Spatiotemporal Prediction of Ionospheric Total Electron Content Based on ED-ConvLSTM

Abstract

Total electron content (TEC) is a vital parameter for describing the state of the ionosphere, and precise prediction of TEC is of great significance for improving the accuracy of the Global Navigation Satellite System (GNSS). At present, most deep learning prediction models just consider TEC temporal variation, while ignoring the impact of spatial location. In this paper, we propose a TEC prediction model, ED-ConvLSTM, which combines convolutional neural networks with recurrent neural networks to simultaneously consider spatiotemporal features. Our ED-ConvLSTM model is built based on the encoder-decoder architecture, which includes two modules: encoder module and decoder module. Each module is composed of ConvLSTM cells. The encoder module is used to extract the spatiotemporal features from TEC maps, while the decoder module converts spatiotemporal features into predicted TEC maps. We compared the predictive performance of our model with two traditional time series models: LSTM, GRU, a spatiotemporal mode1 ConvGRU, and the TEC daily forecast product C1PG provided by CODE on a total of 135 grid points in East Asia (10°–45°N, 90°–130°E). The experimental results show that the prediction error indicators MAE, RMSE, MAPE, and prediction similarity index SSIM of our model are superior to those of the comparison models in high, normal, and low solar activity years. The paper also analyzed the predictive performance of each model monthly. The experimental results indicate that the predictive performance of each model is influenced by the monthly mean of TEC. The ED-ConvLSTM model proposed in this paper is the least affected and the most stable by the monthly mean of TEC. Additionally, the paper compared the predictive performance of each model during two magnetic storm periods when TEC changes sharply. The results indicate that our ED-ConvLSTM model is least affected during magnetic storms and its predictive performance is superior to those of the comparative models. This paper provides a more stable and high-performance TEC spatiotemporal prediction model.

1. Introduction

The ionosphere is a crucial component of the Earth’s upper atmosphere, containing a large number of charged particles that can significantly affect the propagation of radio waves [1]. The spatiotemporal variations in the ionosphere directly affect the accuracy of the Global Navigation Satellite System (GNSS) in positioning, navigation, timing, and other applications [2,3,4,5,6]. Total electron content (TEC) is a vital parameter for describing the state of the ionosphere. Thus, studying the changes of TEC and establishing prediction models for TEC are of utmost significance for improving the accuracy of GNSS.

However, due to the complex spatiotemporal variability of the ionosphere, which is also influenced by multiple factors such as solar activity, geomagnetic activity, and low-level atmospheric disturbances, establishing a high-precision ionospheric prediction model based on physical processes remains a challenging task. Currently, there are three main categories of short-term ionospheric prediction methods: ionospheric empirical models, statistical models, and artificial neural network models. The ionospheric empirical models mainly include the International Reference Ionosphere (IRI) [7,8,9], NeQuick model [10,11], Bent model [12], etc. The main drawback of these models is the inaccuracy in predicting the instantaneous change of TEC [13]. Statistical models mainly include autoregressive moving average (ARMA), autoregressive integrated moving average (ARIMA) models, and so on. For example, Ratnam et al. [14] developed a TEC prediction model utilizing a multivariate ARMA. The model incorporated various features, including solar extreme ultraviolet (EUV), geomagnetic activity, and so on. Mandrikova et al. [15] proposed a TEC prediction model based on a combination of wavelet transform and ARIMA. Kutubuddin et al. [16] used a linear time series model to predict TEC at ten sites in Japan. While these methods capture the trend of TEC over time based on short-term TEC data for linear modeling, they cannot capture the nonlinear changes of TEC [17].

In recent years, artificial neural network (ANN) has gained popularity as a tool in ionospheric TEC prediction because of its strong nonlinear representation ability [18]. In particular, the recurrent neural network (RNN), as a chain connected neural network that recursively progresses in the direction of sequence evolution, has become the mainstream method for time series prediction. Yuan et al. [19] proposed a single-station TEC prediction model based on RNN, with a prediction error of 0.49~1.46 TECU lower than the predictions obtained from other ANN methods such as the backpropagation (BP) [20] artificial neural network. However, when predicting long time series, RNN has the problem of gradient vanishing, leading to forgetting previous data. Long short-term memory (LSTM) neural networks [21,22,23] adopt a gating mechanism to remember information in long time series, resolving the problem of data forgetting in RNN and improving the accuracy of long time series prediction. Wen et al. [24] proposed an LSTM-based TEC prediction model with better prediction performance than BP and IRI-2016. Xiong et al. [25] proposed a TEC prediction model based on ED-LSTM, which has better prediction performance than ARMA and IRI-2016. Tang et al. [26] proposed a TEC prediction model based on multivariate LSTM and added an attention mechanism, which has better prediction performance than NeQuick and LSTM. Ruali et al. [27] combined LSTM with convolutional neural networks (CNNs) to achieve high accuracy in predicting TEC, and experiments demonstrated better performance than traditional neural networks. Although LSTM has shown some success in TEC prediction, it is limited by its structure and can only fit TEC in the temporal dimension without considering the spatial correlation between a given site and its neighboring sites. To address this limitation and balance the spatiotemporal characteristics of time series data, Shi et al. [28] introduced convolutional operations into LSTM and designed a ConvLSTM structure, which effectively utilizes spatiotemporal correlation in time series prediction. Liu et al. [29] proposed an innovative image-based ConvLSTM model to predict storm time ionospheric irregularities. The ConvLSTM structure outperforms the time series prediction model in precipitation prediction. Inspired by this study, we propose an encoder–decoder ConvLSTM model (ED-ConvLSTM) and apply it to TEC map prediction in East Asia.

