Analysis of rst four moderate geomagnetic storms of the 2015 year

This essay investigates of rst four moderate geomagnetic activities (04 January storm, 07 January storm, 17 February storm, and 24 February storm) of 2015 in the 24 th solar cycle. It tries to understand these storms with the aid of the zonal geomagnetic indices. It predicts the zonal geomagnetic indices (Dst, ap, AE) of the storms by an articial neural network model. The phenomena that occurred in January and February are discussed on the solar wind parameters (B z , E, P, N, v, T) and the zonal geomagnetic indices obtained from NASA. In the study, after glancing at the 2015-year general appearance, binary correlations of the variables are indicated by the covariance matrix, and the hierarchical cluster of the variables are presented by the dendrogram. The articial neural network model is governed by the physical principles in the paper. The model uses the solar wind parameters as inputs and the zonal geomagnetic indices as outputs. The causality principle forms the models by cause-effect association. Back propagation algorithm is specied as Levenberg– Marquardt (trainlm) and 35 neural numbers are utilized in the articial neural network. The neural network model predicts the Dst, ap, and AE indices of January and February geomagnetic storms with an accuracy that deserves discussion. Estimating the geomagnetic activities may support interplanetary works.

. Polarized magneto sonic waves and CME straightly turn out the SW parameters (Gonzalez et al. 1999). One of the governor SW parameters is the magnetic eld B z component. The negative B z magnetic eld replaces from the northward to the southward. This orientation and decreasing negatively direction cause of the terrestrial magnetic eld by causing disturbances with magnetic reconnections. Turbulences and uctuations in the magnetic eld controlled by the storm disturbance storm time index (Dst) (Dungey. 1961;Sugiura. 1964) from ZG indices can be called storm after the minimum peak B z . Storms may be de ned in 3-phases: The initial phase (sudden commencement), the main phase, and the recovery phase. In the initial phase, in which the storm begins, the Dst index decreases from positive values to negative values supporting the magnetic eld. In the main phase, the Dst index indicates negative values. When the negative values show the minimum values, it is followed by the recovery phase. Lastly, the geomagnetic storm nishes with the recovery phase when the uctuating in the magnetic eld ends and the Dst index indicates to the initial values. In moderate storms, following the B z parameter of the Dst index with a delay (Burton, 1975) of 5-6 hours is the response of the ring current to the SW. To better understand a geomagnetic storm (Mayaud 1980;2011;Eroglu, 2018;Eroglu, 2019;Inyurt and Sekertekin, 2019;Inyurt, 2020;Koklu, 2020;Eroglu, 2020), the author considers to models between the SW parameters and the ZG indices. This paper utilizes hourly versions of the SW parameters and the ZG indices.
This essay tries to investigate 04 January, 07 January, 17 February, and 24 February (2015) storm based on their physical requirements via an ANN model by meticulously governing the causality principle (Eroglu, 2011;Eroglu et al., 2012a;2012b, Eroglu, 2021. The ANN is a precious method; it may be utilized as an operative approach for forecasting in scienti c disciplines (Elman, 1990;Gleisner et al., 1996;Boberg et al., 2000;Gleisner and Lundstedt, 2001;Karayiannis and Venetsanopoulos, 2013). ANN model(s) application has been remarking in current decades owing to its distinctives such as learning capability, adaptation to changes, and ease of tools.
