Low Ionosphere Under Influence of Strong Solar Radiation: Diagnostics and Modeling

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Article Low Ionosphere under Inﬂuence of Strong Solar Radiation: Diagnostics and Modeling

Vladimir A. Srećković 1,* , Desanka M. Šulić 2, Ljubinko Ignjatović 1 and Veljko Vujˇcić 3

1 Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia; [email protected] 2 Faculty of Ecology and Environmental Protection, University Union—Nikola Tesla, 11000 Belgrade, Serbia; [email protected] 3 Astronomical Observatory, Volgina 7, 11060 Belgrade, Serbia; [email protected] * Correspondence: [email protected]; Tel.: +381-(0)11-37-13-000

Featured Application: The presented data can be used in practice in different areas of science and in several possible ways: for an analysis of the Earth atmosphere; for the investigation of coupling atmospheric electricity with biological systems; for the identification and classification of solar X-ray flares; for obtaining the daytime atmosphere parameters induced by extreme solar radiation; and for understanding and preventing extreme space weather.

Abstract: Solar ﬂares (SFs) and intense radiation can generate additional ionization in the Earth’s atmosphere and affect its structure. These types of solar radiation and activity create sudden ionospheric disturbances (SIDs), affect electronic equipment on the ground along with signals from space, and potentially induce various natural disasters. Focus of this work is on the study of SIDs induced by X-ray SFs using very low frequency (VLF) radio signals in order to predict the impact of

SFs on Earth and analyze ionosphere plasmas and its parameters. All data are recorded by VLF BEL stations and the model computation is used to obtain the daytime atmosphere parameters induced

Citation: Srećković,V.A.; Šulić,D.M.; by this extreme radiation. The obtained ionospheric parameters are compared with results of other Ignjatović,L.; Vujˇcić,V. Low authors. For the first time we analyzed physics of the D-region—during consecutive huge SFs which Ionosphere under Influence of Strong continuously perturbed this layer for a few hours—in detail. We have developed an empirical model Solar Radiation: Diagnostics and of the D-region plasma density and gave a simple approximative formula for electron density. Modeling. Appl. Sci. 2021, 11, 7194. https://doi.org/10.3390/app11167194 Keywords: observations; solar radiation; sun activity; atmosphere; disturbances; modeling

Academic Editor: Harry D. Kambezidis

Received: 5 July 2021 1. Introduction Accepted: 1 August 2021 Published: 4 August 2021 In today’s science, special attention is given to the extreme weather events, climate change, preservation, and protection, because they have been identiﬁed as crucial for sus-

Publisher’s Note: MDPI stays neutral tainable development in our century. Consequently, a very important question nowadays with regard to jurisdictional claims in in modern society is: can we predict the magnitude of impact of explosive solar events published maps and institutional afﬁl- (such as solar ﬂares) on Earth, humans, electronic equipment, and nature in general? By iations. analyzing past instances of these phenomena, we cannot predict the occurrence of each new event itself with certainty, but we can statistically estimate the consequences of phenomena on ionospheric parameters, perhaps predict damage to electronic equipment, predict disruption of GPS, etc. The ionosphere is a part of the atmosphere that contains ionized gases with various Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. kinds of particles, ions, and tens of different species [1–4] with the degree of ionization This article is an open access article which depends mainly on the incident radiation that is solar extreme ultraviolet and X-ray distributed under the terms and radiation [5,6]. This ionizing solar radiation depends on the Sun activity during the solar conditions of the Creative Commons cycle and varies around order of magnitude during the solar minimum and the solar Attribution (CC BY) license (https:// maximum. Furthermore, ionosphere as a huge segment of atmosphere has a tendency to be creativecommons.org/licenses/by/ constantly separated in different regions D, E, and F, with different physical characteristics 4.0/). and chemistry [7–11] which depend on the incident radiation. During stronger solar activity,

Appl. Sci. 2021, 11, 7194. https://doi.org/10.3390/app11167194 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 7194 2 of 17

the violent solar radiation and activity can induce sudden ionospheric disturbances (SIDs) as well as affect electronic equipment on the ground and signals from space, disrupt GPS, and bring damage to power grid components as a consequence [12–15]. Furthermore, many investigations indicate potential connections between this extreme activity and natural disasters such as tropical cyclones or forest fires (see e.g., [16–18]). Signals of very low frequency (VLF) in the narrow band (3–30 kHz) of electromagnetic (EM) spectrum are generated in Earth’s atmosphere by natural sources such as lightning discharges and meteor showers, and likewise VLF EM can be created by man-made sources, e.g., radio emitters [19,20]. The sensitivity of propagation of man-made VLF signals in the lower ionosphere makes them an ideal tool for remote monitoring of this medium under unperturbed/perturbed conditions [9,21]. During solar flares (SFs) and consequently SID events, an increase in ionospheric electron concentration and other ionospheric parameters at all altitudes is noticeable. As a result of radiation effects, the solar-induced SID and plasma irregularities cause perturbations in the received amplitude and phase of VLF EM signals mainly in the D-region which is part of the ionosphere. In this contribution, we focus on amplitude and phase data of radio signals recorded by BEL system (Belgrade, Serbia) [22–24]. Emitted VLF signals [25] are constantly recorded by the equipment at BEL site since 2003. Intensity of X-ray flux during SFs, which are monitored by Geostationary Operational Environmental Satellite (GOES), are simultaneously analyzed with recorded data by BEL system of receivers. For these events, amplitude and phase perturbations are measured and analyzed during the daytime. The aim of this study is to accurately model the perturbed D-region. We determine ionospheric parameters during huge SFs which may continuously perturb this region for several hours. Furthermore, for the perturbed ionospheric D-region, we give a simple approximative formula for altitude-dependent electron density which makes results easy for use. The results presented here are ready for further use with a particular emphasis on the astrophysical applications, more precisely in the rapid investigation of the low ionosphere under the influence of strong solar radiation. The paper is structured as follows: in Section2 we describe techniques for monitoring the D-region and models for determination of electron densities; in Section3 we present and discuss the results of the investigation; and in Section4 conclusions are presented.

2. Methods 2.1. VLF Technique for Monitoring Low Altitude Ionosphere At ionosphere altitudes from 50 km up to 90 km (D-region), measurements mainly rely on EM wave propagation techniques [26]. In our study, synchronal monitoring of phase and amplitude of VLF narrow band radio signal data by the receivers during SFs occurrences were used to obtain daytime ionospheric parameters. For this reason, the perturbation of the VLF phase and amplitude was estimated as a difference between values of the perturbed signal induced by solar X-ray flare and signal in the normal condition. The analysis of VLF data was carried out simultaneously with the examination of the correlative solar X-ray fluxes collected from GOES satellite (see e.g., Figure S1). The intensity of X-ray irradiance was recorded by GOES satellite by X-ray sensors in the band 0.1–0.8 nm. We based our study on investigation of series of stronger flares, i.e., flares of C-, M-, and X-classes. For our study, the effects of A- and B-class flares on VLF signals are rarely recorded and were non-essential. During ionospheric disturbances, a standard numerical procedure for obtaining ionospheric daytime parameters and electron densities was used. It was based on a comparison of the recorded changes of amplitude and phase with the corresponding values obtained in simulations by the LWPC numerical software package [27,28] and Wait’s two-component exponential model, as presented in [26,29]. Appl. Sci. 2021, 11, 7194 3 of 17