In order to effectively leverage the spatiotemporal characteristics of TEC, this paper establishes a grid of 135 neighboring stations in East Asia (10°–45°N, 90°E–130°E), where the TEC data of all stations at the same time in the grid form a TEC map. Subsequently, the proposed method employs seven consecutive days of historical TEC maps in the region to predict the TEC map for the following day within the region.

We propose an encoder-decoder ConvLSTM (ED-ConvLSTM) model based on ConvLSTM, which includes an encoding module and a decoding module. The encoding module compresses and encodes the historical TEC map data, while extracting TEC spatiotemporal features, and the decoding module converts these spatiotemporal features into a predicted TEC map. We compare our proposed model with classical time series prediction models such as LSTM, gated recurrent unit (GRU), ConvGRU, and the 1-day prediction product C1PG provided by CODE, and evaluate the predictive performance of each model during high, normal, and low solar activity years. The experimental results show that the ED-ConvLSTM model proposed in this paper outperforms the C1PG, LSTM, GRU, and ConvGRU in all kinds of solar activity years. In addition, we also discussed the predictive performance of various models during the magnetic storm period. The experimental results showed that our model’s predictive performance was much less affected by geomagnetic storm interference than the other four comparative models, and the predictive performance was better. The remaining sections of this paper are structured as follows: Section 2 introduces the TEC dataset provided by IGS and the preprocessing process performed on the dataset to generate the experimental samples. Section 3 introduces the proposed ED-ConvLSTM model, including ConvLSTM, and encoder-decoder structure. Section 4 describes the experimental setup and presents the comparison results of different models, and analyzes the experimental results. In Section 5, we discuss the experiments in this paper and provide conclusions. Finally, in Section 6, we conclude this paper.

2. Dataset and Data Preprocessing

The TEC data utilized in this paper are the Final TEC product provided by the International GNSS Service (IGS). These data are characterized by higher accuracy and reliability [30]. IGS TEC data are stored in IONEX files, each of which contains one day of global TEC grid data with a time resolution of 2 h. The longitude range of these grid data is 180°W–180°E, with a spatial resolution of 5° and a latitude range of 87.5°N–87.5°S, with a spatial resolution of 2.5°. This paper focuses on a portion of Southeast Asia, coordinates 10°–45°N, 90°–130°E, thus considering a TEC map given by 135 grid points. By updating data every 2 h, a total of 12 TEC maps per day is achieved. For instance, Figure 1 illustrates the TEC map of the study area at UT 06:00 on 27 March 2019.

This paper selects a 3-year period of high solar activity data (2013–2015), a 3-year period of low solar activity data (2017–2019), and a normal solar activity year (2016) within the study area. The research work of Lin et al. shows that in TEC forecasting, the optimal time span used is one week or one month [31]; therefore, we use 8 consecutive days of TEC maps data as a sample, with 84 TEC maps from the first 7 days as the input and 12 TEC maps from the 8th day as the output of the sample. A sliding window method is employed to segment different samples, sliding for 1 day each time. The sample production process is shown in Figure 2, where each block represents 12 TEC maps for 1 day. In total, 1088 samples are generated during both high and low solar activity years, and 366 samples in normal solar activity year. In this article, samples from four years (2013, 2014, 2017, 2018) are used as training samples, and samples from three years (2015, 2016, 2019) are used as testing samples.

The final training set consists of 1446 samples, comprising 723 samples from the high and low solar activity years each. The test set consists of a total of 1096 samples, with 365 samples from the high solar activity year, 365 samples from the low solar activity year, and 366 samples from a normal solar activity year. The distribution of the final samples is shown in

Table 1. Distribution of experimental samples in this paper.

Data Set	Training Set		Test Set
	High Solar Activity (2013, 2014)	Low Solar Activity (2017, 2018)	High Solar Activity (2015)	Normal Solar Activity (2016)	Low Solar Activity (2019)
Number of samples	723	723	365	366	365
Total	1446		1096

.

3. Method

ConvLSTM is an advanced variant of the LSTM model that addresses the limitations of LSTM in extracting spatial features by replacing the fully connected layer in LSTM units with a convolutional layer. It has been proved to have excellent data modeling capability of spatiotemporal series [32,33,34]. In this paper, we combine the encoder–decoder structure with the ConvLSTM model, and propose an ED-ConvLSTM TEC prediction model. The basic framework is shown in Figure 3.

