Global Ionosphere Total Electron Content Prediction Based on Bidirectional Denoising Wavelet Transform Convolution

Abstract

The Denoising Wavelet Transform Convolutional Long Short-Term Memory Network (DWTConvLSTM) is a novel ionospheric total electron content (TEC) spatiotemporal prediction model proposed in 2025 that can simultaneously consider high-frequency and low-frequency features while suppressing noise. However, it also has flaws as it only considers unidirectional temporal features in spatiotemporal prediction. To address this issue, this paper adopts a bidirectional structure and designs a bidirectional DWTConvLSTM model that can simultaneously extract bidirectional spatiotemporal features from TEC maps. Furthermore, we integrate a lightweight attention mechanism called Convolutional Additive Self-Attention (CASA) to enhance important features and attenuate unimportant ones. The final model was named CASA-BiDWTConvLSTM. We validated the effectiveness of each improvement through ablation experiments. Then, a comprehensive comparison was performed on the 11-year Global Ionospheric Maps (GIMs) dataset, involving the proposed CASA-BiDWTConvLSTM model and several other state-of-the-art models such as C1PG, ConvGRU, ConvLSTM, and PredRNN. In this experiment, the dataset was partitioned into 7 years for training, 2 years for validation, and the final 2 years for testing. The experimental results indicate that the RMSE of CASA-BiDWTConvLSTM is lower than those of C1PG, ConvGRU, ConvLSTM, and PredRNN. Specifically, the decreases in RMSE during high solar activity years are 24.84%, 16.57%, 13.50%, and 10.29%, respectively, while the decreases during low solar activity years are 26.11%, 16.83%, 11.68%, and 7.04%, respectively. In addition, this article also verified the effectiveness of CASA-BiDWTConvLSTM from spatial and temporal perspectives, as well as on four geomagnetic storms.

1. Introduction

The Global Navigation Satellite System (GNSS) provides users worldwide with all-weather, all-day, high-precision positioning, navigation, and timing services [1,2]. However, GNSS services are affected by many factors, resulting in errors [3]. The largest source of error comes from the ionosphere [4]. The ionosphere is located 60 to 1000 km above the Earth’s surface, where air molecules are partially ionized into charged particles by high-energy solar radiation and cosmic rays [5]. When the electromagnetic wave signals emitted by GNSS pass through the ionosphere, they will undergo physical bending, refraction, attenuation, and polarization rotation because of these charged particles, resulting in ionospheric delay [6]. To improve the accuracy of GNSS, it is necessary to first calculate the ionospheric delay and then correct it. Since ionospheric delay is directly proportional to total electron content (TEC), high-precision TEC prediction can effectively correct ionospheric delay errors, thus enhancing the positioning precision of GNSS-dependent systems [7,8]. In addition, extreme space weather and geological disasters can also manifest in the ionosphere [9]. TEC prediction can help to detect ionospheric anomalies in advance, monitor and warn of extreme space weather and geological disasters, and reduce their impact on humans [10]. Therefore, TEC prediction is of great significance.

Due to the influence of solar activity, geomagnetic activity, geographical location, and seasons, TEC exhibits complex spatiotemporal variations, mainly manifested as various irregular structures and abnormal phenomena in Global Ionosphere Maps (GIMs) [11,12], making TEC prediction very challenging.

Despite the difficulties in TEC prediction, researchers have developed a large number of prediction methods, which can be roughly divided into four categories: empirical models, traditional time series models, shallow machine learning models, and deep learning models [13]. The ionospheric empirical models are based on mathematical fitting of a large amount of observational data, including the International Reference Ionosphere (IRI) [14], the NeQuick model [15,16], the Klobuchar model [17], the Bent model [18,19], etc. The main drawback of ionospheric empirical models is that they are not effective enough in predicting disturbances and irregular changes in the ionosphere [20]. TEC prediction has relied on traditional time series models, including the Autoregressive (AR) model [21], Autoregressive Integrated Moving Average (ARIMA) [22,23,24], Autoregressive Moving Average (ARMA) [25], etc. While outperforming empirical models in short-term TEC forecasting, these conventional approaches remain fundamentally linear and thus incapable of characterizing TEC’s intricate nonlinear spatiotemporal dynamics [26].

