Detecting Ionospheric TEC Disturbances by Three Methods of Detrending through Dense CORS During A Strong Thunderstorm

Satellite navigation and communications system can substantially be disturbed by ionospheric perturbations. Consequently, monitoring ionospheric anomalous has great significance. In this study, we focus on the short-term irregular disturbances through a strong thunderstorm in Wuhan City, Hubei, China by using ground-based GNSS observations from dense Continuously Operating Reference Stations (CORS) with a sampling rate of 1s. The total electron content (TEC) was used to find possible perturbations after biases have been calibrated for the derived TEC. Additionally, the geomagnetic conditions and the state of solar radiation was checked in the study period to recognize the causes for the ionospheric disturbances. The maxima and minima values of TEC deviations were ~ 2.5 and 0.5 TECU, respectively. Three methods of Detrended Fluctuations Analysis (DFA) were applied to assess the ionospheric disturbances over GNSS CORS stations; “Multi-step numerical difference”(MSND), “6 th order polynomials fitting” (PF), and “one-week average difference”(AD). The analyzed results showed that MSND has the lowest performance. Meanwhile, the fitted TEC data with 6 th order polynomials technique presented an improvement and a discrepancy related to MSND. To resolve this discrepancy, we proposed AD technique, it accomplished the best performance related to the TEC disturbances and was compared with the other two techniques. The research findings showed that ionospheric disturbed electrons can be generated with various rates and different velocities through lightning influences. assessment part was conducted by three methods of Detrended Fluctuations Analysis: (1) Multi-step numerical difference, (2) 6 th order polynomials fitting, (3) One-week average difference and was compared with STEC disturbances. The three techniques which were applied in this study represented a fundamental and substantial


Introduction
Reliable and fast knowledge about ionospheric variations has become increasingly important. GNSS users of single-frequency receivers need accurate corrections to remove signal degradation caused by the ionosphere. The ionospheric variations can be categorized as systematic and non-systematic. Systematic variations either takes place in cycles or does not. Consequently, it can be pre-modulated or predicted with reasonable accuracy [Rama Rao et al., 2006]. On the other hand, irregular variations which happen due to some phenomena such as earthquakes, tsunamis, and underground nuclear explosions (UNE) could not be expected [Amieri-Simkooei and Asgari, 2012;Jain, Vijay, and Gwal, 1996;Park et al., 2011;Salem et al., 2015;Savastano et al., 2017;Yu et al., 2015;. There are many studies dealing with ionospheric disturbances which respond to the aforementioned hazards [Amieri-Simkooei and Asgari, 2012;Calais & Minster, 1995;Jain et al., 1996;Park et al., 2011;Salem et al., 2015;Savastano et al., 2017;Yu et al., 2015;. The common factor for these hazards is a unique epicenter, where we can obtain the epicenter and determine its starting time clearly according to the different research centers. In addition, it is a chance to focus on the coupling between the solid-Earth and atmosphere [Liu and Jin, 2019]. On the other side, ionospheric disturbances could be associated with lightning. However, it is quite difficult to deal with this issue where lightning has multi epicenters and different starting times.
Although the ionospheric anomalies have been observed through GPS TEC for about three decades [Calais and Minster, 1995], insufficient studies have been conducted on dealing with ionospheric response during lightning and their thunderstorm. With the increase of Continuously Operating Reference Station (CORS), it supplies not only abundant measurements to observe the pattern and evolution of ionospheric disturbances, but also a magnificent opportunity for studying more details about the coupling between the tropospheric activities and higher atmosphere. The electromagnetic fields produced by natural thundercloud activities energy can transfer from the troposphere mainly through wave activity, i.e., gravity waves (GWs) and infrasonic waves [Blanc, 1985;Chimonas, 1971;Sentman et al., 2003]. Therefore, the studies of ionospheric disturbances during lightning activity have been interested in exploring as well as monitoring the effect of this phenomenon through the ionosphere, where the lightning activity could disturb the TEC in the ionosphere. A statistical study was conducted on it in 2005 which found a relationship between lightning activity and the sporadic E layer intensification [Davis and Johnson, 2005]. During the lightning, the ionosphere was substantially disturbed by electrical activity, which can cause variations in electron density through heating the electrons [Layet al., 2013].
Consequently, Barta et al. [2013] have shown that the electron density of the sporadic E layer has decreased significantly associated with lightning based on infrared maps and lightning observations over the ionospheric station of Rome. On the other side, Lay et al. [2013] have fitted the GPS total electron content (TEC) data with a 6 th order polynomial, therefore, the variations are calculated by subtracting this fit from the data. So, anomalous TEC changes were closely associated with space and time to the large underlying thunderstorms. Similar to the method described above, 6 dual frequency GPS stations have been used with lightning data obtained from World-Wide Lightning Location Network (WWLLN) over southern Africa. The results have indicated that ~ 1 TECU varied in TEC which corresponding to periods of lightning activity intensification in the studied regions [Amin,

