Correlation Analysis Between Total Electron Content and Geomagnetic Activity: Climatology of Latitudinal, Seasonal and Diurnal Dependence

Abstract

The basic concept of this study is to investigate, by correlation analysis, the relationship between geomagnetic activity and Total Electron Content (TEC) for the period from 1994 to 2023. The global TEC data used have been recalculated to a coordinate system with a modip latitude and geographical longitude. In the analysis of the parameters used, the global index of geomagnetic activity, Kp, and TEC were converted into relative values, showing the deviation from stationary (quiet) conditions. The investigation defined theoretical cross-correlation functions that allow estimating the time lag constant from the shift of the maximum cross-correlation. The seasonal dependence of the ionospheric response was investigated by splitting it into three monthly segments centered on the equinox and solstice months. The dependence of the ionospheric response on local time was studied by creating time series, including those longitudes at which, at a given moment, the local time coincides with the selected one. The results show the following peculiarities in the TEC response: the type of ionospheric response (positive or negative) in each of the latitudinal zones (auroral ovals, mid-latitude and low-latitude) depends on the season, the local time of the geomagnetic storm and the specific physical mechanism of impact.

1. Introduction

The physical mechanisms of the impact of geomagnetic activity on the electron density of the ionosphere are based on effects related to the entry of particle precipitation of the solar wind into the polar latitudes of the Earth, which causes variations in the Earth’s magnetic field [1,2,3]. The ways in which the magnetosphere and the solar wind interact are through dynamic pressure and an electric field. Pressure establishes the size and shape of the system, while the electric field transfers energy, mass and momentum to the magnetosphere. The coupling between the solar wind and the magnetosphere is controlled by the magnetic field in the solar wind through the process of magnetic reconnection [4]. It is a well-known fact that changes in the solar wind can cause disruptions of space and ground-based systems caused by enhanced currents flowing into the ionosphere and increased radiation in near-Earth space [5].

Under the conditions of the disturbed magnetic field because of solar wind and magnetospheric energy inputs to the Earth’s upper atmosphere, the result leads to so-called geomagnetic storms, which in some cases are accompanied by ionospheric storms [6]. This phenomenon appears as a result of considerably increased auroral particle precipitation and high-latitude ionospheric electric fields and currents lasting several hours or more during magnetospheric disturbances [7,8].

One of the main mechanisms that cause variations in electron density and, accordingly, in TEC is the heating of the neutral atmosphere in the Earth’s auroral ovals and the redistribution of gases in the thermosphere [9]. Changing the ratio between atomic oxygen and molecular nitrogen changes the recombination coefficient and consequently causes a decrease in electron density. Warmed air from polar latitudes also spreads to mid-latitudes, where it causes a negative ionospheric response [10,11,12,13,14].

The ionospheric response at low latitudes is determined by the disturbed meridional wind created as a result of the transport of heated air from the auroral oval, which, under the action of Coriolis acceleration near the equator, acquires a zonal direction and causes vertical drift of the plasma [15]. This vertical drift causes plasma transport from the equator to mid-latitudes by the “fountain effect” mechanism, which should be mostly associated with electric fields [16]. The manifestation of this phenomenon is expressed by lifting the plasma from the magnetic equator to higher altitudes, and then it diffuses down along magnetic field lines to higher latitudes, forming two ionization crests on both sides of the magnetic equator [17]. The sign of the TEC response in this case depends on the longitudinal distribution of the disturbed meridional wind direction. Depending on the intensity of the disturbed meridional wind and the intensity of the transport of heated air from the auroral oval at mid-latitudes, there is a region in which responses from both mechanisms operate simultaneously.

This paper presents the dependence of variations in ionospheric TEC on the geomagnetic activity on a global scale using correlation analysis based on a significantly long data series (from 1994 to 2023). The aim of the study is to determine the basic patterns of the ionospheric response depending on the geographical or magnetic latitude, season and local time. The use of correlation analysis requires representing the ionospheric response as a random process correlated with another random process, namely geomagnetic activity. Geomagnetic activity indices provide quantitative information about the solar wind energy entering the Earth’s atmosphere, but in each specific case, the ionospheric response is also determined by the given state of the atmosphere in the corresponding time interval. Correlation relationships calculated based on sufficient statistical material can therefore characterize the average or most probable ionospheric response to specific geomagnetic disturbances.

