Statistical features of TEC and ionospheric scintillation over the low latitude of China

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ScienceDirect Advances in Space Research 64 (2019) 2164–2175 www.elsevier.com/locate/asr

Statistical features of TEC and ionospheric scintillation over the low latitude of China L. Xu, J. Cheng, J.S. Xu ⇑ School of Electronic Information, Wuhan University, Wuhan 430072, China Received 1 February 2019; received in revised form 18 June 2019; accepted 10 July 2019 Available online 19 July 2019

Abstract In this paper, a new index is established which is defined by the standard deviation of total electron content (TEC) fluctuation and denoted by the symbol rtec. It is demonstrated that the index rtec is equivalent to the phase scintillation index and can serve as an indicator of the strength of the phase scintillation. The receiver transiently loses lock on the signal, leading to cycle slips and jumps in the TEC time series. In order to obtain continuous TEC data in the situation of the disturbed ionosphere, a batch processing method is developed to detect and correct cycle slip. Based on the methods mentioned above, we investigate the statistical features of the phase scintillations and cycle slips by means of the data from a scintillation observation network in the south-central region of China during 2012–2015. The results show that the variations of phase scintillation occurrences with local time and season display very similar features to those of the cycle slip occurrences, implying that cycle slips are closely related to phase scintillations. Phase scintillations occur mainly during the night, most frequently before midnight and seldom in the daytime. It is found that phase scintillations occur mainly in equinox months but seldom in solstice months in the crest of the ionization equatorial anomaly and its adjacent regions, and an equinoctial asymmetry that phase scintillations occur more frequently in Spring than in Autumn is also found. Besides, a comparison of the TEC fluctuation index (rtec) and amplitude scintillation index (S4) indicates that there is close relation between the rtec and S4, indicating the co-existence of large and small scale irregularities in equatorial irregularity structures. Ó 2019 Published by Elsevier Ltd on behalf of COSPAR.

Keywords: Low latitude ionosphere; TEC fluctuation index; Phase scintillation; Irregularity; Cycle slip

1. Introduction Transionospheric radio waves propagating through ionospheric irregularities experience rapid random fluctuations in phase and amplitude of the signal at the receiver. This phenomenon is called scintillation. Over the years, many researchers have investigated the morphological feature of GPS L-band signal scintillations in the equatorial and low-latitude ionosphere based on GPS beacon observations. Series of significant results have been obtained on the scintillation activity and its correlation with the ⇑ Corresponding author.

E-mail address: [email protected] (J.S. Xu). https://doi.org/10.1016/j.asr.2019.07.011 0273-1177/Ó 2019 Published by Elsevier Ltd on behalf of COSPAR.

solar activity, geomagnetic disturbance, season and local time (Kintner et al., 2007; Adewale et al., 2012; Akala and Doherty, 2012; Deng et al., 2013; Huang et al., 2014; Amabayo et al., 2014; Akala et al., 2014; Liu et al., 2015; Seba and Gogie, 2015; Olwendo et al., 2016; Cheng et al., 2018, Prasad and Kumar, 2017; Kumar et al., 2007; Kumar and Gwal, 2000). The ionospheric irregularity and its strength have been investigated widely, based on GPS dual-band beacon measurements. In order to quantify the level of the ionospheric irregularity and scintillation, various indices have been derived. Among these indices, the two most widely used are the rate of TEC (ROT) proposed by Wanninger (1993), and the standard deviation of ROT (ROTI)

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proposed by Pi et al. (1997). It was found that ROT and ROTI describe the phase fluctuations and ionospheric irregularities (Pi et al., 1997; Basu et al., 1999). Based on ROT and ROTI, some indices in other forms were proposed. For example, Du et al. (2000) proposed the proxy amplitude scintillation index which is obtained by using ROTI and an elevation-weighted coefficient. Mendillo et al. (2000) introduced an hourly fp index, for individual satellite number, which is mainly the median value of the ROT values over the four 15-min intervals for each onehour period. Jakowski et al. (2012) derived a disturbance ionospheric index (DIX) by using a TEC derivative at higher sampling rate, which can be used as a potential alarm index for satellite communication and navigation applications. Tiwari et al. (2013) deduced the analogous phase scintillation index based on an elevation-weighted function and the normalized standard deviation of the high-pass filtered ROT. At the beginning,the ROT and ROTI were calculated from TEC data with 30-sec sampling rate. However, many researchers (Aarons, 1997; Kintner et al., 2002; Carrano and Groves, 2007; Alfonsi et al., 2011; Jakowski et al., 2012; Tiwari et al, 2013) suggested that, in order to obtain better sensitivity and better understanding on the physics when studying the small-scale irregularity, it would be better to use high sampling rate TEC data, such as 1 Hz TEC data. ROT and ROTI have been widely used on the study of small-scale irregularities (Basu et al., 1999;Beach and Kintner, 1999; Bhattacharya et al., 2000; Kintner et al., 2002; Carrano and Groves, 2007; Jakowski et al., 2012; Tiwari et al., 2013). However, the ROT is obtained based on the time derivative of TEC, which includes the effect of the satellite movement and the ionospheric irregularity drift. Consequently, there exists some uncertainty for ROT and ROTI to obtain quantitative estimates of scintillation and ionospheric irregularity. To avoid the influence of the satellite motion and the ionospheric irregularity drift, TEC fluctuation (dTEC) is proposed as a characteristic parameter in this paper, and an index is set up using the standard deviation of dTEC, named TEC fluctuation index (rtec). In the following sections, distribution of observatory network and data preprocessing methods are described, with a special emphasis on a batch processing method for cycle slip detection and correction that is applied to eliminate the influence of the cycle slip and to obtain continuous TEC data. Then, the method of obtaining dTEC and rtec is

