Introduction
The propagation of radio signals in the form of plane waves through a
drifting ionosphere with inhomogeneities in the electron density distribution
may produce phase and amplitude scintillations (Aarons, 1982; Yeh and Liu,
1982). These scintillations (or fluctuations) are interpreted on the ground
as temporal variations in the amplitude and phase of a received power signal.
Inhomogeneities in the ionosphere can be produced by plasma-depleted
irregularity structures, also known as plasma bubbles. Plasma bubble
irregularities develop in the equatorial ionosphere shortly after sunset and
rise up above the magnetic equator to altitudes that can exceed 1200 km. The
upper height limit above the magnetic equator will define the latitudinal
extent in which the bubbles map to off-equatorial regions (Abdu et al.,
1983). As the field-aligned plasma bubbles propagate away from the Equator
towards low latitudes, they intersect the regions of the equatorial
ionization anomaly (EIA). Once the spatial distribution and strength of the
scintillations are dominated by the background electron density, the most
intense scintillations are expected to occur around 15–20∘ from the
magnetic equator at latitudes of the crests of the EIA. Moreover, the
latitudinal variation in the intermediate-scale length (from hundreds of
meters to a few kilometers) irregularity spectrum within a plasma bubble may
also contribute to strong scintillations near the crests of the EIA
(Bhattacharyya et al., 2017).
The climatology, morphology, and dynamics of ionospheric irregularities at
the EIA region are among the major research topics studied in ionospheric
physics during the past 4 decades (Aarons, 1982; Sobral et al., 2002). Sobral
et al. (2002) reported 22 years (1977–1998) of plasma bubble climatology
over Cachoeira Paulista (22.4∘ S; 45.0∘ W) in Brazil, and
presented one of the most comprehensive studies of the occurrence of
irregularities at the southern crest of the EIA. In the earlier study of
Aarons (1982), the author stressed the importance of better knowledge of the
characteristics of ionospheric scintillations in order to develop models to
minimize the fading problems in Earth–space communications. The work of
Aarons (1982) clearly depicts how the scintillation intensities, produced by
the smaller-scale irregularity structures coexisting with the plasma bubbles,
are maximized in the regions of the Appleton anomaly. More recently, relevant
features of ionospheric radio-wave scintillations at the equatorial anomaly
region have been extensively investigated for different longitudinal sectors
(Spogli et al., 2013; Chatterjee and Chakraborty, 2013; Bhattacharyya et al.,
2014; Akala et al., 2015; Cesaroni et al., 2015; Zhang et al., 2015;
Srinivasu et al., 2016; Moraes et al., 2017). In the South American sector,
particularly for the L-band frequencies, the occurrence characteristics of
scintillation-producing irregularities have been demonstrated using
ground-based global navigation satellite system (GNSS) receiver networks
(e.g., de Paula et al., 2007; Akala et al., 2011; Muella et al., 2013, 2014).
The work of de Paula et al. (2007) presented, for one low-latitude station
located in the Brazilian east sector, the local time and seasonal occurrence
of global positioning system (GPS) L-band scintillations. The study was
conducted during the ascending phase of solar cycle 23 (1997–2002) and
clearly demonstrated that the scintillation occurrence over Brazil has a
seasonal component that departs from other longitude sectors, with the
irregularity activity being more intense during the December solstice
(summer) months. However, in the western sector of South America, the study
of Akala et al. (2011) showed that the highest frequencies and the longest
durations of events of scintillations are mostly observed during the March
equinox. Common to both longitudinal sectors are the observed least
frequencies of occurrence near the June solstice (winter) months. More
recently, Muella et al. (2013, 2014) investigated the L-band scintillation
occurrence over Brazil at latitudes between the north and south crests of the
EIA and close to the magnetic equator. The authors showed that the patch
duration of scintillations and their occurrence tended to increase with solar
activity and that they increased from the magnetic equator toward the crests
of the EIA. However, around the southern crest of the EIA the scintillation
occurrence during solar maximum years was ∼ 10 % higher than that
observed for the northern crest, which suggested a possible influence of the
South Atlantic magnetic anomaly (SAMA) on the scintillation activity over
South America. However, previous studies in the Brazilian sector were not
extended to a quantitative investigation of the long-term climatology of
ionospheric scintillation over a station located under the crest of the EIA.
An understanding of the climatology of ionospheric scintillations is best
achieved by knowing the spatial and temporal variation in the zonal drift of
the irregularities. In the South American sector, the zonal drift of
scintillation-producing irregularities has been studied in the last few
decades through the detection of VHF geostationary satellite signals (Abdu et
al., 1985; Basu et al., 1996; Bhattacharyya et al., 2001; de Paula et al.,
2010), from UHF geosynchronous satellite measurements (Valladares et al;
2002; Sheehan and Valladares, 2004), and through an L-band GPS-spaced antenna
system (Kil et al., 2000, 2002; Ledvina et al., 2004; Kintner et al., 2004;
Muella et al., 2013, 2014). Basu et al. (1996) estimated the zonal drift of
the kilometer-scale irregularities causing VHF scintillations above the
equatorial site of Ancón (MLAT 1.46∘ N) in Peru and at the
low-latitude station of Agua Verde (MLAT 11.3∘ S) in Chile. They
presented evidence of a latitudinal gradient in the irregularity zonal
velocities associated with the vertical shear of the zonal drift in the
topside equatorial ionosphere. Also using a VHF system, de Paula et
al. (2010) estimated the zonal drift of irregularities at two magnetic
conjugate sites in the Brazilian sector and showed that the magnitude of the
eastward zonal velocities in the SAMA region may be ∼ 12 % larger
than at the conjugate point owing to the weakening of the total magnetic
field intensity. Valladares et al. (2002) showed strong correlation in the
nighttime variations in UHF scintillation zonal drifts and thermospheric
zonal winds, indicating the importance of neutrals in controlling the plasma
motion during nighttime. Kil et al. (2002) investigated the latitudinal
variations in GPS scintillation activity over Brazil and showed a negative
gradient of the irregularity zonal drifts with increasing geomagnetic
latitude, which implied decreasing eastward zonal velocities with increasing
altitude when it was projected on the F region in the equatorial plane.
Muella et al. (2014) investigated the climatology of irregularity zonal
drifts over Cuiabá (MLAT 6.2∘ S) in Brazil from 2000 to 2006 and
argued that the magnitude of the zonal velocities might be reduced at the
inner regions of the EIA due to the latitudinal variations in the ion drag
force. However, in these studies a more complete scenario of the seasonal and
solar cycle variation in the zonal drift velocities of
scintillation-producing irregularities was not reported for a site located at
latitudes of the southern crest of the EIA.
