Part II MAPPING THE IONOSPHERE WITH GPS
description
Transcript of Part II MAPPING THE IONOSPHERE WITH GPS
Civil and Environmental Engineering and Geodetic Science
Part II
MAPPING THE IONOSPHERE WITH GPS
GS894G
Civil and Environmental Engineering and Geodetic Science
References
Wielgosz, P. The impact of ionospheric effects on GPS data reduction, PhD dissertation, UWM, Poland, 2002 (in Polish)Bosy, J, M. Figurski, P. Wielgosz. The strategy of GPS data processing in precise local networks during high solar activity, GPS Solutions, 2003 (in
print)Schaer, S. Mapping and Predicting the Earth's Ionosphere Using the Global Positioning System, PhD thesis, University of Bern, 1999.
Ron Muellerschoen, R. and Powers, E. Errors in GPS due to Satellite C1-P1 Code Biases
Hajj, G. A. et al. (2000): COSMIC GPS Ionospheric Sensing and Space Weather, TAO, Vol. 11, No. 1, pp. 235-272.
http://www.spaceweather.com/
http://www.ips.gov.au/Main.php?CatID=8http://nssdc.gsfc.nasa.gov/space/model/models_home.htmlhttp://www.cx.unibe.ch/aiub/ionosphere.htmlhttp://www.sunspotcycle.com/
Civil and Environmental Engineering and Geodetic Science
• The ionosphere is the part of the upper atmosphere where free electrons occur in sufficient density to have a substantial influence on the propagation of radio frequency electromagnetic waves (such as GPS)
• The ionization depends primarily on the solar activity
• Ionospheric structures and peak densities in the ionosphere vary greatly with time and location, and thus, must be monitored
Introduction to the ionosphere
Civil and Environmental Engineering and Geodetic Science
• The spatial and temporal distributions of ionospheric disturbances, such as storms and Traveling Ionospheric Disturbances (TIDs), are of primary interest in their own scientific context, but they are also of special interest to communication, surveillance and radio-navigation, since they affect the skywave signal channel characteristics.
• Thus, the communication and navigation systems (GPS) relying on trans-ionospheric propagation must be able to account for the effects of the abrupt changes in total electron content (TEC), associated with the storm time disturbance effects, including the occurrence of the ionospheric trough at mid-latitudes.
• Conversely: if the GPS receiver’s location is known, GPS observable may allow to track ionospheric properties
Why do we need to study ionosphere?
Civil and Environmental Engineering and Geodetic Science
• As our dependence on technology in space grows, continuous and global sensing of the Earth’s atmosphere is becoming a technological necessity.
• The awareness of the potentially hazardous effects of space weather on technological systems motivated the creation of the National Space Weather Program (NSWP)
• NSWP places particular emphasis on the need to provide timely, accurate, and reliable space environment observations, specifications, and forecasts
• These requirements are similar to what is already accomplished with a great measure of success in the Numerical Weather Prediction (NWP) – currently exclusively relying on remote sensing techniques.
Why do we need to study ionosphere?
Civil and Environmental Engineering and Geodetic Science
Accurate specification and forecasting of space weather phenomena is very difficult because it requires:
• accurate modeling of the coupling between the sun, the magnetosphere, the thermosphere, the ionosphere, and the mesosphere,
• continuous, reliable and accurate observations of all of these regions
• the ability to assimilate the data into the models in an optimal and self-consistent manner.
Current challenges
GPS can contribute greatly by providing near real-time, high resolution, global TEC estimates
Civil and Environmental Engineering and Geodetic Science
• Ionization is caused by:
X-ray radiation
ultraviolet radiation
corpuscular radiation from the Sun
Ionospheric structures and peak densities vary with:
time (sunspot cycle, season, local time, i.e., day vs. night)
geographic location (polar, auroral zones, mid-latitudes (lowest ionospheric variability), and equatorial regions (the largest electron content))
certain solar-related ionospheric disturbances
The motion and distribution of the electrons is affected by Earth magnetic field
Electrons move along magnetic lines of force
Thus, electron distribution is described in terms of geomagnetic coordinates
north geomagnetic pole: 79.41 and –71.64 (epoch 1998.5) slowly moving (0.03 and 0.07 per year)
Civil and Environmental Engineering and Geodetic Science
Solar – Earth connection
Influence of the solar wind on earth’s magnetosphere
Civil and Environmental Engineering and Geodetic Science
Why do we need to study ionosphere?
• Peak values of electron density are encountered in the equatorial region, normally in the early afternoon
• Region with very high electron concentration at geomagnetic latitudes of about +/- 20 deg during early evening (maxima are referred to as equatorial anomaly)
• The mid-latitude ionosphere shows the least variations. It is also best observed as most of the ionosphere sensing instruments are located in this region.
