GPS derived TEC Measurements for
Plasmaspheric Studies: A Tutorial
and Recent Results
Mark Moldwin
LD Zhang, G. Hajj, I. Harris,
T. Mannucci, X. PI
GPS Orbit
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28 Satellites
55º inclination orbit
6 orbital planes
4.2 RE orbit
2 radio signals
Measurements from GPS
• Dual Frequency f1 and f2
-gives pseudoranges P1 and P2 and Phase
information (pseudo due to offsets in clocks
and ionosphere/plasmasphere)
• Single freq GPS is what is used for civilian
receivers to give you position (or accurate
time).
...
2
1
Earth
• Multiple ground stations can 6-8 GPS sats at a time
• 10 second cadence
• For limited areas of Earth have dense arrays and able to
make global ionospheric/plasmaspheric TEC maps
• Data Assimilation and Tomography possible
Global TEC Maps
Sparse Ground-based Coverage
Relative Contribution to TEC
LEO-GPS TEC Measurements
• Global Coverage due to dozens of satellites
with dual frequency receivers
• Can be used to measure the ionospheric and
plasmaspheric contribution to TEC
• Data can be ingested into same algorithms
developed for ground-based TEC studies
LEO-GPS Technique
• Dozens of current and future LEO satellites with
dual-frequency GPS receivers (Topex, GPS/MET,
GFO, CHAMP, SAC-C, JASON-1, GRACE,
COSMIC, NPOES etc.)
LEO-GPS Technique
G PS 1
Elevat ion
G PS 2
LEO
Ionospher4e
Horizon of LEO
Earth
Ionosphere
• LEO sats have
different antennas to
look up fore and aft
• Hundreds of
occultations per day
LEO-GPS comparison with Ionosonde
Jakowski et al
PCE-C, 2001
LEO-GPS Results
3D Global Modeling
• We can go beyond TEC maps due to the
large number of receivers and individual ray
paths.
• Can do tomography and data assimilation
techniques to develop a time-dependent 3D
global model of the plasma density within
the GPS orbit (4.2 Re)
...
2
1
Earth
• 6-10 ray paths per LEO satellite
• 10 second cadence
• Advantage over ground is global coverage (though less
dense coverage)
• Data Assimilation and Tomography possible
Data Assimilation and Tomography
In tomography, the ionosphere or plasmasphere is divided
up into finite elements of appropriate shape. A TEC
measurement, j, is related to the density in each element
via the equation
TECj 
N
 n(r )d   n h
i
ij
i 1
(1)
where the integral is along the line-of-sight, and n(r) is the
electron density at a point r along the ray path. The
integral is discretized and written as the sum over all
volume elements (or “voxels”), with ni corresponding to
the average electron density at voxel i, and hij
corresponding to the length of ray j in voxel i.
Equation (1) can be written in matrix form as
(2) TEC Hxe n
where TEC is a vector containing the individual
measurement values, x is a vector containing the unknown
state parameters (electron density in a voxel), H is an
“observational” matrix geometrically relating the
measurements to the state, and e and n are the
measurement and “representativeness” noises
respectively. The latter reflects error incurred by the
discretization process.
Data Assimilation
Equation (2) is ill-posed due to wide and irregular spacing.
Data Assimilation combines a priori knowledge of the
plasmasphere state at a given time, it’s a priori covariance
matrix with new observations.
Global Assimilative Ionospheric Model (GAIM) [Hajj et al.
2000] starts with a model and iterates until the difference
between the model and all observables is minimized.
Solution not unique - but with a large number of observations
with good spatial coverage (and a good starting model - either
empirical or physics-based) can converge to a robust solution.
Kalman Filter
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Powerful Way of Assimilating Data into a TimeDependent, Physics-Based Model.
Performs a Recursive least-Squares Inversion of all
Data Types for Ne Using the Physics-Based Model as a
Constraint.
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It has the least Expected Error Given the
Measurements, Model, and Error Statistics.
GAIM's Approach
GAIM uses a Physis-Based Ionosphere-Plasmasphere
Model as a Basis for Assimilating a Diverse Set of RealTime (or Near Real-Time) Measurements. GAIM will
Provide Both Specifications and Forecasts on a Global,
Regional, or Local Grid.
UCLA-JPL Approach
• Combine LEO-GPS TEC measurements
with ULF mass density observations and
IMAGE EUV data
• IMAGE EUV gives us plasmapause
location and dynamics
• Create a global 3D mass and number
density model
Webb and Essex
Hardware Bias
Conclusions
• LEO-GPS possible new data source for near-real
time monitoring of plasmaspheric density.
• Expands ground-based TEC measurements.
• Coupled with ULF techniques and IMAGE EUV
the most complete sampling (in time, space, and
plasma parameter space) to date.
• Potential for first time dependent global model of
inner magnetospheric density.