2.2. Simulated VLF Signals The LWPC program package [30] can be used for simulation of VLF propagation along any particular great circle path (GCP) under various diurnal, seasonal, and solar cycle variations in the ionosphere. This program package commonly executes the calculations for all possible modes and was tested with experimental data. In the published papers, there are few models for simulation of VLF propagation in the Earth-ionosphere waveguide (EIWG), such as the FDTD method, modefinder, etc. [31,32]. These models have been applied in many studies for calculations of various ionospheric parameters when characteristics and the ionospheric state allow applying some approximations. In this contribution, by applying the LWPC code, the propagation of VLF signal was simulated for normal ionospheric condition, with the aim to estimate the best fitting pairs of Wait’s parameters H’nor and βnor (reflection height and slope of sharpness, respectively; nor denote normal ionosphere condition) to obtain values of VLF amplitude and phase as close as possible to the recorded data for a selected day [33]. The next step was to simulate propagation of VLF signal through EIWG in the perturbed lower ionosphere during the flare event induced by an increased X-ray flux. For this step, we needed monitored, i.e., observed, VLF data to examine the signal perturbations during the solar X-ray flare. We selected the pair of H’ and β and used it as input parameter in the LWPC code to obtain the VLF signals, i.e., the simulated data of amplitude and phase at the receiver site. The process was rerun until differences between the simulated signal (∆Asim and ∆Psim) for the disturbed and normal condition matched the measured ones ∆A and ∆P. After accomplishing a fair matching: ∆Asim ≈ ∆A and ∆Psim ≈ ∆P, the corresponding pair of H’per and βper was finally obtained (sim means simulated, per denote perturbed condition). The corresponding pair of H’per and βper was used for calculation of the electron density at a function of height for moments during the solar flare event (see schematic presentation in Figure S2). Electron densities were resolved from the observed VLF amplitude and phase perturbations by a trial-and-error method where density profile was adjusted until the simulated amplitude and phase paired with observed disturbed data, as explained in the above paragraph. In this way, by processing data, the acquired Wait’s parameters H’per and βper were used for our further calculations.

2.3. Procedure for Determination of Electron Density: Two-Component Exponential Model The procedure was based on the Wait’s two-component exponential model [34], which uses time-dependent parameters H’ with values 74–50 km and β with values 0.3–0.6 km−1, to describe the electron density height profile in the lower ionosphere. We note that there is a lack of agreement for sharpness values obtained by different models and techniques. Although the values of the β parameter are in the range between 0.3–0.6 km−1, in some papers β values are higher i.e., 1.0 km−1 at daytime and ~3.0 km−1 at nighttime conditions (see e.g., [35]). Such a deviation illustrates the general deficiency of precision in the research of the ionosphere D-region and the need for new and more precise methods and techniques for its investigation. This two-parameter system provides a model of a vertically stratified ionosphere with an electron density profile Ne that increases exponentially with altitude:

0 13 0 −3 Ne(h, H , β) = 1.43 · 10 exp(−β · H ) exp[(β − 0.15) · h] [m ]. (1)

Here, Ne and h are given in m−3 and km, respectively. The model [34] was successfully used in previous comparisons of VLF measurements and theory (e.g., [9,33]) and we also use it in our work. Important plasma quantities used for describing the characteristics of the D-region are height dependent conductivity parameter; ωr(h) deﬁned as

2 5 0 ωr(h) = ωp/ν(h) = 2.5 · 10 exp(β · (h − H )), (2) Appl. Sci. 2021, 11, 7194 4 of 17

−1 where ωp [s ] is defined as the plasma frequency and ν(h) is the effective electron- neutral collision frequency. Quantity H’ is the reflection height, meaning height at which 5 ωr(h) = 2.5 × 10 rad/s. The positive ion density can be approximated to be equal to the electron density at high altitudes where electron density has values larger than 108 m−3, while at lower altitudes the positive ion density is around 108 m−3 or can be calculated based on charge neutrality. As it was noted, the electron densities can be obtained from the observed VLF amplitude and phase perturbations by a trial-and-error method (see Sections 2.1 and 2.2) where density profile is adjusted until the simulated amplitude and phase (using LWPC code) match with observed data. In this way, the obtained Wait’s parameters H’per and βper can be used in Equation (1) for further calculations.

3. Results In this research we studied the amplitude (A) and phase (P) data, obtained by monitoring VLF signals emitted by worldwide transmitters during solar-induced SIDs. The VLF signals which we examined are so-called sky waves, which travel via Earth-ionosphere duct and fluctuate in real-time due to the physical conditions through duct [34]. On the contrary, so-called ground waves closely follow and interact with terrestrial surface, and are attenuating. This category of EM waves is not investigated here. All the data were registered by two receiver systems at the Belgrade site: AbsPAL and AWESOME. The stations can monitor VLF signals under different time resolutions. These kind of monitored data must be independently methodized and differently processed. The receivers can simultaneously collect several signals emitted by different emitters (located at different countries and territories) at the fixed frequencies. This makes it possible to monitor huge regions of the Earth and enables detection of local and global perturbations. The quality of the monitored data depends on the characteristics of the emitters, i.e., the geophysical location and the emitted power. Furthermore, the quality of the recorded data depends on the length of the VLF route, physical properties of the Earth-ionosphere duct, electromagnetic pollution, etc. The technicalities and description of the Belgrade site are presented in [22]. Location of emitters and the receiver site and GCPs of subionospherically propagating VLF signals are provided in Figure1 and also in Table S1 in online material. Here, we present our results of amplitude and phase perturbations on the GQD/22.10 kHz radio signal observed over a long time period. Behaviors of amplitude and phase data on VLF radio signals Appl. Sci. 2021, 11, x FOR PEER REVIEWinduced by different intensity of solar X-ray fluxes and observed on Belgrade5 of 20 site were

examined. These results are presented.

FigureFigure 1. 1. TheThe geographic geographic location location of Belgrade of Belgrade system of system VLF receivers of VLF (blue receivers circle) (blueand the circle) GQD and the GQD transmitter (red circles) (54.73° N, 2.88° W) Anthorn UK with GCP of sub‐ionospheric propagating transmitter (red circles) (54.73◦ N, 2.88◦ W) Anthorn UK with GCP of sub-ionospheric propagating VLF signal. VLF signal. The signal propagates from the GQD transmitter to the receiver site over the great circle distance of 1982 km along a short and mostly overland great circle path that covers two time zones (propagating from Anthorn (54.72° N, 2.88° W), UK to Belgrade (44.85° N, 20.38° E)—see Figure 1. The GQD transmitter is located in the UK, but a great segment of the radio signal propagates over path in the same time zone where the receiver is. We investigated VLF signal changes and observed that the shape of the signal curve changes dramatically with time. Characteristic examples of SID event that happened dur‐ ing occurrence of strong SF is presented in Figure 2. SF X3.6‐class on 9 October 2005 lasted from 09:42–10:08 UT with a peak at 09:59 UT. The dramatical changes of GQD amplitude and phase values at peak time can be observed.

Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 of 20

Figure 1. The geographic location of Belgrade system of VLF receivers (blue circle) and the GQD transmitter (red circles) (54.73° N, 2.88° W) Anthorn UK with GCP of sub‐ionospheric propagating VLF signal. Appl. Sci. 2021, 11, 7194 5 of 17

The signal propagates from the GQD transmitter to the receiver site over the great circle distance of 1982 km along a short and mostly overland great circle path that covers The signal propagates from the GQD transmitter to the receiver site over the great two time zones (propagating from Anthorn (54.72° N, 2.88° W), UK to Belgrade (44.85° N, circle distance of 1982 km along a short and mostly overland great circle path that covers 20.38°two E)—see time zones Figure (propagating 1. The GQD from Anthorntransmitter (54.72 is◦ N,located 2.88◦ W),in the UK UK, to Belgrade but a great (44.85 ◦segmentN, of the radio20.38◦ E)—seesignal propagates Figure1. The over GQD path transmitter in the is same located time in the zone UK, where but a great the segmentreceiver of is. theWe radio investigated signal propagates VLF signal over path changes in the and same observed time zone that where the the shape receiver of is.the signal curve changesWe dramatically investigated with VLF signaltime. changesCharacteristic and observed examples that the of shapeSID event of the that signal happened curve dur‐ ing changesoccurrence dramatically of strong with SF is time. presented Characteristic in Figure examples 2. SF X3.6 of SID‐class event on 9 that October happened 2005 lasted during occurrence of strong SF is presented in Figure2. SF X3.6-class on 9 October 2005 fromlasted 09:42–10:08 from 09:42–10:08 UT with UT a peak with at a peak09:59 at UT. 09:59 The UT. dramatical The dramatical changes changes of GQD of GQD amplitude andamplitude phase values and phase at peak values time at can peak be time observed. can be observed.

Figure 2. Example of VLF signal variations of GQD signal recorded at Belgrade station due to SF event X3.6-class at 09 Oct 2005 (start 09:42, peak 09:59, end 10:08 UT). At peak time the measured variations of amplitude and phase ∆A = 7.25 dB and ∆P = 50 deg, respectively.

The monitoring and investigation of VLF data was carried out simultaneously with the examination of the corresponding incoming solar X-ray fluxes [36,37]. The intensity of X-ray flux Ix is recorded by GOES satellite in the band 0.1–0.8 nm, available from [38] and [36]. SFs can be classified in categories based on the peak emission recorded by GOES satellite in the 0.1–0.8 nm band, namely from A-, B-, C-, M-, and X-classes. In the presence of SIDs, a standard numerical procedure for the estimation of plasma parameters is based on comparison of the recorded changes of amplitude and phase with the matching values acquired in simulations by the LWPC numerical software package [27,30] as explained in [26,29,39]. Furthermore, for details, see Section2.

3.1. Recorded Variations of VLF Amplitude and Phase Data In this paper we analyzed around 200 solar X-ray flares events starting from the year 2003. Intensity of those X-ray flares were in range from C1- to X17-class, 1 × 10−6 Wm−2 to 1.7 × 10−3 Wm−2, respectively. For each flare, we measured amplitude and phase perturbations on VLF signal, except when the transmitter was off-air. The amplitude perturbations were estimated as a difference between values of the perturbed amplitude Appl. Sci. 2021, 11, 7194 6 of 17

induced by X-ray flux and amplitude in the normal ionospheric condition ∆A = Aper − Anor. Phase perturbations were estimated as ∆P = Pper − Pnor. Data points of the observed GQD/22.10 kHz are shown in Figure3—amplitude and phase perturbations as a function of solar X-ray intensity. The range of size in amplitude and phase perturbations varies for different X-ray solar flares. The amplitude perturbations of GQD/22.10 kHz radio signal are distributed between enhancement and attenuation, which depends on signal frequency and the angle of reflection in a function of intensity of solar X-ray flux (see also [40]). On the GQD-BEL path, amplitude decreases during Appl. Sci. 2021, 11, x FOR PEER REVIEW occurrences for C-class solar flares (see Figure3). The size of amplitude perturbations is 7 of 20

proportional to the intensity of solar X-ray ﬂux. A phase change on this path is complicated, displaying an increase or decrease during independent to SF-class. During M-class solar ﬂares, amplitude perturbation is between rising and falling but there are more cases of rising, while during X class SF amplitudes always have positive enhancement.

Figure 3. (left) Observed amplitude perturbations on GQD/22.10 kHz radio signals due to solar Figure 3. (left) Observed amplitude perturbations on GQD/22.10 kHz radio signals due to solar X‐ X-ray flares, measured at Belgrade station during period (2003–2017) as a function of X-ray flux. ray flares,(right measured) Observed at phase Belgrade perturbations station underduring same period conditions. (2003–2017) Two hundred as a function events of of X solar‐ray X-ray flux. (right) Observedflares phase were examined. perturbations under same conditions. Two hundred events of solar X‐ray flares were examined. In order to visualize the distribution of the amplitude and phase data, we give Figure4. InIn order Figure 4to, a visualize rug plots ofthe VLF distribution data are displayed of the amplitude as marks along and anphase axis. data, A small we tick give on Figure 4. In Figurethe edge 4, of a the rug rug plots plot representsof VLF data each are individual displayed observation. as marks The along influence an axis. of different A small tick classes of SF explains the shape of the rug plots. Some grouping of ticks around ∆A = −2, on the edge of the rug plot represents each individual observation. The influence of dif‐ −1, −0.3, 0.8 dB can be noticed, which correspond to the influence of C-class of SF and ferentaround classes 3.4, of 6, SF 7 dB, explains which isthe due shape to M-class of the and rug X-class plots. SF, Some respectively. grouping Similarly, of ticks for around∆P, a ΔA = −2, −grouping1, −0.3, 0.8 of ticksdB can around be noticed, 3 and 5 degwhich can correspond be noticed, due to tothe C-class influence SF and of alsoC‐class around of SF and around−20 3.4, and 6, 20 7 dB, deg which correspond is due to M to‐class M-class. and Around X‐class 40, SF, 60 respectively. deg, some grouping Similarly, exists for ΔP, a groupingdue to X-classof ticks SF. around 3 and 5 deg can be noticed, due to C‐class SF and also around −20 and 20 deg which correspond to M‐class. Around 40, 60 deg, some grouping exists due to X‐class SF. Appl.Appl. Sci. Sci.2021 2021, 11, 11, 7194, x FOR PEER REVIEW 8 of 20 7 of 17

FigureFigure 4. A 4.rugA plot rug of plot two hundred of two hundreddata points. data (upper points. panel) ( Deltaupper amplitude panel) distribution. Delta amplitude (lower distribution. (lower panelpanel) Delta) Delta phase phase distribution, distribution, that appears that in appearsblue along in the blue X‐axis. along The points the X-axis. are sampled The from points are sampled from the kernel smooth distribution shown in black. the kernel smooth distribution shown in black. 3.2. Long Lasting Intense Solar Radiation: An Analysis of Strong SF 3.2. Long Lasting Intense Solar Radiation: An Analysis of Strong SF M3.7‐class SF that occurred on 9 September 2017 is an illustrative example of long‐ lasting intenseM3.7-class solar radiation SF that (~60 occurred min) which on 9induced September SID and 2017 caused is variation an illustrative in VLF example of long- signal.lasting Furthermore, intense solarthis example radiation is good (~60 for showing min) which the methodology induced SID of our and analysis. caused variation in VLF signal.In Figure Furthermore, 5, we present thissimultaneous example variations is good of for X‐ray showing flux, amplitude, the methodology and phase of our analysis. of GQD/22.10 kHz signals against universal time during the occurrence of M3.7‐class SF on 9 SeptemberIn Figure 2017.5, The we lower present panel simultaneous shows observed variations amplitude perturbations of X-ray flux, on GQD amplitude, and phase radioof GQD/22.10signals measured kHz at signalsthe Belgrade against station universal with calculated time values during (red the line). occurrence Middle of M3.7-class SF panelon 9shows September observed 2017. and calculated The lower phase panel perturbations shows observed(red line). Time amplitude variation perturbationsof X‐ on GQD rayradio flux measured signals measuredby the GOES at‐15 the satellite Belgrade on 9 September station with2017 is calculated on the upper values panel. (red line). Middle Shapespanel of showsthe VLF observedsignal parameters and calculated are observably phase modified perturbations similar to the (redshape line). of the Time variation of X‐ray flux. X-rayWe simulated flux measured propagation by theof VLF GOES-15 radio signal satellite through on the 9 September waveguide in 2017 the per is on‐ the upper panel. Appl. Sci. 2021, 11, x FOR PEER REVIEWturbedShapes D‐region of the induced VLF signalby additional parameters X‐ray radiation are observably for resolution modified of 1 min during similar9 of the 20 to the shape of the

flareX-ray duration ﬂux. using a procedure which relies on LWPC code.

