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Statistical distribution of GPS amplitude scintillations
Journal of Atmospheric and Solar-Terrestrial Physics 74 (2012) 199–211
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Statistical distribution of GPS amplitude scintillations A.O. Akala a,b,n, P.H. Doherty a a b
Institute for Scientific Research, Boston College, Chestnut Hill, MA, USA Department of Physics, University of Lagos, Akoka, Yaba, Lagos, Nigeria
a r t i c l e i n f o
abstract
Article history: Received 13 July 2011 Received in revised form 10 November 2011 Accepted 12 November 2011 Available online 23 November 2011
This study presents complementary cumulative distribution function (CCDF) as a statistical distribution apparatus for fitting GPS scintillations data. Three years of data at three levels of solar activity, 2002 (high), 2004 (moderate) and 2008 (low) from an equatorial anomaly crest station; Bogota (4.41N, 74.11W, dip 16.01N) [Colombia] in the West Coast of South America were used for the investigation. These data were grouped into daily, monthly and seasonal sets at three levels of solar activity, and tests were introduced on them to reject data from non-ionospheric sources of scintillation, such as multipath. Before fitting each set of data on a CCDF, the data were first visualized with the aid of scatter plots whereby the distributions exhibit non-Gaussian behavior. As a case study, at S4¼ 0.3 threshold, during the year 2002 and 2004, the months of May–July showed probability of occurrence of the order of 0.01 (1% of the observed samples of a given set) for each month, while in 2008, this trend persisted to August (May–August, probability of occurrence of 0.01 or less (1%)). The tails of January and March’s distributions were observed to be the heaviest at S4 ¼ 0.3, although, a relatively heavy tail at this threshold was also observed during the month of November in the year 2004, and during March Equinox and December Solstice in terms of seasons. The heaviness of the tail at this threshold relaxes as solar activity decreases. The calculated probability of occurrences and those derived from the statistical distribution scheme show good consistency. The results presented in this study may be of assistance for future modeling and simulation studies. & 2011 Elsevier Ltd. All rights reserved.
Keywords: GPS Scintillations CCDF Solar activity
1. Introduction One notable challenge that is delaying the implementation of space based navigation for aviation applications on global level is ionospheric scintillations. In order to resolve ionospheric scintillation issue, aviation agencies, such as, Federal Aviation Administration (FAA), European Space Agency (ESA), Japanese Civil Aviation Bureau (JCAB) etc, under the auspices of the International Civil Aviation Organization (ICAO) have supported the coordination of relevant ionospheric research efforts at the international level. Cardinal in the laid down roadmaps for these efforts is the characterization of the ionosphere, most especially the equatorial ionosphere so as to provide scientific answers to the causes and behavior of ionospheric scintillations (ICAO, 2006). The overall objective is to provide mitigation measures on their impacts on systems’ performances. Ionospheric scintillations are rapid fluctuations in the amplitude and/or phase of radio signals that traverse the ionosphere, and they are largely due to the scattering effects imposed on the
n Corresponding author at: Department of Physics, University of Lagos, Akoka, Yaba, Lagos, Nigeria. Tel.: þ234-8055419769. E-mail address: [email protected] (A.O. Akala).
1364-6826/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jastp.2011.11.006
signals by the irregularities in the ionosphere. During post-sunset hours, the F-region of the ionosphere often becomes turbulent and develops electron density irregularities (Woodman and LaHoz, 1976). Ionospheric scintillations degrade the performance of satellite-based communication and navigation systems (Groves et al., 1997; Basu et al., 1999, 2002; Doherty et al., 2002). At an intense level, scintillation can cause signals to fade below the threshold margin of the receiver, in which case the signal becomes buried in noise, leading to signal loss and cycle slips, and these behaviors are strong at high latitudes, weak at midlatitudes and intense at the equatorial region during solar maximum (Aarons, 1982; Basu et al., 1988). Many authors have explained the interplay of the physical processes leading to the formation and evolution of ionospheric irregularities (e.g. Woodman, 1970; Woodman and LaHoz, 1976; Keskinen and Ossakow, 1983; Kelley, 1989; Fejer, 1991; Titheridge, 1995; Heelis, 2004; Valladares et al., 1996, 2004). According to Fejer (1991) and Valladares et al. (1996), the F-region vertical and zonal plasma drifts showed the largest night-time variations during March Equinox and December Solstice, and the least variations during June Solstice. These drifts also showed solar and magnetic activity dependence. To pursue the characterization of ionospheric scintillations, especially from behavioral stand point, proper understanding of
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the distributions of ionospheric scintillation parameters on different time scales is necessary. Matsunaga et al. (2002) previously showed the statistics of GPS scintillations over Japan using a network of two GPS receivers during solar maximum (2001–2002), but with no definite distribution scheme for characterization. To this end, the present study suggests a complementary cumulative distribution function (CCDF) as a statistical apparatus for fitting GPS scintillations data. This investigation may be relevant for future modeling and simulation studies.
2. Data and methodology The amplitude scintillation data that were used for this research were acquired at a South American equatorial anomaly crest station: Bogota (4.41N, 74.11W, dip 16.01N) using a single frequency CRS1000 Leica GPS receiver at a sampling rate of 10 Hz. The GPS receiver is being managed by the Boston College. The data sets cover three years at three different levels of solar activity; high solar activity (HSA) year (2002) with average annual sunspot number (Rz) of 104, moderate solar activity (MSA) year (2004) with Rz: 41 and low solar activity (LSA) year (2008) with Rz: 03. To ensure a reliable statistics, we introduced three data criteria: (i) data for only equatorial scintillation hours (1800 LT– 0600 LT) were used (Aarons, 1982; Basu et al., 1988, 2002; Ezquer et al., 2003) (ii) only satellites with elevation angles greater or equal to 301 were used, so as to reject data from non-ionospheric scintillation effects such as multipath (Carrano and Groves, 2010; Matsunaga et al., 2002) and (iii) for, each minute of data, the data from the satellite with the severest scintillation impacts has been recorded as the event for that minute. The amplitude scintillation is quantified by S4 (standard deviation of the factor I//IS, where I is the intensity of the received signal and /IS is its average value over a 60 s interval). Data were grouped into daily and monthly sets and further into different seasons using the associated 3 months of data for each season: December Solstice (November–January), March Equinox (February–April), June Solstice (May–July) and September Equinox (August–October). Although during the HSA year, data were not available for the months of March and April. Consequently, only February data were used as a representative of March Equinox for the HSA year. We used scatter plots as a visualization apparatus to study the observational data with a view to establishing a statistical distribution function on which they could be best fitted. On different time scales, the data were fitted into CCDF. We defined the cumulative distribution function (CDF) as CDF ¼ 1
Z
S04
f ðS4 ÞdS4
ð1Þ
0
where f(S4) is a function of S4, the term in integral in Eq. (1) represents the CCDF, and the upper limit of the integration, S04 is the highest S4-value in a given data population. Each raw data sample was first fitted into CDF, and each CDF sample was in turn subtracted from unity to obtain the CCDF sample. This was thereafter employed for the entire data set at different time scales. The CCDF plots define the probabilities of scintillation occurrences, which could be easily determined at any given S4 threshold of interest. On the other hand, the calculated probability of scintillation occurrence at a given threshold for each time scale was determined based on the number of available samples that are greater than or equal to the threshold, and the overall number of samples of the entire population during the time scale.
