Indian Journal of Radio & Space Physics

Vol. 36, August 2007, pp. 278-292

Ionospheric total electron content (TEC) studies with GPS in the

equatorial region

A DasGupta1, 2

, A Paul2 & A Das

1

1 S K Mitra Center for Research in Space Environment, University of Calcutta, 92 A P C Road, Calcutta 700 009, India 2 Institute of Radio Physics and Electronics, University of Calcutta, 92 A P C Road, Calcutta 700 009, India

Email: adg1bkpr@hotmail.com

Received 2 April 2007; accepted 14 May 2007

This paper essentially deals with the effects of equatorial ionization anomaly gradient on space-based navigation

systems like GPS. The equatorial region of the ionosphere, which extends about ±30οdip about the magnetic equator, is

characterized by a steep latitudinal gradient, not only in the maximum ionization but also in the total electron content (TEC),

through a major part of the day. This region also accounts for about one-third of the global electron content. The high

ambient TEC results in large range errors for a major part of the day, affecting navigation and position-fixing using GPS.

The gradient of the equatorial ionization anomaly between the trough and the crest is very sharp, which results in large

temporal and spatial variation of the ionospheric electron content. A prediction of the range error introduced by the

ionosphere in the equatorial zone is very difficult. Identification of a suitable ionospheric model for prediction of these

errors in the geophysically sensitive equatorial region is necessary prior to the introduction of Indian SBAS network,

GAGAN (GPS And Geo Augmented Navigation). For this purpose, ionospheric TEC measured from Calcutta, situated

underneath the northern crest of the equatorial anomaly, has been compared with values generated by models like PIM1.6

and IRI-95 during 1977-1990. The equatorial anomaly gradient not only extends in the horizontal direction but with altitude

also. Problems related to conversion of vertical to slant TEC and vice versa, as required for ionospheric range error

corrections in satellite-based navigation with GPS, have been indicated and diagnostics suggested. It has been observed that

sharp latitudinal gradient of TEC during the afternoon hours of equinoctial months of high sunspot number years is usually

followed by generation of irregularities over the magnetic equator in the form of ‘bubbles’ or depletions. These depletions

have sharp edges resulting in large range error rates on GPS links. Characteristics of bubbles, namely, amplitude and leading

and trailing edge slopes, have been studied using GPS TEC data recorded at the Giant Meterwave Radio Telescope (GMRT)

site during the vernal equinox of 2004. Use of GPS TEC measurements as a tool for studying ionospheric response to

earthquakes has also been indicated.

Keywords: Total electron content (TEC), Global positioning system (GPS), Ionospheric TEC, GAGAN, SBAS, GMRT

PACS No.: 94.20.Yx; 94.20.Vv; 94.20.Ww

1 Introduction The ionosphere is the main source of range and

range-rate errors for users of satellite-based radars and

navigation systems like the Global Positioning

System (GPS). At times, the range errors of the tropo-

sphere and the ionosphere can be comparable, but the

variability of the earth’s ionosphere is much larger

than that of the troposphere, and is more difficult to

model. In terms of ambient electron density variations

and characteristics of density irregularities, the earth’s

ionosphere may be divided into three latitude zones:

(i) the equatorial region, covering about ±30ο dip

around the magnetic equator, (ii) the high latitude

region covering latitudes above 60ο dip around the

magnetic poles, and (iii) the mid-latitude region, lying

in between. The equatorial ionosphere is characterized

by two very prominent features: (i) the equatorial

ionization anomaly and (ii) intense irregularities in

electron density distributions. Propagation of micro-

wave L-band signals from GPS satellites is subject to

two major degrading effects: (i) introduction of an

error in the estimated range due to the group delay of

the signal traversing the ionosphere, and (ii) fluctua-

tions in the signal characteristics, i.e. amplitude and

phase, caused by irregularities in electron density

distribution. The above two effects are most severe in

the equatorial ionosphere. The Indian subcontinent

essentially covers the equatorial zone in the South-

Asian longitudes, with the magnetic equator touching

the southern tip of the peninsula near Trivandrum.

DASGUPTA et al.: EQUATORIAL IONOSPHERIC TEC STUDIES WITH GPS

279

The northern crest of the equatorial anomaly roughly

lies around the line joining Calcutta and Ahmedabad.

A location near the crest of the equatorial anomaly

provides the worst-case scenario and severely tests the

reliability of any fail-safe communication and navi-

gation system.

The group delay of the ionosphere produces range

errors (∆r), which can be determined from the relation

∆r = 40.3 × NT / f 2 m

where NT is the TEC in electrons/m2 integrated from

the observer to each GPS satellite and f the frequency

of transmission in Hz, which in the case of GPS may

be the L1 transmission at 1575.542 MHz.

As a radio signal traverses the ionosphere, the

phase of the carrier of the radio frequency trans-

mission is advanced from its velocity in free space.

The carrier phase advance, as compared with the

received carrier phase in the absence of an iono-

sphere, can be expressed as

∆φ = 40.3 × NT / c × f

where c is the velocity of light in vacuum.

In practice, the amount of this phase advance

cannot be measured readily on a single frequency

unless both the transmitter and the receiver have

exceptional oscillator stability and the satellite orbital

characteristics are extremely well known. Usually two

coherently derived frequencies are required for this

measurement. In case of GPS, the L1 and L2 trans-

mitted carriers are phase coherent, both being derived

from a common 10.23 MHz oscillator. The carrier

phase advances at the two frequencies could be repre-

sented as ∆φ1=40.3×NT/c×f1 and ∆φ2=40.3×NT/c×f2

respectively.