FigureFigure 5. Simultaneous 5. Simultaneous variations variations of X‐ray flux, of delta X-ray amplitude, ﬂux, delta and amplitude, phase of GQD/22.10 and phase signal of GQD/22.10 signal against universal time during occurrence of M3.7‐class solar flare on 9 September 2017. (lower panelagainst) Observed universal amplitude time perturbations during occurrence on GQD, radio of M3.7-class signals measured solar ﬂareat the onBelgrade 9 September station 2017. (lower panel) andObserved calculated values. amplitude (middle perturbations panel) Observed on and GQD, calculated radio phase signals perturbations. measured (upper at panel the) Belgrade station and Timecalculated variation of values. X‐ray irradiance (middle measured panel) Observedby GOES‐15 and satellite. calculated phase perturbations. (upper panel) Time variationThe procedure of X-ray is explained irradiance in detail measured in Section by GOES-15 2. Parameters satellite. were obtained when the calculated amplitude and phase perturbations matched as well as possible with observed data (see lower panels of Figure 5). The obtained Wait’s parameters βper and H’per were used for our further calculations of ionosphere parameters. In Figure 6, calculated parameters are shown (obtained by the method explained in Section 2): time dependent effective reflection height H’, sharpness β, and electron density at reference height during occurrences of M3.7‐class solar flare on 9 September 2017 from lower to upper panel, respectively. Appl. Sci. 2021, 11, 7194 8 of 17

We simulated propagation of VLF radio signal through the waveguide in the perturbed D-region induced by additional X-ray radiation for resolution of 1 min during the flare duration using a procedure which relies on LWPC code. The procedure is explained in detail in Section2. Parameters were obtained when the calculated amplitude and phase perturbations matched as well as possible with observed data (see lower panels of Figure5). The obtained Wait’s parameters βper and H’per were used for our further calculations of ionosphere parameters. In Figure6, calculated parameters are shown (obtained by the method explained in Section2): time dependent effective reflection height H’, sharpness β, and electron density Appl. Sci. 2021, 11, x FOR PEER REVIEW 10 of 20 at reference height during occurrences of M3.7-class solar flare on 9 September 2017 from lower to upper panel, respectively.

FigureFigure 6. 6. TheThe sharpness sharpness β,β effective, effective reflection reﬂection height height H’,H and’, and electron electron density density at reference at reference height height h = 74 km during occurrences of M3.7‐class solar flare on 9 September 2017 from lower to upper panel, h = 74 km during occurrences of M3.7-class solar ﬂare on 9 September 2017 from lower to upper respectively. panel, respectively.

TheThe variation variation of of HH’(t)’(t)with with time time has has expected expected behavior, behavior, i.e., i.e., after after starting starting SF, SF, it it drops drops droppeddropped rapidly rapidly to to minimum, minimum, as as expected, expected, and and after after peak peak time time of of X X-ray,‐ray, it it slowly keeps risingrising to to referent referent value value (see (see Figure Figure 66 middle middle panel). panel). The The behavior behavior of β of(t) βplot(t) plot is in is correla in cor-‐ tionrelation with with changes changes of X‐ ofray X-ray flux. flux. At 11:04 At 11:04 UT, peak UT, peak of the of solar the solar X‐ray X-ray flux reached flux reached Ix = −5 −2 3.78Ix =∙10 3.78 Wm× 10−, and5 Wm induced−2, and perturbations induced perturbations of amplitude of amplitude and phase and ΔA phase= 5.6 dB∆A and= 5.6 ΔP dB = −and5.6 deg,∆P = respectively.−5.6 deg, respectively. For the sharpness, For the we sharpness, obtained values we obtained β = 0.49 values km−1 and,β = 0.49for reflec km−‐1 tion,and, height for reflection, H’= 62.5 height km. ThisH’= means 62.5 km. that This during means this that SF duringthe reflection this SF height the reflection drops by height 11.5 km.drops We by obtained 11.5 km. that We the obtained electron that density the electron increased density at reference increased height at referenceh = 74 km height from 2.2h =∙10 748 m km−3 fromto 6.7 2.2∙1010× m10−38. m−3 to 6.7 × 1010 m−3.

3.3.3.3. Intense Intense Solar Solar Radiation: Radiation: Consecutive Consecutive Strong Strong SF SF WeWe analyzed datadata forfor 10 10 June June 2014 2014 as as an an example example of of a day a day with with several several strong strong and and suc- successivecessive SFs SFs that that induced induced SIDs SIDs and and dramatically dramatically affected affected the the VLF VLF radio radio signal. signal. Speciﬁcally, Specifi‐ cally,on 10 on June 10 2014, June the 2014, Sun the released Sun released several consecutiveseveral consecutive SFs including SFs including two major two X-class major solar X‐ classﬂares solar that flares occurred that one occurred after the one other after as the shown other in as Table shown1. in Table 1.

Table 1. Data of amplitude and phase perturbations of VLF signal induced by different SF events on 10 June 2014.

SID VLF Data Time [UT] at Peak Time ΔP Ix max Active Re‐ SF Start Peak End ΔA [dB] [deg] XL[Wm−2] gion C3.9 08:17 08:25 08:32 −1.5 0.1 3.97 × 10−6 2087 C5.1 09:17 09:31 09:40 −2 −7 5.18 × 10−6 2087 C5.0 10:04 10:17 10:25 −0.5 −9 5.06 × 10−6 2087 X2.2 11:36 11:42 11:44 7.3 32 2.22 × 10−4 2087 X1.5 12:36 12:52 13:03 7.4 15 1.55 × 10−4 2087 Appl. Sci. 2021, 11, x FOR PEER REVIEW 11 of 20