• In the high latitudes and auroral zones the peak electron densities are smaller than in lower latitudes. However, this sector is extremely rich in plasma instabilities, which implies that short-term variations in the electron density are more pronounced there than at lower latitudes
• At polar caps, where the solar zenith angle is essentially constant, a diurnal variation is still detectable, indicating that apart from solar illumination there are other factors that affect the state of the ionosphere
Civil and Environmental Engineering and Geodetic Science
Global TEC map at 14:30 UT September 11, 1994.Clearly visible equatorial anomaly (National Space Science
Data Center)
Civil and Environmental Engineering and Geodetic Science
Why do we need to study ionosphere: ionospheric irregularities
• significant variations in electron density are caused by traveling ionospheric disturbances (TIDs)
• large-scale TIDs, periods of 30 min to 3 hours, and horizontal wavelengths exceeding 1000 km
• medium-scale TIDs, periods from 10 min to 1 hour, and horizontal wavelength of several hundreds of km
• small-scale TIDs, periods of several minutes, and horizontal wavelength of tens of km
• smallest-scale structures in the electron density distribution cause scintillation1 effects, rapid variations in the line-of-sight electron content (equatorial, high-latitude and polar regions)
• ionospheric storms: vast and massive ionospheric events, often coupled with severe disturbances in the magnetic field and intense solar eruptions (flares)
• usually results in a tremendous increase of electron content
Civil and Environmental Engineering and Geodetic Science
Vertical electron distribution
• Vertical regions
• Peak density in F region
• Different distribution during day and night
Ne
-
Civil and Environmental Engineering and Geodetic Science
Vertical electron distribution
• Region F starts at ~150 km
• Consists of F1 and F2• formed primarily due to ultraviolet radiation
• Regions E and D are due to X-ray radiation
• Effect of D on GPS signal propagation are negligible
• F1 combined with E effects accounts for 10% of GPS ionospheric delay
• F2 has the highest electron concentration (250-450 km) and largest variability, and accounts for up to 80% of GPS ionospheric delay
• Upper boundary of ionosphere is not clearly defined, however, above 1000 km the electron density is very low
• The ionospheric delay caused by the layer above 1000 km amounts to about 10% of the total effect during the day and ~50% during the nigh
Civil and Environmental Engineering and Geodetic Science
Sunspots (February 2000)
The Sun - The dark areas are the sunspots
Civil and Environmental Engineering and Geodetic Science
050
100150200250300350400
1952
1955
1959
1962
1965
1969
1972
1976
1979
1982
1986
1989
1992
1996
1999
Year
SS
N
SSN=10g+s,
where:g – number of groups of sunspots,s – number of individual spots.
SSN - Sunspot Number
Civil and Environmental Engineering and Geodetic Science
Current cycle of solar activity
SSN
year
Civil and Environmental Engineering and Geodetic Science
Solar flareCME
(Coronal Mass Ejection)
Solar events
Civil and Environmental Engineering and Geodetic Science
Solar wind speed during disturbances
Civil and Environmental Engineering and Geodetic Science
Kp 0o 0+ 1- 1o 1+ 2- 2o 2+ 3- 3o 3+ 4- 4o 4+ap 0 2 3 4 5 6 7 9 12 15 18 22 27 32 Kp 5- 5o 5+ 6- 6o 6+ 7- 7o 7+ 8- 8o 8+ 9- 9oap 39 48 56 67 80 94 111 132 154 179 207 236 300 400
Indices of geomagnetic activity
Kp 4 - quiet magnetosphereKp = 4 - active magnetosphereKp = 5 - minor stormKp 6 - major storm
Kp and ap are derived every 3 hours from magnetometric observations
Civil and Environmental Engineering and Geodetic Science
Geomagnetic activity during November 2001
Civil and Environmental Engineering and Geodetic Science
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
1 31 61 91 121 151 181 211 241 271 301 331 361
DOY 1999
TE
CU
, 0
.1 S
SN
GPS TEC at 1:00 UT
SSN
Correlation between SSN and TEC: global average
Civil and Environmental Engineering and Geodetic Science
Wave propagation in the ionosphere
The refractive index - n describes the wave propagation in given medium.
v
cn
Where:c – the speed of the light in the vacuumv - the speed of the light in the medium
nion > 1 for code GPS observable (code delay) nion < 1 for phase GPS observable (phase advance)
Civil and Environmental Engineering and Geodetic Science
The refractive index nion can be expanded in the reciprocal frequency f of the electromagnetic wave as:
422
30
2
8cos
221 fN
CfHN
CCfN
Cn e
xe
yxe
xion
With the constants:
,4 0
2
2
e
xm
eC
ey m
eC
20
Where:
Ne – electron density, H0 – magnetic field strength, – angle between the propagation direction of the electromagnetic wave and the vector of the geomagnetic field, e – charge of one electron, 0 – electric permittivity1 in the vacuum, me – mass of electron, 0 – magnetic permeability2 in the vacuum.