Since 1998, the International GNSS Services (IGS) ionospheric working group has been continuously releasing Global Ionospheric Maps (GIMs) to the world. These GIMs have facilitated the flourishing of machine learning-based methods in TEC prediction. Initially, researchers developed some shallow machine learning models to predict TEC, such as support vector machine (SVM) [27], artificial neural networks (ANN) [28], random forests [29], Gradient Boosting Decision Tree (GBDT) [30], eXtreme Gradient Boosting (XGBoost) [31], nearest neighbor [32], etc. These shallow machine learning models learn complex nonlinear mappings from input to output, with a minimal loss on the training set. However, they do not consider the temporal dependencies of data. TEC prediction is essentially a sequence-based modeling problem. Without considering temporal dependencies, shallow machine learning models are inferior to recurrent neural networks (RNNs) in TEC prediction.

In the past five years, a large number of deep learning models, specifically recurrent neural networks, have been developed for TEC prediction. Such models may be systematically classified as either temporal sequence deep learning models or spatiotemporal sequence deep learning models. Time series deep learning models assume that the TEC sequences of different sites are independent when predicting TEC. They initially trained a deep learning model using historical TEC sequences from a specific station, subsequently employing the trained model to forecast future TEC values at that station. Models in this type are mainly built using Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), Recurrent Neural Network (RNN) and their variants, including LSTM [33], ED-LSTM [34], Ion-LSTM [35], BiLSTM [36], LSTM-CNN [37], LSTM-Attention [38], attention-BiLSTM [39], Att-CNN-BiLSTM [40], Mixed CNN-BiLSTM [41], DBO-BiLSTM [42], GRU [43], CNN–GRU [44], RNN [45,46], etc. The drawback of time series deep learning models is that they ignore the spatial correlation of TEC between adjacent sites during modeling, which limits their performance. Spatiotemporal series deep learning models treat TEC prediction as a map sequence prediction problem. They typically embed two-dimensional convolution into LSTM, GRU, and their variants, with two-dimensional convolution extracting TEC spatial features and LSTM/GRU extracting temporal features. At present, the mainstream spatiotemporal series deep learning models in TEC prediction are mainly constructed based on ConvLSTM, ConvGRU, PredRNN, and their variants, including ConvLSTM [47], RA-ConvLSTM [48], SegED-ConvLSTM [49], CGAOA-STRA-BiConvLSTM [50], SAM-ConvLSTM [51], ED-ConvLSTM [52,53], ConvGRU [54], attention Bi-ConvGRU [55], PredRNN [56], Multichannel ED-PredRNN [57], etc. Recent studies have shown that in TEC modeling, spatiotemporal deep learning models consistently achieve superior performance to purely temporal models, owing to their dual capacity to capture both temporal evolution and spatial correlations in TEC variations [43].

In summary, empirical models are unable to capture ionospheric disturbances and irregular variations. Traditional time series models are fundamentally linear and fail to describe the nonlinear spatiotemporal dynamics of TEC. Shallow machine learning models can learn nonlinear relationships but neglect temporal dependencies. Even current spatiotemporal deep learning models based on ConvLSTM, ConvGRU, and PredRNN still face challenges: they cannot simultaneously consider both low-frequency and high-frequency features, and are susceptible to noise.

The recently proposed DWTConvLSTM can effectively extract high-frequency and low-frequency features and reduce the influence of noise bands. However, it only considers one-way time dependence and relies entirely on past information in the spatiotemporal prediction process, which limits the accuracy of the model. To overcome this drawback, this paper introduces a bidirectional structure and proposes a BiDWTConvLSTM model. By simultaneously modeling temporal dependencies from both forward and backward directions, BiDWTConvLSTM is able to capture rich spatiotemporal dependencies from the past and the future, thus compensating for the inherent limitations of unidirectional DWTConvLSTM. Then, this article also integrates the recently proposed CASA mechanism to adaptively enhance salient spatiotemporal features and suppress redundant information. Our final TEC spatiotemporal prediction model is named CASA-BiDWTConvLSTM.