STEC Calculation
Ionospheric observables have been extensively discussed by Mannucci et al. [Ciraolo et al., 2007;Mannucci et al., 1998]. In fact, the ionosphere can cause an ionospheric delay on the GNSS signals, depending on their frequencies ƒ as well as STEC values extended along the line of sight (LoS) between the receiver and satellite. In this study, the STEC was derived from the dual-frequency GNSS observation from HBCORS as follows: (1) Where and indicate satellite and receiver, respectively; TEC is the STEC along LoS; and are the carrier phase and pseudorange measurements, respectively; 1 and 2 are the frequencies of the carrier phases of 1 and 2 , respectively; B S and B r are the satellite and receiver hardware delay of the pseudorange code, respectively; b S and b r are the satellite and receiver hardware delay of carrier phase, respectively; ,1 and ,1 are carrier-phase ambiguity.
Although the ionospheric observations can be derived directly from both pseudorange code or carrier phase measurement, the pseudorange measurement contains more noise than that of carrier phase. Therefore, the ,4 = ,1 -,2 = - precision of the carrier phase is more accurate than that of the pseudorange. Moreover, it presents the additional problem of biased by unknown ambiguities [Mannucci et al., 1998]. Therefore, the so-called "leveling carrier to code" algorithms in this work are applied to minimize the noise of the pseudorange and to remove the ambiguity of the carrier phase [Ciraolo et al., 2007]. The differential carrier phase increases measurements precision of STEC while pseudorange gives the absolute scale of it [Ugur and Ibrahim, 2013]. This form can be represented as: Ŀ I,arc = L I,arc -(L I,arc -P I ) arc = TEC + B r + B S + (ε p ) arc + ε L , Where Ŀ Larc is the ionospheric observable of carrier-phase "leveled" to the code-delay one, L I,arc is the ionospheric observable obtained from carrier-phase; B r and B S are the same as Eq.
(1), ε p and ε L are the noise and multi-path for the code-delay measurements and for the carrier-phase ionospheric observations, respectively.
Based on Eq.
(2), taking leveling process into consideration: "(1) IFBs for carrier-phase are replaced by the corresponding code-delay IFBs" [Ciraolo et al., 2007]; (2) multi-path and noise presented in the code-delay measurements could affect the leveled carrier-phase ionospheric observable, in case these do not average to zero over the same continuous arc. In this study, we employed GPS data observed above 10° cut off angle in order to have the longest arc as possible to check ionospheric disturbances with non-ionospheric related tracking errors.
After processing all GNSS data, we can plot the STEC variation values versus time to detect the perturbations in the ionosphere without detrending. The previous method is conducted with an assumption that ionospheric perturbations have the same systematic error or STEC includes constant bias [X. .
The spatial distribution of TEC has been modeled by the spherical harmonic expansion based on single layer model as follow: ( Where and are the geomagnetic latitude and solar-fixed longitude for Ionospheric Pierce Points (IPP), respectively; ( , ) is the vertical ionospheric TEC at IPP. VTEC is converted from STEC using a mapping function (MF) [Deng et al., 2016;Schaer, 1999]. n max is the max degree of the spherical function; represents the fully normalized Legendre function of degree n and order m; and are the fully normalized spherical coefficients of degree n and order m [Zhang and Zhao, 2019].
Before estimating STEC from GPS observations, the TurboEdit algorithm was used to detect cycle slips. The established algorithm by Blewitt, can identify cycle slips, correct cycle slips wherever possible, even more, delete data outliers [Blewitt, 1990]. Based on the limited number of receivers and the study area, the expansion of spherical harmonics with order 3 is applied. The shell (single layer) has an altitude of about 450km. In this method, we have computed the differential code biases (DCBs) as a constant value per day as well as zero-average conditions are adopted for all observed satellites of each system in order to disconnect the DCBs of satellites and receivers from each other. Therefore, the cleaned STEC are extracted after separating the DCBs which can be applied for measuring and analyzing the ionospheric disturbances through this work. After obtaining the corrected STEC, we can get a STEC time series as follows: STEC 1 , STEC 2 ,⋯, STEC n . Where the subscripts 1, 2, …, n introduce the epoch number started from one at midnight based on UT and end at 86400, where the total number of epochs represents for a whole day by seconds.