dnion distance measured
Civil and Environmental Engineering and Geodetic Science
Approximated values of the terms in equation below:
2nd = 210-4 - delay/advance (we account for this part only)3rd = 210-7 - bending (neglected in the ion computation)4th = 210-8 - different ray paths (neglected in the ion computation)
422
30
2
8cos
221 fN
CfHN
CCfN
Cn e
xe
yxe
xion
Civil and Environmental Engineering and Geodetic Science
• the signal delay depends on the total electron content (TEC) along the signal’s path and on the frequency of the signal itself as well as on the geographic location and time and solar activity, as explained earlier
• integration of the refractive index renders the measured range, and the ionospheric terms for range and phase are as follows:
• TEC is the line-of-sight TEC in electrons per square meter. Usually expressed in TECU (TEC Units), where one TECU corresponds to 1016 electrons contained in a cylinder aligned along the line of sight with a cross-section of one square meter, so 1 TECU = 1016 el/m2
range geometric theis where]mper electrons [10 )(TEC
TECcontent electron total where3.40
distance measured
0216
0
2
0
dN
TECf
dn
e
ion
ionion
Civil and Environmental Engineering and Geodetic Science
Wave propagation in the ionosphere
2
2x
ion
CTECf
ion – path delay due to the ionosphere
Cx/2 40.3 m3s-2 (40.3 1016 ms-2 TECU-1) – constant corresponding to the square of the plasma frequency divided by the electron density ( = e2/(420m ) = 40.3
Ne is the electron density (number of electrons per cubic meter) along the signal’s path
Naturally, if ion is known, TEC value can be estimated
( )eTEC N d
Civil and Environmental Engineering and Geodetic Science
Integrated electron density
• For the propagation of microwaves through the ionosphere the electron density integrated along the ray path, generally called TEC (Total Electron Content), is the important ionospheric quantity
• Ne is the electron density (number of electrons per cubic meter) along the signal’s path
• The term TEC is often used to designate the VTEC (Vertical TEC) – slant TEC reduced to the vertical using mapping function F(z), which is a ratio of slant TEC to VTEC
3.40
)(3.40
22VTEC
fzFTEC
fion
Civil and Environmental Engineering and Geodetic Science
SLM – Single Layer Model
SLM assumes that all free electrons are contained in a shell of infinitesimal thickness at altitude H
VTEC
TECzF )(
'sin1
1)(
2 zzF
z’ is elevation angle at ionosphere piercing point
zHR
Rz sin'sin
Civil and Environmental Engineering and Geodetic Science
Ionospheric path delay caused by 1TECU of free electrons
Linearcombination
path delay / 1 TECU
m cycles
L1
L2
L3 (iono. Free)L4 (geo. free)
L5 (wide-lane)
0.1620.267
0-0.105-0.208
0.8531.095
0-1.948-0.248
Define a constant
that gives the ionospheric path delay per TECU referred to the first GPS frequency f1 (also denoted as 1)
MHzfTECUmfCx
E 42.1575/162.02 1
21
The path delays expressed in meters per TECU are equal to
Where , 4 and 5 equal to
EEEE 54 ,,,
283.12
15
f
f647.014 647.12
2
21
f
f
Civil and Environmental Engineering and Geodetic Science
-150 -100 -50 0 50 100 150
-50
0
50
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
-150 -100 -50 0 50 100 150
-50
0
50
-150 -100 -50 0 50 100 150
-50
0
50
1 1 .0 8 .1 9 9 9 g .1 3 :0 0
1 1 .0 8 .1 9 9 9 g .1 5 :0 0
1 1 .0 8 .1 9 9 9 g .1 7 :0 0
Sze
roko
ść
D łu g o ść
TECU
13 UT
15 UT
17 UT
Global TEC maps
Lati
tude
longitude
Civil and Environmental Engineering and Geodetic Science
-1,0-0,8-0,6-0,4-0,20,00,20,40,60,81,0
0 4 8 12 16 20 24
UT hours
Cyc
les
L5
-1,0
-0,8-0,6
-0,4-0,2
0,0
0,20,4
0,60,8
1,0
0 4 8 12 16 20 24
Godziny UT
Cyk
le L
5
DD residual ionospheric delay on wide-line
combination for 300 kmbaseline
Processing without ionospheric information from the maps
Processing with ionospheric information from the maps
Cycl
es
L5
Cycl
es
L5
UT hours
UT hours
Civil and Environmental Engineering and Geodetic Science
2max
1
cos2 fzR
VTECCxl
lion
Where lion is the iono-induced distance bias to be expected, and l is the baseline vector
R is the length of the geocentric receiver vector (approximately the Earth radius)
zmax is the maximum satellite zenith distance imposed in the processing
Negative sign implies an apparent reduction in baseline length
Civil and Environmental Engineering and Geodetic Science
Influence of the Antarctic ionosphere on static GPS positioning: example
Data processing:
