Modelling complexity in the upperatmosphere 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

ALT

ITU

DE

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

1000kms

sb

sb

Time varying

Electron density Ne

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

[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

Chapman functions

z

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

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

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.

12

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