Investigations of earth-sun interaction, geomagnetic activities (Gleisner et al., 1996;Boberg et al., 2000;Gleisner and Lundstedt, 2001), weather estimations, etc. with ANNs (Gardner and Dorling, 1998;Lundstedt et al., 2005;Pallocchia et al., 2006) is effective in terms of space costs-times. ANN models founded by inferring geomagnetic storms' CMEs (Uwamahoro et al., 2012, Singh andSingh, 2016) give reasonable results with high forecasting ratio of storms. Long term time data ANN models involving SW parameters not only forecast the Dst index (Lundstedt, 1992;Lundstedt and Wintoft, 1994;Gleisner et al., 1996;Fenrich and Luhman, 1998;O'Brien and McPherron, 2000;Lundstedt et al., 2002;Bala, 2012;Uwamahoro, 2012;Singh and Singh, 2016) also estimates geomagnetic activities phases (Gleisner et al., 1996). One may see the trouble of the forecasting of the Dst index, without high-capacity computers with an 84% accuracy. At the '90s, such an amazing estimation has guided the new ANN models (Gleisner et al., 1996). The another ZG indicator Kp index is estimated by the SW parameters as the proton density (N), the ux velocity (v), and the B z magnetic eld. The Kp index ANN model displays a remarkable estimation ratio (Boberg et al., 2000;Lundstedt, 1992). The ap index signi cant model also utilizes the SW parameters as proton density and magnetic eld (Altadill et al. 2001). The auroral electrojet index AE model uses the proton density (N), the ux density (v), and the magnetic eld (B). One may realize from the ANN model estimation more than of 70% of the monitored the AE index (Gleisner and Lundstedt, 2001).
This paper investigates separately different moderate storms. Governing the ANN model by the SW parameters, the ZG indices shapes the investigation. In the examination of the rst four moderate storm, the correlation matrix speci es binary relation of the variables, the dendrogram illustrates of the hierarchical cluster of the data. The events that visualized with graphics is exhibited to the reader. The SW scattering time from bow shock to magnetosphere-ionosphere are not considered in the study when it is utilized the ZG indices from ground stations.
After searching the literature by introduction, in Section 2 yearly ZG indices appearances are seen besides variables ve-day scattering of them is announced. In Section 3 the ANN model and some properties of data are discussed. The paper is completed with a discussion in Section 4.

Data
SPEDAS is used in this essay. Before launching the rst four moderate storms of the 2015 year (day by day), one needs a glance annual appearance of the ZG indices. One can nd observed and estimated values of the 2015 year in Figure 1  Geomagnetic storms are classi ed according to the strength of the Dst index (Loewe and Prölss 1997). If Dst index is between -50 nT and -30 nT then it is weak. When it is between -100 nT and-50 nT, then it is called moderate, and from -200 nT to -100 nT then it is named the strong (intense-severe) storm. Figure 2 is a 120-hour view of some data related to the activities. The storm day is placed in the middle of the ve days.
It would be appropriate to discuss Figure 2' summary.
04 January 2015 Storm: On 04 January at 14:00 UT when the B z magnetic eld is at its minimum value of -8.8 nT, the Dst orients to -56 nT, the electric eld E shows to its maximum value of 3.53 mV/m.
Simultaneously, the proton density N signs to 6.9/cm 3 , the plasma ow speed v shows 401 km/s, and the pressure P reaches 2.63 nPa. As a response after two hours, at 16:00 UT, the Dst index and the auroral electrojet AE index hit the minimum-maximum peak values -62 nT and 866 nT, respectively.
On 03 January at 00:00 UT when the rst CME is burst out to the interplanetary medium, instant instability of the dynamic pressure P reaches its maximum value of 8.36 nPa in addition to indicating to the proton density N maximum value of 33.0 1/cm 3 and the ow speed v minimum value of 379 km/s. 07 January 2015 Storm: Four hours before, on 07 January at 07:00 UT, the Dst index indicates its peak value of -99 nT, the last CME is burst out. Meantime, the dynamic pressure P jumps from 6.05 nPa to its highest value of 12.36 nPa and the proton density N hits its maximum value of 29.4 1/cm 3 . After two hours, on 07 January at 9:00 UT the B z magnetic eld decreases to its minimum value (-17.04 nT), the electric eld E ranges to its highest value of 8.16 mV/m, the AE index shows its maximum value of 1327 nT, and the ap ZG index hits its maximum value of 94 nT. at 04:00 UT with the sudden commencement in the dynamic pressure P, then the proton density N peaks immediately its maximum value of 21.9 1/cm 3 . On 17 February at 21:00 UT, before three hours the Dst ZG index taking its minimum value of -62 nT, the magnetic eld B z component indicates its peak value of -12.0 nT and the electric eld (E) hits its maximum value of 4.54 mV/m. After three hours, at 00:00 UT, the ap index, the AE index, and the Dst index indicate their maximum values of 48 nT, 579 nT, and -62 nT, respectively.