• IGS observations
• 24-hour sessions with 1 hour overlap
• 7 deg. elevation mask
• Elevation-dependent observation weighting
• QIF (Quasi Ionosphere Free) ambiguity resolution
Civil and Environmental Engineering and Geodetic Science
272 276 280 284 288 292 296 300 304 308 312 316 320 324 328 332 336
D O Y 2001
1.5
2
2.5
3
3.5
4rm
s er
rors
of
am
big
uiti
es
[mm
]
5
10
15
20
25
30
35
40
45
Ave
rag
ed T
EC
(C
AS
1,D
AV
1) [T
EC
U]The rm s errors o f the am bigu ities
m 0 24h m ov.aver. (TE CC AS 1
+TE CD A V 1
)/2
C A S 1-D A V 1
1 2 1 6 2 0 2 4 2 8 3 2 3 6 4 0 4 4
A v e r a g e d T E C ( C A S 1 , D A V 1 ) [ T E C U ]
1 .5
2
2.5
3
3.5
4
rms
erro
rs o
f a
mbi
gu
itie
s [m
m]
C oef of determ ination, R -squared = 0 .34
Correlation between averaged TEC over a baseline and rms of obtained ambiguities
Civil and Environmental Engineering and Geodetic Science
280 290 300 310 320 330
DO Y2001
6
8
10
12
14
16
18
20
Dis
tanc
e-1
,39
7,6
36,0
00 [
mm
]
9 0
8 0
7 0
6 0
5 0
4 0
3 0
2 0
% r
ozw
iaza
nych
nie
ozna
czon
osc
i
DAV1-C AS1
2 0 4 0 6 0 8 0
% r o z w i a z a n y c h n i e o z n a c z o n o s c i
8
1 2
1 6
2 0D
ista
nce-
1,3
97,
636
,000
[m
m] 273-334 D O Y2001 D AV1-C AS1
R =0.28
% of resolved ambiguities
% o
f re
solv
ed a
mbig
uit
ies
Correlation between% of resolved ambiguitiesand obtained length of the vector
Civil and Environmental Engineering and Geodetic Science
TEC estimation with GPS
Civil and Environmental Engineering and Geodetic Science
• Ionospheric delay observed by the ground-based permanently tracking stations
• almost impossible to derive height-dependent ionospheric profile
• Observed GPS delay by the Low Earth Orbiter (LEO) at the instant of GPS satellite occultation by Earth limb
• GPS signal bent and delay are associated with the vertical profiles of atmospheric parameters
• With full GPS constellation several hundreds of daily occultations can be observed by a single LEO
• A constellation of LEOs is needed for global coverage
• Ionosphere tomography
• Only ground-based solution is considered here
Civil and Environmental Engineering and Geodetic Science
Civil and Environmental Engineering and Geodetic Science
• Only ground-based solution is considered here
• For ground-based absolute TEC mapping, the TEC along the vertical is of main interest
• GPS provides in principle slant TEC, so mapping function is needed to convert it to VTEC
• to refer the resulting VTEC to specific solar-geomagnetic coordinates, the single-layer (thin shell) model is usually adopted for the ionosphere
• Assume that free electrons are all contained in a shell of infinitesimal thickness at altitude H (350, 400 or 450 km)
TEC estimation with GPS
Civil and Environmental Engineering and Geodetic Science
• Difference in ionospheric delay between the observables on L1 and L2 is used
• Each 1 meter of differential delay between L1 and L2 corresponds roughly to 10 TECU1
• Geometry-free combination is most commonly used
• Relative TEC – from carrier phase
• Absolute TEC – from pseudorange
TEC estimation with GPS
Civil and Environmental Engineering and Geodetic Science
SLM – Single Layer Model
'sin1
1)(
2 zzF
VTEC
zTEC
E
zEzF
v
)()()(
SLM assumes that all free electrons are contained in a shell of infinitesimal thickness at altitude H
Civil and Environmental Engineering and Geodetic Science
zHR
Rz sin'sin
z and z’ are zenith distance at GPS receiver and ionosphere piercing point (IPP); R is geocentric distance to the receiver and H is the assumed height of the ionospheric layer (here assumed at 450 km)
'sin1
1)()(
2 zVTEC
zTECzF
Assuming the homogeneous satellite distribution over the entire sky, the semi diameter of the ionospheric cap probed by a single receiver is defined by the maximum central angle zmax.
Civil and Environmental Engineering and Geodetic Science
The number of stations sufficient to sound out the entire Earth ionosphere equals to:
maxcos1
24
zAnA
So, for zmax=80 deg, nA = ~ 80 stations
The steradian (symbolized sr) is the Standard International (SI) unit of solid angular measure. There are 4 pi, or approximately 12.5664, steradians in a complete sphere.
A steradian is defined as conical in shape, as shown in the illustration. Point P represents the center of the sphere. The solid (conical) angle q, representing one steradian, is such that the area A of the subtended portion of the sphere is equal to r2, where r is the radius of the sphere.
