Discussing Total Electron Content over the Solar Wind Parameters

Modeling and forecasting of Total Electron Content (TEC) values by an Artificial Neural Network model (ANNm) have high agreement on November 2003, 2004 superstorms. &e work discusses Solar Wind Parameters (SWp) from OMNI (Operating Missions as a Node on the Internet) and TEC (TECU) data (International Reference Ionosphere) IRI-2012, IRI-2016 onNovember 20, 2003 (Dst� –422 nT) and on November 08, 2004 (Dst� –374 nT) Geomagnetic Storms (GSs). &e paper commences with a 120-hour GS exhibition of SWp and proceeds with the correlation data of the variables, their hierarchical tracks, and inner dispersions. &e ANNm with SWp as the input and TEC data as the output are introduced. &e performance of the ANNm for 2003 and 2004 superstorms is adequate. &e Correlation Coefficient (R) and Root Mean Square Error (RMSE) of the ANNm are 97.5%, 1.17 TECU (IRI-2012), and 97.9%, 1.09 TECU (IRI-2016) for the 2003 GS and 97.0%, 0.89 TECU (IRI-2012), and 98.0%, 1.61 TECU (IRI-2016) for 2004 GS. Parameters effect of the R constant of TEC data points out to the dynamic pressure (nPa), the magnetic field Bz component (nT), the flow speed (km/s), and the proton density (1/cm). Besides, the absolute total error and the variance of the predicted TEC data for November 2003 and November 2004 GSs are 0.06 (0.30%) with 0.013 variance (IRI-2012), 0.09 (0.49%) with 0.016 variance (IRI-2016) for 2003 storm and 0.13 (0.73%) with 0.033 variance (IRI-2012), and 0.11 (1.06%) with 0.035 variance (IRI-2016) for 2004. It means that the paper models TEC data with considerable consistency over the SWp.