This investigation analyzes the effects of additional ionization in the region of penetration of particle precipitation of the solar wind into the atmosphere. Additional ionization leads to a positive response in night and winter conditions, when the electron density at these latitudes is insignificant.

The obtained results, providing information on the climatology of latitudinal, seasonal and diurnal dependence between ionospheric response and geomagnetic activity, can be used to improve existing models for predicting ionospheric behavior in order to improve forecast accuracy.

2. Data and Methods

The vertical total electron content is the total amount of free electrons in a vertical column with a height up to the upper boundary of the ionosphere (usually assumed to be up to about 1000 km). This ionospheric characteristic is important for determining the so-called ionospheric correction when using Global Navigation Satellite Systems (GNSS).

The ionospheric TEC is obtained by mapping the slant path delay of the signal from dual frequencies received by the global networks of the International GNSS Service (IGS). Usually, the single ionospheric layer assumption is considered to convert the slant path TEC to vertical TEC with a mapping function. This study used TEC data for the period 1994–2023 received from NASA JPL (Jet Propulsion Laboratory, California Institute of Technology, La Cañada Flintridge, CA, USA) freely available at: https://www.izmiran.ru/ionosphere/weather/grif/Maps/TEC/ (accessed on 1 April 2025). The fully available TEC data series covering the 23rd–25th solar cycles was used. The time resolution of this type data is 1 h, with a spatial grid in geographic coordinates between 87.5° S and 87.5° N.

TEC data used in the present investigation are converted to a coordinate system with modip latitude and geographical longitude [18]. The advantage of using such a modification is related to the effects in the ionosphere. The use of a new coordinate system for modeling the ionosphere, adapted to the real magnetic field, leads to an improvement in the accuracy of the representation of the ionospheric response at low and mid-latitudes. This is due to the observed variability of the densest part of the ionosphere, particularly at mid- and low latitudes.

The modip latitude μ is defined by: $\mathit{tan}\mu ={\displaystyle \raisebox{1ex}{$I$}\!\left/ \!\raisebox{-1ex}{$\sqrt{\mathit{cos} \phi }$}\right.}$ where I is the magnetic inclination at a height of 350 km and φ is the geographic latitude.

The K-index quantifies anomalies in the behavior of the horizontal component of Earth’s magnetic field, and it is widely used to characterize the magnitude of geomagnetic storms. The three-hourly planetary Kp index is obtained by averaging the standard K index from 13 geomagnetic observatories located between 44° and 60° northern or southern geomagnetic latitude. According to the accepted classifications, the range of the three-hourly Kp index is from 0 to 9. The NOAA Geomagnetic Storm Scale indicates the severity of geomagnetic storms. It is denoted by a G followed by a number from 1 to 5, with 1 being a minor event and 5 being an extreme event (https://www.spaceweather.gov/noaa-scales-explanation, accessed on 1 April 2025). This scale can be used to see the effects on humanity for three event types: geomagnetic storms, solar radiation storms and radio blackouts.

The geomagnetic activity, represented by the Kp-index, which characterizes the magnitude of geomagnetic storms, is available at https://omniweb.gsfc.nasa.gov/form/dx1.html (accessed on 1 April 2025).

The calculation of the relative deviation of TEC (denoted by rTEC) is based on the following formula:

$$rTEC\left(t\right)={\displaystyle \frac{TEC\left(t\right)-{TEC}_{med}\left(UT\right)}{{TEC}_{med}\left(UT\right)}}$$

(1)

where TEC(t) denotes the TEC value at the moment t, and TECmed(UT) is the median TEC obtained from the TEC values for universal time UT coinciding with universal time at the moment t during a 27-day period, centered on the current day.

The values of the geomagnetic activity index Kp are similarly modified into relative deviations, denoted by rKp:

$$rKp\left(t\right)={\displaystyle \frac{Kp\left(t\right)-{Kp}_{mean}\left(UT\right)}{{Kp}_{mean}\left(UT\right)}}$$

(2)

where Kp(t) is the value of Kp at time t, and Kp_mean is the mean value of Kp for a period of 27 days, centered on the current time t.