Civil and Environmental Engineering and Geodetic Science
Ionospheric delay in GPS equations
ik bb ,
-satellite and receiver hardware delays in units of time; normally ignored as they cannot be separated from the clock errors. Clock errors compensate for hardware delays
)( ki ttc - satellite and receiver clock errors wrt GPS time
kiB 1,
-constant bias expressed in cycles; in principal, it contains the initial carrier phase ambiguity; it is a real-valued number containing the integer ambiguity, effect of phase windup1and satellite and receiver hardware delays
Civil and Environmental Engineering and Geodetic Science
Introducing the ionosphere variable Iik ( ), which represents the ionospheric
delay related to first frequency, 1 (notice that 1 corresponds to our earlier notation f1)
kioni ,
Civil and Environmental Engineering and Geodetic Science
Pseudorange smoothing
Smoothed, dual frequency pseudorange at epoch t
and
The noise on smoothed pseudorange is reduced by sqrt(n), where n is the number of epochs used in the smoothing process; it is used in ionosphere estimation
Civil and Environmental Engineering and Geodetic Science
Double difference equations
Ambiguities, N, are integers, as clock errors and hardware biases were eliminated (greatly reduced) by differencing.
Civil and Environmental Engineering and Geodetic Science
Geometry free linear combination (LC): of vital interest to ionosphere estimation
In un-differenced mode
4 1 2L L L cancels frequency independent errors
Civil and Environmental Engineering and Geodetic Science
What are DCBs and what is the reason for non-zero DCBs?
• P1-P2 and P1-C1 biases
• must be estimated for satellites and receivers
Civil and Environmental Engineering and Geodetic Science
ICD-GPS-200, Revision C, Initial Release, 10 October 1993
3.3.1.8 Signal Coherence. All transmitted signals for a particular SV shall be coherently derived from the same on-board frequency standard; all digital signals shall be clocked in coincidence with the PRN transitions for the P-signal and occur at the P-signal transition speed. On the L1 channel the data transitions of the two modulating signals (i.e., that containing the P(Y)-code and that containing the C/A-code) shall be such that the average time difference between the transitions does not exceed 10 nanoseconds (two sigma).
Civil and Environmental Engineering and Geodetic Science
User Error Problem
• GPS control segment uses GPS P-code measurements to compute the broadcast GPS orbits and clocks corrections.
• For a CA only user, using the P-code based broadcast parameters results in range error
• CA-code user would subtract from his P-code based broadcast/differential clock a P1-C1 bias.
– but this effects phase residuals too
• This bias can be estimated via a network solution
• P-C1 code bias +/- 50 cm max; known with accuracy of ~ 5cm
Civil and Environmental Engineering and Geodetic Science
-0.4
-0.2
0
0.2
0.4
0 100 200 300 400 500
Hourly Solutions of CA-P for the First 6 PRNs
prn1prn2prn3prn4prn5prn6
CA
-P C
ode
Bia
s (
met
ers
)
time ( hours )
Civil and Environmental Engineering and Geodetic Science
Potential Effect on User Error
• If the user had perfect knowledge of the clocks/orbits/ionosphere/troposphere, what would be effect of ignoring the P1-CA bias ?
– use IGS orbits and IGS CA clocks.
– use pre-computed zenith troposphere delay for model.
– use phase only to smooth the multipath in the range data.
– kinematically position a dual-freq. P code receiver
• case 1.) account for P1-C1 code bias
• case 2.) don’t account for P1-C1 code bias
Civil and Environmental Engineering and Geodetic Science
-4
-3
-2
-1
0
1
2
3
4
0 4 8 12 16 20 24
Potential Vertical User Error from CA/P Bias
not accounting for CA/P bias: 0.75 m rms.
accounting for the CA/P bias: 0.65 m rms.ve
rtic
al
erro
r (
met
ers
)
time ( hours )
Civil and Environmental Engineering and Geodetic Science
Differential code bias
• Both P1-P2 and P1-C1 biases are estimated for satellites and receivers
• Daily P1-P2 repeatability is about 0.2 ns RMS
• Contain the information about long term stability of instrumental biases
• Experience little variation and are usually assumed constant (usually known to within 1-2TECU)
• http://www.cx.unibe.ch/aiub/ionosphere.html
Civil and Environmental Engineering and Geodetic Science
CODE'S 30-DAY P1-P2 DCB SOLUTION ENDING DAY 095, 2003 09-APR-03 14:26
--------------------------------------------------------------------------------
DIFFERENTIAL (P1-P2) CODE BIASES FOR SATELLITES AND RECEIVERS:
PRN / STATION NAME VALUE (NS) RMS (NS)
*** **************** *****.*** *****.***
G01 -1.568 0.009
G02 -2.731 0.009
G03 -0.952 0.007
G04 0.191 0.011
G05 -1.161 0.008
CODE'S 30-DAY P1-C1 DCB SOLUTION ENDING DAY 095, 2003 09-APR-03 14:26
--------------------------------------------------------------------------------
DIFFERENTIAL (P1-C1) CODE BIASES FOR SATELLITES AND RECEIVERS:
PRN / STATION NAME VALUE (NS) RMS (NS)
*** **************** *****.*** *****.***
G01 -0.132 0.007
G02 -1.013 0.010
G03 0.168 0.007
G04 1.491 0.008
Civil and Environmental Engineering and Geodetic Science
CODE'S 30-DAY P1-P2 DCB SOLUTION ENDING DAY 095, 2003 09-APR-03 14:26
--------------------------------------------------------------------------------
DIFFERENTIAL (P1-P2) CODE BIASES FOR SATELLITES AND RECEIVERS:
PRN / STATION NAME VALUE (NS) RMS (NS)
*** **************** *****.*** *****.***
G01 -1.568 0.009
G02 -2.731 0.009
………………………………………………….
