Analysis of cosmic ray dynamics and ionospheric parameters during increased solar activity and magnetic storms

. Based on the ground station data, the paper investigates the dynamics of space rays and ionospheric parameters during strong and moderate magnetic storms 2018. The research was carried out applying new methods for modeling and data analysis suggested by the authors. In the course of investigation, anomalous changes in ionospheric parameters preceding and accompanying magnetic storms were detected. When they were compared with the data of cosmic rays and interplanetary magnetic field, correlation was observed. It confirms the solar nature of the detected ionospheric effects. Application of regression methods confirmed the assumption on statistically significant effect of interplanetary magnetic field parameters on ionospheric parameter dynamics during increased solar activity. The results are of interest in the tasks of space weather forecast.


Introduction
Investigation of ionospheric parameters and space weather data is of interest in the tasks of solar-terrestrial physics and applied studies associated with space weather. Changes of the conditions on the Sun, in the solar wind, Earth magnetosphere and ionosphere significantly affects the operation and reliability of satellite and ground technological systems and threatens human health and lives. By the present time, the problem of real-time and accurate forecast of space weather has not been solved [1]. It is very important to create automatic methods for recorded data analysis to make online forecast of space weather.
In order to investigate space ray dynamics, space and ground data of neutron monitor global network data are used [2]. The recorded variations of cosmic rays are a complicated nonlinear dependence. On the Earth surface, cosmic ray intensity depends on air temperature, pressure, observation site latitude and geomagnetic field state, electromagnetic situation in the solar system and physical conditions in the Galaxy [1]. Initial cosmic ray variation amplitude depends on particle energy and interplanetary magnetic field strength. Classical methods for neutron monitor data analysis (spectral methods [3], smoothed methods [4]) are not effective enough. Modern methods, for example station circle method [5] allows one to determine the basic characteristics of cosmic ray variations with acceptable accuracy. However, these methods require labor-consuming calculations and they have not been automatized. Taking into account incomplete knowledge on the processes in the near-earth space and, as a consequence, on the recorded data inner  20 20 2 2 structure, the paper applies neural network apparatus to analyze neutron monitor data. It is known that neural networks are capable of approximating data complicated non-linear dependences without complete a priori knowledge on inner relations and dependences [6]. A significant advantage of this apparatus is the possibility of numerical realization that is important for the tasks of real-time data analysis. The approach used in the paper was firstly suggested in the paper [7] and is based on the application of neural networks of vector quantization [8]. This paper is the continuation of the investigations in this directions. The results confirmed the possibility of application of the developed approach in the problems of detection of anomalous changes in cosmic ray dynamics including those of low amplitude.
Cosmic ray data were analyzed together with ionospheric parameters in the paper. Ionospheric parameter regular changes depend heavily on the time of a day and season, on solar and geomagnetic activities, geographical location (polar and aurora zones, midlatitudinal and equatorial regions) and on other factors [9]. The most prominent irregular changes are observed in the ionosphere during solar flare events and magnetic disturbances and cause ionospheric inhomogeneity formations (ionospheric storms). Ionospheric storms have complicated spatial-time distribution and may have positive and negative phases [9]. The tasks of ionospheric data analysis and ionospheric process investigations are solved by many authors [9]. Among the main approaches, it is possible to emphasize the meridian method, physical models, ionosphere empirical models and neural network models [9]. Application of traditional methods based on smoothing techniques allows us to study data stable characteristics but causes losses of information on fast nonstationary changes [10]. The efficiency of modern methods (empirical, physical and neural network ones) is determined by the presence of qualitative real-time data of geophysical monitoring and decreases significantly during disturbed periods. The approach used at the laboratory is based on the application of wavelet transform and adaptive threshold functions. The developed calculation solutions has multiply proved their efficiency in the problems of ionospheric data real-time analysis and detection of ionospheric disturbances of different intensity [10,11]. The results of the work showed high sensitivity of the developed method and the possibility to apply it in the problems of geophysical data complex analysis and detection of space weather effects. In the course of investigation, we confirmed the possibility of occurrences of weak anomalous changes in ionospheric parameters preceding and accompanying magnetic storm periods. When compared with cosmic ray data and interplanetary magnetic field parameters, correlation was noticed confirming solar nature of detected ionospheric effects. Application of regression methods confirmed the suggestion on statistically significant effect of interplanetary magnetic field parameters on ionosphere dynamics during increased solar activity.