3. Results and discussions Figs. 1, 2, 3 show the scatter plots of the S4 data for all the months of the HSA, MSA and LSA years, respectively. Typically, in all the plots, larger proportion of the data clustered within the range S4¼0.1–0.18, and sparsely distributed at higher values. At unity and beyond, the data were extremely rare, even during active periods of scintillations. During the HSA year, all the months with which data were available experienced weak scintillation (0.3 rS4o0.4) of various degrees of occurrences. At moderate and intense levels (i.e. S4Z0.4); there were no events at all during the months of June and July, and sparsely distributed events during May and August. All other months; January, February, September–December recorded scintillation events at moderate and intense levels, and these events were generally localized within 1930 LT–2400 LT, although, the distributions were observed to extend to around 0300 LT during January, February and December. For the MSA year, all the months also experienced weak scintillation of various degrees of occurrences. At moderate and intense levels, there were no events at all during the months of May and June, and sparsely distributed events during April, July and August. All other months, January–March, September–December recorded scintillation events at moderate and intense levels, and they were observed to extend to around 0300 LT. During the LSA year, all the months also experienced weak scintillation of various degrees of occurrences. At moderate and intense levels, there were no cases of events during the months of May–August, and events were sparsely distributed during the months of April, and September–December. The months of January–March recorded reasonable distributions of scintillation events at moderate and intense levels, and they were localized within 1930 LT–2400 LT on daily scale. Fig. 4(a)–(d), Fig. 5(a)–(d) and Fig. 6(a)–(d) show the scatter plots of intense and moderate scintillations during the equinoctial and solstitial seasons at high, moderate and low levels of solar activity, respectively. The data distribution spreads from the local sunset (1900 LT) to the early morning hours (0400 LT), although with obvious concentration of data around 1930 LT–2400 LT. During these hours of the day, the ionospheric density is largely dependent on the recombination rate and the magnetic meridional winds (Titheridge, 1995). Additional important drivers are the enhanced eastward electric fields (Rishbeth et al., 1963; Woodman, 1970; Rishbeth, 1998; Heelis, 2004). At local sunset in equatorial region, the zonal neutral wind and the rapid decay of the E-region density interact to develop an enhanced eastward electric field on the day-side of the terminator and a westward electric field on the nightside (Anderson and Haerendel, 1979; Kelley, 1989; Basu et al., 2002; Heelis, 2004). The enhanced eastward electric field, otherwise known as the pre-reversal enhancement in the zonal electric field, causes vertical up-welling of the F-region, steepens the bottomside density gradient to trigger the Rayleigh–Taylor instability (Kelley, 1989; Rishbeth, 1998; Heelis, 2004). Consequently, the low-density plasma from the bottomside percolates into the topside ionosphere to develop a plethora of plasma bubbles that transform to a cascade of irregularities of different scale sizes, and cause scintillation of radio signals. The data cluster is denser during the HSA year, less dense during the MSA year and sparse during the LSA year. It is important to note that data were not available for the months of March and April during the HSA year. Seasonally, at all levels of solar activity, the data for December Solstice and March Equinox dominate the distribution, although with a degree of concentration that increases with solar activity, while the data for the June Solstice were sparingly populated with a significant scantiness during the LSA year. Fig. 7(a), (b) and (c) show the scatter plot of intense and moderate scintillations during all the seasons of the
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NOVEMBER, 2002, n=10721
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DECEMBER, 2002, n=10623
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JULY, 2002, n=13396
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29
LT (Hr)
LT (Hr)
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OCTOBER, 2002, n=12135
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S4
S4
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0
26
LT (Hr)
MAY, 2002, n=15256
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25
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0.4
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24
SEPTEMBER, 2002, n=6406
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S4
S4
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LT (Hr)
FEBRUARY, 2002, n=10143
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Fig. 1. Scatter plots of S4 data for all the months (January–December, no data for March and April) during the HSA (2002).
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JULY, 2004, n=21315
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NOVEMBER, 2004, n=19547
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OCTOBER, 2004, n=21088
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SEPTEMBER, 2004, n=21540
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MARCH, 2004, n=20909
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AUGUST, 2004, n=21156
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FEBRUARY, 2004, n=18718
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Fig. 2. Scatter plots of S4 data for all the months (January–December) during the MSA (2004).
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1 0.8 0.6 0.4 0.2 0
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Fig. 3. Scatter plots of S4 data for all the months (January–December) during the LSA (2008).
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LT (Hr) Fig. 4. Scatter plots comparing intense and moderate scintillations (S4 Z0.4) during the HSA year (a) March Equinox (b) June Solstice (c) September Equinox (d) December Solstice.
HSA, MSA and LSA years, respectively. Here, the data from the HSA year dominate the distribution, followed by the MSA year and those of the LSA year were sparse. In other words, the chances of intense/strong scintillation occurrences increase with solar activity.
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LT (Hr) Fig. 5. Scatter plots comparing intense and moderate scintillations (S4Z 0.4) during the MSA year (a) March Equinox (b) June Solstice (c) September Equinox (d) December Solstice.
Fig. 8 shows the CCDF of S4 data for all the months of the HSA, although with the exception of March and April with no data. Generally, the low S4 values (S4r0.18) dominate the distributions. At S4 ¼0.3, the months of January, February, September and
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Fig. 7. Scatter plots comparing intense and moderate scintillations (S4 Z0.4) for all seasons, during (a) HSA, (b) MSA and (c) LSA.
DEC SOLSTICE
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LT (Hr) Fig. 6. Scatter plots comparing intense and moderate scintillations (S4 Z 0.4) during the LSA year (a) March Equinox (b) June Solstice (c) September Equinox (d) December Solstice.
November recorded the highest probabilities of scintillation occurrences, 15%, 14%, 11% and 11%, respectively. The least probabilities of scintillation occurrences were recorded in the months of May–August (1% each). For the months of October and
December, the probabilities of scintillation occurrences were recorded as 7% and 10%, respectively. The months of January, February, October, November and December had the longest tails, S4¼ 1.23, 1.12, 1.13, 1.11 and 1.15, respectively, and the shortest in the months of June and July, S4¼0.36 for each month. Fig. 9 shows the CCDF of S4 data for all the months of the MSA. At S4¼0.3, the months of January, February, March, September, October and November recorded the highest probabilities of scintillation occurrences, 6%, 5%, 6%, 5%, 6% and 9%, respectively. The least probabilities of scintillation occurrences were recorded in the months of May–August (1% each). For the month of April and December, the probabilities of scintillation occurrences were recorded as 1.5% and 4%, respectively. The months of January, February, March, September and November had the longest tails, S4¼ 1.25, 1.19, 1.22, 1.19 and 1.20, respectively, and the shortest in the months of May and June, S4 ¼0.36 for each month. Fig. 10 shows the CCDF of S4 data for all the months of the LSA. At S4¼ 0.3, the probability of scintillation occurrence was recorded to be less than 1% for all the months (precisely 0.5%). However,
A.O. Akala, P.H. Doherty / Journal of Atmospheric and Solar-Terrestrial Physics 74 (2012) 199–211
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
JANUARY, 2002, n=15744
CCDF
CCDF
206
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
FEBRUARY, 2002, n=10143
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
MAY, 2002, n=15256
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
CCDF
CCDF
JUNE, 2002, n=12454
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
JULY, 2002, n=13396
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
S4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1.1 1.2 1.3 1.4
OCTOBER, 2002, n=12135
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1.1 1.2 1.3 1.4
NOVEMBER, 2002, n=10721
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1.1 1.2 1.3 1.4
S4
CCDF
CCDF
S4 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
SEPTEMBER, 2002, n=6406
S4
S4 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
1.1 1.2 1.3 1.4
S4
CCDF
CCDF
S4 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
S4
CCDF
CCDF
S4
AUGUST, 2002, n=7904
1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
DECEMBER, 2002, n=10622
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
S4
Fig. 8. Complementary cumulative distribution function (CCDF) of S4 data for all the months (January–December, no data for March and April) during the HSA (2002).
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
JANUARY, 2004, n=12851
CCDF
CCDF
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
CCDF
MARCH, 2004, n=20909
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
S4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
MAY, 2004, n=20387
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
CCDF S4
NOVEMBER, 2004, n=19547
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
S4
JUNE, 2004, n=21539
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
S4
CCDF
CCDF CCDF
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 OCTOBER, 2004, n=21088
S4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
SEPTEMBER, 2004, n=21540
APRIL, 2004, n= 15134
S4 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
S4
CCDF
CCDF CCDF
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
AUGUST, 2004, n=21156
S4
S4 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
S4
FEBRUARY, 2004, n=18718
CCDF
CCDF
S4
JULY, 2004, n=21315
1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
DECEMBER, 2004, n=20732
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
S4
Fig. 9. Complementary cumulative distribution function (CCDF) of S4 data for all the months (January–December) during the MSA (2004).
