7. Conclusions and Perspectives

[44]  In this paper on the basis of the artificial neural networks (ANN) we developed algorithms of forecasting of the critical frequency of the ionospheric F2 layer to time intervals 1, 2, and 3 hours and longer. To do this, a search for the valid training multitude and ANN architecture was performed. The main result of the conducted complex study of the operation of the created ANN for forecasting of the critical frequency of the ionospheric F2 layer was an increase of the efficiency of the forecast if the parameters of the solar wind, interplanetary magnetic field, and geomagnetic indices are additionally used. This made it possible to find the peculiarities of the physical process determining the behavior of the critical frequency and, first of all, to determine its characteristic time. The practical value of the performed work is a possibility of application of its results for real-time specification of the ionospheric model needed for providing the shortwave communication.

[45]  As a result, some problems concerning the development of ANN are determined and practical conclusions are drawn having an applied importance:

[46]  1. Because of nonlinear internal memory the application of a double-layer neuron network with the Elman feedbacks is the most proper instrument for forecasting time sequences. The Levenberg-Marquardt algorithm of ANN training on the basis of the method of backpropagation of the error showed itself as the most reliable while working with a large number of the input databases (three and more). Its application made it possible to tune the neural network parameters in such a way that the at introducing into the network of new unknown test data the network was able to adapt quickly to the new conditions. The success of the ANN in forecasting of ionospheric parameters in the online regime will essentially depend on the abilities of the network to be adapted to dynamically changing external factors.

[47]  2. The forecasting of the critical frequency to 1 hour may be successfully performed after training by two sets of the initial data: by the sequence of the critical frequencies and its first derivative. The accuracy of the forecast in this case is: PE = 92% and R = 0.96. The decrease of the forecast accuracy at the nighttime and evening hours can be explained by the peculiarities of the ionosphere F2 -layer behavior due to the reformation of the ionosphere.

[48]  3. At the calculation of the forecast to hour, an addition of any parameter out of Dst and DI leads to an increase of PE by about 1%. Introduction into the training sequence of the values of the hydrodynamic pressure or z component of the magnetic field with a delay by 1 hour leads to the same increase in PE. The added parameters increase the forecast accuracy at the evening and night hours.

[49]  4. The most effective delay of the IMF and PSW parameters relative to the rest of the data is the delay by 2 hours. The delay by 3 hours and more makes the training of the neuron network difficult and that leads to a low quality of the forecast. This result agrees with the physical causes of the delay.

[50]  5. At the calculation of the forecast to 2 hours, the adding of the global geomagnetic activity index Dst to the sequence of the critical frequencies and derivatives increases PE from 78% to 80%. The addition of the IMF modulus and its z component is the most effective: it increases PE up to 81%.

[51]  6. Solving the problem of an increase of the accuracy of the 3-hour forecast, the addition of Dst to the sequence of the critical frequencies and derivative increases PE and R from 59% to 60% and from 0.78 to 0.8, respectively. The addition of DI or hydrodynamic pressure shows no significant influence.

[52]  7. In some cases a more long-term forecast of the critical frequencies with the efficiency up to 89% is possible. On the whole, the addition of the delayed by 2.5-hour IMF and PSW parameters (hydrodynamic pressure) and the Dst index improve the forecasts for the periods in question, increasing PE by about 1%. The accuracy of the forecast to 24 hours increases by 8% if DI or the averaged sequence of frequencies is included into the training sequence.

[53]  8. The number of the ANN training parameters should correspond to the physical processes occurring in the solar-terrestrial relations and should be limited enough to avoid an overloading of the network, i.e., adaptation to vast data volume and increase of the training time.

[54]  All the results obtained in the work are summarized in Table 2.

[55]  Application of artificial neuron networks is able to provide an universal automatic forecast of parameters of ionospheric processes on the basis of continuous satellite data, magnetic measurements on the ground, and results of the vertical and oblique ionospheric sounding. Currently the necessary data may be obtained in the online regime. In a perspective a computer installation including ANN and service facilities may be created. Such installation would make it possible to forecast to a few hours in advance with high reliability in an automatic regime parameters of the ionospheric shortwave channel using the oblique sounding data. The installation would make it possible to find the relation between the radio channel parameters to the changing solar and geomagnetic situation, taking into account the space weather phenomena caused by solar activity.

[56]  The application of the ANN method transforms forecasting of the required value from some formal, established in advance with some accuracy, operation to an intellectual process. This process is permanently fitted to changing solar-terrestrial conditions, taking into account the features of the entire prehistory. Thus the process has both quick and slow memory. Combination of various forecasting methods and ionospheric data correction using both the technical means of sounding and developed computation algorithms, broadens considerably the possibilities of providing a high quality of forecasting of the ionospheric shortwave channel.

[57]  Thus forecasting of the ionospheric parameters on the basis of the ANN method makes it possible to obtain reliable results without attracting a description of the physical process. The network training should be provided by the continuous flow of the data needed. The results of the performed forecast were already used for correction of the ionospheric model and synthesis of the oblique sounding ionograms at the Inskip (England)-Nizhny Novgorod path [Barkhatov et al., 2003]. The comparison of the experimental and computed ionograms demonstrated an improvement of the quality of the forecasted ionograms as compared to the old models.

[58]  Concluding it is worth mentioning that the method ANN developed for forecasting of ionosphere parameters we plan to use further for forecasting of the main parameters of the ionospheric SW channel: maximum usable frequency (MUF) and optimal working frequency (OWF) using the data of the oblique LFM (linearly frequency modulated) sounding obtained at the Inskip (England)-Rostov on Don path. The observations at this path are carried out around the clock during more than half a year and a vast database (about 5000 ionograms) needed for training the neuron network in various geophysical conditions is compiled. Using the vast database of the oblique ionospheric sounding, on the basis of the forecast the range of variations in the key parameters of the solar wind and interplanetary magnetic field will be evaluated. These parameters determine the development of magnetic storms. They are manifested in negative disturbances of the electron concentration leading to a reduction of the forecasting accuracy and HF radio communication reliability. Recommendation on the change of the strategy of the LFM ionosondes network operation during disturbances (changes in the sounding intervals and obtaining of the sounding data in the real time) to adapt radio electronic systems to the current state of the ionosphere will be formulated. We consider this aim very actual because of the development of the Russian network of the LFM sounding paths for providing effective operation of various radio electronic systems. Applied to this aim the ANN method would optimize the work of the LFM sounding for providing high quality of the forecast to various time intervals in different geophysical conditions.