Multicomponent model and ionospheric parameter analysis algorithm
Ionospheric parameter time series can be represented in the form [11] ( )  , ( ) is a noise one during ionospheric calm periods. The technique for identification of model (1) components was described in the papers [11,12]. In this paper we use an anomalous component of the model ( ), identification of which is based on the application of threshold functions [11]: T  determines ionospheric disturbances of scale  of high intensity.
Taking into account the ionospehric process changeability, we introduced adaptive thresholds , and coefficients (ratio (2)) are accepted to be equal -If ( ) | | , then we consider that during the time interval ( ), an anomaly of scale was observed, its duration is determined as .

Data pre-processing based on multiscale wavelet decomposition:
-Assuming that the initial time series () j ft belongs to a space with resolution 0 j  , based on the multiscale wavelet decomposition () 0 ft to the level m we obtain [13]: (2 ) , -In order to recover the initial resolution of a function we perform wavelet reconstruction operation [13]: corresponds to the function resolution before the wavelet reconstruction operation).
-To exclude the boundary effect influence, we remove the first and the latest 2* m q counts from the reconstructed set (vicinity size, containing the boundary effect at the decomposition level m , is determined by the formula 2* j hq j  , where q is the carrier applied by the basic function).

Architecture and operating principles for LVQ neural network
LVO neural network consists of 2 layers. The architecture applied in the work is illustrated in Fig. 1 [6]. The first layer is the Kohonen one (competitive layer [8], Fig. 2), the second layer is a linear one and it is formed during the neural network training. The second layer determines the correspondence between the neuron numbers of the 1-st layer (clusters) k and respective classes l [8]  Input vector clustering into a defined number of classes is carried out with the metrics where X is the input vector; k W is the weight vector of neuron k of the first competitive layer, I is the input vector dimension. NN output vector has the dimension equal to the number of classes L (in the paper 3 L , classes are described below). Cluster number was chosen empirically and was equal to 20.
In case of correctly a trained network, one element of an output vector is equal to 1 and the rest are zero. Thus, NC allows us to solve the problem of belonging of an output vector to one of a priori known classes.

Determination of neural network classes and a scheme to solve the problem of data classification
According to the problem under investigation, we defined the following NN classes in the paper [7,14]: -«Calm» class -absence of sporadic layers. «C lm» cl i ch r c erized by (1)  (2) weak disturbances in the magnetosphere (K-index is 3, 4).
-«Disturbed» class -presence of sporadic layers of high amplitude. «Disturbed» class is characterized by: (1) penetration of disturbed high-velocity fluxes of solar wind and/or a shock wave associated with it to the Earth near-space; (2) magnetic storm occurrence and presence of strong disturbances in the magnetosphere (K-index is ≥5).
Based on the suggested approach, solution of data classification problem can be represented in the form of a scheme illustrated in Fig. 2.