The effectiveness of our improvements is first verified through ablation experiments. We conduct a comprehensive performance evaluation of the proposed CASA-BiDWTConvLSTM against four established baseline models (ConvLSTM, ConvGRU, PredRNN, and C1PG) through multi-dimensional comparative experiments. Among the four comparative models, the first three are the mainstream spatiotemporal prediction models currently used in TEC prediction; the last, C1PG, is the TEC daily prediction product provided by the Center for Orbit Determination in Europe (CODE).

The rest of this paper is structured as follows: Section 2 describes the data and data preprocessing; Section 3 presents the methodology; Section 4 provides the experimental results; Section 5 summarizes the paper.

2. Data and Data Preprocessing

The GIMs used in this study are from the International GNSS Service (IGS). These maps are generated every 2 h and contain 12 maps per day. In space, these data are discretized into a 71 × 73 grid with resolutions of 5° (longitude) and 2.5° (latitude).

The GIMs in this paper span 11 years, from UT 0:00, 1 January 2009 to UT 22:00, 31 December 2019, with 7 years of GIMs selected as the training set, 2 years as the validation set, and 2 years as the testing set. The detailed division of the dataset is shown in Figure 1, and it can be seen that all three datasets contain GIMs for both high solar activity years and low solar activity years. The training set, validation set, and test set are mutually exclusive, meaning that the training set, validation set, and test set are unseen to each other, so as to ensure the reliability of the results.

3. Methodology

This article extends DWTConvLSTM by introducing a bidirectional structure to overcome its limitation of relying only on unidirectional time information, thereby capturing the forward and backward dependencies in TEC sequences. In addition, we also embed the recently proposed CASA technique to adaptively enhance important features and suppress unimportant features. This section will introduce these technologies separately.

3.1. Denoising Wavelet Transform Convolutional Long Short-Term Memory (DWTConvLSTM)

The Denoising Wavelet Transform Convolutional Long Short-Term Memory Network, abbreviated as DWTConvLSTM, is an efficient spatiotemporal feature extraction unit that was proposed in 2025 [13]. It can simultaneously extract high-frequency and low-frequency features and exhibits robust noise resistance. Its core is the denoising wavelet transform convolution (DWTConv), and its calculations are as follows:

$$\left[X_{LL},X_{LH},X_{HL},X_{HH}\right]=\mathrm{W}\mathrm{T}\left(X\right)$$

(1)

$$\left[Y_{LL},Y_{LH},Y_{HL},Y_{HH}\right]=\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{v}\left(\left[X_{LL},X_{LH},X_{HL},X_{HH}\right]\right)$$

(2)

$$LF=\mathrm{I}\mathrm{W}\mathrm{T}\left(\left[Y_{LL},Y_{LH},Y_{HL},0\right]\right)$$

(3)

$$HF=\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{v}\left(X\right)$$

(4)

$$Z=LF+HF$$

(5)

Among them, $X$ is the original input image; $\mathrm{W}\mathrm{T}$(.) and $\mathrm{I}\mathrm{W}\mathrm{T}$(.) represent the Haar wavelet transform and inverse Haar wavelet transform, respectively.$\left[X_{LL},X_{LH},X_{HL},X_{HH}\right]$ are the 4 sub-band images obtained through Haar wavelet decomposition. $\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{v}$(.) denotes a standard convolution with a size of 3 × 3. $LF$ and $HF$, respectively, represent the low-frequency features and high-frequency features of the input image. $Z$ is the final fused feature, which contains both low-frequency and high-frequency features.

DWTConv supports multi-level implementation, with the computational procedure for the $i$-th level expressed as:

$$Z={LF}^1+HF$$

(6)

$${LF}^i=\mathrm{I}\mathrm{W}\mathrm{T}\left(\left[{LF}^{i+1}+Y_{LL}^i,Y_{LH}^i,Y_{HL}^i,0\right]\right),i\ge 1$$

(7)

where $i$ represents the number of levels in the cascade. When cascading the $i$-th level, ${LF}^{\mathrm{i}+1}$ is set to 0.

