Introduction
The global age-long interest in the ionosphere is apparently being sustained
due to its tremendous applications in radio communications (Rama Rao et al.,
1997; Rabiu et al., 2013). The variation in ionosphere with time and
location on earth necessitates its study at several points on earth for a
long time. The equatorial and low-latitude ionosphere manifests a number of
unique phenomena, such as the equatorial electrojet (EEJ), equatorial spread
F (ESF), equatorial plasma bubble (EPB), and equatorial ionization anomaly
(EIA) among others, and is characterized by large transient variations
(Bagiya et al., 2009; Mukherjee et al., 2010; Chauhan et al., 2011; Bolaji
et al., 2012). The equatorial ionosphere is highly dynamic and consequently
poses serious threats to communication and navigation systems (Akala et al.,
2010, 2011, 2012).
The ionospheric parameter that has an overbearing influence on GPS-based communication and navigation systems is the total electron content
(TEC) (Akala et al., 2013). TEC is the number of electrons in the column of 1 m2 cross section
that extends from a GPS satellite to a GPS receiver. This important
parameter is a by-product of GPS data, which can also be used to survey the
ionosphere and can be used to provide an overall description of the
ionosphere (Mukherjee et al., 2010).
Bilitza (2001) rightly noted that a good description of the variability in
ionospheric magnitudes is a necessary prerequisite for improvement of the
performance of the ionospheric models. Studies on diurnal variation in TEC
reveal useful information about the physical processes responsible for the
ionospheric behaviour and TEC is fast becoming an important parameter for
both geophysical and engineering applications (Pandey et al., 2001; Mukherjee
et al., 2010). In Nigeria, Bolaji et al. (2012) reported that during low
solar activity the TEC over Ilorin, a station close to the trough of the EIA,
exhibits consistent minimum diurnal variation during pre-sunrise hours
between 05:00 and 06:00 LT, rises steeply during the sunrise period
(07:00–09:00 LT), and subsequently rises very slowly from 10:00 LT to the
peak during the daytime, mostly around 12:00–16:00 LT. Bagiya et al. (2009)
had earlier reported similar diurnal variation patterns during low solar
activity periods near the crest region of the EIA
in India and confirmed that the diurnal characteristics of TEC depend on
season, solar activity, geomagnetic activity, and latitude.
The F2 layer in the vicinity of the magnetic dip equator is characterized by
a depression, or trough, in the ionization density at the equator and two
humps, one on each side of the equator (at about ±17∘ magnetic
latitude) during the day that lasts for several hours after sunset. This
interesting phenomenon is called the equatorial ionospheric anomaly (EIA)
or the Appleton anomaly (Appleton, 1946). The cause of the anomaly is often
attributed to the so-called fountain effect, whereby an eastward electric
field at the equator gives rise to an upward E×B drift
during the daytime. After the plasma is lifted to greater heights it is able
to diffuse downward along magnetic field lines under the influence of gravity
and pressure gradient forces. The net result is the formation of a plasma
fountain, which produces an enhanced plasma concentration (crest) at
higher latitudes and a reduced plasma concentration (trough) at the equator.
The daytime dynamo-generated eastward electric field combined with the
northward geomagnetic field lifts the equatorial ionosphere from 700 km up to
over 1000 km. After losing momentum, the electrons diffuse
along the field lines to either side of the equator to form two crests (Yeh
et al., 2001).
Rama Rao et al. (2006a) studied the temporal and spatial variations in GPS
TEC using simultaneous measurements from the Indian GPS network of receivers
during the low solar activity period and observed that the diurnal variation
in the EIA region reaches its maximum value between 13:00 and 16:00 LT,
whereas near the equator the daytime maximum is broad and its peak is delayed and
occurs around 16:00 LT. Similarly, the daytime minimum in GPS TEC occurs between
05:00 and 06:00 LT at all stations from the equator to the EIA crest region.
However, beyond the crest region an extended day minimum is found to occur,
which is flat during most of the nighttime hours, a feature that is similar
to that at mid-latitudes. The diurnal variation in GPS TEC shows a minimum to
maximum variation in about 5–50 TECU at the equator and from 5 to 90 TECU
at the EIA crest region.
