1. MAPPING THE IONOSPHERE WITH GPS
Part II
MAPPING THE IONOSPHERE WITH GPS
GS894G

2. 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

3. Introduction to the ionosphere
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

4. Why do we need to study ionosphere?
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

5. Why do we need to study ionosphere?
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.

6. Current challenges
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.
GPS can contribute greatly by providing near real-time, high resolution, global TEC estimates

7. 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 ) slowly moving (0.03  and 0.07  per year)

8. Solar – Earth connection
Influence of the solar wind on earth’s magnetosphere

9. 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

10. Global TEC map at 14:30 UT September 11, 1994.
Clearly visible equatorial anomaly (National Space Science Data Center)

11. 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
Another phenomenon, linked to the geomagnetic disturbances, are the time variations in phase, amplitude and angle of arrival of radio waves propagating through the ionospheric medium, known as ionospheric scintillations. Scintillations are due to the diffraction caused by rapid irregularities in ionospheric plasma density.

12. Vertical electron distribution Ne- Vertical regions
Peak density in F region
Different distribution
during day and night
Ne-

13. 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 ( 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

14. The Sun - The dark areas are the sunspots
 Sunspots (February 2000)
The Sun - The dark areas are the sunspots

15. SSN - Sunspot Number SSN=10g+s, where:
g – number of groups of sunspots,
s – number of individual spots.

16. Current cycle of solar activity
SSN
year

17. (Coronal Mass Ejection)
Solar events
CME
(Coronal Mass Ejection)
Solar flare

18. Solar wind speed during disturbances

19. Indices of geomagnetic activity
Kp 0o o o o o 4+ ap
Kp o o o o o ap
Kp and ap are derived every 3 hours from magnetometric observations
Kp  quiet magnetosphere
Kp = active magnetosphere
Kp = minor storm
Kp  6 - major storm
Kp is a logarithmic scale and ap is a linear scale
Both indices reflect the change in the geomagnetic activity level
For example: Kp= 5- means 4.66 and Kp= 5+ means 5.33

20. Geomagnetic activity during November 2001

21. Correlation between SSN and TEC: global average

22. Wave propagation in the ionosphere
The refractive index - n describes the wave propagation in given medium.
Where:
c – the speed of the light in the vacuum
v - the speed of the light in the medium
nion > 1 for code GPS observable (code delay)
nion < 1 for phase GPS observable (phase advance)

23. The refractive index nion can be expanded in the reciprocal frequency f of the electromagnetic wave as:
With the constants:
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.
1 ability to penetrate
2 the ratio of the capacitance of a capacitor, in which a substance is the dielectric to its capacitance with a vacuum between the plates; dielectric constant
Capacitor is a circuit element composed of two metallic plates separated by a dielectric (nonconductor of electricity), used to store a charge temporarily
Capacitance is the ratio of charge to potential on an electrically charged, isolated conductor; also: the property of a circuit element that permits it to store charge

24. Approximated values of the terms in equation below:
2nd = 2 delay/advance (we account for this part only)
3rd = 2 bending (neglected in the ion computation)
4th = 2 different ray paths (neglected in the ion computation)

25. 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

26. Wave propagation in the ionosphere
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/(420m ) = 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

27. 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

28. SLM – Single Layer Model
z’ is elevation angle at ionosphere piercing point
SLM assumes that all free electrons are contained
in a shell of infinitesimal thickness at altitude H

29. Ionospheric path delay caused by 1TECU of free electrons
Define a constant
that gives the ionospheric path delay per TECU referred to the first GPS frequency f1 (also denoted as 1)
Linear
combination
path delay / 1 TECU m
cycles L1 L2
L3 (iono. Free)
L4 (geo. free)
L5 (wide-lane)
0.162
0.267
-0.105
-0.208
0.853
1.095
-1.948
-0.248
The path delays expressed in meters per TECU are equal to
Where , 4 and 5 equal to

30. 13 UT
TECU
Latitude
15 UT
Global TEC maps
17 UT
longitude

31. DD residual ionospheric
delay on wide-line
combination for 300 km
baseline
Cycles L5
UT hours
Processing without ionospheric information from the maps
Cycles L5
UT hours
Processing with ionospheric information from the maps

32. Negative sign implies an apparent reduction in baseline length
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

33. 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

34. Correlation between
averaged TEC over
a baseline and rms
of obtained ambiguities

35. % of resolved ambiguities and obtained length of the vector
Correlation between
% of resolved ambiguities
and obtained length
of the vector
% of resolved ambiguities

36. TEC estimation with GPS

37. 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

39. TEC estimation with GPS
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)

40. TEC estimation with GPS
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
1 this is (L1-L2)/4/E=1/0.647/0.163=9.5 TECU
SEE FOLLOWING SLIDES FOR MORE DETAILS
E is the coefficient pre-multiplying TEC in the observation equation
4 converts the ionospheric delay in L4 to that of the first frequency L1

41. SLM – Single Layer Model
SLM assumes that all free electrons are contained
in a shell of infinitesimal thickness at altitude H

42. 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.
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)

43. So, for zmax=80 deg, nA = ~ 80 stations
The number of stations sufficient to sound out the entire Earth ionosphere equals to:
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 , 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.

