An Analysis of Ionospheric Conditions during Intense Geomagnetic Storms (Dst ≤ − 100 nt) in the Period 2011–2018 †

: The layer of the Earth’s atmosphere known as the ionosphere presents a signiﬁcant obstacle to global satellite navigation systems (GNSS) due to its ability to introduce errors. To address this challenge, various navigation systems have introduced new signals designed to minimize the errors caused by the ionosphere. These signals not only aid in error reduction but also facilitate the examination of electron content behavior. This study focuses on the analysis of vTEC plots obtained from RINEX data collected at the INEG station in Aguascalientes, Mexico, from 2011 to 2018, with a particular emphasis on highly intense geomagnetic storms characterized by values below − 100 nT. Our analysis of these plots employed the Probability Density Function (PDF), which allows for the graphical representation of data distribution. This distribution is then examined in conjunction with the station’s Total Electron Content (TEC) values and the Dst index during the corresponding geomagnetic storm events. The ﬁndings establish the correlation between each of these parameters during such events.


Introduction
The ionosphere's influence on the signals of Global Navigation Satellite Systems (GNSS) has long been recognized as a primary source of errors in satellite-based positioning.However, its significance extends far beyond mere technical challenges, encompassing a pivotal role in global communications and a susceptibility to various factors, most notably solar events [1].Within the framework of GNSS, the dual-frequency capabilities of systems like GPS play a crucial role in characterizing ionospheric behavior.This capability allows for the assessment of ionospheric effects and facilitates the determination of Total Electron Content (TEC), providing insights into electron density variations along the satellite-receiver path.Furthermore, the Sun, as a celestial powerhouse, exerts a profound influence on the ionosphere [1][2][3].Solar phenomena such as coronal mass ejections, solar flares, and solar energetic particle events can instigate disruptive consequences, affecting telecommunications, radiocommunications, and satellite-based systems [4,5].The objectives of this study were to investigate ionospheric behavior during intense geomagnetic storms and to explore its interplay with solar and seasonal cycles.Drawing from historical contexts, in this paper, we delve into the evolution of ionospheric research, its ionization processes, and the pivotal role that GNSS have played in advancing our comprehension of this enigmatic layer of Earth's atmosphere [1,6].Furthermore, a hypothesis is formulated, suggesting that geomagnetic storms can induce significant ionospheric disturbances, and a statistical tool, the Probability Density Function (PDF), is proposed for event classification and analysis.By addressing these key aspects, this manuscript contributes to a deeper understanding of the ionosphere's multifaceted role and its implications for both navigation and global communication systems.With a focus on 22 intense geomagnetic storms occurring between 2011 and 2018, characterized by Dst index values of less than −100 nT, this study aims to unravel the ionospheric behavior during these disruptive events.By investigating the interplay between geomagnetic storms, solar cycles, and seasonal variations, this manuscript seeks to advance our understanding of the ionosphere's multifaceted role, ultimately benefiting global navigation and communication systems.

Data Used and Methodology
In this study, data for the Dst index were acquired from the website of the Center for Data Analysis for Geomagnetism and Space Magnetism at the University of Kyoto.A Python code was developed to plot the data.The criteria for obtaining the Dst index data focused on geomagnetic storms with Dst index values less than −100 nT.After identifying the events, RINEX data for the selected station were downloaded, and the Total Electron Content (TEC) was calculated using GPSTEC software version 2.9.5.These TEC data were used to create vTEC plots.Subsequently, Probability Density Functions (PDFs) were applied to the ionospheric plots using MATLAB R2017b.Our analysis involved categorizing ionospheric storms as positive or negative, examining maximum TEC values, minimum Dst index values, solar and seasonal cycles, and local time.
For TEC calculation, the dual-frequency nature of the GPS system was utilized to assess ionospheric effects.The Total Electron Content (TEC) can be calculated using phase measurements, where TEC = 9.52(R2 − R1), or pseudorange measurements, where TEC = 9.52(R2 − R1) [7].The phase-based TEC calculation provides precise temporal variations, while the pseudorange method offers absolute values.The GPS observations were adjusted for satellite and receiver delays, multipath effects, and receiver noise [8].Additionally, the PDF was used to analyze the probability distribution of variable values.The PDF identifies regions of higher and lower probabilities for a continuous random variable [9,10].The PDF for a distribution can be obtained by differentiating the cumulative distribution function (CDF) [10].The PDFs for transformed variables were computed using the Jacobian matrix.Moments and statistics were also considered to derive asymptotic PDFs.