………………………………………………….
G ALBH 40129M003 21.892 0.065
G ALGO 40104M002 6.129 0.144
G ALIC 50137M001 24.355 0.111
G ALRT 40162M001 -2.289 0.053
Civil and Environmental Engineering and Geodetic Science
Geometry free linear combination (LC): of vital interest to ionosphere estimation
Ambiguities, N, are integers, as clock errors and hardware biases were eliminated (greatly reduced) by differencing. If ambiguities N can be fixed to integers (for example using wide-lane LC), the term is known.kl
ijB 4,
This takes care of differential ionosphere estimation, however, absolute ionosphere estimation is not that straightforward
Civil and Environmental Engineering and Geodetic Science
Absolute TEC estimation with geometry free LC
To rewrite the geometry free LC for absolute TEC estimation, let’s denote:
MHzfTECUmfCx
E 42.1575/162.02 1
21
Civil and Environmental Engineering and Geodetic Science
Absolute TEC estimation
And the observation equations can be written as:
kiL 4,
105.04 EkiB 4,
m/TECU - constant
- zero difference L4 observable
- bias parameter
kiP 4, - zero difference phase-smoothed P code observable
)( ik bbc - satellite and receiver DCBs (Differential Code Bias)
Civil and Environmental Engineering and Geodetic Science
Corresponding double-differenced equation
The unknowns in the above equations (smoothed code and un-differenced and double difference carrier phase, geometry free LCs) are
• absolute TEC (Ev(,s))
• the satellite and receiver differential code biases (DCBs)
• the ambiguity (bias) terms and
• Consequently, one cannot directly derive absolute TEC information from single-epoch GPS data. To separate TEC from DCBs or ambiguity parameters, it is necessary to process data accumulated over certain time span.
ik bb
kiB 4,
klijB 4,
Civil and Environmental Engineering and Geodetic Science
Alternative observation equations used for TEC estimation: single differences
d corresponds to Cx/2 in our earlier notation
Civil and Environmental Engineering and Geodetic Science
Alternative observation equations used for TEC estimation: single differences
Civil and Environmental Engineering and Geodetic Science
Most commonly used LC for TEC estimation: summary
Relative (r) precise (p) TEC
B is a constant bias, v is a noise
Absolute (a) noisy (n) TEC
C is a sum of transmitter and receiver DCBs, is a noise
Relative (r) noisy (n) TEC from single frequency data
B’ is a constant bias, is a noise
Civil and Environmental Engineering and Geodetic Science
TEC parameterization
• L4 – geometry-free linear combination to determine TEC at ionosphere pierce points of SLM
o Network of points allows for global (local) model derivation
o Spherical harmonic expansion 1515
o Spatial resolution 100 – 200 km
o Temporal resolution at least 5 minutes
Civil and Environmental Engineering and Geodetic Science
n
mmnmnmn
n
nv msSmsCPsE
0,,,
0
))sin(~
)cos(~
)((sin~
),(max
– geomagnetic (or geographic) latitude of IPP
s=-0 – sun-fixed longitude of IPP
– longitude of IPP
0 – longitude of the Sun
nmax – maximum degree of SH expansion
– normalized associated Legendre function
Nnm – normalization function
Pnm – classical, unnormalized Legendre function
– unknown SH coefficients
Global TEC representation: spherical harmonics (SH)
nmnmmn PNP ,
~
mnC ,
~mnS ,
~
Model resolution:
Where:
maxn
max
2
ms
Vertical TEC is represented in terms of spherical harmonic coefficients of specific degree/order
Civil and Environmental Engineering and Geodetic Science
-150 -100 -50 0 50 100 150
-50
0
50
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
-150 -100 -50 0 50 100 150
-50
0
50
-150 -100 -50 0 50 100 150
-50
0
50
1 1 .0 8 .1 9 9 9 g .1 3 :0 0
1 1 .0 8 .1 9 9 9 g .1 5 :0 0
1 1 .0 8 .1 9 9 9 g .1 7 :0 0
Sze
roko
ść
D łu g o ść
TECU
13 UT
15 UT
17 UT
Global TEC maps: SH representation
Lati
tude
longitude
Civil and Environmental Engineering and Geodetic Science
Civil and Environmental Engineering and Geodetic Science