44. Ionospheric delay in GPS equations
- satellite and receiver clock errors wrt GPS time
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
1GPS satellites transmit right circularly polarized (RCP) radio waves and therefore, the observed carrier-phase depends on the mutual orientation of the satellite and receiver antennas. A rotation of either receiver or satellite antenna around its bore axis will change the carrier-phase up to one cycle (one wavelength), which corresponds to one complete revolution of the antenna. This effect is called “phase wind-up”. The phase wind-up correction has been generally neglected even in the most precise differential positioning software, as it is quite negligible for double difference positioning on baselines/networks spanning up to a few hundred kilometers. Although, it has been shown that it can reach up to 4 cm for a baseline of 4000 km. However, this effect is quite significant for undifferenced point positioning when fixing IGS satellite clocks since it can reach up to one half of the wavelength.
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

45. Introducing the ionosphere variable Iik ( ), which represents the ionospheric delay related to first frequency, 1 (notice that 1 corresponds to our earlier notation f1)

46. 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

47. Double difference equations
Ambiguities, N, are integers, as clock errors and hardware biases were eliminated (greatly reduced) by differencing.

48. Geometry free linear combination (LC): of vital interest to ionosphere estimation
cancels frequency independent errors
In un-differenced mode

49. 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

50. ICD-GPS-200, Revision C, Initial Release, 10 October 1993
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).

51. 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

53. 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

55. 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)

56. 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)
*** **************** *****.*** *****.*** G G G G G
CODE'S 30-DAY P1-C1 DCB SOLUTION ENDING DAY 095, APR-03 14:26
DIFFERENTIAL (P1-C1) CODE BIASES FOR SATELLITES AND RECEIVERS:
PRN / STATION NAME VALUE (NS) RMS (NS)
*** **************** *****.*** *****.*** G G G G

57. 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)
*** **************** *****.*** *****.*** G G
………………………………………………….
G ALBH 40129M
G ALGO 40104M
G ALIC 50137M
G ALRT 40162M

58. 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.
This takes care of differential ionosphere estimation, however, absolute ionosphere estimation is not that straightforward

59. Absolute TEC estimation with geometry free LC
To rewrite the geometry free LC for absolute TEC estimation, let’s denote:

60. Absolute TEC estimation
And the observation equations can be written as:
- zero difference phase-smoothed P code observable
- zero difference L4 observable
m/TECU
- constant
- bias parameter
- satellite and receiver DCBs (Differential Code Bias)

61. 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.

62. Alternative observation equations used for TEC estimation: single differences
d corresponds to Cx/2 in our earlier notation

63. Alternative observation equations used for TEC estimation: single differences

64. 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

65. TEC parameterization
L4 – geometry-free linear combination to determine TEC at ionosphere pierce points of SLM
Network of points allows for global (local)
model derivation
Spherical harmonic expansion 1515
Spatial resolution 100 – 200 km
Temporal resolution at least 5 minutes

66. Global TEC representation: spherical harmonics (SH)
Vertical TEC is represented in terms of spherical harmonic coefficients of specific degree/order
Where:
 – 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
Model resolution:

67. Global TEC maps: SH representation 13 UT 15 UT 17 UT TECU Latitude
longitude

69. Gauss-type exponential functions Cells of constant TEC
Alternative models of Global TEC representation
Uniform grid
Gauss-type exponential functions
Cells of constant TEC
Spherical wavelets (recent)
Broadcast ionosphere model

70. 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

71. Relevant international activities
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

72. Relevant international activities
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)

75. The response of the ionosphere over Europe to the geomagnetic storm on March 31, 2001
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.

76. 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.

77. Data source: ~60 permanent european GPS stations

78. Diurnal variations of TEC
at different stations

79. 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

80. Quiet-time TEC maps over Europe (March 16, 2001)
Latitude
Longitude
TECU

81. Storm-time TEC maps over Europe (March 31, 2001)
Latitude
Longitude
TECU

82. Average quiet-time TEC maps over Europe (March 15-17, 2001)
TECU

83. Storm–time TEC maps over Europe on March 31, 2001
TECU

84. Differential TEC maps for the first day of the storm (March 31, 2001)
relative to quiet time %

85. TEC maps with 10 min interval on 07:00 – 09:30 UT, March 31, 2001
TEC maps with 10 min interval on 07:00 – 09:30 UT, March 31, The maps demonstrate the presence of large scale structures at high latitude ionosphere during the storm
TECU

86. Storm-time dynamics of
latitudinal TEC profiles:
quiet day
March 17, black line
disturbed day
March 31, 2001 – red line
April 1, blue line

87. Map of high latitude GPS stations used in this study
Phase fluctuations of GPS signals at high latitude ionosphere during the storm
Map of high latitude GPS stations used in this study

88. Red and blue lines are the boundaries of the auroral oval
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.