Analysis of ionospheric parameters by the software system “Aurora”

The paper presents methods of modeling and analysis of ionospheric parameters, which realized in the program system of complex analysis of geophysical parameters “Aurora”. The methods allow to analyze of characteristic changes in the ionospheric parameters and allocate the anomalous features during periods of ionospheric disturbances. The algorithm parameters are adapted for analyzing the ionospheric data of the Paratunka station (Kamchatka) and based on results of the estimates (station data of Yakutsk, Gakona, etc. were analyzed). Methods can be applied for the mid-latitude region. The system is implemented in the public domain (http://aurorasa.ikir.ru:8580). The research was supported by RSF Grant, project No 14-11-00194.


Introduction
The realm of the research concerns the problems of the theory of direct experimental data processing. It is associated with the monitoring and the prediction of the state of near-Earth space. At the present time, the databases of various geophysical parameters (National Geophysical Data Center; MAGBAT; SuperMAG) were formed and provided with the means of primary processing and updating. However, the tasks of effective methods creating for the data analysis, the interpretation of the obtained results and their correspondence to model constructions remain largely open. The influence of solar activity on the magnetosphere and the Earth's ionosphere is complex, many aspects of which have not been sufficiently studied so far [1][2][3][4][5][6]. The most strong and complex ionospheric disturbances (irregularities) are formed during solar flares and geomagnetic storms. They manifest themselves as significant changes of electron concentration in comparison to some characteristic (calm) level and reflect in the ionospheric parameters [1,2,[7][8][9]. Methods and computational algorithms developed by the authors for processing of the ionospheric data and the detection of ionospheric irregularities are described in the present paper. Ionospheric data of IKIR FEB RAS chain located in the northeast of Russia were used for the testing of software tools based on the methods and the algorithms. The software is presented in the paper.
suppressed on the basis of ionospheric data preprocessing by wavelets. This operation allows improving the efficiency of neural networks for the ionospheric irregularities detection [7]. To more detailed study of the ionospheric parameter dynamics in "Aurora" system, the computational solutions based on the continuous wavelet transform (CWT) are used [17]. The CWT application allows the detection of different scale anomalies in the ionosphere and the estimation of their occurence time, duration, and intensity.
2 Methods for analysis of ionospheric parameters by the software system "Aurora"

Modeling of ionospheric parameter time variations based on MCM
Modeling of ionospheric parameters in the program system "Aurora" is performed on the basis of following operations: 2.1.1 Using the multiresolution wavelet decomposition (MRA) [17 , 20, 21], the f 0 F2 time series is represented as components: to third level of the wavelet decomposition (decomposition level was determined by algorithm [17]), and ) (t e is noise. The wavelet decomposition (Eq. (1)) is carried out by the orthonormal wavelet basis Daubechies of third order (the basis was determined by minimization of the approximation error) [ where 3 are the order and parameters of the  th component autoregression, km radius from the station), were used as estimates. The estimation of the model parameters was carried out separately for high and low levels of solar activity and for different seasons. The solar activity was estimated according to the average monthly radio radiation at a wavelength of f10.7 (for f10.7 < 100, the activity was considered low, while for f10.7 > 100, it was considered high). Modeling of the foF2 data in the program system "Aurora" is performed for winter (high and low SA) and summer (high and low SA) seasons. The following models are used: -for winter (high and low SA): The models (see Eq. (2)) describe typical variations of the ionospheric parameters, during the anomalous changes, the model errors increase. Thus, in the program system the detection of anomalies is carried out by the estimation of the model errors:

Approximation of ionospheric data based on the wavelet transform and neural network
Approximation of the ionospheric parameter time variations in the program system "Aurora" is performed by the following operations: 2.2.1 Using MRA the data time series is represented as (1)). [21], the reconstruction of the initial resolution 0 j  is carried out for component Hourly values of the foF2 from 1968 to 2010 were used for neural networks training. The data with significant gaps were not used in the training, and slight gaps in the data were filled with median values, which calculated for the corresponding hour. To approximation of the foF2 typical variations, the data for the periods without strong magnetic disturbances and seismic activity in Kamchatka were used during neural networks training. The construction of NN was performed separately for different seasons and different levels of solar activity (see 1.2). The quality criterion of the NN training was the condition: The constructed neural networks carry out the advance of the data by the following transformation:   (Fig. 3, graphs с and d). During the magnetic storm, the NN errors significantly increase, indicating the disturbances of the ionospheric parameter typical variations (Fig. 3, graphs c and d).

Anomaly detection in the ionospheric data based on the continuous wavelet transform
To detailed analysis of the ionospheric parameters in the system "Aurora", we use following computing solution: 1. Performance of the continuous wavelet transform of data: where a is a scale and  is a basis wavelet.

Conclusions
The methods of the ionospheric parameter analisis, presented in the article, are realized in the ionospheric component of the program system "Aurora". The system is available to users on the website at http://aurorasa.ikir.ru:8580. The following functions are realized in the software system:  Modeling of time variations by the MCM, based on the multiresolution wavelet decompositions and ARIMA methods;  Approximation of the ionospheric data based on the wavelet transform and neural networks;  Detection of ionospheric anomalies and the estimation of their intensity. The algorithm parameters were adapted for the processing of the Paratunka station data (53.0 N, 158.7 E). Approbation of the algorithms was also performed and positive results were obtained for Magadan station (60.0 N, 151.0 E). The paper was supported by RSF Grant No. 14-11-00194. The authors are grateful to the organizations carrying out the registration of ionospheric and magnetic data which were applied in the paper.