24 February 2015 Storm: In the ve days storm discussion period, when the rst CME is burst out on 23 February at 03:00 UT with the sudden commencement in the dynamic pressure P, then the proton density N hits immediately value of 20.3 1/cm 3 . After eight hours at 08:00 UT, when the second CME is burst out, the dynamic pressure (P) hits 5.46 nPa, the proton density (N) indicates 20.0 1/cm 3 . Within four hours the magnetic eld B z component hits its peak value of -7.7 nT (11:00 UT), the dynamic pressure (P) increases its maximum value of 8.81 nPa (12:00 UT), and the proton density (N) shows its maximum value of 31.7 1/cm 3 (at 12:00 UT).

Modeling
Binary relationships with correlation matrix for the data of moderate 04 and 07 January, 17 and 24 February storms are indicated in Table 1a and 1b. The Pearson correlation matrix shows the relationship of variables. When the constants in Table 1a and 1b are close to ± 1, mutual correlation strengthens. Dendrogram of these moderate storms variables and scattering of data are speci ed in Figure 3a, 3b, Figure 4, respectively.  After the mathematical introductory discussion, it can be appropriate to remember the frame of the model of an ANN. The ANNs have inspired from the working principles of the human brain. This complicated and trainable neural system, which is shaped by linking many neurons with several interface levels, imitates the brain. Studies rstly have involved to model neurons in the human brain mathematically. With increasing awareness, the ANN has become a scienti c discipline today and it has been used in many different elds.
The ANN, which observes information and data in different structures and procedures by recognizing them very rapidly, can reveal unknown and di cult to notice correlation between data. It permits modeling without the necessity for any preparation or info among inputs and outputs (Elman, 1990). Basically, inputs and corresponding outputs are speci ed to the network ( Figure 5).
Training or educating of the ANN is provided by learning the relationship between input-output. This approach, called instructional learning, is a common approach (Peng et al., 1992). As an architectural con guration involving of some layers, the ANN uses data with a pre-determined number of arti cial neural cells. The initial layer is generally the input layer. This layer is usually not numbered owing to the lack of weight factors and initiation functions of the inputs in the input layer. The second mid-layers, called the hidden layer, can be founded so many as needed. Using one hidden layer (Elman, 1990;El-Din & Smith, 2002) is usual besides researchers to change into more than one hidden layer for adapting the target function. The layer called the output layer is the last layer. In this paper, the estimations are completed by the back propagation (Rumelhart et al., 1986) ANN algorithm. The typical back propagation algorithm applying a feedback learning structure is the gradient descent algorithm that moves the network weights in the direction of the negative gradient of the performance function. Many backpropagation algorithms appropriate for nearly all problem in ANNs are driven by standard optimization methods such as gradient descent and the Newton approach (Lipmann, 1987). Feedback learning using continuous input diminishes the error caused by backward agglomeration. The author utilizes the widely performed Levenberg-Marquardt (trainlm) learning algorithm.
After the creation of the learning algorithm, the number of neurons of the hidden layer have to be speci ed.
The number of neurons should be determined as needed. Too few neurons cause the pattern unable to be learned by the network, and a large number of neurons cause memorizing by the network, as well. A small enough number of neurons forces the ANN to improve generalization facility (Stern, 1996). In the paper, the hidden layers' neurons numbers are determined to be thirty-ve. In this neuron number, the mean square error (MSE) value begins to indicate no substantial change.
The work consists of three layers: The input layer, hidden layer, and output layer ( Figure 5). In harmony with the causality principle, the SW parameters (B z , E, P, N, v, T) are variables of the input layer and the ZG indices (Dst, ap, AE) are variables of the output layer. For the ANN model to be able to learn well without memorizing, the sigmoid transfer function is selected as the neural transition function (Fausett, 1994). A Linear transfer function is used in the output layer. Where a total of 120 ( ve days) data is investigated, 84 data are utilized for training ANN (70%), 12 data for validation (10%) and 24 data for testing (20%) (Haykin 1994).