Observational studies of ionospheric scintillations and estimations of their
zonal drifts are important to validate the theoretical formulation of
scintillations and to mitigate space weather effects on transionospheric
radio-wave signals. Physics-based, statistical, and climatological models
with ingestions of real data have been developed with the aim of describing
the physical mechanisms giving rise to scintillations, studying the
morphology of scintillations, predicting the strength of radio scintillations
as a function of time, latitude, longitude, and geophysical condition, and
estimating the severity of scintillation effects on receiver operation
(Priyadarshi, 2015, and the references therein). The statistical modeling of
scintillations has the advantage of being computationally inexpensive and
simpler in terms of the number of input parameters (Humphreys et al., 2009).
Hence, higher-order statistical models can be used to understand the impact
of amplitude and phase scintillations on GNSS receiver operations, which is
important to the technical community involved in the development of
mitigation tools useful to the current positioning and navigation
technologies. Following the demonstrations of Fremouw et al. (1980), in the
work of Hegarty et al. (2001) a scintillation signal model statistically
based on the Nakagami-m distribution was developed for the GPS L1-frequency
intensity scintillation. Humphreys et al. (2009) assumed the GPS amplitude
scintillations following the Rice distribution and proposed a model that can
be used to test phase-tracking loops for scintillation robustness evaluation.
More recently, Moraes et al. (2014) demonstrated that the α-μ
distribution best describes the variability in the signal amplitude during
scintillations and used the same model to evaluate the impact of
scintillations on GNSS receiver operations through radio-channel
characterization.
In the present study, data recorded by ground-based GPS receivers located
under the southern crest of the EIA in the Brazilian sector were used to
investigate the occurrence statistics of L-band scintillations. In addition,
two GPS receivers were also arranged in a spaced-antenna configuration and
aligned magnetically in the east–west direction with the objective of
estimating the irregularity zonal drift velocity. We present with these
analyses a climatological study of ionospheric scintillations and the
dynamics of scintillation-producing irregularities based on ∼ 17 years
of observations at the EIA crest region. Finally, the α-μ model
distribution was used to evaluate first- and second-order statistics of GPS
signal amplitude scintillation during periods of different solar activity
levels. We use the α-μ fading model to statistically characterize
the amplitude scintillation behavior at different levels of the solar cycle.
Data and method
Scintillation monitoring and irregularity drift estimations
Ground-based GPS scintillation monitoring systems deployed at the Brazilian
low-latitude station of Cachoeira Paulista (22.4∘ S;
45.0∘ W; dip latitude 16.9∘ S) have collected, since
September 1997, signal power L1 C/A (1575.42 MHz) amplitude scintillation
data samples (at 50 Hz). By using post-processing computer software these
scintillation monitors (named SCINTMON), exclusively configured to operate
during nighttime, have calculated for each interval of 60 s the S4
amplitude scintillation index for all GPS satellites tracked from 18:00 to
06:00 LT (UT = LT + 3 h). The S4 index represents the
normalized RMS deviation of the received signal power intensity. The large
data set of amplitude scintillation measurements at Cachoeira Paulista
allowed us to study the approximately 17-year climatology (1997–2014) of
ionospheric scintillations at the EIA crest region. In the absence of data at
Cachoeira Paulista, we used data from the closest station (∼ 100 km)
of São José dos Campos (23.1∘ S; 45.8∘ W; dip
latitude 17.3∘ S) to complement the analysis. The same type of GPS
scintillation monitor is installed at both stations and it has been
previously described by Beach and Kintner (2001).
The occurrence statistics of the GPS L1-frequency amplitude scintillations
were analyzed for the observatory of Cachoeira Paulista during the period of
September 1997–November 2014. This period includes most of solar cycle 23
(that occurred between May 1996 and October 2008) and solar cycle 24 (since
around November 2008). The general influence on the climatology of
scintillations of the long sunspot cycle 23, the unusual depth and duration
of the last solar minimum (2007–2009), and the comparatively weaker solar
cycle 24 is briefly analyzed. The possible influence of the secular variation
in the dip latitude of Cachoeira Paulista on the scintillation climatology
due to the motion of the magnetic dip equator was also discussed. For the
station of Cachoeira Paulista, about 6000 nights of L1 amplitude
scintillation data were used in the analysis. Only data from geomagnetically
quiet days with daily (3-hourly planetary) ΣKp index < 24 were
considered in the climatologic study.
At the site of Cachoeira Paulista two SCINTMON receivers also operated
simultaneously from 1998 to 2007. The antennas of the scintillation monitors
were separated by a distance of 55 m along the magnetic east–west
direction. By measuring the amplitude scintillation patterns, the east–west
drifts of the irregularities across the signal path from the satellites to
the spaced SCINTMON antennas were inferred by the ground receivers. This
configuration was used to measure the zonal scintillation pattern velocity
(Vscint) in the coordinate frame of the two spaced antenna
receivers. The values of Vscint were obtained from the
cross-correlation functions of the data measured by the two spaced receivers
and for all scintillating satellite signals. The estimations were limited to
measurements made from satellites with an elevation angle higher than
40∘ and for a scintillation index S4 > 0.2. This threshold
of the S4 index may be considered to be above the level of noise and
multipath effects. The cross-correlation function C(τ) between the time
sequences S1 and S2 of two signal intensities is given as (Kil et
al., 2000)
Cτ=∑kS1tkS2tk-τ∑kS12tk∑kS22tk-τ,
where k is an index into the time series and τ is the time lag with
optimal values that occur when it maximizes C(τ). In order to reduce
any effect of the apparent velocities in the Vscint calculations,
as detailed by Kil et al. (2002) and Muella et al. (2014), we considered in
the analysis a high threshold of 0.9 for the peak cross-correlation. Then,
the mean ionospheric irregularity zonal drift velocities (Vzonal)
are inferred by averaging the Vscint velocities measured from the
various scintillating GPS satellite signals. The method used here to estimate
Vzonal was primarily described in the study of Ledvina et
al. (2004), and a modified form was applied more recently in the studies of
Muella et al. (2013, 2014). To estimate Vzonal we used the
following relation:
Vzonal=hsat-hipphsatVscint+hipphsatVsatx+qy/qxVsaty+qz/qxVsatz,
where hsat is the satellite height, hipp denotes the mean
scattering height of the irregularities (assumed as 350 km) above the
receivers' horizontal plane, Vsatx, Vsaty, and
Vsatz respectively represent the zonal, meridional, and vertical
components of the satellite velocity, and the ratios (qy/qx) and
(qz/qx) are the mapping factors that rotate all vectors into the
receivers' coordinate system as a function of the satellite zenith and
azimuth angles and the magnetic dip and declination angles of the magnetic
field at the hipp. In this study, the mean zonal drift velocities
(Vzonal) of the scintillation-producing irregularities were
inferred during 281 geomagnetically quiet nights. The Vzonal values
were obtained during the December solstice (summer) months (1999–2001;
2003–2007) and during the equinoctial months (1999; 2001; 2003–2005).