Multi-step numerical difference
For a given STEC sequence, Hernandez-Pajares et al., [2006] have extracted ionospheric disturbances by applying a numerical difference method with an order of 1. Recently, other researchers have applied the multi-step multi-order with higher orders 2 and 3 [Park et al., 2011;. The multi-order numerical difference is defined: Where t is the sampling rate of the data, τ is the time step, which was chosen to detect the possible variations Assuming TEC trendlines have linear changes during a short period. In other words, the applied method will detect ionospheric disturbance periods of 600S (A'=2A) with significant sensitivity, and periods between (400-1200)S where (A'=A), will be quite efficient [Hernandez-Pajares et al., 2006;. Mostly, this type of problems happens in all detrending procedures commonly, so in this study, we investigate the suitability of a deterministic technique to display the strong thunderstorm fluctuations by employing two more of detrending methods; they are described in sections 2.3.2 and 2.3.3, respectively.

Six order polynomials fitting
In this strategy, the TEC data are fitted with a 6 th order polynomial as a second method to detrend the data, in order to sensitively observe TEC fluctuations.
(6) 6 th order being the highest that can be displayed with the trend line. The disturbed TEC is computed by subtracting this fitting from the STEC data. We got that ionospheric perturbations as a function in TEC variations are closely correlated in space and time during the strong underlying electrical storm. The aforementioned process removes the gross offset, as well as the detrended values, are mostly related to the carrier phase TEC around 0.01 to 0.1 TECU accuracy [Burrell et al., 2009].

One-week average difference
The following is the proposed method employed to detect ionospheric disturbances based on the average of one week before the phenomena day. Subtraction of the average simultaneous observations from a certain day can lead to an observable residual, in other words, removing an aspect from the dataset arise some kind of distortion or disturbance can appear in the behavior of the output. As mentioned above, the mathematical process for this kind of detrending can be described in the next simple equations.
Where Ḱ is the average value of STEC for period one week before electrical storm, V is the residuals between a certain day and average value. In the assumption, TEC trendlines have linear changes during a short period.
Furthermore, the Dst index, geomagnetic Kp index, and the solar radio flux F10.7 index during the study period were quite steady, based on Figure 1. So, the values of TEC for the average simultaneous observations supposed to be almost close to each other. The difference between TEC value for average and a certain day should be smooth

Geomagnetic index Dst, Kp, and solar activity index F10.7
The Disturbance storm-time (Dst) index, geomagnetic Kp index, and the solar radio flux F10.7 index during 12 Days (Doy53-Doy65) are depicted below in Figure 1.