Alternative models of Global TEC representation
• Uniform grid
• Gauss-type exponential functions
• Cells of constant TEC
• Spherical wavelets (recent)
• Broadcast ionosphere model
Civil and Environmental Engineering and Geodetic Science
Alternative models of Global TEC representation
• Broadcast ionosphere model:
Eight ionospheric coefficients are broadcast by the GPS satellites; they represent the amplitude and the the period of the cosine function by cubic polynomials
Civil and Environmental Engineering and Geodetic Science
• International GPS Service (IGS) provides
- precise GPS ephemeris
- Earth Rotation Parameters (ERPs)
• x, y polar motion and length of day (LOD)
- IGS tracking station coordinates in SINEX format (Solution IN-dependent EXchange format)
- satellite and station clock information
- since 1997 also station-specific tropospheric zenith delay estimates
Relevant international activities
Civil and Environmental Engineering and Geodetic Science
• IGS Ionosphere working group to coordinate GPS-based work on ionosphere (1998)
• Result distribution:
- IONEX files (grid)
• IONosphere Map EXchange Format
- ionospheric maps
- SH coefficients
- CODE provides regularly 12 2-hourly global TEC solutions and satellite-specific differential code biases (DCBs)
• http://www.cx.unibe.ch/aiub/ionosphere.html
Relevant international activities
Civil and Environmental Engineering and Geodetic Science
Civil and Environmental Engineering and Geodetic Science
Civil and Environmental Engineering and Geodetic Science
The response of the ionosphere over Europe to the geomagnetic storm on March 31, 2001
27.03
0
2
4
6
8
10
Kp
28.03 29.03 30.03 31.03 1.04 2.04 3.04 4.04
27.03 28.03 29.03 30.03 31.03 1.04 2.04 3.04 4.04
-400
-300
-200
-100
0
100
Dst
[nT
]
Day/month
The Dst or disturbance storm time index is a measure of geomagnetic activity used to assess the severity of magnetic storms. It is expressed in nanoteslas and is based on the average value of the horizontal component of the Earth's magnetic field measured hourly at four near-equatorial geomagnetic observatories.
Civil and Environmental Engineering and Geodetic Science
The Dst or disturbance storm time index is a measure of geomagnetic activity used to assess the severity of magnetic storms. It is expressed in nanoteslas and is based on the average value of the horizontal component of the Earth's magnetic field measured hourly at four near-equatorial geomagnetic observatories.
Civil and Environmental Engineering and Geodetic Science
- 2 0 - 1 0 0 1 0 2 0 3 0 4 0
4 0
5 0
6 0
7 0
Data source: ~60 permanent european GPS stations
Civil and Environmental Engineering and Geodetic Science
0
2 0
40
60
TE
CU
0
30
60
TE
CU
0
30
60
TE
CU
0
30
60
TE
CU
0
30
60
TE
CU
0
3 0
60
90
TE
CU
0
3 0
60
90
TE
CU
N YAL (79 o N , 12 o E)
T RO1(70 o N , 19 o E )
VIL 0 (65 o N , 16 o E)
ON S A (57 o N , 12 o E )
L AM A (54 o N , 20 o E)
OR ID (41 o N , 21 o E)
L AM P (35 o N , 17 o E )
2 7 2 8 2 9 3 0 31 1 2 3 4
Diurnal variations of TECat different stations
Civil and Environmental Engineering and Geodetic Science
6 7 7 8 8 90
20
40
60
TE
CU
2 0 2 2 2 4 2 6 2 8long itude
62
64
66
68
70
6 7 8 9 100
20
40
6018 20 22 24 26
long itude
5 8
6 0
6 2
6 4
6 6
6 8
7 0
latit
ude
5 6 7 8 90
20
40
60T
EC
U3 0 3 2 3 4 3 6 3 8
5 8
6 0
6 2
6 4
6 6
6 8
7 0
6 7 8 9 1 00
2 0
4 0
6 02 8 3 0 3 2 3 4 3 6
5 6
5 8
6 0
6 2
6 4
6 6
6 8
latit
ude
5 6 7 8 90
20
40
60
TE
CU
4 0 4 4 4 8 5 2
6 4
6 6
6 8
7 0
7 2
7 4
7 6
6 7 8 9 1 0 1 10
2 0
4 0
6 03 8 4 2 4 6 5 0 5 4
6 2
6 4
6 6
6 8
7 0
7 2
7 4
latit
ude
5 6 7 8 9U T
0
20
40
60
TE
CU
3 0 3 2 3 4 3 6 3 8
6 6
6 8
7 0
7 2
7 4
7 6
6 7 8 9 1 0 1 1U T
0
20
40
6024 28 32 36 40
64
66
68
70
72
74
latit
ude
TROM
VARS
TRDS
VAAS
Variations of TEC along single satellite passes observed at different stations on:• March 30 (blue line)• March 31 (red line) - storm day
Locations of the satellites’ traces on the ionospheric layer are also presented (black line with crosses every 5 min.)
