secondary irregularities may grow on the eastern
wall [Makela et al., 2006]. There is also substantial evidence that coherent radar backscatter at
the meter-scale range occurs from the center of depletions [Tsunoda, 1980; Otsuka et al., 2004b].
Furthermore, the km-scale irregularities that cause radio wave scintillation are difficult to locate
because scintillation is an effect that results from the combined action of electron density gradient
and irregularity scale [Yeh and Liu, 1982].
Coupling to/from Mid-Latitude Instabilities
The fourth, and final, question regards the coupling between low-latitude processes and mid-latitude
processes. Mid-latitude medium scale traveling ionospheric disturbances (MSTIDs) are often ob-
served in airglow images in association with what appear to be ordinary equatorial plasma depletions
16
that have surged poleward from the equatorial arcs. Does the depletion trigger a mid-latitude pro-
cess? Is the the observed “MSTID” truly a MSTID or just a collapsing depletion? Can a mid-latitude
process trigger a depletion?
1.6.2 Contribution
This dissertation is devoted to techniques that can assist in answering the questions outlined in the
previous section, particularly using multiple remote sensing techniques together and bringing the
data into a common format for study. There are primarily three new and significant contributions
in this work: The first is to locate scintillation-causing irregularities in three dimensions using
radio occultation and airglow imaging. This study suggests that the radio occultation technique
for identifying and locating scintillations benefits greatly from additional information. The second
contribution is a long-term study of equatorial plasma irregularities from the central Pacific sector.
This study confirmed some of the climatological observations from in situ probes and the Jicamarca
radar in the American sector while uncovering new and interesting details, as well. One of these
interesting details is the third contribution: A secondary peak in depletion activity was identified
post-midnight during the November—January period at solar minimum. This was correlated with
a high incidence of MSTID structures in the airglow. A physical explanation is provided suggesting
that most (if not all) post-midnight depletions are associated with MSTID structures that propagate
past the equatorial anomaly crests.
1.7 Outline
Chapter 1 has concerned the general state of ionospheric research and the relationship of this dis-
sertation to it. Chapter 2 surveys the main ionospheric remote sensing techniques utilized in this
work, with special attention to radio occultation, coherent backscatter radar, and optical airglow
imaging. Chapter 3 develops the basis for the field-aligned airglow observation technique. Chapter
4 proposes a fusion technique to localize irregularities in three dimensions using radio occultation
and optical airglow imaging. Chapter 5 discusses a long-term study of airglow and radar data from
Haleakala, Maui, Hawaii, and Christmas Island, Kiribati. Chapter 6 presents evidence uncovered
during the work presented in Chapter 5 of an alternate depletion seeding process that may explain
deviations in the depletion climatology. Chapter 7 concludes with a synthesis of equatorial irregu-
larity formation and detection, placing this work in the larger context and providing some ideas for
17
future directions. A collection of appendices follow at the end, containing information on the data
processing approach, the fielding of imaging instruments, and the relative accuracy of geomagnetic
field models.
18
CHAPTER 2
IONOSPHERIC OBSERVATIONS AND
REMOTE SENSING
2.1 Introduction
The ionosphere and thermosphere are relatively inaccessible to in situ measurements, and the phe-
nomena they host are often best observed remotely. Indeed, the ionosphere was discovered due to
its effects on radio waves: refraction, absorption, and scattering. The ionosphere is also the source
of naturally occuring airglow emissions that may be used as tracers of plasma and neutral dynam-
ics. This chapter is devoted to these two major ionospheric remote sensing modalities, radio and
optical. The radio occultation, coherent radar backscatter, and airglow imaging techniques, which
are principal subjects of this dissertation, are covered in detail. Finally, the chapter concludes with
some open questions.
2.2 Radio Techniques
2.2.1 Ionosondes
The ionosonde is a simple radar that was originally designed to test the theories of the ionosphere’s
existence [Breit and Tuve, 1925]. An ionosonde transmits RF pulses vertically and detects the delay
(2τ) between transmitted and received pulses in order to compute the virtual (constant velocity)
heights (h0) of plasma density layers given a known wave velocity (c0),
h0 = 2c0τ. (2.1)
Modern ionosondes transmit coded pulses over a range of frequencies (usually 1–20 MHz) and
are capable of identifying different layers and propagation modes automatically. The ionosonde
is an important instrument for making HF radio link decisions and for making temporally coarse
ionospheric measurements of parameters such as hmF2 and nmF2 (the height and maximum density of
the F region peak, respectively), especially over extended periods of time. However, other radars are
19
superior for studying specific phenomena, such as irregularities associated with equatorial spread-F .
An example comparing equatorial spread-F observed by ionosonde and coherent radar backscatter
is given in Section 1.4.
2.2.2 Backscatter radar
Phenomenon and Theory
In contrast to ionosondes which leverage the rapidly changing refractive index of the ionospheric
plasma in the HF (3–30 MHz) range, backscatter radars are used to study the ensemble behavior
of free electrons in the plasma by scattering pulses off of them. These radars operate at higher
power levels and higher frequencies, usually in the VHF (30–300 MHz) and UHF (300–3000 MHz)
ranges. Frequency choice is motivated by the availability of suitable high-power and low-noise
components, location far above the plasma frequency, the ease of creating large aperture antennas,
radar wavelength exceeding the plasma Debye length, and the required instrument resolution.
The incoherent backscatter radar was conceived in the late 1950s as a way to understand the
ionospheric plasma physics at a more fundamental level [Gordon, 1958; Bowles, 1958]. The incoher-
ent scatter theory is that the scattered spectra from an ensemble of charged particles in the plasma
contain information about the plasma density and temperature. By observing the spectra at dif-
ferent ranges, the electron temperature (Te) and density (ne) profiles may be inferred. A complete
discussion of incoherent scatter theory, particularly the modeling and inverse problems that must
be solved to recover the plasma parameters, is beyond the scope of this work. However, a functional
description of the backscatter measurement and the understanding that temperatures and densities
may be estimated from incoherent scatter measurements are essential.
For the sake of a non-rigorous illustration, consider a scalar wave with Eb the backscattered
electric field at the scattering electrons. The scattered field, Es, observed at the radar is the
superposition of the backscattered fields, Eb, over the scattering volume propagated back to the
antenna,
Es = −re
∑
p
Eb
e−jk0rp
rp
. (2.2)
The term re is the classical electron radius and rp is the range from the antenna to electron p. Since
the scattering region is small, assume that the amplitude variation is small and that only phase
differences are consequential (paraxial approximation). Therefore, the backscattered field may be
approximated by the product of the incident field, Ei, at the electrons and a phase term representing
20
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Figure 2.1: Range-time-intensity (RTI) plot of backscatter SNR for the Christmas Island 50-MHz
radar on the night of 4 August 2003.
the propagation delay from the transmitter,
Eb = Eie−jk0rp . (2.3)
Combining Equations (2.2) and (2.3) yields
Es = −reEi
∑
p
e−j2k0rp
rp
≈ −re
r
Ei
∑
p
e−j2k0rp , (2.4)
relating the scattered field to the incident field. Notable in Equation (2.4) is the Bragg wavenumber,
kBragg = −2k0 = −4pi
λ0
. (2.5)
For the purpose of this dissertation, the Bragg wavelength is important because it represents the
scale of plasma irregularities that are detectable as coherent radar backscatter. Coherent backscatter
can and does occur during incoherent scatter measurements, although study of irregularities that
cause it is a research field in itself. Coherent backscatter data are typically aggregated in a range-
time-intensity (RTI) or range-time-velocity (RTV) plot, such as that in Figure 2.1, with time on
the abscissa, range on the ordinate, and intensities (Doppler velocities) plotted at each point. For
equatorial plasma depletions, such a plot represents a “slit camera” observation of irregularities that
drift through the radar beam. Figure 2.1 illustrates backscatter from irregularities in both equatorial
plasma depletions (above 250 km) and the electrojet (near 100 km).
The “slit camera” observation is a liability in understanding the dynamics which lead to the
21
tFigure 2.2: A cartoon illustration of the slit camera problem in backscatter radar. The ten panels
across the top represent snapshots of an irregularity process that moves left-to-right and evolves
with time. The bottom panel is the aggregate of strips from the center of each of the ten panels. It
is clear that changes in velocity smear the slit panel image. Irregularities also enter the left side of
of the beam fully formed or continue developing once they exit the right side.
formation of depleted plumes and the associated strong coherent backscatter. Figure 2.2 illustrates
two of the problems with the slit camera. The first problem is that changes in irregularity velocity
cause the RTI plot to smear. This is particularly prominent during periods of increased geomagnetic
activity, when the zonal drift may reverse one or more times; but it also skews the interpretation
of regular RTI plots, particularly during the growth stages of backscatter plumes when the velocity
vector varies rapidly. The second difficulty is observing irregularity developments and precursors.
Even if the beam were wide enough to view a large portion of the ionosphere, the resolution would
be poor.
Although the considerations in the previous paragraph can be factored into the analysis of
RTI plots, the radio imaging technique can alleviate some of the difficulties and provide additional
insight into the formation of plasma depletions. Originally, radio imaging was developed by radio
astronomers wishing to observe distant radio sources with useful resolution. The first application
to ionospheric backscatter radars was in the study of electrojet instabilities [Kudeki and Su¨ru¨cu¨,
1991]. Radar images are constructed by illuminating the ionosphere with a relatively wide beam
and synchronously sampling the backscattered field at multiple locations. Sampling the field over
a small region creates (by diffraction) a lens. By way of analog to the pinhole lens in optics, the
inversion is related to the Fourier transform [Woodman, 1997]. Although this technique creates
high-resolution images in space and time, it does not have comparable spatial extent to airglow
imaging, for instance.
22
Figure 2.3 illustrates a sample of frames from a coherent backscatter imaging experiment at
Jicamarca, Peru´, in 2006 using a maximum-entropy (ME) inversion technique [Hysell , 1996; Hysell
et al., 2008a]. The intricacy of the irregularities and the level of detail afforded by the imaging radar
are quite stunning in comparison to what can be resolved with an RTI plot. Although the radar
images have not, as of yet, been rigorously verified by any secondary technique, they are thought to
be a good representation of the physics.
Coherent backscatter from irregularities in equatorial plasma depletions is also highly aspect
sensitive. That is, the radar beam must be pointed very nearly perpendicular to the geomagnetic
field in order to detect coherent backscatter. The 50-MHz radar at Jicamarca, Peru´, cannot steer the
beam far enough off perpendicular to avoid detecting coherent backscatter. However, one equatorial
radar, the ALTAIR (ARPA Long-Range Tracking and Instrumentation Radar) on Roi-Namur island
in the Kwajalein Atoll, is capable of steering its beam on and and off-perpendicular to the geomag-
netic field. This was used to test the theory that coherent backscatter comes from the depleted
portions of equatorial plasma depletions [Tsunoda, 1980].
Coherent backscatter, particularly imaging coherent backscatter, is an important tool for under-
standing irregularity processes. However, it is limited to detecting irregularities at the Bragg scale
within the typically narrow radar beam. Other instruments are therefore important in understanding
irregularity development, location, and motion.
Christmas Island Radar
The Christmas Island Radar (CXI; geographic: 2.0 N, 202.6 E; geomagnetic: 3.1 N, 273.6 E) is a
50-MHz system presently operated by the U. S. Air Force Research Laboratory (formerly operated
by SRI International between 2002–2007) in Kiribati. The antenna is a 100-m × 100-m co-co type
array. Two stationary beams (each with symmetric half-power beam-width of 2.3◦) have been
operational since 2002 (east) and 2003 (north). The east beam (elevation: 60.5◦; azimuth: 90.0◦)
provides backscatter data slightly to the east of the CNFI field of view. The north beam (elevation:
84.5◦; azimuth: 0.0◦) provides observations within the same geomagnetic volume as a pair of airglow
imagers operating from Hawaii (discussed in Section 2.3.3). That is, the range gate centroid locations
of the north beam reside on geomagnetic field lines that intersect the airglow observed by the imagers
north of the geomagnetic equator. In its present configuration, the radar provides backscatter SNR
and Doppler velocities at 100× 10-km (in altitude) range gates on each of the two beams every 75
seconds.
23
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24
2.2.3 Satellite beacons
Forward scatter, or bistatic, measurements utilize a transmitter and receiver at different locations.
For this work, we are interested primarily in forward scatter measurements made with either the
transmitter or receiver (or both) on spacecraft. The first artificial Earth satellites employed radio
beacons to facilitate tracking. It was soon discovered that rapid variations (much more rapid and
irregular than the Doppler shift) were present on the received satellite signal. Although the first
recorded observation of scintillation came from radio star (pulsar) observations a decade earlier,
artificial satellite beacons provided a calibrated means to observe irregularities in the ionosphere.
Satellite beacons on multiple frequencies far above the plasma frequency can also be used to
determine the total electron content (TEC) along the path between the transmitter and receiver via
the dispersive properties of the plasma. From the Appleton-Hartree formula in the high-frequency
limit,
n(z) =
√
1− ω
2
p(z)
ω2
. (2.6)
The plasma frequency, ωp, can be derived by slightly displacing a parcel of plasma of known density
ne and allowing it oscillate at its natural frequency,
ωp =
√
neq2e
&0me
≈ 2pi√80.6ne, (2.7)
where qe = 1.609 × 10−19 C/e− is the fundamental unit of electronic charge, me = 9.109 × 10−31
kg/e− is the mass of an electron, and &0 = 8.854 × 10−12m−3 · kg−1 · s4 · A2 is the permittivity of
free space. Let the group path (Sg) be the effective distance traveled by a wave packet through the
dispersive plasma in the course of the group delay (τ),
Sg = c0τ =
∫ z0+z
z0
dz′
n(z′)
. (2.8)
Dividing through by c0 and taking a Taylor series approximation for the group refractive index
(ng = 1/n) yields
τ ≈ 1
c0
∫ z0+z
z0
(
1 +
1
2
ω2p(z′)
ω2
)
dz′, (2.9)
which can be simplified to
τ ≈ z
c0
+
1
2c0ω2
∫ z0+z
z0
ω2p(z
′)dz′. (2.10)
25
We solve Equation (2.7) for ne and integrate to obtain TEC,
TEC =
∫ z0+z
z0
ne(z′)dz′ =
&0me
q2e
∫ z0+z
z0
ω2p(z
′)dz′. (2.11)
That is, ∫ z0+z
z0
ω2p(z
′)dz′ =
q2e
&0me
TEC. (2.12)
We can insert this result into Equation (2.10) to obtain
τ ≈ z
c0
+
q2e
2c0&0meω2
TEC. (2.13)
Given two temporally coincident (phase-coherent at the transmitter) group delays (τ1, τ2), we can
compute the TEC as
TEC ≈ 2c0&0me (τ1 − τ2)
q2e
ω21ω
2
2
ω21 − ω22
. (2.14)
Converting the frequencies from angular (rad/s) to time (Hz) and applying the approximation from
Equation (2.7) yields
TEC ≈ c0 (τ1 − τ2)
40.3
f21 f
2
2
f21 − f22
. (2.15)
TEC is typically specified in e−/m2 or in “TEC units” (TECU, 1016 e−/m2). When observed
over a path that traverses the entire ionosphere such as Earth’s surface to the Global Positioning
System (GPS), TEC serves as a relative measure of plasma density over the surface of the Earth. For
comparison, TEC measurements are often projected onto the surface normal vector of the Earth.
This product is called vertical TEC (VTEC). The plasmasphere also contributes some electron
density to TEC observations made using GPS. This contribution is generally small during the
day, but may become significant at night during solar minimum conditions when the ionospheric
contribution to TEC is low. TEC is also useful in “ray” tomography problems [e.g., Austen et al.,
1988; Kunitsyn and Tereshchenko, 2003; Lee et al., 2008]. A special case of the ray tomography
problem is radio occultation, discussed in Section 2.2.3.
One of the problems with the TEC technique is removing the biases introduced by the transmit-
ter and receiver circuitry when determining the actual delays, τ1 and τ2. In the case of GPS, the
correction terms are broadcast regularly, but the receiver biases must also be removed. For ground-
based receivers, a simple technique normalizes all of the observations made by a given receiver to the
lowest TEC observed just before dawn. There are also estimation and filtering techniques that may
26
be applied to this problem given sufficient data. For the case of space-based receivers and trans-
mitters, the TEC can be plotted as a function of distance between the two satellites. Extrapolating
the distance to zero yields both the transmitter and receiver biases directly (P. Bernhardt, personal
communication, 2007). This extrapolation technique does not work well when distances are large
or slowly varying, as is the case for GPS. However, it is useful with many of the low-Earth orbiting
beacon transmitters and receivers.
The Global Positioning System
GPS provides precision location and altitude information world wide through a constellation of 32
satellites. Each satellite broadcasts coded time signals on several frequencies, which are combined
at the receiver to determine location. As a remote sensing tool, the GPS is fundamentally similar to
other satellite beacons. However, it has the advantage of a synchronized, stable clock system, and
global coverage. GPS is particularly interesting for ionosphere studies because it is both a remote
sensing tool and an application space for the results of ionospheric research.
GPS operates on the principle of time-of-arrival (TOA), illustrated in Figure 2.4. Synchronized
pulses from three transmitters {A,B,C} at known locations are received at Z. The estimated range
to a given satellite under assumption of a known constant propagation velocity (c0, the speed of light
in a vacuum) is called the pseudorange. Equation (2.16) is a simplified version of the pseudorange
equation. In the pseudorange equation, ρ is the true range to the satellite, ε is the error (including
ionospheric TEC and hardware biases, discussed earlier, among others) in the pseudorange, and τ
is the measured time delay between the satellite and the receiver.
P = ρ+ ε = c0τ. (2.16)
Orbital information for each satellite is provided in the form of ephemerides broadcast by the
satellites. This allows the satellite position to be accurately fixed during solution for the user
location. Most of the components of the error term ε are corrected using information included
with the ephemerides. However, environmental errors not associated with satellite hardware are
often difficult to parameterize. Particularly of interest are the delays introduced by variations in
the refractive indices of the Earth’s atmosphere and ionosphere. Herein lies the problem of interest.
Through the delay mechanism discussed above in association with TEC measurements, the presence
of electron density gradients causes GPS navigation solutions to become inaccurate on the order
of a few meters. Large gradients, such as those observed during major storms, may degrade the
27
navigation solution further to the order of tens of meters. Although scintillation is usually associated
with gradients in electron density, the rapid fading may also cause the tracking algorithm in the
receiver to lose lock on the GPS signal.
A
Z
C
B
Figure 2.4: Illustration of the time-of-arrival principle applied to GPS. Three transmitters labeled
{A,B,C} produce synchronized pulses that are received at Z. By computing the transit times of
the pulses, the location of Z can be fixed.
The GPS signal is spread-spectrum BPSK with a 50-Hz data rate. Two different frequencies are
presently used for GPS. Consumer-grade GPS units lock onto the Coarse / Acquisition (C/A) code
broadcast on the GPS L1 frequency of 1.57542 GHz. Another code, the so-called Precise-Encrypted
(PY) code, inaccessible to civilian users, is broadcast both at L1 and at frequency L2, 1.22760 GHz.
Although the coded data from L2 are not accessible to civilians, receivers with high-stability local
oscillators can track the phase difference between the L1 and L2 signals without decoding L2. This
technology allows TEC measurements through the technique discussed in the previous section (e.g.,
Equation (2.15)). The two frequencies may also be used to correct for dispersive transmission delays
in the ionosphere through a related procedure. However, the codeless tracking on L2 requires higher
SNR than the C/A signal on L1 and is more susceptible to scintillation.
Another technique for improving the accuracy of single-frequency GPS receivers is differential
GPS. Differential GPS employs one or more well-surveyed receivers whose observations are combined
with the observations of the unknown receiver to yield a navigation solution with improved accuracy.
A widely deployed differential GPS service is the Wide-Area Augmentation System (WAAS). WAAS
employs a network of reference receivers throughout the United States. While WAAS can correct
for large scale temporal and spatial variations in the ionosphere, its accuracy does break down under
certain cases, particularly during intense geomagnetic storms, when smaller scale electron density
structures often form in the midlatitude ionosphere.
GPS receivers have also been employed as scintillation monitors [Beach and Kintner , 2001]. Since
the irregularities and the satellites are in motion with respect to the receiver, the interpretation of
the data requires careful effort [e.g., Ledvina et al., 2004; Kintner et al., 2004]. One way to mitigate
28
the effect of satellite motion is to use the WAAS signal, which is broadcast from geostationary
orbit [Cerruti et al., 2006; Ledvina and Makela, 2005].
Radio Occultation
The premise behind occultation is that a space-based transmitter and space-based receiver have
established a radio communication link. As one of the two stations passes behind a planet, the
communication signal is lost, or occulted. However, at the immersion and emersion points, where
the transmitting station is just setting and rising, respectively, the signal is bent slightly as it passes
through the planet’s atmosphere. Figure 2.5 illustrates immersion in cartoon form, although the
bending angle is slightly exaggerated.
Occultation has a long history in planetary astronomy. The first suggestion for optical observa-
tions was by Pannekoek [1903]. The idea is that a varying intensity (due to extinction) of a star
occulted by a planet should yield the atmospheric scale height. However, this measurement was im-
practical until photometry advanced sufficiently. Even then, the measurement is noisy due to seeing
conditions1 for terrestrial telescopes. The first radio occultation experiment was completed using
supernova remnant IC 443 and the moon in 1955 [Elsmore and Whitfield , 1955]. This measurement
was repeated in 1956 using the Crab Nebula [Elsmore, 1957]. The modern era of radio occultation
began with the Mariner IV spacecraft as it flew by Mars on 15 July 1965 [Kliore et al., 1965].
V
Disk
Limb
RX
SRC
Figure 2.5: Cartoon of immersion occultation geometry. The bending angle is exaggerated for effect.
In the Mariner experiments, the spacecraft and Earth stations were used as transmitters and
receivers, respectively, to probe the atmospheres of Venus and Mars. The Voyager spacecraft sent
to the outer planets of the Solar System also employed this particular occultation geometry to
study not only planetary atmospheres, but also ring systems [Marouf et al., 1986]. Early in the
U.S. space program, plans were laid for occultation experiments involving two orbiters [Harrington
1Atmospheric turbulence also affects light from extraterrestrial sources. In astronomy circles, “good seeing” is the
qualitative term for little variation in intensity.
29
et al., 1970]. While this was a substantial undertaking for other planets, it suddenly became feasible
for the Earth when space-based navigation systems were installed. The introduction of the Global
Positioning System (GPS) spurred a renaissance for the occultation idea. The GPS/MET satellite
launched in the mid-1990’s was intended as a testbed for GPS occultation technology. Other pro-
grams such as CHAMP and IOX became operational in 2000 and 2001, respectively. More recently,
six COSMIC/FORMOSAT-3 satellites were launched in April 2006 as a partnership between the
University Corporation for Atmospheric Research (UCAR) in the United States and the Taiwanese
Space Agency [Cheng et al., 2006].
Radio occultation leverages phase measurements of phase-coherent signals at two or more dif-
ferent frequencies to obtain either the ray bending angle (for neutral atmosphere) or the TEC (for
ionosphere). Initially, the Mariner phase measurement data were inverted by comparing the obser-
vations to a forward model for the Martian atmosphere [Kliore et al., 1965]. However, subsequent
inversions employed the Abel transform relationship and the assumption of spherical symmetry to
solve for the refractive index profile. The refractive index profile is then inverted via forward model
for the neutral or electron density profile [Fjeldbo et al., 1971].
Occultation is a projection problem in the sense that the properties of the medium along the
ray path at each sample step affect the resulting measurement. In contrast to most other projection
problems such as those in medical imaging, occultation is constrained by instrument density to be
a very limited angle problem. A tomographic reconstruction is not possible in the traditional sense.
However, by modeling the atmosphere as a set of spherically symmetric layers (“voxels” to borrow
the tomography term), the density (refractivity) of each layer can be inverted to produce a profile.
Since the region over which the occultation occurs is a surface (“plane”), it is common to flatten
the problem into two dimensions. In two dimensions the analytical formulation is the so-called Abel
transform. Referring to Figure 2.6, the two-dimensional Abel transform amounts to the projection
(Equation (2.17)) of a circularly symmetric function (f(r)) along a line-of-sight (p) parallel to the
x-axis:
fA(a) =
∫ ∞
−∞
f(r)dx. (2.17)
For any point (x, a), r =
√
x2 + a2. Therefore, we invoke the chain rule to change dx to dr in the
Abel projection integral. Substituting the new differential and noting the symmetry involved, we
write
fA(a) =
∫ ∞
−∞
f(r) r dr√
r2 − a2 = 2
∫ ∞
a
f(r) r dr√
r2 − a2 . (2.18)
30
ar
p
x
y
Figure 2.6: Abel transform geometry.
There are generally two approaches to solving this inverse problem for f(r). The first, and
original, technique is to evaluate the analytical inverse of the Abel transform numerically,