Ionospheric fading model
The S4 index is the indicator of the severity of the amplitude
scintillation and is widely used to quantify the severity of ionospheric
scintillation. Another parameter, which has become of interest in recent
studies (Humphreys et al., 2010; Carrano and Groves, 2010), is the
decorrelation time τ0. This parameter provides temporal information
about scintillation and may be interpreted as the indicator of the fading
rate, defined as the time lag at which the autocorrelation function (Ar)
of amplitude scintillation falls off by exp(-1) from its maximum (zero
lag) value. Thus
Arτ=Er(t)-zr(t+τ)-zσr2,
where z and σr2 are the mean and variance values of the
amplitude r, respectively, and E(.) denotes the expected value operator.
The τ0 is obtained from Arτ0/Ar0=exp(-1). Examples of the variability in the
decorrelation time as computed from GPS L1 amplitude scintillation
measurements can be found in Fig. 2 of the work of Oliveira et al. (2014).
Additionally to the fading rate, the τ0 parameter may be used to
characterize the turbulent ionospheric medium (Carrano et al., 2012) and to
predict GPS receiver cycle slipping rates (Humphreys et al., 2010). For
example, in Moraes et al. (2011), the typical values of probability of cycle
slip for GPS users at low latitudes under amplitude scintillation conditions
were up to 35 %. Therefore, the evaluation of τ0 is important to
describe the receiver performance under scintillation effects and to
characterize the ionospheric medium.
Moraes et al. (2012) proposed the model used in this work for the
transionospheric radio-wave scintillations at the GPS L1 frequency. This
signal fading model is based on a α-μ distribution for intensity
scintillation. According to Yacoub (2007), one advantage of the physical
model for the α-μ distribution is the fact that it takes into
account the inhomogeneities of the propagation medium. Hence, it can be
considered a general fading model in which the received radio signals are
composed of clusters of multipath waves assumed to be scattered with
identical powers. Thus, we take this advantage of the model by associating
the α-μ parameters with the physical fading of the ionospheric
scintillation phenomena. In this study, we initially used the α-μ
signal model to investigate the first-order statistics of the amplitude
scintillation phenomena.
According to Moraes et al. (2012, 2014), the α-μ probability
density function of the normalized amplitude envelope r is given by
f(r)=αrαμ-1ξαμ/2Γμexp-rαξα/2,ξ=ΓμΓμ+2/α,
where Γ(.) is the gamma function, the parameter μ denotes the
number of multipath components in the propagation environment, and the power
parameter α denotes the modulus of the sum of those clusters that
results in the envelope that propagates in the nonhomogeneous environment. A
more detailed description of the physical properties represented by the
α-μ parameters can be found in the work of Yacoub (2007) and
Moraes et al. (2012).
A second advantage in the use of the α-μ distribution represented
by Eq. (4) is the fact that, depending on the values of the parameters
α and μ, it may become a Weibull, an exponential, a Rayleigh, a
one-sided Gaussian, or a Nakagami distribution. Since the α-μ
model has two parameters that are directly described by the physical
properties of the ionospheric medium, it becomes more flexible and
mathematically tractable, ensuring much better agreement with S4 data
whether compared to the popular Nakagami-m or Rice distributions (e.g.,
Moraes et al., 2012).
The α-μ pair of parameters can be estimated from the equality that
involves the moments of α-μ amplitude envelope given by Yacoub
(2007):
E2(rβ)E(r2β)-E2(rβ)=Γ2(μ+β/α)Γ(μ)Γ(μ+2β/α)-Γ2(μ+β/α).
Finally, the values of the α-μ pair that best represent the
amplitude distribution in the scintillation index S4 can be obtained
from the following relation:
S42=ΓμΓμ+4/α-Γ2μ+2/αΓ2μ+2/α.
Another advantage of the α-μ model is the fact that it can also be
used to understand the impact of the irregularities producing scintillations
on GPS receiver operations. In this case, second-order statistics may be
derived from the α-μ model and then used to calculate GPS
radio-channel characterization, such as the average fading duration (AFD) and
the level crossing rate (LCR). Fading is a well-known phenomenon caused by
the superposition of two or more versions of the transmitted signal that may
result in either constructive or destructive interferences. These effects are
interpreted as changes in the amplitude envelope of the received power
signal. Thus, the analysis of the AFD and LCR parameters are devoted here to
the temporal characteristics of these fading events. Moreover, the AFD and
LCR are important in receiver design and model. The former parameter
indicates the average amount of time that the amplitude envelope of the
received power signal spends below a certain threshold, whereas the latter
provides the average number of times within an observation period that the
envelope of a fading signal crosses a certain level in the downward or upward
direction (e.g., Moraes et al., 2014).
According to Yacoub (2007) the AFD (in seconds) for the α-μ
distribution is given by
TR(r)=2πΓ(μ,μρα)exp(μρα)ωμμ-0.5ραμ-0.5,
and the LCR (in crossings per second) for the α-μ distribution is
obtained from
NR(r)=ωμμ-0.5ραμ-0.52πΓ(μ)exp(μρα),
where ω is an empirical parameter used as an offset adjustment of LCR
and AFD function and was introduced by Yacoub (2007). In the present work we
used ω=2 for the cases of solar maximum and moderate solar activity
and ω=3 for the cases of solar minimum. The values of ω used
here are those that provided the minimum absolute error deviation and were
based on the previous work (Table 2 and Eq. 13) of Moraes et al. (2014). As
we are computing the crossing rate for E[r2]=1, the scale factor ρ
for both LCR and AFD can be found as
ρ=rΓ(μ+2/α)Γ(μ)μ-1/α,
where r in Eqs. (7), (8), and (9) is the value of the normalized amplitude
envelope as defined in Eq. (4).
Percentage of scintillation occurrence at Cachoeira Paulista as
a function of Universal Time (UT = LT + 3 h) from September 1997 to
November 2014 for two threshold levels of the S4 scintillation index;
S4>0.2 in panel (a) and S4>0.5 in panel (b). The monthly
mean F10.7 cm solar flux is shown in panel (c).
The complete outlining of the α-μ distribution for scintillations
and for the AFD and LCR calculations can be found in the work of Moraes et
al. (2012, 2014), and therefore their full mathematical description will be
limited to the equations presented above. In the present work, the
scintillations at the low-latitude station of Cachoeira Paulista are modeled
for different values of the S4 index (from 0.4 to 0.9) and during
periods that represent different phases of the solar cycle (solar maximum,
solar minimum, and intermediate level). Finally, second-order statistics are
used to evaluate the AFD and LCR parameters during cases of different solar
activity levels.
