Efficiency of long-short term memory neural network model in prediction of ionosphere time series and comparison with GRNN, GIM and NeQuick

The ionosphere extends from an altitude of 80 to more than 1000 km above the earth. Due to its electrical properties, this layer of the atmosphere has very important and fundamental effects on the electromagnetic waves passing through it. A parameter that can be used to study the ionosphere is the total electron content (TEC). This parameter is the sum of free electrons in a cylinder with a cross section of one square meter between the satellite and the receiver on the ground. The unit of TEC is electron per square meter (ele/m2). The TEC in the vertical direction is called VTEC. Usually, TEC is expressed in terms of TECU, which is equal to 1016 ele/m2.
Different methods have been developed to model the TEC. The simplest and most practical method is to use observations of two-frequency receivers. If there is a proper station distribution, it is possible to obtain accurate TEC and model the ionosphere. The main innovation of this paper is in the long-term prediction of TEC in the period of severe solar activity, as well as the modeling of the ionosphere time series with the long-short term memory (LSTM) neural network model in the Iranian region. This model is used for the first time in Iran to model and predict the time series of the ionosphere. To check the capability of the new model in prediction of TEC in the conditions of severe solar activity, observations from 2007 to 2016 are used for training and the TEC in 2017 is predicted. All the observations are related to the Tehran GPS station, which is one of the stations of the IGS network. To evaluate the accuracy of the model presented in this paper, statistical indicators of relative error, correlation coefficient and root mean square error (RMSE) are used.

Long-short term memory model
Long short-term memory (LSTM) neural network is a special type of recurrent neural network (RNN). RNN is a type of neural network that has internal memory; in other words, this network is a normal neural network that has a loop in its structure through which the output of the previous step, along with the new input, is entered into the network at each step. This loop helps the network to have the previous information along with the new information and can calculate the desired output based on this information’s. One of the problems of RNNs is the vanishing of the gradient when learning from long-term sequences, which reduces the ability to learn in the algorithm. LSTM networks are actually a type of RNNs that have had a change in their block (RNN Unit). This change makes LSTM recurrent neural networks able to manage long-term memory and not have the problem of gradient vanishing.

After the training step, using the trained models, the VTEC value for 2017 has been estimated and compared with the VTEC values obtained from GPS as a reference observation, GIM and NeQuick models. For the test step, the parameters of correlation coefficient, RMSE and relative error were calculated and presented in table (1). It should be noted that the average of all days of 2017 is showed in this table. Also, VTEC values obtained from GPS are considered as reference observations in this table.
Table 1. Statistical values of correlation coefficient, RMSE and relative error in the test step of 2017 for GRNN, LSTM, GIM and NeQuick models.
The correlation coefficient value of LSTM model is higher than other models. Also, the values of RMSE and relative error of LSTM model are lower than other models. This model has the ability to show the ionosphere time series variations with an accuracy of about 87%.

Analysis of the results of the correlation coefficient in 2017 for LSTM, GRNN, NeQuick and GIM models compared to the GPS-TEC was obtained as 0.84, 0.72, 0.77 and 0.71, respectively. The average annual relative error for these four models was calculated as 16.98%, 25.69%, 29.89% and 51.05% respectively. The results of the analysis showed that in the conditions of severe and quiet solar and geomagnetic activities, the accuracy and precision of the LSTM model is higher than the other models evaluated in this paper. The analysis of the coordinate components of Tehran station with PPP method showed that by using the model proposed in this paper, an improvement of about 5.19 to 56.23 mm can be seen in the coordinates of the station compared to other models.