Introduction
Briefly, a geomagnetic storm (GS) [1][2][3][4][5][6][7][8][9][10][11] is the effect of the solar wind to the magnetic field of the Earth. e solar wind traveling through the interplanetary medium has tremendous energy-charge density. e GS is named by the southward peak value of the disturbance storm time (Dst (nT)) zonal geomagnetic index after the B z (nT) magnetic field is rushed from the northward (positive direction) to the southward (negative direction). e GS initiates with the deceleration of the flow wind velocity v (km/s). Meanwhile, the dynamic pressure P (nPa) and the proton density N (1/ cm 3 ) respond with the sudden acceleration called coronal mass ejection (CME). e high-speed solar wind reaches the ionosphere with CME and causes ionospheric instabilities through intense currents [12]. e ionosphere coat, which covers from 50 to 1000 km, is the layer of the Earth's upper atmosphere. e total electron content (TEC) is one of the principal ionospheric parameters. e TEC (TECU) describes the electron density at a cross-section zone of 1 m 2 during the transferring of the signal. e unit of TEC is specified by 10 16 electrons/m 2 [1,[13][14][15]. e electric field fluctuation in lower latitudes induces ionospheric-magnetospheric disturbances that may be classified as negative or positive. While the electron density diminishes in the negative disturbances, the electron density enhances in the positive ones [16]. Ionospheric storms, which alter depending on the solar action, the Earth's turning, and spatial, regular, monthly, and seasonal circumstances, have different impacts in the ionosphere [17,18]. e TEC values, which change over time and ought to be evaluated along with their location in space, are the principal factors for solar activity and ionosphere-magnetosphere-Sun interaction [3,[19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. is essay predicts the TEC values through an artificial neural network model (ANNm) [7,8,[37][38][39][40][41][42][43][44][45] over the superstorms of November 20, 2003 (Dst � -422 nT) and November 08, 2004 (Dst � -374 nT). e predicted TEC values are criss cross checked with the values attained from the IRI-2012 and 2016 [31,[46][47][48] model. e IRI model, which has been incessantly improved after its first version was produced in 1978, was created by the collaboration of the International Union of Radio Science (URSI) and the Committee on Space Research (COSPAR). e last open data-based version of the model is the IRI-2016 model. IRI may introduce various parameters concerned with the ionosphere, holding the TEC value for ionosphere altitudes between 50 km and 2000 km along with time, date, and position [47]. e solar wind parameters (SWp) and the TEC values of the IRI-2012, 2016 model are utilized in the ANNm that performs the backpropagation iteration of Rumelhart et al. [49].
e Scaled Conjugate Gradient (trainscg) training algorithm is used with thirty-five neural members supplying inner dealings of the ANNm. e TEC data is gained as the output while the SWp (B z , E, P, N, v, T) are selected as the input to the ANNm, where B z (nT) is the magnetic field (B) and component (z), N is the proton density (1/cm 3 ), T is the temperature (K), v is the plasma flow velocity (km/s), P is the dynamic pressure (nPa), and E is the electric field (mV/m).
e TEC values are related to the IRI-2012 and 2016 data, and the consistency of the consequence is evaluated with the aid of the correlation coefficient (R) and the root means square error (RMSE (TECU)). After that, the data attained from the ANNm is pictured with the absolute error rate. e purpose of the paper is to model and compare the TEC (TECU) values of the two declared geomagnetic phenomena by the ANN. e work obeys the causality principle [50][51][52]. In the light of this principle, the cause is the SWp and the effect is TEC variables. In the ANNm established, the paper is governed by the physical facts of the GSs. e novelty of this paper is that it predicts TEC data for two superstorms with considerable consistency, obeying the causality principle, based on the solar wind parameters. In estimating IRI-2012 and IRI-2016 TEC data, the same ANN framework has modeled different TEC data with RMSE scores under two and with variance under one. e first part scans the background, the next section tries to comprehend the dynamics of the GSs, and the third part handles the binary relations, hierarchical clusters, and scattering of the SWp, TEC variables. e ANN investigation is utilized for the modeling of the TEC variables. In the last section, the work is concluded by discussions of the results. e hourly version of data is employed in the essay. nasa.gov/modelweb/models/iri2016_vitmo.php). is paper uses "NeQuick" as "electron density profile" at the top, "URSI" as "Ne F-peak (on)", and "AMTB2013" as "F-peak height". e performances of IRI-2012 and IRI-2016 in this paper do not differ significantly. In general, minor differences are expected [53][54][55][56]. Under 300 km [55], the IRI models predict a little less than the observed TEC value. While this deviation in estimation increases for IRI-2016 around the equinoxes, it decreases during solar minimum. So, IRI-2016 is relatively more accurate at the solar minimum than IRI-2012. Again, under 300 km, IRI-2016 is closer to the observed TEC values over the plot for bins [55].

Data
In the modeling of TEC data obtained during the 24th solar cycle from Guntur (India), Sukkur (Pakistan), and Agartala (India), the results obtained with IRI-2016 are more consistent than the results of IRI-2012 [53,54,56]. Figure 1 exhibits the 120-hour (five-day) scene of the SWPs of the two super GSs. e phenomenon day is centered at the five-day storm period. e paper employs SPEDAS (Space Physics Environment Data Analysis Software) to indicate oscillations in the SWp of GSs.
By looking at Figure 1, something can be said about the process of the super GSs. At 07 : 00 UT on November 19, a sudden acceleration in the dynamic pressure (nPa) occurs with the assistance of the proton density (1/cm 3 ). is means that the first CME commences the November 2003 superstorm. Meanwhile, the B z (nT) magnetic field straightly orients from the negative northward to the positive southward. e B z magnetic field immediately catches its deep value (−50.9 nT) and the Dst (nT) index takes place in the center of the storm that the Dst index shows its negative peak values (−422 nT) within a couple of hours. On November 20, 2003, the time shows 20 : 00 UT when the Dst index hits its negative peak. e smallest value time of the Dst index is the main phase of the GS.
Once again, by looking at Figure 1 for the November 2004 superstorm, on November 06, at 15 : 00 UT, the first CME commences with an unpredicted jump in the dynamic pressure (from 1.11 nPa to 5.31 nPa) and the proton density (from 5.3 1/cm 3 to 18.0 1/cm 3 ). e CME of the November 2004 superstorm is far more shocking than that of the November 2003 storm. On November 07, another CME bursts at 03 : 00 UT. November 08 (06 : 00 UT) is the storm day in which the Dst index indicates its supreme value of -374 nT after the orienting of the B z magnetic field from the northward to the southward.