Results and discussion
Ionospheric scintillation climatology
The panels in Fig. 1 show the percentage of occurrence of GPS L1-amplitude
scintillations, as observed for the low-latitude station of Cachoeira
Paulista for the period of September 1997–November 2014. The plots from
Fig. 1 provide a general picture of the climatology of ionospheric
scintillations over a station located in the southern crest of the EIA. The
nocturnal occurrence statistics are presented as a function of universal time
(UT = LT + 3 h) and considering two distinct thresholds of the
S4 scintillation index. Figure 1a shows the occurrence of scintillation
for S4 > 0.2, while Fig. 1b is valid for the threshold of
S4 > 0.5. Data were not available for May 1999, the beginning of
September 1999, and January 2001–March 2001. In the statistics data were
only considered from satellites with an elevation angle higher than
40∘. The variation in solar activity over the period analyzed here
can be visualized in Fig. 1c, as represented by the monthly mean variation in
the solar radio flux in 10.7 cm (F10.7 index). As shown in Fig. 1, we can
observe how the scintillation activity changes with time, month, season,
year, and solar activity level.
The patches of the highest occurrence of scintillations were observed in
Fig. 1a from 23:00 to 04:00 UT (or 20:00 to 01:00 LT) for the threshold
level of S4 > 0.2 and from 23:00 UT until around midnight in
Fig. 1b for the cases when S4 > 0.5. The scintillations also occur
predominantly in the period of September–March and are generally more
intense around the December solstice (summer) months when the longitude of
Cachoeira Paulista is in close alignment between the sunset terminator and
the magnetic meridian due to the large westward magnetic declination angle of
this region. A broad minimum in the seasonal occurrence of ionospheric
scintillations is observed in the June solstice (winter) months. An important
aspect that can be immediately seen in Fig. 1 is the variation in the
percentage of scintillation occurrence during most of solar cycle 23 (that
started in May 1996). The maximum activity period of solar cycle 23 occurred
in 2000–2002. As the statistical series of scintillation begins at the end
of 1997, the increase in the scintillation occurrence during the ascending
phase of solar cycle 23 can clearly be observed in Fig. 1a and b. The maximum
percentages of occurrence of about 80 and 50 % were observed over
Cachoeira Paulista around December 2001 and January–February 2002,
respectively, for the threshold levels of S4 > 0.2 and
S4 > 0.5. Scintillation intensity is known to be a function of both
the electron density deviation of the irregularity (ΔN) and the
thickness of the irregularity layer. In years of high solar flux, the
ionosphere becomes thicker and the background electron density increases at
latitudes of the EIA. Thus, large levels of ΔN are expected to be
formed around the solar maximum years. Consequently, much stronger
scintillations are likely to appear in the latitudes surrounding the crest of
the EIA, under which the site of Cachoeira Paulista is located. The largest
scintillations at latitudes of the EIA also tend to be associated with
regions of intense TEC gradients (Muella et al., 2013, 2014). In addition, as
the large-scale bubbles map down along geomagnetic field lines to
off-equatorial latitudes, the spectrum of the intermediate-scale
irregularities within the bubbles tends to become shallower near the F-region
peak. This factor, based on the recent study of Bhattacharyya et al. (2017),
also contributes to the strong L-band scintillations observed near the crest
of the EIA, particularly in years of high solar activity and during the
December solstice months in the longitude of Cachoeira Paulista.
Figure 1 also shows that the occurrence of scintillation started to subside
with the decline in solar activity. The descending phase of cycle 23 extended
from 2002 until around October–November 2009, which was historically
considered the solar cycle with the longest decline phase since the first
official records. Despite the longevity of the descending phase, the
occurrence of strong levels of scintillation (S4 > 0.5) seemed to be
extremely reduced as early as 2006, while for the overall scintillation
activity a drastic reduction started in 2007 as revealed in Fig. 1a. Another
important effect on the occurrence of scintillations that appears clearly
hallmarked in Fig. 1a and b occurred in the period of
December 2002–February 2003. There is a sudden drop in the frequency of the
occurrence of scintillations, which was recently attributed by de Paula et
al. (2015) to a sudden stratospheric warming (SSW) event. This signature of
scintillation weakening by SSW observed at the low-latitude station of
Cachoeira Paulista can be associated with the following: (a) a reduction in
the growth rate of the plasma instability process during post-sunset hours
owing to the decrease in the equatorial ionospheric vertical drifts; (b) the
presence of an opposing thermospheric wind induced by the SSW in the Northern
Hemisphere that possibly modified the flux-tube-integrated conductivities,
leading to the suppression of the secondary instability processes that
generate smaller-scale irregularities; and (c) an anomalous distribution of
the ionospheric plasma density around the southern crest of the EIA during
the SSW event, which possibly affected the scintillation activity over
Cachoeira Paulista. Some weakening is also evident in Fig. 1b around January
and February of the years 1999, 2000, and 2002, possibly associated with SSW
events, which still needs further investigation.
Another marked effect depicted in Fig. 1a is related to the pronounced
decrease in the overall occurrence of scintillations during the period of
2007–2009. This diminishment is associated with the unusual solar minimum
that hit bottom in 2008. This deep solar minimum period was related to the
lowest values of sunspot numbers registered in about 100 years (Hady,
2013) and an anomalous reduction in solar extreme ultraviolet (EUV)
irradiance (Solomon et al., 2010). According to previous studies, during the
anomalous minimum in the transition of solar cycles 23–24 the global
ionosphere became more contracted in height than other previous solar minimum
conditions, the base altitude of the F layer was the lowest, the ionospheric
electron density was unusually low (Liu et al., 2011), and the fountain
effect was suppressed (Santos et al., 2013). Thus, the reduced ambient
ionization at the EIA during the deep solar minimum period throughout the
years 2007–2009 certainly played an important role in the weakening of the
scintillation activity over Cachoeira Paulista.
The present solar cycle 24 started to increase slowly after October 2008 and
just around the middle of 2010 the monthly values of 10.7 cm radio flux
exceeded 80 sfu. The ascending phase of solar cycle 24 lasted until around
April 2014 when it attained its maximum phase; it is currently considered by
solar physicists as the weakest solar cycle in more than a century. According
to Solanki et al. (2002), the length of a solar cycle can be considered a
good predictor for the maximum sunspot number in the coming cycle. They
argued that as solar cycle 23 was long with a delayed descending phase, the
memory of its length by the solar dynamo was carried into the next cycle, and
consequently it would be expected that the present solar cycle 24 will have a
small number of sunspots. The consequence of this weak solar cycle in the
scintillation occurrence can be clearly seen in Fig. 1. The maximum frequency
of occurrence of ∼ 60 % was observed in 2014 for S4 > 0.2
and ∼ 45 % in 2014 for the highest levels of scintillation when
S4 > 0.5. This represents a reduction of approximately 20 % in
comparison to the solar maximum of cycle 23 during the season of higher
occurrence. Associated with this weakest solar cycle is a reduction in the
solar EUV flux and lower atomic oxygen densities, which led to a reduction in
the ionospheric densities at the EIA region. The measurements of global
average total electron content reported by Hao et al. (2014) confirm the fact
that during the first half of solar cycle 24 the ionosphere was weakly
ionized in comparison to the previous cycle 23. Also as a consequence of the
reduction in the EUV flux, a decrease in the E-region conductivity leading to
decay in the development of equatorial F-region E×B
drifts is expected. Thus, the generation of equatorial plasma bubble
irregularities and the distribution of ionospheric ionization at the crests
of the EIA have possibly been affected during solar cycle 24. As
scintillations require a significant plasma density and strong electron
density fluctuations to occur, the reduced ambient ionization accompanied
with changes in the strength and position of the southern crest of the EIA
are probably limiting the scintillations to levels of comparatively weaker
intensities.