The seasonal variations in vertical TEC are higher during the
equinox than the solstice during low solar activity (Wu et al., 2004; Bagiya et
al., 2009; Chauhan et al., 2011) and high solar activity (Natali and Meza,
2011) at different stations. Rama Rao et al. (2006a) observed that the
seasonal variation in TEC reaches a maximum during the equinoctial months followed by
winter and is at a minimum in the summer, a feature similar to that observed
by Rabiu et al. (2013) in
the Indian EEJ strength for the corresponding seasons. Scherliess and Fejer (1999) had earlier inferred that
daytime E×B drift velocities are larger in the
equinoctial months and winter months than in the summer months, and this
could result in semi-annual variation. Olatunji (1967), Bailey et al. (2000),
and Liu et al. (2006, 2009) found that this semi-annual variation is related
to the variation in the noon solar zenith angle, which is an important factor
in ionization. Wu et al. (2004), Rama Rao et
al. (2006a, b), and Lee et al. (2010) attributed the semi-annual variation to
a combined effect of solar zenith angle and geomagnetic field geometry.
The list of stations used in the study with their respective
geographical and geomagnetic coordinates.
ID
Location
Geo. lat (∘ N)
Geo. long (∘ E)
Mag. lat (∘ N)
Mag. long (∘ E)
RUST
Port Harcourt
4.80
6.98
-4.33
78.76
CLBR
Cross River
4.95
8.35
-4.30
80.09
FPNO
Imo
5.43
7.03
-3.90
78.85
UNEC
Enugu
6.42
7.50
-3.25
79.36
ULAG
Lagos
6.52
3.40
-3.03
75.45
OSGF
FCT
9.03
7.49
-1.64
79.50
FUTY
Yola
9.35
12.50
-1.32
84.31
ABUZ
Kaduna
11.15
7.65
-0.13
79.75
BKFP
Kebbi
12.47
4.23
0.72
76.62
Geo: geographical co-ordinate. Mag: geomagnetic co-ordinate. Lat:
latitude.
Long: longitude.
Quantitative study of transient variations in GPS TEC, involving
simultaneously measured data from multiple stations in Nigeria, has been
hindered over the years due to the dearth of distributed GPS facilities. Recent
deployment of a network of Nigerian GNSS Reference Network (NIGNET) CORS by the
Nigerian Office of the Surveyor General, as well as the reduced costs of microcomputing, provided an essential foundation for this study. The present
study attempts to investigate the diurnal and seasonal variations in GPS TEC
obtained from simultaneous GPS measurements from nine locations in Nigeria, a
region under the equatorial anomaly region, covering geomagnetic coordinates
bounded between geomagnetic longitudes 75.45 and 84.31∘ E and
geomagnetic latitudes -4.33 and 0.72∘ N.
Data and method of analysis
The study locations consisted of nine stations distributed over Nigeria, a
region within the equatorial and low latitudes. The selected locations and
their details, including their geographical and geomagnetic coordinates, are
shown in Table 1 in order of increasing latitude.
A Nigerian map showing the locations of the various selected stations is shown
in Fig. 1. Raw GPS (observable) data in RINEX format for these nine stations
were used for this research work. The Ionospheric GPS TEC was obtained from
the ground-based GPS receiver stations of NIGNET equipment being operated by the Office of the Surveyor General of the
Federation (OSGoF) of Nigeria for the year 2012. Description of the NIGNET
network and the managing agency is given in Rabiu et al. (2014) and Ayorinde et
al. (2016).
The distribution of the NIGNET GPS stations used for the study.
The axes shows the geographical coordinates in degrees; the red solid line
crossing near ABUZ is the magnetic equator.
![]()
The slant TEC (STEC) records obtained from GPS are polluted with satellite differential delay (bS, satellite bias) and receiver differential delay (bR, receiver bias), coupled with receiver inter-channel bias (bRX). This uncorrected STEC measured at every 1 min interval
from the GPS receiver derived from all the visible satellites at all the
stations is converted to vertical TEC (VTEC). VTEC can be expressed as
VTEC=STEC-[bR+bS+bRX]/SE,
where STEC is the uncorrected slant TEC measured by the receiver, S(E) is
the obliquity factor with zenith angle (z) at the ionospheric pierce point
(IPP), E is the elevation angle of the satellites in degrees, and VTEC is
the vertical TEC at the IPP. The S(E) is defined by Mannucci et al. (1993)
and Langley et al. (2002) as follows:
SE=1cosz=1-RE×cosERE+hS2-0.5.