As it may be realized from Figure 6a, the MSE values do not change after 6 updates (step, epoch) for the Dst index, after 8 updates for the ap index, and after 8 updates for the AE index in the 04 January storm (left column). In addition to this, the MSE values do not change after 7 updates for the Dst index, after 8 updates for the ap index, and after 8 updates for the AE index in the 07 January storm (right column). Therefore, learning (training) is nished. Up to these iteration totals, where the best veri cation performance happens, there is no monitoring of memorization owing to error constancy. Because the validation and test set errors show similar behavior and no substantial memorization happens, the network performance is acceptable.
One can see from Figure  In the literature, the signi cant studies in the literature have reached remarkable consequences in the estimation of the Dst, the ap (or the Kp), the AE index. In the Dst ZG index estimations, Gleisner et al. (1996) with 84%, Fenrich and Luhman (1998)  have declared their discussions.
Four moderate storm forecasting model outcomes look similar. It is obvious that the ANN model displays the reliable method and the t output for these moderate geomagnetic activities.
The illustration of the estimated Dst, ap, AE index values and their errors of 04 January moderate storm with actual ones from NASA is exhibited in Figure 8a, respectively. In Figure 1 and Figure 8a The effect of variables (for solar wind parameters) on the ANN model (Gontarski et al., 2000) can be speci ed with the formula % Effect=100.
(1-R n /R dif ) by omitting these variables from the investigation process. The correlation coe cients govern this formula. In the formula; R n is the correlation coe cient attained by excluding input. R dif is the basic correlation coe cient between estimated and observed values.    (Table 2a). The second-high effect belongs to the proton density N (1/cm 3 ) and dynamic pressure P (nPa). The correlation coe cient weakens by 10.37% and 9.43% when omitting the proton density and dynamic pressure P value, respectively (Table 2a). Finally, when ignoring the magnetic eld B z (nT) component, the Dst index is affected by 3.54%. The plasma ow speed v (km/s), the proton density N (1/cm 3 ), the dynamic pressure P (nPa), and the magnetic eld B z (nT) are indispensable estimators for the Dst (nT) index (Burton et al., 1975;Gleisner et al., 1996). Physically, coronal holes created by the instability of hot particles is the origin of the ow speed v (km/s). The SW streams have high-speed. The polarization of the magnetic eld is indicated by the parameters of the SW speed (Tsurutani et al., 2006). Besides orienting the magnetic eld B z (nT) component from southward to northward and indicating its negative values, the ow speed v (km/s) is shaped the geomagnetic storm. The ow speed v (km/s) and the B z (nT) component, with these anomalous replies, show that the Dst (nT) index should decline to negative minimum. With enhancing the proton density N (1/cm 3 ), the high-density plasma dynamic pressure P (nPa), and SW suppress the magnetosphere (Tsurutani et al., 2006). The re ection of the disturbance caused by this compress governed by the ow speed v (km/s) is the Dst (nT) index. Accordingly, one of the principal motivations why the Dst (nT) index inclines to minimums is the ow speed (Gonzalez et al., 1989;Borovsky, 2012;Borovsky and Yakymenko, 2017). The ANN model that shapes the Dst values prediction agrees with the literature (Table 2a and 2b).
The maximum impact on the ap (nT) index forecasting regards the magnetic eld B z (nT) component, the dynamic pressure P (nPa), the ow speed v (km/s), and proton density N (1/cm 3 ). When the magnetic eld and the dynamic pressure are neglected, the correlation ratio declines by 14.66% and 12.64%, respectively (Table 2a). The ow speed v (km/s) and the proton density N (1/cm 3 ) are also other high parameters for the ap index. If these variables are omitted from the ap forecasting, the model correlation constant diminishes by 8.91% and 8.40%, respectively. Physically, the magnetic eld polarizations indicate parallel effects with the dynamic pressure P (nPa), the ow speed v (km/s), and the proton density N (1/cm 3 ) while the ap index nonlinearly responses to the instabilities (Altadill et al. 2001;Eroglu, 2018;2019;2021;Inyurt, 2020;Koklu, 2020). The noticeable relation between B z (nT) magnetic eld, the dynamic pressure P (nPa), the ow speed v (km/s), and proton density N (1/cm 3 ) and the ap (nT) index may be perceived in Table 2a.