As mentioned before, the latitudinal extent of the equatorial plasma bubbles
is crucial in determining the scintillation activity around the anomaly
crest. This extent depends on the upper height limit attained by the bubble
above the magnetic dip equator. Also, the strength of nocturnal
scintillations seems to be well correlated with the resurgence of EIA driven
by pre-reversal enhancement E×B drift and the location of
the EIA crest (Chatterjee and Chakraborty, 2013). These factors are known to
be intimately related to the location of the dip equator. According to
Rangarajan and Barreto (2000), in the American zone the dip equator is moving
westward at a rate of ∼ 0.22∘ per year and in the Brazilian longitudinal sector an
unmistakable northward drift is also noteworthy due to the configuration of
the magnetic equator. This means that in addition to the solar cycle
dependence, the occurrence climatology of scintillations depicted in Fig. 1
is possibly under the influence of changes in the dip latitude of Cachoeira
Paulista over ∼ 17 years. For example, Fig. 2 presents the variation in
the dip latitude of Cachoeira Paulista (line with circles) during the period
of 1997–2014 as calculated from the International Geomagnetic Reference
Field (IGRF) model. The results revealed a change in the dip latitude from
∼ 16.5∘ S in 1997 to ∼ 19.7∘ S in 2014. The
plot inserted in the upper right corner of Fig. 2 also shows how the dip
equator in the longitude range of the magnetic meridian of Cachoeira Paulista
moved in relation to the geographic Equator in 1997 (dashed line) and in 2014
(solid line). Hence, it is possible that the percentage of scintillation
occurrence observed in Fig. 1 is also being modulated by migratory changes in
the location of the magnetic dip equator and with the increase in the dip
latitude of Cachoeira Paulista. For example, the field line apex over the dip
equator that maps to the F region at the latitudes of Cachoeira Paulista
increased from around 850–900 km in 1997 to over 1100 km in 2014. This
means that the site of Cachoeira Paulista that was under the crest of the EIA
in 1997 is now located further along the poleward edge of the southern EIA
region. Consequently, the bubbles have to extend somewhat beyond the EIA
crest to be detected over Cachoeira Paulista, which also possibly leads to
comparatively fewer occurrences of scintillation around the solar maximum
year of 2014.
Variations in the dip latitude of Cachoeira Paulista (line with
circles) and in the magnetic dip equator (panel in the top corner) during the
period from 1997 to 2014.
Nocturnal variations in the irregularity zonal (eastward) drift
velocities estimated at Cachoeira Paulista during the equinoctial periods of
the years 1999 and 2001 (a), 2003 and 2004 (b), and
2005 (c).
Ionospheric irregularity zonal drift velocities
To infer the average zonal drift velocities of the ionospheric
irregularities, the amplitude fluctuations registered in the measurements of
the signal power intensity by the ground receivers were arranged for two
seasonal periods, equinoxes (March–April and September–October) and
December solstice (summer) months (November–February). No calculations were
performed during the June solstice (winter) months due to the much reduced
occurrence of scintillations through that season. As mentioned in Sect. 2.1,
only data from geomagnetic quiet days were used in the zonal drift
estimations. The irregularity zonal drift estimations here are based on 207
nights during the summer months (years 1999–2001 and 2003–2007) and 74
nights during the equinoxes (years 1999, 2001, and 2003–2005). The panels in
Figs. 3 and 4 respectively show the nocturnal variations in the mean zonal
drift velocities (positive eastward) during the equinoxes and December
solstice months. As shown in the plots, the irregularity drift velocities
were averaged for each 30 min bin and plotted here as a function of the
local time. The number of drift estimates for each bin is presented close to
the respective symbols. The standard deviations of the inferred drift
velocities were plotted as vertical bars and are shown in the graphs.
Nocturnal variations in the irregularity zonal drift velocities
estimated at Cachoeira Paulista during the December solstice months of the
years 1999–2001 and 2003–2007 (from top to bottom panels).
As can be seen in Figs. 3 and 4, the prevailing characteristic of the mean
irregularity zonal drift velocities over Cachoeira Paulista during the
equinoxes and December solstice months is the reduction in the amplitude of
the eastward velocities with the progression of night. This behavior is in
agreement with earlier observations reported at equatorial and low-latitude
regions (e.g., Otsuka et al., 2006; Muella et al., 2013, 2014; Liu et al.,
2015). According to theoretical formulations, this is a direct result of the
post-sunset weakening of the vertical electric fields mapped to
off-equatorial latitudes. However, we further note that the drift velocities
may present clearly distinct time, seasonal, and solar cycle variations. For
example, in Fig. 3c the irregularity zonal velocity during the equinoxes of
the year 2005 showed an increase from the early evening of
∼ 70 m s-1 until its maximum of ∼ 160 m s-1 at
around 23:00 LT, which rapidly decreased from then on. Before attaining its
maximum value, a deep reduction in the zonal drift with a magnitude of
∼ 110 m s-1 was observed at around 22:00 LT. Such behavior was
not observed in a similar way during the equinoxes of the years 1999 to 2004
when the maximum velocities were observed earlier, at around
20:00–20:30 LT, followed by a decrease toward the later hours of the night.
In contrast, the irregularity zonal drifts estimated during the December
solstice months of the years 2004 to 2007 presented quite similar behavior to
that observed during the equinoxes of the year 2005. The marked differences
are the comparatively larger mean velocities during early evening (from
∼ 100 to 120 m s-1) followed by a brief initial increase until
reaching the peak velocities between 21:00 and 22:00 LT.
Table 1 summarizes the averaged irregularity zonal drifts (Vzonal‾) during nighttime for each seasonal period throughout the
years 1999–2007, the maximum velocity of the nocturnal variations in mean
zonal drifts (Vmax), and its time of occurrence (tmax) as taken
from the plots of Figs. 3 and 4, and the average values of the F10.7 index
(in units of 10-22 W m-2 Hz-1) during the days used to
compute the mean irregularity drifts. A more detailed inspection of the
results presented in Figs. 3 and 4 and Table 1 reveals that the average
nocturnal irregularity drifts during the December solstice months are larger
than during the equinoctial periods. They are more pronounced in the years
close to solar maximum (mainly between 2001 and 2003) and tend to decrease in
the years of moderate solar cycles (2004 and 2005). Considering only a
particular season, it is possible to observe that Vzonal‾ for the December solstice period is larger in the years of high solar flux
units (sfu) and tends to decrease toward solar minimum. However, during the
years of moderate solar activity in the ascending and descending phases of
the solar cycle, the values of Vzonal‾ seem not to change
significantly. Conversely, for the equinoxes the dependence with solar flux
is not as evident as observed for the December solstice months.