RE is the mean radius of the earth measured in km and
hs is the
height of the ionosphere from the surface of the earth, which is
approximately equal to 350 km. These analyses from Eqs. (1) and (2) were
implemented in the GPS TEC analysis software developed and freely distributed
by the Institute for Scientific Research, Boston College, MA, USA. The
GPS TEC software runs on a Windows operating system with the availability of
internet. The raw RINEX GPS data were processed using this GPS TEC
analysis software. This software reads raw data, processes cycle slips in
phase data, reads satellite biases from International GNSS Service (IGS) code
file (if not available, it calculates them), calculates receiver bias, and
calculates the inter-channel biases for different satellites in the receiver.
To eliminate the effect due to multipath, a minimum elevation angle of
20∘ is used. The VTEC data estimated are then subjected to a two-sigma
(2σ) iteration, which is a
measure of GPS point positioning accuracy (95 % confidence level).
Research efforts that have utilized this GPS TEC software include the works
of Bolaji et al. (2012, 2013), Olwendo et al. (2013), Rabiu et al. (2014),
and Ayorinde et al. (2016), among others.
Contour plots of the diurnal variation in GPS TEC measured at the
study areas in Nigeria. The white sections in the plots show unavailability of
data.
![]()
Results and discussion
Diurnal variation in total electron content of the ionosphere over
Nigeria
The processed TEC data obtained from GPS TEC analysis software developed by
the Institute of Scientific Research, Boston College, USA, gave GPS TEC data
at minute intervals in ASCII format. These minute GPS TEC data were scaled down
to hourly values for all the stations used. The time convention for these
analyses is in local time (LT). Nigeria is 1 h ahead of Greenwich meridian
time GMT; 01:00 UT is 02:00 LT in Nigeria. The hourly values of GPS TEC for
each individual hour for all the days of the year from 1 January to 31 December 2012
were collated together to obtain the diurnal variation. The hourly
values of GPS TEC were plotted against local time to examine the hourly
variation (diurnal) and this was done for the entire nine stations using
surfer software package to generate the local TEC maps for each station as
shown in Fig. 2. Surfer software has a built-in kriging function that enables
it to account for missing data using appropriate interpolation techniques.
However, only six stations out of the nine stations had consistent data that
could translate to meaningful GPS TEC maps. The other three stations were
afflicted with missing data due mainly to occasional power outages and so are
not reported in Fig. 2. The diurnal variations in GPS TEC in all stations in
Nigeria show characteristics typical of the low-latitude ionosphere (e.g. Rama
Rao et al., 2006a, b and Rabiu et al., 2014). It is clearly shown from the
plots that TEC exhibits consistent minimum diurnal variation during the
pre-sunrise hours 04:00 to 05:00 LT with magnitude of 0 to 5 TECU, rises
steeply during the sunrise period (07:00 to 09:00 LT), and then rises very
slowly from 10:00 LT with the intensity of the sun to an afternoon maximum
between 12:00 and 16:00 LT. It then falls to its minimum just before
sunset. Large variations in GPS TEC are observed in daytime, while nighttime
variations are found to be minimal at all the stations.
Hourly variation in GPS TEC in all the months along latitude.
Data from all stations were used in this figure, except RSUT,
CLBR, and FPNO, which were not used to derive maps for the months of March Equinox.
Also, RSUT and FPNO were not used to derive maps for the months of December
Solstice due to poor data quality.
![]()
Fig. 2 shows that the magnitude of GPS TEC is generally high
during daytime at all locations. The early morning increase in GPS TEC is
relatively faster at all stations than the evening decrease in GPS TEC. The
daytime GPS TEC values are generally greater than the nighttime values. This can be
attributed to the absence of solar radiation at nighttime. It is observed
that during the equinoctial days the late afternoon decrease in GPS TEC is
equally steep, with occasional post sunset peaks at all the stations. Likewise, during nighttime, the ionosphere maintains an average GPS TEC
value of about 15 to 20 TECU. During the solstice days, similar features are
also seen but with a reduced intensity of 10 to 15 TECU. It can be concluded
that TEC increases as the intensity of the sun increases with the time of
day. Also, minimum TEC occur around the same time (05:00 LT) on all the days
at all the stations, which shows that as the intensity of the sun decreases,
TEC decreases. The trend of this result is in accordance with the diurnal
variation in TEC at some other locations in the earlier works of Rastogi et
al. (1971), Warnant (2000), Rama Rao et al. (2006a, b), Bagiya et al. (2009),
Bolaji et al. (2012), and others, which showed that the diurnal variation in
TEC shows a short-lived predawn minimum, a steady early morning increase,
followed by an afternoon maximum and gradual fall after sunset.