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introduced, and it is confirmed that there is the quantitative relationship between the TEC fluctuation index and phase scintillation index. Using the observations in the southcentral region of China during 2012–2015, the statistical features of phase scintillations and cycle slips are analyzed and compared. Besides, the correlation between rtec and S4 index is investigated. 2. Data description and preprocessing methods 2.1. Observatory network description The data used in this paper are from GPS ionospheric scintillation observation network established by the Ionospheric Scintillation Research Group of Wuhan University in the south-central region of China. This network consists of six observation stations. The names, codes, geographic and magnetic coordinates of the stations are listed in Table 1. Observation data from 2012 to 2015 are used for statistical analysis, covering the most recent solar maximum years. As listed in Table 1, the six stations can be qualitatively divided into three groups according to their locations. The SY station, representing the first group, is located near the magnetic equator, where is the valley of the equatorial ionization anomaly (EIA). The second group is located around the EIA crest, including the GL, GZ, NN and HK stations. The WH station, recognized as the third group, is located in the transition region from low latitude to mid latitude. 2.2. TEC acquisition and cycle slip correction There are two ways to compute TEC along the propagation path, which are dual-frequency differential pseudo range and differential phase, respectively, TEC a ¼ 9:52  Dq þ eq ;

ð1aÞ

TEC r ¼ 279:2  ðU1 =m1  U2 =m2 Þ þ TEC ro þ eu

ð1bÞ

where TECa is TEC obtained by the dual-frequency differential pseudo range and TECr is TEC obtained by dualfrequency differential phase, the unit is TECu (1 TECu = 1016/m2). Dq is dual-frequency differential pseudo range, with unit of meter. U1 and U2 are carrier phases of L1 and L2, with unit of radian. m1 = 154 and m2 = 120 are the ratio of L1 and L2 frequencies to the base frequency, respectively. TECro is an unknown constant which

Table 1 Observation stations and their coordinates. Name (code)

Longitude (°E)

Latitude (°N)

Magnetic Longitude (°W)

Magnetic latitude (°N)

WuHan (WH) GanZhou (GZ) GuiLin (GL) NanNing (NN) HongKong (HK) SanYa (SY)

114.36 114.92 110.33 108.23 114.21 109.58

30.54 25.84 25.29 22.84 22.42 18.28

173.58 172.93 177.22 179.19 173.53 177.85

20.74 16.07 15.48 13.08 12.66 8.49

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is caused by the unknown initial phase and cycle slip, eq and eu are measurement errors, respectively. The eq in formula (1a) includes the systematic error and random error. The systematic error is caused by the differential code bias (DCB) related to the receiver and the satellite. Generally, effects of DCB on differential pseudo range measurements are very remarkable that needs to be removed in order to determine the reasonable absolute TEC (Prasad and Kumar, 2017). Sudden variations of the electron density or other factors in the space environment may cause an apparent Doppler shift that sometimes exceeds the bandwidth of the phase lock loop in the receiver. When this situation occurs, the receiver loses lock on the signal, causing abrupt change of the carrier phase with integer cycles. This phenomenon is called cycle slip. The cycle slip leads to jump of TEC data, which seriously reduces the quality of TEC data. Obtaining valuable ionospheric information from GPS measurements inevitably requires a proper handling of cycle slips in TEC data preprocessing. It inevitably requires a proper handling of cycle slips to obtain valuable ionospheric information from GPS measurements. Many methods have been developed for cycle slip detection and correction (Banville et al., 2010). Based on single-frequency phase observation data, polynomial fitting, high-order difference, and kalman filtering are generally adopted (Beutler et al., 1984; Bastos and Landau, 1988; Ji et al., 2013). The method of the phase and pseudo-range combination is also a very common method, such as MW combination method (Melbourne, 1985; Wu¨bbena, 1985, Blewitt, 1990). Liu (2011) simultaneously used the wide-lane combination and ionospheric combination to detect the cycle slip. Based on the previous research results, a batch processing algorithm of the cycle slip detection and correction is designed in this paper. The developed method is simple in principle and easy to operate. It is especially suitable for batch processing of large amounts of data without human intervention. For the different method of cycle slip detection, the detected parameter can be different. The method used in this paper chooses the differential TEC (DTEC) as the detected parameter. The time sequence contains a piece of a continuous arc or a series of short continuous arcs. There are some transient interrupts (shorter than 30 sec.) between short continuous arcs because of losses of lock on the signals. The sequence generally changes smoothly with time when there is no cycle slip. Whenever the sequence presents jumps, we think that there are cycle slips. Define DTEC at epoch k as DTECðkÞ ¼ TECðkÞ  TECðk  1Þ

ð2Þ

Because relative TEC is derived from measurements of the dual-frequency differential phase, the detected parameter DTEC obtained by the difference of TEC between adjacent epochs no longer include the influence of the non-dispersive factors such as satellite-receiver distance, clock difference, initial phase, and so on. When no cycle

slip occurs, the value of DTEC can be regarded as a random variable subject to the normal distribution. We use statistical method to detect DTEC. When the following two conditions are met simultaneously, we judge that a cycle slip occurs at epoch k, jDTECðkÞj > e