The proposed model includes an encoder module and a decoder module, both of which consist of ConvLSTM layers. The principles of ConvLSTM and encoder–decoder are introduced separately below.

3.1. ConvLSTM

ConvLSTM, similar to LSTM, is a type of recurrent neural network, which mainly consists of three gates (input gate $i_t$, forget gate $f_t$, and output gate $o_t$) and a memory unit ($C_t$). Figure 4 shows the structure of a ConvLSTM cell, as can be seen at time $t$: a ConvLSTM cell receives the output $h_{t-1}$ and memory unit $C_{t-1}$ transmitted by the ConvLSTM cell at the previous time $t-1$, as well as the spatiotemporal input data of the current time sequence $X_t$, and calculates the output $h_t$ and memory unit state $C_t$ at time $t$, and passes them to the next ConvLSTM cell, continuously recursively calculating. The calculation process inside an ConvLSTM cell can be divided into the following steps:

• The first step of ConvLSTM is to determine what information can be obtained through the cell state. This decision is controlled by the “forget gate” through sigmoid function, which generates a forget gate $f_t$ value between 0 and 1 based on the output $h_{t-1}$ from the previous time and the current input $X_t$. The calculation formula for the forgetting gate is as follows:

  $$\begin{array}{c}{f}_t=\sigma \left(W_{xf}\ast X_t+W_{hf}\ast h_{t-1}+b_f\right)\end{array}$$

  (1)

  where $\ast$ is convolution operation, $\sigma$ represents the sigmoid function, $W_{xf}$, $W_{hf}$ represents the weight matrix of $X_t$, $h_{t-1}$ is the output of ConvLSTM cell at time $t-1$, and $b_f$ is the bias of the forgetting gate.
• The second step is to generate new information that we need to update. This step consists of two parts. The first is an “input gate” (represented by $i_t$) that uses sigmoid function to determine which values to update, and the second is a tanh function that generates new candidate values $\widetilde{c_t}$, which may be added to the cell state as candidate values generated by the current layer. We will combine the values generated from these two parts to update them. The calculation formulas for $i_t$ and $\widetilde{c_t}$ are as follows:

  $$\begin{array}{c}{i}_t=\sigma \left(W_{xi}\ast X_t+W_{hi}\ast h_{t-1}+b_i\right)\end{array}$$

  (2)

  $$\begin{array}{c}\widetilde{c_t}=\tanh \left(W_{xc}\ast X_t+W_{hc}\ast h_{t-1}+b_c\right)\end{array}$$

  (3)
• The third step is to update the old cell state $C_t$ as follows.

  $$\begin{array}{c}{C}_t=f_t\odot C_{t-1}+i_t\odot \widetilde{c_t}\end{array}$$

  (4)

  where $\odot$ is Hadamard product.
• Finally, we calculate the output gate $o_t$, and then calculate the output $h_t$ of the ConvLSTM cell based on $o_t$ and $C_t$ as follows:

  $$\begin{array}{c}{o}_t=\sigma \left(W_{xo}\ast X_t+W_{ho}\ast h_{t-1}+b_o\right)\end{array}$$

  (5)

  $$h_t=o_t\odot \tanh \left(C_t\right)$$

  (6)

3.2. Encoder–Decoder Structure

The encoder–decoder structure is a deep learning model structure that consists of two main components:

• Encoder: receives a TEC sample input into the model, compresses the high-dimensional sample, and performs feature extraction to convert the high-dimensional input sample into low-dimensional spatiotemporal feature vectors which contain important features of the input sample.
• Decoder: decodes the spatiotemporal feature vector obtained by the encoder and convert it into outputs, which are the predicted TEC maps corresponding to the input sample.

The data-processing process of the encoder–decoder structure can be described by Formulas (7) and (8):

$$\begin{array}{c}{v}_1,v_2,\cdots ,v_m=Encoder\left(X_i\right)\end{array}$$

(7)

$$\begin{array}{c}{Y}_i=Decoder\left(v_1,v_2,\cdots ,v_m\right)\end{array}$$

(8)

where $X_i=\left(x_i,x_{i+1},\dots ,x_{i+83}\right)$ represents the input vector of the sample $i$, which contains 84 TEC maps, $v_1,v_2,\cdots ,v_m$ represents low-dimensional spatiotemporal feature vectors, and $Y_i=\left(y_i,y_{i+1},\cdots ,y_{i+11}\right)$represents the predicted TEC maps of the input sample $X_i$.

