4. Numerical Experiments for 1 Hour Ahead

Figure 2

[26]  The first series of the numerical experiments was performed to obtain the forecast 1 hour ahead. The first numerical experiment was aimed at forecasting the process prehistory. The training sequence contained two parameters: the sequence of f _cr (t) and its first derivative d f _cr (t)/dt. The choice of the derivative was due to the wish to concentrate the "attention" of the network at irregular variations in the critical frequency. In this case, there is no sense in the delay at the network entrance, and the delay block was switched off. The forecasting results were satisfactory: PE = 92% and R = 0.96. As an example, Figure 2 shows the parallel pieces of the forecasted and real sequences of the critical frequency for 4 days out of the entire test interval.

Figure 3

[27]  One can see that the forecasting was successful. However, the diurnal behavior of the correlation coefficient showed that the forecast reliability is low in the morning and evening time. The variations in the diurnal behavior of the forecast accuracy are most probably related to various physical processes supporting the electron concentration N_e level in the upper ionosphere in the daytime and at night. In the daytime the N_e level in the F region is determined by the intensity of the solar ionizing radiation, whereas at night it is supported by the plasma fluxes from the protonosphere and by thermosphere winds [Brunelly and Namgaladze, 1988]. Some role in the depletion of the forecast accuracy in the evening and nighttime hours may be played by occurrence of diffuse reflections of the F spread type. In the intermediate period (morning, evening) when the rebuilding of the ionosphere occurs combination of different factors (the relative role of each of them demonstrate considerable variations) is manifested in the depletion of the accuracy of the ionospheric critical frequency forecasting. Figure 3 shows the dynamics of the R coefficient.

[28]  To increase the forecast accuracy in the evening and morning hours for the 1 hour ahead forecasting, we decided to involve an extra parameter. As such an added set in the further numerical experiments of the series we used the index of the global geomagnetic activity Dst, DI and hydrodynamic pressure of the solar wind. The latter was obtained by multiplication of the data sets of N (the concentration of the interplanetary plasma) by V² (the solar wind velocity squared). In the latter case the solar wind parameters were involved with different delay (1, 2, and 3 hours) and the efficiency of this delay was studied. The following results were finally obtained. The adding of the Dst index increases PE from 92% to 92.8% with insignificant increase in the total correlation coefficient from 0.96 to 0.97. The adding of DI increases PE up to 93.1% also with an insignificant increase in the total correlation coefficient up to 0.97. The introduction of the hydrodynamic pressure with the delay of 1 hour provided no significant influence on the forecast quality. However, at the 2-hour delay, PE and R increased up to 93.1% and 0.97, respectively. At the delay of the considered set by 3 hours the network stopped learning. This fact indirectly shows that the delay of this parameter was too large for the considered problem.

Figure 4

[29]  Further search for a valid training multitude led to finding one more successful combination of the input data. A high accuracy of the forecast to 1 hour ahead was provided by the sequence: IMF modulus, z  components of IMF, and the sequence of the critical frequencies and its first derivative. The most successful was the delay of the IMF parameters by 2.5 hours. The forecast accuracy in this case was PE = 93.9% and R = 0.97. Figure 4 shows the forecast result. In the same way as in the previous experiment, the 3-hour delay leads to an interruption of the network operation.

[30]  The realization of other combinations of input databases provided no improvement of the results. At the same time, the optimal time delay in PSW and IMF of 2.5 hours was confirmed. The increase of this time up to 3 hours more usually leads to impossibility of the neuron network training.