In this study, a new multicomponent model (MCM) to determine the time variation of ionospheric parameters is suggested. The model was based on the combination of wavelets with autoregressive-integrated moving average model classes and allowed the study of the seasonal and diurnal variations of ionospheric parameters and the determination of anomalies occurring during ionospheric disturbances. To investigate in detail anomalous changes in the ionosphere, new computational solutions to detect anomalies of different scales and estimate their parameters (e.g., time of occurrence, duration, scale, and intensity) were developed based on a continuous wavelet transform. The MCM construction for different seasons and periods of solar activity was described using ionosphere critical frequency f o F2 data from Kamchatka (Paratunka Station, 52°58′ N, 158°15′ E, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS). A comparison of the MCM with the empiric International Reference Ionosphere (IRI) model and the moving median method for the analyzed region showed that the suggested method was promising for future research, since it had the advantage of providing quantitative estimates for the occurrence time, duration, and intensity of the anomalies, characterizing the ionospheric state and disturbance degree with a higher accuracy. Geomagnetic storms from 17 March and 2 October 2013 were analyzed using the suggested method, and it was shown that the ionospheric disturbances were at maximum during the strongest geomagnetic disturbances. An increase in the electron concentration in comparison with the background level, under calm or weakly disturbed geomagnetic field conditions, was identified before the analyzed magnetic storms.

In the present paper, we propose a wavelet-based method of describing variations in the Earth's magnetic field, such as the horizontal component of the geomagnetic field, in addition to methods for evaluating changes in the energy characteristics of the field and for isolating the periods of increased geomagnetic activity. Based on a combination of multiresolution wavelet decompositions with neural networks, we propose a method of approximation of the cosmic ray time course and the allocation of anomalous variations (Forbush effects) that occur during periods of high solar activity. During the realization of the method, an algorithm was created for selecting the level of the wavelet decomposition and adaptive construction of the neural network. By using the proposed methods, we performed a joint analysis of the geomagnetic field and cosmic rays during periods of strong magnetic storms. The strongest geomagnetic field perturbations were observed in periods of abnormal changes in cosmic ray level. Assessment of the intensity of geomagnetic disturbances on the eve of and during magnetic storm development allowed us to highlight local increases in intensity of the geomagnetic field occurring at different frequency ranges prior to the development of the storm's main phase. Implementation of the proposed method with theoretical tools in combination with other methods will improve the estimation accuracy of the geomagnetic field state during space weather forecasting.