f(r) = − 1
pi
∫ ∞
r
dfA(a)
da
da√
a2 − r2 . (2.19)
One such numerical technique is termed “onion peeling.” The assumption is that the area over
which spherical (circular) symmetry is required is smallest at the highest altitude shell for which
data are available. As the name suggests, onion peeling starts at the highest shell and works down,
evaluating Equation (2.19) by quadrature, layer by layer. Although the error response of such a
technique is relatively good on the topside, errors compound rapidly as the ray descends and the
size of the required region of symmetry grows. The second technique recognizes that the discrete
form of the integral transform in Equation (2.18) can be cast as
fA = G f . (2.20)
In this case, there may exist a whole host of generalized inverses G† for the transform G, each with
different smoothing and noise response properties. At the time of this writing, the COSMIC and
CHAMP occultation data were processed using a form of the onion peeling algorithm [Lei et al.,
2007]. The only known study of matrix inverse methods for this problem was performed on modeled
data [Hysell , 2007].
The input, fA(a), of Equation (2.19) for ionospheric problems is the calibrated suborbital total
electron content: the TEC within the satellite orbit ellipse. This is obtained by measuring the
31
TEC from the receiver to the GPS satellite as a function of ray tangent altitude on either side of
the ray tangent point. On each side of the tangent point, there is a TEC measurement with the
same tangent altitude. The difference between these measurements approximates the TEC below
the receiver orbit. Naturally, this estimate is considerably better if the occultation is (nearly) in the
orbit plane of the receiver. The value of the suborbital TEC is constrained to approach zero as the
ray tangent altitude approaches the satellite altitude. This motivates the onion-peeling inversion
by starting with the shortest ray paths (those supposed to have the most local spherical symmetry)
and working downward.
In the absence of other data sources, classical radio occultation utilizing spherically symmetric
shells is a credible technique. However, as we will soon see, the spherical symmetry assumption is
easily violated. Figures 2.7 and 2.8 illustrate the effects of the spherical symmetry assumption under
daytime conditions with few irregularities and nighttime conditions with irregularities, respectively.
Each of these figures has three panels containing occultation data from the COSMIC experiment.
On the left is the suborbital TEC as a function of ray tangent altitude. The center is the Abel
electron density inversion provided as a data product by the UCAR COSMIC program. The right is
the SNR reported by the receiver as a function of ray tangent altitude. The inversion in Figure 2.7 is
both relatively smooth and mostly positive. However, the inversion in Figure 2.8 is both ragged and
negative up to 225 km. The presence of negative values (or unrealistic positive ones) suggests that
the inverse Abel transform has redistributed the electron density in the spherical shells to explain
meridional or longitudinal gradients in electron density. Notice also in Figure 2.8 that the GPS L1
SNR undergoes scintillation from about 175 to 350 km. This suggests that small-scale electron-
density irregularities are present, likely in conjunction with large-scale equatorial plasma depletions.
This was confirmed by an airglow imaging system operating on the ground.
The spherical symmetry problem is an invitation to creativity in assimilating data from other
sources. A few researchers have combined ground-based GPS VTEC data with GPS occultation
data [Herna´ndez-Pajares et al., 2000]. This can also be accomplished as a tomography problem,
which relies on a high density of ground receivers in addition to one or more well-placed occulta-
tions (J. Lee, personal communication, 2007).
The SNR and excess phase measured at the occultation receiver can also be used to study ir-
regularities. This is a relatively recent development that requires special attention to detail because
the transmitter, receiver, and irregularities, are all in motion. Furthermore, the data rates (typically
1-Hz) provided by the early radio occultation satellites tended to under-sample irregularities. Scin-
32
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E
"
03F;0'GH0IJFJK
Figure 2.8: Nighttime occultation inversion in the presence of irregularities at many scales. The
left plot shows the calibrated TEC as a function of the ray tangent altitude. The center plot is the
inverted electron density profile. Notice that the inverted profile is negative up to 225 km. This is an
artifact of the spherical symmetry assumption in an atmosphere that is not spherically symmetric.
The right plot is the 1-Hz SNR on the GPS L1 frequency. Large, rapid fluctuations occur over
most of the occultation. This suggests that small-scale irregularities (which may be associated with
equatorial plasma depletions) are present. Data provided courtesy of the UCAR COSMIC Project
Office.
33
tillation indices such as the S4 cannot be interpreted in the same way for these measurements as for
the 50-Hz sampled ground-based measurements. This is because both the satellite and the receiver
are in motion, whereas terrestrial scintillation observations only have the satellite moving (in the
Earth frame). However, as we will see in Chapter 4, a short-time increase in the SNR variance does
indicate the presence of irregularities along the ray path [Miller and Makela, 2008]. The geographic
distribution and magnetic aspect angles of scintillation irregularities have been studied in a coarse
manner utilizing the SNR variance (called “S4” by the authors) [Straus et al., 2003; Anderson and
Straus, 2005]. However, the assumption is made that the irregularities are occurring at the ray
tangent point.
2.2.4 Irregularity imaging with occultation
The irregularity localization problem can also be approached from the standpoint of diffraction
tomography or inverse scattering [Sokolovskiy et al., 2002; Gorbunov et al., 2002; Gorbunov and
Gurvich, 1998; Bojarski , 1982]. Fundamentally, this amounts to invoking Huygens’ principle, which
arises from solving the Helmholtz equation
(∇2 + k2)u = 0. (2.21)
Given samples of the complex field along the perimeter of a region, we can reconstruct the irregu-
larities within the region. If the field is stationary in time and is uniformly sampled along a straight
line in a two-dimensional plane, the problem reduces to a phase-shift in Fourier space,
F{u} = F{u0} exp
(
−jz k
2
x
2k
)
, (2.22)
where F{·} is a Fourier transform operator, z is the distance from the sample line, kx is the angular
displacement [−pi,pi] along the samples u0(kx), k is the radio-frequency wavenumber, and u(kx, z)
is the unknown field [e.g., Ratcliffe, 1956]. Figure 2.9 illustrates an example of this kind of recon-
struction. The forward diffraction field (top) is generated for a thin phase screen of irregularities at
x = 100 and the radio source at x→ −∞. The forward field is sampled at x = 200 and reconstructed
(bottom). The point (x = 100) in the reconstructed field at which the rays appear “focused” with
minimum amplitude variation is the location of the irregularities.
Since satellite orbits are elliptical, it is sensible to attempt a solution of Equation (2.21) in two
34
Forward Model
x [arb. units]
y
 [
a
rb
. 
u
n
it
s
]
50 100 150 200 250 300
20
40
60
80
100
120
Inverse Model
x [arb. units]
y
 [
a
rb
. 
u
n
it
s
]
50 100 150 200 250 300
20
40
60
80
100
120
Figure 2.9: Forward (top) and inverse (bottom) models of diffraction due to irregularities at x = 100.
The forward field was sampled at x = 200. In the inverse model, the reconstructed field exhibits a
focusing effect at x = 100. This indicates the position of the irregularities.
dimensions. After Gorbunov and Gurvich [1998], the solution is
u(x) =
√
k
2pi
∫
S
u0(y) cosψxy exp(−jk|x− y|+ jpi/4)√|x− y| dSy, (2.23)
where u0(y) are the samples of the field along the satellite orbit, x is the location of the reconstructed
field, y is the location of the satellite, and ψxy is the angle between the vector x− y and the normal
to the curve, aˆn. The complex field samples u0(y) are obtained from the GPS receiver SNR and
excess phase measurements.
In order to take advantage of the spatial reduction to two dimensions, it is necessary to assume
that the irregularities are field-aligned [Sokolovskiy et al., 2002]. The two-dimensional flattening also
destroys the physical interpretation of the reconstructed field. However, if the irregularities form
a thin phase screen, they can be detected by the focusing technique described above. Figure 2.10
illustrates the geometry of this problem when flattened to two dimensions. The diffraction tomog-
raphy approach has never been directly verified against other techniques. Some of its proponents
claim to have detected irregularities at an altitude of 1300 km [Sokolovskiy et al., 2002]. While
scintillation-scale irregularities have been detected near 800 km using forward-scatter [MacDougall ,
1981] (mid-latitude case) and rocketry [Jahn and LaBelle, 1998] (equatorial case), this claim seems
to be somewhat dubious. Refinement of this technique or a complimentary technique might allow
35
Figure 2.10: Geometry of the two-dimensional diffraction tomography (“back propagation”) prob-
lem. The receiver is in low-Earth orbit over the eastern Caribbean. The GPS satellite is far below
the figure. The 2-D solution is computed in the plane drawn tangent to Earth’s surface.
it to become more robust, and therefore more valuable, in the future. One such complimentary
technique is presented in Chapter 4.
2.3 Optical Imaging Techniques
Optical remote sensing of the ionosphere predominantly occurs through airglow detection. Airglow
is light given off as ions in the ionosphere change energy levels due to ion-electron recombination
or high-energy particle impacts. The aurorae, which are the most commonly recognized airglow
emissions, are primarily due to high-energy particle impact. However, at lower latitudes, the pri-
mary airglow emissions of interest are due to recombination. During the day, solar radiation drives
production. After sunset, the ions and electrons recombine to form neutral species again. These
recombination processes yield airglow emissions used as dynamic tracers in the low- and mid-latitude
ionosphere. Because airglow emissions at low and mid-latitudes tend to be rather weak (below the
threshold of human perception), narrow bandwidth color filters are used in conjunction with long
(on the order of minutes) exposure times and sensitive photon counters.
As equatorial depletions grow in altitude, internal polarization electric fields map efficiently along
the geomagnetic field (an effect that will be discussed in Chapter 3), pushing them into the low-
and mid-latitude regions north and south of the geomagnetic equator. There, the depleted plasma
appears as a dark region in the airglow, allowing wide-area spatial maps to be made of the depletions.
Airglow observations represent a complex product of sensor and optics, observation geometry,
chemistry, neutral dynamics, and electrodynamics. In the following subsections, we will investigate
many of these relationships, especially plasma chemistry, instrumentation, calibration, and signal
36
processing. The details of geomagnetic field-aligned imaging will be reserved for discussion in Chap-
ter 3. A short discussion of the practical aspects of installing and operating an airglow imager is
found in Appendix B.
2.3.1 Airglow chemistry
There are predominantly two airglow emission lines that are useful for ground-based F -region studies
in the equatorial region. One is the 630.0-nm “red” line. The other is the 777.4-nm line in the
infrared. These emissions arise from atomic oxygen energy transitions, as illustrated in Figure 2.11.
D1
S1
P3
P5
S5
0
2
4
6
8
10
12
14
16
777.4
135.6
557.7
630.0
eV
ionized states
Figure 2.11: Simplified OI transition diagram showing commonly observed equatorial airglow emis-
sions. This figure is a considerably simplified version of Figure 1 in Tinsley et al. [1973]. There are
a number of high-energy states with transitions that populate the 1D and 5P states that are not
shown here.
The 630.0-nm “red” line that results from the dissociative recombination of O+2 is easiest to
observe, although the chemistry and dynamics are a little more complex. This discussion is based
on work by Makela and Kelley [2003b]; Garc´ıa [1999]; Link and Cogger [1988]. O+2 is formed from
the collision between O+ and molecular oxygen (O2),
O+ +O2 → O+2 +O. (2.24)
37
One dissociative recombination reaction of O+2 yields
O+2 + e
− → O(1D) +O(3P ) + 4.99 eV. (2.25)
Although O(1D) may be lost through several mechanisms, the 630.0-nm emission arises from the
relaxation
O(1D)→ O(3P ) + hν. (2.26)
The O(1D) state has a lifetime of 110 s. This is important because the O(1D) population may be
advected by dynamics, causing the image to blur.2 The transition produces a photon (hν) at 630.0
nm.
The volume emission rate of the 630.0-nm emission has contributions from a number of sources,
which are summarized in this rate equation [Link and Cogger , 1988]:
η630.0 =
0.76β1Dk1[O+][O2]
1 + (k3[N2] + k4[O2] + k5ne)/A1D
. (2.27)
The values of the coefficients [from Link and Cogger , 1988] are given in Table 2.1. Coefficient k1
relates the production of O+2 ions to the densities O+ and O2, which are dominant ion and neutral
components at F -region altitudes. Coefficient β1D reflects the rate of production of O(1D) from the
dissociative recombination reaction in Equation (2.25). Dissociative recombination of O+2 also yields
significant populations of O(3P ) and O(1S), which can be seen in the context of airglow emissions
in Figure 2.11.
Table 2.1: Reaction Rate Coefficients for the 630.0-nm Emission
Reaction Coefficient Value
O+2 + e− → O(1D) +O(3P ) + hν β1D 1.1
O+ +O2 → O+2 +O k1 3.23× 10−12 exp
(
3.72·300
Ti
− 1.87·3002
T 2i
)
cm3·s−1
O(1D) +N2 → O(3P ) +N2 k3 2.0× 10−11 exp
(
111.8
Te
)
cm3·s−1
O(1D) +O2 → O(3P ) +O2 k4 2.9× 10−11 exp
(
67.5
Te
)
cm3·s−1
O(1D) + e− → O(3P ) + e− k5 1.6× 10−12T 0.91e cm3·s−1
O(1D)→ O(3P ) + hν A1D 6.81× 10−3 s−1
A typical emission profile of the 630.0-nm red line emission generated from Equation (2.27)
is shown in Figure 2.12 along with the electron and molecular (diatomic) oxygen densities. The
peak emission altitude and the altitude of peak electron density are marked, as well as one neutral
2This might be something, however impractical, to explore as a remote sensing technique.
38
scale-height below the electron density peak.
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Figure 2.12: 630.0-nm emission profile compared to ne and [O2] profiles. Peak emission/density
altitudes are indicated by the horizontal line and marker (◦). In the oxygen profile, the electron
density peak altitude and scale-height are indicated.
The 777.4-nm emission arrises from the radiative recombination of O+,
O+ + e− → O(5P ). (2.28)
And a photon is given off at 777.4 nm,
O(5P )→ O(5S) + hν. (2.29)
The 777.4-nm emission occurs promptly. From Equation (2.28) and Figure 2.11, it is apparent that
the rate of O(5P ) production, and hence 777.4-nm photon production, is related to the product
of the O+ and electron densities. Given that the dominant ion at the F region peak is O+ and
assuming that the ionosphere is electrically neutral, such that ne = ni ≈ [O+], the volume emission
rate of 777.4-nm photons is proportional to the square of the electron density, as described by
Equation (2.30). This is also true of the 135.6-nm emission observed by the GUVI and IMAGE
instruments, which comes from a related reaction [e.g., DeMajistre et al., 2004]. The 135.6-nm
39
emission also has a different constant (α) relating its volume emission rate to the electron density.
η777.4 ≈ α5Sn2e. (2.30)
There is also an ion-ion recombination contribution to the 777.4-nm emission that is frequently
negligible and beyond the scope of this work.
2.3.2 Intensity interpretation
Whereas the volume emission rate, and therefore the intensity, of the 777.4-nm emission is directly
related to the electron density, the emission rate for the 630.0-nm emission is jointly dependent on
the density of O2 and electrons. Because O2 is a neutral species, its distribution is not strongly
influenced by electrodynamic processes. As the electrons (in the F -region peak) move upward, there
is less O2, and the 630.0-nm emission becomes weaker. Likewise, as the F region descends, the
630.0-nm emission intensifies.
This ambiguity becomes particularly important when differentiating classes of structures, no-
tably MSTIDs (medium-scale traveling ionospheric disturbances) and equatorial plasma depletions.
MSTIDs are predominantly observed as undulations in the ionosphere height and to a lesser ex-
tent changes in density, whereas depletions exhibit considerably larger electron density variations.
However, to the untrained eye, they may appear to have similar characteristics in an airglow image.
In an all-sky imaging system, the optical extinction of the atmosphere and the thickness of the
airglow layer become important. At low elevation angles, the ray path lengths in the atmosphere
and the airglow layer are longer than they are at zenith. For a narrow-field imaging system such as
those predominantly utilized in this work, this consideration is less important. For a discussion of
these effects, consult Garc´ıa [1999].
2.3.3 Instrumentation
An airglow imaging system consists of several major components (see Mendillo and Baumgardner
[1982] for an early example of this architecture). Light enters the system through an objective lens.
It is then re-imaged to be approximately telecentric as it passes through a narrow filter to select the
emission wavelength of interest. Filters are switchable using a rotating wheel. The final block of
optics focuses light exiting the filter onto the detector. The earliest airglow images were obtained
with film or intensified television cameras. However, developments in charge-coupled device (CCD)
40
Figure 2.13: KEO architecture all-sky airglow imager fitted with a CCD camera (back). PICASSO
architecture all-sky airglow imager (front).
technology over the past two decades have made it the sensor of choice for modern airglow imagers.
At least two architectures of airglow imagers are in use worldwide. Examples of each are shown
together in Figure 2.13. The original is the KEO3 architecture, which was developed using mostly
off-the-shelf photographic components. While many contributions were made using the KEO archi-
tecture, these imagers are large and require considerable infrastructure to operate. A more recent
imager architecture is the PICASSO (Portable Ionospheric Camera and Small-Scale Observatory).
PICASSO utilizes custom optics that reduce the length of the optical train from about 1.3 m for a
KEO system to 0.3 m. The PICASSO imager can be operated from a laptop in a small weatherproof
enclosure of 0.5× 0.5× 0.5 m.
Two narrow-field imagers and one all-sky imager are predominantly used in this work. The
narrow-field imagers are located in Hawaii and Chile, respectively. The all-sky imager is co-located
with the narrow-field imager in Hawaii.
The airglow imager (“CTIO” or “PICASSO2”) used in the Chapter 4 has a narrow field of view,
80◦×60◦, which covers about 18 degrees of magnetic longitude or 2000 km. This increases the spatial
resolution of the imager compared with the all-sky systems at the expense of a more limited field of
view. The imager is installed at the Cerro Tololo Inter-American Observatory (CTIO; geographic:
30.17 S, 289.19 E; geomagnetic 16.72 S, 0.42 E) near La Serena, Chile, and has been operating since
August 2006. It consists of custom optics, a five-position filterwheel to select the emission line of
interest, and a 2184 × 1472 CCD array cooled to −30 ◦C and binned 3× 3 on-chip. The imager is
oriented such that the lines of sight are parallel to the geomagnetic field at the altitude of the peak
3Named for KEO Consultants of Brookline, MA, now KEO Scientific, Ltd., Calgary, AB.
41
airglow emission, as illustrated in Figure 2.14. The physical motivation for this technique will be
discussed in Chapter 3. In such an orientation, the imager can observe the effects of the polarization
electric fields along an entire magnetic field line projected onto the local (off-equatorial) airglow
layer.
−90 −80 −70 −60
−10
−20
−30
Geo. Longitude [deg]
Ge
o.
 L
at
itu
de
 [d
eg
]
a b
CTIO FOV
CTIO “Geomagnetic FOV”
Mag. Equator
CTIO FOV
Airglow
Figure 2.14: (a) Geographic view of the PICASSO narrow-field imager at Cerro Tololo, Chile
(CTIO). The field of view assumes a 250-km emission altitude for the airglow. (b) This figure
shows the meridional cross-section, highlighting that the lines of sight are nearly parallel to the
geomagnetic field.
The narrow-field and all-sky imagers used in the Chapter 5 and 6 studies are located at the U. S.
Air Force’s Maui Space Surveilance Complex on Mount Haleakala on the Hawaiian island of Maui.
The Cornell Narrow-Field Imager (CNFI; geographic: 20.71 N, 203.83 E; geomagnetic 21.03 N,
271.84 E) has been operational since December 2001 [Kelley et al., 2002]. This system is oriented in
the field-aligned viewing geometry discussed in Chapter 3. The imaging system has a narrow (47◦)
field of view that yields high native resolution compared to ordinary wide-field or all-sky imaging
systems. CNFI has a liquid-cooled, low-noise CCD detector and a filterwheel containing several
narrowband filters that allow observation of the 630.0-nm and 777.4-nm emissions, as well as a slice
of the background continuum. The Cornell All-Sky Imager (CASI) is colocated with CNFI and
oriented at zenith. In addition to the airglow lines observed by CNFI, it also has filters for 557.7 nm
(“green” line) and 589.0 nm (sodium). The fields of view of these instruments at 250 km altitude
are shown in conjunction with the beams of the Christmas Island 50-MHz radar in Figure 2.15.
2.3.4 Flat field calibration
As with any wide aperture, wide angle lens, vignetting, or intensity roll-off, occurs near the edges of
the image. For certain experiments, the absolute or relative airglow intensity across an image is an
important observable. Therefore, it is necessary to correct for the vignetting using a flat-field image.
42
!170 !160 !150
0
10
20
Geo. Longitude [deg]
G
e
o
. 
L
a
ti
tu
d
e
 [
d
e
g
]
a b
CXI East CXI North
Mag. Equator
CNFI “Geomagnetic FOV”
CNFI FOV
Airglow
CASI FOV
CNFI FOV
CASI FOV
CXI beams
Figure 2.15: (a) Geographic view of several instruments in the central Pacific. The CASI curve is
the field of view for CASI at 250 km altitude and 15◦ elevation. The CNFI curve is the CNFI field
of view at 250 km. The dashed curves in between −150◦ and −155◦ are beams of the CXI radar
mapped along the geomagnetic field into the off-equator ionosphere at 250 km. (b) Meridional-
cut view of the CNFI-CASI-CXI geometry. The approximately parallel family of curves are the
geomagnetic field. The CXI beams are oriented ⊥ B just north of the geomagnetic equator. CNFI
(oblique) and CASI (zenith) fields of view are indicated. Notice that the CNFI lines of sight are
nearly parallel to the geomagnetic field.
In principle, this correction is accomplished by obtaining an image of a known constant source over
the entire field of view of the imager. An integrating sphere is a convenient and accurate constant
intensity source that yields a flat-field image directly. Data images are divided by the flat-field
image to obtain the corrected image. Even when photometry is a secondary consideration, flat-field
correction yields more visually appealing images.
In the absence of an integrating sphere, a calibrated Lambertian light source may be employed
at every azimuth and elevation angle. A curve is then fit to the observed intensity as a function
of angle (pixel location) in each direction. Assuming that the azimuthal variation is constant for a
high-quality lens system, the flat-field image is equal to the fitted curve rotated about the optical
axis:
ΥFF = axay cos θx cos θy. (2.31)
2.3.5 Spatial calibration
Perhaps the most important calibration for all airglow imaging applications is the mapping from
pixel coordinates to geographic coordinates in the airglow layer. This is a two-step procedure that
begins with identifying known stars in the airglow images. Given the location for the imager, the
date and time, and the locations of a few stars, an azimuth and elevation map is generated to relate
the pixel locations to the azimuth and elevation [e.g., Garc´ıa, 1999]. The second step is to convert
43
the azimuth and elevation to latitude and longitude in the airglow layer. By assuming an altitude
for the centroid of the emission layer, the intersection point for each ray can be computed using
spherical geometry.
The procedure outlined here is iterative. The first step is to propose a model of the imaging
system and its orientation. Second, a guess is made (based on an observed star field or known
surveying of the site) as to how the imager is oriented at the site. Third, the position from the on-
site GPS receiver is used in conjunction with the previous two steps to create an azimuth/elevation
map for each pixel in a candidate airglow image. Now, the timestamp of the airglow image is utilized
with the aid of a star catalog to find the actual positions of stars within the imager’s field of view.
The final step is to compare the locations of the stars within the field of view from the star catalog to
those stars in the candidate image. This procedure is iterated4 until the ensemble distance between
the stars in the candidate image and the catalog image is negligible.
Figure 2.16 illustrates the five parameters of the installed imager system required to estab-
lish a spatial calibration: optical axis azimuth (ξ, North-definite) and elevation (ε), CCD rotation
with respect to optical axis (γ), and CCD translation (δx, δy) from the optical axis. Addition-
ally, because the PICASSO-type imagers use custom non-telecentric optics, each unit has a specific
function relating the angle between the optical axis and the radial distance on the CCD. This
function is specified by the designer in the form of radial distances (0, in pixels) at optical angles
{0◦, 15◦, 30◦, 45◦, 60◦, 75◦, 80◦}. These are fit to a cubic spline function, ψ(0), to map each radial
distance (in pixels) on the detector to its angle with the optical axis.
The center pixel offset is applied to each pixel (i, j)→ (xij , yij),
xij = i− δx, (2.32)
yij = j − δy. (2.33)
Next, the distance from each of the offset pixels (xij , yij) to the center pixel (x0, y0) is computed,
∆ij =
√
(xij − x0)2 + (yij − y0)2, (2.34)
where x0 = .max i/2/, y0 = .max j/2/. The azimuth (αij) and elevation (εij) of each pixel are
4There are commercial software tools which can perform this operation automatically. In the case of the PICASSO
systems, it has been performed semi-automatically with a human operator in the feedback loop to assess the goodness
of fit and tune the update parameters.
44
NZ AX
εξ
δx
δy
Figure 2.16: Illustration of the rotational and translational parameters for orienting an imaging
system. North is indicated by N , zenith by Z, and the optical axis of the imager by AX. The
optical axis is defined by the geographic location of the imager and its azimuth (ξ) and elevation
(ε). The orientation of the CCD with respect to the optical axis is defined by a rotation γ and a
translational offset (δx, δy).
readily obtained:
αij = arctan
yij − y0
xij − x0 , (2.35)
εij =
pi
2
− ψ(∆ij). (2.36)
In order to perform the orientation portion of the calibration, we treat each pixel azimuth/elevation
pair as a unit vector and convert to Cartesian coordinates,
xij = sin(pi/2− εij) cosαij , (2.37)
yij = sin(pi/2− εij) sinαij , (2.38)
zij = cos(pi/2− εij). (2.39)
Now, we use the specified (ξ, ε) orientation of the imager itself to orient the bundle of pixel unit
vectors correctly. As a matter of notational simplicity, we will consider each of the unit vectors
45
individually, although in practice this is easily vectorized. Initially, rotate about the y-axis by ε:
v1,ij =