ð3Þ

jDTECðkÞ  X j > nr

ð4Þ

where X and r represent the mean value and standard deviation of time sequence of DTEC in the duration of 1 min before epoch k, respectively, e is a given small quantity, and n is an integer greater than 1. If the standard deviation of DTEC data in a certain period before time k is particularly small, due to the phase measurement error, formula (4) may be true for this data even if there is no cycle slip. The addition of formula (3) can effectively prevent the misjudgment caused by this situation. In formula (3), e depends on the accuracy of the carrier phase measurement and its value should be determined according to the actual observations. Based on the practical experience of the cycle slip detection for a large amount of measured data, we find that, for a small amount of specific data, there is no effect on the results of cycle slip detection without formula (3). For batch processing of a large amount of long-term data, however, formula (3) is indispensable if there is no manual operation, otherwise, it will lead to serious misjudgment. In this paper, we choose e being equal to 0.02 TECu, which is roughly equivalent to the magnitude of the random measurement error. For the value of n in formula (4), referring to Liu (2011), we take the fluctuation within four times of standard deviation as the normal variation, otherwise, we judge that the cycle slip occurs. According to the above criteria, if a cycle slip is detected at epoch k, the TEC change at epoch k after the cycle slip correction is given by DTEC0 (k) = X. Thus, the TEC measurement error caused by the cycle slip can be obtained as eTEC ¼ DTECðkÞ  DTEC 0 ðkÞ;

ð5Þ

By subtracting this error from the TEC at time k and subsequent time, the results of cycle slip correction can be obtained. The detection and correction of cycle slips are successively carried out from front to back until to the end of the time sequence. Fig. 1 gives two examples of TEC variation with time before (Fig. 1a and b) and after (Fig. 1c and d) cycle slip correction. The data used in Fig. 1 are obtained from the satellite observations at HK and NN stations. Fig. 1a and b are the relative TEC obtained by dual-frequency differential phase, and Fig. 1c and d are the absolute TEC obtained by leveling processing with dual-frequency differential pseudo range measurements (Wilson and Mannucci, 1993). The cycle slip detection and correction are successively carried out by the methods described above. As shown in Fig. 1a and b, there are many transient losses of lock and cycle slips, which lead to jump of TEC

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Fig. 1. Examples of TEC time sequences before (a, b) and after (c, d) the correction of cycle slips.

variations. Such data cannot be used without cycle slip correction. It can be seen from Fig. 1c and d that the TEC jump is eliminated in full after cycle slip correction. Besides, it can be also seen that the variation feature of the TEC time sequence without cycle slips does not change except for the up and down translation caused by the leveling process. In the period of cycle slips occurring, the obvious depleted structures in TEC variation can be seen after the cycle slip correction. Without cycle slip correction, however, the pattern of TEC depletions could not be identified due to a lot of transient losses of lock and cycle slips, and these data will be of no use and may be completely disregarded. These examples show that the method developed in this paper is effective for cycle slip detection and correction. It should be noted that, in our method, the 1-min average value of the differential TEC right before the cycle slip is used as the differential TEC at the time of the cycle slip. The corrected TEC is derived from the sum of two values, i.e., TEC(k) = TEC(k-1) + X, where X is the averaged differential TEC during the 1 min before the cycle-slip. Doing so may lose some details of the true TEC variation. However, the overall trend of the TEC variation obtained is generally reliable.

In this study, the sampling interval of the TEC data is 1 sec and the TEC average value at time ti is computed by the average of the data within one minute centered at time ti. Before calculating dTEC, the TEC data need to be preprocessed. The key step of preprocessing is to eliminate data jumps in the time series of TEC caused by temporary losses of lock and the cycle slips. The method has been introduced in the previous section. The TEC fluctuation index, rtec is defined as the standard deviation of dTEC, which is calculated in formula (7), qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi  rtec ¼ dTEC 2  hdTEC i2 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !2 u i¼N i¼N u1 X 1 X t 2 ¼ dTEC i  dTEC i ð7Þ N i¼1 N i¼1

3. TEC fluctuations and phase scintillations

du ¼

The observed TEC data generally contain the long-term background variations and the short-term rapid fluctuations. The latter is mainly caused by ionospheric electron density irregularities. By eliminating the long-term TEC background variations from the observed TEC data, the short-term TEC fluctuations can be obtained. For a fixed station, the TEC rapid fluctuation is obtained from the difference between the instantaneous value and the average value of data during certain time period. It is calculated by the following formula,

where c is light speed, f is carrier frequency in Hertz, the unit of du is radian and the unit of dTEC is TECu, 1 TECu = 1016/m2. For GPS satellites, L1 frequency is f1 = 1.57542 GHz, the phase fluctuations at GPS L1 frequency are obtained as formula (9),

dTECðti Þ ¼ TECðti Þ  hTEC i ¼ TECðti Þ 

j¼iþN X 1 TECðtj Þ 2N þ 1 j¼iN

where symbol hi represents the arithmetic average.

ð6Þ

In our data processing procedure, the index rtec is computed at intervals of 1 min. For the carrier with a given frequency, the optical path fluctuation (dP) is proportional to the phase fluctuation (du), du = dP/k, where k is the carrier wavelength. Under high frequency approximation, the phase fluctuation caused by irregularities can be obtained as formula (8), 40:3 dTEC: cf

du1 ¼ 0:85  dTEC

ð8Þ

ð9Þ

Formula (9) indicates that, there is a linear relationship between TEC fluctuation and the phase fluctuation caused by irregularities. It can be inferred that the measurement of phase fluctuations is equivalent to that of TEC fluctuation. According to the definition, the phase scintillation index is the standard deviation of the phase fluctuation per minute,

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ru1 ¼

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qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hdu21 i  hdu1 i2

ð10Þ

where du1 is the phase fluctuation of the L1 frequency, ru1 is the phase scintillation index of the L1 frequency. Substituting formulas (7) and (9) into formula (10), the relationship between the phase scintillation index and the TEC fluctuation index can be derived as formula (11), ru1 ¼ 0:85  rtec