Disturbances by STEC observations
According to Wuhan Meteorological Observatory, the lightning warning classified as yellow signal besides their strong thunderstorm occurred at 09:00 UT (05:00 pm LT) on 2 nd March 2018 as shown in Table 1 for more details we can refer to (https://www.timeanddate.com/weather/china/wuhan/historic?month=3andyear=2018). Based on code-delay and Dual-frequency carrier phase GPS observations are combined to obtain ionospheric observables represented as the STEC along the LoS between satellite and receiver. Both the transmitting and the receiving hardware cause differential code biases (DCB) could have an effect on observations [Ciraolo et al., 2007]. These biases have been estimated and eliminated from the data to adjust the experimental STEC. However, assuming STEC still contains bias, it is supposed to have a constant bias . According to this assumption, we analyzed the STEC to detect the ionospheric disturbances then verified the results with VTEC. Finally, the ionospheric disturbances are assessed with three detrending methods. Generally, the behavior of the ionosphere is in steady-state during the night. Some ionospheric layers going to disappear, so STEC supposed to decrease or at least become a fixed value in normal conditions [Zolesi and Cander, 2014]. Consequently, the ionospheric disturbances in these times may be caused by lightning and their thunderstorms effects, especially this phenomenon happened after the sunset with respect to China local time (UT+8h). The red arrows in Figure    The ionospheric STEC series also contains a significant disturbances during 15:00-15:45UT, as shown in Figure 3 the perturbations can be considered as extreme values of ionospheric disturbances which happened up to 45min separately over most of the ground-based stations. Based on Figure 2, 3 we can see that ionospheric disturbances over WH04 moved quicker than other points. Where the "B" arrow refers to an earlier time of ionospheric disturbances than the red arrows for all panels in Figure 3. By referring to Figure 4, we can interpret ionospheric disturbances moved quickly in N-E direction over WH04 located 58km close to the city center of Wuhan.
Where the turbulence reached the highest value at 15:03UT. However, the XG01 10km closer than WH04 to the city center, but the highest perturbations have delayed about 11min at 15:14UT. For the N-W direction, the detectable large ionospheric disturbances were nearly 40min overdue than WH04, where the furthest station named as XF05 located about 323km in the same direction from Wuhan city center. In accordance with the above results, the detected ionospheric disturbances have different horizontal velocity, period, direction, waveform and observed time compared with the reflected lightning and their thunderstorms time period. Furthermore, a possible recurrent ionospheric disturbance has been checked, we also verified that there were not significant perturbations for one week before the day of the phenomenon at the same study times.
Based on the main concept of TEC during the night, it should be discharged and decrease because of nonexistance of solar radiation to recharge it. However, solar radiation is the major element which associates in recharge ionospheric particles. As it is known, through the nighttime there are some ionospheric layers such as D and E which disappear [Zolesi and Cander, 2014]. Therefore, in the steady states, the TEC values decrease. However, TEC values have increased during nighttime which is likely to support our interpretation that electrical energy generated by lightning could contribute in ionospheric fluctuations by vertical coupling between troposphere activities and higher atmosphere. As a result, the TEC has been disturbed. These results can confirm that the observed ionospheric disturbances in Figure 3 is triggered by the electrical energy that have been generated by lightning waves for the next reasons (1) The detected ionospheric disturbances happened during the nighttime where no solar radiation which is the main factor to recharge ions in the ionosphere.
(2) As we can see in Figure 1, during the whole day of the event (DOY 61), no presence of strong geomagnetic activity or solar activity is observed so no effect came from DST, Kp, and F10.7. In the next section, we used detrended methods to remove the effects of accumulated errors to display individually the ionospheric changes in TEC values.

Results of Detrended methods
In order to assess the ionospheric disturbances explained in section 3.2. It is worth considering the removal of the effects of accumulated errors to display individually the ionospheric changes in TEC values. Therefore, multiple detrending techniques are applied in the next sections which show their results, discussion, and analysis listed below.

Multi-step numerical difference
Based on the results shown in Figure 5, two types of ionospheric disturbances were detected by the GPS station It is interesting to note that using time step 300 s is more sufficient to detect the ionospheric disturbance which is an indication of ionospheric response to a strong thunderstorm . As we can see in Figure   5,   It is acknowledged that the chosen time step could be relevant to the detectable period, so a certain time step may skip detectable perturbations. Using the same criteria, there are no detectable perturbations over the other two stations XG01 and XN01, although there are detectable ionospheric disturbances over the same stations in Figure 3. As a result, we need to apply other techniques, where the pre-analysis mentioned based on Figure 3 indicates the aforementioned stations have disturbance common with the time period of lightning over Wuhan.
Consequently, Multi-step numerical difference is not enough to assess the detectable ionospheric turbulences response to the studied phenomena overall disturbed stations.