cos(pi/2− ε) 0 sin(pi/2− ε)
0 1 0
− sin(pi/2− ε) 0 cos(pi/2− ε)


xij
yij
zij
 . (2.40)
Now, rotate around the z-axis by ξ:
v2,ij =

cos ξ sin ξ 0
− sin ξ cos ξ 0
0 0 1
v1,ij . (2.41)
Then, rotate around the new optical axis (ux, uy, uz) = v2,0 (that is, the v2 value corresponding to
the center pixel) by γ:
v3,ij =

1 + (1− cos γ)(u2x − 1) (1− cos γ)uxuy − uz sin γ (1− cos γ)uxuz + uy sin γ
(1− cos γ)uxuy + uz sin γ 1 + (1− cos γ)(u2y − 1) (1− cos γ)uyuz − ux sin γ
(1− cos γ)uxuz − uy sin γ (1− cos γ)uyuz + ux sin γ 1 + (1− cos γ)(u2z − 1)
v2,ij .
(2.42)
Finally, convert the Cartesian v3,ij = [vx, vy, vz]T back to spherical coordinates:
Eij =
pi
2
− arctan

√
v2x + v2y
z
 , (2.43)
Aij =
pi
2
− arctan
(
vy
vx
)
, (2.44)
where Eij and Aij are elements of matrices E and A, respectively. In summary, Equations (2.32)—
(2.44) are encapsulated as a function that returns E and A given the CCD geometry and the five
parameters that define the orientation of the system: optical axis azimuth (ξ, North-definite) and
elevation (ε), CCD rotation with respect to optical axis (γ), and CCD translation (δx, δy) from
optical axis.
The star catalog employed for this work is the Yale Catalogue of Bright Stars, hereafter referred
to as BSC5 [Hoffleit and Jaschek , 1991]. It contains, in astronomical coordinates (right ascension,
α, and declination, δ), the locations of all stars magnitude 6.5 and brighter, 9110 objects in all. The
catalog is sorted by magnitude, brightest stars first, and the positions of the stars are computed
46
for the site location and capture time of the calibration image. The conversion from astronomical
coordinates to horizon coordinates is straightforward and given here using units of degrees: Compute
the Julian date (JD) from the Gregorian calendar (M/D/Y, h:m:s):
JD = D+
⌊
153M + 2
5
⌋
+365Y +
⌊
Y
4
⌋
−
⌊
Y
100
⌋
+
⌊
Y
400
⌋
−32045+ s+ 60m+ 3600(h− 12)
86400
(2.45)
Compute the Greenwich Mean Sidereal Time from the Julian date of the observation:
GMST = 280.46061837◦ + 360.98564736629◦JD. (2.46)
Compute the local MST for the site longitude (λ) from the GMST:
MST ≡ (GMST + λ) mod 360◦. (2.47)
Compute the hour angle (H) of the object at this site and time:
H = MST− α. (2.48)
Determine elevation (ε) and azimuth (ξ) of the object for this observation:
sin ε = sin δ sin θ + cos δ cos θ cosH (2.49)
and
cos ξ =
sin δ − sin ε sin θ
cos ε cos θ
. (2.50)
The brightest stars with elevation angles above the local horizon (usually choose 10–15◦) are
retained for calibration. These points are utilized to initialize the search for the nearest stars in the
star field of the calibration image. An example of this is shown in Figure 2.17. The triangles mark
the estimated locations of BSC5 stars using the imager model. The circles are stars found in the
vicinity of the triangles.
A distance measure such as the following is useful in establishing the end of iteration:
ρ =
∑
n
√
(Cεn −O εn)2 + (Cξn −O ξn)2, (2.51)
where (Cξn,C εn) are the catalog star locations and (Oξn,O εn) are the locations of stars found in
47
100 200 300 400 500 600 700
50
100
150
200
250
300
350
400
450
Figure 2.17: Example calibration iteration from the imaging system near Sangre Grande, Trinidad
(similar to the Bonaire system discussed in Appendix B). The triangles are locations of stars from
BSC5 given the proposed orientation of the imager. The circles are stars found in the image.
the image. For Figure 2.17, ρ = 100.3.
Once the azimuth and elevation associated with each pixel are determined, these values are
mapped to arbitrary layer altitudes to match the emission centroid of the emission of interest. This
computation is performed by computing the intersection of the look direction from each pixel with
a spherical shell of given altitude. In order to compute the intersections, we define first a differential
angle α, which measures the absolute (that is, jointly in latitude and longitude) displacement angle
of the intersection from the imager location. This geometry is illustrated visually in Figure 2.18a in
the two-dimensional plane containing the imager and intersection vectors, OA and OX, respectively.
A little bit of manipulation yields
α = arccos
[
Re cos &
Re + h
]
− &, (2.52)
where Re is Earth’s radius, h is the layer altitude, & is the elevation angle, and α is the differential
angle. A given elevation & angle corresponds to a unique α for all azimuths. Therefore, the latitude
and longitude are separable. We consider first the latitude by defining OP as the vector through the
North Pole of a spherical Earth. The procedure is illustrated by the spherical triangle in Figure 2.18b.
Given the imager site colatitude (∆A), the pixel azimuth from the site (ξ), and the differential angle
48
(a) (b) (c)
X
h
R e
!
"
"
O
A
A
O
P
AX
!
"
"
#
X
!
"
#
$%
O
A
P
Figure 2.18: (a) Illustration of the differential angle α in the two-dimensional plane containing the
intersection vector OX and the imager location vector OA. Re is the Earth radius, h is the layer
altitude, & is the elevation, and α is the differential angle. (b) Derivation of the actual latitude of
a pixel. XA appears to have a constant latitude only as a matter of illustrative convenience. In
practice, XA may be any great circle that connects X and A. (c) Derivation of the actual longitude
of a pixel. δλ represents the differential longitude added to the site longitude for a given azimuth
and elevation (via differential angle α).
(α), we can compute the colatitude of the pixel (∆) by
cos∆ = cosα cos∆A + sinα sin∆A cos ξ. (2.53)
By converting from colatitude (cos∆) to latitude (sin δ), we can rewrite this as
δ = arcsin (cosα cos δA + sinα sin δA cos ξ) . (2.54)
The final computation is for the longitude. In a spherical triangle, the law of sines represents the
relationships between the angles with vertices at the origin O ({a, b, c}, not illustrated) and the
corresponding vertex angles on the surface of the sphere ({A,B,C}),
sinA
sin a
=
sinB
sin b
=
sinC
sin c
. (2.55)
Considering Figure 2.18c, we can write the law of sines for this figure as
sin δλ =
sin ξ sinα
sin∆
=
sin ξ sinα
cos δ
. (2.56)
To obtain the actual longitude, we add δλ to the site longitude,
λ = arcsin
(
sin ξ sinα
cos δ
)
+ λsite. (2.57)
49
This mapping from pixel coordinates to geographic coordinates permits the interpretation of airglow
images as maps of ionospheric irregularities. Figure 2.19 illustrates one such map. A detailed
interpretation of this map will be offered in Chapter 3.
Figure 2.19: Airglow image from Cerro Tololo, Chile, from 15 September 2006 mapped to geographic
coordinates at 250-km altitude. Note the dark irregularity bands stretching approximately from
north to south.
2.3.6 Post-processing
Some post-processing can clarify the features of airglow images. Both destructive and non-destructive
processing may be performed. That is, some techniques improve clarity at the expense of voiding
the photometric interpretation of the intensity data, for example, adaptive histogram equalization.
Most effort, however, is directed toward reducing noise in the images. For the purpose of this dis-
cussion, there are three sources of noise: dark current in the CCD, read-out noise in the CCD, and
stars.
Figure 2.20 illustrates a typical approach to denoising airglow images, with each step providing
slightly better SNR than the previous one. This example is of the 630.0-nm emission from a narrow-
field airglow imager at the Cerro Tololo Inter-American Observatory (CTIO) near La Serena, Chile,
at 0336 UT on 16 (259) September 2006 [Makela and Miller , 2008]. Figure 2.20a is the raw image
from the CCD, with only the contrast adjusted. The first step is to remove the dark noise (and
readout noise) by taking a dark image (Figure 2.20b) with the same exposure length as the observed
image. The difference (Figure 2.20c) between the observed image and the dark image gains about
10.1 dB SNR over the original.
The stars (and hot pixels not removed by the dark subtraction) may be removed by locating the
brightest points in the image and selectively applying a median filter to the surrounding region [e.g.,
50
Lim, 1990]. As shown in Figure 2.20d, this gains an additional 3.4 dB of SNR over the image with
the dark noise subtracted. Perhaps the biggest remaining gain in SNR may be obtained by applying
a wavelet filter (Figure 2.20e). The wavelet used for this filtering is a Daubechies type 3 wavelet
applied using the MATLAB software package [Daubechies, 1992]. The Daubechies denoising filter
improves the SNR another 5.8 dB to 19.2 dB over the original. This is quite good considering the
nominal amount of effort required for these denoising steps.
Clearly, the image in Figure 2.20f has undergone contrast distortion and the pixel intensities are
no longer photometrically meaningful. However, this adaptive histogram equalization step brings
out details that are not evident in the unequalized images, notably the depletion to the right of the
packet of depletions in the center of the image. While in Figure 2.20e the depletion just appears to
be a dark patch in the airglow, the bifurcations are clearly evident in the equalized image.
Alternatively, a sequence of airglow images may be processed jointly to produce even better
denoising results [Atkinson et al., 2006]. An example of an image processed using this technique is
presented in Figure 2.21. The small-area SNR estimation shows only a 0.7 dB increase in SNR over
the sequence described in the previous paragraphs. However, a visual inspection of Figures 2.20e
and 2.21 suggests that the technique of Atkinson et al. [2006] indeed produces more visually appealing
images with particularly fewer dark pixels.
2.3.7 Keogram representation
In order to aggregate an entire night of airglow data into a printable (as opposed to a sequence of
frames) format, the so-called “keogram” was developed. A keogram is constructed by taking strips
from the same location in each image. The strips are assembled into a time series, as shown in
Figure 2.22.
In the example of Figure 2.22, the cut was made along constant geomagnetic meridian (88◦
W magnetic longitude) with magnetic latitude as the spatial variable. The coherent dark curved
structures particularly evident between 7–11 UT are equatorial plasma depletions. The slope of the
depleted regions is indicative of their velocity and shape in much the same manner as the slit-camera
model for radar backscatter. The lighter, less-coherent objects in the image are clouds.
In Chapter 4, we will see a distorted keogram whose spatial variable is the tangent point altitude
of a radio occultation ray path. By plotting the received SNR on the radio link along side this
plot, the altitude of scintillation-causing irregularities may be read directly off the plot. Finally, in
Chapter 5, we will see a keogram with a the geomagnetic field line apex as the spatial variable. This
51
Dark imageRaw CCD Image (global contrast adjusted, 0 dB)
Stars removed (13.4 dB)Dark noise subtracted (10.1 dB)
Daubechies wavelet denoising (19.2 dB) Adaptive histogram equalization
a b
c d
e f
Figure 2.20: Airglow images from Cerro Tololo, Chile, from 16 September 2006 in CCD pixel
coordinates showing (a) no denoising, (b) dark frame, (c) subtraction of dark frame, (d) star removal,
(e) Daubechies wavelet denosing, and (f) histogram equalization. Each image processing step (c)–(f)
is performed on the results of the previous step.
52
Asymptotically blind denoising (19.9 dB)
Figure 2.21: Airglow image from Cerro Tololo, Chile, from 15 September 2006 in CCD pixel co-
ordinates. This image has had the dark noise removed and has been processed with the denoising
algorithm presented by Atkinson et al. [2006].
!"#$%&'()*+#,%*-.&'/
0
(
1
2*
3
(
42
*-
5
%
1
/
6789*:;<2<*",*!*==*>%?4%,@%&*ABCDE*B<<B*!*FF
°
*G*,(12*)H"1#4I5%
*
*
: J F K =< == =B =; =D
=D
=:
=F
B<
9"
4%
"
'
#4
L
*-
M
4'
/
=<<<
=C<<
B<<<
BC<<
;<<<
;C<<
D<<<
Figure 2.22: Example keogram of 630.0-nm airglow data collected at Haleakala, Hawaii, on 11
September 2002.
allows radar backscatter to be compared with the airglow.
2.4 Conclusion
In this chapter, we have reviewed several radio and optical remote sensing techniques for the iono-
sphere. VHF radar backscatter is capable of detecting coherent echoes from Bragg-scale plasma ir-
regularities, as well as providing estimates of plasma temperature and density via incoherent echoes
from ensembles of free electrons in the plasma. Although this work leverages theories and models
developed using incoherent backscatter data, we will be primarily interested in coherent backscat-
ter from F -region irregularities near the geomagnetic equator. The excellent frequency stability
and good geographic coverage combined with inexpensive commercial receivers have made forward-
scatter ionospheric observations using the Global Positioning System practical. These observations
53
are either dispersive multi-carrier observations of the ionospheric plasma density or signal power
and phase observations to detect diffraction from 100-meter scale irregularities. One innovative use
of GPS receivers is radio occultation, which involves placing them in low-Earth orbit (LEO) to
gather plasma (and neutral) density profiles from regions that are ordinarily sparsely probed. This
technique may also be useful for imaging or locating diffraction-causing irregularities.
Images of airglow emissions provide snapshots of a large (100s or 1000 km) geographic region of
the ionosphere with relatively high spatial (1–10 km) and temporal (1–2 min) resolution. Several
emission lines are useful for observing F -region irregularities, although most of the work in this
dissertation is focused on the 630.0-nm emission. Imaging systems are calibrated using the star field
to determine the extent of the ionosphere observed within their field of view. As with any low-light
photometry process, noise is an important consideration. Several steps were outlined, including
subtracting a dark frame and wavelet filtering, to improve the signal-to-noise ratio by almost 20 dB.
The next chapter describes how the geomagnetic-field-aligned nature of irregularities may be
exploited to infer the three-dimensional extent of plasma density structures from two-dimensional
airglow images. This assumption also links data from radio observations and optical airglow imag-
ing in a common geomagnetic coordinate system. The remaining chapters discuss applications to
ionospheric problems.
54
CHAPTER 3
ELECTRIC FIELD MAPPING AND THE
FIELD-ALIGNED AIRGLOW IMAGING
TECHNIQUE
3.1 Introduction
Observation of the equatorial ionospheric irregularities discussed in Chapter 1 using the airglow
techniques of Chapter 2 depends on the “impression” of electric fields associated with the irregulari-
ties on the airglow emission layer. Due to the high anisotropy of the ionospheric conductivity tensor,
particularly in the F region, electric fields map efficiently along the geomagnetic field. However, at
small scales and lower altitudes, the Pedersen and Hall conductivity terms begin to play an impor-
tant role. The field-aligned nature of the irregularities suggests a special imaging geometry which
is optimal for observing longitudinal structures. This chapter explores the efficiency of mapping
electric field structures of different scales from the geomagnetic equator into the off-equator regions
where depletions are observed in the airglow as well as the field-aligned imaging geometry and the
geomagnetic interpretation of airglow images.
3.2 Electric Field Mapping
Fundamentally, the mapping of electric fields is a classic problem first tackled rigorously by Farley
[1959]. The present chapter contains a review of Farley’s work utilizing modern computer solution
techniques and ionosphere models. The results are compared and discussed. The technique is
extended to two cases of interest to this work. The first is the simpler case in which irregularities
are generated in the local (mid-latitude) ionosphere and mapped to the geomagnetic equator as
suggested by the observations presented in Makela et al. [2009]. A similar case was considered
by Saito et al. [1995]. The second case is more complicated and more relevant to this work in
general: mapping of electric fields from the geomagnetic equator over the entire airglow imager field
of view. This suggests the “sweet spots” for observing fine structure.
55
3.2.1 Physical derivation
In a companion set of two papers, Farley [1959, 1960] derived relationships for the impact of electric
fields of different scales acting at different heights in the ionosphere. He was interested in the effects
of electric fields generated in the E region on the F region. In the first paper, he developed the “polar
case” illustrated in Figure 3.1a to determine the attenuation of the potential field φ(x, y, z) in the
plane perpendicular to the geomagnetic field, B, with altitude. In the second paper, he developed the
“middle latitude case” illustrated in Figure 3.1b by keeping the potential field parallel to the Earth’s
surface and projecting it along the magnetic field. An approximate “equatorial case,” illustrated
in Figure 3.1c, was also developed in the second paper under the assumption that the small-angle
approximation for the tangent is valid for the dip angle and that Earth’s magnetic field may be
approximated by the dipole term of the multi-pole expansion. In each of the “polar” and “middle
0
B
0
B
dipIN
0
B
(a) (b) (c)
Figure 3.1: The (a) polar, (b) middle latitude, and (c) equatorial geometries.
latitude” cases, the geomagnetic field line is assumed to be approximately linear over the region
of interest. Due to the scarce computing resources available at the time, analytical solutions were
favored. In the present analysis, computational resources are no longer a primary concern and a
technique similar to that employed in the polar case is utilized over many small, discrete regions, to
perform the mapping between any two arbitrary points on the same field line.
In a coordinate system with aˆz parallel to B and aˆx perpendicular to B in the plane of B, the
ionospheric conductivity tensor is defined as
σ¯ =