ð11Þ

Formula (11) indicates that, there is a quantitative relationship between the phase scintillation index and the TEC fluctuation index. The phase scintillation intensity can be measured by the rtec index. Ionospheric irregularities can cause the rapid random fluctuation of radio wave phases propagating across the ionosphere, i.e. phase scintillations. Kintner et al. (2007) pointed out that phase scintillations are typically produced by ionospheric irregularities at small wave numbers and near the first Fresnel radius. The former quantity (small wave numbers) can be thought of as being refractive effect and produced by fluctuations in the TEC along the signal path. The latter quantity (near the first Fresnel radius) is the result of interference between different phases exiting the thin screen. It is generally recognized that amplitude scintillations are dominated by ionospheric irregularities near the first Fresnel radius and essentially are the diffraction pattern. Unlike amplitude scintillations, however, phase scintillations are dominated by large-scale irregularities and the contribution of small-scale irregularities is lesser (Yeh and Liu, 1982). It must be noticed that formula (11) is deduced under the condition of ignoring the effect

of the interference caused by small-scale irregularities near the first Fresnel radius. Fig. 2 shows the temporal variation of ionospheric irregularities and scintillations in the night of March 12, 2014 at NN (column 1), GL (column 2), HK (column 3) and GZ (column 4), observed by GPS PRN08 satellite. The local time can be converted to the universal time by LT = UT + 8 in Fig. 2 (similarly hereinafter). 12 March 2014 is a magnetic quiet day with the maximal Kp value of 2.67. It can be seen from Fig. 2b, large-scale TEC depletion structures have been observed around the midnight on March 12, 2014 at NN, GL, HK and GZ in the ionospheric region where GPS PRN08 satellite passes. By comparing Fig. 2b to f, it can be seen that, the time of the appearance and disappearance of the large-scale TEC depletion structure is almost the same as those of the small-scale irregularities and scintillation activities for each station. This feature indicates that the ionospheric amplitude and phase scintillation are caused by the large-scale TEC depletion structure and the irregularities of different scales contained in it. There is a direct causal relationship between them. A large number of phase scintillation events have been analyzed and the results show that the feature shown in Fig. 2 is universal for the scintillation activity occurring at night. That is, for vast majority of night scintillation events, TEC depletion and its rapid fluctuation always correspond well with the rapid fluctuation of the CNR and the enhancement of the amplitude scintillation index, S4. Their accompanying appearance indicates that both amplitude and phase scintillations are caused by TEC depleted plasma bubbles. The increase of indices ru and S4 in the

Fig. 2. Temporal variation of ionospheric irregularities and scintillation observed by GPS satellite PRN 08 on 12 March 2014 at NN (column 1), GL (column 2), HK (column 3) and GZ (column 4).

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same period indicates that phase and amplitude scintillations exist simultaneously. According to Yeh and Liu (1982), the main contribution to the amplitude scintillation is the irregularity of sizes no greater than the size of the first Fresnel radius, while the phase scintillation is dominated by the large-scale irregularity. The coexistence of phase and amplitude scintillations indicates that the irregularities near the first Fresnel radius coexist with large-scale irregularities. 4. Statistical characteristics of ionospheric irregularities at low latitudes Combining the carrier phase and pseudo range measurements of GPS dual-frequency beacons, as well as cycle slip identification and correction, the piecewise continuous and accurate TEC data can be obtained. Based on preprocessed TEC data, dTEC and rtec can be calculated. The statistical characteristics of ionospheric irregularities and phase scintillations are then analyzed by using rtec as the characteristic parameter. The statistical characteristics of cycle slip event are also analyzed and compared with that of phase scintillations. In order to reduce the influence of multipath effect caused by non-ionospheric factors, a cut-off elevation angle is usually applied. Some scholars chose 50° as the cut-off elevation angle (Prasad and Kumar, 2017). In this study, we use 35° as the cut-off elevation angle. When rtec is very small, such as rtec < 0.1, rtec is approximately evenly distributed and the local time dependence and seasonal dependence of rtec can hardly be seen. As a threshold, only the scintillation activities with rtec equal to or greater than

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0.1 and lasting at least 10 min were taken into account as scintillation events. When two activities for the same satellite had an interval less than 10 min, they were considered as one event. The duration limit can eliminate some temporary disturbances caused by non-ionospheric factors, and result in a relatively low occurrence of scintillations but would not change the essential feature of the statistical results. It is worth mentioning that there are still enough events to ensure the reliability of the statistical results with the above-mentioned data criteria. The data criteria for the statistics of cycle slip events are similar to those for scintillation statistics. Figs. 3 and 4 are scatter plots of the TEC fluctuation index rtec measured at NN and HK stations, respectively, from January 2013 to December 2014 (solar maximum years), respectively. We assume that data of rtec < 0.1 represent the background variation and are not shown in the Figures. Those panels marked with ’no data’ mean that the observation data are missing for the whole month or most days of the month. As shown in Figs. 3 and 4, the occurrence of irregularities is significantly seasonal dependent. Irregularities appear most frequently in March and April. In the months when the irregularities frequently appear, they mainly occur around 20:00 LT after sunset, and end around 04:00 LT predawn. Strong irregularities with higher value of rtec appear mainly before the midnight. According to statistical theory, the probability density function (PDF) of random data is defined as the probability that the instantaneous data value falls within a specified range. For limited discrete experimental data, we define the ratio of data points with their value within each specified

Fig. 3. Scatter plots of magnitude and occurrence of the TEC fluctuation index measured from January 2013 to December 2014 at NN.