The differential carrier phase (∆δφ) is related to

TEC (NT) by

∆δφ = 40.3 × NT × (1 – m) / (c × f1)

where m = f1/f2, f1 = L1 = 1575.442 MHz and f2 = L2 =

1227.60 MHz.

Although differential carrier phase provides a very

precise measure of changes in relative TEC during a

satellite pass, because of the unknown number of

differential cycles of phase, absolute TEC values must

be obtained from differential group delay measure-

ments at GPS L1 and L2 frequencies. A dual frequency

GPS receiver measures the difference in ionospheric

time delays at (L2 – L1) referred to as δ(∆t). Thus

δ(∆t) = 40.3 × NT × [(1/f22) – (1/f1

2)] / c

= ∆t1× [(f12 – f2

2) / f2

2]

where ∆t1 is the ionospheric time delay at L1.

The relationship between group delay and carrier

phase is simply given by ∆φ = – f ∆t.

In the case of GPS L1 frequency, one cycle of

carrier phase advance is equivalent to 0.635 ns of

group delay. The minus sign indicates that the

differential code group delay and the differential

carrier phase advance move in opposite directions.

A prediction of the range error introduced by the

ionosphere in the equatorial zone is very difficult. The

low-cost stand-alone single frequency standard preci-

sion GPS receivers normally employ the Klobuchar

model of the ionosphere for correction of the iono-

spheric group delay. This and other models used so

far are empirical in nature and are based on TEC data

measured at several locations in the mid-latitudes,

mostly in the American and European zones. Data

from the equatorial stations are sparse and are

primarily from the South American sector. The

validity of these models in the equatorial region,

particularly the Indian longitude sector, is yet to be

tested. For operation of navigational systems with

accurate estimates of error, real-time data on TEC

have to be provided.

The group delay, which is directly proportional to

the ionospheric TEC, is practically omnipresent

throughout the day in varying degree. The TEC in the

equatorial region is characterized by large temporal

and spatial gradients in the earth’s ionosphere under

normal as well as disturbed conditions1. The error due

to group delay is normally taken care of in differential

GPS (DGPS) by measuring the difference between the

observed pseudo range and the geometrical range

from a reference station whose position is accurately

known. The error data are transmitted to users in the

neighborhood of the reference station. Because of the

effects described above in the equatorial zone, the

range over which the error data are valid from a

reference station is limited. An extension of the DGPS

is the Wide Area Augmented System (WAAS). A

number of such systems are planned/operational in

continental USA, European continent (EGNOS –

European Geostationary Navigation Overlay System),

Japan (MSAS – Multi-functional Transport Satellite

(MTSAT) Satellite-based Augmentation System) and

India (GAGAN – GPS And Geo Augmented Navi-

gation), where a number of reference stations distri-

buted over a large area will monitor TEC data.

INDIAN J RADIO & SPACE PHYS, AUGUST 2007

280

In India, GAGAN is being set up by the Indian

Space Research Organization (ISRO) in collaboration

with Airport Authority of India (AAI) with 20 dual

frequency GPS receivers stationed at different airports

all over India. Locations of GAGAN stations are

shown in Fig. 1. A 5ο×5

ο grid has been suggested by

the International Civil Aviation Organization (ICAO)

for navigation by civilian aircrafts. Within this grid,

the GPS satellite data are received and processed at

widely dispersed Wide-Area Reference Stations

(WRS), which are strategically located to provide

coverage over the required SBAS service volume.

Data are forwarded to a Wide-Area Master Station

(WMS), which processes the information from

multiple WRSs to determine the integrity, develops

differential corrections, validates results and calcu-

lates errors like the Grid Ionosphere Vertical Error

(GIVE) and User Ionospheric Vertical Error (UIVE)

for each monitored satellite and for each predeter-

mined ionospheric grid point (IGP).

In GAGAN, a Master Control Center would be set

up near Bangalore. Multiple WMSs are sometimes

provided to eliminate single-point failures within the

SBAS network. Information from a WMS is sent to

an earth station which uplinks the SBAS message

containing the different ionospheric errors like GIVE

and UIVE via C-band to geostationary satellites. The

user receives the downlink transmission in one

channel of the GPS receiver at L1 frequency. When a

user like an aircraft enters a grid, it receives data

about the ionospheric error in the vertical direction at

the grid point and the nature of distribution of the

vertical error over the grid. From the GIVE,

ionospheric errors along the slant path to different

GPS satellites would be calculated. The problem thus

essentially translates into conversion of the recorded

slant TEC from reference stations to equivalent

vertical TEC values and the reverse process from the

equivalent vertical TEC to slant TECs.

In the mid-latitudes, where the TEC normally

shows a smooth spatial variation, slant TEC could be

calculated by multiplication of the equivalent vertical

TEC with the geometrical factor sec χ at the 350 km

sub-ionospheric point, where χ is the zenith angle. In

the equatorial zone, in view of the large gradients of

TEC and its variability with geophysical conditions,

such a simple conversion is not appropriate. In

addition, the applicability of the same grid size of

5ο×5

ο, used in the relatively quiet ionosphere over the

mid-latitudes, to the very dynamic equatorial iono-

sphere is an issue yet to be addressed.

The large gradient of the equatorial ionization

anomaly persists in the local post-sunset hours till

about 2100 hrs LT. Frequently during the afternoon

hours of equinoctial months of high sunspot number

years, the gradient between the trough and the crest of

the equatorial anomaly becomes abnormally steep. On

majority of those days, equatorial F-region irregula-

rities are found to develop in the early evening hours.