It is well known that at low latitudes the field-line-mapped ionospheric
vertical electric field is responsible for the zonal motions of the ambient
plasma (Haerendel et al., 1992). Since the maximum contribution of the
scintillation-producing irregularities occurs at the heights of peak electron
density, any change in the evening peak of the F region is expect to affect
the dynamic evolution of these irregularities. Theoretical formulations have
predicted that the nighttime eastward irregularity drift, which can be
considered equivalent to the background plasma drift, depends essentially on
a ratio of flux-tube-integrated Pedersen conductivity weighted by the
F-region zonal neutral wind velocity (Anderson and Mendillo, 1983; Haerendel
et al., 1992; Eccles, 1998; Santos et al., 2016). Thus, the years with larger
mean irregularity zonal velocities during the December solstice (summer)
months over Cachoeira Paulista are possibly associated with a stronger
vertical polarization electric field owing to a larger thermospheric zonal
wind, which then drives the irregularities zonally. Moreover, at the
latitudes of Cachoeira Paulista the ion drag forces imposed by the enhanced
electron density structures of the EIA may also play an important role in
neutral wind dynamics (Martinis et al., 2003; Muella et al., 2014), which in
turn could affect the plasma dynamics and the irregularities in them. It is
worth mentioning that the zonal drifts estimated here only over Cachoeira
Paulista cannot be used to infer the altitude variation in the vertical
electric fields; simultaneous measurements at different latitudes along the
same magnetic meridian would be necessary.
Averaged irregularity zonal drifts (Vzonal‾),
time of occurrence (tmax) of maximum velocity of the nocturnal
variations in mean zonal drifts (Vmax), and the average values
of the F10.7 index (in units of 10-22 W m-2 Hz-1) during
the days used to compute the seasonal variations in irregularity zonal drift
velocities throughout the years 1998–2007.
Equinoxes
F10.7‾
Vzonal‾ (m s-1)
Vmax (m s-1)
tmax (LT)
1999
170.8
135.2
171.5
20:00
2003
157.7
112.6
168.2
20:30
2004
137.1
108.9
133.6
20:00
2004
113.7
131.1
176.4
20:00
2005
80.3
115.7
158.3
23:00
Dec. solstice
F10.7‾
Vzonal‾ (m s-1)
Vmax (m s-1)
tmax (LT)
1999
132.2
124.9
176.8
20:30
2000
178.3
134.6
150.1
21:00
2001
163.9
150.4
185.1
20:00
2003
146.3
126.1
168.9
20:30
2004
127.1
126.1
154.6
21:00
2005
100.6
125.8
153.9
21:00
2006
87.2
112.6
160.6
22:00
2007
86.2
96.5
125.5
21:30
In Fig. 5 the mean values of the irregularity zonal drift velocity (between
22:00 and 24:00 LT) throughout the entire period analyzed in this study were
used to correlate with the daily mean values of the F10.7 index (Fig. 5b) and
the daily mean values of full solar disk EUV flux (in units of photons cm-2 s-1)
at 1 AU (wavelength range of 0.1–50 nm)
obtained from the SEM sensor aboard the SOHO spacecraft (Fig. 5a). We have selected the period of
22:00–24:00 LT because throughout this time the scintillation-producing
irregularities can be considered for practical purposes to drift at
comparable velocities with the background plasma (Kil et al., 2000, 2002;
Engavale et al., 2005). Before 22:00 LT, due to the presence of perturbation
electric fields associated with the Rayleigh–Taylor instability, the
irregularities are still growing and the values of Vzonal may
present great variability (Bhattacharyya et al., 2001; Engavale et al.,
2005), whereas after 24:00 LT the scintillation-producing irregularities
start to decay faster by cross-field diffusion (Basu et al., 1978). The
tendency for the irregularity drift velocities to increase with increasing
EUV and F10.7 cm solar fluxes can clearly be seen in the plots of Fig. 5.
Such an increase in Vzonal is also in agreement with the
observations of Engavale et al. (2005) and Fejer et al. (2005), who
respectively reported pre-midnight irregularity drift and zonal drift in the
equatorial F-region plasma as increasing with the solar flux.
Linear fit (red line) and polynomial fit (blue line) of the daily
mean zonal drift velocity of the irregularities estimated at Cachoeira
Paulista from 22:00 to 24:00 LT versus daily values of the EUV
flux (a) and F10.7 index values (b).
Figure 5 also shows that the cross-correlation coefficients (linear fit) for
both EUV flux (R=0.65) and the F10.7 index (R=0.70) are quite similar and
can be used to investigate solar cycle effects on the irregularity drift
velocity. The mostly marked difference is depicted in Fig. 5b; the tendency
for Vzonal to become nonlinear as the F10.7 index values increase
can clearly be seen from the polynomial fit (red line). However, for
Vzonal versus the F10.7 index, the parabolic fit (R=0.51) also
suggests that the saturation level of the irregularity drift velocities may
exist for higher flux levels. We may note for the Vzonal versus EUV
case (Fig. 5a) that the relationship is strongly linear, with the parabolic
curve adjusting moderately (R=0.42). A direct correlation between EUV flux
and the F10.7 index has been reported by Santos et al. (2013), and the
authors observed a slower rate of increase in F10.7 in comparison to the
increase in the EUV flux for high solar flux values, which might explain the
nonlinearity feature depicted here in the plot of Vzonal versus the
F10.7 index. The solar flux effects on irregularity zonal velocities have
also been studied by Sobral et al. (2009) based on the formulations presented
by Haerendel et al. (1992) and Eccles (1998). They discussed the fact that
around solar maximum years the magnitude of the thermospheric zonal wind
velocities tends to be larger owing to an enhanced solar thermal tide.
Therefore, for higher solar flux levels the increase we have observed in the
irregularity zonal motion is possibly associated with an increase in the
Pedersen-conductivity-weighted F-region zonal neutral wind.
Statistical characterization of amplitude scintillation
This section presents, for the proposed α-μ model, the results of
the first- and second-order statistical characterization of amplitude
scintillation at the equatorial anomaly crest region. We intend with this
analysis to provide statistical values that a GNSS user might be susceptible
to when dealing with geophysical conditions similar to those found in this
study. We have chosen GPS scintillation data available during specific years
that represent three different levels of solar activity, i.e., near the solar
maximum (year 2000), a moderate or intermediate level during the descending
phase of cycle 23 (year 2005), and near the solar minimum (year 2010). The
cases for solar maximum cover the period January–February 2000; for the
intermediate cycle the cases are within the period of
November–December 2005, and for solar minimum the cases selected occurred in
the months of February–March and November–December 2010. All measurements
of the GPS L1 amplitude scintillation used as input in the model were
conducted at Cachoeira Paulista.