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Fig. 4. Scatter plots of magnitude and occurrence of the TEC fluctuation index measured from January 2013 to December 2014 at HK.

range to the total data points as PDF. Using rtec calculated from TEC data at HK and NN between September 2012 and August 2015, we obtained the probability density function of rtec. In the calculation, select 0.1 as the minimum value of rtec, and step at 0.1 interval and all data points of rtec > 1:0 are ignored. Fig. 5 shows the variation of probability density function of rtec at NN and HK. As shown from Fig. 5, the PDF variation pattern of rtec at NN and HK is quite similar. With the increase of rtec values, the probability decreases gradually. We consider 0:1 6 rtec < 0:3 as a weak irregularity, 0:3 6 rtec < 0:6 as a moderate irregularity, 0:6 6 rtec 6 1:0 as a strong irregularity. Statistical analysis shows that for NN and HK, the cumulative probability of weak irregularities is about 68%, that of moderate irregularities is about 22%, and that of strong irregularities is about 10%. To obtain the diurnal variation of the occurrence of phase scintillations and cycle slips, we divide one day into 48 time intervals, and each interval is 30 min. Fig. 6 shows the daily average percentage occurrence of phase scintillations (Fig. 6a) and cycle slips (Fig. 6b) in every interval during 2012–2015 at the six stations listed in Table 1. The daily average occurrences are number of minutes of scintillation (cycle slip) occurrences in each time interval, which are obtained by the cumulative occurrences of scintillations (cycle slips) in the time interval divided by the number of observing day. It can be seen from Fig. 6a that the diurnal variations of phase scintillation occurrences at all six stations are similar. The occurrence of phase scintillations begins at about 20:00 LT and reaches its peak value quickly, and then decreases gradually until predawn. The occurrence of phase scintilla-

Fig. 5. Variation of probability density function of rtec at NN and HK. The rightmost point represents the sum of PDFs with rtec P 2:0.

tions is most frequent during the several hours before midnight and seldom in the daytime. On the whole, the occurrence of phase scintillations depends on latitude, the closer to the magnetic equator, the more frequently scintillations occur. Besides, with the increase of latitude, phase scintillations appear slightly later and end slightly earlier. At the SY station, the scintillations begin to appear at about 19:30 LT and last until about 04:00 LT. At the northernmost WH station, the beginning time of the

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Fig. 6. Local-time variations of the daily average percentage occurrence of phase scintillations (a) and cycle slips (b) at all six stations listed in Table 1.

scintillation is about 20:30 LT, and almost no phase scintillation is observed after 02:00 LT. These facts indicate that scintillations at low latitudes are primarily associated with irregularities from the magnetic equator. It is generally accepted that, a steep upward plasma density gradient often appears at the bottom of the F2 layer after sunset, and the equatorial F layer will become unstable due to the corporate action of the electric field, neutral wind and magnetic field, which result in the so-called Rayleigh-Taylor (R-T) instability (Kelley, 1989). The development of the R-T instability can cause the generation of ionospheric irregularities such as plasma bubbles and plumes. These irregularities drift upward over the magnetic equator and then diffuse to low-latitude regions along the magnetic Flux Tubes. The phase scintillations in the low latitude ionosphere are primarily caused by the irregularities produced over the magnetic equator. These irregularities occur almost after sunset, which explains the local time distribution of scintillation occurrences. Previously, some authors investigated the local time dependence of amplitude scintillation occurrences over the low-latitude region of China (Deng et al., 2013; Huang et al., 2014; Liu et al., 2015), and pointed out that the amplitude scintillation in the equatorial and low-latitude ionosphere is a nighttime phenomenon. The result in Fig. 6a confirms, similar to the amplitude scintillation, the phase scintillation is also a nighttime phenomenon. By comparing Fig. 6a and b, it can be seen that the local time distribution of the occurrence of cycle slips is very similar to that of phase scintillations. Cycle slips also occur mainly at night, and most frequently between 21:00 LT and 23:00 LT. The cycle slips detected before midnight are much more than after midnight. The occurrence of daily average cycle slips also varies with latitudes. For example, cycle slips occur more frequently at HK and NN than at GZ and GL. The similarity between the diurnal variations of phase scintillation and cycle slip occurrences indicates

that there are close connections between them and the phase scintillation is an important factor causing cycle slips. However, there are some subtle differences between the diurnal variations of scintillations and cycle slips. The phase scintillation occurrence at SY is most frequent among all the six stations, but the cycle slip occurrence at SY is slightly lower than that at HK and NN. In addition, the peaks of scintillation occurrences and cycle slip occurrences are not always at the same local time interval. For example, the scintillation occurrence at NN reaches its peak between 22:00 LT and 23:00 LT, but the cycle slip occurrence at NN reaches its peak at about 21:00 LT. These differences are understandable, because the phase scintillation is not the only factor that causes the cycle slip, and only strong phase scintillations may cause cycle slips. Yue et al. (2016) reported that only about 23% of cycle slips are caused by irregularities in E layer and F layer. Xiong et al. (2016) found that all the total loss of GPS signal events at low latitudes are related to equatorial plasma irregularities that show absolute density depletions larger than 10  1011 m3. Fig. 7 shows the monthly variation of the daily average percentage occurrence of phase scintillations (Fig. 7a) and cycle slips (Fig. 7b) at all six stations listed in Table 1. It can be seen from Fig. 7 that, at GZ, GL, NN and HK that are located around the crest region of the EIA, the seasonal variation features of daily average occurrences of phase scintillations and cycle slips are very similar. Phase scintillations and cycle slips occur most frequently in spring (March and April), then in autumn (September and October) and the least in summer (June and July) and winter (December and January). In addition, the daily average occurrences of the phase scintillations and cycle slips at these four stations show a significant spring-autumn asymmetry. The seasonal variation of the daily average occurrence of phase scintillations and cycle slips at SY is similar to that at GZ, GL, NN and HK, but the

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Fig. 7. Monthly variation of the daily average percentage occurrence of phase scintillations (a) and cycle slips (b) at all six stations listed in Table 1.