Irregularities develop in the evening at F-region

altitudes of the ionosphere in the form of depletions,

frequently referred to as ‘bubbles’. These ‘bubbles’

develop over the magnetic equator and extend in both

horizontal and vertical directions. The bubbles are

upwelled by electrodynamic E × B drift over the

magnetic equator and map down to off-equatorial

locations along magnetic field lines. As the bubbles

move, normally from west-to-east across a satellite

Fig. 1—Location of GPS receivers in India under the GAGAN

program

DASGUPTA et al.: EQUATORIAL IONOSPHERIC TEC STUDIES WITH GPS

281

link, ionization depletions and scintillations are

usually encountered. The characteristics of the

bubbles, which extend several hundred kilometers on

the topside, could be studied from depletions in the

ionospheric TEC, which gives a height-integrated

profile of ionization. The time rate of change of TEC

(ROT) and its standard deviation (ROTI) measured

using GPS transmissions at Ascension Island (lat:

7.95οS, long: 14.41

οW geographic; magnetic lat:

16οS) have been shown to be indicators of the

presence of scintillation-causing irregularities2. The

GPS TEC and carrier phase measurements also show

equatorial depletions. An estimate of the range error

and ionization gradients at GPS L1 frequency

measured in the equatorial region provides an

indication for possible GPS system outages.

Increased reliance of modern society on space-

based communication and navigation system such as

GPS since the late 1980s led to formal recognition of

the International GPS Service (IGS), presently the

International GNSS Service, in 1993 by the Inter-

national Association of Geodesy (IAG) and began

routine operations on 1 Jan. 1994. The IGS is a

voluntary federation of more than 200 worldwide

agencies that pool resources and permanent GPS and

GLONASS station data to generate precise GPS and

GLONASS products. At present, the IGS tracking

network consists of 379 stations and 336 active

stations distributed around the world. The IGS global

system of satellite tracking stations, data centers, and

analysis centers provide high quality GPS data. These

include GPS satellite ephemeris, GLONASS satellite

ephemeris, earth rotation parameters, IGS tracking

stations coordinates and velocities, GPS satellite and

IGS tracking station clock information, zenith

tropospheric path delay estimates, global ionospheric

maps, etc. and data products on-line in near real-time

to meet the objectives of a wide range of scientific

and engineering applications and studies.

Figure 2 shows the IGS tracking network. A

snapshot of the global TEC using data from about 200

GPS/GLONASS sites of the IGS for 1000 hrs UT of

19 May 2006 are shown in Fig. 3. The high values of

TEC within ±30οN geographic latitudes around this

time should be noted. The number of IGS stations in

the geophysically sensitive Indian longitude sector is

very few and far between, the only one being located

at Bangalore (13.02οN, 77.57

οE geographic). The

Indian SBAS network GAGAN could fill up the void

when operational. While IGS provides a synoptic map

of different atmospheric products, a more detailed

picture over a certain region of the globe could be

obtained from a regional SBAS network like

GAGAN. Figure 4 shows a sample plot of slant TEC

measured along the paths joining all visible GPS

satellites to ground station Calcutta (one of the 20

operational stations of GAGAN) on 16 Apr. 2004.

The large variability of the curves, particularly during

the daytime is related to differing look angles of the

GPS satellites and transmitter and receiver clock

biases, among other factors. In addition, as the GPS

satellites are slowly drifting, the temporal and spatial

variations of any measured parameter always conta-

minate each other.

In some cases, a high-density GPS monitoring

station network could be effectively used to forecast

natural calamities like earthquake where extremely

Fig. 2—IGS global tracking network (379 stations and 336 active

stations as on 23 Apr. 2006)

Fig. 3—Global ionospheric TEC map generated using IGS data

for 1000 hrs UT of 19 May 2006

INDIAN J RADIO & SPACE PHYS, AUGUST 2007

282

small-scale tectonic movements could be identified.

The GPS ionospheric monitoring using dense, conti-

nuous networks such as GEONET in Japan3 has

proved to be an efficient technique to observe small-

scale perturbations. Development of high-density

GPS networks has made possible imaging of traveling

ionospheric disturbances (TIDs). Since the 1960s,

numerous observations of acoustic-gravity waves in

the ionosphere induced by solid earth events, such as

earthquakes, mine blasts or explosions have been

published4-9

. Near surface sources causing large

vertical displacement of the earth surface during

strong earthquakes are often known to excite the

atmospheric infrasonic waves that propagate upward

with increasing amplitude. As the gravity wave pro-

pagates upward, it will interact with the ionospheric

plasma through different mechanisms. The possibility

of tsunami detection by the way of coupled atmos-

pheric gravity waves has been proposed by Peltier and

Hines10

. Some early work by Yeh and Liu11

extended

this formalism to ionospheric heights, including the

effect of the Lorentz force due to the magnetic field,

and the ion-neutral particle collision terms. This

gravity wave-ionosphere interaction is one of the

main sources of TIDs. The measurement of

ionospheric TEC by using GPS transmission have

been used

by Calais and Minster7 to show the

ionospheric response to the Northridge earthquake

(Southern California) on 17 Jan. 1994 (Mw = 6.7). The

TIDs were detected at the arrival time of a tsunami

generated by the Peru earthquake on 23 June 2001

using GEONET in Japan. A preliminary study on

ionospheric perturbations observed subsequent to the

recent catastrophic 26 Dec. 2004 earthquake has been

performed by the Satellite Beacon Group of the

University of Calcutta12

.

The present paper reviews the deleterious effects of

the steep gradients of TEC prevalent in the equatorial

ionosphere, particularly the Indian longitude zone

almost throughout the day, resulting in large range

errors and range error rates on satellite-based radars

and navigation systems. Application of GPS moni-

toring of the ionosphere for studying solid earth

events like earthquakes has been indicated.

2 Effects of large spatial and temporal gradient

of TEC on satellite based augmentation system

grid size in the low latitudes

Ionospheric TEC measured using Faraday Rotation

technique at Calcutta during 1977-1990 from

geostationary ETS-II is available with the Satellite

Beacon Group of the University of Calcutta. Com-

parison of the measured TEC with those calculated

from models like the Parameterized Ionospheric

Model (PIM1.6) and International Reference Iono-

sphere (IRI-95) under varying solar activity condi-

tions and different seasons would help understand the

applicability of these models to the equatorial

region13

. Identification of an ionospheric model for

the equator and low latitudes for estimation of SBAS

grid size in this zone form one of the most essential

tasks prior to operation of satellite based navigation

systems.