It is well known that very intense signal fluctuation associated with
scintillation can cause GNSS receivers to stop tracking the signals from the
satellites, provoking the so-called loss of lock. It happens when the
carrier-to-noise (C / N0) ratio for the receiver to continue
tracking a satellite goes below 26–30 dBHz for the L1 frequency (Kintner et
al., 2007; de Paula et al., 2007). Thus, we have chosen cases with no
occurrence of loss of receiver lock, which was considered a difficult task
and reduced the set of data to be analyzed, since loss of lock is a very
common process during the occurrence of strong scintillation. Loss of
receiver lock during very strong scintillation events tends to occur more
frequently when there is a close alignment between the magnetic field lines
and the satellite-to-receiver signal paths (DasGupta et al., 2004; Moraes et
al., 2017). However, this geometrical factor should not be considered a
general rule. In order to increase the number of cases for the statistical
characterization, we also included in the analysis the satellites with
elevation angles greater than 30∘. We then selected data sets in
which the S4 index values varied from 0.4 ± 0.025 to at least
0.9 ± 0.025. A total of 21 days met these criteria and were considered
in the analysis: 6 days for solar maximum (10, 28, 29 January and 4, 10,
17 February 2000), 8 days for moderate solar activity (23 November and 2, 4,
7, 8, 17, 23, 30 December 2005), and 7 days for solar minimum (17,
21 February, 11, 20 March, 12, 18 November, and 29 December 2010). For these
days, Table 2 summarizes the number of cases (in intervals of 60 s) that
attained the different levels of the S4 index.
(a) Case of amplitude scintillation with S4=0.8 for
satellite PRN2 on 4 February 2000. (b) Theoretical α-μ
model based on the moment estimation of Eq. (4) in comparison with the
measured occurrences from panel (a).
As previously discussed, the decorrelation time τ0 is an important
parameter that provides information about receiver vulnerability. In order to
calculate the τ0 it is necessary to compute the autocorrelation
coefficients by using Eq. (3). As pointed out by Moraes et al. (2012), a time
series of signal fading with similar values of the S4 index may present
distinct decorrelation time, revealing the importance of the estimation of
this parameter due to its implications for GNSS receiver performance. Table 3
presents the average values of decorrelation time E[τ0] for the data
sets shown in Table 2. According to the results presented in the table, it is
possible to observe that E[τ0] tends to decrease with an increasing
S4 index. Also, the values of E[τ0] are in close agreement for
almost all cases analyzed during the three different periods of solar
activity. The only exception occurred for S4=0.7 for the solar minimum
period, but the E[τ0] is still in agreement with the typical expected
values, as presented by Moraes et al. (2012). Analyzing Table 3 it is also
possible to observe that the amplitude scintillation fades are decorrelated
between a range of 0.50 and 0.90 s. Shorter or longer decorrelation times
may be found. As discussed by Kintner et al. (2004), under particular
conditions in which the user and the satellites are coupled with the
irregularity and moving in the same direction, longer fades with slower
temporal variations are expected, which may result in higher values of
τ0. The opposite situation is also applicable with a satellite signal
crossing the irregularity in the opposite direction of its displacement.
Total of cases analyzed for different levels of the S4
scintillation index during the periods of maximum (Max), moderate (Mod), and
minimum (Min) solar activity levels.
S4 (±0.025)
0.4
0.5
0.6
0.7
0.8
0.9
Max
136
86
74
45
40
11
Mod
40
21
7
5
4
2
Min
54
27
13
7
3
1
In the next step, the shapes of the α-μ model distributions for
the normalized amplitude envelope are investigated for the different values
of the S4 index and during different phases of solar activity. Figure 6a
shows a case of amplitude scintillation with S4=0.8 for solar maximum.
Using the α-μ model with the coefficients estimated by the
equality of moments in Eq. (5), Fig. 6b illustrates the successful adjustment
of the model to the empirical distribution. This case was obtained for the
satellite PRN 2 on 4 February 2000. In particular, it is possible to note
that the α-μ distribution adjusts fairly well with the normalized
amplitude scintillation data, mainly in the tail region of the distribution,
providing a realistic estimate for the statistics of the received signal.
This adaptability is one of the advantages of this model, which is considered
to outperform other probability density functions with only one coefficient,
such as Nakagami-m or Rice. It is important to mention that the α-μ model tends to raise the tail as the α parameter increases,
taking the lower region of intensity values where the probabilities are
higher. Therefore, the increased α coefficient for the same S4
value represents a harsher scenario for propagation, with a higher chance of
the occurrence of deep fades. More details about the fit capability and
approximations for theoretical work can be found in Moraes et al. (2012) and
Oliveira et al. (2014).
Average value of decorrelation time E[τ0] (in seconds)
as a function of the S4 scintillation index for the periods of maximum
(Max), moderate (Mod), and minimum (Min) solar activity levels.
S4 (±0.025)
0.4
0.5
0.6
0.7
0.8
0.9
Max
0.82
0.80
0.73
0.71
0.63
0.62
Mod
0.83
0.87
0.81
0.77
0.69
0.72
Min
0.80
0.79
0.70
0.50
0.46
0.40
For a more complete scenario and using the data sets of cases listed in
Table 2, Fig. 7 depicts the empirical distribution of amplitude scintillation
for the S4 index varying from 0.4 up to 0.9. It is worth pointing out
that most of the distributions agree very well for solar maximum (red line),
moderate activity (blue line), and solar minimum (green line) periods, in
particular for S4 < 0.8. For strong scintillation of the wave field
with S4 = 0.8 and S4 = 0.9, the empirical distributions
during the different periods of solar activity tend to show some differences,
mainly in the tail region. Possible reasons for this may be the distinct
spatial variations in the electron density through the medium and the drift
velocities of scintillation during different periods of the solar cycle. The
regime of strong scintillation of the wave field is known to be the combined
result of the effects of multiple scattering and diffraction by the
irregularities inside the ionospheric layer (Zernov and Gherm, 2015), which
introduces significant changes in the statistical characteristics of
propagating waves. Therefore, multiple deep fading levels tend to
characterize the L1 signal amplitude fluctuations. Additionally, as discussed
in Kintner et al. (2004), those variations result in different Fresnel
lengths and propagation paths that directly affect the scintillation pattern.
Average values of the fading coefficient α as a function of
the S4 scintillation index for different solar activity levels.
S4
0.4 ± 0.025
0.5 ± 0.025
0.6 ± 0.025
0.7 ± 0.025
0.8 ± 0.025
0.9 ± 0.025
Max
1.76
1.22
1.08
0.73
0.78
0.67
Mod
1.99
1.89
1.07
0.52
2.50
3.6
Min
1.56
1.21
1.1
0.99
0.40
0.36
Distribution of measured normalized amplitudes for the S4 index
from 0.4 to 0.9 for the different periods of solar activity (solar maximum,
moderate level, and solar minimum).