The process of feature extraction using a two-level DWTConv is shown in Figure 2.

Replacing the standard convolution in ConvLSTM with DWTConv constitutes DWTConvLSTM. The calculation process of DWTConvLSTM is shown as follows.

$${ f}_t=\sigma \left(W_{xf}▲X_t+W_{hf}▲h_{t-1}+b_f\right)$$

(8)

$$i_t=\sigma \left(W_{xi}▲X_t+W_{hi}▲h_{t-1}+b_i\right)$$

(9)

$${ \tilde{c}}_t=tanh\left(W_{xc}▲X_t+W_{hc}▲h_{t-1}+b_c\right)$$

(10)

$${ C}_t=f_tʘC_{t-1}+i_tʘ{\tilde{c}}_t$$

(11)

$${ o}_t=\sigma \left(W_{xo}▲X_t+W_{ho}▲h_{t-1}+b_o\right)$$

(12)

$${ h}_t=o_tʘ{tanh(C}_t)$$

(13)

Among them, $▲$ represents WTDConv. The other symbols are exactly the same as those in ConvLSTM. The structural comparison between DWTConvLSTM and ConvLSTM is presented in Figure 3, where the DWTConv is located within the red rectangle.

3.2. Bidirectional Denoising Wavelet Transform Convolutional Long Short-Term Memory Network (BiDWTConvLSTM)

DWTConvLSTM enhances feature extraction through denoising convolution, but its unidirectional structure limits its ability to extract TEC features. To overcome this drawback, we propose a bidirectional spatiotemporal feature extraction unit, Bidirectional Denoising Wavelet Transform Convolutional Long Short-Term Memory Network (BiDWTConvLSTM), by connecting forward and backward DWTConvLSTM. The structure of a BiDWTConvLSTM unit is presented in Figure 4, where $h_{t\left(fwd\right)}$ is the output of a forward DWTConvLSTM, $h_{t\left(bwd\right)}$ is the output of a backward DWTConvLSTM, and $h_t$ is the output of a BiDWTConvLSTM.

3.3. Convolutional Additive Self-Attention (CASA)

The BiDWTConvLSTM introduced in the previous subsection is used to extract spatiotemporal features from TEC map sequences. Numerous existing studies have shown that not all features are equally important in deep learning applications. Attention technology can highlight key features and suppress unimportant features [58,59]. Adding attention techniques to deep learning tasks can improve the efficiency of feature utilization, thereby enhancing the performance of the model.

Convolutional Additive Self-Attention (CASA) is a lightweight variant of self-attention, which replaces the time-consuming paired queries in self-attention by performing lightweight spatial and channel interactions on features to reduce the time complexity [60]. Considering the efficiency and performance of CASA, we add it to our model to weight the spatiotemporal features extracted by BiDWTConvLSTM.

The schematic diagram of CASA is shown in Figure 5. Its core components are the spatial interaction (Figure 5a) and the channel interaction (Figure 5b). The spatial interaction part is designed similar to spatial attention. Specifically, it receives the input and mixes the spatial information in the input through a two-dimensional convolution layer (Conv2D) with a size of 3 × 3. Next is the batch normalization layer (BatchNorm2D), which is used to normalize the features in each batch to reduce the internal covariate shift and accelerate the training convergence speed of the network. Then, the ReLU activation function is used to enhance the nonlinear representation capability. Subsequently, it uses a 1 × 1 Conv2D layer and a sigmoid activation function to obtain the attention. Finally, this attention is multiplied onto the input, weighting the input from a spatial perspective. The channel interaction can be considered channel attention. It receives the input and then uses a global average pooling layer (AdaptiveAvgPool2D) to aggregate the input along the channel. Next, it uses 1 × 1 convolution and a sigmoid function to generate the channel attention. Finally, the channel attention is multiplied onto the input, weighting the input from a channel perspective. In CASA, the input feature $X$ is first linearly transformed independently to obtain three matrices $Q$, $K$, and $V$. Then, perform spatial interaction on $Q$ and $K$ separately to obtain $Q_s$ and $K_s$. Then, perform the channel interaction to obtain $Q_c$ and $K_c$. Afterwards, $Q_c$ and $K_c$ are integrated through additive operation. Finally, perform a two-dimensional convolution on the addition result to generate the attention and multiply this attention by $V$ to obtain the weighted feature $X^{\prime }$.