Figure 1 shows a comparison between the Kp index and the relative rKp index for one selected month, namely January 2005. This month was selected due to the fact that several geomagnetic storms occurred during this period, according to the accepted NOAA classification of the Kp index, which describes the significance of the effects of this phenomenon for different systems (detailed information can be seen at the following link: https://www.spaceweather.gov/noaa-scales-explanation, accessed on 2 March 2025). The figure shows that the relative Kp index (rKp) exactly repeats the variations of the Kp index but represents an alternative quantity in sign, similar to the relative TEC. The chosen time interval, which is illustrated in Figure 1, is due to the fact that three strong geomagnetic storms were registered in January 2005. Furthermore, no major sudden stratospheric warming (SSW) was registered during this period, and January 2005 is given in the literature as an example of a “normal” year. As can be seen from the behavior of Kp and rKp, demonstrated in Figure 1, the three geomagnetic storms occur in the following periods: (i) 7–8 January, (ii) 17–19 January and (iii) 21–22 January.

The present study is based on the assumption that geomagnetic activity and ionospheric TEC represent random processes. When using correlation analysis of time-limited series, it is necessary that they possess the property of stationarity. This means that their probabilistic characteristics do not depend on the localization of the finite-length time series, i.e., the processes under consideration are represented satisfactorily accurately by a sufficiently long sample of them. Removing the seasonal and diurnal variation of TEC by converting it into a relative deviation and removing the dependence of the average Kp on the level of solar activity by converting it into a relative one helps to improve the stationarity of the two time series.

The calculations of normalized autocorrelation and cross-correlation functions are performed according to the traditional formulas, where, for simplicity, the “reason” process (rKp) is denoted as x(t), and the “consequence” process (rTEC) is denoted as y(t). The two time series are practically centered, and their mean value is practically zero:

$$\begin{array}{c}{\rho }_{xx}\left(\tau \right)={\displaystyle \frac{M\left[x\left(t\right)x\left(t+\tau \right)\right]}{{\sigma }_x^2}}\\ {\rho }_{yy}\left(\tau \right)={\displaystyle \frac{M\left[y\left(t\right)y\left(t+\tau \right)\right]}{{\sigma }_y^2}}\\ {\rho }_{xy}\left(\tau \right)={\displaystyle \frac{M\left[x\left(t\right)y\left(t+\tau \right)\right]}{{\sigma }_x{\sigma }_y}}\end{array}$$

(3)

The operator M denotes the average value in the considered ensemble, σ denotes the corresponding standard deviation and τ is the time lag.

The cross-correlation function provides information about the similarity of the behavior of the two processes over time. For this reason, it is appropriate to determine theoretically the type of cross-correlation function and properties for the specific study. In the study by Muhtarov et al., 2002 [19], an approximate model of the ionospheric response to geomagnetic activity was proposed. This work is based on the idea that the ionospheric response has the character of an inertial process, which is described by a first-order linear differential equation. Mukhtarov et al., 2013 [20] make further development of this model in their article. A significant part of the ionospheric response processes is related to the consequences of the heating of neutral air in polar latitudes by the solar wind, which justifies this assumption. The Wiener-Lee theorem makes it possible to determine theoretically the cross-correlation function between the thus defined “input” (in this case the geomagnetic activity index) and “output” (TEC response) processes [21]. According to Korn, G. A., and Korn, T. M., 2000 [21], a counting process, in which the number of points of the process is a Poisson random variable, has an exponential autocorrelation function.

The empirical autocorrelation function of the index Kp, shown in Figure 2a, is sufficiently close to the exponential, which means that Kp can be considered a Poisson random process.

$${\rho }_{xy}\left(\tau \right)={\displaystyle \frac{{\sigma }_x}{{\sigma }_y}}{\int }_{-\infty }^{\infty }h\left(\zeta \right){\rho }_{xx}\left(\tau -\zeta \right)d\zeta$$

(4)

The transition functions h of the differential equation is

$$\begin{array}{c}h\left(t\right)={\displaystyle \frac{1}{T}}exp\left(-{\displaystyle \frac{t}{T}}\right);t\ge 0\\ h\left(t\right)=0;t<0\end{array}$$

(5)

T denotes the time lag constant. The condition h(t) = 0; t < 0 is related to the requirement for a physically realizable process.

Figure 2a shows the empirical autocorrelation function of rKp, which can be represented sufficiently accurately by the exponent

$${\rho }_{xx}\left(\tau \right)=exp\left(-{\displaystyle \frac{\left|\tau \right|}{T_g}}\right)$$

(6)

where Tg = 12 h.