Fig. 4—Diurnal variation of slant TEC (STEC) at Calcutta measured at Calcutta on 16 Apr. 2004 under the GAGAN program

DASGUPTA et al.: EQUATORIAL IONOSPHERIC TEC STUDIES WITH GPS

283

It is important to distinguish between the true

content and the Faraday or ionospheric content. In the

measurement of TEC using phase techniques, the

effect of the geomagnetic field is a second-order or

less effect. On the other hand, Faraday rotation is

directly affected by the magnitude and direction of the

geomagnetic field. As the geomagnetic field decays

approximately as the inverse cube of the radial

distance, electrons at altitudes greater than about 2000

km contribute little or nothing to the Faraday rotation

and, conversely are not detected by the Faraday

rotation technique. Calculations with a wide variety of

electron density profiles and geostationary satellite to

ground ray paths14

show that the Faraday rotation

technique measures the content up to an altitude of

about 2000 km. This content is called the Faraday

content or the ionospheric content. For comparing the

measured TEC with models, an altitude of 1600 km

was used for PIM11.6. PIM essentially provides

Faraday content of the ionosphere. The phase techni-

ques measure the total electron content up to the

source. The difference between the total content and

the Faraday content gives the protonospheric, or

plasmaspheric content from about 2000 km to the

satellite15, 16

. For a major part of the day, excepting

near the pre-sunrise time, the plasma-spheric electron

content is a very small fraction of the total electron

content in the equatorial region.

Figure 5(a) shows the diurnal variation of

measured monthly mean equivalent vertical TEC

along with those calculated from PIM1.6 and IRI-95

for the month of September 1979, equinoctial month

of a high sunspot number year. Error bars are drawn

at ±1σ level on the measured TEC. It is found that

although PIM overestimates the original data, it

follows the nature of variation closely. The IRI in

general does not correspond to the variation of the

ETS-II TEC data almost throughout the day, rather

smoothes out the variations. The difference between

the measured TEC and PIM values is least during the

late night and early morning hours. However

significant deviations between the two are noted

around the time of diurnal maximum. Figures 5(b)

and (c) show similar plots for September 1983, a

moderate sunspot number year and September 1986, a

low sunspot number year respectively. Differences

between the original values and the models still

persist. But as the ambient ionization level is low

during these periods, the deviations are not that

marked.

Large gradients of ionization in the equatorial

ionosphere exist in vertical directions also as observed

from the ionogram data from the topside sounder

satellite Alouette 1 recorded at Singapore (1οN,

104οE)

17 in 1963. Plots of the electron concentrations

at a series of fixed heights between 390 km and 650

km obtained during a pass over Singapore on a

magnetically quiet day, 10 Sep. 1963 and a magneti-

cally disturbed day, 15 Sep. 1963 are shown in Fig. 6.

It should be noted that on 10 Sep. 1963, the equatorial

Fig. 5—Comparison of monthly mean equivalent vertical TEC measured by ETS-II (136 MHz) at Calcutta with midmonth values

obtained from PIM 1.6 and IRI-95 for (a) September 1979, a high sunspot number year, (b) September 1983, a moderate sunspot number

year, (c) September 1986, a low sunspot number year (LT = UT + 0600 hrs)

INDIAN J RADIO & SPACE PHYS, AUGUST 2007

284

Fig. 6—Plots of electron concentrations at various fixed heights

on a quiet day and a disturbed day from topside sounder data of

Alouette 1 recorded at Singapore17

anomaly arch penetrates further into the ionosphere,

up to 850 km instead of 600 km, and its feet are about

15ο from the magnetic equator.

In the Indian longitude sector, sharp latitudinal

gradients of TEC are noted from GPS data recorded at

the GMRT site (lat: 19.1οN, long: 74.05

οE geogra-

phic; dip: 24οN magnetic) near Pune using a semi-

codeless dual frequency GPS receiver. Figure 7 shows

the TEC contours measured from different GPS

satellites along the signal propagation paths on 15

Apr. 2004. Ionospheric models like PIM provide good

correspondence with actual measured data in the

Indian longitude zone and show a similar picture as

evident from Fig. 8. Vertical TEC contours of 15 Apr.

2004, equinoctial month of a moderate sunspot

number year, show the latitudinal gradients of TEC

present in this region.

The problems arising out of the regular large

gradient of ionization or latitudinal gradient of TEC is

frequently compounded during the equinoctial months

of high sunspot number years when an abnormally

steep slope of the equatorial anomaly from the trough

to the crest is encountered. Figure 9 shows that during

August through October 2000, when the latitudinal

gradient of TEC exceeds 8 TEC unit/deg, on majority

of the days, intense L-band scintillations with S4max >

0.4 are also observed from Calcutta, a station situated

under the northern crest of the anomaly in the Indian

longitude sector. The corresponding threshold value18

for February through April 2001 was 6 TEC unit/deg.