3.3. Implementation Details

The detailed structure of our ED-ConvLSTM proposed in this paper is shown in Figure 5, which includes two parts:

Encoder: This module consists of a combination of three paired ConvLSTM layers and BatchNorm layers that work together to extract the spatiotemporal features of the input TEC map sequence. This module receives input samples, each containing 7 consecutive days of TEC map within the study area, with dimensions (84, 15, 9), where 84 represents a total of 84 TEC maps within 7 days, and 15 and 9 represent the number of grid points in the study area. Then, the combination of ConvLSTM and BatchNorm is used to extract the features of the input TEC map sequence. Each ConvLSTM is composed of 16 convolution kernels. The BatchNorm layer is used to regularize the output results of the ConvLSTM layer, thereby preventing gradient disappearance and explosion. The ConvLSTM layer passes $h_t^l$ and $C_t^l$ backward along the time direction, where $t$ (time) and $l$ (the number of layers) and allows the upper layer ConvLSTM cell to acquire higher-level spatiotemporal features by exchanging information between layers. After processing with three ConvLSTM+BatchNorm combinations, the input (84, 15, 9) dimensional data are converted into a (1, 15, 9) dimensional vector, which contains historical spatiotemporal information and represents the 7-day spatiotemporal characteristics of the input samples, which are essential for predicting the TEC.

Decoder: This module consists of a combination of three paired ConvLSTM and BatchNorm layers, as well as one convolutional layer. The three paired ConvLSTM and BatchNorm layers are combined to decode the spatiotemporal feature vectors transmitted by the encoder module. Finally, a convolutional layer with a single convolutional kernel is used to generate the prediction TEC map for the eighth day.

4. Results

As described in Section 2, we use TEC maps from 2013 to 2014 (high solar activity years) and 2017 to 2018 (low solar activity years) as training samples, and TEC maps from 2015 (high solar activity year), 2016 (normal solar activity year), and 2019 (low solar activity year) as testing samples. We compared the predictive performance of various models in high, low, and normal solar activity years, as well as in two magnetic storm events. There are four comparative models in this paper: two mainstream time series prediction models (LSTM, GRU), one spatiotemporal prediction model (ConvGRU), and C1PG. C1PG is the one-day TEC prediction provided by the Center for Orbit Determination in Europe (CODE). It has been reported that the global TEC map prediction accuracy of C1PG is higher than that of two other International Analysis Centers (IAACs), namely, the European Space Agency (ESA) and the University of Bern (UPG) [35].

Since LSTM and GRU models can only predict the TEC of a single station and cannot directly output the TEC map, we separately trained and predicted the LSTM and GRU at each station in the research area. The prediction results were then converted into TEC maps for comparison with the experimental results.

Our proposed model is built with TensorFlow. During model training, the adaptive motion estimation (ADAM) optimizer is used. The initial learning rate is set to 0.001, and is adjusted during the training process. The learning rate is reduced by 0.5 times every 50 iterations. The structural similarity index measure (SSIM) [36] loss function is used as the loss function of the model. A total of 300 iterations are performed during the model training process.

4.1. Matrices Evaluation Indicators

The evaluation indicators used in this paper include two categories. The first category is error indicators, including mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE), where MAE and RMSE are absolute errors, and MAPE is relative error. The smaller the error, the better the prediction performance of the model. The second type of indicator is the similarity index measure, called SSIM [36], which is used to evaluate the spatial approximation of two TEC maps. The larger the SSIM, the better the spatial fit between the predicted TEC map and the true one. When SSIM is 1, it indicates that the predicted TEC map is identical to the real one. The formula for calculating each indicator is as follows:

$$\begin{array}{c}\mathrm{MAE}\left(y_i,{\widehat{y}}_i\right)=\frac{1}{m}{\displaystyle {\displaystyle \sum }_{i=1}^m}\left|y_i-{\widehat{y}}_i\right|\end{array}$$

(9)

$$\begin{array}{c}RMSE\left(y_i,{\widehat{y}}_i\right)=\sqrt{\frac{1}{m}{\displaystyle {\displaystyle \sum }_{i=1}^m}{\left(y_i-{\widehat{y}}_i\right)}^2}\end{array}$$

(10)

$$\begin{array}{c}MAPE\left(y_i,{\widehat{y}}_i\right)=\frac{100\%}{m}{\displaystyle {\displaystyle \sum }_{i=1}^m}\left|\frac{y_i-{\widehat{y}}_i}{y_i}\right|\end{array}$$

(11)

$$\begin{array}{c}SSIM\left(y_{\left(i,j\right)},{\widehat{y}}_{\left(i,j\right)}\right)=\frac{1}{m}\frac{1}{12}{\displaystyle {\displaystyle \sum }_{i=1}^m}{\displaystyle {\displaystyle \sum }_{j=1}^{12}}\frac{\left(2{\mu }_{y_{\left(i,j\right)}}{\mu }_{{\widehat{y}}_{\left(i,j\right)}}+c_1\right)\left(2{\sigma }_{y{\widehat{y}}_{\left(i,j\right)}}+c_2\right)}{\left({\mu }_{y_{\left(i,j\right)}}^2+{\mu }_{{\widehat{y}}_{\left(i,j\right)}}^2+c_1\right)\left({\sigma }_{y_{\left(i,j\right)}}^2+{\sigma }_{{\widehat{y}}_{\left(i,j\right)}}^2+c_2\right)}\end{array}$$

(12)