Using the equality of moments in Eq. (5) to estimate the α-μ pair
of values, Table 4 summarizes the average values of the α coefficient
as a function of S4 for the different periods of solar activity. We note
that the α values in most of the cases are less than 2, which
supports the use of the α-μ model since there is an infinite
number of α and μ values that satisfy Eq. (6). It is known that
the Nakagami-m distribution can be obtained from the α-μ model
by setting α=2. Thus, the present results suggest that the fades
have a tail that is less raised than in the Nakagami-m case. Furthermore,
the Nakagami-m model may be considered as a conservative approach based on
the analysis presented here. It can also be interpreted from Table 4 that for
a given scintillation index S4, the α-μ model may describe
different patterns of scintillation during different solar activity levels.
This is an advantage of the α-μ model against the popular
Nakagami-m distribution, as also addressed by Oliveira et al. (2014).
Empirical LCR (crossings per second; panels a, c, e) and
AFD (in seconds; panels b, d, f) during the three distinct phases
of solar activity level versus the scintillation severity as estimated by
the theoretical α-μ model (Eq. 5) for S4=0.67.
The second-order statistical evaluation of the ionospheric scintillation
amplitude fading events, designated level crossing rate (LCR) and average
fading duration (AFD), is also presented for the three periods of solar
activity levels. As mentioned before, the LCR and AFD parameters are
connected to the temporal characteristics of fading events. According to
Moraes et al. (2014), these parameters may help to estimate how often the
fades will exceed certain thresholds of the amplitude envelope r and how
long they are expected to last. Figure 8 shows an example of the theoretical
formulation of Eqs. (7) and (8) versus the empirical LCR and AFD values for
the cases in which S4=0.67 ± 0.025. The plots in the top, middle,
and bottom pairs of panels respectively correspond to periods of solar
maximum, moderate, and minimum. The solid line in magenta is the formulation
of Eqs. (7) and (8) for α=1.67 repeated in the three respective
plots for comparison. We used this optimum α value based on the
previous results of Moraes et al. (2014), who reported an α range of
1.64–1.69 for the S4 index value around 0.67. By comparing the
theoretical formulation of LCR and AFD against scintillation data, the
authors concluded that for moderate and weak levels of scintillation
(S4 < 0.7) the α-μ model agrees quite well with the
values of amplitude envelope r. Otherwise, for S4 > 0.7 the model
tends to become more conservative, which means that it predicts longer fades
and also more crossings for the deeper region of the fades.
In the panels on the left side of Fig. 8, it is possible to note that the LCR
for the three solar activity periods has similar behavior. For the AFD plots
on the right side it is possible to note again the good fit between the field
data and the theoretical formulation. These results clearly suggest that the
statistical characteristics of scintillation remain similar throughout the
solar cycle, and one cannot assume that the number of fades and their time
duration will be different from solar maximum to solar minimum. In other
words, the severity of scintillation seems not to be directly linked with
solar activity itself, but with the scale size and strength of the
irregularities, mainly with the signal propagation path along the
irregularity structure. In terms of GPS channel characterization, the typical
AFD and LCR values shown in Fig. 8 for the anomaly region might help GNSS
receiver developers to estimate outage rate and duration, evaluate GNSS
receiver vulnerabilities under scintillating environments, and design more
robust receivers that are less susceptible to the effects of ionospheric
scintillation.
Conclusions
This study investigated the climatology and modeling of ionospheric
radio-wave scintillations over Cachoeira Paulista, a Brazilian GNSS station
located under the southern crest of the EIA.
The occurrence of scintillations observed from the climatological analysis
showed that the Fresnel-scale irregularities causing scintillations at the
amplitude of GPS L1 signals are more frequent from September to March, mainly
during pre-midnight hours. The observed seasonal distribution of
scintillation occurrence follows the longitudinal characteristics of the
occurrence of equatorial plasma bubbles for the eastern coast of South
America, with a maximum in the scintillation occurrence around the December
solstice months. This is due to the large magnetic declination angle over the
region, with a good alignment between the sunset terminator and the magnetic
meridians around the summer months.
The mostly marked aspect resulting from the climatological analysis of
ionospheric scintillations was their solar activity variations throughout
solar cycle 23 until the maximum of the present solar cycle 24. The largest
frequency of occurrence of ∼ 80 % was observed in 2001–2002 around
the solar maximum of cycle 23. After the year 2002, the overall occurrence
and strength of scintillations tended to subside with the decrease in solar
activity. Following the long declining phase of solar cycle 23 is the deep
solar minimum period that occurred from 2007 to 2009 when the lowest
occurrence of scintillations was attributed to the suppression of the
fountain effect and the anomalous reduction in the background electron
density observed at the EIA region. In the first half of solar cycle 24,
considered to be the weakest solar cycle in more than a century, the maximum
occurrence of scintillations was ∼ 20 % lower than that observed
during the maximum of the previous solar cycle.
The dip latitude of Cachoeira Paulista increased ∼ 3.2∘ from
1997 to 2014 and it is possible that, in addition to the solar cycle
dependence, the occurrence climatology of scintillations is also being
modulated by the drifts in the magnetic dip equator. The crest of the EIA
displaced northward of Cachoeira Paulista from 1997 to 2014, which means that
the site is currently located further under the poleward edge of the southern
EIA region. Consequently, in the present solar cycle for the plasma bubbles
to extend to the site of Cachoeira Paulista, they have to rise to
comparatively much higher altitudes above the magnetic equator, thus
affecting the local scintillation activity.
The average magnitude of the nocturnal GPS-estimated eastward drift
velocities of the irregularities over the low-latitude station of Cachoeira
Paulista was larger during the December solstice months than during the
equinoxes. The results revealed the tendency for the irregularity drift
velocities to increase with increasing EUV and 10.7 cm solar fluxes.
Depending on the season and solar activity level, the irregularity zonal
drifts tended to peak from 20:00 to 23:00 LT.
In terms of scintillation modeling, the results showed that the shape of the
distribution of measured normalized amplitudes and the statistical profile of
the scintillating signals do not change significantly through the solar
cycle. The values of the parameter τ0, which is a temporal indication
of fading characteristics, decreases with the increasing S4 index
independently of the solar activity. Furthermore, for the same value of the
S4 index the decorrelation time tends to decrease with the decline in
the solar activity. The formulation for the α-μ distribution was
revisited and the estimated pairs of fading coefficients α-μ also
supported the fact that the statistical characteristics of scintillation
remain stable during periods of different solar activity levels.
The field data have also been analyzed for second-order statistics,
designated level crossing rate (LCR) and average fading duration (AFD), and
again the results showed that the α-μ formulation fits very well
for most of the range of the amplitude envelope measured during different
levels of solar activity. This result shows that for the same value of the
S4 index the statistical characteristics of scintillation are similar
independently of the solar activity level.