Hourly variation in total electron content<?xmltex \hack{\break}?> along latitude
An interesting feature in the geographic location of Nigeria is the magnetic
equator that passes through the northern part of the entire country
providing a unique opportunity for studying important ionospheric phenomena,
such as TEC variation, the EEJ,
the EIA, the equatorial ionization and temperature
anomaly (EITA), and the occurrence of intense scintillations.
Figure 3, which displays the hourly variation in TEC as a function of
latitude,
reveals an occurrence of obvious variation in the hourly plots of TEC along
latitudes in all the months in year 2012. Figure 3 was also obtained using
surfer software package to generate the local TEC maps for each month. The
hourly variation shows a short, steep increase of about 10 to 16 TECU of TEC
occurring between 01:00 and 02:00 LT, a sharp and short-lived daytime minimum of
about 0 to 2 TECU occurring between 04:00 and 06:00 LT, and a daily maximum of
TEC occurring between 12:00 and 14:00 LT. A similar variation was
observed for all the months of the year except for the equinox months of
March, April, September, and October, which had a sharp and rapid decrease in TEC
observed at 20:00 LT with subsequent enhancement at 23:00 LT.
After the occurrence of post-sunset enhancement at 23:00 LT, TEC across all
the geomagnetic latitudes further gradually and smoothly decayed through
midnight until the pre-sunrise hours. The magnitude of TEC post-sunset variation
is always greater than its sunrise variation. This post-sunset decrease and
enhancement could be attributed to abrupt onset scintillations, plasma
bubbles, and the spread-F phenomenon, which was also observed in the work of Bolaji
et al. (2012).
Hourly variation in GPS TEC in all the months along longitude.
Data from all stations were used in this figure, except RSUT,
CLBR, and FPNO, which were not used to derive maps for the months of March Equinox.
Also, RSUT and FPNO were not used to derive maps for the months of December
Solstice due to poor data quality.
![]()
However, the spread of GPS TEC at the low-latitude stations in Nigeria is
at a minimum during the nighttime and at a maximum during the daytime, which may be
attributed to the high ionization due to intense solar radiation. In all the
months, a comparatively high value of GPS TEC above 40 TECU was observed
between 12:00 and 16:00 LT at all the latitudes except in the month of
December when the recorded GPS TEC value was below 40 TECU. This could be due
to inhibition of EIA, which is completely inhibited on the day of the counter
electrojet, resulting in a lower TEC value. Dabas et al. (1984) and Aravindan
and Iyer (1990) reported that the EEJ has a pronounced influence on TEC over
a large latitudinal belt from the equator to the 25∘ N dip
latitude. Rama Rao et al. (2006a) have shown that the EEJ
controls the altitude of lifted plasma and the location of the crest of the
equatorial ionization anomaly. It can be concluded that during the daytime the
GPS TEC variability at low latitudes is mainly driven by variations in the
equatorial electric fields. The equatorial ionization anomaly is a result of
the so-called fountain effect, which gives rise to lifting of the equatorial
plasma to higher altitudes, during most of the daytime hours. This plasma
subsequently diffuses along the geomagnetic field lines to either side of the
magnetic equator, owing to the effects of ambipolar diffusion, gravity, and
pressure gradients and giving rise to an accumulation of ionization at the
F-region altitudes around ±15∘ geomagnetic latitudes. This
results
in the formation of crests of ionization, while simultaneously depleting the
ionization over the magnetic equator.
Hourly variation in GPS TEC across longitudes
The hourly variations in GPS TEC across geomagnetic longitudes in all the
months of the year 2012 were examined using contour plots as shown in Fig. 4.
