modelling complexity in the upper atmosphere using gps data chris budd, cathryn mitchell, paul...
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Modelling complexity in the upperatmosphere using GPS data
Chris Budd, Cathryn Mitchell, Paul Spencer Bath Institute for Complex Systems, University of Bath
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Ground-receiver
tomography
Instrumentation
Have.
Networks of GPS receivers at mid-latitudes over continental regions of the Northern Hemisphere
Problem:
Atmosphere is a highly complex and multi-scale, time-evolving system.
It is vital to know the state of all levels for meteorology and navigation
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LATITUDE
Ionospheric Imaging
Measured –
relative values of total electron content TEC
Find –
3D time-evolving
electron density Ne
ALT
ITU
DE
Multi-Instrument Data AnalysiS
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Acknowledgements: IGS network
MIDAS – Northern Hemisphere GPS receivers
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6 moving satellites S
100 receivers R
Measure the differential phase change between dual frequency radio signals from S to R at 2 minute intervals over one hour
is directly proportional to the total electron content (TEC) of the ionosphere over the path s
Ionosphere
1000kms
sb
sb
Time varying
Electron density Ne
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R
S
s dstrNetb ),,,()(
Ne : electron concentration along the I = 6*100 paths s at the initial time (order 100 G electrons/metre cubed)
Set up 3D grid of J = 20 [height] *360*360 [angle] voxels,
x electron density in each voxel, matrix A of path lengths in each voxel
bAx Ill-conditioned .. Use a-priori information to solve
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[electron density] = [model electron density] [coefficients]
MIDAS algorithm
The electron density (x) distribution is formed from the weighted (W) sum of orthonormal basis functions, X:
4*50 Spherical Harmonics in latitude and longitude and
3 empirical functions Chapman Profiles in height z
XWx
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Chapman functions
z
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bAXW 1)(
bAXWAx Obtain least squares best fit for W using the regularised SVD to calculate the generalised inverse
XWx Initial estimate of the electron density
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Update this estimate every 2 minutes by assuming small change y in x, c in the measured TEC b and D in the ray path matrix A. To leading order have
Mapping matrix, X, transforms the problem to one for which the unknowns are the linear changes in coefficients G (y = XG) of the orthonormal basis functions
DxceAy
eAXGeA(XG) 1)(
MIDAS – time-dependent inversion
Improve with a Kalman filter
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Horizontal Variation
Spherical Harmonics
Model (eg IRI)
Height profile (to create EOFS)
Thin Shell (variable height) Chapman profiles Epstein profiles Models (eg IRI)
TIME:
None Zonal/Meridional Zonal/Meridional & Radial
Co-ordinate frame
Geographic Geomagnetic
Inversion type
2-D (latitude-height or thin shell) 3-D (2-D with time evolution or latitude-longitude-altitude)4-D (latitude-longitude- altitude-time)
Graphics options
Vertical profiles of Ne
Horizontal profiles of Ne
TEC maps
Electron concentration images (latitude vs height) at one longitude.
Electron concentration images (longitude vs height) at one latitude.
TEC movies
Electron concentration movies
MIDAS algorithm
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Electron density North America Longitude 70 W
Vertical TEC b Electron density Ne
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Vertical TEC b
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Observations of mid-latitude ionospheric storms
• Near global view of TEC distributions
• Observations of storm enhanced density
• Uplifts in layer height over Europe and North America
• Poleward movement of the anomaly
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Imaging Issues
What is the spatial resolution?
What is the temporal resolution?
What is the accuracy of the imaged electron density?
What scientific information can we derive directly from the images?
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Radar backscatter
Verification of the peak height uplift over the USA
MIDAS
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Combining imaging with first-principle modeling
How can we relate the images the underlying physics?
• Imaging alone cannot get at the underlying physics
• Simply reproducing localized image features with modeling does not uniquely determine the physical drivers
• Future aim – develop methods that constrain the physical models with full 4D imaging
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Acknowledgements to:
GPS RINEX data from SOPAC, IDA3D images from ARLUT, EISCAT
Collaboration with Cornell University
Support from BAE SYSTEMS, the UK EPSRC, BICS and PPARC
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MIDAS – Northern Hemisphere
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Coverage of Input Data
ionosonde
Polar NIMS
GPS
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• Is the TEC movie showing convection?• If so, the plasma over Europe originates from the USA
TEC over the Northern Hemisphere
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F2 layer uplifts move horizontally westwards, that is, firstly, in the European sector, then the east coast of the USA, and around an hour later, occurring in the west coast of the USA.
12
3
East-west progression of layer height uplift
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Equatorial imaging
(with Cornell University)
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Polar imaging
• Observations of patches over ESR
• IDA3D imaging appears to show patches convecting from Sondestrom to ESR
• Imaging alone cannot show the convection
• Combine AMIE convection patterns with trajectory analysis into IDA3D
• Provides strong evidence of plasma transport from Sondestrom to ESR
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IDA3D Ne at 400 km 2005 UT
Patch
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Results from Europe
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Ionospheric Measurements
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Observations over ESR
Patch at 20 UT