On the application of meteorological data assimilation techniques to
radio occultation measurements of the ionosphere
Matthew Angling
Centre for RF Propagation and Atmospheric Research
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Ionospheric data assimilation
• To provide a high accuracy and timely specification of the ionosphere
for use in RF systems
• Increased accuracy of ground and space based trans-ionospheric
sensors
− EWR, SAR, AMTI/GMTI, satellite geolocation systems
• Improved accuracy of single frequency navigation systems
− GPS, Galileo
• Improved LPI/LPJ characteristics of HF communications
• Significant reduction in the errors for HF position finding systems
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2
Estimation
LT persistence
Forecast
Empirical
•IRI
•RIBG
•PIM
Shells
•Single
•Multiple
Non-optimal
•Profile adjustment
•Tomography
•ART, MART, etc
Physical
•Ionospheric
•Coupled
3D basis functions
•Horiz harmonics
•Vertical EOFs
3D grid
•Geographic
•Geomagnetic
Optimal
•DIT
•GMKF
•Approx Kalman
•Full Kalman
•Variational methods
covariances
Representation
No
covariances
Model
Physical
forecast
Data assimilation models
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Estimation
LT persistence
Forecast
Empirical
•IRI
•RIBG
•PIM
Shells
•Single
•Multiple
Non-optimal
•Profile adjustment
•Tomography
•ART, MART, etc
Physical
•Ionospheric
•Coupled
3D basis functions
•Horiz harmonics
•Vertical EOFs
3D grid
•Geographic
•Geomagnetic
Optimal
•DIT
•GMKF
•Approx Kalman
•Full Kalman
•Variational methods
covariances
Representation
No
covariances
Model
Physical
forecast
JPL GIM
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Estimation
LT persistence
Forecast
Empirical
•IRI
•RIBG
•PIM
Shells
•Single
•Multiple
Non-optimal
•Profile adjustment
•Tomography
•ART, MART, etc
Physical
•Ionospheric
•Coupled
3D basis functions
•Horiz harmonics
•Vertical EOFs
3D grid
•Geographic
•Geomagnetic
Optimal
•DIT
•GMKF
•Approx Kalman
•Full Kalman
•Variational methods
covariances
Representation
No
covariances
Model
Physical
forecast
IonoNumerics
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5
Estimation
LT persistence
Forecast
Empirical
•IRI
•RIBG
•PIM
Shells
•Single
•Multiple
Non-optimal
•Profile adjustment
•Tomography
•ART, MART, etc
Physical
•Ionospheric
•Coupled
3D basis functions
•Horiz harmonics
•Vertical EOFs
3D grid
•Geographic
•Geomagnetic
Optimal
•DIT
•GMKF
•Approx Kalman
•Full Kalman
•Variational methods
covariances
Representation
No
covariances
Model
Physical
forecast
USU GAIM
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Estimation
LT persistence
Forecast
Empirical
•IRI
•RIBG
•PIM
Shells
•Single
•Multiple
Non-optimal
•Profile adjustment
•Tomography
•ART, MART, etc
Physical
•Ionospheric
•Coupled
3D basis functions
•Horiz harmonics
•Vertical EOFs
3D grid
•Geographic
•Geomagnetic
Optimal
•DIT
•GMKF
•Approx Kalman
•Full Kalman
•Variational methods
covariances
Representation
No
covariances
Model
Physical
forecast
Electron Density Assimilative Model
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Electron Density Assimilative Model
• PIM used for background model
− Electrons only
• Designed to be scalable
− Can assimilate single or multiple measurements
• Low demands on computer resources
• Simple evolution
− Exponential decay of electron density grid differences
• Uses sun-fixed geomagnetic coordinate system
• Model Variances are propagated, covariance are estimated as
required
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Best Linear Unbiased Estimator
Most probable atmospheric state (xa) is obtained by modifying
background state (xb) with differences between the observation
vector (y) and the background state
xa  xb  K(y  Hx b )

K  BH HBH  R
T
T

1
xa = most probable atmospheric state
xb = a priori (background) atmospheric model
y = observations
B = background error covariance matrix
H = observation operator
R = observation error covariance matrix
K = weight matrix
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Radio Occultation
• GPS transmitter, LEO receiver
vGPS
• Global coverage with high
vertical, low horizontal resolution
βGPS
GPS
φGPS
• In the ionosphere bending angles
are small
• Estimating slant TEC from L1/L2
phase difference removes clock
and POD errors

rGPS
a
r
• Assimilation of sTEC has
v
potential to overcome limitations
of Abel Transform
lEO
• RO provides important height
information

a
βLEO
φLEO
rlEO
Earth
LEO
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foF2/hmF2 testing
• Previous study has shown that
EDAM can improved foF2
performance
• But hmF2 performance is
relatively poor
• Can RO data improve
representation of vertical
structure in EDAM?
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Assimilation tests
• Assimilations run for 19-20 August and 4, 10 September 2006
− Disturbed, moderate and quiet conditions
• Assimilate COSMIC podTEC data
− Calibrated slant TEC
− Reduced sampling rate at high elevations
− Constellation is not yet fully deployed
• Runs with just RO data, just IGS data and with RO + IGS data
• Test using vertical profiles
− ionPRF files from UCAR-CDAAC
− Abel Transform vertical profiles
− True height profiles from AFRL vertical ionosonde network
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IGS and DISS stations
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Example ionPRF vertical profile
• RMS error in electron density
calculated at 4 km intervals
• Little quality control of ionPRF
− Values must be positive
• Not comparing similar
measurements
− ionPRF is a distributed
measurement
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IonPRF RMS errors
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IonPRF RMS errors
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Example VI vertical profile
• RMS error in electron density
calculated at 4 km intervals
• Little quality control of VI profile
− Autoscaled data
− Values must be positive
• No attempt to limit VI data to that
close to RO measurements
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VI RMS errors
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VI RMS errors
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Conclusions
• COSMIC podTEC data has a positive effect on EDAM analysis
• For moderate and disturbed conditions, assimilation of podTEC
improves the electron density RMS error at all heights from 200 to
500 km
• The interaction between podTEC and ground based TEC requires
further investigation
• Modest improvements, limited by
− Difficult test
− COSMIC constellation
− Autoscaled vertical ionosonde data
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