Among them, $y_i=\left\{y_{\left(i,1\right)},y_{\left(i,2\right)},\cdots ,y_{\left(i,12\right)}\right\}$ represents the i-th test sample, which consists of TEC maps at 12 different times in a day; ${\widehat{y}}_i=\left\{{\widehat{y}}_{\left(i,1\right)},{\widehat{y}}_{\left(i,2\right)},\cdots ,{\widehat{y}}_{\left(i,12\right)}\right\}$ represents the model’s prediction of the i-th sample; $m$ is the total number of test samples; ${\mu }_{y_{\left(i,j\right)}}$ represents the mean of the j-th TEC map of the i-th test sample; ${\mu }_{{\widehat{y}}_{\left(i,j\right)}}$is the mean of the predicted TEC map; ${\sigma }_{y{\widehat{y}}_{\left(i,j\right)}}$ represents the covariance between the true and predicted TEC maps; ${\sigma }_{y_{\left(i,j\right)}}^2$and ${\sigma }_{{\widehat{y}}_{\left(i,j\right)}}^2$represent the variance of the true and predicted values separately, ${\mathrm{c}}_1={\left({\mathrm{k}}_{1}L\right)}^2$ and ${\mathrm{c}}_2={\left({\mathrm{k}}_{2}L\right)}^2$ are constant used to maintain stability, L is the maximum value in the TEC map, $k_1=0.01$, and $k_2=0.03$.

4.2. Experiments

4.2.1. Comparison of Prediction Performance under Different Solar Activities

Table 2. Predictive assessment results under different solar activities.

Solar Activity	Model	RMSE (TECU)	MAE (TECU)	SSIM	MAPE (%)
High (2015)	C1PG	4.9	3.4	0.9362	13.77
	LSTM	5.2	3.4	0.8968	12.61
	GRU	5.1	3.5	0.9216	13.69
	ConvGRU	4.7	3.2	0.9388	12.12
	Ours	4.7	3.2	0.9390	12.02
Normal (2016)	C1PG	3.5	2.4	0.9177	14.24
	LSTM	3.5	2.4	0.8924	13.41
	GRU	3.5	2.4	0.9094	14.48
	ConvGRU	3.4	2.3	0.9200	13.02
	Ours	3.4	2.2	0.9244	12.70
Low (2019)	C1PG	1.8	1.3	0.9365	11.75
	LSTM	2.4	1.2	0.9157	10.91
	GRU	1.9	1.3	0.9267	13.01
	ConvGRU	1.7	1.2	0.9392	10.71
	Ours	1.6	1.1	0.9432	10.15

shows the predictive performance of five models under various solar activity conditions. It can be seen that our model has significant advantages over time series prediction models (LSTM and GRU) in all solar activities. In high solar activity years, our model’s RMSE decreased by 9.62% and 7.84%, respectively; MAE decreased by 5.88% and 8.57%, respectively; MAPE decreased by 4.68% and 12.20%, respectively; SSIM increased by 4.71% and 1.89%, respectively. In normal solar activity year, our model’s RMSE decreased by 2.86% and 2.86%, respectively; MAE decreased by 8.3% and 8.3%, respectively; MAPE decreased by 5.29% and 12.29%, respectively; SSIM increased by 3.59% and 1.65%, respectively. In low solar activity years, our model’s RMSE decreased by 33.33% and 15.79%, respectively; MAE decreased by 8.3% and 15.38%, respectively; MAPE decreased by 7.0% and 21.98%, respectively; SSIM increased by 3.00% and 1.78%.

Compared with the one-day TEC prediction product C1PG provided by CODE, the prediction performance of our model is also significantly improved. In high solar activity years, compared to C1PG, our model’s RMSE decreased by 4.08%, MAE decreased by 5.88%, MAPE decreased by 12.71%, and SSIM increased by 0.3%. In the normal solar activity years, our model’s RMSE decreased by 2.86%, MAE decreased by 8.3%, MAPE decreased by 10.81%, and SSIM increased by 0.73%. In low solar activity years, our model’s RMSE decreased by 11.11%, MAE decreased by 15.38%, MAPE decreased by 13.62%, and SSIM increased by 0.72%.

Compared with the spatiotemporal prediction model ConvGRU, our model’s MAPE decreased by 0.83% in high solar activity years, while other indicators were similar. In normal solar activity years, our model’s MAE decreased by 4.35%, MAPE decreased by 2.84%, and SSIM increased by 0.48%; In low solar activity years, our model’s RMSE decreased by 5.88%, and MAE reduced by 8.30%, MAPE decreased by 5.23%, and SSIM increased by 0.43%.

From Table 2, it can also be seen that the spatiotemporal prediction models (ConvGRU and ED-ConvLSTM) have better prediction performance than the time series prediction models (LSTM and GRU) and the C1PG products of CODE. In spatiotemporal prediction models, our ED-ConvLSTM outperforms ConvGRU.

Figure 6, Figure 7 and Figure 8 further demonstrate the statistical distributions of prediction errors between our model and four comparative models in low, normal, and high solar activity years. In these three figures, a, b, c, and d, respectively, represent the comparison of error distribution between our model and C1PG, LSTM, GRU, and ConvGRU. The x-axis denotes the prediction error and the y-axis represents the proportion of each error interval.