3.4. Overall Structure of the Proposed TEC Spatiotemporal Prediction Model

In this section, we integrate BiDWTConvLSTM (used for feature extraction) and CASA (used for feature weighting) to design a TEC spatiotemporal prediction model, CASA-BiDWTConvLSTM, whose detailed structure is shown in Figure 6. In this paper, both the input sequence and the output sequence consist of 12 TEC maps. So, both input and output tensors share the (12, 1, 71, 73) dimensional structure, where “12” represents the temporal sequence length for both input and output, “1” indicates the singular input channel, “71” and “73” correspond to the latitudinal and longitudinal grid points, respectively, in each TEC map. First, three pairs of BiDWTConvLSTM + LayerNorm are used to extract spatiotemporal features from the input. Here, LayerNorm is used for data normalization to reduce the risk of potential gradient vanishing and explosion caused by changes in data scale. Each BiDWTConvLSTM layer contains two tunable hyperparameters: the number of convolutional kernels and their size dimensions. In this work, we implement the model using Python 3.9 and PyTorch 2.2.2 with CUDA 11.8. In this article, Bayesian optimization is used to optimize them: (i) the number of convolutional kernels, with the search ranging from 8 to 64; (ii) the convolution kernel size, with the search space of {3 × 3, 5 × 5, 7 × 7}. The optimization objective was to minimize the validation $RMSE$. For each candidate configuration, the model was trained for 15 epochs, and the performance on the validation set was recorded. The optimization was run for 50 iterations. The search was conducted on an NVIDIA GeForce RTX 3090 GPU (manufactured by NVIDIA Corporation, Santa Clara, CA, USA), with each trial requiring about 45–55 min, and the entire optimization process consumed approximately 42 h. Finally, the best kernel number is 13 and the best size is (5, 5). Since each kernel can be viewed as a bidirectional feature extractor, it can generate two feature maps, one forward and one backward. A total of 13 kernels will generate 26 feature maps. Therefore, the output tensor size of these BiDWTConvLSTM + LayerNorms is (12, 26, 71, 73). Then, these feature maps are processed by the CASA module to perform adaptive feature weighting. Finally, the feature channels are adjusted through a Conv3D layer to generate 12 predicted TEC maps.

3.5. Evaluation Metrics

In this paper, Root Mean Square Error ($RMSE$) and Mean Absolute Percentage Error ($MAPE$) are used as the evaluation metrics; their calculations as presented as follows.

$$RMSE=\sqrt{{\displaystyle \frac{1}{m}}{\sum }_{i=1}^m{{(y}_i-{\widehat{y}}_i)}^2}$$

(14)

$$MAPE={\displaystyle \frac{1}{m}}{\sum }_{i=1}^m|{\displaystyle \frac{y_i-{\widehat{y}}_i}{y_i}}|\times 100\%$$

(15)

Among them, $m$ represents the total number of grid points within the test dataset. For each grid point $i$, ${\widehat{y}}_i$ denotes the predicted value, while $y_i$ signifies the corresponding true value, without considering the position and the timestamp.

4. Experiment and Analysis

The model is trained using the Adam optimizer with an initial learning rate of 0.001 and $RMSE$ as the loss function. We have adopted a ReduceLONPlateau dynamic learning rate scheduler: when the validation loss does not improve for 10 consecutive epochs, the learning rate will decay by a coefficient of 0.7. This dynamic learning rate adjustment strategy can effectively avoid the overfitting phenomenon.