spring-autumn asymmetry is not very significant. At WH located in the transition region from low latitude to mid latitude, the level of daily average occurrences of phase scintillations and cycle slips is very low and their seasonal variation is different from that at the other five stations. It shows that the daily average occurrence of phase scintillations appears the most in spring, followed by summer, and the cycle slip occurrence is most frequent in summer (July), followed by spring. In autumn and winter, almost no activity of phase scintillations and cycle slips is observed. Previously, Cheng et al. (2018) analyzed and compared the statistical characteristics of amplitude scintillations and GPS signal cycle slips in the south-central region of China from 2012 to 2015. Comparing their results with Figs. 6 and 7 in this paper, it can be seen that the statistical characteristics of the ionospheric amplitude scintillations and phase scintillations in the south-central region of China is quite similar regarding their local time and seasonal dependency. 5. Comparisons between S4 index and rtec index The relationship between the S4 index and rtec index is investigated for the observation data at specific station and specific satellite in a given time interval. Fig. 8 shows four examples of the comparison of the local-time variations between S4 index and rtec index, where solid line denotes the S4 index and dashed line denotes the rtec index. Fig. 8a–d show data from GPS PRN06 satellite at GL on 8 March 2012, data from GPS PRN18 satellite at GZ on 3 April 2015, data from GPS PRN13 satellite at NN on 18 March 2013 and data from GPS PRN08 satellite at HK on 6 April 2013, respectively. The S4 index and rtec index in Fig. 8 share the left ordinate, where the unit of rtec is TECu. Slightly different from Basu et al. (1999), in this paper, rtec and S4 indices are calculated within 1-min interval based on 1-sec sampling rate TEC data. Therefore, the time interval of S4 and rtec is the same, i.e. 1 min.

As shown in Fig. 8, the overall feature of the temporal variations of S4 and rtec is consistent. When the ionosphere is in a quiet state and no scintillation occurs, the magnitude of both S4 index and rtec index is very small. Especially when no scintillation occurs, the background variation of rtec index is close to zero. When the ionosphere is in a disturbed state and scintillations occur, the value of S4 index increases, and the value of rtec index increases almost simultaneously. From the details of the change, however, there are still slight difference between the temporal variations of S4 and rtec. One possible reason is that S4 index represents the strength of amplitude scintillations associated with Fresnel scale irregularities and rtec is related to the strength of phase scintillations associated with largescale irregularities. The evolution of irregular structures of different scales is different. Based on all the GPS satellite data observed in the night (from 18 LT to 06 LT) from September 2012 to August 2015 at HK and NN, we made a statistical analysis on the relationship between S4 index and rtec index. Average processing of data has been done in two steps before the statistical analysis. Firstly, data of S4 index and rtec index are averaged in 15-minute interval. Secondly, the rtec index with values greater than 0.05 is binned at a step of 0.01, and the average S4 of all points falling within each rtec bin is calculated. Because the data points with higher value of rtec are very few, all data points with rtec P 1 are grouped in a bin. Fig. 9a and 9b show the scatter plot of rtec index and S4 index reckoned from all GPS satellite data in the night from September 2012 to August 2015 at NN (Fig. 9a) and HK (Fig. 9b), respectively. The solid lines in Fig. 9 denote the least square fitting of the scatter points. The numbers of data points used to draw Fig. 9a and 9b are about 7400 and 7200 for NN and HK stations, respectively. It can be seen from Fig. 9 that the average S4 index increases approximately linearly with the increase of rtec index, and the correlation coefficient of linear fitting reaches 0.96, which indicates there is a significant positive

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Fig. 8. Examples of the comparison of the local-time variation between S4 index and rtec index.

Fig. 9. Scatter plot of rtec, the standard deviation of the TEC fluctuation and the average amplitude scintillation index, S4 from all GPS satellite data in the night from September 2012 to August 2015 at NN (a) and HK (b).

correlation between two indices. For the data from HK and NN, the least square fitting of S4 and rtec is almost the same, and can be expressed as S4 ¼ 0:47rtec þ 0:1 In Section 3, we have proved that the phase scintillation index, ru and the TEC fluctuation index, rtec are equivalent. Therefore, the relationship between S4 and rtec actually reflects the relationship between the amplitude scintillation index and the phase scintillation index. Earlier, Basu et al. (1999) compared the relationship between TEC fluctuations and amplitude scintillations by using ROTI index and S4 index that were obtained from data of the Ascension Islands Observatory between

February and April 1998. The result shows that, in view of the co-existence of large and small-scale irregularities in equatorial irregularity structures, during the early evening hours and small magnitude of irregularity drifts, ROTI measurements can be used to predict the presence of amplitude scintillation caused by irregularities. Due to variations of the ionospheric projection of the satellite velocity and the ionospheric irregularity drift, however, the quantitative relationship between S4 and ROTI varies considerably and ratios of S4 to ROTI vary between 2 and 10 (Basu et al., 1999). Unlike ROTI, rtec does not include variations of the ionospheric projection of the satellite velocity and the ionospheric irregularity drift. From the typical event analysis shown in Fig. 8, it can be