207
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1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
JANUARY, 2008, n=20670
CCDF
CCDF
208
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
JULY, 2008, n=20270
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
S4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
FEBRUARY, 2008, n=20522
CCDF
CCDF
S4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
AUGUST, 2008, n=19598
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
S4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
MARCH, 2008, n=20392
CCDF
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1.1 1.2 1.3 1.4
S4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
SEPTEMBER, 2008, n=18533
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
S4
APRIL, 2008, n=18748
CCDF
CCDF
CCDF
S4
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
OCTOBER, 2008, n=16344
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
S4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
MAY, 2008, n=17851
CCDF
CCDF
S4
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
NOVEMBER, 2008, n=9324
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
JUNE, 2008, n=18558
CCDF
CCDF
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
S4
1.1 1.2 1.3 1.4
S4
S4
1
1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
DECEMBER, 2008, n=7918
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
S4
1.1 1.2 1.3 1.4
Fig. 10. Complementary cumulative distribution function (CCDF) of S4 data for all the months (January–December) during the LSA (2008).
A.O. Akala, P.H. Doherty / Journal of Atmospheric and Solar-Terrestrial Physics 74 (2012) 199–211
209
the June Solstice was characterized with extremely light tails. During the HSA year, at S4¼0.3, the probabilities of scintillation occurrences are 13%, 14%, 0.5% and 6% for the December Solstice, March Equinox, June Solstice and September Equinox, respectively. For the MSA year, at S4¼0.3, the probabilities of scintillation occurrences are 6%, 5%, 0.5% and 5% for the December Solstice, March Equinox, June Solstice and September Equinox, respectively. During the LSA year, at S4¼0.3, the probabilities of scintillation occurrences are 1% each for the December Solstice, March Equinox and September Equinox and 0.5% for the June
the months of January, March and October had the longest tails, S4 ¼0.76, 0.83 and 0.76, respectively, and the shortest in the months of May, June and July, S4 ¼0.4, 0.38 and 0.39, respectively. Fig. 11(a), (b) and (c) shows the CCDF of S4 data during the equinoctial and solstitial seasons at HSA, MSA and LSA years, respectively. All the plots have the same features, but for the relaxation of the heaviness of the tails of the distributions within the range S4¼0.2–0.8 as the solar activity decreases. In addition, the tails of the December Solstice and March Equinox distributions were observed to be the heaviest within this range, whereas,
BOGOTA, 2002
1 0.9 0.8
DEC SOLS MAR EQUI JUN SOLS SEP EQUI
CCDF
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7 S4
0.8
0.9
1
1.1
1.2
1.3
1.4
BOGOTA, 2004
1 0.9 0.8
DEC SOLS MAR EQUI JUN SOLS SEP EQUI
CCDF
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
0.9
1
1.1
1.2
1.3
1.4
S4 BOGOTA, 2008
1 0.9
DEC SOLS MAR EQUI JUN SOLS SEP EQUI
0.8
CCDF
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
S4 Fig. 11. Complementary cumulative distribution function (CCDF) of S4 data during the equinoctial and solstitial seasons at (a) HSA, (b) MSA and (c) LSA.
A.O. Akala, P.H. Doherty / Journal of Atmospheric and Solar-Terrestrial Physics 74 (2012) 199–211
0.2
2002 2004 2008
0.16
0.12 0.08 0.04
OCT
SEP
AUG
JUL
JUN
MAY
APR
MAR
FEB
JAN
DEC
0 NOV
Probability of occurrence (%), S4>1
210
20
Cal. Emp.
18 16 14
NO DATA
12 10 8 6 4
2 DEC
NOV
OCT
SEP
AUG
JUL
JUN
MAY
APR
MAR
DEC
NOV
OCT
SEP
AUG
This study investigated the statistical distributions of GPS scintillations data at Bogota (an equatorial anomaly crest station). Three years of data at three levels of solar activity, high (2002), moderate (2004) and low (2008) were used for the investigation. The study concludes as follows:
JUL
JUN
MAY
APR
MAR
Cal. Emp.
FEB
% Probability of occurence S4≥0.3
20
4. Conclusions
JAN
% Probability of occurence S4≥0.3
20 18 16 14 12 10 8 6 4 2 0
FEB
0 JAN
Cal. Emp.
18 16 14 12 10
8 6 4 2 DEC
NOV
OCT
SEP
AUG
JUL
JUN
MAY
APR
MAR
JAN
0 FEB
% Probability of occurence S4≥0.3
Fig. 12. Bar plots of the probability of scintillation occurrences at S4 41.0 threshold during the HSA (2002), MSA (2004) and LSA (2008).
Solstice. For the HSA, MSA and LSA years, the distribution tailed off at S4 ¼0.8, 0.6 and 0.3, respectively. These features confirm the vulnerability of the ionosphere to scintillations during December Solstice and March Equinox, most especially during the HSA year at Bogota, and June Solstice can be regarded as a non-scintillation season. Fig. 12 shows the bar plots of the probability of occurrences of S441.0. The probability of occurrences is very rare at this threshold, with no event during the months of May–August for the HSA year, April–August for the MSA year and no event at all during any of the months of the LSA year. During the HSA year, the highest occurrence was recorded during the months of January (0.15%) and February (0.11%), and during the months of January and November for the MSA year with 0.04% for each month. Due to very low chances of the occurrences of scintillation at this threshold (S441.0), the distribution curve seems to tail off along the S4 axis, ending at the maximum observed value. Conclusively, a significant rareness of data was observed at this threshold even during the HSA year and active months of scintillations. It is also important to mention that at lower S4 values (o0.15), all the plots, irrespective of the month, season or solar activity depict congruent feature as they were all seen to superimpose. The inference is that, the inherent receiver’s noise by design is fixed at the 0.15 level. Fig. 13(a), (b) and (c) shows the Bar plots that compare the calculated and the CCDF probabilities of scintillation (S4Z0.3) occurrences for all the months during HSA, MSA and LSA, respectively. The calculated probability of occurrences and those derived from the statistical distribution scheme show good consistency. The little variances between the calculated and the CCDF probabilities of scintillations were commonly observed when the probability is significantly low (less than 1.0), and this is suspected to be a matter of precision.
Fig. 13. Bar plots comparing the calculated (Cal.) and CCDF (Emp.) probabilities of scintillations (S4Z 0.3) occurrences for all the months during (a) HSA, (b) MSA and (c) LSA.
(i) Complementary cumulative distribution function (CCDF) is a suitable statistical apparatus for fitting GPS scintillation data. The apparatus is also typical in figuring out the inbuilt receiver’s noise level. (ii) GPS amplitude scintillation data exhibit non-Gaussian behavior. The rarity of the distributions increases with S4 value, with a significant rarity in the neighborhood of unity, even during solar active periods. In other words, low-valued S4 (S4 o0.2) samples dominated the entire data. By implication, samples deviations from the mean seem asymmetric around the mean. Consequently, using central tendencies or measures of dispersion for reliable statistical inference on GPS scintillation data seems impracticable. For instance, unlike other ionospheric parameters (e.g. foF2, TEC) where the hourly mean could be relatively representative of the subminutes data of the hour, scintillation data will not support such representation. This is because scintillations exhibit extreme variability in space and time (Basu et al., 2002). (iii) GPS amplitude scintillation is a post-sunset event with a daily trend of occurrence during the hours of 1900 LT–0400 LT, although with distributions that are largely localized at 1930 LT–2400 LT. On a monthly scale, March and January had highest probabilities of occurrences, while the months of
A.O. Akala, P.H. Doherty / Journal of Atmospheric and Solar-Terrestrial Physics 74 (2012) 199–211
May–July were observed as non-scintillation months. Seasonally, March Equinox and December Solstice showed the highest probabilities of occurrences, while June Solstice was observed as non-scintillation season. On a solar activity scale, the probabilities of occurrences increase with solar activity. The observed monthly, seasonal and solar activity variations of scintillation occurrences could be attributed to the associated night-time variations in F-region vertical and zonal plasma drifts. Overall, the calculated probability of occurrences and those derived from the statistical distribution scheme show good consistency. These results were in reasonable agreement with earlier statistical observations carried out by Matsunaga et al. (2002), Beniguel et al. (2009). The results presented in this study may be of assistance for future modeling and simulation studies.