4.1. Ablation Experiment

This subsection presents ablation studies to verify the functional importance of both the bidirectional structure and the CASA modules. In the ablation experiments, DWTConvLSTM is the basic model. By combining bidirectional modeling, we obtained BiDWTConvLSTM and finally added CASA to form CASA-BiDWTConvLSTM. For fair comparison, all models were optimized to their optimal performance using a Bayesian optimization algorithm. The experimental results are represented in

Table 1. Ablation experiment results (bold indicates superior performance).

Solar Activity	Model	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}$ (TECU)	$\mathit{M}\mathit{A}\mathit{P}\mathit{E}$
2015 (High)	DWTConvLSTM	3.5917	15.26%
	BiDWTConvLSTM	3.2961	14.49%
	CASA-BiDWTConvLSTM	3.1788	13.57%
2019 (Low)	DWTConvLSTM	1.2992	14.15%
	BiDWTConvLSTM	1.2573	13.82%
	CASA-BiDWTConvLSTM	1.1959	12.12%

, in which the best results are highlighted in bold. The percentage improvements are shown graphically in Figure 7.

First, we verify the effectiveness of the bidirectional structure by comparing DWTConvLSTM and BiDWTConvLSTM. From the experimental results in 2015 and 2019, it can be seen that the $RMSE$ of BiDWTConvLSTM decreased by 8.23% and 3.22%, and the $MAPE$ decreased by 5.04% and 2.33%. This demonstrates the effectiveness of the bidirectional structure in capturing richer temporal dependencies.

Second, we validate the effectiveness of CASA by comparing CASA-BiDWTConvLSTM and BiDWTConvLSTM. The results indicate that the CASA-BiDWTConvLSTM reduces $RMSE$ by 3.55% and 4.88%, and $MAPE$ by 6.34% and 12.3% in 2015 and 2019, compared with BiDWTConvLSTM. This improvement is only due to the addition of CASA, which verifies its effectiveness.

Further analysis based on Figure 7 reveals that compared with the improvements in low solar activity years, the bidirectional structure has greater improvements in high solar activity years. The reason for this phenomenon may be that during high solar activity, the ionospheric TEC experiences frequent and intense large-amplitude disturbances. This makes the temporal evolution of TEC more complex, involving not only interactions with past states but also interactions with subsequent changes. Unidirectional models may not be able to fully capture these dependencies, while bidirectional structures can simultaneously utilize past and future information. Therefore, it provides more comprehensive time feature extraction and achieves greater improvement in prediction accuracy under such interference conditions.

In general, the experimental results provide evidence of the effectiveness of the two proposed modules: the bidirectional structure and CASA. The synergistic combination of the two modules yields optimal prediction performance.

4.2. Comparison with Other Models

The preceding analysis has systematically verified the efficacy of each proposed enhancement. In this subsection, the performance of CASA-BiDWTConvLSTM will be evaluated through multi-faceted comparisons with alternative prediction methods. The comparative models include ConvGRU, ConvLSTM, PredRNN, and C1PG. Specifically, the first three are the mainstream deep learning models used for TEC spatiotemporal prediction, and C1PG is the TEC one-day prediction product provided by CODE. Among these comparative models, C1PG is the predictive product and can be directly used for comparison, while the other models are optimized by a Bayesian optimization algorithm to ensure their best performances.

4.2.1. Overall Quantitative Comparison

This subsection first provides a quantitative comparison of various models across all test samples, as shown in

Table 2. Overall quantitative comparison.