PRN 4 PRN 24
Civil and Environmental Engineering and Geodetic Science
Lati
tude
Longitude
TECU
Quiet-time TEC maps over Europe (March 16, 2001)
Civil and Environmental Engineering and Geodetic Science
Lati
tude
Longitude
TECU
Storm-time TEC maps over Europe (March 31, 2001)
Civil and Environmental Engineering and Geodetic Science
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 0 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 1 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 2 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 3 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 4 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 5 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 6 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 7 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 8 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 9 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 0 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 1 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 2 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 3 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 4 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 5 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 6 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 7 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 8 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 9 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
2 0 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
2 1 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
2 2 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
2 3 U T
0 4 8 1 2 1 6 2 0 2 4 2 8 3 2 3 6 4 0 4 4 4 8 5 2 5 6
Average quiet-time TEC maps over Europe (March 15-17, 2001)
TECU
Civil and Environmental Engineering and Geodetic Science
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 0 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 1 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 2 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 3 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 4 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 5 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 6 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 7 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 8 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 9 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 0 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 1 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 2 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 3 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 4 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 5 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 6 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 7 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 8 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 9 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
2 0 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
2 1 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
2 2 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
2 3 U T
0 4 8 1 2 1 6 2 0 2 4 2 8 3 2 3 6 4 0 4 4 4 8 5 2 5 6 TECU
Storm–time TEC maps over Europe on March 31, 2001
Civil and Environmental Engineering and Geodetic Science
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 0 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 1 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 2 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 3 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 4 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 5 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 6 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 7 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 8 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
0 9 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 0 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 1 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 2 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 3 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 4 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 5 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 6 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 7 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 8 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
1 9 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
2 0 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
2 1 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
2 2 U T
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
2 3 U T
- 1 5 0- 1 0 0 - 7 5 - 5 0 - 2 5 - 1 0 0 1 0 2 5 5 0 7 5 1 0 0 1 5 0 %
Differential TEC maps for the first day of the storm (March 31, 2001)
relative to quiet time
Civil and Environmental Engineering and Geodetic Science
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
7 : 0 0
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
7 : 1 0
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
7 : 2 0
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
7 : 3 0
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
7 : 4 0
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
7 : 5 0
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
8 : 0 0
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
8 : 1 0
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
8 : 2 0
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
8 : 3 0
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
8 : 4 0
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
8 : 5 0
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
9 : 0 0
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
9 : 1 0
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
9 : 2 0
- 1 0 0 1 0 2 0 3 0 4 04 0
5 0
6 0
7 0
9 : 3 0
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56TECU
TEC maps with 10 min interval on 07:00 – 09:30 UT, March 31, 2001. The maps demonstrate the presence of large scale structures at high latitude ionosphere during the storm
Civil and Environmental Engineering and Geodetic Science
40 50 60 700
10
20
TE
CU
40 50 60 70 40 50 60 70
40 50 60 70 40 50 60 70 40 50 60 70
40 50 60 70 40 50 60 70 40 50 60 70
40 50 60 70 40 50 60 70 40 50 60 70
40 50 60 70 40 50 60 70 40 50 60 70
40 50 60 70 40 50 60 70 40 50 60 70
40 50 60 70 40 50 60 70 40 50 60 70
0
10
20
30
40
010203040506070
0
10
20
TE
CU
01020304050
0102030405060
0
10
20
TE
CU
0102030405060
0102030405060
0
10
20
TE
CU
01020304050
01020304050
0
10
20
TE
CU
01020304050
0
10
20
30
40
0
10
20
30T
EC
U
01020304050
0
10
20
30
40
0
10
20
30
TE
CU
01020304050
0
10
20
30
0
10
20
30
40
TE
CU
01020304050
0
10
20
30
40 50 60 70Latitude
40 50 60 70Latitude
40 50 60 70Latitude
00 U T
01 U T
02 U T
03 U T
04 U T
05 U T
06 U T
07 U T
08 U T
09 U T
10 U T
11 U T
12 U T
13 U T
14 U T
15 U T
16 U T
17 U T
18 U T
19 U T
20 U T
21 U T
22 U T
23 U T
Storm-time dynamics of latitudinal TEC profiles:
• quiet day March 17, 2001- black line
• disturbed day March 31, 2001 – red line
• disturbed day April 1,2001 - blue line
Civil and Environmental Engineering and Geodetic Science
Map of high latitude GPS stations used in this study
Phase fluctuations of GPS signals at high latitude ionosphere during the storm
Civil and Environmental Engineering and Geodetic Science
Location of TEC fluctuations derived from GPS measurements at northern hemisphere during two disturbed days: September 12 and 15, in Geomagnetic local time and Corrected Geomagnetic Latitude.
Red and blue lines are the boundaries of the auroral oval