Six order polynomials fitting
Hereinafter, the results of detrending by polynomial fitting for TEC have displayed through the same 6 CORS stations. The disturbed TEC is computed by subtracting this fitting from the STEC data.
The satellite has the given GPS pseudo-random number (PRN) 28. In Figure 7, the measured STEC has large deviations from the fitted curve between ~14:30 and 16:00 UTC. The vertical green lines show the period of the STEC deviations from the fitted curve. This time range indicates that may detectable ionospheric disturbances can be found based on the large deviations. In addition, the corresponding time ionospheric disturbances which detected by the first method "Multi-step numerical difference". The applied method is more reliable for higherfrequency variations, in other words, it acts to filter out the lower-frequency changes [Lay et al., 2013].
By deducting the observed TEC from the best fit 6 th order polynomial, the deviation can be detected easily. The performance of this kind of detrending for the six disturbed stations has more efficiency than the method of "Multi-step numerical difference" which mentioned separately in section 3.3.1. The ionospheric disturbances over the stations XG01, XG04, WH04, XF05, and XG04 are successfully detected by the current method as shown in Figure 8. However, the first two stations (XG01, XG04) are non-detectable by "Multi-step numerical difference" method, and the last three stations (WH04, XF05, and XG04) are detected by both techniques. Although the current technique using best fitting polynomials apparently has a better performance than the first one. "Multistep numerical difference" has found a detectable ionospheric disturbance over the station XF01, which was not observed by subtracting the fitted-curve method from the data. Polynomial fitting acts to filter out the lowerfrequency changes so it cannot detect the lower values disturbances. For this reason, we proposed a third detrending method to avoid these defects.
12 Figure 7. The deviations between the measured TEC and the 6 th order polynomial fitted curve for the given GPS pseudo-random number (PRN) 28 over station WH04.