The solution to (4) is

$$\begin{array}{c}{\rho }_{xy}\left(\tau \right)={\displaystyle \frac{1}{T}}\sqrt{{\displaystyle \frac{T_g+T}{T_g}}}{\displaystyle \frac{T{T}_g}{T_g-T}}\left(exp\left({\displaystyle \frac{-\tau }{T_g}}\right)-{\displaystyle \frac{2T}{\left(T_g+T\right)}}exp\left({\displaystyle \frac{-\tau }{T}}\right)\right);T\ne T_g\\ {\rho }_{xy}\left(\tau \right)={\displaystyle \frac{\sqrt{2}}{T}}\left(\tau +{\displaystyle \frac{T}{2}}\right)exp\left(-{\displaystyle \frac{\tau }{T}}\right);T=T_g\end{array}$$

(7)

Figure 2b shows an ensemble of theoretical cross-correlation functions between rKp and rTEC, calculated by Formula (6) at different time lag constants of the ionospheric response. As the time lag constant of the maximum increases, the maximum itself decreases.

Figure 2c demonstrates the empirical cross-correlation function between rKp and rTEC at the equator at local time 12 h, which is close in shape to the theoretical cross-correlation at a lag time constant of about 16 h. This allows for an approximate estimate of the time lag constants of the ionospheric response based on the time lag of the delay in the empirical cross-correlation.

Figure 3a illustrates the theoretical dependence of the time lag of the maximum cross-correlation on the time lag constant. This dependence can be used to estimate the delay of the ionospheric response from the empirical cross-correlation.

Figure 3b shows the dependence of the maximum cross-correlation on the time lag constants. In cases where the time lag constant approaches zero, which means a non-inertial reaction, the maximum cross-correlation approaches one, i.e., the two processes turn out to be identical. Physical processes in the ionosphere cannot be treated as deterministic, i.e., they cannot be described by deterministic transition functions, regardless of the assumption made. The probabilistic character of the time constant T, as well as the presence of variations in the electron density, independent of geomagnetic activity, leads to a reduction in the empirical cross-correlation compared to the theoretical one.

3. Results

After the theoretical analysis presented above, which shows the dependence between geomagnetic activity and the ionosphere, a detailed study of the climatology of latitudinal, seasonal and diurnal dependence between the considered parameters is necessary. In this section, the seasonal dependence of the TEC response to geomagnetic disturbances is investigated by sampling the full database of individual seasons (referring to the Northern Hemisphere). The resulting samples include three-month segments centered on the calendar months of the equinox and solstice, respectively: (a) winter is represented by the months of November, December and January; (b) spring by the months of February, March and April; (c) summer illustrates May, June and July and (d) autumn by the months of August, September and October.

Figure 4 shows the seasonal dependence of the cross-correlation between rKp and the zonal average rTEC. The modip latitude range is clearly divided into several regions. The sign and delay of the ionospheric response in these regions indicate the dominant physical processes in the ionosphere in the presence of solar wind influence on the Earth’s auroral regions. In the winter hemisphere (Northern Hemisphere in winter, Southern Hemisphere in summer), a distinct region of positive ionospheric response is observed at a modip of about 60–70° with almost zero delay. The positive ionospheric response, which means an increase in TEC with an increase in Kp, can be explained by the presence of additional ionization under the action of particle precipitation in the Earth’s atmosphere. This ionization causes an increase in electron density, and therefore in TEC, which is especially noticeable due to the fact that, in winter conditions, sunlight at these latitudes is insignificant and TEC values are small [22]. In the corresponding summer hemispheres at these latitudes, a negative response is observed, with a delay of about 10 h. Due to the presence of sunlight almost throughout the day and correspondingly high TEC values, the additional electron density turns out to be insignificant, and the increase in recombination appears as a dominant process. This is related to the redistribution of neutral gases under the influence of their heating by ionospheric currents. At latitudes corresponding to the auroral oval, the heating is direct, without the transfer of warm air; therefore, the response delay should be associated primarily with the delay in the heating process. The observed time lag corresponds to a time constant of about 4 h (see Figure 3a).