Modeling
Dual relation with the Pearson correlation matrix for the variable of the November 20, 2003, and November 08, 2004, super GSs are displayed in Tables 1 and 2. Tables 1 and 2 tell the mutual relation of the variables. Table 1  After that, in the statistical corporation of data, one can need to recall the ANNm (Figure 4).
1 1 e ANNm is inspired by the human brain that connects via neurons. e ANNm has sheets that are named input, hidden, and output layers ( Figure 4) as they resemble the brain regions. is complex organization learns by training with the support of mathematical instruments, especially nonlinear ones. e ANN inputs-outputs do not need any info or homework for modeling [37].
is ANNm employs the following equation: where w is the weight vector, y is the independent variable of the activation function (as an output), x is the input, and B is the bias. e sigmoid transfer function [57] is f: where f is the logistic function. e instructional learning technique is extensively used [58]. e ANN background includes some layers and a predefined quantity neural cell that is utilized for inner contact. e input layer is commonly the first layer. e hidden layer [37] is the other layer. One hidden layer is frequently preferred rather than multiple layers [59]. e last layer is the output layer. While the input layer includes the independent variables (SWp: B z , T, N, v, P, E), the output layer comprises the dependent variable (TEC) in this essay. e output layer utilizes the sigmoid transfer function. e author employs 120 (hours) data totally; 84 hours (70%) are used for training ANN, 24 hours (20%) for testing, and 12 hours (10%) for validating. e essay commits the backpropagation algorithm that learns feedback reiteration for the prediction. e gradient reduction method that utilizes the weights of the variables piles up the all iterations. Newton's approach [60] and gradient decrease are commonly used as a standard optimization in backpropagation algorithms. Feedback training-learning employing constant input minimalizes the total error residue by backward cluster.
e work uses the Scaled Conjugate Gradient (trainscg) training algorithm.
After generating the training algorithm, the amount of the hidden layer of the neurons ought to be assigned. e number of neurons is stated as an involved amount. While few neurons reason insufficient learning, large numbers of neurons cause memorizing the ANNm. e appropriate amount of neurons allows the ANN to develop its generalization facility [61,62]. e number of the layer's neurons is addressed as thirty-five, in which the Mean Square Error (MSE) value inclines to be stable. e MSE is as follows: e ANN yields satisfactory results after its own training. All updates should be as free from memorization as possible. Updates of the time series are interrupted as soon as they reach the stability of the training-test-validation iterations ( Figure 5). When the MSE (equation (3) optimization model reaches stability, the iteration (period, update)) step is terminated. Figure 5  We consider that our consequences merit the readers' evaluation. e relatively small RMSE (TECU) rates, with the margin of error of the prediction reliability of the TEC data, are exhibited in Figure 5  One may discover R correlation constant of some forecasts in Tulunay et al. [35] with 99.0%, Ansari et al. [19] with 91.6%, Inyurt and Sekertekin [42] with 88.0%, Razin and Voosoghi [45]  e TEC values ANN estimation model outcomes of the super GSs seem comparable. e model not only exhibits the suitability of the IRI (2007)-estimated TEC outputs but also shows the reliability of the consequences.
Validation of the ANN model: In this part, one can see to validate the ANN model with the null hypothesis and different location extrapolation. Except for the locations discussed in the paper, the ANN model can be validated for the North Pacific, Hawaii, 5.581°N/150.88°W and Australia offshore, Coral Sea, 21.759°S/156.38°E. Figure 7 shows that the ANN model is also useful in many different locations.
Are the R coefficients obtained in the paper significant and purely event-related, or are they calculated by accidental (random)?
is significance test can be done with the classical null hypothesis (H 0 ) and t-score.
ree separate steps should be followed: (i) e null hypothesis is put forward. (ii) e t score is calculated. (iii) A comparison of the t-score with the table value is made. If the t-score is greater than the table value, the hypothesis is rejected. If it is less, it is accepted.   e formula (4) [63] relates to the effect of the variables. It is expressed as follows: Equation (4) is employed by ignoring the variables from the investigation. In this way, the impact strength of the relevant variable is revealed. e R correlation constant is centered in equation (4). R n is the correlation rate attained by assuming the related input. R dif is the basic correlation ratio between predicted and observed variables in equation (4). e variables' impact on the ANNm can be seen in Table 3.
In addition to the training, validation, and testing R correlation coefficients of the investigation (result) can be In Table 2, B z (nT), N (1/cm 3 ), v (km/s), P (nPa) SWp are the magnetic field (B z ), the proton density, the flow speed, and the dynamic pressure, respectively. e two superstorms to be handled separately:

November 20, 2003, Superstorm
(i) IRI-2012 TEC values: e prediction model of the TEC (TECU) data is substantially influenced by the B z (nT), the v (km/s), the P (nPa), and the N (1/ cm 3 ) SWp. When these SWp are ignored, the R rate of the TEC is influenced by 20.89%, 14.12%, 12.42%, and 11.69%, respectively (Table 2). is means that the R constant is much exceedingly

Mathematical Problems in Engineering 7
influenced by the B z (nT) and highly influenced by the v (km/s), the P (nPa), the N (1/cm 3 ). e B z (nT), the v (km/s), the P (nPa), and the N (1/cm 3 ) are dynamic-effective estimator for the TEC [64][65][66][67][68]. Physically, after the decrease in the flow velocity of high-speed (v) energetic particles, the GS commences with an unexpected rise in the dynamic pressure (P) and the proton density (N). en in a few hours, the SW speed begins to increase. at is, the directing of the B z magnetic field from the negative northward to the positive southward corresponds to the sudden acceleration of the SW speed [2]. In the main phase of the GS, which begins directly after the mentioned time period, the TEC data reacts (Figure 7-black arrow) to this situation with a serious decrease [67]. Accordingly, in the main phase of the GS following the sudden commencement, TEC data answer back to a raise in the dynamic pressure (P), the proton density (N), and the flow speed (v) with a decrease like there were a quadruple physical mechanism. At last, in the main phase of the GS is an ascendant plasma flow that decreases the ionospheric electron density till the magnetic reconnection [61] procedure initiates, which reestablishes the pressure stability [64][65][66][67]. (ii) IRI-2016 TEC values: e ANN prediction model of the TEC is considerably influenced by the B z (nT), the N (1/cm 3 ), the P (nPa), and the v (km/s) SWp. When these SWp are ignored, the R rate of the TEC is influenced by 21.31%, 12.26%, 12.06%, and 11.18%, respectively (    Mathematical Problems in Engineering is much highly influenced by the B z (nT) and highly influenced by the N (1/cm 3 ), the P (nPa), and the v (km/s).

November 08, 2004, Superstorm
(i) IRI-2012 TEC values: e prediction model of the TEC (TECU) data is substantially affected by the P (nPa), the B z (nT), the v (km/s), and the N (1/cm 3 ) SWp. When these SWp are neglected, the R rate of the TEC is influenced by 12.78%, 12.27%, 10.76%, and 9.07%, respectively (Table 3). One can realize that the R constant is much exceedingly influenced by the P (nPa) and highly influenced by the B z (nT), the v (km/s), and the N (1/cm 3      Works on the modeling-predicting of TEC values give way to a better comprehension of the relationship between the Earth's crust and the ionosphere.

Conflicts of Interest
e author declares no conflicts of interest.

Authors' Contributions
Data are collected and analyzed by the author. All interpretations and explanations belong to the author. e author read and approved the final manuscript.