Acknowledgments The first author thanks the U.S. Government for the Fulbright Scholarship Grant, and the Institute for Scientific Research, Boston College for hosting him. He also thanks Dr. Constantin Adronache and Chuangi Zhu of the Information Technology Services of Boston College for their useful discussions on MATLAB programming and Charles Carrano for his useful discussions on this paper. The authors also thank the Reviewers for their useful comments and suggestions, which has improved the paper. References Aarons, J., 1982. Global morphology of ionospheric scintillations. In: Proceedings of the IEEE 70, 360–378. Anderson, D., Haerendel, G., 1979. The motion of depleted plasma regions in the equatorial ionosphere. Journal of Geophysical Research 84, 4251–4256. Basu, S., MacKenzie, E., Basu, Su, 1988. Ionospheric constraints on VHF/UHF communications links during solar maximum and minimum periods. Radio Science 23, 363–378.
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Basu, S., Groves, K.M., Quinn, J.M., Doherty, P., 1999. A comparison of TEC fluctuations and scintillations at Ascension Island. Journal of Atmospheric and Solar–Terrestrial Physics 61, 1219–1226. Basu, S., Groves, K.M., Basu, Su., Sultan,, J.P., 2002. Specification and forecasting of scintillations in communication/navigation links: current status and future plans. Journal of Atmospheric and Solar–Terrestrial Physics 64, 1745–1754. Be´niguel, Y., et al., 2009. Analysis of scintillation recorded during the PRIS measurement campaign. Radio Science 44, RS0A30. doi:10.1029/2008RS004090. Carrano, C.S., Groves, K.M., 2010. Temporary decorrelation of GPS satellite signals due to multiple scattering from ionospheric irregularities. In: Proceedings of the 2010 ION GNSS Meeting. September 21–24, Portland, OR. Doherty, P.H., Dehel, T., Klobuchar, J., Delay, S.H., Datta-Barua, S., de-Paula, E.R., Rodrigues, F.S., 2002. Ionospheric effects on low-latitude space based augmentation systems. In: Proceedings of the ION GPS-2002, Portland, OR. Ezquer, R.G., Kintner, P.M., Cabrera, M.A., Radicella, S.M., Forte, B., 2003. Scintillations observed at Tucuman as from GPS signals: first results. Advances in Space Research 31, 741–747. Fejer, B.G., 1991. Low latitude electrodynamics plasma drifts: a review. Journal of Atmospheric and Terrestrial Physics 53, 77–693. Groves, K., et al., 1997. Equatorial scintillation and systems support. Radio Science 32, 2047–2064. Heelis, R.A., 2004. Electrodynamics in the low and middle latitude ionosphere: a tutorial. Journal of Atmospheric and Solar–Terrestrial Physics 66, 825–838. International Civil Aviation Organization (ICAO), 2006. Navigation Systems Panel’s Report on Ionospheric Effects on GNSS Aviation Operations. Montreal, Canada, 10–20 October. Kelley, M.C., 1989. The Earth’s Ionosphere. Academic Press Inc., London. Keskinen, M.J., Ossakow, S.L., 1983. Theories of high-latitude ionospheric irregularities: a review. Radio Science 18, 1077–1091. Matsunaga, K., Hoshinoo, K., Igarashi, K., 2002. Observation of ionospheric scintillation on GPS signals in Japan. In: Proceedings of the ION NTM. 28–30 January 2002, San Diego, CA. Rishbeth, H., Lyon, A.J., Peart, M., 1963. Diffusion in the equatorial F layer. Journal of Geophysical Research 68, 2559–2569. Rishbeth, H., 1998. How the thermospheric circulation affects the ionospheric Flayer. Journal of Atmospheric and Solar–Terrestrial Physics 60, 1385–1402. Titheridge, J.E., 1995. Winds in the ionosphere: a review. Journal of Atmospheric and Terrestrial Physics 57, 1681–1714. Valladares, C., Sheehan, R., Basu, S., Kuenzler, H., Espinoza, J., 1996. The multiinstrumented studies of equatorial thermosphere aeronomy scintillation system: climatology of zonal drifts. Journal of Geophysical Research 101, 26839–26850. Valladares, C.E., Villalobos, J., Sheehan, R., Hagan, M.P., 2004. Latitudinal extension of low-latitude scintillations measured with a network of GPS receivers. Annales Geophysicae 22, 3155–3175. Woodman, R., 1970. Vertical drift velocities and east–west electric fields at the magnetic equator. Journal of Geophysical Research 75 (31), 6249–6259. Woodman, R.F., La Hoz, C., 1976. Radar observations of F-region equatorial irregularities. Journal of Geophysical Research 81, 5447–5466.
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Statistical distribution of GPS amplitude scintillations A.O. Akala a,b,n, P.H. Doherty a a b
Institute for Scientific Research, Boston College, Chestnut Hill, MA, USA Department of Physics, University of Lagos, Akoka, Yaba, Lagos, Nigeria
a r t i c l e i n f o
abstract
Article history: Received 13 July 2011 Received in revised form 10 November 2011 Accepted 12 November 2011 Available online 23 November 2011
This study presents complementary cumulative distribution function (CCDF) as a statistical distribution apparatus for fitting GPS scintillations data. Three years of data at three levels of solar activity, 2002 (high), 2004 (moderate) and 2008 (low) from an equatorial anomaly crest station; Bogota (4.41N, 74.11W, dip 16.01N) [Colombia] in the West Coast of South America were used for the investigation. These data were grouped into daily, monthly and seasonal sets at three levels of solar activity, and tests were introduced on them to reject data from non-ionospheric sources of scintillation, such as multipath. Before fitting each set of data on a CCDF, the data were first visualized with the aid of scatter plots whereby the distributions exhibit non-Gaussian behavior. As a case study, at S4¼ 0.3 threshold, during the year 2002 and 2004, the months of May–July showed probability of occurrence of the order of 0.01 (1% of the observed samples of a given set) for each month, while in 2008, this trend persisted to August (May–August, probability of occurrence of 0.01 or less (1%)). The tails of January and March’s distributions were observed to be the heaviest at S4 ¼ 0.3, although, a relatively heavy tail at this threshold was also observed during the month of November in the year 2004, and during March Equinox and December Solstice in terms of seasons. The heaviness of the tail at this threshold relaxes as solar activity decreases. The calculated probability of occurrences and those derived from the statistical distribution scheme show good consistency. The results presented in this study may be of assistance for future modeling and simulation studies. & 2011 Elsevier Ltd. All rights reserved.
Keywords: GPS Scintillations CCDF Solar activity
1. Introduction One notable challenge that is delaying the implementation of space based navigation for aviation applications on global level is ionospheric scintillations. In order to resolve ionospheric scintillation issue, aviation agencies, such as, Federal Aviation Administration (FAA), European Space Agency (ESA), Japanese Civil Aviation Bureau (JCAB) etc, under the auspices of the International Civil Aviation Organization (ICAO) have supported the coordination of relevant ionospheric research efforts at the international level. Cardinal in the laid down roadmaps for these efforts is the characterization of the ionosphere, most especially the equatorial ionosphere so as to provide scientific answers to the causes and behavior of ionospheric scintillations (ICAO, 2006). The overall objective is to provide mitigation measures on their impacts on systems’ performances. Ionospheric scintillations are rapid fluctuations in the amplitude and/or phase of radio signals that traverse the ionosphere, and they are largely due to the scattering effects imposed on the
n Corresponding author at: Department of Physics, University of Lagos, Akoka, Yaba, Lagos, Nigeria. Tel.: þ234-8055419769. E-mail address: [email protected] (A.O. Akala).