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seen that the change range of the ratio of S4 to rtec is obviously smaller than that of S4 to ROTI. Such feature can also be seen from the statistical results. In this sense, rtec may be more effective than ROTI in predicting the existence of irregularities causing scintillation. 6. Summary In this study, TEC fluctuation, dTEC is proposed as a characteristic parameter to avoid the influence of the ionospheric projection of the satellite velocity and the ionospheric irregularity drift, and a new index, named TEC fluctuation index, rtec is established using the standard deviation of dTEC in the 1-min interval. It has been demonstrated that the TEC fluctuation index is equivalent to the phase scintillation index and can serve as an indicator of the strength of the phase scintillation. When the ionosphere is in the disturbed state and strong scintillations occur, transiently discontinuous cycle slips in the TEC time series often appear. In order to obtain continuous TEC data, a processing method for the detection and correction of cycle slips is developed. The method is simple in principle and easy to operate. It is especially suitable for batch processing of large amount of data without human intervention. The practical application of cycle slip detection and correction for large amount of data observed in our network during 2012–2015 shows that the method developed in this study is effective for cycle slip detection and correction. In this paper, the statistical characteristics of ionospheric irregularities and phase scintillations are analyzed by using rtec as the characteristic parameter. The statistical characteristics of occurrences of cycle slips are compared with that of phase scintillations. The data used for the analysis were observed in the ionospheric scintillationmonitoring network in the south-central region of China from September 2012 to August 2015. Besides, we also compare the S4 index of GPS amplitude scintillations with the TEC fluctuation index (rtec) values and, thereby investigate the evolution of large and small-scale irregularities at scale lengths of a few kilometers and the first Fresnel radius, respectively. The statistical characteristics of ionospheric irregularities and phase scintillations and their relation to cycle slips are summarized as follows: 1. With the increase of rtec values, the occurrence probability decreases gradually, the cumulative probability of weak irregularities with 0:1 6 rtec < 0:3 is about 68%, that of moderate irregularities with 0:3 6 rtec < 0:6 is about 22%, that of strong irregularities with 0:6 6 rtec < 1:0 is about 10%. 2. On average, the closer to the magnetic equator, the more frequently phase scintillations occur and the earlier the onset time of scintillations is, indicating that the scintillations are caused by ionospheric irregularities originating at the magnetic equator.

3. In the south-central region of China located in the crest of the EIA and its adjacent region and during September 2012 to August 2015, phase scintillations occur mainly during the night, most frequently before midnight and seldom in the daytime. It is found that phase scintillations occur mainly in equinox months but seldom in solstice months, and an equinoctial asymmetry that phase scintillations occur more frequently in spring than in autumn is also found. 4. The variations of cycle slip occurrences with local time and season are very similar to those of phase scintillation occurrences in the crest of the EIA and its adjacent region, implying that cycle slips are closely related to phase scintillations. This similarity indicates that there are close connections between them and the phase scintillation is a key factor causing cycle slips. 5. A comparison of the TEC fluctuation index (rtec) and S4 index indicates there is close relation between the rtec and S4, signifying the co-existence of large and small scale irregularities in equatorial irregularity structures and rtec measurements can be used to predict the presence of amplitude scintillation caused by irregularities.

Acknowledgements The work of this paper is supported by the National Natural Science Foundation of China (Grant No. 41774163). References Aarons, J., 1997. Global positioning system phase fluctuations at auroral latitudes. J. Geophys. Res. 102, 17219–17231. Adewale, A., Oyeyemi, E., Adeloye, A., Mitchell, C., Rose, J., Cilliers, P., 2012. A study of L-band scintillations and total electron content at an equatorial station, Lagos, Nigeria. Radio Sci. 47, RS2011. https://doi. org/10.1029/2011RS004846. Akala, A., Doherty, P., 2012. Statistical distribution of GPS amplitude scintillations. J. Atmos. Solar-Terr. Phys. 74, 199–211. https://doi.org/ 10.1016/j.jastp.2011.11.006. Akala, A., Amaeshi, L., Doherty, P., Groves, K., Carrano, C., Bridgwood, C., Seemala, G., Somye, E., 2014. Characterization of GNSS scintillations over Lagos, Nigeria during the minimum and ascending phases (2009–2011) of solar cycle 24. Adv. Space Res. 53, 37–47. https://doi.org/10.1016/j.asr.2013.09.034. Alfonsi, L., Spogli, L., De Franceschi, G., Romano, V., Aquino, M., Dodson, A., Mitchell, C., Bipolar, N., 2011. Climatology of GPS ionospheric scintillation at solar minimum. Radio Sci. 46, RS0D05. https://doi.org/10.1029/2010RS004571. Amabayo, E., Edward, J., Cilliers, P., Habarulema, J., 2014. Climatology of ionospheric scintillations and TEC trend over the Ugandan region. Adv. Space Res. 53, 734–743. https://doi.org/10.1016/j. asr.2013.12.015. Banville, S., Langley, R., Saito, S., Yoshihara, T., 2010. Handling cycle slips in GPS data during ionospheric plasma bubble events. Radio Sci. 45, RS6007. https://doi.org/10.1029/2010RS004415. Bastos, L., Landau, H., 1988. Fixing cycle slips in dual-frequency kinematic GPS- applications using Kalman filtering. Manuscr. Geod. 13 (4), 249–256.