σP −σH 0
σH σP 0
0 0 σ0
 , (3.1)
where σ0 is the specific conductivity along B, σP is the Pedersen conductivity perpendicular to B in
the plane swept out by B, and σH is the Hall conductivity perpendicular to both B and the plane
swept out by B. In the absence of a neutral wind, the current due to an applied electric field E can
56
be computed from the electromagnetic form of Ohm’s law, neglecting wind-driven currents:
J = σ¯ ·E. (3.2)
Next, we exploit the fact that the electric field can be written as the gradient of a potential dis-
tribution, E = −∇φ. Furthermore, over a short time scale, the current J is constrained to be
divergence-free,
∇ · J = −∇ · (σ¯ ·∇φ) = 0. (3.3)
The expanded divergence of the product evaluates to
∂2φ
∂x2
+
∂2φ
∂y2
+
1
σP
∂
∂z
(
σ0
∂φ
∂z
)
= 0. (3.4)
3.2.2 Solution
We now introduce a coordinate transformation
x′ = x
y′ = y
dz′ =
√
σP
σ0
dz
. (3.5)
Note that because z′ is defined in terms of differentials, it must be referenced to a certain height.
In Farley [1959], z′ = 0 at z = 300 km, which corresponds to the observation height. After some
algebra and recognizing that ∂/∂n(lnu(n)) = (1/u(n))∂u(n)/∂n, we can let ∇′2 be the Laplacian
in the new coordinate system and rewrite Equation (3.4) as
∇′2φ+ ∂
∂z′
ln (
√
σ0σP )
∂φ
∂z′
= 0. (3.6)
In the interest of finding a tidy solution, we introduce the geometric mean conductivity
σm =
√
σ0σP ≈ Cec0z′ , (3.7)
yielding the analytical form
∇′2φ+ c0 ∂φ
∂z′
= 0. (3.8)
57
If we consider the boundary condition that the potentials with source at z′0 decay to zero as z′ →∞,
we recognize that potentials will have solutions of the form
φ = φ0 exp (j (kxx′ + kyy′)) exp (−γ (z′ − z′0)) . (3.9)
The decay and growth parameters α and β are the solutions to the characteristic polynomial in γ,
letting k2 = k2x + k2y and solving Equation (3.7) for c0:
α =
√
c20+4k
2+c0
2
β =
√
c20+4k
2−c0
2
. (3.10)
Farley [1959] divided the ionosphere into three discrete regions by height, setting the source field
at z′0 and observing the mapped field at z′ = 0. We extend Farley’s solution to an ionosphere with N
regions, allowing us to consider more general problems. We assume that each region has a solution
of the form
φi = Φ(x′, y′)
[
Gi exp(−αi(z′ − z′i−1)) +Hi exp(βi(z′ − z′i−1))
]
. (3.11)
At the source, where z′ = z′0, the following boundary condition exists:
φ1 = Φ(x′, y′). (3.12)
At the other region interfaces, we assume continuity of φ and ∂φ/∂z′. Recalling that the potential
decays to zero as z′ → ∞, the growing solution should be suppressed at the observation point.
Therefore, the final Hi is constrained to be zero and is not solved. For N regions, this yields a
system of 2N − 1 equations and unknowns, which can be represented in matrix form as
i = Ax, (3.13)
where i is a (2N−1)×1 column vector with one in the first position and zeros elsewhere, representing
the boundary condition at the source. The x column vector contains the Gi’s and Hi’s. The matrix
A is a (2N − 1) × (2N − 1) sparse matrix encoded with the interfacial boundary conditions. We
are really only interested in G = GN , which corresponds to the decaying solution in the last region.
58
There is no HN , per the decaying boundary condition. The attenuation factor (A) is obtained as
A = GN exp
(−α2N−1(z′N − z′N−1)) . (3.14)
Note now that given a well-characterized ionosphere or model ionosphere, we have a solution method
not only for the polar case, but for any field-aligned trajectory over which the variation in the
conductivities is dominated by the position along the field line. This interpretation is fundamentally
similar to that of Saito et al. [1995], although employing a slightly different form written in the
terms of Farley [1959].
3.2.3 Model ionosphere
For the purpose of modeling the conductivity tensor at an arbitrary point (both spatial and tem-
poral) in the ionosphere, it is helpful to begin with an empirical model of the plasma and neutral
constituents plus the Earth’s magnetic field. The International Reference Ionosphere (IRI2007) [Bil-
itza, 2001; Bilitza and Reinisch, 2008], the NRLMSIS00E [Picone et al., 2002], and the International
Geomagnetic Reference Field (IGRF) [Maus et al., 2005] are employed to provide plasma ion and
electron densities, neutral densities, and magnetic field intensities, respectively, as a function of
position and time.
The electron-ion and electron-neutral collision frequencies are computed using the Chapman
formulas in Farley [1959] and Kelley [1989]. Te is the electron temperature in K; ne and nn are the
electron and neutral densities in cm−3, respectively:
νei =
(
34 + 4.18 log10
(
T 3e
ne
))
× neT−3/2e (3.15)
νen =
(
5.4× 10−10)nn√Te (3.16)
νe = νei + νen. (3.17)
The ion-neutral collision frequency is computed following Makela and Kelley [2003b]:
νin =
(
0.393
√
Tn + Ti
2
[O] + 6.9[N2] + 6.7[O2]
)
× 10−10. (3.18)
Finally, the specific conductivity, parallel to the geomagnetic field, is computed using Chapman’s
59
formula
σ0 = neq2e
(
1
meνe
+
1
miνin
)
. (3.19)
The Pedersen conductivity (S/m) perpendicular to B is also computed from the Chapman formulas:
σP = neq2e
(
νin
mi (Ω2i + ν2in)
+
νe
me (Ω2e + ν2e )
)
. (3.20)
The electron and ion gyro frequencies (Ωe and Ωi, respectively), are derived from the Lorenz force
law and Newton’s second law [e.g., Heelis, 2004]. The fundamental unit of electronic charge is
qe = 1.602× 10−19 C.
3.2.4 Results
Polar case
To perform a first-order evaluation of the method outlined above, we reproduce the result of
Farley [1959]. Using the empirical model described in the previous section, a vertical rocket trajec-
tory is simulated from Fort Churchill, Manitoba, at noon local time under solar maximum condi-
tions. Figure 3.2 illustrates the result for wavenumbers k = {0.1, 0.25, 0.5, 1.0, 2.0, 4.0, 8.0}, where
λ = 2pi/k. As expected, small scale sizes (large wavenumbers) are attenuated more aggressively
than larger scales. Attenuation is lower for all scales when the source is located at a higher altitude.
The ionosphere model used by Farley differs slightly from that used in this analysis. However, the
salient features are visible in both plots.
Transequatorial case
For the transequatorial case, a geomagnetic field line approximately linking sites at Cerro Tololo,
Chile (geo 30.17◦ S, 289.19◦ E; mag 16.72◦ S, 0.42◦ E), and Villa de Leyva, Colombia (geo 5.57◦
N, 287.37◦ E, mag 17.79◦ N, 0.13◦ W), is modeled using the suite of models discussed above. The
conditions are early evening (2000 LT) in September during high solar activity and quiet geomagnetic
field. Figure 3.3a illustrates the effect of mapping different scale sizes from a variety of source heights
(E-region all the way to apex at the equator) in the southern hemisphere to 250 km (approximately
the layer height for the 630.0-nm airglow emission) in the northern hemisphere. Large scales are
well-preserved, while smaller scales are not. For all scale sizes, the attenuation decreases for sources
at higher altitudes near the equator. The adjacent Figure 3.3b shows the trajectory of the field line
and the background plasma density.
60
100 120 140 160
10
10
10
100
height of source field (km)
0.1
0.25
0.5
1.0
2.0
4.0
8.0
(a) (b)
Figure 3.2: (a) Reduction of field strength reduction at 300 km for different wavenumbers. (b)
Original result of Farley, 1959. (Reproduced with permission of the American Geophysical Union.)
50 100 150 200 250 300 350 400 450 500 550
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
F
ie
ld
-s
tr
e
n
g
th
 r
e
d
u
c
ti
o
n
 i
n
 n
o
rt
h
e
rn
 h
e
m
is
p
h
e
re
 a
t 
2
5
0
 k
m
 
 
2.0 km
4.0 km
8.0 km
16.0 km
32.0 km
height of source field in southern hemisphere (km) Geographic Latitude
A
lt
it
u
d
e
 (
k
m
)
 
 
0
0
100
200
300
400
500
600
0
2
4
6
8
10
12
10
e
lo
g 
   
 n
   
 (m
   
 )
-3
(a) (b)
Figure 3.3: (a) Relative strength at 250 km in the Northern hemisphere for field sources of different
scale sizes at different heights in the Southern hemisphere. (b) Geometry of the field line with
log10 ne in the background (units of m−3).
61
Airglow imaging case
This case is for the Cornell Narrow-Field Imager system located atop Mt. Haleakala (CNFI; geo-
graphic: 20.71◦ N, 203.83◦ E; geomagnetic 21.03◦ N, 271.84◦ E) on the Hawaiian island of Maui.
This system was installed particularly for the purpose of studying field-mapped irregularities such
as the ones described in this chapter. The ionosphere was modeled for a day in September 2005
with relatively quiet geomagnetic conditions.
Figure 3.4 illustrates, over CNFI’s entire geographic field of view, the efficiency of mapping
electric fields at the geomagnetic equator to the local ionosphere, similar to Figure 3.3a. At 8 km
scales, the crest region of the equatorial anomaly permits the strongest response in the airglow layer.
This is frequently observable in practice, particularly with very high resolution imagers. Nothing
else is particularly noteworthy about this in light of the previous results, except perhaps that it
explains the difficulty in observing the bottom-type layers described by Hysell and Burcham [1998]
with airglow imagers.
3.2.5 Discussion
One of the drawbacks to the Farley model and similar models is that current continuity is enforced
at the source and response points under the assumption that no current flows in the regions beyond
these points, as illustrated in Figure 3.5. This model is conceptual only and does not completely
consider that Equation (3.8) is not reversible. That is, in the model and the actual ionosphere,
exchanging the positions of the source and observation points may not yield exactly the same
attenuation for the same-size structure.
Unfortunately, there are several interesting special cases in the growth of equatorial plasma
depletions that are ignored under this assumption. The most notable cases are when the E region
at one or both ends of the flux tube (magnetic field line) is highly conductive. This could occur
because the E region is still in sunlight or due to the presence of a sporadic-E layer. This situation
might effectively be approximated by adding an additional equivalent Pedersen conductivity term
representing the rest of the flux tube at each end point. In both of these circumstances, we expect
the field to disappear completely by driving currents perpendicular to B.
62
1
9
0
1
9
5
2
0
0
2
0
5
2
1
0
5
1
0
1
5
2
0
  