Fig. 7—Slant TEC (× 1016 electron/m2) contours from GPS data recorded at GMRT site near Pune on 15 Apr. 2004 during 1500-1600 hrs

IST (IST = UT + 0530 hrs)13

DASGUPTA et al.: EQUATORIAL IONOSPHERIC TEC STUDIES WITH GPS

285

Fig. 8—Vertical TEC (× 1016 electron/m2) contours within the zone of reception of GMRT obtained using PIM1.6 on 15 Apr. 2004 at

0000, 0600, 1200 and 1800 hrs IST (IST = UT + 0530 hrs)

Fig. 9—Latitudinal gradients of equivalent vertical TEC (TEC slope) measured on different days of August through October 2000 from

LEO NOAA14 transmission at Calcutta [The filled-in circles correspond to days with post-sunset equatorial scintillations on

geostationary L-band link with S4max > 0.4, while the crosses are for days with no scintillations. A ‘threshold’ value of 8 TEC unit/deg of

the gradient, indicated by a horizontal line, shows a highly significant association with L-band scintillations. (LT = UT + 0600 hrs)]18

INDIAN J RADIO & SPACE PHYS, AUGUST 2007

286

The equatorial ionization anomaly is not confined

to the height of maximum ionization but extends

several hundred kilometers in the topside of the iono-

sphere. Because of the large gradients of ionization in

the equatorial region, simple geometric conversion of

vertical to slant TEC and vice versa is unsuitable. An

alternative method of conversion involves integrating

the ionization along the signal propagation path

joining the satellite to the ground station, referred to

here as the path integrated (PI) slant TEC13

. The PI

slant TEC takes into account the spatial distribution of

the electron density distribution occurring in the

equatorial ionosphere. Figure 10 shows a represen-

tative sample plot for September 1979 where the slant

ETS-II values, (sec χ conversion), slant PIM values

(sec χ conversion) and path integrated PIM values

(ionization integrated along signal propagation path)

are plotted. While there is substantial difference

between the model values and actual TEC data, it

should be noted that the PI slant TEC values provide a

marginally improved solution than simple geometri-

cally converted TEC, the improvement being of the

order of 10-20 TEC units. This translates to a better

accuracy in range error of 1.6-3.2 m at GPS L1

frequency.

An optimum grid size for the Indian SBAS has

been estimated from PIM for three different latitudes:

(i) at 10οN near the magnetic equator, (ii) at 22.58

οN,

near the northern crest of the anomaly, and (iii) at

17.7οN in between the magnetic equator and the

northern crest over the Indian subcontinent along the

meridian of Calcutta (88.38οE) as shown in Fig. 11.

The results obtained as one goes off the zenith to 80ο,

70ο and 60

ο elevation angles, north and south of each

station, are represented by bars drawn against sub-

ionospheric latitudes. It is of interest to note that from

particular latitude along a meridian, the PI slant TEC

values at elevation angles greater than 80ο differ very

little from the vertical TEC values. For elevation

angles in the range 70ο-80

ο, the PI slant values when

converted to equivalent vertical TEC differ from the

vertical TEC at the corresponding 350 km sub-

ionospheric latitude by about 10 TEC units. At L-

band this implies a range error of about 1.6 m. The

pierce point latitude range over which the vertical

TEC lies within 1-2 TEC unit of the PI slant values

(as one goes off from the zenith to lower elevation

angles) is thus limited to 1ο.

Figure 12 shows the result of a similar exercise

performed at the latitude of Calcutta (22.58οN) at

overhead position and 80ο, 70

ο and 60

ο elevations,

east and west of the station, which yielded a sub-

ionospheric longitude range of about 1.2ο over which

the difference between the vertical TEC and PI values

is negligible. Similar results were obtained when the

same computations were performed at 0930 and 2130

hrs LT. Thus model calculations using PIM yield a

Fig. 10—Comparison of monthly mean slant TEC measured by ETS-II (136 MHz station) at Calcutta with mid-month values of slant

TEC and PI slant TEC obtained from PIM 1.6 and IRI-95 for September 1979, a high sunspot number year. Differences between the sec χ

converted slant TEC and PI slant TEC are highlighted in the top frame (LT = UT + 0600 hrs)13

DASGUPTA et al.: EQUATORIAL IONOSPHERIC TEC STUDIES WITH GPS

287

Fig. 11—Comparison of TEC, obtained from PIM 1.6 for three different locations along the same meridian (88.38ο) at 1530 LT of 15

Mar. 2004 [The results obtained as one goes off the zenith to elevations of 80ο, 70ο and 60ο north and south of each location are

represented by bars drawn against pierce point latitudes. The topmost panel shows the result obtained from the present station, Calcutta at

22.58οN, 88.38οE, the second at a location 17.7οN, 88.38οE, and the third from a location at 10.0οN, 88.38οE. (LT = UT + 0600 hrs)]13

Fig. 12— Comparison of TEC calculated from PIM 1.6 from the latitude of Calcutta at overhead position and 80ο, 70ο and 60ο elevations,

east and west of the station, at 1530 hrs LT of 15 Mar. 2004, represented by bars against pierce point longitudes (LT = UT + 0600 hrs)13

INDIAN J RADIO & SPACE PHYS, AUGUST 2007

288

grid size of 1ο×1.2

ο for the Indian subcontinent, which

is considerably smaller than the 5ο×5

ο size used in

WAAS and EGNOS.

3 Effects of large gradients of TEC in the

equatorial region on satellite-based communi-

cation and navigation links

Irregularities develop in the evening hours at F-

region altitudes in the form of depletions. The edges

of the depletions are very sharp resulting in large time

rate of change of TEC (ROT) in the equatorial iono-

sphere, even during magnetically quiet conditions.

Satellite links operating through such steep edges

experience large range error rates, which pose serious

problems for position-fixing using GPS in the

equatorial region.

The dual-frequency semi-codeless GPS receiver

operational at GMRT site near Pune provides since

April 2003 TEC measured from group delay as well

as carrier phase, and signal-to-noise ratio at L1

frequency recorded at a sampling interval of 1s. The

location of this receiver situated in between the

magnetic equator and the northern crest of the

equatorial ionization anomaly, is ideally suited for

studying equatorial bubbles. The GPS links towards

the north of the station normally look through the

northern crest of the equatorial anomaly and would

frequently encounter the northern limit of the

equatorial irregularity belt. Looking towards the

south, an end-on view of field-aligned bubbles over a

longer path can be possible in the satellite-to-ground

propagation path. GPS data for the equinoctial period

February through April 2004 has been presented in

DasGupta et al.19

to highlight the problems associated

with GPS links operating through the steep gradients

of ionization on the walls of the irregularities.