The negative response also spreads to mid-latitudes, with the time lag increasing to about 24 h in the summer hemispheres. The resulting increase in the ionospheric response time lag is caused by the time required for warm air to transfer from high to mid-latitudes. In the winter hemispheres, the meridional circulation has a direction from the equator to the pole and does not allow the penetration of warmed air at low latitudes.

In the two equinoctial seasons (spring and autumn), a practically symmetrical ionospheric response is observed in both hemispheres. In these cases, it turns out that the positive response in polar latitudes is slightly noticeable. The results from Figure 4 show that the negative response spreads to mid-latitudes less than in the summer season due to the weakening of the meridional circulation in the process of its transition from winter to spring and from autumn to winter.

During the equinox seasons, a symmetrical latitudinal distribution of the dominant positive response at low latitudes is observed. At the magnetic equator, the correlation has a time lag of about 6 h, which corresponds to a time constant of less than 4 h.

In the results of some studies, the authors obtain an increase in the O/N₂ ratio at low latitudes during geomagnetic storms, which they explain may cause an increase in electron density due to a decrease in recombination [23,24,25]. The explanation given by Yu et al., 2023 for the O increase is that this effect resulted from the downwelling at high latitudes and then was propagated to middle–low latitudes by the horizontal advection [25]. In their investigation showing a similar result of an increase in the O/N₂ ratio from the equator to mid-latitudes during geomagnetic storms, the authors explain the obtained result with thermospheric neutral composition disturbances [24].

In the equinox seasons, symmetrically located cross-correlation maxima are observed at latitudes ±40° with a time lag of about 3 h. These responses can be explained by the “fountain effect” caused by the disturbed dynamo [26]. Such a response is also observed in the winter hemisphere. In the summer hemispheres, this response is probably suppressed by the opposite-sign reaction associated with the equatorward spreading influence of the decrease in the O/N₂ ratio.

The results of the cross-correlation of geomagnetic activity and zonal mean rTEC actually provide information about the predominant response at a given latitude, i.e., averaged over longitude and local time. Due to the fact that the impact of the solar wind is localized predominantly in the night sector of the auroral oval, it is appropriate to study the response depending on the local time. For this purpose, rTEC time series containing its values at that longitude at which they have been created, at a given moment in universal time, when the considered local time is equal to the specified one.

The results of the cross-correlation analysis for the four considered seasons are shown in Figure 5, Figure 6, Figure 7 and Figure 8.

For the equinox seasons, spring and autumn at selected local times, shown in Figure 5 and Figure 6, the positive response at latitudes corresponding to auroral ovals is concentrated in the night hours, between 21LT and 3LT. This gives reason to make a statement that this response is due to additional ionization by particle precipitation of the solar wind entering the atmosphere, practically without delay. In daytime conditions (from 9LT to 15LT), the ionospheric response is negative, with a time lag of 12 h. In zonal meaning, the two responses are compensated, which can be seen in Figure 4.

An interesting result can be seen from the figures below, which show that during the night hours, along with a positive ionospheric response at ±65°, a thin latitudinal band zone appears, between 50° and 60°, in which the ionospheric response is negative. This latitude zone is characterized by the lack of a clearly expressed maximum (in absolute value) of the cross-correlation function, which means that for individual events (geomagnetic storms), the delay values vary widely. There is research that shows that similar effects are observed during specific geomagnetic storms [22]. It can be assumed that in this latitudinal region the summation of the two mechanisms with opposite signs of ionospheric response occurs, namely, additional ionization and increased recombination under the action of Joule heating.

The positive ionospheric response at low and mid-latitudes is evident in the daytime hours and in both equinoctial seasons—spring (see Figure 5) and autumn (see Figure 6). In the early daylight hours (around 6LT), a significant positive ionospheric response is observed around the equator with increasing delay from around 6 to 12 h. The two symmetrically located areas of additional positive ionospheric responses appear later, between 9LT and 18LT, with a shift of about 6 h. The change in the time lag during the day can be interpreted as a consequence of the effects in specific geomagnetic storms, as shown by the authors Bojilova and Mukhtarov (2024) in their study of selected cases of geomagnetic disturbances [27]. In the three specific events considered, the maxima of the positive ionospheric response at mid-latitudes move westward, but with a speed significantly slower than the Earth’s rotation speed, i.e., than the movement of the midnight meridian along the Earth’s surface.

The present correlation analysis, applied on the basis of a significantly long statistical data set (30 years), shows that this phenomenon has a recurring behavior over the years and, in general, a common character.