2
 k
m
 
 
00
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63
Source
Below Source Beyond Response PointRegion of Solution
Response
Figure 3.5: Circuit model of two magnetic field lines showing the specific (series) and Pedersen
(shunt) conductivities. This model is inaccurate in the sense that the flux tube might be better
modeled with dependent sources mixed among the resistors to represent other current sources. The
c0∂φ/∂z′ term in Equation (3.8) belies this condition. This model is conceptual only and does not
accurately model all aspects of the ionosphere circuit. See text.
3.3 Interpretation of Airglow Images
3.3.1 Equatorial plasma depletions
Once an airglow image of one or more equatorial plasma depletions has been mapped into geographic
coordinates, it can be interpreted physically in the following way. As discussed in the previous
section, large-scale polarization electric fields associated with the depletion map efficiently along
the geomagnetic field. Due to these mapped polarization fields, the depletion expands into its
characteristic wedge shape. Where this wedge punctures the airglow layer, it is observable in airglow
images. It is important to recall that even when the airglow emission diminishes, the depletion may
still be present, although not visible. This is particularly true of the 630.0-nm emission.
Since the depletion in the airglow is the result of electric fields that map along the geomagnetic
field, the airglow image may also be mapped along the geomagnetic field to the apexes of the field
line [Mendillo and Tyler , 1983]. For sufficiently large scales, this concept may be generalized to any
point along the field line [e.g., Otsuka et al., 2002]. Figure 3.6a shows an airglow image projected onto
a spheroidal shell at 250 km altitude in geographic coordinates. Figure 3.6b is a three-dimensional
map of the depleted wedges extruded from the airglow image.
One convenient representation of the field-aligned nature of equatorial plasma depletions is to
convert the latitude and longitude of the pixels in an airglow image to a “geomagnetic” coordi-
nate system. One example of a geomagnetic coordinate system is AACGM, the Altitude-Adjusted
Corrected GeoMagnetic coordinate system [Baker and Wing , 1989]. In a geomagnetic coordinate
system, the latitude, longitude, and altitude define a geomagnetic field line rather than a point in
a grid mapped onto a surface. The geomagnetic equator is defined as the apex point of each field
line. This representation allows images to be mapped from the airglow layer to the geomagnetic
equator, where the images may be directly compared with radar backscatter maps. AACGM has
64
(a) (b)
Figure 3.6: (a) A field-aligned 630.0-nm airglow image from Cerro Tololo, Chile, projected onto the
assumed emission layer at 250 km. (b) The same image as (a) with the airglow depletions extruded
along the geomagnetic field to produce a three-dimensional map of the irregularities.
the advantage that it is quite fast in converting between geographic and geomagnetic coordinates,
something that is vital when processing a large quantity of data. However, it was developed for
use at high latitudes and is not presently maintained. Whenever possible, it is better to use IGRF,
the International Geomagnetic Reference Field [Maus et al., 2005]. A discussion of IGRF versus
AACGM and field tracing steps in IGRF is presented in Appendix C.
3.4 Field-Aligned Imaging Geometry
A traditional airglow imaging system utilizes a zenith-pointing camera with a wide field of view.
This type of system offers a view of nearly the entire sky. One of the major drawbacks to this
imaging technique is that, for field-aligned density depletions, the ray (integration) paths for each
pixel tend to cross magnetic field lines in the airglow layer rather than nearly parallel to them.
This leads to spatial blurring as the rays cross both dense and depleted regions. Since depletions
are field-aligned, an airglow imager with ray paths that are parallel to the geomagnetic field in the
airglow layer gives the optimal viewing geometry [Tinsley , 1982]. This configuration is depicted in
Figure 3.7. Several months’ data were collected from Hawaii in the late 1980s using the field-aligned
imaging geometry [Rohrbaugh et al., 1989]. A more comprehensive data set has come from the CNFI
and CASI systems operating at Haleakala, Hawaii, since 2001 [Kelley et al., 2002]. The details of
these instruments were discussed in Chapter 2.
No imager has been created that can have all of its rays parallel to the geomagnetic field.
Therefore, some parts of the image will be subject to more or less spatial blurring than others.1 The
1In principle, this relates to the field-aligned irregularity assumption discussed in §2.2.4 and Sokolovskiy et al.
65
Mag. Equator
“Geomagnetic FOV”
CNFI
Airglow
Figure 3.7: Field-aligned imaging geometry from Haleakala, Maui, Hawaii.
amount of spatial blurring has been quantified as the minimum-scale resolvable feature and can be
computed through geometry [Tinsley , 1982]. Figure 3.8 is an example of the spatial blur across the
field-of-view of the imager operating at Cerro Tololo, Chile [Makela and Miller , 2008]. In practice,
it is best to interpret the contours as a relative measure of the blurring rather than a strict scale
limit.
Figure 3.9 is an illustration of the same spatial blurring estimation performed on the CNFI system
in Hawaii. This is particularly interesting to compare with Figure 3.4. It is clear that there is a
“sweet spot” near 12◦ N, 202◦ W. Although this spot does not approach the native imager resolution
(about 3 km with 2×2 binning) in that part of the image, it does suggest that field-aligned features
below 10 km can be identified there.
Comparing Figures 3.8 and 3.9 illustrates something that has been observed in practice. In the
case of the PICASSO2 system at Cerro Tololo, depletions are rarely observed in the western 25%
of the image, approximately west of the 283◦ meridian. Rather, they slide into view fully formed
near this point. This behavior is less common at Haleakala, where the CNFI system has a narrower
field of view. This suggests that PICASSO’s field of view might be a little too wide for its location,
resulting in wasted CCD space. On the other hand, the wider field of view permits spacing between
multiple packets of depletions to be estimated [Makela and Miller , 2008].
[2002].
66
275 280 285 290 295 300
−30
−28
−26
−24
−22
−20
−18
−16
−14
−12
20
20
20 40
40
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60
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60
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10
0
100
100
12
0
120
14
0
140
CTIO field of view; Geographic coordinates
G
eo
. L
at
. [d
eg
]
Geo. Long. [deg]
Figure 3.8: Relative spatial blurring across the field-of-view of the PICASSO2 narrow-field imager
operating at Cerro Tololo, Chile. In theory, the contours refer to the smallest resolvable feature
dimension. In practice, it is best to interpret them as a relative measure.
192 194 196 198 200 202 204 206 208 210
4
6
8
10
12
14
16
18
20
10
10
10
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202
0
20
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50 50
60
60
60
60
70
70
80
80
90
CNFI field of view; Geographic coordinates
G
eo
. L
at
. [d
eg
]
Geo. Long. [deg]
Figure 3.9: Relative spatial blurring across the field-of-view of the Cornell Narrow-Field Imager
operating at Haleakala, Hawaii.
67
3.5 Conclusion
Large-scale electric fields associated with equatorial irregularities map efficiently along the geomag-
netic field from hemisphere to hemisphere. This allows the irregularities to grow in a wedge-shape
and create an observable impression on the airglow layer. As a consequence of this impression, a
three-dimensional map of the irregularities observed in the airglow layer may be created by extrud-
ing the image along the geomagnetic field, sweeping out the entire depleted channel. In order to
reduce blurring from ray paths that pass through both depleted and normal regions of plasma which
are field-aligned, it is advantageous to align imaging systems such that their ray paths are parallel
to the geomagnetic field in the airglow layer for this kind of analysis.
68
CHAPTER 4
LOCALIZATION OF
SCINTILLATION-CAUSING REGIONS
4.1 Introduction
There are at least two compelling motivations for locating irregularities in three dimensions. The
first is to understand the physics of the irregularity formation and distribution. The second is to
compliment, verify, and refine observations made solely from the ground or space.
One common measurement apparatus for scintillation patterns associated with the passage of
equatorial plasma bubbles is an array of single-frequency GPS receivers installed on the ground,
frequently along a line in the magnetic East-West direction [e.g., Kintner et al., 2004]. For such a
system operating at the GPS L1 frequency (1.57542 GHz), the Fresnel scale is approximately 240
m when the irregularities occupy a slab between 250 and 350 km (z = 350 km, L = 100 km, in
Equation (1.8)). For such a system, with the source at zenith, an error of 100 km in altitude results
in an error of about 40 m, or 17%, in Fresnel scale. It can be shown that the relative error sensitivity
in Fresnel scale is frequency independent. The sensitivity of the irregularity velocity estimate is more
difficult to quantify because it involves both geometry- and satellite-dependent terms. Depending on
the satellite trajectory with respect to the receiver and irregularities, Cerruti et al. [2006] calculated
sensitivities from less than 6 m/s for a 100 km altitude error to as much as 36 m/s for the same
100-km error in altitude when using the GPS L1 signal. For typical zonal irregularity velocities on
the order of 150 m/s [e.g., Kintner et al., 2004], this represents an error of 4–24%, respectively.
Occultation experiments are designed to take high resolution vertical cuts through the ionosphere,
making them good candidates for observing the altitude of irregularities. However, occultation
measurements lack a reliable method of locating irregularities along a ray path to the transmitting
satellite. As Straus et al. [2003] point out, one cannot simply assign the scattering region to the
ray tangent point under scintillation conditions. The argument can be made that the most intense
scattering occurs at the location of highest background electron density, which is the F -peak [Yeh
and Liu, 1982]. As evidenced by reports of scattering regions at high altitudes [Sokolovskiy et al.,
2002; Cerruti et al., 2006], this may not strictly be the case.
69
Another possible analysis technique in the presence of irregularities is to perform a back-
propagation inversion on the amplitude and phase data in the phase-screen approximation
[Sokolovskiy et al., 2002]. While elegant in principle, this inversion assumes stationarity of the sam-
pled complex field and that a single, well-defined phase screen is the cause of the observed scintilla-
tion. Pure radio techniques involving tomographic reconstructions have been proposed [Bernhardt
and Siefring , 2006]. However, in order to obtain useful resolution, they require sufficient density of
instruments, something which is not readily achieved in practice.
In contrast to these techniques that rely solely on data from radio instrumentation, a compli-
mentary technique based on data from a radio instrument and another modality, in this case an
optical imager, can be used to reduce the number of assumptions that have to be made in analyzing
data in the presence of irregularities. Furthermore, such a dual-modality technique can provide the
context of the irregularity regions that cannot easily be obtained from radio-only measurements.
In this chapter, a novel technique for three-dimensional localization of irregularities using GPS ra-
dio occultation and a ground-based airglow imager is presented. This demonstrates the field-mapped
extent of equatorial plasma depletions and associated irregularities. Furthermore, it provides an
independent method to estimate the altitude of an irregularity layer. We begin with a detailed
discussion of the instrumentation and technique. Then, we apply the technique to measurements
from the American sector during the September–October equinox period in 2006. A discussion of
the results and associated caveats is presented.
4.2 Instrumentation and Analysis
For this study, the CTIO narrow-field imager described in Chapter 2 observes the 630.0-nm line due
to its relatively high volume emission rate, even during solar minimum. Launched in April 2006,
the COSMIC/FORMOSAT-3 constellation of six satellites in low-Earth orbit (LEO) is designed to
provide in excess of 2000 radio occultation measurements daily using Integrated GPS Occultation
Receivers [Cheng et al., 2006]. Initially, the satellites were placed in a low-altitude orbit at about
515 km. Later, they were raised to final orbits at 800 km one at a time. The data products are
provided for each occultation in a variety of formats. Two products of interest to this work are the
ionospheric signal-to-noise ratio (SNR) and excess phase data (1-Hz sampling), and the atmospheric
SNR and excess phase data (50-Hz sampling). However, the high-rate atmospheric data are only
provided for tangent altitudes up to about 150 km, making them less useful for the purposes of this
70
work, which is focused on irregularities at altitudes above 150 km.
Rather than inverting the entire occultation data set from an occultation through irregularities,
it is instead instructive to consider other metrics from the data. For example, variation of the
received signal strength can be used to compute the normalized variance of the SNR. We infer that
radio links exhibiting higher SNR variance traverse irregularities. The SNR variance is computed
from the familiar S4 formula,
σ2 =
〈I2〉 − 〈I〉2
〈I〉2 . (4.1)
The ray tangent point moves at a velocity on the order of 3000 m/s. At 1-Hz sampling, this
suggests that spatial sampling distance is longer than the Fresnel scale, which varies from about
200 to 1200 m for practical occultation geometries. Thus, for the purposes of this technique the
SNR variance can serve only as a tracer for the presence of irregularities along the path and not a
measure of scintillation intensity or characteristics. Equation (4.1) utilizes the symbol σ to avoid
ambiguous interpretation of the results.
In order to corroborate data from the occultations, ground-based scintillation observations from
two sites are also considered. The SCINDA (Scintillation Network Decision Aid) station at Anco´n,
Peru´, samples VHF (approximately 250 MHz) beacon signals from the FLEETSAT 7 and 8 satellites
at 50 Hz. The approximate ionospheric pierce points of the VHF ray paths are plotted in Figure 4.1.
(See Groves et al. [1997], Sheehan and Valladares [2004], and Valladares et al. [1996] for details on
the SCINDA instruments.) There are also two GPS scintillation monitors co-located with the
airglow imager at Cerro Tololo, Chile. These receivers monitor the GPS L1 and WAAS (Wide Area
Augmentation System) signals for scintillation at a 50-Hz sampling rate. The scintillation monitors
are similar to those described in Beach and Kintner [2001].
Figure 4.1 outlines the new analysis technique proposed in this chapter. Initially, airglow images
captured by the imager at Cerro Tololo, Chile, in which equatorial plasma depletions are visible,
are selected for study. COSMIC/FORMOSAT-3 radio occultation events are then selected from the
same time and region. Each airglow image can be projected onto the layer representing the peak
airglow emission altitude, nominally 250 km for 630.0-nm, as shown in Figure 4.1a. A depletion
mask containing the region of the image in which a depletion is present is created from each of the
airglow images nearest to the times of occultation. The depletion mask is then projected onto the
airglow layer. In order to reduce computational complexity when handling the geomagnetic field
lines (discussed below), the masks are binned-down by 16 × 16, yielding a horizontal resolution of
71
Figure 4.1: Illustration of the three-step extrusion procedure used in this work. (a) The airglow
image is projected onto the assumed airglow layer height of 250 km. The locations of the ionospheric
pierce points (x) of two look directions of the SCINDA station at Anco´n, Peru´, and the imager (o)
at Cerro Tololo, Chile, are marked. (b) The field lines corresponding to depletions in the airglow
are selected to create a three-dimensional map of the field-aligned depletion. (c) Occultation ray
paths connecting a GPS satellite and a COSMIC/FORMOSAT-3 satellite have been added. The
COSMIC/FORMOSAT-3 satellite is orbiting over the western coast of South America and over
Panama. The ray paths in red correspond to σ > 0.10, indicating some irregularities are present
along the ray path. Note that these ray paths are also crossing the geomagnetic field lines associated
with the depletion.
approximately 20–150 km at the airglow layer altitude of 250 km. The field lines with the lowest
apex altitudes yield the better resolutions. It is well-understood that large-scale (> 10s of km)
electric fields associated with depletions map efficiently along the geomagnetic field lines from the
geomagnetic equator to low latitudes [e.g., Farley , 1960; Otsuka et al., 2002]. At smaller scales, this
approximation breaks down. Since this scale is of the same order as the horizontal resolution above,
that approximation is valid. Invoking this assumption, the resulting projection is extruded along
the geomagnetic field using the AACGM (altitude-adjusted corrected geo-magnetic) model with
epoch 2000 coefficients [Baker and Wing , 1989]. Extrusion along the geomagnetic field represents
the three-dimensional space occupied by the depletion, as shown in Figure 4.1b.
Neglecting diffraction and refraction effects, which should be negligible, the straight line between
the COSMIC/FORMOSAT-3 and GPS spacecraft define a ray path. The occultation ray paths that
cut through the extruded depletion map are located by computing the intersection between the ray
paths and the affected field lines. The present algorithm only locates intersections below the satellite
orbit. This computation is performed at each time step, regardless of the variance at the time, and
the resultant ray paths are sorted by intersection altitude and SNR variance. The variance (σ2,
Equation (4.1)) is computed from the SNR of the GPS signal received during occultation. For this
work, the variance was taken on L2 over twenty 1-Hz samples. Figures 4.1c and 4.2 show example
composites of SNR variance, ray paths, and airglow, for the same event on 15 September 2006.
72
Figure 4.2: Three-dimensional view illustrating the problem geometry. The cyan curves represent
the depletion region as estimated by extruding the airglow image. The black curve above the LEO
(COSMIC/FORMOSAT-3) orbit on the top (left) ends of the ray paths is a relative measure of
SNR variance. Only every 10th ray path is shown for clarity. The ray paths highlighted in red have
increased SNR variance, suggesting that they host irregularities. Only the portions of the ray paths
that are below the orbit of the LEO are shown. Blue dots are placed at the tangent point for each
ray path. This illustrates the distance (∼ 500 km) between the bubble intersection and the tangent
point.
These illustrate clearly the increase in SNR variance as the ray paths cut through the depleted
wedges of field lines.
An alternate viewing geometry is that in Figure 4.3. The airglow image has been mapped along
the geomagnetic field onto the surface formed by the occultation ray paths. Doing so allows the
intersection altitude between the occultation ray paths and bubbles to be easily inferred. The
broken and solid lines indicate the beginning and end of fading on the GPS signal received during
the occultation. Intersections with three bubbles are also indicated by dots. Note that due to the
geometry and projections involved in creating this figure, part of the image is mapped to physically
unrealistic low altitudes. However, note that there are no SNR variations associated with ray path
intersections at these low altitudes. Finally, Figure 4.3 illustrates the amount of each ray path
that passes through the imager’s extruded field of view. The most suitable occultation events were
selected for this study by requiring that at least 50% of the segment of each ray path below the LEO
orbit be within the field-aligned volume observable by the imager. This ensures the best possible
chance of unambiguously observing the irregularities.
It is evident from Figures 4.2 and 4.3 that ray paths frequently cross multiple depletions, partic-
ularly on East-West ray paths. In this work, we take the mean altitude of intersections that occur
on ray paths with “shallow” slopes that vary less than 50 km over the depleted region. For example,
73
Figure 4.3: The top panel shows an example of an airglow image mapped along the geomagnetic
field onto the surface swept out by the occultation ray paths. This extrusion allows the altitude of
the irregularities to be read off the plot directly. COSMIC GPS L1 SNR is shown in the bottom
panel. The dashed and solid lines correspond to the beginning and end of irregularities inferred from
the COSMIC occultation SNR data, respectively. Corresponding lines are drawn on the projected
airglow image in the top panel. Markers indicate the position of depletions in the airglow image.
The mean altitude of the intersection of the ray path and airglow depletions is recorded as the
irregularity altitude for that ray path. Thus, irregularities are inferred to occur over a range of
210–350 km.
in the case of the end of the irregularity observation (solid line) shown in Figure 4.3, intersections
are found at 190 km, 210 km, and 230 km. A value of 210 km is recorded for that ray path. Ray
paths that cut through depletions over a range of altitudes larger than 50 km are not included in
this analysis. Figures 4.2 and 4.3 also show the distance from the tangent point to irregularities.
Although the tangent point is not specifically marked in Figure 4.3, it is at the point of minimum
altitude in each of the ray paths. It is clear that the irregularities may be some distance, in this
case ∼ 500 km, from the tangent point.
4.3 Results and Discussion
The temporal distribution of airglow images (thick colored bars) and occultation measurements
(points) considered in this study is plotted in Figure 4.4. During the study period, 7 September–27
October 2006 (days 254–300), there were 14 individual occultation events (marked by blue circles)
that substantially crossed the “geomagnetic” field-of-view of the imager when bubbles were observed.
Several of the events are nearly temporally coincident and therefore indistinguishable on the plot. All
of these occultation events exhibited some increase in SNR variance over a portion of the altitudes
74
Figure 4.4: The temporal distribution of selected occultation events and the availability of airglow
imagery data. Individual occultation events are marked with a blue dot. By default, the imager
collects data between sunset and moonrise or between moonset and sunrise, as the case may be.
The relative lack of coincident airglow and occultation data for days 260–289 is mostly a function
of data availability, not a lack of bubble activity. The Kp index is plotted along the bottom.
covered by the occultation. Geomagnetic activity, plotted through the Kp index at the bottom of
Figure 4.4, was relatively quiet on the days of interest, so this study focuses on quiet behavior of
irregularities associated with bubbles and scintillation. In Figure 4.4, the lack of events during days
260–289 is because there were no coincident examples of bubbles and occultations in the data sets.
The time period from 276–282 has no imaging data due to moon-up conditions.
The data fall cleanly into pre-midnight (UT < 0400) and post-midnight (UT ≥ 0400) bins. The
altitude distribution inferred from the pre-midnight events is shown in Figure 4.5. The envelope
of the plot shows the number of occultation ray paths intersecting plasma bubbles in each altitude
bin. Intersections are considered all the way down to the Earth’s surface, although the irregularity
electric fields dissipate with decreasing altitude. Ray paths are considered to intersect irregularities
if the SNR variance σ > 0.10, which is larger than the apparent noise floor of the COSMIC GPS
occultation receivers. These irregularities are seen to be constrained between 200 and 375 km with
a mean altitude for σ > 0.10 is 306 km and a standard deviation of 50 km.
After midnight, shown in Figure 4.6, the data become more interesting. Notice that the relative
proportion of high-altitude intersections (any shading, not just irregularities) is greater than before
midnight. This is indicative of mature plasma depletions observed in the airglow that have grown
to high altitude, but no longer contain irregularities at the correct scale to cause scintillation of
75
Figure 4.5: Distribution of intersection points with altitude and σ in the pre-midnight (UT < 4) time
frame. Due to the availability of coincident data, this corresponds to data taken during days 254–270.
The “All” statistics show all intersections between identified depleted flux tubes and occultation ray
paths, regardless of σ. The “Irregularity” statistics show the distribution of intersections between
depleted flux tubes and occultation ray paths that exhibit σ > 0.10.
Figure 4.6: Similar to Figure 4.5. Due to the availability of coincident data, this corresponds to
data taken during days 280–300.
76
the GPS signal. As observed in airglow images, these depletions will persist until ion production
resumes at sunrise. The mean altitude for the post-midnight events with σ > 0.10 is 278 km with a
standard deviation of 46 km.
There is also an abrupt decrease in the number of intersections at 500 km since we have only
computed intersections below the satellite orbit altitude. Most of the COSMIC/FORMOSAT-3
satellites were in a low-altitude holding orbit of 515 km during the observation period. This upper
limit will be improved for dates after all of the satellites reached their final 800 km orbit altitude
in Fall 2007. At that point, the particular imager used in this study will limit the useful altitude to
about 700 km. However, this restriction is not universal and there are imaging systems whose fields
of view map to higher apex altitudes.
Together, the irregularities detected pre- and post-midnight span an altitude range of 175-375
km. Detection of irregularities along the occultation link would require sufficient electron density
at the irregularity layer, implying that for the lower end of our height estimates to be valid, the
F peak would have to descend to a relatively low altitude. Using the Jicamarca incoherent scatter
radar, Hysell et al. [2008b] have shown that the F layer can indeed descend to low altitudes at
night, approximately 250 km, during solar minimum conditions, such as those prevalent during our
observations. This suggests that the lower irregularity heights obtained from our method are indeed
feasible although we lack direct evidence.
In order to verify that ground-based scintillation was observed coincident to that on the occul-
tation paths, 250-MHz and L-band scintillation observations from the SCINDA station at Anco´n,
Peru´, were studied. Scintillation index (S4) data are plotted for the VHF links in Figure 4.7. The
black dashed lines correspond to occultation events considered in this study. Since some of the
occultation events are nearly coincident in time, some of the lines are indistinguishable. Each oc-
cultation event identified in this study corresponds to 250-MHz S4 > 0.25 at the SCINDA site. No
scintillation was observed at L-band for this station (not shown). However, a GPS L1 scintillation
monitor co-located with the airglow imager at Cerro Tololo, Chile, did observe increased S4 around
most of the events, including several at S4 ≈ 0.4. These S4 data are plotted in Figure 4.8. The
difference in L-band scintillation at the two sites probably arises from ∇N/N differences for ray
paths to the two stations. Anco´n lies in the lower density region between the equatorial arcs, while
Cerro Tololo lies near the southern edge of the southern arc.
One of the assumptions made in this new technique is the altitude of the airglow emission layer.
As mentioned above, deviation from the assumed layer height will affect the spatial characteristics
77
Figure 4.7: VHF scintillation recorded by the SCINDA station at Anco´n, Peru´. The heavy vertical
dashed lines correspond to the times of occultations used in this study. Each occultation corresponds
to scintillation on one or both of the VHF links; see text for discussion. Note that several of the
occultations are nearly coincident in time and are not distinguishable on these plots.
Figure 4.8: L-band scintillation recorded by a GPS scintillation monitor at Cerro Tololo, Chile.
Occultations are marked with dashed vertical lines. Notice that Cerro Tololo’s position below the
equatorial arcs affords greater opportunity to observe scintillations due to increased background
electron density. See text.
78
inferred from the images. Thus, it may be reasonable to expect these errors to affect our results.
To examine the effects of our assumed airglow emission altitude, we performed a simple numerical
experiment. The error in the predicted field line apex altitude between two layer heights can be
considered an upper-bound for the altitude error due to an incorrect airglow layer height estimate.
Emission layer modeling using NRLMSIS-2000E [Picone et al., 2002] and IRI 2000 [Bilitza, 2001]
suggest that a height perturbation of ± 10 km is common in the region of interest. However, for the
purpose of demonstration, we have perturbed the emission height by 50 km up to 300 km. From the
AACGM with 2000 coefficients, we computed the field line apex altitudes using the 250 km and 300
km layer heights and the viewing geometry from the imaging system at CTIO. Most of the errors
were considerably lower than the layer perturbation of 50 km, with 92% of errors being 30 km or
less. For a more typical height perturbation of 10 km, an error of less than 12 km is expected. Note
that these errors do not necessarily scale linearly. Thus, the results presented here can be viewed
with confidence even if the actual height of the airglow layer varies significantly.
The present results are in agreement with the forward-scatter observations of Bhattacharyya
et al. [2001] of an irregularity layer near 350 km in western South America using data from the
Anco´n SCINDA station. However, our data suggest that irregularities may be present over a wider
range of altitudes, 200–375 km. Our technique also confirms the assertion of Straus et al. [2003] that
the scattering region may be far from the ray tangent point, as evidenced in Figure 4.2 in which the
tangent location is far to the east of the intersections observed by the imaging system. Although the
technique presented here does require a ground-based imager, no geostationary satellite is required
as a reference data source as in Cerruti et al. [2006]. Perhaps the most important feature of this
technique is that unlike the others cited, it does not require 50-Hz GPS data to be stored for analysis.
Variance indices computed internally from 50-Hz data or from even lower sampling frequencies such
as those used here are acceptable, although irregularity scale and scintillation parameters may be
difficult to interpret from under-sampled measurements such as these.
4.4 Summary
In this chapter, a novel technique for localizing scintillation-causing irregularities in the equatorial
ionosphere using radio occultation and field-aligned airglow images was discussed. Data collected
during days 254–300 of 2006 suggest that most ionospheric scintillation during this time period
occurred due to irregularities in the 200–375 km altitude range. The present results indicate that
79
higher-altitude irregularities are uncommon during relatively quiet geomagnetic conditions.
80
CHAPTER 5
RELATIONSHIP BETWEEN COHERENT
BACKSCATTER AND AIRGLOW
DEPLETIONS
5.1 Introduction
The post-sunset equatorial ionosphere is capable of extreme volatility due to the abrupt transition
from the daytime E-region dynamo to the nighttime F -region dynamo. This transition manifests
itself in the pre-reversal enhancement of the zonal eastward electric field and various irregularities
known collectively as equatorial spread-F [Kudeki et al., 2007]. Both forward-scatter radio scintil-
lation observations and in-situ rocket and satellite density probes suggest that a broad spectrum of
irregularity scales are present. These measurements also suggest that there are at least two different
spectral characteristics, one at smaller scales (≤ 100 m), and the other at larger scales. In response
to this observation, it has been theorized that there are two or more irregularity process classes
operating [e.g., Chapter 1; Woodman and Basu, 1978; Yeh and Liu, 1982; Kelley , 1989; Hysell and
Farley , 1996, and references therein].
The larger irregularity scales are widely supposed to be the result of an interchange instability, as
first suggested by Dungey [1956]. The smaller scales are thought to be a drift wave operating within
the depleted regions and driven by non-linear coupling to a larger-scale interchange instability [Hysell
and Farley , 1996]. Another suggested mechanism is a wind-driven gradient-drift instability—either
meter-scale or in cascade [Sekar et al., 2007]. Although the irregularities represent a continuum of
scales, most remote techniques for observing them are sensitive to particular scales. Radio scintil-
lation and coherent radar echoes are due to smaller scale irregularities at the Fresnel and Bragg
scales, respectively. Optical airglow imaging and incoherent radar backscatter are able to detect the
larger-scale structures, on the order of a few kilometers and larger. It is well-known that the meter-
scale irregularities observed via coherent backscatter decay more rapidly than the 100-meter-scale
irregularities responsible for scintillation [Basu et al., 1978]. This also extends to the even larger
depletions observed in the airglow, which frequently remain until ionization resumes at sunrise [e.g.,
Makela, 2006].
The first comparative study of the relationship between Bragg-scale irregularities causing coher-
81
ent echoes and plasma depletions was undertaken by Tsunoda [1980] using the ALTAIR (ARPA
Long-range Tracking and Identification Radar) system on Kwajalein Atoll in the Marshall Islands.
This study utilized the steerable capability of ALTAIR to confirm the aspect sensitivity of coherent
backscatter echoes to the geomagnetic field. Furthermore, the aspect sensitivity of coherent echoes
was leveraged to perform an incoherent backscatter analysis of the off-perpendicular returns and
confirm that the coherent backscatter emanates from the depleted regions. More recently, this type
of work has been extended to optical airglow imaging systems and coherent backscatter in the East
Asian Sector [Otsuka et al., 2004b; Saito et al., 2008]. In both cases, the data have come from limited
periods of time due to instrument availability (notably ALTAIR) and, in the later studies, atmo-
spheric observing conditions at the airglow imaging site. Given the manifest variety of formations
in which equatorial irregularities appear, it is compelling to consider a long-term data set.
In this chapter, a long-term coincident study of airglow and radar data is presented from a
field-aligned airglow imaging system (CNFI) at Mount Haleakala, Hawaii, and a 50-MHz coherent
backscatter radar at Christmas Island, Kiribati (CXI). Several interesting examples are considered,
as well as a reduction of the entire airglow imaging and radar backscatter data set from January
2002–January 2009. The first section treats analysis techniques employed to reduce the data. The
next section discusses the selection of the data and general characteristics. The final section considers
specific geophysical implications.
5.2 Instrumentation and Analysis
Equatorial plasma depletions are observed by the CNFI system described in Chapter 2 through the
impression left by their internal electric fields in the airglow emission layer (nominally 250-km alti-
tude for the 630.0-nm emission). In Chapter 3, we saw that electrostatic modeling and observations
suggest that electric fields associated with irregularities of scales greater than approximately 10 km
map efficiently along the geomagnetic field, affecting a wedge-shaped region that extends from the
northern to southern hemisphere. Given that the range gates of the CXI radar are also spaced at
10-km intervals in altitude and that the integrations occur every 75 seconds (assuming an eastward
drift of 100 m/s, this works out to 7.5 km in the zonal direction), we are comfortable making the
approximation that irregularities observed in the airglow can be extruded along the geomagnetic
field for comparison with the radar as described in Chapter 4 and Appendix C.
The extrusion is performed by mapping the pixels of the imaging sensor to an assumed peak
82
emission altitude of the airglow, 250 km for this work, unless specified otherwise. That is, the ray
path corresponding to each pixel is traced until it intersects the airglow layer. The intersections
are recorded in geographic coordinates. For the purpose of this work, the centroid location of each
range gate on the north beam of the Christmas Island radar has been traced along the geomagnetic
field until it insects the airglow layer as well. This allows the airglow intensity corresponding,
geomagnetically speaking, to each range gate to be interpolated. Thus, for each radar integration
time step, there are 100 backscatter range gates and 100 airglow intensities. These may be assembled
in a standard range-time-intensity (RTI) backscatter map [Woodman and Hoz , 1976] and a so-called
keogram of the airglow. We will refer to the combination of an RTI map and a keogram, examples
of which are shown in Figure 5.1, as an “RTI gram.” This kind of representation was first employed
by Makela et al. [2009].
Furthermore, we have extracted an estimate of the plasma drift velocity as a function of time
and apex altitude from the sequence of airglow images. This technique is a modification of those
described by Makela and Kelley [2003a] and Yao and Makela [2007]. The drift velocity extraction
procedure begins by detecting the brightest stars in the image and applying a median filter to their
vicinities to remove them. Next, the image is convolved with a 3× 3 Sobel edge-detection operator.
Pixels corresponding to the desired field-line apex altitude are selected to produce a one-dimensional
slice of the image, which is filtered with a boxcar filter (length 16, corresponding to about 40 km)
to reduce noise. The correlation between slices at adjacent time steps can be used to estimate the
drift velocity by converting the lag from pixel space to geographic space to linear distance. While
this technique for computing the drift velocity is not new, applying it to different apex altitudes
provides insight into the types of drifts observed and may be an important classification tool in the
future. A quality-of-fit index is assigned to each velocity computation based on the strength of the
correlation. Presently, this is the value of the maximum correlation at the lag used to compute the
velocity. The velocity and quality-of-fit data are combined as altitude-time series for plotting on
axes similar to the RTI gram.
The drift velocity estimation is important primarily from a classification standpoint. It allows
different structures to be detected in the airglow, notably clouds, depletions, and MSTIDs. This
permits the reader to quickly identify the relationship between the structures seen in the RTI gram
(both radar and airglow) and their motions in the airglow.
83
5.3 Data
The data selected for daily study come from 2004 and 2005, all during the period 12 August through
12 September, which is during the season in which equatorial irregularities are typically prevalent
in the central Pacific as shown in previous climatology studies from Haleakala and the U.S. Defense
Meteorological Satellite Program (DMSP) [Makela et al., 2004; Gentile et al., 2006]. There are two
consecutive days selected from 2004 and six consecutive in 2005, plus one other that is interesting.
These days were picked for their illustrative value or because they were representative, not because
they constitute a valid statistical sample. Most of the days correspond to relatively quiet geomagnetic
conditions and clear or mostly clear observing conditions at Haleakala. There is one storm day, 24
August 2005, with Kp = 8+ observed at 0900 UT. All daily plots have a header that indicates
the year, day-of-year, and date, in addition to a plot of 11 days’ Kp data, five preceding and five
following the day of interest. The bars are color-coded with the usual green for Kp ≤ 3, yellow for
3 < Kp < 5, and red for Kp ≥ 5. A small gray box behind the bars indicates the exact time period
for the optical and radar data shown, which corresponds to approximately 0600–1500 UT every day.
Figure 5.1 shows composite RTI gram and drift velocity estimates (from the airglow) on 19–20
August 2004. In order to make a meaningful comparison between the keogram (top for each day),
RTI gram (middle), and velocigram (bottom), the altitude coordinates have been transformed to
the field line apex altitude. Unless specifically described otherwise, this will be the standard display
format for all daily data in this chapter.
233
0
5
9
K p
B 
Ap
ex
 [k
m
]
 