One-week average difference
In the assumption, TEC trendlines have linear changes during a short period. Furthermore, the Dst index, geomagnetic Kp index, and the solar radio flux F10.7 index during the study period were quite steady, based on Figure 1. So, the values of TEC for the average simultaneous observations supposed to be almost close to each other.
The average value calculated from Doy54 to Doy60, afterward, the mean values subtracted from Doy60 (Day before phenomena) and Doy61 (Day of phenomena), respectively. The results of these experiment shown in Figure 9 below.
The anomalous TEC changes are found closely associated in space and time to the strong underlying lightning and their thunderstorms. The TEC variations are observed with maxima and minima to be ~2.5 and 0.5 TECU, respectively, through typical hours of darkness background value of numerous TECUs. The changes close to the thunderstorm appear to have a quick response than those away from the storm. In addition, there was a highfrequency content over the nearest neighbors' stations, especially in the N-E direction from Wuhan city center with periods of minutes to tens of minutes. The ionospheric disturbances lasted for a longer time than South direction by a few minutes, based on the results over XG04 and XN01 in the North and South of Wuhan city center, respectively. The TEC perturbations have ended in the N-W direction over XF05 station later than other stations around the Area of interest (AOI). These findings are warranted by the pre-analysis over the same station which located about 323km (all distances measured from Wuhan city center).
Indeed, the turbulences are coming later comparing to other stations, taking into consideration the direction and the farther distance away from Wuhan city center. With ingesting deep, the N-W direction seems to have the last detectable large ionospheric disturbances, was nearly 40min overdue than WH04. The detectable localized TEC variations for XF05 is observed at night of the strong thunderstorm. It was found that the TEC perturbations finished with minutes to tens of minutes after other stations. Emphatically, both results of the large and last ionospheric disturbances which can be detectable coincide with the ionospheric disturbances moved quickly in N-E direction on the other side, shifted little faster in the N-W direction. As a result, Multiple epicenters of the lightning and their thunderstorm might be concentrated near to the center of the city and to N-E direction during that night.
Moreover, ionospheric disturbances can travel with different velocities in the case of thunderstorms depending on the direction as well as the remoteness from the electrical storm.
By comparing the results of the second and third detrending technique, where both techniques agree in more than 80% of the detectable ionospheric disturbances. Around 5 CORS stations have detected ionospheric disturbances except for XF01 station discovered only by the third method. Based on the results for both methods, the 6 th order polynomial technique delayed within mins to tens of mins from the mean method for detecting ionospheric disturbances. The only non-detectable ionospheric disturbance for station XF01 by the fitting technique which has variations less than 1TECU during the common time with phenomena effect. Emphatically, this finding agrees with the concept of fitting is acted more sensitive only for the higher-frequency variations [Lay et al., 2013].
It is worthy of mentioning that under large ionospheric electron disturbances based on lightning and their thunderstorms, significant ionospheric disturbances maybe in some detrending styles. On the basis of this study results, and according to Table 2 the third method called "one-week average difference" has the best performance agree with our pre-analysis. Where the third method has detected the ionospheric disturbances over the 6 CORS stations. This type of detrending technique is more significant especially in mid-latitude locations with quite steady solar radio flux F10.7 and moderate geomagnetic storm Kp based on research findings.
It is known that the tropospheric activities like thunderstorms could disturb the lower ionosphere of height range 60 to 90 km through lightning-generated electric fields [(Cheng et al., 2007;Davis and Lo, 2008;Lu, 2006;Pasko et al., 1997;Mende et al., 2005] as well as the convective atmospheric gravity waves (GWs) [Lay and Shao, 2011;Sentman et al., 2003;Taylor and Hapgood, 1988]. Besides, [Davis and Johnson, 2005;Yu et al., 2015] have found that the ionospheric sporadic E of altitude ∼100 km could be affected by lightning. Recently, researchers have reported that the roles of ionization enhancements could happen through the lightning, and thunderstorms can trigger atmospheric gravity waves (AGWs) and propagate upwards to the ionosphere [Yue and Lyons, 2015]. It is known that GWs are considered as a crucial part of the atmosphere's dynamics process. GWs influence temperature and atmospheric winds distribution where it mainly contributes to moving momentum and energy between the different layers of the atmosphere. Once GWs arrive at the upper atmosphere and interact with the plasma of ionosphere, the density of plasma is disturbed, electron density is also changed according to the law of conservation of charge, and causes the ionospheric disturbances. In 2017, Yu et al. have tried to find the relation between Earth's atmosphere and ionosphere interactions, their results indicated that electric field effects and GWs likely the mechanisms responsible enhancement of Na layer [Yu et al., 2017]. Subsequently, Yu, B. et al. have concluded that the dynamical process of the ionosphere's sporadic E layers and Na layer dominantly effect by atmospheric tides.
Their findings indicated that metallic layered has been intensified by atmospheric tides or in other words the troposphere-mesosphere-ionosphere coupling [Yu et al., 2019].  Figure 9. Detecting ionospheric disturbances series by One-week average difference technique over the six stations, (left) differences of the day before the event day, (right) differences of the event day.
In this paper, the present results can confirm the ionospheric disturbance was observed in the TEC through three methods, the mechanism responsible for these disturbances above the strong thunderstorms in Wuhan could be the generated electric fields from lightning and convective AGWs produced by thunderstorms.
It is unfortunate we lack information about simultaneous ionosonde observation associated with the lightning in our data. Subsequently, since STEC derived from GNSS observation is only total electron content along the path from station to satellite, it is not easy to determine accurately the height of the occurrence of ionospheric disturbance resulting from a lightning strike. Yue et al., [2016] have concluded that the ionospheric disturbance is mostly observed in the E and F region based on combined GNSS rays from LEO-based GNSS and the ground-based receivers to get good global resolution in the topside ionosphere during a geomagnetic storm. As the F region is located too high to be associated with lightning, meanwhile, it is worthy of indicating that the ionospheric perturbations were preceding revealed in the ionospheric Es region. In 2005, Davis and Johnson have concluded that electrical discharge is likely responsible for any ionospheric enhancement and the lightning is concerned with the disturbance ionospheric Es layer which represented as the localized enhancement of electron density [Davis and Johnson, 2005]. A dominant response after few hours of lightning has existed. It was a result of GWs generated by the thunderstorm which has a large vertical wavelength. However, the waves' vertical component is small compared with their horizontal velocity [Chimonas, 1971;Johnson and Davis, 2006]. In 2008, Davis and Lo have investigated the response to lightning strokes in the ionospheric Es layer by a superposed epoch study.
It has been revealed that the dominant cause of the observed ionospheric disturbance in the sporadic layer was related to cloud-to-ground lightning [Davis and Lo, 2008]. Although [Johnson and Davis, 2006] have discussed the potential mechanisms summarized by [Rycroft, 2006] in relation to the enhancement of the Es layer at 100 km is associated with sprites. While [Davis and Lo, 2008] suggested that this unlikely whereas their results were lack to the peak current which accompanying the lightning. Recently, [Yu et al., 2017] have followed the conclusion by [Inan et al., 1996] which indicated that the local ionosphere can be effected by lightning over a distance of up to 150 km to study the connection between neutral metal Na layer and thunderstorms.
The few minutes difference between disturbance for the aforementioned CORS stations may be due to their different locations where the geographic location of lightning affect the influence of thunderstorms on the ionosphere. [Chimonas, 1971] was expected the formation of the lower and higher Es layers depend on the Eastwest gravity waves and northerly waves, respectively. In 2006, Johnson and Davis have extended the limits of the data set, used by them in 2005, to 400 km from Chilton where it was revealed a direct effect of the lightning on the ionosphere beyond the previous limits (200 km). In addition, the enhancement in the Es layer revealed not only related to the location geographic of lightning but also the position of lightning as well such as cloud-to-ground or inter-cloud lightning [Davis and Lo, 2008].