In the ANN estimation model for the AE (nT) index, the highest impact relates with magnetic eld B z (nT) component. One may see when neglecting the B z (nT) magnetic eld, the correlation constant decreases by 12.16% (Table 2a). The magnetic eld is accompanied by the ow speed v (km/s) and proton density N (1/cm 3 ) during the calculation of the AE (nT) index correlation ratio. It is realized that the value of R declines by 6.94% and 4.60% when the ow speed v (km/s) and proton density N (1/cm 3 ) are subtracted from the ANN model of the AE index, respectively (Table 2a) (Gleisner and Lundstedt, 2001).
07 January Storm: Parallel conclusions can also be realized in 07 January moderate storm. In the demonstrating of the Dst index estimation, the highest effect belongs to the dynamic pressure P (nPa), the ow speed v (km/s), and the B z (nT) magnetic eld. The correlation coe cient diminishes by 12.35%, 10.53%, and 10.02% when neglecting the mentioned SW parameters value, respectively (Table 2a).
According to Table 2a, the proton density N (1/cm 3 ) affects the Dst (nT) index with a value of 8.81%.
The maximum impact on the ap (nT) index forecasting regards the proton density N (1/cm 3 ) and the ow speed v (km/s). When the proton density and the ow speed are omitted, the correlation constant value decreases by 17.32% and 16.04%, respectively (Table 2a). Secondly, the other main factors are the B z magnetic eld (nT) and the dynamic pressure P (nPa) for the ap (nT) index. If they are omitted from the ap (nT) forecasting, the model correlation ratio decreases by 10.25% and 10.05%, respectively (Table 2a).
In the discussion for the estimation of the AE (nT) index, the highest effect belongs to the proton density N (1/cm 3 ). One can perceive when neglecting the proton density, the correlation constant value decreases by 13.11% (Table 2a). Besides the proton density, it is perceived that the value of R decreases by 9.76% and 9.55% when the magnetic eld B z (nT) component and the ow speed v (km/s) are subtracted from the AE index model, respectively (Table 2a).
17 February Storm: This moderate storm also re ects similar effects. The Dst (nT) index estimation responses to neglect the ow speed v (km/s), the proton density N (1/cm 3 ), the dynamic pressure P (nPa), and the B z (nT) magnetic eld. The correlation constant decreases by 8.20%, 7.48%, 7.07%, and 6.86% when neglecting mentioned SW parameters value, respectively (Table 2b).
The maximum effect on the ap (nT) index estimation regards the proton density N (1/cm 3 ), the B z magnetic eld (nT), the dynamic pressure P (nPa), and the ow speed v (km/s). When the mentioned SW parameters are omitted, the correlation constant value decreases by 10.72%, 10.11%, 9.81%, and 9.00%, respectively (Table 2b).
In the discussion for the estimation of the AE (nT) index, the highest effect belongs to the ow speed v (km/s), the magnetic eld B z (nT) component, and proton density N (1/cm 3 ). One can realize when neglecting these parameters, the correlation constant value decreases by 7.73%, 7.40%, and 6.80%, respectively (Table 2b).
24 February Storm: Eventually, according to 24 February moderate storm, demonstrating of the Dst (nT) index estimation is deeply related to the B z (nT) magnetic eld, the dynamic pressure P (nPa), the proton density N (1/cm 3 ), and the ow speed v (km/s). The correlation coe cient diminishes by 23. 36%, 13.04%, 8.19%, and 8.03% when neglecting these SW parameters, respectively (Table 2b).
The maximum impact on the ap (nT) index estimation regards the proton density N (1/cm 3 ), the ow speed v (km/s), the B z magnetic eld (nT), and the dynamic pressure P (nPa). When the mentioned SW parameters are omitted, the correlation constant value decreases by 18.10%, 12.59%, 8.02%, and 7.41%, respectively (Table 2b). Secondly, the other factor is the electric eld E (mV/m) for the ap (nT) index by affecting 2.23% (Table 2b).