Event 1 (6 August 2011)
On 6 August 2011, a geomagnetic storm with a Dst index of −115 nT occurred (considered intense).Negative ionospheric disturbances were observed during this storm, with a vTEC value of 35.34 TECU being recorded the day before, while during and after the storm, values of 16.91 and 18.42 TECU were reached, respectively.The vTEC and Dst index graph for this event is shown in Figure 1.The Probability Density Function (PDF) results for this event, displayed in Figure 1, demonstrate the range of vTEC values before, during, and after the event.
of less than −100 nT, this study aims to unravel the ionospheric behavior durin disruptive events.By investigating the interplay between geomagnetic storms, s cles, and seasonal variations, this manuscript seeks to advance our understandin ionosphere's multifaceted role, ultimately benefiting global navigation and comm tion systems.

Data Used and Methodology
In this study, data for the Dst index were acquired from the website of the Ce Data Analysis for Geomagnetism and Space Magnetism at the University of Kyoto thon code was developed to plot the data.The criteria for obtaining the Dst ind focused on geomagnetic storms with Dst index values less than −100 nT.After iden the events, RINEX data for the selected station were downloaded, and the Total E Content (TEC) was calculated using GPSTEC software version 2.9.5.These TEC da used to create vTEC plots.Subsequently, Probability Density Functions (PDFs) w plied to the ionospheric plots using MATLAB R2017b.Our analysis involved categ ionospheric storms as positive or negative, examining maximum TEC values, mi Dst index values, solar and seasonal cycles, and local time.
For TEC calculation, the dual-frequency nature of the GPS system was uti assess ionospheric effects.The Total Electron Content (TEC) can be calculated usin measurements, where TEC = 9.52(R2 − R1), or pseudorange measurements, wher 9.52(R2 − R1) [7].The phase-based TEC calculation provides precise temporal var while the pseudorange method offers absolute values.The GPS observations w justed for satellite and receiver delays, multipath effects, and receiver noise [8].Ad ally, the PDF was used to analyze the probability distribution of variable values.T identifies regions of higher and lower probabilities for a continuous random v [9,10].The PDF for a distribution can be obtained by differentiating the cumulativ bution function (CDF) [10].The PDFs for transformed variables were computed u Jacobian matrix.Moments and statistics were also considered to derive asymptoti

Event 1 (6 August 2011)
On 6 August 2011, a geomagnetic storm with a Dst index of −115 nT occurre sidered intense).Negative ionospheric disturbances were observed during this with a vTEC value of 35.34 TECU being recorded the day before, while during an the storm, values of 16.91 and 18.42 TECU were reached, respectively.The vTEC index graph for this event is shown in Figure 1.The Probability Density Functio results for this event, displayed in Figure 1, demonstrate the range of vTEC values during, and after the event.

Event 2 (26 September 2011)
The 26 September 2011 storms caused significant ionospheric alterations, with vTEC values reaching 77.32 TECU during the storm.Before the storm, the TEC value was 40.01 TECU, and they quickly recovered to 39.29 TECU after the storm, indicating a positive ionospheric storm.Although intense, this geomagnetic storm had a Dst index of −118 nT, suggesting it was not as perturbing as other events from the same solar cycle.Figure 2 illustrates the variations in vTEC and the geomagnetic index for this event.The PDF results in Figure 2 show uniform alterations in vTEC throughout the study region during the event.