As can be seen from Figure 6 (2015, high solar activity year), the prediction error ratio of ED-ConvLSTM around 0 is significantly higher than those of C1PG and GRU, and slightly higher than that of LSTM, approximate to that of ConvGRU. From Figure 8 (2019, low solar activity year), it can be seen that the prediction error of ED-ConvLSTM is mainly distributed between −2 TEC and 1 TECU, and its prediction error ratio near 0 is higher than that of the other three models.

From Figure 7, it can be seen that in a normal solar activity year, the proportion of errors in our model around 0 is much higher than that of C1PG, GRU, and LSTM, and is similar to that of ConvGRU.

From Figure 8, it can be seen that in a low solar activity year, the proportion of errors in our model around 0 is significantly higher than that of C1PG, GRU, LSTM, and ConvGRU.

The paper also discusses the prediction performance monthly during different solar activity periods, and discusses the relationship between prediction performance and TEC monthly mean. The results are shown in Figure 9, Figure 10, Figure 11 and Figure 12.

From Figure 9, it is evident that TEC monthly average exhibited an initial increase followed by a subsequent decrease throughout the high solar activity year of 2015. The TEC monthly average attained its maximum value of 44.87 TECU in April and its minimum value of 19.16 TECU in December. Comparing the prediction results of each model, it is notable that the absolute error RMSE and MAE of each model follow the same trend as that of the TEC mean value. Specifically, in the months when the TEC monthly mean value is high, the absolute error RMSE and MAE are also high. However, the relative errors of MAPE and SSIM of each model remain relatively stable. The comparison results between our proposed model, ED-ConvLSTM, and classical time-series prediction models LSTM and GRU show that the prediction errors (MAE, RMSE) of ED-ConvLSTM are significantly lower than those of LSTM and GRU in January, February, March, April, July, and October, and slightly better in the remaining months. In April, when the TEC monthly average was the highest, the MAE index of ED-ConvLSTM decreased by 11.03% and 14.91% compared to LSTM and GRU, while the RMSE index decreased by 8.65% and 9.71%. In terms of similarity index, SSIM, when the monthly mean of TEC is high in March and April, the SSIM index of LSTM and GRU significantly decreases, while ED-ConvLSTM remains stable throughout the year and higher than those of LSTM and GRU. In terms of relative prediction error, the MAPE index of ED-ConvLSTM mainly fluctuates between 10.5% and 12.75%, which is more stable compared to the 10.5% to 15% of LSTM and the 12% to 16% of GRU. This indicates that during the high solar activity year, when TEC mean fluctuates significantly, the prediction performance of ED-ConvLSTM is relatively stable and superior to LSTM and GRU.

Compared with C1PG, the MAE index of ED-ConvLSTM is better in January, February, April, July, September, October, November, and December. The superiority of our model is most evident in January and February, with MAE reduced by 25.51% and 15.14% compared to C1PG, respectively. In terms of MAPE indicator, the MAPE of C1PG fluctuated significantly during January, February, November, and December, while our ED-ConvLSTM’s MAPE was more stable and significantly lower than that of C1PG.

From Figure 9, it can also be seen that in a high solar activity year, the spatiotemporal prediction model ConvGRU and ED-ConvLSTM have similar prediction performance, outperforming LSTM and GRU throughout the year, surpassing C1PG in most months. Especially in terms of MAPE and SSIM indicators, our ED-ConvLSTM has significantly better stability than the LSTM, GRU, and C1PG.

Figure 10 shows the predictive performance of various models in a normal solar activity year (2016). It can be seen that in March, April, June, and July, our model is slightly inferior to ConvGRU, but significantly superior to LSTM, GRU, and C1PG. In the remaining months, our model outperforms all comparative models.

Figure 11 shows the predictive performance of our model and LSTM, GRU, and C1PG in 2019. It can be seen that the TEC monthly mean changes in 2019 are similar to those in 2015. The TEC monthly mean reached its highest value of 14.31 TECU in April and its lowest value was 9.09 TECU in December. The prediction error indicators (MAE, RMSE, MAPE) of various models vary with the monthly mean of TEC, while the similarity index SSIM is relatively stable. The MAE and RMSE of ED-ConvLSTM are lower than those of GRU throughout the year, and are lower than those of LSTM in most months. Especially in May, when TEC are relatively high, our ED-ConvLSTM had a 15.99% and 19.37% decrease in RMSE and MAE compared to GRU; compared with LSTM, our model reduces MAE and RMSE by 10.19% and 14.83%, respectively. In terms of MAPE indicators, our ED-ConvLSTM’s MAPE is significantly lower than that of the comparative models. In terms of SSIM indicators, all models showed a decrease in April and May, which is related to the TEC monthly average reaching the maximum value of the year in April and May. During these two months, our ED-ConvLSTM model showed a smaller decrease in SSIM compared to LSTM and GRU.