Figure 7 presents simultaneous variations of X‐ray flux, amplitude, and phase of GQD radio signal against universal time during five successive flares on 10 June 2014. Appl. Sci. 2021, 11, 7194 From Figure 7, one can see that VLF and X‐ray flux peaks happened simultaneously, i.e., 9 of 17 intense radiation instantly disturbed ionosphere, creating SIDs and resulting in perturbed VLF signal. Accurately, variation of amplitude and phase on GQD signals during X‐class SFs re‐ actTable as 1.a wellData‐defined of amplitude enhancement and phase that perturbations follows the ofX‐ VLFray radiation signal induced maximum. by different SID VLF SF events on changes10 June 2014. at the time of the maximum of SF of X2.2‐ and X1.5‐classes are ΔA ~ 7.3 dB, ΔP ~ 32° and ΔA ~ 7.4 dB, ΔP ~ 15°, respectively. During C‐class SFs, perturbations of amplitude SID VLF Data and phase are notTime well [UT]‐defined but they exist. These C‐class SFs with similar characteris‐ at Peak Time tics produce increased ionization in the ionospheric D‐region, generating amplitude per‐ ∆P I max Active turbationsSF of StartGQD radio Peak signal with End a decrease∆A [dB]in amplitude up to 2 dBx with changes in [deg] XL [Wm−2] Region phase up to ΔP = 10 deg. C3.9 08:17 08:25 08:32 −1.5 0.1 3.97 × 10−6 2087 For the first X‐class flare, it should be emphasized that the development to the max‐ C5.1 09:17 09:31 09:40 −2 −7 5.18 × 10−6 2087 imum flux of X‐ray lasted 6 minutes, and after 2 minutes, the additional radiation was C5.0 10:04 10:17 10:25 −0.5 −9 5.06 × 10−6 2087 completed. The graph of measured phase changes is characterized by a turning point X2.2 11:36 11:42 11:44 7.3 32 × −4 2087 when the phase stops declining and begins to rise, but not so well‐defined2.22 as10 for another × −4 event.X1.5 During 12:36 this X2.2‐class 12:52 flare, 13:03the height of7.4 reflection dropped15 from1.55 74 km10 to 59.1 km2087 following the increase in β from 0.30 km−1 to 0.53 km−1. DuringFigure 7the presents time interval simultaneous of 16 minutes, variations X‐ray radiation of X-ray of flux, the second amplitude, X‐class and flare phase of reachedGQD radio a maximum. signal against During the universal same interval, time during the shape five of successive the phase changes flares on is more 10 June 2014. noticeableFrom Figure with7, well one‐defined can see turning that VLF points and on X-ray the graph flux peaks of measured happened phase simultaneously, values as a i.e., functionintense radiationof time. Throughout instantly disturbedthis X1.5‐class ionosphere, flare, the creatingheight of SIDsreflection and resultingdropped from in perturbed −1 −1 74VLF km signal. to 60.85 km following the increase in β from 0.30 km to 0.54 km

Figure 7. 7. SimultaneousSimultaneous variations variations of X of‐ray X-ray flux, flux,amplitude, amplitude, and phase and of phase GQD/22.10 of GQD/22.10 radio signal radio signal against universal universal time time during during five five successive successive flares flares on 10 onJune 10 2014. June (lower 2014. panel (lower) Perturbation panel) Perturbation of of amplitude; (middle panel) Perturbation of phase; (upper panel) X‐ray flux. amplitude; (middle panel) Perturbation of phase; (upper panel) X-ray flux. Figure 8 shows calculated values of time‐dependent effective reflection height H’ and Accurately, variation of amplitude and phase on GQD signals during X-class SFs react the sharpness β (with the time resolution of one minute) for the time period 08:00 to 14:30 UTas a during well-defined occurrences enhancement of five solar that flare follows on 10 June the X-ray 2014. radiation maximum. SID VLF changes at the time of the maximum of SF of X2.2- and X1.5-classes are ∆A ~ 7.3 dB, ∆P ~ 32◦ and ∆A ~ 7.4 dB, ∆P ~ 15◦, respectively. During C-class SFs, perturbations of amplitude and phase are not well-defined but they exist. These C-class SFs with similar characteristics produce increased ionization in the ionospheric D-region, generating amplitude perturbations of GQD radio signal with a decrease in amplitude up to 2 dB with changes in phase up to ∆P = 10 deg. For the first X-class flare, it should be emphasized that the development to the maximum flux of X-ray lasted 6 minutes, and after 2 minutes, the additional radiation was completed. The graph of measured phase changes is characterized by a turning point when the phase stops declining and begins to rise, but not so well-defined as for another event. During this X2.2-class flare, the height of reflection dropped from 74 km to 59.1 km following the increase in β from 0.30 km−1 to 0.53 km−1. Appl. Sci. 2021, 11, x FOR PEER REVIEW 12 of 20

Appl. Sci. 2021, 11, 7194 10 of 17 During occurrences of X2.2‐ and X1.5‐class SFs, the variation of H’(t) with time has expected behavior: after SF starts, it drops rapidly to a minimum as expected, and after X‐ ray flux peaks, it keeps rising to a referent value (see Figure 8 middle panel). Behavior of β(t) is correlatedDuring thewith time the shape interval of recorded of 16 minutes, increase in X-ray amplitude. radiation Practically of the during second this X-class flare SF of X‐class, it rises rapidly to a maximum as expected after the peak time of X‐ray flux reached a maximum. During the same interval, the shape of the phase changes is more and drops to a referent value. At 11:42 UT, during peak time of X2.2‐class SF, with the solarnoticeable X‐ray flux with Ix = well-defined2.22∙10−4 Wm−2, turning the reflection points height on the lowers graph by 14.9 of measured km to a value phase of values as a H’=function 59.1 km ofand time. the sharpness Throughout values this rises X1.5-class to β = 0.53 km flare,−1. At the peak height time of12:52 reflection UT, during dropped from −1 −1 X1.574‐ kmclass to SF 60.85 with kmthe solar following X‐ray flux the increaseIx = 1.55∙10 in−4 βWmfrom−2, the 0.30 reflection km to height 0.54 lowers km to H’= 60.85Figure km and8 shows the sharpness calculated values values rises of to time-dependent a same value as for effective X2.2. During reflection C‐class height H’ and SFs,the the sharpness variation ofβ (withreflection the height time resolution H’ and the sharpness of one minute) β are in for correlation the time with period X‐ray 08:00 to 14:30 flux.UT during occurrences of five solar flare on 10 June 2014.