Event 2 (26 September 2011)
The 26 September 2011 storms caused significant ionospheric alterations, wit values reaching 77.32 TECU during the storm.Before the storm, the TEC value w TECU, and they quickly recovered to 39.29 TECU after the storm, indicating a ionospheric storm.Although intense, this geomagnetic storm had a Dst index of − suggesting it was not as perturbing as other events from the same solar cycle.F illustrates the variations in vTEC and the geomagnetic index for this event.The sults in Figure 2 show uniform alterations in vTEC throughout the study region the event.

Event 3 (25 October 2011)
On 25 October 2011, the strongest geomagnetic storm of 2011 occurred, wit index reaching −134 nT and peaking at 6:00 UT.This storm led to positive iono disturbances, as evident in Figure 3, along with an increase in standard deviation estingly, the largest data dispersion is not observable at the peak of the storm bu during other times.Figure 3 shows the PDF results for this event, highlighting th increase in the study region, with a small area preserving its previous values due uniformity the day before the storm.

Event 4 (9 March 2012)
The event on 9 March 2012 had an intensity of −145 nT, peaking at 9:00 UT. ranking as the fifth most intense storm of Solar Cycle 24, it resulted in negative iono disturbances, as shown in Figure 4.The PDF results in Figure 4 reveal changes in th range during the event.Although the ionosphere experienced higher variations in gion after the event, its recovery was rapid, as the event only negatively impac ionosphere for one day.

Event 3 (25 October 2011)
On 25 October 2011, the strongest geomagnetic storm of 2011 occurred, with a Dst index reaching −134 nT and peaking at 6:00 UT.This storm led to positive ionospheric disturbances, as evident in Figure 3, along with an increase in standard deviation.Interestingly, the largest data dispersion is not observable at the peak of the storm but rather during other times.Figure 3 shows the PDF results for this event, highlighting the vTEC increase in the study region, with a small area preserving its previous values due to their uniformity the day before the storm.

Event 2 (26 September 2011)
The 26 September 2011 storms caused significant ionospheric alterations, wit values reaching 77.32 TECU during the storm.Before the storm, the TEC value w TECU, and they quickly recovered to 39.29 TECU after the storm, indicating a ionospheric storm.Although intense, this geomagnetic storm had a Dst index of − suggesting it was not as perturbing as other events from the same solar cycle.F illustrates the variations in vTEC and the geomagnetic index for this event.The sults in Figure 2 show uniform alterations in vTEC throughout the study region the event.

Event 3 (25 October 2011)
On 25 October 2011, the strongest geomagnetic storm of 2011 occurred, wit index reaching −134 nT and peaking at 6:00 UT.This storm led to positive iono disturbances, as evident in Figure 3, along with an increase in standard deviatio estingly, the largest data dispersion is not observable at the peak of the storm bu during other times.Figure 3 shows the PDF results for this event, highlighting th increase in the study region, with a small area preserving its previous values due uniformity the day before the storm.

Event 4 (9 March 2012)
The event on 9 March 2012 had an intensity of −145 nT, peaking at 9:00 UT. ranking as the fifth most intense storm of Solar Cycle 24, it resulted in negative iono disturbances, as shown in Figure 4.The PDF results in Figure 4 reveal changes in th range during the event.Although the ionosphere experienced higher variations in gion after the event, its recovery was rapid, as the event only negatively impac ionosphere for one day.The event on 9 March 2012 had an intensity of −145 nT, peaking at 9:00 UT.Despite ranking as the fifth most intense storm of Solar Cycle 24, it resulted in negative ionospheric disturbances, as shown in Figure 4.The PDF results in Figure 4 reveal changes in the vTEC range during the event.Although the ionosphere experienced higher variations in the region after the event, its recovery was rapid, as the event only negatively impacted the ionosphere for one day.