L. Xu et al. / Advances in Space Research 64 (2019) 2164–2175 Basu, S., Grovesa, K., Quinna, J., Dohertyb, P., 1999. A comparison of TEC fluctuations and scintillations at Ascension Island. J. Atmos. Sol. Terr. Phys. 61, 1219–1226. Beach, T., Kintner, P., 1999. Simultaneous global positioning system observation of equatorial scintillation and total electron content fluctuations. J. Geophys. Res. 104, 22553–22565. Beutler, G., Davidson, D.A., Langley, R.B., Santerre, R., Vanicek, P., Wells, D.E., 1984, Some theoretical and practical aspects of geodetic positioning using carrier phase difference observations of GPS satellites, Tech. Rep. 109, Univ. of New Brunswick, New Brunswick, Canada. Bhattacharya, A., Beach, T., Basu, S., Kintner, P., 2000. Nighttime equatorial ionosphere: GPS scintillations and differential carrier phase fluctuations. Radio Sci. 35 (1), 209–224. https://doi.org/10.1029/ 1999RS002213. Blewitt, G., 1990. An automatic editing algorithm for GPS data. Geophys. Res. Lett. 17 (3), 199–202. https://doi.org/10.1029/GL017i003p00199. Cheng, J., Xu, J.-S., Cai, L., 2018. A comparison of statistical features of ionospheric scintillations and cycle slips in the south-central region of China. Chin. J. Geophys. 61 (1), 18–29. https://doi.org/10.6038/ cjg20180065. Carrano, C., Groves, K., 2007. TEC gradients and fluctuations at low latitudes measured with high data rate GPS receivers. In: 63rd Annual Meeting of The Institute of Navigation. The Institute of Navigation, Cambridge, MA, pp. 156–163. Deng, B., Huang, J., Liu, W., Xu, J., Huang, L., 2013. GPS scintillation and TEC depletion near the northern crest of equatorial anomaly over South China. Adv. Space Res. 51, 356–365. https://doi.org/10.1016/j. asr.2012.09.008. Du, J., Caruana, J., Wilkinson, P., Thomas, R., Cervera, M., 2000. Determination of equatorial ionospheric scintillation S4 by dual frequency GPS. IPS Radio and Space Services, NSW1240; Surveillance System Division, Defense Science and Technology Organization, Sydney. Huang, L., Wang, J., Jiang, Y., Chen, Z., Zhao, K., 2014. A study of GPS ionospheric scintillations observed at Shenzhen. Adv. Space Res. 54, 2208–2217. https://doi.org/10.1016/j.asr.2014.08.023. Jakowski, N., Borries, C., Wilken, V., 2012. Introducing a disturbance ionosphere index. Radio Sci. 47, RS0L14. https://doi.org/10.1029/ 2011RS004939. Ji, S., Chen, W., Weng, D., Wang, Z., Ding, X., 2013. A study on cycle slip detection and correction in case of ionospheric scintillation. Adv. Space Res. 51, 742–753. https://doi.org/10.1016/j.asr.2012.10.012. Kelley, M.C., l989. The Earth’s Ionosphere. Academic Press, San Diego, Califomia, USA. Kintner, P., Kil, H., Deehr, C., 2002. Simultaneous total electron content and all-sky camera measurements of an auroral arc. J. Geophy. Res. 107 (A7), 1127. https://doi.org/10.1029/2001JA000110. Kintner, P., Ledvina, B., de Paula, E., 2007. GPS and ionospheric scintillations. Space Weather 5, S09003. https://doi.org/10.1029/ 2006SW000260. Kumar, S., Kishore, A., Ramachandran, V., 2007. Ionospheric scintillations on 3.925 GHz signal from Intelsat (701) at low latitude in the

2175

South Pacific region. Phys. Scr. 75 (3), 258. https://doi.org/10.1088/ 0031-8949/75/3/005. Kumar, S., Gwal, A., 2000. VHF ionospheric scintillations near the equatorial anomaly crest: solar and magnetic activity effects. J. Atmos. Sol. Terr. Phys. 62 (3), 157–167. Liu, Z., 2011. A new automated cycle slip detection and repair method for a single dual-frequency GPS receiver. J. Geod. 85, 171–183. https:// doi.org/10.1007/s00190-010- 0426-y. Liu, K., Li, G., Ning, B., Hu, L., Li, H., 2015. Statistical characteristics of low-latitude ionospheric scintillation over China. Adv. Space Res. 55, 1356–1365. https://doi.org/10.1016/j.asr.2014.12.001. Melbourne, W.G., 1985. The case for ranging in GPS based geodetic systems. In: Proc. of the 1st International Symposium on Precise Positioning with the Global Positioning System, pp. 373–386. Mendillo, M., Bosheng, L., Aarons, J., 2000. The application of GPS observation to equatorial aeronomy. Radio Sci. 35 (3), 885–904. Olwendo, O., Baki, P., Cilliers, P., Doherty, P., Radicella, S., 2016. Low latitude ionospheric scintillation and zonal plasma irregularity drifts climatology around the equatorial anomaly crest over Kenya. J. Atmos. Sol.-Terr. Phys. 138–139, 9–22. https://doi.org/10.1016/ j.jastp.2015.12.002. Pi, X., Mannucci, A., Lindqwister, U., Ho, C., 1997. Monitoring of global ionospheric irregularities using the worldwide GPS network. Geophys. Res. Lett. 24 (18), 2283–2286. Prasad, R., Kumar, S., 2017. Day and nighttime L-Band amplitude scintillations during low solar activity at a low latitude station in the South Pacific region. J. Atmos. Sol. Terr. Phys. 165–166, 54–66. Seba, E., Gogie, T., 2015. Characterization of ionospheric scintillation at a geomagnetic equatorial region station. Adv. Space Res. 56, 2057–2063. https://doi.org/10.1016/j.asr.2015.07.035. Tiwari, R., Strangeways, H., Tiwari, S., Ahmed, A., 2013. Investigation of ionospheric irregularities and scintillation using TEC at high latitude. Adv. Space Res. 52, 1111–1124. https://doi.org/10.1016/j. asr.2013.06.010. Wanninger, L., 1993. Ionospheric monitoring using IGS data, paper presented at the IGS workshop. Inst. of Geol. Sci, Bern, Switzerland. Wilson, B., Mannucci, A., 1993. Instrumental biases in ionospheric measurements derived from GPS data, paper presented at the 6th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GPS 1993), Salt Lake City, Utah. Wu¨bbena, G., 1985. Software developments for geodetic positioning with GPS using TI4100 code and carrier measurements. In: Proc. of the 1st International Symposium on Precise Positioning with the Global Positioning System, pp. 403–412. Xiong, C., Stolle, C., Lu¨hr, H., 2016. The Swarm satellite loss of GPS signal and its relation to ionospheric plasma irregularities. Space Weather 14, 563–577. https://doi.org/10.1002/2016SW001439. Yeh, K., Liu, C., 1982. Radio wave scintillations in the ionosphere. Proc. IEEE 70 (4), 324–360. Yue, X., Schreiner, W., Pedatella, N., Kuo, Y., 2016. Characterizing GPS radio occultation loss of lock due to ionospheric weather. Space Weather 14, 285–299. https://doi.org/10.1002/2015SW001340.