# Modelling complexity in the upper atmosphere using GPS data Chris Budd, Cathryn Mitchell, Paul Spencer Bath Institute for Complex Systems, University of.

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Modelling complexity in the upper atmosphere using GPS data Chris Budd, Cathryn Mitchell, Paul Spencer Bath Institute for Complex Systems, University of Bath

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

LATITUDE Ionospheric Imaging Measured – relative values of total electron content TEC Find – 3D time-evolving electron density Ne ALTITUDE Multi-Instrument Data AnalysiS

Acknowledgements: IGS network MIDAS – Northern Hemisphere GPS receivers

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 1000km s Time varying Electron density Ne

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 Ill-conditioned.. Use a-priori information to solve

[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

Chapman functions z

Obtain least squares best fit for W using the regularised SVD to calculate the generalised inverse Initial estimate of the electron density

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 MIDAS – time-dependent inversion Improve with a Kalman filter

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

Electron density North America Longitude 70 W Vertical TEC b Electron density Ne

Vertical TEC b

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

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?

Radar backscatter Verification of the peak height uplift over the USA MIDAS

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

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

MIDAS – Northern Hemisphere

Coverage of Input Data ionosonde Polar NIMS GPS

Is the TEC movie showing convection? If so, the plasma over Europe originates from the USA TEC over the Northern Hemisphere

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. 1 2 3 East-west progression of layer height uplift

Equatorial imaging (with Cornell University)

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

IDA3D Ne at 400 km 2005 UT Patch

Results from Europe

Ionospheric Measurements

Observations over ESR Patch at 20 UT

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