6. Numerical Experiments for the Forecast to 12 and 24 Hours

[39]  One of the advantages of the ANN method is its use in automatic forecasting of ionospheric parameters with permanent tuning to the changing external conditions and with taking into account the prehistory of the studied process. Thus an important part of this study is performing numerical simulations of long-term forecasts 12 and 24 hours ahead. Below the results concerning the process prehistory are presented.

Figure 9

Figure 10

Figure 11

[40]  The results were the following. For the forecast to 12 hours (see Figure 9) at the input of the sequence of the critical frequencies and the derivative the forecast accuracy was PE = 57% and R = 0.8. For the forecast for a day (see Figure 10) at the same input data the accuracy was higher (  PE = 80.3% and R = 0.9 ). There is nothing astonishing in the fact that the forecast to a day was more reliable. The matter is that the training of the neural network and the further work on the forecast to a day were to recalculate each point of the critical frequency sequence into a similar (by value) point just shifted by one day. This result is close to the results of a "naive" forecast which is performed by substitution of the forecasting value by the previous one. Figure 11 illustrates the dependence of the quality of the critical frequency prediction on the forecasting versions: only on the basis of the process prehistory, on the basis of the prehistory completed by the IMF and PSW parameters, and by the "naive" forecast method.

[41]  At forecasting by the "naive" forecast method to 12 and 32 hours, high negative values of the correlation coefficient correspond to the regression equation line that is almost perpendicular to the regression equation line for the maximum correlation. In this case we may state that there is no correlation and the "naive" forecast should not be applied.

[42]  Further search for a valid training multitude led to the following results. For the 12-hour forecast the successful combination of the input sequences is the sequence of the critical frequencies, hydrodynamic pressure (the 2.5-hour delay in PSW), derivative, and the values of the Dst index. This combination led to an increase of PE and R from 57% to 57.1% and from 0.8 to 0.9, respectively. The sequence of the critical frequencies, derivative, magnetic filed modulus, and the z component of IMF with a delay by 2.5 hours also in combination with the values of the Dst index increased considerable PE and R up to 58% and 0.9, respectively.

[43]  The quality of the 24-hour forecast was increased using the only combination of the training data. This combination was the sequence of the critical frequencies, its first derivative, and the values of DI (the difference between the observed and mean values of the critical frequency). This combination increased the forecast reliability considerable. The values of PE and R increased from 80% to 89% and from 0.9 to 0.94, respectively. All other combinations and inclusion of other parameters brought no useful information into the training process and was not able to influence the diurnal forecast. In the same way as in other numerical simulations, it was confirmed that the delay of the PSW and IMF relative the other parameters by 3 hours and more cannot train the neural network well and the optimum delay time is 2.5 hours.