1364-6826/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jastp.2011.11.006
signals by the irregularities in the ionosphere. During post-sunset hours, the F-region of the ionosphere often becomes turbulent and develops electron density irregularities (Woodman and LaHoz, 1976). Ionospheric scintillations degrade the performance of satellite-based communication and navigation systems (Groves et al., 1997; Basu et al., 1999, 2002; Doherty et al., 2002). At an intense level, scintillation can cause signals to fade below the threshold margin of the receiver, in which case the signal becomes buried in noise, leading to signal loss and cycle slips, and these behaviors are strong at high latitudes, weak at midlatitudes and intense at the equatorial region during solar maximum (Aarons, 1982; Basu et al., 1988). Many authors have explained the interplay of the physical processes leading to the formation and evolution of ionospheric irregularities (e.g. Woodman, 1970; Woodman and LaHoz, 1976; Keskinen and Ossakow, 1983; Kelley, 1989; Fejer, 1991; Titheridge, 1995; Heelis, 2004; Valladares et al., 1996, 2004). According to Fejer (1991) and Valladares et al. (1996), the F-region vertical and zonal plasma drifts showed the largest night-time variations during March Equinox and December Solstice, and the least variations during June Solstice. These drifts also showed solar and magnetic activity dependence. To pursue the characterization of ionospheric scintillations, especially from behavioral stand point, proper understanding of
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the distributions of ionospheric scintillation parameters on different time scales is necessary. Matsunaga et al. (2002) previously showed the statistics of GPS scintillations over Japan using a network of two GPS receivers during solar maximum (2001–2002), but with no definite distribution scheme for characterization. To this end, the present study suggests a complementary cumulative distribution function (CCDF) as a statistical apparatus for fitting GPS scintillations data. This investigation may be relevant for future modeling and simulation studies.
2. Data and methodology The amplitude scintillation data that were used for this research were acquired at a South American equatorial anomaly crest station: Bogota (4.41N, 74.11W, dip 16.01N) using a single frequency CRS1000 Leica GPS receiver at a sampling rate of 10 Hz. The GPS receiver is being managed by the Boston College. The data sets cover three years at three different levels of solar activity; high solar activity (HSA) year (2002) with average annual sunspot number (Rz) of 104, moderate solar activity (MSA) year (2004) with Rz: 41 and low solar activity (LSA) year (2008) with Rz: 03. To ensure a reliable statistics, we introduced three data criteria: (i) data for only equatorial scintillation hours (1800 LT– 0600 LT) were used (Aarons, 1982; Basu et al., 1988, 2002; Ezquer et al., 2003) (ii) only satellites with elevation angles greater or equal to 301 were used, so as to reject data from non-ionospheric scintillation effects such as multipath (Carrano and Groves, 2010; Matsunaga et al., 2002) and (iii) for, each minute of data, the data from the satellite with the severest scintillation impacts has been recorded as the event for that minute. The amplitude scintillation is quantified by S4 (standard deviation of the factor I//IS, where I is the intensity of the received signal and /IS is its average value over a 60 s interval). Data were grouped into daily and monthly sets and further into different seasons using the associated 3 months of data for each season: December Solstice (November–January), March Equinox (February–April), June Solstice (May–July) and September Equinox (August–October). Although during the HSA year, data were not available for the months of March and April. Consequently, only February data were used as a representative of March Equinox for the HSA year. We used scatter plots as a visualization apparatus to study the observational data with a view to establishing a statistical distribution function on which they could be best fitted. On different time scales, the data were fitted into CCDF. We defined the cumulative distribution function (CDF) as CDF ¼ 1
Z
S04
f ðS4 ÞdS4
ð1Þ
0
where f(S4) is a function of S4, the term in integral in Eq. (1) represents the CCDF, and the upper limit of the integration, S04 is the highest S4-value in a given data population. Each raw data sample was first fitted into CDF, and each CDF sample was in turn subtracted from unity to obtain the CCDF sample. This was thereafter employed for the entire data set at different time scales. The CCDF plots define the probabilities of scintillation occurrences, which could be easily determined at any given S4 threshold of interest. On the other hand, the calculated probability of scintillation occurrence at a given threshold for each time scale was determined based on the number of available samples that are greater than or equal to the threshold, and the overall number of samples of the entire population during the time scale.
3. Results and discussions Figs. 1, 2, 3 show the scatter plots of the S4 data for all the months of the HSA, MSA and LSA years, respectively. Typically, in all the plots, larger proportion of the data clustered within the range S4¼0.1–0.18, and sparsely distributed at higher values. At unity and beyond, the data were extremely rare, even during active periods of scintillations. During the HSA year, all the months with which data were available experienced weak scintillation (0.3 rS4o0.4) of various degrees of occurrences. At moderate and intense levels (i.e. S4Z0.4); there were no events at all during the months of June and July, and sparsely distributed events during May and August. All other months; January, February, September–December recorded scintillation events at moderate and intense levels, and these events were generally localized within 1930 LT–2400 LT, although, the distributions were observed to extend to around 0300 LT during January, February and December. For the MSA year, all the months also experienced weak scintillation of various degrees of occurrences. At moderate and intense levels, there were no events at all during the months of May and June, and sparsely distributed events during April, July and August. All other months, January–March, September–December recorded scintillation events at moderate and intense levels, and they were observed to extend to around 0300 LT. During the LSA year, all the months also experienced weak scintillation of various degrees of occurrences. At moderate and intense levels, there were no cases of events during the months of May–August, and events were sparsely distributed during the months of April, and September–December. The months of January–March recorded reasonable distributions of scintillation events at moderate and intense levels, and they were localized within 1930 LT–2400 LT on daily scale. Fig. 4(a)–(d), Fig. 5(a)–(d) and Fig. 6(a)–(d) show the scatter plots of intense and moderate scintillations during the equinoctial and solstitial seasons at high, moderate and low levels of solar activity, respectively. The data distribution spreads from the local sunset (1900 LT) to the early morning hours (0400 LT), although with obvious concentration of data around 1930 LT–2400 LT. During these hours of the day, the ionospheric density is largely dependent on the recombination rate and the magnetic meridional winds (Titheridge, 1995). Additional important drivers are the enhanced eastward electric fields (Rishbeth et al., 1963; Woodman, 1970; Rishbeth, 1998; Heelis, 2004). At local sunset in equatorial region, the zonal neutral wind and the rapid decay of the E-region density interact to develop an enhanced eastward electric field on the day-side of the terminator and a westward electric field on the nightside (Anderson and Haerendel, 1979; Kelley, 1989; Basu et al., 2002; Heelis, 2004). The enhanced eastward electric field, otherwise known as the pre-reversal enhancement in the zonal electric field, causes vertical up-welling of the F-region, steepens the bottomside density gradient to trigger the Rayleigh–Taylor instability (Kelley, 1989; Rishbeth, 1998; Heelis, 2004). Consequently, the low-density plasma from the bottomside percolates into the topside ionosphere to develop a plethora of plasma bubbles that transform to a cascade of irregularities of different scale sizes, and cause scintillation of radio signals. The data cluster is denser during the HSA year, less dense during the MSA year and sparse during the LSA year. It is important to note that data were not available for the months of March and April during the HSA year. Seasonally, at all levels of solar activity, the data for December Solstice and March Equinox dominate the distribution, although with a degree of concentration that increases with solar activity, while the data for the June Solstice were sparingly populated with a significant scantiness during the LSA year. Fig. 7(a), (b) and (c) show the scatter plot of intense and moderate scintillations during all the seasons of the
A.O. Akala, P.H. Doherty / Journal of Atmospheric and Solar-Terrestrial Physics 74 (2012) 199–211
1.4 1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
18
19
20
21
22
23
24
25
26
AUGUST, 2002, n=7904
1.2
S4
S4
1.4
JANUARY, 2002, n=15744
1.2
27
28
29
0
30
18
19
20
21
22
LT (Hr) 1.4 1
1 0.8
0.6
0.4
0.2
0.2 19
20
21
22
23
24
25
26
27
28
29
0
30
18
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20
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22
LT (Hr) 1.4
1
0.8
0.8
0.6
0.4
0.2
0.2 19
20
21
22
23
24
25
26
27
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29
0
30
18
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1.4 1
1
0.8
0.8
S4
S4
23
24
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30
23
24
25
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27
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29
30
0.6
27
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30
27
28
29
30
0.6
0.4
0.4
0.2
0.2 18
19
20
21
22
23
24
25
26
NOVEMBER, 2002, n=10721
1.2
27
28
29
0
30
18
19
20
21
22
LT (Hr) 1.4
1.4
0.8
S4
1
0.8 0.6
0.4
0.2
0.2 20
21
22
23
24
LT (Hr)
25
26
0.6
0.4
19
24
25
26
DECEMBER, 2002, n=10623
1.2
1
18
23
LT (Hr)
JULY, 2002, n=13396
1.2
S4
30
1.4 JUNE, 2002, n=12456
1.2
0
29
LT (Hr)
LT (Hr)
0
28
0.6
0.4
18
27
OCTOBER, 2002, n=12135
1.2
S4
S4
1.4
1
0
26
LT (Hr)
MAY, 2002, n=15256
1.2
25
0.6
0.4
18
24
SEPTEMBER, 2002, n=6406
1.2
S4
S4
1.4
0.8
0
23
LT (Hr)
FEBRUARY, 2002, n=10143
1.2
201
27
28
29
30
0
18
19
20
21
22
23
24
25
26
LT (Hr)
Fig. 1. Scatter plots of S4 data for all the months (January–December, no data for March and April) during the HSA (2002).