From Figure 11, it can also be seen that in low solar activity years, compared to C1PG, the MAE and RMSE of ED-ConvLSTM are better than those of C1PG throughout the year, especially when the monthly mean TEC value is high. For example, in May, the RMSE and MAE of ED-ConvLSTM significantly decreased by 15.98% and 17.93% compared to C1PG. In terms of SSIM indicators, when the monthly mean of TEC increases, such as in March, April, May, and June, the SSIM indicators of ED-ConvLSTM and C1PG both decrease, but ED-ConvLSTM decreases less and is more stable.

To sum up, in terms of absolute error (MAE and RMSE), all models are affected by the TEC mean value in both high and low solar activity years, but our model is the least affected. In terms of the predicted relative error MAPE and similarity index SSIM, LSTM and GRU are more affected by solar activity, followed by C1PG, and ED-ConvLSTM is the least affected by solar activity. Whether in high or low solar activity years, the performance of our model is relatively stable, and the prediction results are more reliable.

Figure 12 shows the predictive performance of ED-ConvLSTM and ConvGRU. In 2019, in February, March, April, May, and October, when the monthly mean TECs are high, there is no significant difference in performance between ED-ConvLSTM and ConvGRU. In other months with lower monthly mean TEC, ED-ConvLSTM is significantly better than ConvGRU.

We also calculated the average absolute error MAE of the predicted values every two hours in one day in 2015, 2016, and 2019, and the results are shown in Figure 13, Figure 14 and Figure 15.

From Figure 13, it can be seen that in the high solar activity year, between UT 2:00 and UT 16:00, the TEC values in the middle and low latitudes of the study area are relatively large, and the MAE of each model in this area is also relatively large at that time. The ED-ConvLSTM has the best performance. The conclusions in a normal solar activity year (Figure 14) and in a low solar activity year (Figure 15) are similar to those in a high solar activity year (Figure 13).

4.2.2. Impact of Magnetic Storms on Prediction Performance

Magnetic storms can cause significant fluctuations in the ionospheric TEC [26], which can affect the accuracy of ionospheric TEC prediction [37]. The Dst index can describe the degree of magnetic storms and serves as a standard for classifying geomagnetic storm levels [38]. Based on the Dst, geomagnetic activity can usually be categorized into five categories: quiet (>−30 nT), minor storm (−50 nT < Dst ≤ −30 nT), moderate storm (−100 < Dst ≤ −50), major storm (−200 < Dst ≤ −100), and severe storm (Dst ≤ −200), as shown in

Table 3. Classification of geomagnetic activity.

Dst/nT	Geomagnetic Activity
−50 < Dst ≤ −30	Minor storm
−100 < Dst ≤ −50	Moderate storm
−200 < Dst ≤ −100	Major storm
Dst ≤ −200	Severe storm

. In order to compare the predictive performances of our ED-ConvLSTM model with LSTM, GRU, and C1PG during magnetic storms, this paper selected two magnetic storm events during 2015: DOY73~DOY79 and DOY171~DOY177. The Dst index peaked at DOY76 and DOY174, reaching −234 nT and −198 nT, respectively, corresponding to severe storm and major storm levels. We evaluated the predictive performance of each model during the two magnetic storms, and the results are shown in Figure 13 and Figure 14.

Figure 16 illustrates the variances in Dst over the duration from DOY73 to DOY79, along with the daily predictive performance of the four models. Notably, the magnetic storm attained its peak intensity at DOY76 and persisted until DOY77, emerging as a severe storm. Prior to DOY77, the predictive performances of all five models were relatively similar. However, when the magnetic storm occurred at DOY77, the RMSE and MAE of all five models rose significantly. The RMSE of C1PG, ED-ConvLSTM, ConvGRU, LSTM, and GRU escalated to 21.5 TECU, 16.1 TECU, 18.4 TECU, 21.6 TECU, and 19.2 TECU, respectively, while the MAE attained values of 15.9 TECU, 11.4 TECU, 13.7 TECU, 16.2 TECU, and 14.7 TECU, respectively.

However, our ED-ConvLSTM model outperformed the other three methods significantly in term of RMSE and MAE. Specifically, compared to C1PG, LSTM, GRU, and ConvGRU, our model’s RMSE decreased by 25.12%, 25.46%, 16.15%, and 12.50%, respectively, while the MAE decreased by 28.30%, 29.63%, 22.45%, and 16.79%, respectively. Regarding relative error, the MAPE of ED-ConvLSTM is 55.03%, which is 23.89%, 26.59%, 19.76%, and 14.40% lower than those of C1PG, LSTM, GRU, and ConvGRU, respectively. Moreover, during magnetic storms, the SSIM of all five models in DOY77 also significantly decreased. The SSIM of ED-ConvLSTM was 0.7005, which was 12.60%, 22.08%, 11.53%, and 7.00% higher than those of C1PG, LSTM, GRU, and ConvGRU, respectively. Therefore, it is evident that our ED-ConvLSTM model has better anti-interference performance during large magnetic storms.