Figure 13(a) shows a typical sample of signal-to-

noise ratio of the satellite link (SNR-CA), operated in

the coarse acquisition (C/A) mode, showing intense

scintillations and associated depletions in TEC calcu-

lated from group delay (TECtau) of GPS satellite

SV15 on 16 Mar. 2004. The 90-min moving average

of TECtau (TEC-mov-avg) is shown along with

TECtau. Large fluctuations in TECtau near the ends

of the track could be ascribed to multipath effects at

low elevation angles. The TEC depletion, which

occurred from 1441-1523 hrs UT had amplitude of 28

TEC units over an ambient of 61 TEC units. The

SNR-CA records were clear prior to and after the

bubble.

Figure 13(b) shows the distribution of the TEC

depletions in equatorial plasma bubbles observed

from GMRT site within the selected elevation swath

(greater than 60ο) during February through April

2004. It may be noted that out of the observed 45 bite-

outs, the maximum amplitude was found to be about

33 TEC units over an ambient of 40 TEC units and a

median depletion of about 9 TEC units against an

ambient 33 TEC units. The maximum amplitude

corresponds to a range error of about 5.3 m at GPS L1

frequency and the median to about 1.4 m range error.

Fig. 13—(a) A typical sample record from GPS satellite SV16

observed19 from GMRT site on 16 Mar. 2004 [The line labeled 1

refers to the elevation angle of the satellite during its transit, 2

represents the TEC calculated from the group delay (TECtau), 3 is

the 90-min moving averaged TECtau (TECtau-mov-avg) and 4

shows the signal-to-noise ratio for the satellite link operated in the

coarse-acquisition (C/A) mode (SNR-CA), (b) amplitude

distribution of TEC depletions observed from GMRT site along

the tracks of different GPS satellites during February-April 2004

at elevation angles exceeding 60ο

DASGUPTA et al.: EQUATORIAL IONOSPHERIC TEC STUDIES WITH GPS

289

The observed bubbles often show asymmetry

between the leading (eastern) and trailing (western)

edges. Figure 14(a) and (b) compare the slopes of

eastern and western walls of the bubbles. It may be

noted that in general, the trailing slope, i.e. the

western wall is sharper than the leading slope, i.e. the

eastern wall. The leading edge slope has a maximum

value of 3 TEC unit/min with a median of about 1

TEC unit/min. While the maximum corresponds to a

range error rate of 0.48 m/min, the median yields a

range error rate of 0.16 m/min. The noted maximum

value of the trailing edge slope of 14.4 TEC units/min

and median of 1.8 TEC unit/min in Fig. 14(a) and (b)

conforms to the idea of asymmetric edges of the

bubble. In this case, the maximum value produces a

range error rate of 2.3 m/min and the median

0.29 m/min.

4 Ionospheric perturbations observed by GPS

subsequent to occurrence of earthquakes Under the GAGAN program, 20 dual frequency

GPS receivers stationed all over India measure TEC

along the slant ray path (STEC). The data contains

STEC, as well as azimuth, elevation, satellite PRN

number, time in UTC, S4 and phase scintillation index

at 1-minute interval in RINEX format20

. By measu-

ring the carrier phase at the two frequencies the STEC

is obtained21

along the path from satellite to the

receiver.

On 26 Dec. 2004, at 00:58:53 hrs UT, a strong

earthquake (Mw = 9.15) originated in the Indian Ocean

Fig. 14—Distribution of (a) leading (eastern wall of the

irregularity) edge and (b) trailing (western wall of the irregularity)

edge, of the bite-out in TEC observed19 from GMRT site along the

tracks of different GPS satellites during February-April 2004 at

elevation angles exceeding 60ο.

Fig. 15—Comparison of STEC deviations at three stations:

Calcutta (22.58οN, 88.38οE), Vishakhapatnam (17.72οN, 83.22οE)

and Aizwal (23.83οN, 92.62οE) on satellite SV3 on 26 Dec. 2004

data with those of 25 Dec. 2004 (one day before the quake) and 27

Dec. 2004 (one day after the quake) and five day average before

the earthquake. The arrow indicates the commencement of the

earthquake

INDIAN J RADIO & SPACE PHYS, AUGUST 2007

290

just north of Simeulue island, off the western coast of

northern Sumatra, Indonesia. This earthquake gene-

rated Tsunami that was among the deadliest disasters

in modern history. The hypocenter of the quake was

3.31οN, 95.85

οE, some 160 km west of Sumatra at a

depth of 30 km below the mean sea level. The

epicenter of the quake was 3.29οN and 95.94

οE.

Among the GAGAN stations, Vishakhapatnam

(17.72οN, 83.22

οE), Calcutta (22.58

οN, 88.38

οE) and

Aizwal (23.83οN, 92.62

οE), located in the eastern part

of India recorded prominent perturbations of STEC on

four different satellites (SV3, SV13, SV19 and SV23)

links in the morning hours around 0136-0145 hrs UT

for 26 Dec. 2004, nearly one hour after the

earthquake. This perturbation also showed time delays

that increase with the distance from the epicenter. The

deviations of STEC from the 90-min moving average

were calculated. In Fig. 15, STEC deviations for 26

Dec. 2004, the day of the quake was compared with

those of (i) the average value of STEC for 20-25 Dec.

2004 (ii) STEC for 25 Dec. 2004, the day prior to the

earthquake, and (iii) STEC for 27 Dec. 2004, the day

after the quake, for SV3 from three different stations,

namely Calcutta, Visakhapatnam and Aizwal. The

marked deviations of the STEC perturbations on

December 26 could be well identified from the rest.

Figure 16 shows the STEC deviations obtained from

Calcutta, Visakhapatnam and Aizwal on GPS links

SV3, SV13, SV19 and SV23. The propagating nature

of the ionospheric disturbance could be noted from

the time delays of STEC peaks on different GPS

links, progressively from the east to the west.