Results of method application
In the experiments we applied neutron monitor minute data from Moscow station [2], analyzed strong and moderate storms occurred in 2018. When constructing a training sampling, data selection for each introduced class (Section 2.2.3) was based on the analysis of geomagnetic activity indicators, A-, K-and Dst-indexes were used [15]. The «calm» class was formed from the data for those time intervals during which A-index was <7, Kindex was <3, Dst-index was within ± 4. The «weakly-disturbed» class was formed from the data for those time intervals during which A-index was < 18, K-index was < 5, Dstindex was within ± 8. The «disturbed» class included the time intervals during which Aindex was >18, K-index was >5, Dst-index was out of ± 8. We used 20 vectors to train the neural networks, they are: 10 vectors, the geomagnetic indexes of which corresponded to he «c lm» cl ; 6 vec or corre ponded o the «weakly disturbed» class; 4 vectors corresponded to the «disturbed» class. To test the network, we used 36 vectors (data were not used during network training), they are: 10 vectors, the geomagnetic indexes of which corre ponded o he «c lm» cl ; 21 vec or corre ponded o he «we kly di urbed» cl ; 5 vec or corre ponded o he «di urbed» cl . E ch vector is a three-day interval containing minute data of neutron monitor (NM). Data multi-scale wavelet decompositions were carried out with Koiflet wavelet functions, the choice of which was explained in the paper [16]. According to the work [16] function expansion was carried out to the expansion 1-st level. The results with the least error were obtained applying the Koiflet wavelet functions of order 3. Taking into account the NM data diurnal variation and with the aim of the possibility of processing the data in a moving time window (we used the time window step equal to 3 hours), 8 neural networks were constructed. On each of them we supplied the input vectors of the size of N=4320 counts (corresponds to three days) with the displacement of M=180 counts (corresponds to 3 hours). Comparison of the neural network operation results with cosmic weather data and wavelet spectrum (Fig. 3b) confirms the accuracy of network solution. Analysis of ionospheric data processing (Fig. 3 e -g) shows a long positive anomaly occurrence (red color) before the magnetic storm. The anomaly was of low intensity with the maximum during the second part of the day on August 24 (UT). We should note that the time of ionospheric anomaly intensity maximum (Fig. 3g) coincides with the time of cosmic ray intensity increase (Fig.  3d) and IMF fluctuations increase (Fig. 3h). During the main phase of the magnetic storm, electron concentration oscillations are observed in the ionosphere. First, the concentration decre ed h n n « emp » of recovery w ob erved (from 01.00 till 12.00 UT on August 26). From August 26 to 27, a multiscale negative (blue color) anomaly is observed in the ionosphere at the recovery phase of the magnetic storm (Fig. 3f,g). The occurred negative ionospheric storm lasted for more than one day and a half and was the most intensive at 14.00 UT on August 27. Comparison of anomalous changes in the ionosphere with IMF and SWV data during the event shows the correlation, oscillations in the ionosphere are observed during Bz component fluctuations increase and SWV growth.  Based on the results of neural network operation (Fig. 4d), small-scale sporadic effects («we kly-di urbed» cl ) appeared in the dynamics of cosmic rays before the magnetic storm (March 12). The network referred the period of March 14-20 to the «disturbed» class that corresponds to large sporadic effects and confirms the accuracy of the solution. Ionospheric data processing results (Fig. 4e-g) show the occurrences of large-scale ionospheric anomalies during the period under analysis. A negative ionospheric anomaly of low intensity occurred during a weak magnetic storm on March 15-16 and had intensity maximum close to average statistical values during geomagnetic disturbances (Fig. 4g). The anomaly lasted for about one day and a half. At the background of anomalous decrease of electron concentration in foF2 data, oscillations (positive anomalies) of small scales are observed (Fig. 4 f, g). Similar to the event described above, changes in ionospheric parameter dynamics correlate with IMF fluctuation amplitude increases. Before the strong magnetic storm during the second half of the day on March 17, a positive anomaly occurred in the ionosphere. It reached the intensity maximum at about 02.00 UT on March 18. During the recovery phase, electron concentration in the ionosphere significantly decreased (negative anomaly on March 19).   (Fig. 5d), small-scale sporadic effects were observed in cosmic ray dynamics on October 4-7 before the magnetic storm. The period from 00 on October till the noon on Oc ober 8 w referred o he «di urbed» cl by he ne work hat corresponds to large sporadic effects and confirms the accuracy of the solution. The results of ionospheric data processing ( Fig. 5e-f) show the occurrence of a short positive anomaly of average intensity (at the boundary of October 5-6 (UT), Fig. 5g) before the magnetic storm. The anomaly was of short duration (within 8 hours) and had statistically high intensity for a calm period. The second positive anomaly of weak intensity occurred several hours before the magnetic storm beginning. In the vicinity of Dst amplitude maximum (Fig. 5c), electron concentration in the ionosphere decreased and a negative anomaly of average intensity occurred (anomalies are shown by blue color in Fig. 5 f,g). During the storm recovery phase, electron concentration of the ionosphere remained decreased. The effect is likely to be determined by thermosphere warming up and lift that causes recombination rate increase and, as a sequence, ionization depletion [18]. has been constructed. We analyzed the periods when IMF Bz component had the values less than -8 nTl. Taking into account the possible duration of ionospheric disturbances [19], ionospheric data were analyzed in a 3-day time window, each beginning from 00:00 UT. Thus, for the ionospheric data we processed the periods including the date of the event in IMF and the two following days. Gaps in ionospheric data were filled with median values (for 10 preceding days) taking into account the diurnal variation. When a gap was long (more than a day), the event was removed from the statistics. Gaps in IMF data were filled by the neighbor method [20]. When the total duration of gaps in IMF data was more than 30% of the period under analysis or the dap duration was 15% and more, the event was removed from the statistics.
In the course of ionospheric data processing for the period under analysis (three days for one event), maximum intensity for negative ionospehric storms was determined. As long as the duration of the analyzed periods for IMF parameters was one day and for foF2 data it was three days, the highest values for the period under analysis were used during the periods of long disturbances in IMF parameters (assumed that they contributed the most to ionospheric disturbances).
Based on the chosen criteria for the processing, 46 events were selected: 14 storms of G0 class (weakly-disturbed geomagnetic state), 10 storms of G1 class (weak geomagnetic storm), 17 storms of G2 class (moderate magnetic storm), 4 storms of G3 class (strong magnetic storm) and 1 storm of G4 class (very strong magnetic storm). These events corresponded to negative ionospheric storms of different intensity. Events with positive ionospheric storms were not included into the analysis. Correlation estimated coefficient is The obtained characteristics confirmed the statistical significance of the estimated parameters and model validity that indicated the statistically significant effect of IMF parameters on ionospheric data parameters (confidence coefficient is 95%).