Conclusions
The influence of lightning and their thunderstorms could transfer to the high atmosphere so, it is a good way to understand the upper atmosphere coupling by detecting the response of the ionosphere to this phenomenon.
In this study, we investigated the ionospheric response by using ground-based GNSS observations from dense CORS during strong thunderstorms over Wuhan city. Before estimating STEC from GPS observations, the TurboEdit algorithm was used to detect cycle slips, correct cycle slips wherever possible and delete data outliers [Blewitt, 1990]. The STEC was derived from the dual-frequency GPS observation from HBCORS. The code-delay and Dual-frequency carrier phase were combined to obtain ionospheric observables represented as the STEC along the LoS between satellite and receiver. Assuming STEC still contains a constant bias after calibrating it , the STEC were checked to find the possible ionospheric disturbances with respect to maxima and minima values to check the periods of extreme disturbance and first arriving of lightning influence on the ionosphere. The research has found that the ionospheric disturbances have different velocities based on thunderstorm activities. Based on the distance and direction of each CORS station from Wuhan city center. The assessment part was conducted by three methods of Detrended Fluctuations Analysis: (1) Multi-step numerical difference, (2) 6 th order polynomials fitting, (3) One-week average difference and was compared with STEC disturbances. The three techniques which were applied in this study represented a fundamental and substantial Mohamed Freeshah et al.
mechanism in the detrended dataset during strong thunderstorms. Applying only one method have some defects, so we used different methods to avoid these defects as possible. Thereby, this issue is very worthy of discussing because maybe misleading results could do dissipation or impediment in detecting the ionospheric fluctuations depending upon the applied detrending technique. On the other hand, considering one day as a reference for subtracting from the day of phenomenon maybe be not enough for the detectable ionospheric TEC disturbances, where it depends mostly upon the latitude of the study area, especially in low latitude regions where ionospheric variability is more dynamic and complex as compared to mid-latitudes [Maruyama et al., 2007]. The analyzed results for the three detrending methods showed that the MSND method has the lowest performance. Meanwhile, the fitted TEC data with 6 th order polynomials technique presented an improvement and a discrepancy related to the MSND method. The AD method has satisfied the best performance comparing with TEC disturbances.
Based on results of the three detrending methods, further studies are therefore necessary to evaluate more ways with different phenomena, investigating various case studies for the further improvement could lead to a fast and efficient algorithm for detecting of duration and frequency of ionospheric perturbations can be proposed, where it will be more suitable for certain phenomena and regions.