5 Discussion Regular as well as irregular gradients of equatorial

ionization anomaly play a dominant role in charac-

terizing the performance of satellite based communi-

cation and navigation systems such as GPS. A

comparison of the equivalent vertical TEC values

with those generated by the models clearly establishes

the fact that the applicability of these models to the

equatorial latitudes is limited. While the IRI model

does not follow the trend of the actual data at all

under most geophysical conditions (different months

and different sunspot number years), the PIM model

could be used with some restriction. It fits reasonably

well with the measured data in the late night and early

morning hours of high solar activity years until about

0830 hrs LT. The lack of correspondence near the

diurnal maximum and the decay phase of the anomaly

could be attributed to the fact that the electrodynamic

drift parameters used in PIM are climatic in nature

averaged over a large data base and obtained from the

American longitude sector. Comparison of measured

TEC with model values has been reported earlier22

.

However, the study conducted at the University of

Calcutta13

is based on a much longer interval of data

covering more than one solar cycle (1977-1990).

Model calculations with PIM show that within the

anomaly region, because of the large spatial gradients

of ionization, the slant TEC approximates the vertical

TEC for a very limited (~10ο) angle around the zenith.

It should be noted that model calculations yield a grid

size of 1ο×1.2

ο for the Indian subcontinent, which is

considerably smaller from the 5ο×5

ο size as used in

the WAAS or EGNOS.

Fig. 16—Variation of STEC deviations at three stations, Calcutta,

Visakhapatnam, and Aizwal on GPS satellites SV3, SV13, SV19

and SV23 during the period 2330-0500 hrs UT of 26 Dec. 2004

[The tracks of the satellites from Calcutta are also shown.]

DASGUPTA et al.: EQUATORIAL IONOSPHERIC TEC STUDIES WITH GPS

291

The characteristics of the ionospheric bubbles,

namely the amplitude and asymmetric edges, which

determine the range error and range error rate respec-

tively, had been studied earlier using observations

from geostationary satellites23, 24

. The depletions in

TEC associated with VHF amplitude scintillations at

137 MHz recorded at Arequipa (lat: 16.4οS, long:

71.5οW geographic; magnetic dip: 9

οS), Peru during

the solar maximum period 1979-1980 have usually

been found to have an amplitude less than 5 TEC

units, although depletions with amplitude as large as

20 TEC units had sometimes been encountered23

.

Examples of TEC depletion events registered on a

136 MHz VHF beacon recorded at equatorial and

low-latitude stations in the Brazilian longitude sector

during the equinoctial and local summer December-

January months of 1982-1983 using Faraday Rotation

technique show steep rate of change24

of the order of

7ο/min. The sharper western wall of the irregularity

measured at GMRT site may in part be attributed to

the effect of the neutral wind25

.

The maximum gradient of the western wall has

been found to be 14.4 TEC units/min. Such steep

edges of TEC depletions are quite frequent even

under magnetically quiet conditions in the equatorial

ionosphere, particularly during the equinoctial months

of solar maximum period. However, in the mid-

latitudes, enhancements with such sharp edges are

usually associated with magnetically disturbed iono-

sphere. During the magnetic super-storm of 30 Oct.

2003, a large storm-enhanced density (SED) plume

extended over the continental US and Canada in a

southeast to north-west direction, with the largest

TEC exceeding 200 TEC units in the western US.

Large TEC fluctuations of the order of 5 TEC

unit/min, in a quasi-magnetic east-west direction

along lines of geomagnetic latitude and also in a

south-east to north-west direction following the large

TEC gradients of the SED were noted26

. The median

value of the amplitude of TEC bite-out observed from

GMRT site, which corresponds to 1.4 m range error at

GPS L1 frequency, coupled with the sharp edges of

the depletions result in high range error rates ~ 0.30

m/min and may pose serious problems for position-

fixing using GPS in the equatorial region, even under

magnetically quiet conditions19

.

The GPS TEC measurements have become a very

useful tool for studying ionospheric response to

earthquakes. Ionospheric effects have been observed

on the slant TEC from different stations near the east

coast of the Indian subcontinent subsequent to the

Sumatra-Andaman earthquake of 26 Dec. 2004. A

significant perturbation of the TEC (1.5-2 units of

TEC) approximately 45 min after the earthquake was

recorded on a number of satellites from stations like

Vishakhapatnam, Hyderabad, Raipur, Calcutta,

Guwahati, and Aizwal. No such perturbation was

recorded in TEC plot at stations in the northern and

western parts of the country. The observed iono-

spheric variation is thus regional in nature.

Although such ionospheric perturbations are attri-

buted to seismic activities, the mechanism of coupling

of the ionosphere to earthquake is yet to be fully

understood. In the earliest formulation based on

coupled atmospheric gravity waves, a vertical

displacement of the sea surface due to a Tsunami can

be a source of gravity wave in the atmosphere. The

surface gravity wave propagates obliquely upward

with an increase in the wave amplitude due to the

exponential decrease of the atmospheric density and

manifests as travelling ionospheric disturbances (TID)

in the upper atmosphere27, 11

. Amplitude of ionization

perturbations due to TID has been estimated to be up

to 10% of the background28

. In order to establish any

definitive cause-effect relationship of severe seismic

activity event and ionospheric response numerical

models based on physical processes and the severity

of seismic activity has to be developed.

Acknowledgement This research has been sponsored in part by the

Indian Space Research Organization (ISRO) through

the S K Mitra Center for Research in Space Environ-

ment, University of Calcutta, Kolkata 700 009.

References 1 Klobuchar J A, Doherty P H, DasGupta A, Sivaraman M R,

& Sarma A D, Equatorial anomaly gradient effects on a

space-based augmentation system, Proceedings of the

International Beacon Satellite Symposium, Boston (USA),

2001.