Conclusions
The method suggested in the paper to analyze neutron monitor data has shown its efficiency when applied in the tasks of investigation of cosmic ray dynamics and detection of sporadic effects. On the example of considered events for 2018, the possibility of application of the method in the problems of real-time analysis of neutron monitor data and detection of different-scale sporadic effects, including those of low amplitude, has been confirmed. The method for ionospheric parameter analysis allowed us to investigate ionospheric process dynamics during disturbed periods in detail. Ionospheric disturbances were detected in the regions under analysis. These disturbances preceded and accompanied magnetic storm periods. The analysis confirmed the possibility of occurrence of pre-increase effect in the ionosphere that agrees with multiple observations described in the papers [9,10,11]. Comparison with cosmic ray data and IMF parameters gives us the ground to assume solar nature of the detected anomalous effects in the ionosphere.
During the magnetic storm main phases, oscillations, correlating with IMF variations, were observed in the ionosphere. Statistical significance of IMF parameter effect on ionospheric data dynamics and ionospheric anomaly occurrences has been quantitatively confirmed (confidence coefficient is 95%). At the magnetic storm recovery phase, ionospheric process dynamics changed and anomalous decrease of electron concentration was observed. It is likely to be determined by thermosphere warming up and lift causing recombination rate increase and, as a sequence, ionization depletion [18].
In the future the authors plan to continue the investigation in this direction applying a wider spectrum of data recording sites and extending the statistical material.