On DOY77, the magnetic storm reached its maximum value, and the predicted residuals of each model during that day are shown in Figure 17. It can be seen that our ED-ConvLSTM prediction has the smallest residual errors.

Figure 18 shows predicted performance comparisons during the DOY171−DOY177 magnetic storm in 2015. From the Dst chart, the magnetic storm reached major storm level on DOY174. At this time, the RMSE of C1PG, ED-ConvLSTM, ConvGRU, LSTM, and GRU reached 7.9 TECU, 6.8 TECU, 7.2 TECU, 7.7 TECU, and 6.9 TECU, respectively, and the MAE reached 6.3 TECU, 5.4 TECU, 6.0 TECU, 6.3 TECU, and 5.7 TECU, respectively. The RMSE of the ED-ConvLSTM model was reduced by 13.92%, 11.69%, 1.45%, and 5.56% compared to C1PG, LSTM, GRU, and ConvGRU, respectively, and its MAE was reduced by 14.29%, 14.29%, 3.57%, and 10.0%, respectively. By comparing the relative error indicators, it can be seen that the MAPE of ED-ConvLSTM is 30.22%, which is 4.22%, 5.9%, 2.91%, and 5.48% lower than those of C1PG, LSTM, GRU, and ConvGRU, respectively. Additionally, the SSIM indicators for the four models showed a decrease on DOY174, with ED-ConvLSTM achieving a higher value of 0.8746, representing an improvement of 3.70%, 10.53%, 1.89%, and 1.19% over C1PG, LSTM, GRU, and ConvGRU, respectively.

In summary, the TEC spatiotemporal prediction model ED-ConvLSTM proposed in this paper can better resist magnetic storm interference during magnetic storms, and its prediction performance is superior to the comparison model.

Figure 19 shows the residuals predicted by various models during the maximum geomagnetic storm on DOY174 in 2015. It can be seen that our ED-ConvLSTM model has the best prediction performance.

5. Discussion

This article designed a TEC spatiotemporal prediction model, ED-ConvLSTM, based on the encoder-decoder structure. The encoder part of our model was used to extract spatiotemporal features from 84 TEC maps inputted for 7 consecutive days, obtaining spatiotemporal feature vector from the historical TEC map sequence inputted into the model. The decoder part was used to convert the spatiotemporal feature vector into 12 predicted TEC maps for the next day. In the paper, 1446 samples (723 each in the high and low years of solar activity) were selected to train our model. We compared our model with LSTM, GRU, ConvGRU, and C1PG on 1096 test samples (365 from high solar activity years, 366 from normal solar activity years, and 365 from low solar activity years). The results indicate that the predictive performance of our proposed model is superior to that of the comparative models under all solar activities. We also provided detailed error distributions for all models and found that our model had a higher proportion of errors near 0 than the comparison models. We also analyzed the predictive performance of each model month by month and compared it with the TEC monthly mean values. We found that the predictive performance of each model is affected by the TEC monthly mean values, and our model outperformed the comparison models in the vast majority of months. We also calculated the MAE predicted by each model every 2 h in 2015, 2016, and 2019. The results indicate that between UT 2:00 and UT 16:00, the TEC mean is relatively large in the middle and low latitudes of the study area, and the predictive performance of each model is also poor, while the predictive performance of the model in this paper is the best.

We also discussed the comparison of the predictive performances of various models during two magnetic storms in 2015. The results showed that our ED-ConvLSTM is significantly better than the other four comparative models during the occurrence of magnetic storms.

6. Conclusions

We propose a TEC map prediction model, ED-ConvLSTM, which can simultaneously consider spatiotemporal characteristics when predicting TEC. We apply the proposed model to predict TEC map in the East Asian region (10°–45°N, 90°–130°E). We compared our model with ConvGRU, LSTM, GRU, and the 1-day forecast product C1PG provided by CODE. The experimental results indicate that:

• Under all solar activities, our ED-ConvLSTM is superior to ConvGRU, LSTM, GRU, and C1PG in terms of RMSE, MAE, MAPE, and SSIM.
• We compared the predictive performance of various models in 2015, 2016, and 2019 month by month. It was found that the MAE and RMSE of the five models are significantly influenced by the TEC monthly mean and fluctuated synchronously with it. The MAPE and SSIM indicators are less affected by the monthly TEC mean. Our ED-ConvLSTM is the least affected by the monthly mean of TEC, and the prediction results are the most stable.
• The predictive performance of all five models decreased during magnetic storms, but our ED-ConvLSTM had the least impact during magnetic storms and is significantly better than the comparison models.

The ED-ConvLSTM model proposed in this article is based on the encoder–decoder architecture. Due to its structural limitations, the historical TEC map spatiotemporal variation information encoded by the encoder is stored in a spatiotemporal feature vector, which may result in the loss of information and affect the prediction performance of the decoder. Therefore, our future work will improve the structure of the model, minimize the loss of spatiotemporal information, and establish a more accurate TEC map prediction model.