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1.4 1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
18
19
20
21
22
23
24
25
26
JULY, 2004, n=21315
1.2
S4
S4
1.4
JANUARY, 2004, n=12851
1.2
27
28
29
0
30
18
19
20
21
22
23
LT (Hr) 1.4 1
1
0.8
0.8
0.6
0.4
0.2 0
0.2 19
20
21
22
23
24
25
26
27
28
0
29 30
18
19
20
21
22
23
LT (Hr) 1.4 1
1 0.8
0.6
0.4
0.2
0.2
0 20
21
22
23
24
25
26
27
28
0
29 30
18
19
20
21
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LT (Hr) 1.4 1
1 0.8
0.6
0.4
0.2
0.2 19
20
21
22
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24
25
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27
28
29
0
30
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LT (Hr) 1.4 1
1 0.8
0.6
0.4
0.2
0.2 19
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24
25
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27
28
0
29 30
18
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20
21
22
LT (Hr) 1.4 1
1 0.8
0.6
0.4
0.2
0.2 0
19
20
21
22
23
24
LT (Hr)
26
27
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29 30
24
25
26
27
28
29 30
23
24
25
26
27
28
29
30
0.6
0.4
18
25
25
26
DECEMBER, 2004, n=20732
1.2
S4
S4
1.4
0.8
0
24
LT (Hr)
JUNE, 2004, n=21539
1.2
29 30
0.6
0.4
18
28
NOVEMBER, 2004, n=19547
1.2
S4
S4
1.4
0.8
0
27
LT (Hr)
MAY, 2004, n=20387
1.2
26
0.6
0.4
18
25
OCTOBER, 2004, n=21088
1.2
S4
S4
1.4
0.8
0
24
LT (Hr)
APRIL, 2004, n=15134
1.2
29 30
0.6
0.4
19
28
SEPTEMBER, 2004, n=21540
1.2
S4
S4
1.4
0.8
18
27
LT (Hr)
MARCH, 2004, n=20909
1.2
26
0.6
0.4
18
25
AUGUST, 2004, n=21156
1.2
S4
S4
1.4
FEBRUARY, 2004, n=18718
1.2
24
LT (Hr)
27
28
29 30
18
19
20
21
22
23
24
25
LT (Hr)
Fig. 2. Scatter plots of S4 data for all the months (January–December) during the MSA (2004).
26
27
28
29 30
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1 0.8 0.6 0.4 0.2 0
JULY, 2008, n=20270
0.8 S4
S4
1
JANUARY, 2008, n=20670
0.6 0.4 0.2
18
19
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21
22
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25
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27
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0
30
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LT (Hr) 1
0.4 0.2 18
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0.6
S4
S4
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0.2 18
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24
24
25
26
27
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30
25
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30
SEPTEMBER, 2008, n=18533
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0.4
26
27
28
29
0
30
18
19
20
21
22
23
LT (Hr)
24
25
26
LT (Hr) 1
APRIL, 2008, n=18748
0.8
0.8
0.6
0.6
S4
S4
30
0.8
0.4 0.2
OCTOBER, 2008, n=16344
0.4 0.2
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19
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21
22
23
24
25
26
27
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30
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LT (Hr) 1
24
25
26
LT (Hr) 1
MAY, 2008, n=17851
0.8
0.8
0.6
0.6
S4
S4
29
LT (Hr) 1
1
0.4 0.2
NOVEMBER, 2008, n=9324
0.4 0.2
18
19
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30
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LT (Hr) 1
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25
26
27
28
29
30
27
28
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30
LT (Hr) 1
JUNE, 2008, n=18557
0.8
0.8
0.6
0.6
S4
S4
28
0.4
0
30
MARCH, 2008, n=20391
0.8
0.4 0.2 0
27
0.2
1
0
26
0.6
LT (Hr)
0
25
AUGUST, 2008, n=19598
0.8 S4
S4
1
0.6
0
24 LT (Hr)
FEBRUARY, 2008, n=20522
0.8
0
203
DECEMBER, 2008, n=7918
0.4 0.2
18
19
20
21
22
23
24 LT (Hr)
25
26
27
28
29
30
0
18
19
20
21
22
23
24 LT (Hr)
Fig. 3. Scatter plots of S4 data for all the months (January–December) during the LSA (2008).
25
26
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1.4
1.4 MAR EQUINOX
1 0.8 0.6 0.4 0.2
MAR EQUINOX
1.2 S4>=0.4
S4>=0.4
1.2
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S4>=0.4
S4>=0.4
0.8 0.6 0.4 18
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LT (Hr) 1.4
SEP EQUINOX
1.2
SEP EQUINOX
1.2
1
S4>=0.4
S4>=0.4
28
0.4
1.4
0.8 0.6 0.4
1 0.8 0.6 0.4
18
19
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30
LT (Hr)
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LT (Hr)
1.4
1.4
DEC SOLSTICE
1.2
DEC SOLSTICE
1.2
1
S4>=0.4
S4>=0.4
27
JUN SOLSTICE
LT (Hr)
0.8 0.6 0.4 0.2
26
1.2
1
0.2
25
1.4 JUN SOLSTICE
1.2
0.2
24 LT (Hr)
1 0.8 0.6 0.4
18
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24
25
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29
30
LT (Hr) Fig. 4. Scatter plots comparing intense and moderate scintillations (S4 Z0.4) during the HSA year (a) March Equinox (b) June Solstice (c) September Equinox (d) December Solstice.
HSA, MSA and LSA years, respectively. Here, the data from the HSA year dominate the distribution, followed by the MSA year and those of the LSA year were sparse. In other words, the chances of intense/strong scintillation occurrences increase with solar activity.
0.2
18
19
20
21
22
23
24
25
26
27
28
29
30
LT (Hr) Fig. 5. Scatter plots comparing intense and moderate scintillations (S4Z 0.4) during the MSA year (a) March Equinox (b) June Solstice (c) September Equinox (d) December Solstice.
Fig. 8 shows the CCDF of S4 data for all the months of the HSA, although with the exception of March and April with no data. Generally, the low S4 values (S4r0.18) dominate the distributions. At S4 ¼0.3, the months of January, February, September and
A.O. Akala, P.H. Doherty / Journal of Atmospheric and Solar-Terrestrial Physics 74 (2012) 199–211
1.4
1.4
MAR EQUINOX
1.2
1 S4>=0.4
S4>=0.4
HSA (2002)
1.2
1 0.8 0.6 0.4 0.2
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MSA (2004)
1 S4>=0.4
S4>=0.4
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0.8 0.6 0.4
0.8 0.6 0.4
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LT (Hr)
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SEP EQUINOX
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LSA (2008)
1.2
1 0.8
S4>=0.4
S4>=0.4
24
1.4
JUN SOLSTICE
1.2
0.6 0.4 0.2
23
LT (Hr)
1.4
0.2
205
1 0.8 0.6 0.4
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LT (Hr)
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25
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27
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29
30
LT (Hr)
1.4
S4>=0.4
Fig. 7. Scatter plots comparing intense and moderate scintillations (S4 Z0.4) for all seasons, during (a) HSA, (b) MSA and (c) LSA.
DEC SOLSTICE
1.2 1 0.8 0.6 0.4 0.2
18
19
20
21
22
23
24
25
26
27
28
29
30
LT (Hr) Fig. 6. Scatter plots comparing intense and moderate scintillations (S4 Z 0.4) during the LSA year (a) March Equinox (b) June Solstice (c) September Equinox (d) December Solstice.