2 Basu S, Groves K M, Quinn J M & Doherty P, A comparison

of TEC fluctuations and scintillations at Ascension Island, J

Atmos Sol-Terr Phys (UK), 61(1999) 1219.

3 Hatanaka Y, Iizuka T, Sawada M, Yamagiwa A, Kikuta Y,

Johnson J M & Rocken C, Improvement of the analysis

strategy of GEONET, Bull Geogr Surv Inst (Japan), 49

(2003) 11.

4 Bolt B A, Seismic air waves from the great 1964 Alaska

earthquake, Nature (UK), 202 (1964) 1095.

5 Yuen P C, Weaver P F & Suzuki R K, Continuous traveling

coupling between seismic waves and the ionosphere evident

in May 1968 Japan earthquake data, J Geophys Res (USA),

74 (1969) 2256.

INDIAN J RADIO & SPACE PHYS, AUGUST 2007

292

6 Blanc E, Observations in the upper atmosphere of infrasonic

waves from natural or artificial sources: a summary, Ann

Geophys (UK), 3 (1985) 673.

7 Calais E & Minister J B, GPS detection of ionospheric

perturbations following the January 17, 1994, Northridge

earthquake, Geophys Res Lett (USA), 22 (1995) 1045.

8 Hobara Y & Parrot M, Ionospheric perturbations linked to a

very powerful seismic event, J Atmos Sol-Terr Phys (UK), 67

(2005) 677.

9 Artru J, Ducic V, Kanamori H & Lognonne P, Ionospheric

detection of gravity waves induced by tsunamis, Geophys J

Inst (UK), 160 (2005) 840.

10 Peltier W R & Hines C O, On the possible detection of

tsunamis by a monitoring of the ionosphere, J Geophys Res

(USA), 81 (1976) 1995.

11 Yeh K C & Liu C H, Theory of Ionospheric Waves

(Academic Press, New York), 1972, 402.

12 DasGupta A, Das A, Hui D, Bandyopadhyay K K &

Sivaraman M R, Ionospheric perturbations observed by the

GPS following the December 26th, 2004 Sumatra-Andaman

earthquake, Earth Planets Space (Japan), 58 (2006) 167.

13 Paul A, Chakraborty S K, Das A & DasGupta A, Estimation

of Satellite Based Augmentation System Grid Size at Low

Latitudes in the Indian Zone, Navigation (USA), 52 (2005) 15.

14 Titheridge, Determination of ionospheric electron content

from the Faraday rotation of geostationary satellite signals,

Planet Space Sci (UK), 20 (1972) 353.

15 Davies K, Fritz R B & Gray T B, Measurements of the

columnar electron contents of the ionosphere and the plasma

sphere, J Geophys Res (USA), 81 (1976) 2825.

16 Hargreaves J K, On the presentation of ATS-6 electron

content data, J Atmos Terr Phys (UK), 40 (1978) 493.

17 King J W, Reed K C, Olatunji E O & Legg A J, The behavior

of the topside ionosphere during storm conditions, J Atmos

Terr Phys (UK), 29 (1967) 1355.

18 Ray S, Paul A & DasGupta A, Equatorial scintillations in

relation to the development of ionization anomaly, Ann

Geophys (UK), 24 (2006) 1429.

19 DasGupta A, Paul A, Ray S, Das A & Ananthakrishnan S,

Equatorial bubbles as observed with GPS measurements over

Pune, India, Radio Sci (USA), 41 (2006) RS5S28,

doi:10.1029/2005RS003359.

20 Mannucci A J, Ho C M, Pi X, Wilson B D & Lindqwister U

J, Group delay and phase advance due to ionospheric total

electron content, Proceedings of the workshop on Space

Weather Effects on propagation of Navigation and

Communication Signals edited by E J. Fremouw, COMSAT

corp., Bethesda, Md. (USA), 1997.

21 Klobuchar J A, Global Positioning System: Theory and

Applications, Volume I, edited by B W Parkinson and J J

Spilker Jr., (American Institute of Aeronautics and

Astronautics. Inc.), 1996, 485.

22 Ezquer R G, de Adler, N O & Heredia T, Predicted and

Measured Total Electron Content at Both Peaks of the

Equatorial Anomaly, Radio Sci (USA), 29 (1994) 831.

23 DasGupta A, Basu S, Aarons J, Klobuchar J A, Basu Su &

Bushby A, VHF amplitude scintillations and associated

electron content depletions as observed at Arequipa, Peru, J

Atmos Terr Phys (UK), 45 (1983) 15.

24 Abdu M A, Batista I S, Sobral J H A, de Paula E R & Kantor

I J, Equatorial ionospheric plasma bubble irregularity

occurrence and zonal velocities under quiet and disturbed

conditions, from polarimeter observations, J Geophys Res

(USA), 90 (1985) 9921.

25 Tsunoda R T, Time evolution and dynamics of equatorial

backscatter plumes: 1. Growth phase, J Geophys Res (USA),

86 (1981) 139.

26 Basu Su, Basu S, Makela J J, Sheehan R E, MacKenzie E,

Doherty P, Wright J W, Keskinen M J, Pallamraju D, Paxton

L J & Berkey F T, Two components of ionospheric plasma

structuring at mid-latitudes observed during the large

magnetic storm of October 30, 2003, Geophys Res Lett

(USA), 32 (2005) L12S06, doi:10.1029/2004GL021669.

27 Clark R M, Yeh K C & Liu C H, Interaction of internal

gravity waves with the ionospheric f2-layer, Phys Earth

Planet Inter (UK), 33 (1971) 1567.

28 Kirchengast G, Elucidation of the physics of the gravity

wave-tid relationship with the aid of theoretical simulations,

J Geophys Res (USA), 101 (1996) 13353.