Figure 4 was obtained using the Surfer software package to generate the local TEC
maps for each month. The hourly variation shows an early morning steep of
about 12 to 14 TECU occurring between 01:00 and 02:00 LT in longitudes
75.45–80.09∘ E and a short-lived predawn minimum of 0–2 TECU occurring
between 04:00 and 06:00 LT at all the longitudes. TEC increases with time
across all the longitudes until noontime; a postnoon maximum is observed in all
the months at about 14:00 LT. TEC decreases gradually as intensity of the
solar radiation decreases along all the longitudes. Generally, the hourly
variations in TEC along the longitudes show a predawn minimum followed by
an early morning steady increase, an afternoon maximum, and then a post-sunset
gradual reduction in TEC, with the equinoctial months of March and April
depicting nighttime enhancement more prominently at 23:00 LT. The gradual
increase in TEC to a maximum value at peak hours of the day at equatorial and
low latitudes has been attributed to solar extreme ultraviolet (EUV)
ionization coupled with the vertical E×B drift (Bolaji et
al., 2012).
The nighttime decrease is due to the size of the magnetic flux tubes, which
are so small that electron content in these tubes collapses rapidly after
sunset in response to the low temperatures in the thermosphere at night,
leading to low GPS TEC values. During sunrise, the magnetic flux tubes again
filled up because of their small volume, resulting in a sudden increase in
ionization due to increasing thermospheric temperatures during sunrise (Oron
et al., 2013). The observed nighttime GPS TEC enhancement could be attributed
to the tidal winds, which blow the ionization across the geomagnetic field.
According to Hanson and Mofett (1966), a large-scale electrostatic field is
produced at the low latitudes. The electrostatic field is primarily eastward during the day and
westward, with the eastward fields being responsible for the
upward plasma drift motion and the westward fields during the night, causing
the downward drift motion. This plasma fountain reverses during nighttime hours
and the northward motion of the crest of ionization during the daytime reverses
to a southward motion during the night. The downward motion at the geomagnetic
dip equator and the southward motion of ionization could be responsible for
the nighttime enhancement of GPS TEC observed in these months.
Seasonal mean values of TEC.
ID
Location
March Equinox
June Solstice
September Equinox
December Solstice
Mean ± SD
Mean ± SD
Mean ± SD
Mean ± SD
RSUT
Port Harcourt
–
21.70 ± 13.02
24.00 ± 16.76
–
CLBR
Calabar
–
23.00 ± 14.19
30.96 ± 18.67
25.82 ± 15.22
FPNO
Owerri
–
22.40 ± 14.63
30.00 ± 19.87
–
UNEC
Enugu
30.60 ± 17.02
24.60 ± 14.71
27.90 ± 18.63
23.40 ± 14.93
ULAG
Lagos
28.40 ± 18.07
23.80 ± 15.30
28.60 ± 18.36
22.80 ± 14.51
OSGF
Abuja
28.20 ± 17.38
22.10 ± 14.52
27.50 ± 18.64
23.00 ± 14.74
FUTY
Yola
28.50 ± 18.49
21.60 ± 13.88
26.10 ± 17.56
23.10 ± 15.18
ABUZ
Zaria
28.70 ± 17.71
20.50 ± 8.48
24.60 ± 12.87
23.40 ± 14.88
BKFP
Kebbi
28.20 ± 17.59
22.20 ± 14.95
28.70 ± 19.06
23.60 ± 15.05
The GPS TEC depletions, followed by GPS TEC enhancements, as shown in March and April, are associated with small-scale plasma density irregularities. Such
irregularities, which result in ionospheric scintillations, can cause
trans-ionospheric signal fading, a potential threat to GNSS systems.
According to Burke et al. (2004), this behaviour could be attributed to
plasma bubbles generated from sunset until sunrise. These plasma
irregularities are due to the turbulent ionospheric conditions that give
rise to the equatorial spread F (Paznukhov et al., 2012). Factors responsible
for these spread-F occurrences have been reported to be either due to the
variations in the linear growth rate of the Rayleigh–Taylor instabilities as
a result of the electrodynamics of the ionosphere, or to the atmospheric
gravity waves. It is furthermore reported that for the African equatorial
region, scintillation occurrence is most frequent when the solar terminator
aligns with the geomagnetic field (Paznukhov et al., 2012). The months of
June, July, and December exhibit lower values of GPS TEC with a magnitude of
less than 50 TECU compared to other months, which have more than 50 TECU across
all the longitudes. This implies that the formation of EIA is weaker in those
months with less than 50 TECU.