The time lag of the ionospheric response, which varies throughout the day and is shown by the calculated cross-correlation functions, is the result not only of inert processes. Another explanation for this effect is that it is most likely due to the delayed movement of the structure of the currents flowing in the dynamo region at low latitudes, causing an additional “fountain effect” relative to the movement of the source (the night sector of the auroral oval).

It should be emphasized that the use of the relative TEC deviation effectively filters out the “fountain effect” existing in quiet conditions, caused by the diurnal course of the equatorial zonal wind, which is related to local weather.

The correlations during the winter and summer seasons, shown in Figure 7 and Figure 8, have a well-pronounced symmetry between the two hemispheres.

In the winter hemispheres, the positive ionospheric response at auroral latitudes is strongest during the night hours, with a negligible time lag. In the summer hemispheres at auroral latitudes, the response is strongly negative, at a delay of about 6 h.

The negative ionospheric response at mid-latitudes in the summer hemispheres shows a significant delay of about 24 h, which is due not only to the inertia of the heating but also to the time required for the transport of warm air equatorward.

The ionospheric response at the equator has a similar character to that of the equinoctial months. A well-expressed positive ionospheric response at mid- latitudes is observed in the winter hemisphere, apparently symmetrically in the summer hemisphere, where the effect is suppressed by the negative ionospheric response associated with the transport of warmed air from the equatorward meridional circulation prevailing in the summer season.

Figure 9 shows the cross-correlation values at a fixed time lag of 6 h, depending on the local time. The selection of this value is determined by the predominant delays in the high-latitude and low-latitude regions (see Figure 5, Figure 6, Figure 7 and Figure 8, which present cross-correlation analysis for all seasons at a fixed local time). In the equinox seasons, at latitudes corresponding to the auroral oval, a positive cross-correlation is observed during the night hours, from 21LT to 6LT, and during the daytime, the cross-correlation is negative. This result confirms the suggestion stated above that additional ionization dominates during the night hours, and, during the day hours, the increased recombination effect due to heating dominates. The limited region of negative ionospheric response at high mid-latitudes (between 40° and 60°) extends to about 30° between 3LT and 6LT. This is most likely a result of the fact that, during the equinox months, the meridional neutral circulation is weak. The figure shows that, at the equator, three intensities of the response are observed in the hours between 6LT and 9LT, between 12LT and 15LT and between 18LT and 21LT.

In the summer hemispheres, at high and mid-latitudes, a negative response dominates, which propagates deepest equatorward between 6LT and 9LT for the Northern Hemisphere and around 15LT for the Southern Hemisphere. The resulting asymmetry between the two hemispheres can be due to both the asymmetry in the Earth’s magnetic field and the asymmetry in the neutral meridional circulation. An enhanced positive ionospheric response at the equator between 6LT and 9LT during the summer and winter seasons, as well as at the equinoxes, is observed. The observed positive response is in the winter hemispheres, between 30° and 60°, in daytime conditions and between 9LT and 18LT. The flowing transition of the response at the equator to the response in mid-latitudes is additional evidence for the presence of a “fountain effect” caused by a disturbed dynamo.

4. Discussion

In this investigation, a cross-correlation analysis of the relationship between geomagnetic activity and ionospheric TEC was performed based on a period from 1994 to 2023. The TEC coordinate system has been converted, resulting in the latitude being replaced with modified latitude. The global index of geomagnetic activity Kp and the ionospheric TEC are converted into relative values, reflecting the deviation from stationary conditions, represented by moving medians with a segment of 27 days. By introducing this methodology, the diurnal, seasonal and solar dependence of TEC, and the influence of the solar cycle on the average geomagnetic activity, are filtered out.

The results of the cross-correlation analysis should be interpreted as averaged characteristics of the ionospheric TEC response to low or medium geomagnetic activity. Figure 10 shows the probability that the Kp index is equal to or less than the value illustrated on the horizontal axis. For the selected period in this study, 90% of the Kp values are below 5. For this reason, cases in which a geomagnetic storm was registered have an insignificant impact on the presented results of the cross-correlation analysis. Furthermore, under strong geomagnetic disturbances, the TEC response shows a nonlinear dependence on Kp [20]. For this reason, the results obtained in this study cannot fully describe the ionospheric response to strong geomagnetic storms, for which the statistical material is insufficient.