 
200
1000
I [
co
un
ts]
2000
7000
B 
Ap
ex
 [k
m
]
 
 
200
1000
SN
R 
[d
B]
−20
 20
Universal Time [hrs]
B 
Ap
ex
 [k
m
]
 
 
7 9 11 13 15
200
1000
Ea
st 
Dr
ift 
[m
/s]
−50
0
150
20 August
(233) 2004
CXI / CNFI
232
0
5
9
K p
B 
Ap
ex
 [k
m
]
 
 
200
1000
I [
co
un
ts]
2000
7000
B 
Ap
ex
 [k
m
]
 
 
200
1000
SN
R 
[d
B]
−20
 20
Universal Time [hrs]
B 
Ap
ex
 [k
m
]
 
 
7 9 11 13 15
200
1000
Ea
st 
Dr
ift 
[m
/s]
−50
0
150
19 August
(232) 2004
CXI / CNFI
clouds
Figure 5.1: Composite keogram (top for each day), RTI gram (middle), and airglow velocigram
(bottom) for 19 and 20 August 2004. See text for discussion.
The radar backscatter data in the RTI gram are a classical RTI backscatter map showing SNR
84
as a function of (apex) altitude and time. The relatively solid line of backscatter along the bottom
of the map around 100 km in altitude is due to electrojet instability waves. The blackened regions
in the velocigram correspond to points for which the logarithm of the peak frame-to-frame airglow
correlation value is at least 0.25 standard deviations below the mean for the entire data set. This
condition is an ad hoc indicator that little coherent object motion was tracked in the image at that
time and location. The algorithm also tends to recognize the rapid brightening or dimming of the
airglow as a coherent motion, although it often reports zero velocity. Also note in Figure 5.1 that
saturations (≥ 150 m/s) in the drift velocity tend to correspond to clouds, which appear to move
much faster than the depletions due to the parallax effect. The drift velocity also helps identify
airglow structures that remain in the image after the backscatter ceases.
Figure 5.2 contains data from six consecutive days, 24–29 August 2005 in the same format as
Figure 5.1. This is meant largely to illustrate the day-to-day variability of the structures. The first
two days, 24 and 25 August, show some geomagnetic activity. 24 August (236) 2005 is interesting
because there are two layers of backscatter. This is relatively uncommon and occurs perhaps once
or twice per year. The finger-like structure between 1300 and 1430 UT propagates with a westward
component, as seen in the drift velocity plot. Common structures that propagate with a westward
component are mesoscale traveling ionospheric disturbances (MSTIDs), which propagate to the
southwest in the northern hemisphere under geomagnetic quiet conditions. The next three days,
26–28 August, are typical geomagnetic quiet days. And, finally, 29 August is a day with no bubble
activity included as a control and to illustrate the effectiveness of the airglow velocity extraction
method as a technique for detecting depletions.
Figure 5.3 is a climatological reduction of CNFI and CXI data for 2002–2009. The black regions
in each plot indicate periods when data were unavailable or unusable (poor SNR). The color-coded
percentages correspond to the percentage of days in a 20-day sliding window in which equatorial
plasma bubbles or 3-meter backscatter were observed, respectively. The CNFI airglow images were
classified visually into four categories: clear, cloudy, bubble, or unusable. Cloudy and unusable
days were lumped together as unusable for this presentation. The CXI backscatter was tallied for
received levels of > −10 dB and > 0 dB above the thermal noise level on the CXI east beam. We
have also included the 3-hour Kp index and the daily 10.7-cm solar flux for the period. The Kp
index is sorted into bins and color coded just as it is for the composite RTI grams: green for Kp ≤ 3,
yellow for 3 < Kp < 5, and red for Kp ≥ 5.
85
236
0
5
9
K p
B 
Ap
ex
 [k
m
]
 
 
200
1000
I [
co
un
ts]
2000
7000
B 
Ap
ex
 [k
m
]
 
 
200
1000
SN
R 
[d
B]
−20
 20
Universal Time [hrs]
B 
Ap
ex
 [k
m
]
 
 
7 9 11 13 15
200
1000
Ea
st 
Dr
ift 
[m
/s]
−50
0
150
24 August
(236) 2005
CXI / CNFI
237
0
5
9
K p
B 
Ap
ex
 [k
m
]
 
 
200
1000
I [
co
un
ts]
2000
7000
B 
Ap
ex
 [k
m
]
 
 
200
1000
SN
R 
[d
B]
−20
 20
Universal Time [hrs]
B 
Ap
ex
 [k
m
]
 
 
7 9 11 13 15
200
1000
Ea
st 
Dr
ift 
[m
/s]
−50
0
150
25 August
(237) 2005
CXI / CNFI
238
0
5
9
K p
B 
Ap
ex
 [k
m
]
 
 
200
1000
I [
co
un
ts]
2000
7000
B 
Ap
ex
 [k
m
]
 
 
200
1000
SN
R 
[d
B]
−20
 20
Universal Time [hrs]
B 
Ap
ex
 [k
m
]
 
 
7 9 11 13 15
200
1000
Ea
st 
Dr
ift 
[m
/s]
−50
0
150
26 August
(238) 2005
CXI / CNFI
239
0
5
9
K p
B 
Ap
ex
 [k
m
]
 
 
200
1000
I [
co
un
ts]
2000
7000
B 
Ap
ex
 [k
m
]
 
 
200
1000
SN
R 
[d
B]
−20
 20
Universal Time [hrs]
B 
Ap
ex
 [k
m
]
 
 
7 9 11 13 15
200
1000
Ea
st 
Dr
ift 
[m
/s]
−50
0
150
27 August
(239) 2005
CXI / CNFI
240
0
5
9
K p
B 
Ap
ex
 [k
m
]
 
 
200
1000
I [
co
un
ts]
2000
7000
B 
Ap
ex
 [k
m
]
 
 
200
1000
SN
R 
[d
B]
−20
 20
Universal Time [hrs]
B 
Ap
ex
 [k
m
]
 
 
7 9 11 13 15
200
1000
Ea
st 
Dr
ift 
[m
/s]
−50
0
150
28 August
(240) 2005
CXI / CNFI
241
0
5
9
K p
B 
Ap
ex
 [k
m
]
 
 
200
1000
I [
co
un
ts]
2000
7000
B 
Ap
ex
 [k
m
]
 
 
200
1000
SN
R 
[d
B]
−20
 20
Universal Time [hrs]
B 
Ap
ex
 [k
m
]
 
 
7 9 11 13 15
200
1000
Ea
st 
Dr
ift 
[m
/s]
−50
0
150
29 August
(241) 2005
CXI / CNFI
Figure 5.2: Composite data for each day 24–29 August 2005. The format of the plot is the same as
Figure 5.1.
86
UT (LT)
Pe
rc
en
ta
ge
 o
f n
igh
ts 
wi
th
 b
ub
ble
s >
 4
00
 km
 a
t C
NF
I
 
 
20
02
20
03
20
04
20
05
20
06
20
07
20
08
20
09
6 
(2
0)
8 
(2
2)
10
 (0
)
12
 (2
)
14
 (4
)
16
 (6
)
020406080
UT (LT)
Pe
rc
en
ta
ge
 o
f n
igh
ts 
wi
th
 b
ac
ks
ca
tte
r >
 −
10
dB
 a
t C
XI
 
 
20
02
20
03
20
04
20
05
20
06
20
07
20
08
20
09
6 
(2
0)
8 
(2
2)
10
 (0
)
12
 (2
)
14
 (4
)
16
 (6
)
020406080
UT (LT)
Pe
rc
en
ta
ge
 o
f n
igh
ts 
wi
th
 b
ac
ks
ca
tte
r >
 0
dB
 a
t C
XI
 
 
20
02
20
03
20
04
20
05
20
06
20
07
20
08
20
09
6 
(2
0)
8 
(2
2)
10
 (0
)
12
 (2
)
14
 (4
)
16
 (6
)
020406080
20
02
20
03
20
04
20
05
20
06
20
07
20
08
20
09
0
10
0
20
0
30
0
Da
te
 (y
ea
rs
)
F
10.7
 (SFU, 10
−22
 W m
−2
 Hz
−1
)
K p
 a
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 1
0.
7−
cm
 so
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 flu
x
 
 
F
ig
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5.
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C
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at
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ic
al
re
du
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of
th
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(t
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),
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(b
ot
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)
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he
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da
ys
w
he
n
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re
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la
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ti
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w
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.
87
5.4 Discussion
5.4.1 Depletions and backscatter
Even at a visual glance, the observations in Figures 5.1 and 5.2 appear to confirm assertions that
the most intense backscatter emanates from locations that are geomagnetically connected to the
depleted regions observed in the airglow. A cut across all times at a fixed altitude (single range
gate) illustrates this even better. Figure 5.4a shows normalized cuts of airglow and backscatter
intensity at ranges corresponding to apex altitudes of 300, 450, and 600 km, from 19 August 2004.
The backscatter does appear to be well-correlated with the depleted regions of airglow. In contrast,
Figure 5.4b, from 12 August 2005, exhibits a time-lag between the backscatter and some of the
airglow depletions. This raises two possibilities, assuming proper spatial calibration of the imager
system and radar. The first is that there is indeed backscatter coming from the eastward wall of the
depletion. That is, since the depletion is drifting eastward, irregularities on the wall begin to appear
in the radar beam before the depletion is observed in the airglow image. This theory gains credence
from the observation by Ledvina and Makela [2005] that the eastern walls of depletions contained
more spectral power at small scales than the western walls as they passed a geostationary SBAS
satellite link. The second alternative explanation is that the airglow emission altitude has deviated
from the nominal 250-km estimate. This will be discussed further in the next subsection.
Another compelling observational argument for the majority of the backscatter arising from the
depleted region may be illustrated by the following cartoon. Consider a radar beam convolved with a
medium containing backscattering irregularities frozen onto two walls of a depletion. Next, consider
the same radar beam convolved with a medium containing a single (again frozen) block of scattering
irregularities. Unless the beam is sufficiently wide to illuminate both walls of the depletion, the
signatures of the two structures differ greatly, as illustrated in Figure 5.5. Naturally, this argument
requires that the drift is constant and the morphology of the scatterers remains constant. The
drifts extracted from the airglow, plus the fact that the drifts can be extracted from the airglow
using correlation, suggest that these conditions are approximately met. Notice that the backscatter
envelopes tend to have soft edges, coming to a near maximum in the middle of the envelope before
tapering back to a soft edge on the other side. If backscatter were to be arising from both edges, the
backscatter would be greater at the edges than in the center. A gradient drift instability requires
the wind to be antiparallel to the plasma density gradient in order to grow, which in the case of
an eastward wind, would not occur on the eastward wall of the depletion [Sekar et al., 2007]. It is
88
most likely, therefore, that the 3-meter irregularities are indeed within the depleted region, perhaps
being driven by or propagating from a gradient drift instability on the western wall.
0
0.5
1
In
te
ns
ity
 [a
rb]
19 August 2004 (232)
0
0.5
1
In
te
ns
ity
 [a
rb]
7 9 11 13 15
0
0.5
1
In
te
ns
ity
 [a
rb]
Universal Time [hrs]
600 km
450 km
300 km
0
0.5
1
In
te
ns
ity
 [a
rb]
12 August 2005 (224)
0
0.5
1
In
te
ns
ity
 [a
rb]
7 9 11 13 15
0
0.5
1
In
te
ns
ity
 [a
rb]
Universal Time [hrs]
600 km
450 km
300 km
(a) (b)
Figure 5.4: (a) RTI gram time series cuts from 19 August 2004 corresponding to apex altitudes of
300, 450, and 600 km. The solid (blue) line corresponds to the airglow intensity. The dashed (red)
line corresponds to radar backscatter. These quantities are normalized over ranges of [1000,7000]
counts and [-20,20] dB, respectively, to create the [0,1] scale. Although it is difficult to make out
some of the structure on the low-altitude plot, the higher altitude plots show that the backscatter
coincides with the depleted regions. (b) RTI gram time series cuts from 12 August 2005. In this
case, there appears to be some “phase shift” between the airglow images and the radar backscatter,
e.g., 600 km between 1100 and 1300 UT. See text for discussion.
5.4.2 Airglow layer altitude estimation
One of the well-known limitations of airglow imaging is knowledge of the emission layer altitude. This
problem is particularly vexing with the 630.0-nm emission because, although easy to observe due to
its high emission rate, it is strongly dependent on both neutral density and electron density profiles.
Knowledge of the emission altitude is crucial because it affects the perceived interpretation of the
impact of the irregularities observed in the image when they are transformed from pixel coordinates
to geographic coordinates. Figure 5.6 illustrates the effect of varying the assumed emission altitude
from 220 to 440 km when producing RTI grams of data from 12 August 2005. Notice that the
airglow and backscatter seem to match best at layer altitudes above 300 km on this day. The
brightening around 1300 UT corresponds to the lowering of the ionosphere. Correspondingly, the
little remaining backscatter at 1400 UT seems to match better at lower altitudes again.
Correlations have been computed over a 60-minute window in 20-minute steps to estimate the
layer altitude. In Figure 5.7, these altitudes are compared with an airglow emission profile modeled
89
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Figure 5.5: Series of cartoons that illustrate two example irregularity location scenarios. The top
row illustrates a block of irregularities located in the depleted region (left), convolved with a radar
beam (center), to produce a backscatter map (left). The bottom row of figures is analogous, with
the exception of the differing irregularity structure. This suggests that the irregularities are either
located along one wall or in the center. These plots are for one range gate, just as the plots in
Figures 5.4a and 5.4b.
for 12 August 2005 using IRI 2007 [Bilitza and Reinisch, 2008] and NRL MSIS00-E [Picone et al.,
2002]. The estimated altitude exceeds that of the IRI/MSIS model. Tomographic reconstructions
of plasma densities using the 135.6-nm airglow emission observed by the TIMED/GUVI instrument
suggest that altitude of the peak electron density between depletions may reach as high as 425 km
in the Pacific sector [Comberiate et al., 2007]. Although the Comberiate et al. [2007] example was
during the same season (22 September 2002), it was during near solar maximum conditions. Sahai
et al. [2000] presented ionosonde data showing the F -region virtual height (h′F ) exceeding 500 km
during one night when spread-F was observed during solar minimum. Based on physical models of
the emission emission profile, the 630.0-nm emission peak is typically about one neutral scale height
(50–100 km) below the F -layer electron density peak. The estimated emission altitudes with this
technique are therefore in line with Comberiate et al. [2007] and Sahai et al. [2000]. A more detailed
correlative study with another instrument capable of estimating the airglow layer altitude would be
compelling.
Furthermore, the night of 12 August 2005 is particularly active with depletions continuing
throughout the entire night. The lowering (brightening in the airglow) of the ionosphere, usu-
90
Ap
ex
 [k
m
]
220 km
200
400
600
800
1000
Ap
ex
 [k
m
]
260 km
200
400
600
800
1000
Ap
ex
 [k
m
]
300 km
200
400
600
800
1000
Ap
ex
 [k
m
]
340 km
200
400
600
800
1000
Ap
ex
 [k
m
]
380 km
200
400
600
800
1000
Universal Time [hr]
Ap
ex
 [k
m
]
420 km
6 8 10 12 14 16
200
400
600
800
1000
240 km
280 km
320 km
360 km
400 km
Universal Time [hr]
440 km
6 8 10 12 14 16
Figure 5.6: Series of RTI grams from 12 August 2005 produced with the assumed airglow emission
altitude varied from 220 to 400 km. The height of the airglow layer does change as a function of
time. At different times, different altitudes may match better. See text for detailed discussion.
6 8 10 12 14 16
250
300
350
400
450
Universal Time [hrs]
Es
t L
ay
er
 A
lt [
km
] 12 August (224) 2005 CXI / CNFI
 
 
modeled
extracted
6 8 10 12 14 16
250
300
350
400
450
Universal Time [hrs]
Es
t L
ay
er
 A
lt [
km
]
19 August (232) 2004 CXI / CNFI
 
