1. Ionospheric TEC Gradient Magnitude Distribution over the Brazilian Airspace
Patricia Doherty, Rezy Pradipta and Endawoke Yizengaw
Institute for Scientific Research
Boston College
Image Source:
AGU 100 Fall Meeting Washington, DC December 2018
SA12A Multiscale Ionosphere Structuring Processes and Related Impact on Technology 1

2. The Roles of SBAS/GBAS in Civil Aviation
SBAS/GBAS Benefits
Enabling precision approach at all runways
Increasing safety
Increasing capacity
Reducing delays
Reducing equipment cost
SBAS/GBAS Challenges
Large ionospheric gradients
Scintillation
Demand for Air Travel continues to increase. Aging ground-based radio navigation aides cannot keep up…. ICAO has committed to advancing satellite based navigation.

3. Outline and Summary Ionospheric threats to SBAS/GBAS operations
- midlatitude scenario: storm-enhanced density during geomagnetic storms
equatorial scenario: equatorial plasma bubbles (TEC depletions) at night; scintillation
Studies of large TEC gradients over the Brazilian sector in : representative examples
large TEC gradients due to steep side walls of equatorial plasma bubbles
large TEC gradients due to density irregularities inside equatorial bubbles
Statistical distribution/properties of TEC gradient magnitudes over Brazil in
TEC gradient magnitudes can reach ~1000 mm/km at L1 frequency
2x size of gradients seen in the CONUS SED events
TEC gradient magnitudes follow a power law distribution (a peculiar one)
Compare TEC gradient magnitudes with a scintillation proxy (ROTI)

4. SBAS and GBAS Systems
Play an important role in aviation safety to ensure the accuracy, availability and integrity of navigation information
Broadcast correction messages – allowing navigation and control systems to take ionospheric delays into account for precise positioning calculation
Steep ionospheric gradients and scintillation can threaten these systems
SBAS – Wide-area or regional scale
GBAS – Localized/airport service
(Figures:

5. Midlatitude Threat: Storm-Enhanced Density
Nominal upper bound for CONUS during SED: ~425 mm/km at GPS L1 frequency
Quiet time TEC gradients for CONUS: ~40mm/km or lower
On the average, 30 geomagnetic storms per year, where 30% of them are major geomagnetic storms
(Refs: Datta-Barua et al., 2010; Lekshmi et al., 2011)

6. Low-latitude Threat: Equatorial Plasma Bubbles
Seen as depletions in TEC.
Bubbles of different shapes and sizes.
(Pradipta et al., 2015)
(Pradipta et al., 2015)
EPBs are seeded at the bottom layer of the ionosphere, then plumes of low density plasma rises upward
Gradients can come from the side walls and the irregularities inside the bubble
EPBs can occur night-after-night for the duration of several months
Aircraft can sample much different ionosphere in the vicinity of a bubble

7. GPS Receiver Locations and Timespan of the Study
GPS receivers located in between the geomagnetic equator and -20o geomagnetic latitude
Nighttime TEC gradients most severe in this area
Time span from (solar cycle 24)
January to March: peak season for nighttime EPBs and ionospheric scintillation over Brazil

8. The Brazil Case Study – Measuring Gradients
Two independent ways to estimate the TEC gradients:
The 1st method (station-pair method) gives us the TEC gradient values along a fixed direction dictated by the station geometry.
Advantage: instantaneous measurement of the TEC gradient;
Disadvantage: need two closely-spaced receiver stations;
The 2nd method (single-station method) gives us the TEC gradient values parallel along the IPP trajectory Advantage: not constrained by the availability of station pair;
Disadvantage: intertemporal measurement from consecutive epochs;
Further disadvantage – working in equivalent vertical TEC.
TEC gradients are rather conservative. Slant TEC gradients, esp. at low elevation might be larger.

9. TEC Gradient Case Examples (1 of 2)
The sharp isolated spikes in the TEC gradient indicate that the side walls of the bubbles played the dominant role in this case
(>300mm/km)

10. TEC Gradient Case Examples (2 of 2)
Large TEC gradients due to steep side walls (A, B, C)
Smaller gradients observed inside bubble (F)
(>600mm/km)

11. Distribution Statistics of TEC Gradient Magnitudes over the Brazil (2014-2015) – early results
The TEC gradient magnitudes associated with equatorial plasma bubbles extend up to ~1000 mm/km at GPS L1 frequency.
The TEC magnitude distribution varies with season, but no apparent spatial variability across longitudes within the Brazilian sector.

12. Cumulative Distribution of TEC Gradient Magnitudes over the Brazil - 2014-2015
Follows a form of power law distribution
Exponents of the power law found via linear curve fitting
Slope of the best fit line corresponds to the power law exponent
Different exponents for two different regimes
Break at 200 mm/km
Final drop at 800mm/km
More precise physical mechanism responsible for this power law is subject of ongoing research.
(Pradipta and Doherty, 2016)

13. (double power law exhibited each year)
Distribution Function of TEC Gradient Magnitudes
(double power law exhibited each year)
2 exponents with a break between mm/km
solar cycle variation in the power-law exponents
low sunspot: more negative power law exponents/distribution falls off more rapidly
higher sunspots: less negative exponents/distribution function falls off more slowly creating a heavier tail in the gradient distribution

14. During the observations of large TEC gradients, ROTI was also high.
TEC Gradients and ROTI Comparison
Brasilia January 2013 and Nighttime
ROTI = Std Dev of the TEC time rate of change, calculated over 5 minute window
ROTI: an indicator of ionospheric plasma density irregularities that can lead to scintillation
During the observations of large TEC gradients, ROTI was also high.

15. Summary and Conclusions
Ionospheric TEC gradients associated with equatorial plasma bubbles pose threat to SBAS/GBAS
The nighttime ionospheric TEC gradient magnitudes follow a double-power-law distribution
The power-law exponents vary systematically according to the progression of solar cycles
During a max/peak of the solar cycle, TEC gradients with extreme magnitudes may occur more often
Future work: to investigate more precise origin(s) of the double-power-law behavior and to determine the possibility to possibly extrapolate to other years

16. Thank you for your attention.
Patricia H. Doherty
Phone:
Fax:
We thank the Federal Aviation Administration for support under Cooperative Agreement DTFAWA-17-C-80005
We also thank the Instituto Brasileiro de Geografia e Estatistica (IBGE) for the GPS data form the RBMC network.