The obtained normalized cross-correlation functions are analyzed by introducing the hypothesis that the response of the ionospheric TEC has an inert character with a time constant depending on the season, magnetic and geographic latitude and local time. In Section Data and Methods, it is theoretically proven that the inert ionospheric response leads to a positive time lag of the maximum (in absolute value) cross-correlation. It is well known that the positive cross-correlation corresponds to a response in which an increase in the quantity “reason” leads to an increase in the quantity “consequence”. In cases of negative cross-correlation, an increase in the quantity “reason” leads to a decrease in the quantity “consequence”. Theoretical cross-correlation functions are presented that allow the time lag constant to be estimated from the shift of the maximum cross-correlation (in absolute value).

Seasonal dependence was investigated by splitting the time interval into three-month segments centered on the equinox and solstice months. Local time dependence was investigated by creating time series, including those longitudes where local time coincides with the set time at a given moment.

The latitudinal zones that have specific characteristics of the TEC response are divided into the auroral oval region (60–70° modip latitude), the mid-latitude region (30–50° modip latitude) and the low-latitude region. These zones are conditional in nature, because in different seasons, in some areas, various physical mechanisms of influence on the ionosphere dominate.

In the auroral region, the most significant mechanisms are the direct impact of particle precipitation of the solar wind. In the winter and equinox seasons, the sign of the response depends on the TEC values. In cases where the TEC values are small (winter months and night conditions) the response is predominantly positive due to the additional ionization from particle precipitation. In summer conditions and daytime conditions, in the equinoctial months, the ionospheric response becomes negative due to the insignificant additional electron density and the increase in recombination under the influence of heating of the neutral air.

The positive response has no significant delay, while the negative response shows a delay determined by the inert character of the heating of the neutral air.

In summer conditions, the negative response propagates up to about 30°, with an additional delay due to the time required to transport the heated air from the equatorward-oriented meridional circulation. In winter conditions, the spread of the negative response is limited due to the predominance of poleward meridional circulation. In the equinox seasons, during the reorganization of the meridional circulation, a limited spread of the negative response to mid-latitudes is also observed.

The ionospheric response at the equator and at low latitudes is positive in all seasons. The results show, especially in the equinox months, a positive response at the magnetic equator, which occurs in daytime conditions with a delay of several hours. Two symmetrically located maxima are clearly formed at latitudes around 30°. The vertical drift caused by disturbed wind and the two symmetrically located maxima of the accompanying fountain effect must explain the ionospheric response at the equator. In the winter hemispheres, this additional maximum spreads to high mid-latitudes, and in the summer hemispheres, it is almost absent due to the dominance of the negative response caused by the spread of heated air to mid-latitudes. The ionospheric response, which can be associated with the additional fountain effect caused by geomagnetic disturbances, is observed in daytime conditions, for example, between 9LT and 18LT. The conversion of TEC values into relative values effectively filters out the fountain effect under quiet conditions, which is part of the stationary diurnal behavior of TEC at low latitudes. The obtained dependence of the ionospheric TEC response at low latitudes on local time can be interpreted as a consequence of the deviation of the disturbed wind from the meridional direction and the manifestation of an additional ExB drift at longitudes (respectively local times) different from the midnight sector, where particle precipitation of the solar wind occurs. The positive values of the response at low latitudes are possibly related to the increase in the O/N₂ ratio under the influence of geomagnetic disturbances as well as the influence of Prompt Penetration Electric Fields (PPEFs) [28,29,30]. PPEFs, in addition, create electric fields that can cause additional vertical plasma drift.

5. Conclusions

In the present study, the explanation of positive ionospheric TEC responses obtained at the equator and at low latitudes is because of the induced vertical drift of the plasma under the action of disturbed wind. The influence of the increase in the O/N₂ ratio observed during geomagnetic storms cannot be neglected at low and mid-latitudes in daytime conditions [24]. This increase in atmospheric changes may also be associated with the positive TEC response. Some authors hypothesize that this phenomenon is related to the excitation of wave disturbances in the neutral atmosphere during geomagnetic disturbances [28]. The results of some studies show the influence of PPEF, which creates additional vertical plasma drift in daytime conditions [29,30].

The combined impact of these mechanisms determines the specifics of the TEC response at the equator and at low latitudes under geomagnetic storm conditions.