FigureFigure 8. Simultaneous 8. Simultaneous variations variations of X‐ray of flux, X-ray effective flux, effective reflection reflectionheight H’, and height the Hsharpness’, and the β sharpness β duringduring the the occurrence occurrence of five of successive five successive flares on flares 10 June on 2014 10 June are shown 2014 are in panels shown from in panelsupper to from upper to lower one, respectively. lower one, respectively. It can be noted that it is very difficult to analyze and model the D‐region in the case During occurrences of X2.2- and X1.5-class SFs, the variation of H’(t) with time has of strong SFs. Therefore, the results related to ionospheric parameters of some authors haveexpected some deviations behavior: (see after Section SF starts, 3.5). An it even drops more rapidly difficult to case a minimum for modeling as expected,is when and after weX-ray have fluxconsecutive peaks, flares it keeps which rising are continuously to a referent perturbing value (see the Figure D‐region.8 middle During panel). con‐ Behavior secutiveof β(t) huge is correlated SFs which with repeatedly the shape perturb of recordedthis region increase for a few in hours, amplitude. the ionosphere Practically during lacksthis time SF offor X-class, regeneration it rises and rapidly returns to to a anormal maximum condition. as expected The flares afterfollow the each peak other, time of X-ray literallyflux and sticking drops together to a referent and amplifying value. At their 11:42 influence UT, during in the peak D‐region. time Therefore, of X2.2-class we SF, with the havesolar the X-ray case that flux aI xweaker = 2.22 SF,× i.e.,10− 4X1.5Wm‐class,−2, theinduces reflection similar height changes lowers in amplitude by 14.9 as km to a value theof strongerH’ = 59.1 flare km of class and theX2.2 sharpness (ΔA ~ 7.4 dB values and ΔA rises ~ 7.3, to respectively).β = 0.53 km It −is1 also. At necessary peak time 12:52 UT, toduring point out X1.5-class that the solar SF with zenith the angle solar and X-ray the flux durationIx = 1.55of flare× 10have−4 Wman impact−2, the on reflection the height parameters of the D‐region. lowers to H’ = 60.85 km and the sharpness values rises to a same value as for X2.2. During Parameters H’ and β are used to determine the spatial structures of disturbances in theC-class lower ionosphere. SFs, the variation The change of reflection in distribution height of ionizationH’ and the at sharpnessthe D‐regionβ dueare to in flare correlation with existenceX-ray flux. can be illustrated by the electron density altitude profile changes. We present the heightIt can profile be noted of electron that density it is very at peak difficult time to of analyzefive successive and model flares on the 10 D-region June 2014 in the case of instrong Figure SFs.9. At Therefore, unperturbed the ionospheric results related conditions to ionospheric (black line), parameters there is a moderate of some in authors‐ have creasesome in deviations electron density (see Sectionfrom 2 × 3.5107). m An−3 at even 60 km more height, difficult to about case 2 × for109 m modeling−3 at the upper is when we have barrierconsecutive of the D‐ flaresregion whichi.e., at 90 are km continuously height. These three perturbing lines have the almost D-region. the same During slope. consecutive huge SFs which repeatedly perturb this region for a few hours, the ionosphere lacks time for regeneration and returns to a normal condition. The flares follow each other, literally sticking together and amplifying their influence in the D-region. Therefore, we have the case that a weaker SF, i.e., X1.5-class, induces similar changes in amplitude as the stronger flare of class X2.2 (∆A ~ 7.4 dB and ∆A ~ 7.3, respectively). It is also necessary to point out that the solar zenith angle and the duration of flare have an impact on the parameters of the D-region. Parameters H’ and β are used to determine the spatial structures of disturbances in the lower ionosphere. The change in distribution of ionization at the D-region due to flare Appl. Sci. 2021, 11, 7194 11 of 17

existence can be illustrated by the electron density altitude profile changes. We present the height profile of electron density at peak time of five successive flares on 10 June 2014 in

Appl. Sci. 2021, 11, x FOR PEER REVIEWFigure 9. At unperturbed ionospheric conditions (black line), there13 of is 20 a moderate increase in electron density from 2 × 107 m−3 at 60 km height, to about 2 × 109 m−3 at the upper barrier of the D-region i.e., at 90 km height. These three lines have almost the same slope. Totally different different behavior behavior and slope and have slope lines haveat peak lines times at of X peak‐class times SF (dashed of X-class orange SF (dashed orange andand pink pink lines lines)) are already are already 2∙109 m− 23 at× 6010 km9 m height.−3 at These 60 km variation height. in altitude These profile variation of in altitude proﬁle electronof electron density density are essential are essentialfor the VLF forpropagation the VLF characteristics. propagation characteristics.

FigureFigure 9. 9.TheThe height height profile profile of electron of electron density at density peak time at for peak five time successive for five flares successive on 10 June flares on 10 June 2014. 2014. 3.4. Approximative Expressions 3.4. Approximative Expressions FigureFigure 10 shows10 shows variation variation of X‐ray flux, of X-ray as measured flux, asby measuredGOES‐15 satellite, by GOES-15 and the satellite, and the correspondingcorresponding electron electron density density evaluated evaluated at reference atheight reference 74 km versus height universal 74 km time versus universal time UTUT during during five five successive successive flares on flares 10 June on 2014. 10 The June red 2014. line presents The red results line obtained presents results obtained usingusing simple simple and andaccurate accurate approximative approximative Equation (3) Equationbased on a least (3)‐ basedsquares on method. a least-squares method. Circles presented as Ne are obtained by the method mentioned above. For these explosive Appl. Sci. 2021, 11, x FOR PEER REVIEW Ne 14 of 20 XCircles‐class solar presented flares, electron as densityare obtained grows by almost by the two method orders of mentioned magnitude. above. For these explosive X-class solar flares, electron density grows by almost two orders of magnitude.

FigureFigure 10. Variation 10. Variation of X‐ray of flux, X-ray as measured flux, as by measured GOES‐15 satellite, by GOES-15 and the corresponding satellite, and electron the corresponding electron densitydensity evaluated evaluated at reference at reference height 74 height km versus 74 kmuniversal versus time universal UT during timefive successive UT during flares five successive flares on on 10 June 2014. The red line presents results obtained using simple approximative Equation (3). With10 June circles 2014. are presented The red Ne lineobtained presents by the mentioned results obtained above method. using simple approximative Equation (3). With circles are presented Ne obtained by the mentioned above method. To enable the better and more adequate use of data, we give electron density results obtained using simple approximative formula, which is logarithmic and represented by a second‐degree polynomial with height‐dependent coefficients a1(h), a2(h), a3(h):

2 logNe (, h Ix ) a() h a()log h Ix a()(log) h Ix (3) 12 3 Here, Ix is solar X‐ray flux (Wm−2), and h is height (km). Table 2 presents data of the selected fits. The whole table with smaller step in altitudes is available in the Supplemen‐ tary material (see Table S2.)

Table 2. Data of the selected heights.

Height (km) a1(h) a2(h) a3(h) 50 10.3249 0.97123 0.06168 55 12.94731 1.65399 0.11341 60 15.56972 2.33674 0.16513 65 18.19213 3.0195 0.21686 70 20.81454 3.70226 0.26858 75 23.43695 4.38501 0.32031 80 26.05936 5.06777 0.37203

To obtain a formula that applies to all conditions and input parameters, we analyzed all investigated SF cases from this study and obtained coefficients. We have selected the most appropriate ones (Table 2 and Table S2) that cover all the examples and can honestly satisfy the accuracy. Moreover, in order to check the validity of the formula, we presented the values of the approximative formula together with the calculations from this work and also of other authors in Figure S4. One can see that it is in good agreement with all relevant data. Surely a more complicated formula could have been chosen, but there was no need Appl. Sci. 2021, 11, 7194 12 of 17

To enable the better and more adequate use of data, we give electron density results obtained using simple approximative formula, which is logarithmic and represented by a second-degree polynomial with height-dependent coefﬁcients a1(h), a2(h), a3(h):

2 log Ne(h, Ix) = a1(h) + a2(h) · log Ix + a3(h) · (log Ix) (3)

Here, Ix is solar X-ray ﬂux (Wm−2), and h is height (km). Table2 presents data of the selected ﬁts. The whole table with smaller step in altitudes is available in the Supplementary material (see Table S2.)

Table 2. Data of the selected heights.