 
modeled
extracted
Figure 5.7: Automatically determined airglow peak emission altitude (in 20-km bins) compared
with MSIS/IRI modeled emission altitude for 12 August 2005 and 19 August 2004, left to right,
respectively.
91
ally associated with the MTM (midnight temperature maximum), occurs at 1300 UT, some three
hours after local midnight. The combination of high depletion activity and late layer lowering may
be related to drivers (e.g., tides, a vigorous E×B drift earlier in the day) that exceeded the physical
or statistical basis for the models.
The remaining plots in Figure 5.7 illustrate another example, 19 August 2004 (RTI gram in
Figure 5.1). The high-altitude estimate at the beginning of 19 August 2004 is probably not physical,
although there is some mismatch in Figure 5.1 at that time. It appears to match quite well near
260 km the rest of the night. Apart from the IRI/MSIS model, a direct measurement of the density
or emission profile would lend additional credibility to this technique.
5.4.3 Decaying backscatter
It has been theorized that the Bragg-scale irregularities responsible for coherent backscatter are due
to a flute mode drift wave that is pumped by an additional irregularity [Hysell and Farley , 1996;
Saito et al., 2008]. In the absence of the pump mode, the drift wave irregularities will diffuse rapidly.
Referring to Figure 5.2, under quiet geomagnetic conditions on 26–28 August 2005, the late-night
descent of the ionosphere (brightening of the airglow) appears to coincide with the cessation of 3-
meter backscatter even though the depletions remain. This corroborates the argument of Saito et al.
[2008] that the descent associated with the MTM is associated with dwindling backscatter. Based on
the airglow-derived drifts, it is not entirely clear that the eastward drift approaches stationary until
after the backscatter disappears, if at all. Furthermore, the example in Figure 5.1 from 19 August
2004 shows strong (∼ 100 m/s) drifts even after the 3-m backscatter has ended. This example is
also interesting because the backscatter disappears before any apparent descent of the ionosphere.
There is, however, a descent on 20 August 2004 that appears weakly in the airglow around 1030 UT
between the last two tall radar plumes.
Supposing that it is a gradient drift instability that drives the 3-meter backscatter, the variability
seen here suggests that there may be a threshold in the drift velocity, almost certainly set by the
eastward thermospheric neutral wind, that determines the cessation of backscatter. This may have
particularly interesting implications for 12 August 2005, when high-altitude backscatter persists
after low-altitude irregularities have disappeared. The small patch of backscatter at 400 km at
1200 UT on 12 August 2005 appears to be fairly well matched to the airglow, as seen in Figure 5.6.
However, the backscatter above, presumably from the same depletion, is quite far from the depletion
outline in the airglow, suggesting that the airglow layer might not have a uniform altitude across
92
the image.
5.4.4 Climatology
Figure 5.3 illustrates the seasonal climatology of airglow depletions and 3-m backscatter observed
from 2002 to 2009 by CNFI and CXI. This climatology extends and corroborates work by Makela
et al. [2004], which was only performed for 2001–2003 using data from Maui. It is clear that the
occurrence of airglow depletions and backscatter is seasonal and well-correlated. There is a peak
in activity in the later portion of the year, particularly July–October, surrounding the autumnal
equinox. There is considerably less activity at the vernal equinox, when the sunset terminator is
also aligned with the geomagnetic declination in this longitude sector. This confirms that alignment
may be a necessary, although insufficient, condition for irregularity growth [Tsunoda et al., 1982].
The reason for this asymmetry is not yet known, although Maruyama and Matuura [1984] have
suggested that it may be a consequence of the neutral wind. However, Fabry-Perot interferometer
measurements of the neutral wind in the American sector by Mendillo et al. [2001] suggest that, at
least during the time period considered, there is little direct correlation between the thermospheric
neutral wind and the observation of GPS L1 (fL1 = 1.57542 GHz) radio scintillations and airglow
depletions. More recently, Su et al. [2009] have used ROCSAT-1 satellite drift velocity measurements
to infer that differences in irregularity formation morphology may be more strongly related to
the onset and duration of vertical drifts (through their relationship to the local geomagnetic field
intensity) during different seasons.
As discussed in the previous section, backscatter also decays before the depletions disappear.
This is also quite clear from the climatological data as the depletions tend not to disappear until
sunrise (top of the plots). Unlike previous studies using satellite in situ observations [Huang et al.,
2002] and airglow images [Sahai et al., 2000], these data suggest that the equatorial ionosphere
continues to produce irregularities into solar minimum at a rate comparable to that seen near solar
maximum. However, there are marked differences in the morphology and behavior.
One notable effect is that the seasonal backscatter centroid appears later in the evening toward
solar minimum. It is probable that these depletions go largely undetected by the sun-synchronous
DMSP satellites because they occur late in the evening or early in the morning local time, and
many do not reach the 840-km orbit altitude. Both 3-m backscatter and depletions appear to dwell
longer at solar minimum in this data set as well. As discussed previously, the midnight temperature
maximum, which often coincides with the cessation of backscatter, does not vary greatly in time or
93
intensity as a function of solar cycle. Therefore, it is unlikely to be a source of variability with solar
conditions.
As solar activity decreases, there is also an increase in early-morning backscatter activity in
December–January. This effect is pronounced in 2005–2009 and only visible in the −10 dB category.
These irregularities frequently coincide with activity in the airglow. Although statistics were not
tracked independently for this study, many of the airglow structures observed at the end of the
night in 2008 and 2009 resembled the southwestward propagating undulations often observed at
Arecibo [e.g., Garc´ıa, 1999]. Although the electric fields within these structures are known to map
into the conjugate hemisphere, they are not frequently associated with depletions or Bragg-scale
irregularities [Saito et al., 1995]. There have been some recent examples of VHF backscatter from
these structures at middle latitudes by the MU radar [Otsuka et al., 2009]. Makela et al. [2009] have
argued with an example that under certain conditions, what may be a midlatitude phenomenon
can induce backscatter near the geomagnetic equator. A similar event is shown in Figure 5.2 on 24
August 2005. A study of the anomalous peak in activity, as well as a proposed explanation involving
forcing from mid-latitude MSTID instabilities, is presented in Chapter 6.
5.5 Conclusion
This work presents several interesting conclusions regarding the morphology of plasma depletions
and VHF backscatter during the course of a solar cycle. In a long-term sense, this work confirms
earlier point (space and time) observations suggesting that meter-scale coherent radar backscatter
originates from within the depleted regions of equatorial plasma bubbles and presented examples
showing the variety of conditions under which coherent radar echoes are observed and the capability
of coincident airglow images to contextualize these events.
Over the period January 2002–January 2009, we presented a climatological reduction of the
airglow images and radar data showing that depletion and backscatter activity do not decrease
substantially from solar maximum to solar minimum in the central Pacific. However, as solar
minimum conditions set in, backscatter begins later in the evening and continues longer. These
observations confirm similar observations made from Jicamarca. One anomalous peak in backscatter
and depletion activity has been noted in the November–January period of solar minimum years
(November 2004–January 2009).
94
CHAPTER 6
EVIDENCE OF A MID-LATITUDE SEED FOR
EQUATORIAL PLASMA DEPLETIONS
6.1 Introduction
As discussed in Chapters 1 and 2, irregularities in the post-sunset equatorial F -region ionosphere
have been a source of immense scientific and engineering curiosity since their first reporting by Booker
and Wells [1938]. Among the enduring unknowns regarding equatorial plasma depletions is the
sequence of events linking their formation to the apparently unstructured equatorial ionosphere of the
late afternoon. Although depletions tend to have a well-defined seasonal occurrence (July–October,
March–May, for Hawaii [Makela et al., 2004]) for a given longitude, the day-to-day variability remains
elusive.
Within the depleted regions, polarization electric fields of sufficient scale map efficiently along
the geomagnetic field pushing depleted wedges into low and tropical latitudes, piercing layers of
airglow emission. Imaging observations of the 630.0-nm (dissociative recombination of O+2 ) airglow
have been conducted from Hawaii since December 2001 [Kelley et al., 2002]. These observations
are supported by a 50-MHz radar on Christmas Island, Kiribati. On-going climatological study of
airglow images and radar backscatter from these sites uncovered a minor peak in post-midnight
depletion and backscatter activity in solar minimum years (2005–2009). Although post-midnight
depletions are often associated with geomagnetic activity [Martinis et al., 2005], these events almost
universally occurred under quiet conditions, prompting this investigation. A similar pattern of
post-midnight spread-F was also reported at Hawaii in the climatology by Reber [1954].
In addition to depletions, mesoscale traveling ionospheric disturbances (MSTIDs) are frequently
observed in the 630.0-nm airglow emission over Hawaii, particularly during solar minimum condi-
tions. The MSTID is a propagating perturbation in the altitude of the electron density peak thought
to be related to the Perkins instability [Perkins, 1973]. MSTIDs appear propagating from the north-
east to the southwest with wavefronts aligned in the southeast-northwest direction. Like depletions,
MSTIDs contain polarization electric fields that map into the conjugate hemisphere [Otsuka et al.,
2004a]. However, meter-scale field-aligned irregularities (FAIs) responsible for coherent backscatter
95
are confined to the undulations and are not generally observed at high altitudes [Otsuka et al., 2009].
In this chapter, we examine observational evidence of a relationship between mid-latitude struc-
ture and the development of post-midnight equatorial spread-F during geomagnetic quiet conditions.
We suggest that the polarization electric field associated with the mid-latitude structure maps to
the bottom-size equatorial F region, initiating the development of plasma depletions, as proposed
by Tsunoda [2007]. We will first give a brief overview of the instrumentation, which is amply dis-
cussed in Chapters 2, 3, and 5. Then, we will present two case study events followed by a discussion
of the events and their potential implications for understanding the seeding of equatorial plasma
depletions in general.
6.2 Instrumentation and Observations
The instrumentation employed in this study comprises two airglow imaging (CNFI and CASI)
systems located atop Mount Haleakala and a 50-MHz radar at Christmas Island. These systems are
described in Chapter 2. By tracing the ray paths from each pixel on the CCD imaging sensors in
these systems to the airglow layer height, two-dimensional maps of the airglow emission extending
from 5◦ N to 28◦ N latitude are produced. The radar east beam provides backscatter data slightly
to the east of the CNFI field of view, while the north beam provides observations within the same
geomagnetic volume as CNFI. That is, the range gate centroid locations of the north beam reside
on geomagnetic field lines that intersect the airglow observed by CNFI north of the geomagnetic
equator, as illustrated in Figure 2.15.
During cataloging of the images from Haleakala (reported in Chapter 5) from January 2002 to
January 2009, a high incidence of MSTID structures was noted during the November–January period
during the solar minimum years (from late 2005 onward). Furthermore, the radar climatology (also
presented in Chapter 5) indicates a coincident increase in post-midnight backscatter. This correlation
was not immediately apparent since separate statistics for MSTIDs and plasma depletions were not
being kept. However, a few events provided impetus for further study. Of these, we have selected
two examples to present here: 23 November (327) 2005 and 2 September (246) 2008. Both of these
days are preceded by geomagnetically quiet conditions (Kp < 3), which is representative of all of
the events in the dataset.
The first example, from 23 November 2005, is striking: it is near the end of the normal plasma
bubble season for Hawaii, the airglow data are of high contrast, and the 50-MHz backscatter con-
96
tinues until the radar stops taking data. A composite data summary of this event is presented in
Figure 6.1. The top of the figure contains header information about the date, site, and geomagnetic
activity for ±5 days from the date of interest. The three panels summarize the airglow and radar
data for the night, mapped to the field line apex for comparison using the International Geomagnetic
Reference Field (IGRF) [Maus et al., 2005]. The vertical scale is the apex altitude and the horizontal
scale is Universal Time (leads Hawaiian Standard Time, HST, by 10 hours). The top panel is a
keogram, except that each altitude bin at each time step corresponds to a range gate of the CXI
radar’s north beam. This permits direct comparison of the range-time-intensity (RTI) map from
the radar with the airglow images, which are shown overlaid in the center panel. The dark bands
(indicated by arrow) from upper left to lower right between 2300 and 0000 HST are the signature
of an MSTID passing through the local ionosphere over Haleakala. The bottom panel provides an
estimate of the eastward drift velocity of features in the airglow corresponding to different apex
altitudes using the technique described in Chapter 5. The black regions indicate locations where
no features were tracked. The regions marked with ‘W’ have westward drift components due to the
MSTID.
327
0
5
9
K p
B 
Ap
ex
 [k
m]
 
 
200
400
600
800
1000
I [c
ou
nts
]
3500
7000
B 
Ap
ex
 [k
m]
 
 
200
400
600
800
1000
SN
R 
[dB
]
−20
 20
Universal (Local) Time [hrs]
B 
Ap
ex
 [k
m]
 
 
07 (21) 09 (23) 11 (01) 13 (03) 15 (05)
200
400
600
800
1000
Ea
st
 D
rif
t [m
/s]
−50
0
150
23 November
(327) 2005
CXI / CNFI
W W
Figure 6.1: Data summary “RTI-gram” from 23 November (327) 2005. Headers show Kp index for
±5 days. The three panels contain (top) a keogram of the airglow, (middle) RTI-gram of the airglow
and radar backscatter, and the plasma drift velocity estimated from features in the local airglow
layer (bottom). See text for discussion.
97
Figure 6.2 illustrates the relationship between the light and dark bands of the MSTID structure
and the Doppler velocities observed at the Christmas Island radar. Although it is not a perfect
indicator of the electric field structure, the coherence of the Doppler velocity within the bands
suggests that they are electrified and the polarization fields are driving the 3-meter irregularities by
the E×B mechanism.
327
0
5
9
K p
B 
Ap
ex
 [k
m]
 
 
200
400
600
800
1000
I [c
ou
nts
]
3500
7000
B 
Ap
ex
 [k
m]
 
 
200
400
600
800
1000
D
op
 V
el
 [m
/s]
−150
150
B 
Ap
ex
 [k
m]
Universal (Local) Time [hrs]
 
 
07 (21) 09 (23) 11 (01) 13 (03) 15 (05)
200
400
600
800
1000
D
op
 W
id
 [m
/s]
  0
150
23 November
(327) 2005
CXI / CNFI
Figure 6.2: Supplemental RTI-gram plot similar to Figure 6.1 with Doppler velocities and widths
from the Christmas Island radar. The light and dark bands of the MSTID structure correspond
directly to downward and upward Doppler velocities, suggesting that the structure is electrified and
driving E×B drifts. Broader widths imply more recent development of the irregularities.
Figure 6.3 contains eight selected airglow frames from CNFI and CASI on 23 November 2005.
They ilustrate the appearance of a band structure propagating to the southwest as plasma bubbles
appear at the equator and propagate to the east. The geomagnetic projections of the north and
east beams of the Christmas Island radar along the flux tubes corresponding to each range gate are
plotted as well. A large alternating band structure begins to appear in the all-sky images of the
630.0-nm emission around 2042 HST. The isointensity contours of the MSTID emerge in the airglow
already elongated magnetically northwest to southeast and propagating to the southwest (about
50 degrees off magnetic north). At first, the bands appear to be a large wave. However, by 2153
HST, finer structure begins to appear in the circled region. By 2229 HST, the structure appears to
reach all the way to the southern extent of CNFI’s field of view. This is well-correlated with first
98
1
9
5
2
0
0
2
0
5
2
1
0
08
29
 U
T
22
29
 H
ST
12
16
 U
T
02
16
 H
ST
1
9
5
2
0
0
2
0
5
2
1
0
08
50
 U
T
22
50
 H
ST
14
02
 U
T
04
02
 H
ST
1
9
5
2
0
0
2
0
5
2
1
0
06
42
 U
T
20
42
 H
ST
09
40
 U
T
23
40
 H
ST
1
9
5
2
0
0
2
0
5
2
1
0
07
53
 U
T
21
53
 H
ST
10
15
 U
T
00
15
 H
ST
E
a
s
t 
G
e
o
g
ra
p
h
ic
 L
o
n
g
it
u
d
e
 [
d
e
g
re
e
s
]
North Geographic Latitude [degrees]
05
1
0
1
5
2
0
2
5
3
05
1
0
1
5
2
0
2
5
3
0
23
 N
ov
em
be
r (
32
7)
 2
00
5:
  6
30
.0
-n
m
 H
al
ea
ka
la
 / 
50
-M
H
z 
C
hr
is
tm
as
 Is
la
nd
F
ig
ur
e
6.
3:
Se
le
ct
ed
ai
rg
lo
w
im
ag
es
fr
om
C
N
F
I
an
d
C
A
SI
on
23
N
ov
em
be
r
(3
27
)
20
05
.
Im
ag
es
ar
e
pr
oj
ec
te
d
to
th
e
ai
rg
lo
w
la
ye
r
at
(n
om
in
al
ly
)
25
0
km
al
ti
tu
de
.
T
he
no
rt
h
an
d
ea
st
be
am
s
of
th
e
C
hr
is
tm
as
Is
la
nd
ra
da
r
ar
e
al
so
ov
er
la
id
by
m
ap
pi
ng
al
on
g
th
e
ge
om
ag
ne
ti
c
fie
ld
.
D
ot
s
ap
pe
ar
on
th
e
be
am
s
w
he
n
th
e
re
ce
iv
ed
SN
R
is
>
−1
0
dB
in
di
ca
ti
ng
FA
I.
A
rr
ow
s
co
ar
se
ly
in
di
ca
te
th
e
m
ot
io
n
of
th
e
st
ru
ct
ur
es
.
99
246
0
5
9
K p
B 
Ap
ex
 [k
m]
 
 
200
400
600
800
1000
I [c
ou
nts
]
2300
3300
B 
Ap
ex
 [k
m]
Universal (Local) Time [hrs]
 
