5. Numerical Experiments for the Forecast to 2 and 3 Hours Ahead

Figure 5

[31]  This series of numerical experiments was performed to study the behavior of the neuron network in the conditions of forecasting to large time intervals: to 2 or 3 hours. As in the first series, the analysis of the work with the network started with the experiment aimed at its training by two input parameters: the sequence of the critical frequencies and the first derivative of this sequence. The results were found strongly different: at the forecast to 2 and 3 hours ahead: PE=78.2%, R=0.89 and PE=58.7%, R=0.78, respectively. It should be noted that such a strong difference in the forecast accuracy at the increase of the time only by 1 hour from the very beginning made doubtful a possibility of further increase of the forecast time up to 12 and 24 hours. Below we will show that it is

Figure 6

not so. Figures 5 and 6 show the results of the forecast to 2 and 3 hours, respectively.

Figure 7

[32]  The dynamics of the correlation coefficient for both versions of the forecast showed a low quality of the forecast in some intervals of the day. Figure 7 shows the studied variations of the coefficient R for forecast to 2 and 3 hours ahead.

[33]  Further numerical experiments of the series are dedicated to looking for the extra input databases. At the calculation of the forecast to 2 hours the addition of the global magnetic activity index Dst increased PE and the total correlation coefficient R from 78.6% to 80.6% and from 0.89 to 0.91, respectively. Introduction of the DI sequence produced no significant effect. Addition of the values of the intensity of the X-ray radiation or Kp (global geomagnetic activity) and PC (magnetic activity in the polar cusps) indices does not influence the quality and accuracy of the forecasts. The combination of sequences: sequence of the critical frequencies, first derivative of this sequence, IMF modulus, B_z components of IMF without a delay, provided the forecast quality with the following parameters: PE = 79.7 and R = 0.91. However, it is known that the IMF and PSW parameters are able to impact the general situation in the ionosphere only after some period of time. Physical considerations state that this delay interval should be within 1-3 hours.

[34]  The created model of neutron network made it possible to simulate the delay of the near-Earth parameters relative to the observed critical frequencies with a step of 30 min. Further, we analyzed an introduction of the time delay in the IMF and PSW parameters. The results of this study are presented in Table 1, where the maximum values of the PE coefficients obtained in the series of numerical simulations are presented. One can see that the most acceptable is the delay by 1.5-2.5 hours and 0.5 hour for the forecast to 1 and 2 and 3 hours ahead, respectively. The presence of the extreme for long delay times characterizes complicated relaxation processes in the ionosphere.

[35]  Determination of the optimal time delay for each forecasting version was performed in several stages. At the first stage the input porthole of the neuron network was regulated to simulate the corresponding delay. At the second stage, at each fixed delay the neuron network was once again training and tested, that is, 10 times in a row the testing interval was forecasted and the PE coefficient was calculated. Then the procedure was repeated for the next time delay of the IMF and PSW parameters. At the third stage, out of each 10-element set of the PE values the maximum value was chosen and presented in Table 1. Similar strategy was used for each version of the forecast thrice so three curves are obtained for each group. The maxima in all groups of curves show that for the forecast to 1 hour the most acceptable is the delay of the IMF and PSW parameters by 1.5-2.5 hours, whereas for the forecasts to 2 and 3 hours the delay in the parameters by 0.5 hour is enough. This demonstrates that there is a corresponding physical delay in ionospheric events relative to the IMF parameters. It is worth noting that according to the data of Zevakina and Kiseleva [1985] a 2- to 4-hour delay is observed between the maximum deviation of the critical frequency from the mean value and the maximum value of the Dst geomagnetic index. The combination of sequences: sequence of the critical frequencies, the first derivative over the critical frequency sequence, IMF modulus, and the B_z component of IMF (with the 1-hour delay) is the most effective and increases PE and the total correlation coefficient up to 80.8% and 0.91, respectively.

Figure 8

[36]  Figure 8 illustrates the influence of the general increase in the forecast quality on the diurnal dynamics of the correlation coefficient for the 2-hour forecast with the delay of the IMF parameters by 1 hour. Compared to Figure 7 (line 1), Figure 8 shows an improvement of the forecast in the morning and daytime hours and in the evening around 1900 UT.

[37]  While solving the problem of an increase of the 3-hour forecast, the search for an optimal training multitude led to the following results. The addition of Dst increases PE and R from 58.7% and 0.78 to 60% and 0.79, respectively, whereas the addition of DI and hydrodynamic pressure does not influence. The successful combination for the 2-hour forecast found earlier (the sequence of the critical frequencies, derivative over the sequence of the critical frequencies, modulus of IMF, and the B_z component of IMF with the delay by 1 hour) does not improve the quality of the 3-hour forecast.

[38]  The analysis of the behavior of the diurnal dynamics of the correlation coefficient for the 3-hour forecast showed insignificant changes in the picture as compared to Figure 7 (line 2). Only general increase in the forecast accuracy is observed at addition of new input data.