To obtain a formula that applies to all conditions and input parameters, we analyzed all investigated SF cases from this study and obtained coefficients. We have selected the most appropriate ones (Table2 and Table S2) that cover all the examples and can honestly satisfy the accuracy. Moreover, in order to check the validity of the formula, we presented the values of the approximative formula together with the calculations from this work and also of other authors in Figure S4. One can see that it is in good agreement with all relevant data. Surely a more complicated formula could have been chosen, but there was no need for such accuracy because it is known that the values of the D-region parameters can vary literally by an order of magnitude. The idea was to make the formula easy to use as well as to enable rapid calculations and analysis. During this study, two hundred events of solar X-ray flares were examined. The results were obtained on the basis of VLF and satellite data and static analysis of numerous events. One of the main results is that we can obtain values of electron density at any height, against maximum intensity of X-ray flux by expression (3). Figure 11 shows observed amplitude and phase perturbations on GQD/22.10kHz radio signals, due to solar X-ray flares, measured at the Belgrade station (during 2003–2017), as a function of X-ray flux. Values of electron density at reference height h = 74 km, against maximum intensity of X-ray flux obtained by Equation (3), are presented. The color of the point is proportional to the electron density values. This makes it easier to analyze the D-region during different solar disturbances. In modern times, one of the largest solar flare measured with instruments occurred on 28 October 2003 (X17.2-class, Ix = 1.72 × 10−3 Wm−2). Coronal mass ejection (CME) was associated with the 28 October 2003 X17.2 solar flare. In Figure S3 in Supplementary Material, VLF and satellite data are presented. The approximative Equation (3) allows evaluation of electron density even for this extremely large SF. Lower panels in Figure S3 present perturbations of amplitude and perturbation of phase on the same day. At the peak time, amplitude changes ∆A = 7.2 dB and phase changes ∆P = 76 deg (it is the farthest point on the right in Figure 11). In Figure S3, the upper panel variations of X-ray irradiance are shown, as measured by GOES-15 satellite, as well as the evaluated electron density at reference height versus universal time UT on 28 October 2003 during occurrence of huge X17.2-class SF. Appl. Sci. 2021, 11, x FOR PEER REVIEW 15 of 20

for such accuracy because it is known that the values of the D‐region parameters can vary literally by an order of magnitude. The idea was to make the formula easy to use as well as to enable rapid calculations and analysis. During this study, two hundred events of solar X‐ray flares were examined. The re‐ sults were obtained on the basis of VLF and satellite data and static analysis of numerous events. One of the main results is that we can obtain values of electron density at any height, against maximum intensity of X‐ray flux by expression (3). Figure 11 shows observed amplitude and phase perturbations on GQD/22.10kHz ra‐ dio signals, due to solar X‐ray flares, measured at the Belgrade station (during 2003–2017), as a function of X‐ray flux. Values of electron density at reference height h = 74 km, against Appl. Sci. 2021, 11, 7194 maximum intensity of X‐ray flux obtained by Equation (3), are presented. The color of the13 of 17 point is proportional to the electron density values. This makes it easier to analyze the D‐ region during different solar disturbances.

FigureFigure 11. (left) 11. Observed(left) Observed amplitude amplitude perturbations perturbations on GQD/22.10 on GQD/22.10 radio signals, radio signals, due to duesolar to X solar‐ray X-ray flares, flares,measured measured at Belgrade at Belgrade during during (2003–2017), (2003–2017), as a function as a function of X‐ray of flux. X-ray (right) flux. ( Sameright) as Same left asbut left but for observed phase perturbations. Two hundred events of solar X‐ray flares were examined. Values for observed phase perturbations. Two hundred events of solar X-ray flares were examined. Values of electron density at reference height, against maximum intensity of X‐ray flux obtained by Equa‐ of electron density at reference height, against maximum intensity of X-ray flux obtained by Equation tion (3) are presented. The color of the point is proportional to the electron density values change— darker(3) color are indicates presented. larger The color values of of the electron point is density. proportional to the electron density values change—darker color indicates larger values of electron density.

In3.5. modern Comparison times, of one Obtained of the Ionospheric largest solar Parameters flare measured with instruments occurred on 28 October 2003 (X17.2‐class, Ix = 1.72 × 10−3 Wm−2). Coronal mass ejection (CME) was As it was said in Section2, with the sharpness parameter β, which usually takes associated with the 28 October 2003 X17.2 solar flare. In Figure S3 in Supplementary Ma‐ values 0.3–0.6 km−1, and with a reference height H’ with values in range 74–50 km, one can terial, VLF and satellite data are presented. The approximative Equation (3) allows evalu‐ describe the electron density height profile, rate coefficients, etc. in the lower ionosphere. ation of electron density even for this extremely large SF. Lower panels in Figure S3 pre‐ We noted that there is a lack of agreement for sharpness values obtained by different sent perturbations of amplitude and perturbation of phase on the same day. At the peak models and techniques. Although the values of the β parameter are in the range between time, amplitude changes ΔA = 7.2 dB and phase changes ΔP = 76 deg (it is the farthest 0.3–0.6 km−1, in some papers β values are higher, i.e., 1.0 km−1 at daytime and ~3.0 km−1 point on the right in Figure 11). In Figure S3, the upper panel variations of X‐ray irradiance at nighttime (see e.g., [35]). Such a deviation illustrates the general deficiency of precision are shown, as measured by GOES‐15 satellite, as well as the evaluated electron density at in the ionosphere D-region research and the need for new and more precise methods reference height versus universal time UT on 28 October 2003 during occurrence of huge and techniques for its investigation. Therefore, we presented a comparison of obtained X17.2‐class SF. ionospheric parameters with the other authors. The sharpness parameter β and reflection height H’ (red squares) calculated in present work are plotted in Figures 12 and 13 together with results of other authors [41–44]. In Table S3, one can find the data of amplitude and phase perturbations of the VLF signal and the ionospheric parameters induced by different SF events which were also analyzed in this study. In Figure S4, we also give the electron density at reference height evaluated from the data presented in Figures 12 and 13. We can point out that the results of the sharpness parameter β and reflection height H’ presented in this paper are in good agreement with the results of most authors found in the available literature. Appl. Sci. 2021, 11, x FOR PEER REVIEW 16 of 20

3.5. Comparison of Obtained Ionospheric Parameters As it was said in Section 2, with the sharpness parameter β, which usually takes val‐ ues 0.3–0.6 km−1, and with a reference height H’ with values in range 74–50 km, one can describe the electron density height profile, rate coefficients, etc. in the lower ionosphere. We noted that there is a lack of agreement for sharpness values obtained by different mod‐ els and techniques. Although the values of the 𝛽 parameter are in the range between 0.3– 0.6 km−1, in some papers 𝛽 values are higher, i.e., 1.0 km−1 at daytime and ~3.0 km−1 at nighttime (see e.g., [35]). Such a deviation illustrates the general deficiency of precision in the ionosphere D‐region research and the need for new and more precise methods and techniques for its investigation. Therefore, we presented a comparison of obtained iono‐ spheric parameters with the other authors. The sharpness parameter β and reflection height H’ (red squares) calculated in pre‐ sent work are plotted in Figures 12 and 13 together with results of other authors [41–44]. In Table S3, one can find the data of amplitude and phase perturbations of the VLF signal and the ionospheric parameters induced by different SF events which were also analyzed in this study. In Figure S4, we also give the electron density at reference height evaluated from the data presented in Figures 12 and 13. We can point out that the results of the sharpness parameter β and reflection height H’ presented in this paper are in good agree‐ Appl. Sci. 2021, 11, 7194 ment with the results of most authors found in the available literature. 14 of 17

Appl. Sci. 2021, 11, x FOR PEER REVIEW 17 of 20

FigureFigure 12. 12.TheThe effective effective reflection reﬂection height height (red (red squares) squares) calculated calculated for for this study isis plottedplotted together together withwith the theresults results of other of other authors authors [41–44]. [41–44 ].

Figure 13. Same as in Figure 12 but for the sharpness parameter. Figure 13. Same as in Figure 12 but for the sharpness parameter.