November recorded the highest probabilities of scintillation occurrences, 15%, 14%, 11% and 11%, respectively. The least probabilities of scintillation occurrences were recorded in the months of May–August (1% each). For the months of October and
December, the probabilities of scintillation occurrences were recorded as 7% and 10%, respectively. The months of January, February, October, November and December had the longest tails, S4¼ 1.23, 1.12, 1.13, 1.11 and 1.15, respectively, and the shortest in the months of June and July, S4¼0.36 for each month. Fig. 9 shows the CCDF of S4 data for all the months of the MSA. At S4¼0.3, the months of January, February, March, September, October and November recorded the highest probabilities of scintillation occurrences, 6%, 5%, 6%, 5%, 6% and 9%, respectively. The least probabilities of scintillation occurrences were recorded in the months of May–August (1% each). For the month of April and December, the probabilities of scintillation occurrences were recorded as 1.5% and 4%, respectively. The months of January, February, March, September and November had the longest tails, S4¼ 1.25, 1.19, 1.22, 1.19 and 1.20, respectively, and the shortest in the months of May and June, S4 ¼0.36 for each month. Fig. 10 shows the CCDF of S4 data for all the months of the LSA. At S4¼ 0.3, the probability of scintillation occurrence was recorded to be less than 1% for all the months (precisely 0.5%). However,
A.O. Akala, P.H. Doherty / Journal of Atmospheric and Solar-Terrestrial Physics 74 (2012) 199–211
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
JANUARY, 2002, n=15744
CCDF
CCDF
206
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
FEBRUARY, 2002, n=10143
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
MAY, 2002, n=15256
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
CCDF
CCDF
JUNE, 2002, n=12454
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
JULY, 2002, n=13396
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
S4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1.1 1.2 1.3 1.4
OCTOBER, 2002, n=12135
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1.1 1.2 1.3 1.4
NOVEMBER, 2002, n=10721
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1.1 1.2 1.3 1.4
S4
CCDF
CCDF
S4 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
SEPTEMBER, 2002, n=6406
S4
S4 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
1.1 1.2 1.3 1.4
S4
CCDF
CCDF
S4 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
S4
CCDF
CCDF
S4
AUGUST, 2002, n=7904
1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
DECEMBER, 2002, n=10622
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
S4
Fig. 8. Complementary cumulative distribution function (CCDF) of S4 data for all the months (January–December, no data for March and April) during the HSA (2002).
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
JANUARY, 2004, n=12851
CCDF
CCDF
A.O. Akala, P.H. Doherty / Journal of Atmospheric and Solar-Terrestrial Physics 74 (2012) 199–211
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
CCDF
MARCH, 2004, n=20909
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
S4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
MAY, 2004, n=20387
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
CCDF S4
NOVEMBER, 2004, n=19547
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
S4
JUNE, 2004, n=21539
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
S4
CCDF
CCDF CCDF
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 OCTOBER, 2004, n=21088
S4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
SEPTEMBER, 2004, n=21540
APRIL, 2004, n= 15134
S4 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
S4
CCDF
CCDF CCDF
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
AUGUST, 2004, n=21156
S4
S4 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
S4
FEBRUARY, 2004, n=18718
CCDF
CCDF
S4
JULY, 2004, n=21315
1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
DECEMBER, 2004, n=20732
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
S4
Fig. 9. Complementary cumulative distribution function (CCDF) of S4 data for all the months (January–December) during the MSA (2004).
207
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1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
JANUARY, 2008, n=20670
CCDF
CCDF
208
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
JULY, 2008, n=20270
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
S4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
FEBRUARY, 2008, n=20522
CCDF
CCDF
S4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
AUGUST, 2008, n=19598
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
S4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
MARCH, 2008, n=20392
CCDF
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1.1 1.2 1.3 1.4
S4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
SEPTEMBER, 2008, n=18533
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
S4
APRIL, 2008, n=18748
CCDF
CCDF
CCDF
S4
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
OCTOBER, 2008, n=16344
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
S4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
MAY, 2008, n=17851
CCDF
CCDF
S4
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
NOVEMBER, 2008, n=9324
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
JUNE, 2008, n=18558
CCDF
CCDF
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
S4
1.1 1.2 1.3 1.4
S4
S4
1
1.1 1.2 1.3 1.4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
DECEMBER, 2008, n=7918
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
S4
1.1 1.2 1.3 1.4
Fig. 10. Complementary cumulative distribution function (CCDF) of S4 data for all the months (January–December) during the LSA (2008).
A.O. Akala, P.H. Doherty / Journal of Atmospheric and Solar-Terrestrial Physics 74 (2012) 199–211
209
the June Solstice was characterized with extremely light tails. During the HSA year, at S4¼0.3, the probabilities of scintillation occurrences are 13%, 14%, 0.5% and 6% for the December Solstice, March Equinox, June Solstice and September Equinox, respectively. For the MSA year, at S4¼0.3, the probabilities of scintillation occurrences are 6%, 5%, 0.5% and 5% for the December Solstice, March Equinox, June Solstice and September Equinox, respectively. During the LSA year, at S4¼0.3, the probabilities of scintillation occurrences are 1% each for the December Solstice, March Equinox and September Equinox and 0.5% for the June
the months of January, March and October had the longest tails, S4 ¼0.76, 0.83 and 0.76, respectively, and the shortest in the months of May, June and July, S4 ¼0.4, 0.38 and 0.39, respectively. Fig. 11(a), (b) and (c) shows the CCDF of S4 data during the equinoctial and solstitial seasons at HSA, MSA and LSA years, respectively. All the plots have the same features, but for the relaxation of the heaviness of the tails of the distributions within the range S4¼0.2–0.8 as the solar activity decreases. In addition, the tails of the December Solstice and March Equinox distributions were observed to be the heaviest within this range, whereas,
BOGOTA, 2002
1 0.9 0.8
DEC SOLS MAR EQUI JUN SOLS SEP EQUI
CCDF
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7 S4
0.8
0.9
1
1.1
1.2
1.3
1.4
BOGOTA, 2004
1 0.9 0.8
DEC SOLS MAR EQUI JUN SOLS SEP EQUI
CCDF
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
0.9
1
1.1
1.2
1.3
1.4
S4 BOGOTA, 2008
1 0.9
DEC SOLS MAR EQUI JUN SOLS SEP EQUI
0.8
CCDF
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
S4 Fig. 11. Complementary cumulative distribution function (CCDF) of S4 data during the equinoctial and solstitial seasons at (a) HSA, (b) MSA and (c) LSA.
A.O. Akala, P.H. Doherty / Journal of Atmospheric and Solar-Terrestrial Physics 74 (2012) 199–211
0.2
2002 2004 2008
0.16
0.12 0.08 0.04
OCT
SEP
AUG
JUL
JUN
MAY
APR
MAR
FEB
JAN
DEC
0 NOV
Probability of occurrence (%), S4>1
210
20
Cal. Emp.
18 16 14
NO DATA
12 10 8 6 4
2 DEC
NOV
OCT
SEP
AUG
JUL
JUN
MAY
APR
MAR
DEC
NOV
OCT
SEP
AUG
This study investigated the statistical distributions of GPS scintillations data at Bogota (an equatorial anomaly crest station). Three years of data at three levels of solar activity, high (2002), moderate (2004) and low (2008) were used for the investigation. The study concludes as follows:
JUL
JUN
MAY
APR
MAR
Cal. Emp.
FEB
% Probability of occurence S4≥0.3
20
4. Conclusions
JAN
% Probability of occurence S4≥0.3
20 18 16 14 12 10 8 6 4 2 0
FEB
0 JAN
Cal. Emp.
18 16 14 12 10
8 6 4 2 DEC
NOV
OCT
SEP
AUG
JUL
JUN
MAY
APR
MAR
JAN
0 FEB
% Probability of occurence S4≥0.3
Fig. 12. Bar plots of the probability of scintillation occurrences at S4 41.0 threshold during the HSA (2002), MSA (2004) and LSA (2008).