In the discussion for the estimation of the AE (nT) index, the highest effect is observed by means of the proton density N (1/cm 3 ), the B z (nT) magnetic eld, and the ow speed v (km/s). One can perceive when neglecting these SW parameters, the correlation constant value decreases by 11.66%, 7.20%, and 7.10%, respectively (Table 2b).

Conclusion
Page 12/25 The purpose of the study is to assess the four moderate geomagnetic storms that occurred in 2015 year. After glancing at the 2015 year as a whole, these rst four moderate activities' zonal geomagnetic (ZG) indices are estimated e ciently. When the estimation of geomagnetic storms by the arti cial neural network (ANN) compares with the literature, the conclusions are satisfactory.
For these events, it is notable that the ANN model estimates the zonal geomagnetic (ZG) indices over the solar wind (SW) parameters. A geomagnetic storm strength and its phases may be evaluated by discussing the ZG indices. The paper is based on the method of inputting the SW parameters to the ANN model and yielding the ZG indices as output. The forecasting performance that is agreed with the literature of the ANN model, whose outputs are the ZG indices, is acceptable. The results demonstrate that the model is over 90% consistent in the estimation of these four moderate storms' ZG indices. The essay, in addition to the estimation, handles for these storms the effect of the SW variables on the ANN model, too.
In accordance with the 04 January storm ANN model, for the Dst index, the ow speed (v), the proton density (N), and the dynamic pressure (P) have a high effect, the magnetic eld (Bz) component has the moderate effect. Furthermore, the magnetic eld (Bz), the dynamic pressure (P), the ow speed (v) with the proton density (N) affect the ap index highly. For the auroral electrojet index AE, the magnetic eld (Bz) has a high effect, the ow speed (v) and the proton density (N) have a moderate effect.
According to the 07 January moderate storm ANN model, for the Dst index, the dynamic pressure (P), the ow speed (v), the magnetic eld (Bz), and the proton density (N) has a high effect. Moreover, the proton density (N), the ow speed (v), the magnetic eld (Bz) with the dynamic pressure (P) affect the ap index highly. For the AE index, the proton density (N), the magnetic eld (Bz), and the ow speed (v) have a high effect.
In accordance with the 17 February storm ANN model, for the Dst index, the ow speed (v), the proton density (N), the dynamic pressure (P), and the magnetic eld Bz component has a high effect. Additionally, the proton density (N), the magnetic eld (Bz), the dynamic pressure (P) with the ow speed (v) affect the ap index highly. The electric eld (E) has also a moderate effect on the ap ZG index. In calculating auroral electrojet index AE, the ow speed (v), the magnetic eld (Bz), and the proton density (N) have a high effect.
According to the ANN estimation model of the 24 February moderate storm, for the Dst ZG index, the magnetic eld (Bz) has a very high effect and the dynamic pressure (P), the proton density (N), the ow speed (v) have a high effect. Furthermore, for the ap ZG index, the proton density (N) has a very high effect and the ow speed (v), the magnetic eld (Bz), the dynamic pressure (P) have a high effect besides the moderate effect of the electric eld (E). For the AE index, the proton density (N), the magnetic eld (Bz), and the ow speed (v) have a high effect.
The harmony of the consequences of this study and the agreement with the previous discussions indicates that the reliability of the paper's results. The author expects to contribute to geomagnetic storm estimations by making it easier to understand their dynamics. The forecasted Dst, ap, and AE indices for these storms can also be predicted for other storms. With a similar approach, it will not be di cult for the ANN model to estimate the ZG indices not studied in this discussion for weak, moderate, or severe storms. The indices considered together with the SW parameters prepare the ground for predictable storms. The author hopes to attain the same results for weak, moderate, and severe storms in the next discussions. Figure 1 Annual views of the observed-estimated Dst (nT) index, ap (nT) index, AE (nT) index for 2015 year and their errors. From top of to bottom data shown in the Dst (nT) index, the Bz magnetic eld (nT), the E electric eld (mV/m), the dynamic pressure P (nPa), the proton density N (1/cm3), the ow speed v (km/s) and the ap  The neural network structure for the estimation of ZG indices