It Itcan can be benoticed noticed that, that, when when the theintense intense solar solar flux fluxincreases increases during during SF, values SF, values of the of the reflectionreflection height height H’ Hdecrease.’ decrease. Looking Looking at Figure at Figure 12, generally 12, generally speaking, speaking, there thereis a good is a good agreementagreement in the in the values values of the of reflection the reflection height height from the from literature the literature [41–44]. [ When41–44 ].the When in‐ the tensity of radiation increases from −6 −3 −2 intensity of radiation increases10 from to 1010−6Wmto 10(i.e.,−3 Wm when−2 we(i.e., go when from wenormal go from condi normal‐ tions of the ionosphere to the perturbed ionosphere due to strong X‐class SF), the reflec‐ conditions of the ionosphere to the perturbed ionosphere due to strong X-class SF), the tions go down from 74 km to 50 km. Figure 13 gives the simple dependence for H’ with reflections go down from 74 km to 50 km. Figure 13 gives the simple dependence for H’ the well‐defined slope with the well-defined slope = + · ( ) y ykk12k1 klog(2 log Ix ),Ix ,(4) (4)

where k1 = 36.85032 and k2 =−6.12059. A larger deviation can be noticed only in the results from Pandey et al., where a very strong flare of X‐class with the Ix~10−3 Wm−2 induce a very small decrease in the reflection height (H’~ 65 km), like the M3‐class gives. Looking at the Figure 13, one can see a totally different situation for the results of sharpness parameter. Generally speaking, sharpness parameter β increases with the in‐ crease in X radiation intensity. However, the results are more scattered with the huge dis‐ agreement for the cases of strong X‐class solar flares (right corner of the Figure) due to results of Gavrilov et al. [44]. These results of Gavrilov et al. deviate a lot from the slope obtained from the results of other authors. Excluding the results from Gavrilov et al., we obtain for the β a linear dependence, as in Equation (4), where now k1 = 0.89756 and k2 = 0.09654. Generally, the results show that electron density can be obtained by processing the observed amplitude and phase perturbations with a specially developed method. More precisely, we obtained parameters H’ and β which were further used to obtain the electron density for different classes of SF starting from usual to extreme. The parameters are in good agreement with the most of the existing data from the literature. As expected, the electron density time variation during solar‐induced SIDs follows the variation of the reg‐ istered solar GOES flux. As a conclusion, Ne varies in time and height (few orders of mag‐ nitude) during SFs. Appl. Sci. 2021, 11, 7194 15 of 17

where k1 = 36.85032 and k2 =−6.12059. A larger deviation can be noticed only in the results from Pandey et al., where a very strong flare of X-class with the Ix~10−3 Wm−2 induce a very small decrease in the reflection height (H’~ 65 km), like the M3-class gives. Looking at the Figure 13, one can see a totally different situation for the results of sharpness parameter. Generally speaking, sharpness parameter β increases with the increase in X radiation intensity. However, the results are more scattered with the huge disagreement for the cases of strong X-class solar flares (right corner of the Figure) due to results of Gavrilov et al. [44]. These results of Gavrilov et al. deviate a lot from the slope obtained from the results of other authors. Excluding the results from Gavrilov et al., we obtain for the β a linear dependence, as in Equation (4), where now k1 = 0.89756 and k2 = 0.09654. Generally, the results show that electron density can be obtained by processing the observed amplitude and phase perturbations with a specially developed method. More precisely, we obtained parameters H’ and β which were further used to obtain the electron density for different classes of SF starting from usual to extreme. The parameters are in good agreement with the most of the existing data from the literature. As expected, the electron density time variation during solar-induced SIDs follows the variation of the registered solar GOES flux. As a conclusion, Ne varies in time and height (few orders of magnitude) during SFs.

4. Discussion and Conclusions In this paper we analyzed around 200 solar X-ray flares events during the 2003–2017 period. The perturbed daytime VLF amplitude and phase data are obtained by recording the GQD/22.10 kHz radio signal for a GCP = 1982 km between the transmitter in Anthorn, UK and the receiver in Belgrade, Serbia. We inspect the magnitude of impact of these ~200 SFs on Earth atmosphere and consequences of these explosive events. The VLF data and important Wait’s parameters—during the enhancements of X-ray flux due to these SFs—are presented and discussed. We would like to emphasize that, for the first time, we analyzed the D-region in detail; we obtained ionospheric parameters and electron density profile during consecutive huge SFs which continuously perturbed this region for a few hours. The results show that the impact of subsequent flares can be higher than expected and cannot be analyzed as a stand-alone case without analysis of the state of the ionosphere in the moments before their starts. Furthermore, the results of the ionospheric parameters presented in this paper are compared with the results of other authors in literature and we conclude that they are in good agreement with the findings of most authors. It can be noticed that the intense solar radiation, namely solar extreme events, lead to an increased electron production rate and can increase electron density up to a few orders of magnitude, depending on the flare intensity with distortion of the amplitude and phase VLF signal. In addition, we give a simple approximative formula for altitude electron density profile as a function of X-ray flux which is valid for nonperturbed and also for the perturbed D-region. The results confirmed the advantageous usage of the presented method for investigation of solar-terrestrial coupling processes as well as for detection and analysis of space weather phenomena such as solar explosive events. The analyzed data can be used in studies of the radiation characteristics before its impact on the atmosphere, modeling of VLF radio propagation in the lower ionosphere, modeling of disturbed ionosphere, etc. We note that the research requires multidisciplinary approach together with application of various models [45,46].

Supplementary Materials: The following are available online at https://www.mdpi.com/article/10 .3390/app11167194/s1, Figure S1: X-ray flux, amplitude and phase of GQD signals during occurrence of M3.7 class solar flare on 09 Sep 2017, Figure S2: Schematic presentation of a method for atmosphere electron density modeling. Figure S3: X-ray flux, perturbation of amplitudes and perturbation of phases and the corresponding electron density at reference height on 28 Oct 2003 during X17.2 class solar flare, Figure S4: The electron density at reference height calculated for this study together with Appl. Sci. 2021, 11, 7194 16 of 17

the results of other authors, Table S1: Data of amplitude and phase perturbations of VLF signal and ionospheric parameters induced by different SF events analyzed in this study, Table S2: VLF receiving and transmitting sites, Table S3: Data needed for approximative function. Author Contributions: Conceptualization, V.A.S. and D.M.Š.; Formal analysis, D.M.Š., V.V. and V.A.S.; Validation, V.A.S., L.I., V.V. and D.M.Š.; Visualization, V.A.S., D.M.Š. and V.V.; Writing— original draft, V.A.S. and D.M.Š.; Writing—review & editing, V.A.S., L.I. and D.M.Š. All authors contributed equally to this work. All authors have read and agreed to the published version of the manuscript. Funding: This work was funded by the Institute of Physics Belgrade and Astronomical Observatory Belgrade (contract 451-03-68/2020-14/200002), through the grant by the Ministry of Education and Science of the Republic of Serbia. Also, This article/publication is based upon work from COST Action CA17126 - Towards understanding and modelling intense electronic excitation (TUMIEE), supported by COST (European Cooperation in Science and Technology). Data Availability Statement: Publicly available datasets were analyzed in this study. This data can be found here: https://hesperia.gsfc.nasa.gov/goes/goes_event_listings/, accessed on 10 June 2021, https://satdat.ngdc.noaa.gov/sem/goes/data, accessed on 10 June 2021. Acknowledgments: We wish to thank to Ognyan Kounchev for the shown attention to this work and for a useful discussion. This investigation is also provided within the TUMIEE (CA17126). Conﬂicts of Interest: The authors declare no conﬂict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

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