Solstice. For the HSA, MSA and LSA years, the distribution tailed off at S4 ¼0.8, 0.6 and 0.3, respectively. These features confirm the vulnerability of the ionosphere to scintillations during December Solstice and March Equinox, most especially during the HSA year at Bogota, and June Solstice can be regarded as a non-scintillation season. Fig. 12 shows the bar plots of the probability of occurrences of S441.0. The probability of occurrences is very rare at this threshold, with no event during the months of May–August for the HSA year, April–August for the MSA year and no event at all during any of the months of the LSA year. During the HSA year, the highest occurrence was recorded during the months of January (0.15%) and February (0.11%), and during the months of January and November for the MSA year with 0.04% for each month. Due to very low chances of the occurrences of scintillation at this threshold (S441.0), the distribution curve seems to tail off along the S4 axis, ending at the maximum observed value. Conclusively, a significant rareness of data was observed at this threshold even during the HSA year and active months of scintillations. It is also important to mention that at lower S4 values (o0.15), all the plots, irrespective of the month, season or solar activity depict congruent feature as they were all seen to superimpose. The inference is that, the inherent receiver’s noise by design is fixed at the 0.15 level. Fig. 13(a), (b) and (c) shows the Bar plots that compare the calculated and the CCDF probabilities of scintillation (S4Z0.3) occurrences for all the months during HSA, MSA and LSA, respectively. The calculated probability of occurrences and those derived from the statistical distribution scheme show good consistency. The little variances between the calculated and the CCDF probabilities of scintillations were commonly observed when the probability is significantly low (less than 1.0), and this is suspected to be a matter of precision.
Fig. 13. Bar plots comparing the calculated (Cal.) and CCDF (Emp.) probabilities of scintillations (S4Z 0.3) occurrences for all the months during (a) HSA, (b) MSA and (c) LSA.
(i) Complementary cumulative distribution function (CCDF) is a suitable statistical apparatus for fitting GPS scintillation data. The apparatus is also typical in figuring out the inbuilt receiver’s noise level. (ii) GPS amplitude scintillation data exhibit non-Gaussian behavior. The rarity of the distributions increases with S4 value, with a significant rarity in the neighborhood of unity, even during solar active periods. In other words, low-valued S4 (S4 o0.2) samples dominated the entire data. By implication, samples deviations from the mean seem asymmetric around the mean. Consequently, using central tendencies or measures of dispersion for reliable statistical inference on GPS scintillation data seems impracticable. For instance, unlike other ionospheric parameters (e.g. foF2, TEC) where the hourly mean could be relatively representative of the subminutes data of the hour, scintillation data will not support such representation. This is because scintillations exhibit extreme variability in space and time (Basu et al., 2002). (iii) GPS amplitude scintillation is a post-sunset event with a daily trend of occurrence during the hours of 1900 LT–0400 LT, although with distributions that are largely localized at 1930 LT–2400 LT. On a monthly scale, March and January had highest probabilities of occurrences, while the months of
A.O. Akala, P.H. Doherty / Journal of Atmospheric and Solar-Terrestrial Physics 74 (2012) 199–211
May–July were observed as non-scintillation months. Seasonally, March Equinox and December Solstice showed the highest probabilities of occurrences, while June Solstice was observed as non-scintillation season. On a solar activity scale, the probabilities of occurrences increase with solar activity. The observed monthly, seasonal and solar activity variations of scintillation occurrences could be attributed to the associated night-time variations in F-region vertical and zonal plasma drifts. Overall, the calculated probability of occurrences and those derived from the statistical distribution scheme show good consistency. These results were in reasonable agreement with earlier statistical observations carried out by Matsunaga et al. (2002), Beniguel et al. (2009). The results presented in this study may be of assistance for future modeling and simulation studies.
Acknowledgments The first author thanks the U.S. Government for the Fulbright Scholarship Grant, and the Institute for Scientific Research, Boston College for hosting him. He also thanks Dr. Constantin Adronache and Chuangi Zhu of the Information Technology Services of Boston College for their useful discussions on MATLAB programming and Charles Carrano for his useful discussions on this paper. The authors also thank the Reviewers for their useful comments and suggestions, which has improved the paper. References Aarons, J., 1982. Global morphology of ionospheric scintillations. In: Proceedings of the IEEE 70, 360–378. Anderson, D., Haerendel, G., 1979. The motion of depleted plasma regions in the equatorial ionosphere. Journal of Geophysical Research 84, 4251–4256. Basu, S., MacKenzie, E., Basu, Su, 1988. Ionospheric constraints on VHF/UHF communications links during solar maximum and minimum periods. Radio Science 23, 363–378.
211
Basu, S., Groves, K.M., Quinn, J.M., Doherty, P., 1999. A comparison of TEC fluctuations and scintillations at Ascension Island. Journal of Atmospheric and Solar–Terrestrial Physics 61, 1219–1226. Basu, S., Groves, K.M., Basu, Su., Sultan,, J.P., 2002. Specification and forecasting of scintillations in communication/navigation links: current status and future plans. Journal of Atmospheric and Solar–Terrestrial Physics 64, 1745–1754. Be´niguel, Y., et al., 2009. Analysis of scintillation recorded during the PRIS measurement campaign. Radio Science 44, RS0A30. doi:10.1029/2008RS004090. Carrano, C.S., Groves, K.M., 2010. Temporary decorrelation of GPS satellite signals due to multiple scattering from ionospheric irregularities. In: Proceedings of the 2010 ION GNSS Meeting. September 21–24, Portland, OR. Doherty, P.H., Dehel, T., Klobuchar, J., Delay, S.H., Datta-Barua, S., de-Paula, E.R., Rodrigues, F.S., 2002. Ionospheric effects on low-latitude space based augmentation systems. In: Proceedings of the ION GPS-2002, Portland, OR. Ezquer, R.G., Kintner, P.M., Cabrera, M.A., Radicella, S.M., Forte, B., 2003. Scintillations observed at Tucuman as from GPS signals: first results. Advances in Space Research 31, 741–747. Fejer, B.G., 1991. Low latitude electrodynamics plasma drifts: a review. Journal of Atmospheric and Terrestrial Physics 53, 77–693. Groves, K., et al., 1997. Equatorial scintillation and systems support. Radio Science 32, 2047–2064. Heelis, R.A., 2004. Electrodynamics in the low and middle latitude ionosphere: a tutorial. Journal of Atmospheric and Solar–Terrestrial Physics 66, 825–838. International Civil Aviation Organization (ICAO), 2006. Navigation Systems Panel’s Report on Ionospheric Effects on GNSS Aviation Operations. Montreal, Canada, 10–20 October. Kelley, M.C., 1989. The Earth’s Ionosphere. Academic Press Inc., London. Keskinen, M.J., Ossakow, S.L., 1983. Theories of high-latitude ionospheric irregularities: a review. Radio Science 18, 1077–1091. Matsunaga, K., Hoshinoo, K., Igarashi, K., 2002. Observation of ionospheric scintillation on GPS signals in Japan. In: Proceedings of the ION NTM. 28–30 January 2002, San Diego, CA. Rishbeth, H., Lyon, A.J., Peart, M., 1963. Diffusion in the equatorial F layer. Journal of Geophysical Research 68, 2559–2569. Rishbeth, H., 1998. How the thermospheric circulation affects the ionospheric Flayer. Journal of Atmospheric and Solar–Terrestrial Physics 60, 1385–1402. Titheridge, J.E., 1995. Winds in the ionosphere: a review. Journal of Atmospheric and Terrestrial Physics 57, 1681–1714. Valladares, C., Sheehan, R., Basu, S., Kuenzler, H., Espinoza, J., 1996. The multiinstrumented studies of equatorial thermosphere aeronomy scintillation system: climatology of zonal drifts. Journal of Geophysical Research 101, 26839–26850. Valladares, C.E., Villalobos, J., Sheehan, R., Hagan, M.P., 2004. Latitudinal extension of low-latitude scintillations measured with a network of GPS receivers. Annales Geophysicae 22, 3155–3175. Woodman, R., 1970. Vertical drift velocities and east–west electric fields at the magnetic equator. Journal of Geophysical Research 75 (31), 6249–6259. Woodman, R.F., La Hoz, C., 1976. Radar observations of F-region equatorial irregularities. Journal of Geophysical Research 81, 5447–5466.