Abstract:
The time-varying and uneven spatial distribution of electron density (number of electrons (Ne) in m
3) in the ionosphere retards and refracts electromagnetic waves in different frequency bands, in particular, radio waves from Very Low Frequencies (VLFs) to Very High Frequencies (VHFs). The ionospheric electromagnetic activity is a major factor in the quality of HF communication, satellite communication, Global Navigation Satellite Systems (GNSSs), and other space communications. Globally forecasting the Ne would improve the positioning accuracy of HF communication equipment, particularly in providing necessary conditions for precise positioning of real-time 3D ray tracing. The International Reference Ionosphere (IRI) model is an empirical model based on long-term data records from ground and space observations of the ionosphere. It has undergone extensive validation and is used for a wide range of applications in science, engineering, and education. Extensive publicly available 2016 ionospheric Ne data provided by the IRI model IRI2016 is a time series with three-dimensional spatial characteristics. SHI has confirmed through experiments that the Convolutional Long Short-Term Memory (ConvLSTM) is better than a simple LSTM in handling spatiotemporal data owing to its ability to simultaneously utilize both spatial and temporal information of the data. Based on the high-dimensional spatiotemporal features of Ne data, this study constructs a network model composed of an autoencoder and ConvLSTM to forecast a sequence of global Ne 3D maps without introducing any prior knowledge other than the Earth rotation periodicity. The encoder has three convolutional layers that reduce the spatial dimension, creating coded Ne maps, which are the inputs of ConvLSTM; subsequently, the decoder with three convolutional layers increases the output spatial size back to its original input size. We compare the performance of six optimization algorithms. We compare the root mean square error (RMSE) of three prediction strategies: the global mean RMSE of the 1h to 1h prediction strategy was 1.0 Ne units (NEU), which was 0.4% of the maximum value 243 NEU, whereas the global mean RMSE of the 1h to 24h and 24h to 24h prediction strategies was 6.3 NEU (2.6%). Based on the experimental results, the following conclusions can be drawn: first, Nadam is better for Ne prediction. Second, the performance of the 1h prediction strategy is competitive compared with similar ionospheric TEC prediction studies, achieving an RMSE higher than 1.5 TECU, which is 1% of the TEC maximum value 151 TECU; however, the prediction time is too short and real-time requirements for data are higher. Third, although the two 24h prediction strategies can achieve long-term prediction, their performance is not ideal. Currently, no suitable neural network exists for three-dimensional spatial data. The ConvLSTM network proposed by SHI can reflect only two-dimensional spatial relationships. Although all its inputs, outputs, and intermediate transition states are 3D tensors, only the last two dimensions are spatial (rows and columns), losing the spatial variation characteristics of Ne data at height, which is also one of the factors affecting prediction accuracy. Therefore, further improvement of neural networks, model structures, and prediction strategies are required to achieve long-term and high-precision prediction of three-dimensional spatiotemporal sequences.