 
07 (21) 09 (23) 11 (01) 13 (03) 15 (05)
200
400
600
800
1000
SN
R 
[dB
]
−20
 20
02 September
(246) 2008
CXI / CNFI
Figure 6.4: Data summary from 2 September (246) 2008. Same format as Figure 6.1 except there
are no drifts.
radar echoes occurring at 2250 HST. Bubbles begin to emerge around the time of the last all-sky
image at 2340 HST. The bubble-like features between 200◦ and 202◦ are actually propagating to
the southwest with a wavelength of about 150 km. At 0015 HST, both the plasma bubbles drifting
to the east and the MSTID drifting to the southwest are visible in the same image. The bubbles
grow in altitude (and latitude) and continue to drift east throughout the remainder of the night.
In Figure 6.1, there appears to be a break in the backscatter, which is indicated by the dashed
line in the center panel. This coincides with a shear in the drift velocity as the depletions grow
into a region still affected by the MSTID instability. As the drift slows, secondary structures grow
on the eastern walls of the depletions which are particularly evident in the 0216 HST frame from
Figure 6.3.
Figure 6.4 illustrates the summary data for 2 September 2008. This night exhibits a bottom-type
layer that formed at 2200 HST but did not yield any plumes before decaying around 2330 HST.
In our experience, bottom-type layers never re-form after descending in altitude. This has also
been confirmed by Hysell and Burcham [1998]. However, at 2345 HST, coincident to the passage
of an MSTID in the airglow (indicated by arrows), a packet of depletions emerges along with the
attendant backscatter. Although they are not evident in the keogram, these depletions are visible in
the airglow frames (not shown). Most of the backscatter disappears in conjunction with the lowering
(brightening of the 630.0-nm emission) of the ionosphere around 0300 HST.
100
6.3 Discussion
The event from 2 September 2008 is interesting because the MSTID structure continues in the airglow
until the backscatter vanishes. This is in sharp contrast with the 23 November 2005 example in which
the equatorial irregularities not only grow to high altitudes (latitudes), but the MSTID introduces
a shear in the drift, apparently allowing the cascade to smaller-scale irregularities to continue until
after the radar stopped collecting data at 0600 HST, which is 15 minutes before sunrise at the
CXI site. Although it does not alter the distribution of irregularities, the descent of the ionosphere
at 0300 HST on 2 September 2008 (Figure 6.4) appears to quench the cascade to smaller scales,
corroborating the assertion of Saito et al. [2008].
Among the most compelling recent theories for the initiation of equatorial plasma depletions
just after sunset is a fast-growing mode operating on perturbations with westward-tilting wavefronts
(with maximum growth rate at 45◦) in the equatorial plane put forth by Kudeki et al. [2007]. A
polarization electric field Ep associated with an MSTID structure such as those at 2340 and 0015
HST in Figure 6.3 can drive an Ep ×B drift with westward-tilting wavefronts when mapped to the
equator. This relationship is illustrated in Figure 6.5.
Ep
BVp
Magnetic North
Altitude
Magnetic East
Off-Equator F region
Equatorial F region
bottom side
MSTID
Figure 6.5: A schematic of polarization electric fields (Ep) within a mid-latitude structure driving
a perturbation (via Vp) at the equator.
The (projected) length-scale presented here for 23 November 2005 differs from those suggested
by Kudeki et al. [2007] as providing maximal growth in the post-sunset period (240 km versus 40 km).
And, asKudeki et al. [2007] point out, the collisional-shear instability presented byHysell and Kudeki
[2004] has a similar growth rate to the 240-km wind-driven instability. Although this particular
instability may no longer operate due to the fact that the F -region dynamo constrains the neutrals
and plasma to move at the same rate, the MSTID can generate vertical velocity perturbations on
the order of 80 m/s, which are sufficient to destabilize the equatorial ionosphere. On 23 November
101
2005, the spacing of the depletions is identical to the projected wavelength (240 km × cos 50◦ ≈
150 km, where 50◦ is the angle of MSTID propagation with respect to the magnetic equator) of the
fine-scale MSTID bands indicated at 2340 HST in Figure 6.3, lending credence to this theory.
The principle contribution of this work is to illustrate that seeding of Rayleigh-Taylor instability
responsible for the ultimate growth stage of equatorial plasma depletions need not be the sole
providence of a particular process; rather, the title goes to the highest bidder. That is, the bottom-
side F -region gradient is susceptible to the Rayleigh-Taylor instability for much of the night. In the
hours just after sunset and during periods of peak depletion activity, irregularities growing out of the
evening vortex region are the fastest-growing, and therefore most likely seeds. Later in the evening,
when the ionospheric current system has approached steady state with the F -region dynamo firmly
in control, perturbations may be created by electric fields mapped in from off-equatorial sources.
There are at least a half-dozen more examples of coincident mid-latitude and equatorial events in
the data from November and December 2008 alone. This suggests that these events may be quite
common at solar minimum.
That depletions may be triggered by off-equator processes also underscores the practical im-
portance of understanding the ionosphere at middle latitudes from a space weather perspective.
Scintillations associated with equatorial plasma depletions have negative effects on the availability
and accuracy of satellite-based communication and navigations systems. Users of these systems
would benefit from enhanced prediction and mitigation schemes.
6.4 Conclusion
In this chapter, we have examined two examples of post-midnight equatorial plasma depletions initi-
ated by polarization electric fields from a mid-latitude process mapped into the equatorial ionosphere,
as suggested by Tsunoda [2007]. Airglow images in conjunction with VHF coherent backscatter pro-
vide a four-dimensional (three spatial, one temporal) picture of the initiation of many post-midnight
equatorial plasma depletions observed during quiet periods.
102
CHAPTER 7
CONCLUSION AND FUTURE DIRECTIONS
7.1 Contribution
7.1.1 Data presentation and analysis
The primary aim of this work is to develop synergy between data sets from radio and optical in-
struments, leveraging their strengths and mitigating their weaknesses to understand the physical
implications of the data. Radio instruments excel at providing high-resolution range data through
phase-coherent detection. However, their coverage is generally limited to a narrow beam/ray region.1
Airglow imaging provides considerable information on the two-dimensional (horizontal) spatial struc-
ture at ionospheric altitudes. However, it lacks information on the detailed irregularity structure
and the range. Combination of data from imagers and radars permits the small-scale irregulari-
ties to be contextualized within the larger-scale structures. Combination of data from imagers and
GPS occultation receivers can approximate the location of scintillation-causing irregularities in three
dimensions.
7.1.2 Physics
Three physics contributions have been made in this work. The first is to establish the location of
scintillation-causing regions in three dimensions using radio occultation and airglow imaging. The
second contribution is the long-term climatology of equatorial plasma depletions and the associated
backscatter in the central Pacific using airglow observations from Maui and coherent-scatter radar
observations from Christmas Island. The third and perhaps most significant contribution is evi-
dence of a mid-latitude seed for equatorial plasma depletions that occur post-midnight during quiet
geomagnetic conditions at solar minimum.
During the course of the climatology created using airglow observations from Hawaii and backscat-
ter from Christmas Island, an anomalous post-midnight peak in depletion/backscatter activity was
1Although this restriction has been relaxed considerably by the AMISR systems and radio tomography tech-
niques, there is no significant AMISR installation at middle or equatorial latitudes and tomography requires sufficient
instrument density, which is only recently coming to fruition for long-term observations.
103
Bottom-Type Layers Bottomside Plumes Topside Plume
Stable
Stable
Stable
Mapped E-field Plume
Tim
e since Sunset
Evolution of Irregularities
Figure 7.1: Flow-chart showing the interaction between potential seeding mechanisms for equatorial
plasma depletions.
discovered during November–January during solar minimum. Further investigation yielded an inter-
esting coincidence between mesoscale traveling ionospheric disturbances (MSTIDs) and the forma-
tion of depletions and backscatter post-midnight during geomagnetic quiet conditions. Polarization
electric fields within the MSTIDs drive an E × B drift as the the fields are mapped to the ge-
omagnetic equator. This suggests an alternate seeding method for equatorial plasma depletions
by MSTID structures propagating to low-latitudes. Figure 7.1 illustrates the present post-sunset
seeding theory along with the middle latitude seeding theory put forth in Chapter 6.
7.2 Future Directions
There are two primary areas where this work could be expanded, one in the physics, and the other in
data processing. Although evidence of mid-latitude seeding of equatorial plasma depletions has been
presented, it is mostly a by-product of the analysis techniques at this stage. A more-detailed descrip-
104
tion of the physics would be compelling, although it could perhaps form another dissertation in and
of itself. The 2-D inverse-scattering solution for GPS radio occultation presented by Sokolovskiy
et al. [2002] and discussed in Chapter 2 was not reproducible on coincident airglow observations
discussed in Chapter 4 using standard quadrature integration techniques. This continues to be an
area of potentially fruitful study because it would provide a complete picture of scintillation-causing
irregularities.
7.2.1 Seeding of depletions
There are several more examples of coincidence between MSTID events and the appearance of
equatorial plasma depletions in November and December of 2008. At least one of these examples,
29 November (334) 2008, coincides with the passage of the C/NOFS satellite in the vicinity of Maui
and Christmas Island. CORISS radio occultation profiles for this event, depicted in Figures 7.2a–c,
suggest considerable structure in the equatorial ionosphere at this time, including what may be Es
layers.
Each of Figures 7.2a–c exhibit negative ne over a range of altitudes, particularly up to 200
km. This suggests a gross violation of spherical symmetry. Figure 7.2b not only shows structure
apparently in the E region, it also has jagged structure along the topside portion of the profile.
Although there is coherent backscatter, there is very little L1 scintillation (not depicted here). This
suggests that the structure may be the result of an MSTID structure possibly associated with an
E-F coupled instability as suggested by Cosgrove et al. [2004]; Otsuka et al. [2009]. Further work
on the geometry of the occultation, as well as complementary data sets from the ground and in situ,
may aid complete identification of MSTID structures in radio occultation profiles.
Another important consideration is the growth rate of perturbations caused by electric fields
mapped to the equator from MSTID structures. The differential velocity between the plasma drift
and the neutral wind is an important contributor to the instability suggested by Kudeki et al. [2007].
Since the F -region dynamo should be in control of the equatorial ionospheric current system by local
midnight, this differential velocity would be approximately zero. This suggests that there may be
more to the mid-latitude seeding of depletions than simple E perturbations.
7.2.2 Inverse scattering and radio occultation
As mentioned previously, the work of Sokolovskiy et al. [2002] was not reproducible for comparison
with the irregularity location technique presented in Chapter 4. In brief, this inverse scattering
105
(a) CORISS Radio Occultation Profile - prn 26 - 29 November 2008 - 1136 UT
(b) CORISS Radio Occultation Profile - prn 12 - 29 November 2008 - 1317 UT
(c) CORISS Radio Occultation Profile - prn 9 - 29 November 2008 - 1321 UT
Figure 7.2: Three electron density profiles retrieved from C/NOFS Occultation Receiver for Iono-
spheric Sensing and Specification (CORISS) from the central Pacific on 29 November (334) 2008.
These profiles were produced from the sub-orbital TEC assuming spherical symmetry. See text for
discussion. Figures were provided by Rebecca Bishop and Paul Straus.
106
technique utilizes the SNR and excess phase data from radio occultation measurements to deduce
samples of the complex field scattered by a thin phase screen. One of the principal errors was that
any variation in the received signal amplitude or phase would result in the same solution for the
phase screen location. That is, for a given orbit geometry and the projection into two-dimensions,
any varying complex input signal produced the same phase-screen solution. However, employing the
same technique with the two-dimensional modeled data in Chapter 2 was invertible for the phase
screen locations. This suggests that the projection to two dimensions (from four—three spatial and
one temporal) may have deleterious effects, particularly when the occultation is not particularly
planar.
The scattering problem is quite computationally intensive, especially if a three-dimensional for-
ward model was created to study the effects of projecting to fewer dimension to reduce computational
complexity. One approximation that may be attractive has been presented by Chaubell et al. [2009].
Furthermore, few high-rate 50-Hz occultation examples exhibiting significant scintillation and
significant common volume with the airglow imagers were available for comparison. This should be
rectified with the continued success of the COSMIC/FORMOSAT-3 mission and the possibility for
50-Hz burst mode data on CORISS.
107
APPENDIX A
DATA MANAGEMENT WORKFLOW
A.1 Introduction
This work utilizes data from ground- and space-based airglow imaging systems, ground- and space-
based GPS receivers, and radar systems, as well as models written in FORTRAN. In this chapter,
I outline the workflow used to manage all of these data in a sensible manner.
A.2 Overview
Figure A.1 illustrates the flow of data. Incoming data transit our file server (airglow) as a point
of entry. From there, they are archived and pushed off to other locations for analysis since the file
server does not have sufficient resources to support many analysis sessions. I assembled an 8-node
MOSIX cluster (esf) using surplus workstations from the dormitories for my analysis [Barak et al.,
1993]. The MOSIX environment simulates a symmetric multiprocessing system (SMP) similar to
those supported by modern multi-core processors. This type of cluster is ideal because most of
my analyses are codes that run relatively quickly on a small portion of the data set, but take a
long time when analyzing the entire data set. The codes need not be specifically parallelized in the
same sense that a large weather model might be for a supercomputer. Rather, multiple processes
can be launched and the MOSIX scheduler simply migrates them from node to node for optimum
performance.
108
PERL PERL
Instrument
Data Product Data Product
Instrument Instrument
Data Product
MATLAB
txttxt bin bin/txt
Excel/Gnuplot
Mac OS X Preview Adobe Illustrator
MATLAB
PERL
EPS+PDF
PNG EPS
IDL
Instrument
Data Product Airglow (airglow.csl.uiuc.edu)
MacBook (epb.csl.uiuc.edu)
Cluster (esf.csl.uiuc.edu)
text filematfile
FORTRAN
codes via 
mex interface
Figure A.1: Workflow developed to manage the data presented in this dissertation.
109
APPENDIX B
A CASE STUDY IN FIELDING
INSTRUMENTATION
B.1 Introduction
The purpose of this appendix is to outline the process required to field instrumentation in a remote
location. The instrumentation suite has already been selected: a dual-frequency GPS receiver and
an all-sky airglow imaging system. Although the goal of the research at the Bonaire site is not
directly related to this dissertation, it is an interesting case study because it was not conducted
in conjunction with a university or another research organization. This introduced both challenges
and opportunities. One aspect that will come up again and again is the power of knowing peo-
ple. It is also instructive because, as of this writing, the system represents the state of the art in
portable ionospheric observation. The following topics will be discussed: selecting the site, preparing
the equipment and related hardware, transporting the instrumentation, and installation and data
collection.
B.2 Site Selection
In the case at hand, the instruments needed to be located somewhere in the southwestern Caribbean
since there was already a planned group of instruments in the southeastern Caribbean (Trinidad
and Tobago). This left basically four choices: any of the three ABC (Aruba, Bonaire, Curac¸ao)
islands of the Netherlands Antilles, or one of the coastal islands of Venezuela. Due to the stormy
political situation between the U.S. and Venezuela, it was deemed unsuitable out-of-hand. West to
east, Aruba, Curac¸ao, and Bonaire, each have very different character. Aruba is well known in the
U.S. as a tourist destination and Curac¸ao is becoming more well known for tourism and as a center
of commerce in the region. Bonaire is relatively lesser-known in the U.S. outside diving circles and
has substantially lower population than the other two islands. Correspondingly, Bonaire is the most
rural and has the least light pollution. The Bonaire community is also very eco-concious. In fact,
the entire coastline of the island is a protected marine habitat. This suggested that it would be a
good location.
110
There is one primary difficulty with Bonaire, as well: getting power. An initial visit to Bonaire
made that clear. The best locations on the island do not have power available. I had some contacts
among amateur radio operators who own homes on Bonaire, as well as several who visit there
regularly (Hans van Hese, Noah Gottfried, Jeff Clarke, and Scott Robbins, personal communcation).
These conversations suggested that most of the places with electricity would also have many lights.
None of their properties were suitable for the installation. There was one option on a hill called
Seru Largu in the northeast part of the island. Seru Largu hosts some of the communication (Telbo)
and navigation (Antillean Coast Guard) equipment for the island and so would provide a nearby
power drop. The Seru Largu location was accessible by road, as well, although it would require us to
provide our own secure enclosure for the equipment. I pursued the idea of installing the equipment
in a 20-foot sea container, which is readily available from Amcar Freight in Bonaire (Scott Robbins
and Sue Felix, personal communication). The next step was to obtain a lease for the land.
In Bonaire, there are three types of land rights: outright ownership, short-least land, and long-
lease land (Hans van Hese, personal communication). Most of the privately held land is in housing
developments that are unsuitable for our instruments due to the surrounding light sources and
other view obstructions. Short-lease land is difficult and expensive to obtain and tends to be used
for business purposes. Long-lease land, however, was an attractive option: a few dollars per m2
per year. Most of the hilltop at Seru Largu is long-lease land, so this would work. However, in
preparation for a change in the administration of the Netherlands Antilles, the land office was being
audited. There were so many poorly documented or undocumented land transfers that the process
was held up at least two years for new applicants (Scott Robbins and Hans van Hese, personal
communication). This suggested that an alternative would be attractive.
We started working another angle: find the most suitable site capable of alternative power. Two
sites that I had driven past but not contacted were a butterfly farm and the Bonaire Washington-
Slagbaai National Park (part of the Antillean national park system STINAPA). The butterfly farm
was not responsive. The Washington-Slagbaai staff were not keen on the idea of installing the
instruments and related power generation equipment on Park land. However, Fernando Simal (per-
sonal communication), the manager of the Park, put us in contact with several individuals who own
property in the rural parts of the island. The most receptive of these were Alan Gross and Jane
Townsend, who own about 30 acres in the Bolivia region of eastern Bonaire. Figure B.1 illustrates
the location of the prospective sites.
111
Figure B.1: Composite satellite photograph of Bonaire showing the proposed instrument locations.
The site marked “Alan and Jane” was the final location for installation.
112
!" # $ %
& ' (
)*+!,-./01
23456-1
78*606/39!#
)*+:;<=
236-=33>:8?
@-=
*A/6BC
;DD:#
;DD:"
E/16-.AC--1:B396.311-.
8
F*
8
F*
??D
?331/9G:E09,
E/16-.AC--1
Figure B.2: Schematic of the complete instrument package installed in Bonaire.
Alan and Jane’s entire homestead is powered by solar electricity. Initial measurements of the
PICASSO (S/N A2) imager system with an SBIG CCD, the IBM ThinkPad R60 notebook computer,
and the modified NovAtel GPStation-2 receiver, yielded a power requirement of about 80 watts
during the night and around 40 watts during the day when the CCD was switched off. This exceeded
the projected capacity of the present system. In order to support the additional load, a Whisper
200 wind generator was installed1 prior to the installation of the equipment.
B.3 Equipment Preparation
The center of the instrument package is a notebook computer running a GNU/Linux operating sys-
tem. This system controls the instruments and collects the data. The imager CCD and filterwheel
are controlled via USB interface by CDAS (camera data acquisition software) written by Jonathan
Makela. The GPS receiver is controlled by GPS-SCINDA software from Atmospheric and Environ-
mental Research (AER). Scheduling is handled by the cron daemon and CDAS. Figure B.2 shows a
schematic of the complete system with all components. A hard plastic toolbox serves as a convenient
and readily available housing when a 12-inch acrylic optical dome is installed in the lid, as shown
in Figure B.3.
1The logistical saga surrounding the purchase, installation, and ownership of the wind generator is not discussed
here.
113
Figure B.3: Photograph of the inside of the equipment housing.
When this set of instruments was originally installed in Socorro, NM, Fedora Core 1 GNU/Linux
(2.4 kernel, released in 2003) was installed for compatibility with the Finger Lakes Instruments
filterwheel. Since both the Santa Barbara Instrument Group (SBIG) and Finger Lakes Instruments
(FLI) had released new software for their products, and for compatibility with the USB to RS-232
convertor used by the GPS, it was decided to move to a more modern 2.6-series Linux kernel. The
Xubuntu 8.04.1 LTS GNU/Linux distribution was selected for this installation because it offers
long-term binary support, low graphical overhead, and an easy-to-use interface. The specific details
of the software installation are chronicled electronically with the CDAS software.
The USB interface in the SBIG CCD requires firmware to be downloaded into it every time
the power is cycled. This is accomplished through the Linux udev system, which allows system
commands to be executed on hot-plug events. Both the CCD and the filterwheel are configured to
be accessible to unprivileged users by udev, as well. All of the USB devices are connected by way of
a powered USB hub. The powered hub also allows two external hard drives which are powered via
USB to be attached to the bus without exceeding the power capacity. These drives are configured
to automount and are synchronized daily by rsync.
As illustrated in Figure B.2, power is distributed using a Digital Loggers web power switch. This
device has eight power outlets that are switchable through an embedded world-wide web server. For
the purpose of automation, a Perl script on the computer automatically connects to the web server
to switch outlets ON and OFF. This allows the CCD and filterwheel to be turned OFF during the
114
Table B.1: List of Tools and General Consumables Required for PICASSO/GPS Installation
Tool Application
Leatherman Tool General
Digital multimeter Electronic and electrical troubleshooting
Solder iron and solder Electronic repairs and modifications
Hacksaw blades Cutting holes for dome, cables, and ventillation
Cordless drill and bits∗ Drilling holes and driving screws
Interchangeable screwdriver∗ Driving screws, prying, bits fit in drill
Wrench∗ (4- or 6-inch adjustable) Tightening machine nuts
Hex wrenches Imager adjustments
Flashlight Finding your way in the dark
8-32 stainless machine screws Mounting dome and electrical box
#6 drywall screws Securing wooden shelf
1/4-inch Tapcon R© screws Mounting instruments to concrete
1/4-20 hex bolts Mounting housing to pylons
Unistrut pylons Mounting housing above concrete surface
1/4- x 1-inch fender washers Tapcon screws and Unistrut mounting
Cauk dispenser† and silicone cauk† Sealing the dome and other joints
11-inch Ty-wraps Anchoring cables, fans, etc
Electrical tape UV-/weather-proofing, masking, general
Heavy-duty hook and loop fastener sticking small peripherals to the walls of the enclosure
Duct tape General
Permanent marker General
∗Items were provided by host in Bonaire.
†Items were purchased on-site in Bonaire.
day to conserve electricity. Two fans are installed to move air through the enclosure for 5 minutes
every 15 minutes.
Table B.1 lists basic tools and consumables used in the installation of the imager and GPS. The
local availability and quality of these items varies dramatically from place to place. It is, therefore,
wise to ship these items ahead of time. It is also beneficial to mark the circular hole for the dome
with a compass before the box is transported into the field. White paint or correction fluid usually
suffices in this application.
The final important step before shipping an imaging system is to determine and set the focus
point in the laboratory. This is accomplished by coupling a tungsten light source into a single-mode
fiber optic cable and focusing the camera on the spot of light at the unterminated end of the fiber.
Introducing the dome into the optical path slightly perturbs the focus point on a PICASSO imaging
system. Therefore, it is important to perform the focusing with the dome in-line as well as without.
The focal point with the dome in-line is recorded and the focusing stage locked with a hex wrench
for transport.
115
B.4 Transportation
The PICASSO system moves in two packages. One is the primary container, a Pelican 0350 flight
case, which contains the instrumentation and computer. The second package serves as the housing
and contains the GPS antenna and mast, the optical dome, and miscellaneous hardware that may
or may not be available at the destination. Ordinarily, when working with a host institution, it
is a simple matter to ship all of the equipment and the host will either provide a customs broker
(as was the case with the instruments installed at Cerro Tololo, Chile) or negotiate directly with
Customs (as was the case with the Trinidad and Tobago installation that complimented the Bonaire
instruments). We did not wish to be in the position of paying a high duty or “fast money” as has
been done in Brazil [Ledvina, 2004]. The Bonaire Customs procedures are not uniform, although
they tend to protect locally produced goods (Alan Gross, Hans van Hese, Geoff Howard, personal
communication). At the suggestion of Alan Gross (personal communication), we decided to secure a
carnet (essentially, a merchandise passport) for the equipment. This was confirmed by Mr. Ludwig
Balentien of the Customs office in Bonaire (personal communication). Most standard international
courier services such as FedEx and UPS do not allow the use of carnets. So, the main container
of instruments would be transported as checked baggage. Only the container of hardware was
shipped by courier. At this writing, FedEx has the most reliable international logistics model of any
courier, using local subcontractors to navigate the delivery-end environment (Dan Jordan, personal
communication). This was confirmed by Alan Gross. The package arrived in Curac¸ao less than 24
hours after it was picked up; however, it took a week to get to Bonaire.
The carnet was straightforward to obtain from the U. S. Council for International Business. It
cost about 500 USD and took two business days to arrive with standard processing. The carnet
must be validated by U. S. Customs at the port of exit. This is important. I tried to do this
before my port of exit and was refused. The validation process only takes about 20 minutes once
the equipment is in the Customs area. When checking in for the departure flight, tell the airline
representative that you would like to claim the containers covered by the carnet at the port of exit
because it needs to clear Customs leaving the U.S. If baggage porters are available, they are worth
whatever you pay them to get you to the Customs area, which may or may not be readily accessible
from the insecure zone of the airport. You should not have to pay the excess baggage fee again if
you are continuing on the same airline under the original itinerary. The Customs officer in Bonaire
immediately spotted the flight case and demanded an explanation. When I produced the carnet
document with a U. S. Customs seal on it, he was instantly satisfied and waved me through. This
116
may or may not be representative of other countries.
B.5 Installation
B.5.1 Overview
No installation is typical. However, a typical plan of attack follows:
• Survey the site visually for light sources and view obstructions.
• Select the best position for the instruments.
• Assess needed supplies and (optionally) obtain them from a hardware store.
• Prepare the instrument housing by cutting holes for:
– Dome
– Cable inlet (mount an outdoor electrical box on the surface of the enclosure)
– Ventillation (cover holes with fine fiberglas/plastic mesh)
• Install shelves for imager and computer, studs for web power switch.
• Install dome, fans, and electrical box.
• Seal dome and electrical box with silicone caulk.
• Mount instrument housing (see discussion following this plan).
• Connect and install instruments within the housing.
• Assess image quality:
– Focus
– Light pollution
– Dark noise
• Operate the system for a period of nights.
• Train local host on maintenance and data transport.
117
B.5.2 Specific details
Although much of the installation of airglow imagers and GPS receivers is fairly obvious, there are
some local idiosyncrasies that may complicate things. This section details how to work with concrete
construction, UV radiation, and salt air.
In most of the tropical and equatorial regions, concrete construction is common. In Bonaire,
the site was on top of a concrete above-ground septic tank. The GPS antenna and equipment
enclosure were installed using Tapcon R© concrete screws. These screws are very easy to install: drill
a pilot hole with the provided concrete bit, then insert the screw. In order to make the instrument
enclosure easy to install and keep it above the surface of the concrete for airflow and moisture ingress
considerations, it was mounted on four pylons made of Unistrut channel that were anchored to the
concrete, as shown in Figure B.4. These pylons also allow the enclosure to be removed from the
concrete without drilling additional holes.
Protection from UV radiation is necessary, particularly for power cables. Our host, Alan Gross,
provided some scraps of plastic irrigation tubing to use as conduits. Most varieties of Ty-wraps will
disintegrate, as well. This can be prevented by wrapping them with good quality (3M Scotch R© Super
33+) electrical tape (Geoff Howard, personal communication). Amateur radio operators who own
and maintain stations in the Caribbean are a valuable source of information about UV protection
and salt-air corrosion mitigation (e.g., http://www.pj2t.org/).
Housing
Concrete
Unistrut
Tapcon screw
Fender washer
Hex bolt
Figure B.4: Cross-sectional view of the Unistrut pylon arrangement.
118
B.6 After the Installation
There are two main tasks once the instruments have been installed and determined working: get-
ting the data and ensuring that the instruments are maintained. In the case of the imager/GPS
instruments in both Bonaire (miniature hard drives) and Trinidad (DVD+R), the data are sent
back at regular intervals by courier service. The instruments on Mount Haleakala, Hawaii, and
Cerro Tololo, Chile, are connected to high-speed Internet links. Maintenance can be a considerable
headache, particularly when the computers are not connected to the Internet. Mobile telephone and
video conferencing over a mobile Internet connection has worked relatively well in Trinidad. We
have no experience with Bonaire, as of this writing.
119
APPENDIX C
GEOMAGNETIC FIELD MODELS
C.1 Introduction
As discussed in Chapter 3, electric fields of a certain scale map efficiently along the geomagnetic
field. In order to effectively extrude electrified structures from airglow images, it is necessary to
utilize a geomagnetic field model. There are two models in use for this type of work: the Altitude
Adjusted, Corrected, Geomagnetic (AACGM) coordinate system [Baker and Wing , 1989] and the
International Geomagnetic Reference Field (IGRF) [Maus et al., 2005].
AACGM was primarily designed for high-latitude work as a part of the SuperDARN radar
project. It gives each geomagnetic field line a unique latitude-longitude pair. Although questions
have been raised in the past about the efficacy of AACGM at equatorial latitudes, the field coefficients
of AACGM are no longer actively maintained. IGRF aims to be an accurate specification of the
geomagnetic field and its variation with time. This goal is subtly different from AACGM: IGRF
requires the field line to be traced in order to find points on the same field line. In this appendix,
we briefly explore the relative errors involved in using AACGM versus IGRF as well as changing
step sizes for tracing along the field line.
C.2 Step Size Study
In order to trace a field line, an initial point (δ,λ, z), a step size, step direction (via the sign of the
step size), and the stopping altitude are provided. IGRF provides the magnetic field direction. The
next point is determined by creating a segment of the length of the step size in the direction of the
field. This process is iterated until the stopping altitude is reached.
Figure C.1 compares the absolute error with respect to a standard 100-m step size for the case of
mapping the CXI north beam range gate centroids to the airglow layer at 250 km. The choice of 100
m was largely arbitrary and dictated by computation time. At the equator, one degree of longitude
is approximately equal to 111 km. One degree in latitude is approximately the same at the equator
and drops to about 100 km at 25◦ latitude. Clearly, the largest errors are in latitude. However, they
120
only reach 25 km in the worst presented case (50 km steps) and 5 km in the second-worst case. For
the purpose of this dissertation, a step size of 1 km has been used with the CXI beams.
0 0.05
0
0.05
0.1
0.15
0.2
0.25
500 m
N
 G
e
o
g
ra
p
h
ic
 L
a
ti
tu
d
e
 [
d
e
g
]
0 0.05
0
0.05
0.1
0.15
0.2
0.25
1000 m
0 0.05
0
0.05
0.1
0.15
0.2
0.25
5000 m
E Geographic Longitude [deg]
0 0.05
0
0.05
0.1
0.15
0.2
0.25
10000 m
0 0.05
0
0.05
0.1
0.15
0.2
0.25
50000 m
Figure C.1: Comparison of the error with respect to 100-m step size for steps of 500 m, 1 km, 5 km,
10 km, and 50 km, when mapping CXI north beam range gates to 250 km.
C.3 IGRF vs AACGM
This section highlights the absolute error between AACGM and the 100-m step IGRF trace used
in the previous section. For comparison, the range gate centroids of the CXI north beam were con-
verted from geographic coordinates to AACGM. The resulting magnetic coordinates were converted
back to geographic coordinates using a fixed altitude of 250 km, again the nominal location of the
airglow layer. The latest AACGM epoch 2000 coordinates are compared to IGRF in 2005, which is
representative of the application in this dissertation.
Figure C.2 illustrates that the AACGM error is quite large, on the order of 25 km at some
points. However, AACGM is much faster than IGRF, so this error has been tolerated with some of
the airglow image maps, which have on the order of 103× more points, in the interest of reduced
computational complexity. An adaptive IGRF tracing function might be beneficial to expedite this.
121
!!"# ! !"#
!!"$
!!"#
!!"%
!
!"%
!"#
!"$
!"&
'()*+,-./012(3+4,1567*(87*,9
:
()
*
+
,
-.
/
0
12
(3
.
51
56
7
*
(8
7
*
,
9
;;<)=(>?(@)AB(C#!!D"!E
Figure C.2: Comparison of the error with respect to IGRF tracing with 100-m step size to AACGM,
when mapping CXI east (solid curve) and north (dashed curve) beam range gates to 250 km.
122
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AUTHOR’S BIOGRAPHY
Ethan Schofield Miller was born and raised in Millersburg, Ohio. He was first exposed to electrical
engineering while sitting on his father’s lap as he wrote BASIC code on a HeathKit H-8 micro-
computer. Although he was later fascinated by construction work, automobiles, and airplanes, he
eventually came back to electronics. His work has varied from building mobile robot cleaning devices
to fabricating and evaluating 110-GHz interconnects to tracking insect pests with harmonic radar.
Ethan married Sarah in 2005, and they both began pursuing graduate degrees at the University
of Illinois. His most recent work on remote sensing of the ionosphere has been motivated by a
long-standing interest in amateur radio, as well as a keen interest in configuring instrumentation
and making sense of data. After graduation, he will be employed by the Johns Hopkins University
Applied Physics Laboratory in the Atmospheric and Ionospheric Remote Sensing group.
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