Seasonal variation in GPS total electron content
Seasonal effects were investigated using Lloyd's seasonal classification
(Eleman, 1973); the months of the year were classified into three seasons
based on the movement of the sun: December Solstice or D season (November,
December, January, and February), Equinox or E season (March, April,
September, and October), and June Solstice or J season (May, June, July, and
August). Since E season shows significant variations in months, we
further classified E season into March Equinox (March and April) and
September Equinox (September and October) (Bilitza et al., 2004; Rabiu et
al., 2007; Oladipo et al., 2009). The seasonal values of GPS TEC, plotted in
Fig. 5, were estimated by finding the average of the monthly means of TEC
values under a particular season as shown in Table 2 with their respective
standard deviation (SD).
Seasonal TEC variations across some of the study areas in Nigeria.
![]()
Figure 5 presents the seasonal variation in TEC across some of the study
areas considered for this study. Generally, the seasonal variation depicts a
semi-annual distribution with equinoctial maxima (∼ 25–30 TECU) around
minima in solstices (∼ 20–25 TECU). December Solstice magnitude is
slightly higher than the June Solstice magnitude at all stations (except at
ULAG and UNEC; see Table 2 for a full list of abbreviations), while March Equinox magnitude is also slightly higher than
September Equinox magnitude at all stations. This shows a seasonal asymmetry
in the ionosphere in the solstices and equinoxes. Thus, the seasonal variation
shows a semi-annual pattern, with a maximum in March Equinox, followed by
September Equinox, December Solstice, and June Solstice. Earlier on, a similar
semi-annual variation was observed in TEC by Bolaji et al. (2013) and
Rabiu et al. (2014) while working at stations within Nigeria. The
semi-annual variation in Fig. 5 is significant from ABUZ to FUTY, but became
insignificant from ULAG; this observation could be due to the EIA initiating
redistributions of semi-annual variation as plasma moves along the
southern crest.
Wu et al. (2004) and Rama Rao et al. (2006a) independently argued that the
seasonal variation pattern in GPS TEC could be explained by the seasonal
changes in atmospheric composition. Earlier, Titheridge (1974) reported a
worldwide semi-annual variation in atmospheric composition, with the ratio
O / N2 (the relative densities of atomic oxygen and molecular
nitrogen) at a maximum near the equinoxes. Also, Rama Rao et al. (2006) argued that
the lower values of GPS TEC during the solstice days may be attributed to the
low ionization densities due to the reduced production rates indicated by
the reduced O / N2 ratios owing to the increased scale height of N2
as reported by Titheridge (1974). Rishbeth et al. (2000) and the references
therein attributed the seasonal variations in the ionosphere to changes in
the neutral air composition due to the large-scale thermospheric dynamics,
changes in atmospheric turbulence, inputs from atmospheric waves, and
variations in geomagnetic activities. Several authors, including Quattara et
al. (2009) and Adebesin et al. (2015), have reported distinct seasonal
variations, similar to our findings, in the equatorial ionosphere in the western
African
region using ionosonde measurements.
The semi-annual variation in the GPS TEC could also be due to the combined
effect of the solar zenith angle and magnetic field geometry (Wu et al.,
2004; Bagiya et al., 2008). Rabiu (2004) observed semi-annual variation with
equinoctial maxima in ranges of H, D, and Z components of the geomagnetic
field and suggested the cause may be due to one or more of three models
commonly referred to as axial, equinoctial, and Russell–McPherron mechanisms (for
example Clua de Gonzalez, et al., 1993, 2001; Russell and McPherron, 1973;
Legrand and Simon, 1989; Simon and Legrand, 1989; Crooker and Siscoe, 1986;
Orlando, et al., 1993; and references therein). Olatunji (1967), Scherliess
and Fejer (1999), Bailey et al. (2000), and Liu et al. (2006, 2009)
suggested that daytime E×B drift velocities are larger
in the equinoctial months (February, March, April, August, September, and
October) and winter months (November, December, and January) than in the
summer months (May, June, and July) and this could result in semi-annual
variation. Olatunji (1967), Bailey et al. (2000), and Liu et al. (2006, 2009)
related this semi-annual variation to the variation in the noon solar zenith
angle, which is an important factor for the production of ionization. Wu et
al. (2004), Rama Rao et al. (2006b), and Lee et al. (2010) attributed the
semi-annual variation to a combined effect of solar zenith angle and
geomagnetic field geometry.