Solar Activity	Model	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}$ (TECU)	$\mathit{M}\mathit{A}\mathit{P}\mathit{E}$
High (2015)	C1PG	4.2296	19.88%
	ConvGRU	3.8102	17.10%
	ConvLSTM	3.6752	15.79%
	PredRNN	3.5436	14.98%
	CASA-BiDWTConvLSTM	3.1788	13.57%
Low (2019)	C1PG	1.6186	19.32%
	ConvGRU	1.4380	18.16%
	ConvLSTM	1.3541	14.68%
	PredRNN	1.2865	13.39%
	CASA-BiDWTConvLSTM	1.1959	12.12%

. It can be seen that in 2015, which is a high solar activity year, CASA-BiDWTConvLSTM achieved superior performance with an $RMSE$ of 3.1788 TECU, representing significant reductions of 24.84%, 16.57%, 13.50%, and 10.29% compared with C1PG, ConvGRU, ConvLSTM, and PredRNN, respectively. During the low solar activity period in 2019, the CASA-BiDWTConvLSTM model achieved reductions in $RMSE$ of 26.11%, 16.83%, 11.68%, and 7.04%, respectively. $MAPE$ of CASA-BiDWTConvLSTM decreased by 31.74%, 20.64%, 14.05%, and 9.41% in 2015 and by 37.26%, 33.25%, 17.43%, and 9.48% in 2019 compared with the four models, respectively.

Based on the above comparisons of $RMSE$ and $MAPE$, the proposed CASA-BiDWTConvLSTM is obviously superior to the comparative models.

Figure 8 further illustrates the differences in error distribution between CASA-BiDWTConvLSTM and the comparative model. Among them, the horizontal axis represents the prediction error value, and the vertical axis corresponds to the statistical results of the proportion of each error interval. The left and right subplots, respectively, present comparative data from 2015 and 2019. Based on Figure 8, a larger proportion of prediction errors in CASA-BiDWTConvLSTM cluster around zero relative to the competing models, confirming the superiority of CASA-BiDWTConvLSTM.

4.2.2. Comparison from the Spatial Perspective

The overall quantitative comparison of all the test samples is quite rough, with many details hidden. The distribution of ionospheric TEC is uneven and has complex spatial variations. This subsection will provide comparisons among various models by longitude and latitude, respectively.

First, we discuss the comparison from a latitude perspective. For this purpose, we divide the global TEC map into 18 subregions based on geographical latitude. Calculate the $RMSE$ of each model within each subregion and compare them. Figure 9 shows the performance comparison results of different models, with the top for 2015 and the bottom for 2019. Based on the figure, whether in 2019 or 2015, regardless of which subregion, the $RMSE$ of the proposed CASA-BiDWTConvLSTM is the smallest. This further validates the effectiveness of the model proposed. Figure 9 also reveals that the $RMSEs$ of all models exhibit bimodal anomalies near the equator. This is caused by the equatorial ionization anomaly (EIA) phenomenon. Additionally, it should be noted that C1PG also exhibits $RMSEs$ anomalies in high latitude subregions, especially in high latitude areas of the southern hemisphere.

Then, we discuss the comparison from the perspective of longitude. For this purpose, the world is divided into 15 subregions based on longitude, with each subregion spanning 25°. The comparisons of different longitude regions are shown in Figure 10. It indicates that the $RMSE$ of our model is also the lowest in each longitude region.

The detailed comparisons by longitude and latitude in this subsection further confirm the superiority of our proposed CASA-BiDWTConvLSTM.

4.2.3. Comparison from the Temporal Perspective

Apart from complex spatial variations, the ionosphere also exhibits complex temporal changes. This section validates the predictive ability of CASA-BiDWTConvLSTM from the time dimension. To attain the above-stated objective, we calculate and compare the monthly $RMSE$ and $MAPE$ of each model and represent them in Figure 11, where the x-axis represents the month. The top layer shows the results for 2015, and the bottom layer for 2019. In the figure, the lighter the color, the better the performance. It can be seen that in each month (column) of 2015 and 2019, the $RMSE$ and $MAPE$ of the proposed CASA-BiDWTConvLSTM are the smallest, indicating the effectiveness of CASA-BiDWTConvLSTM from a temporal perspective.

4.2.4. Visually Comparison

After the quantitative comparison, this study further conducted an intuitive comparative analysis. For visual comparison, we compare model predictions at four key times (UT 00:00, UT 6:00, UT 12:00, UT 18:00) using selected days from 2015 (DOY 203) and 2019 (DOY 224). The predictive effects on the selected two days are presented in Figure 12 and Figure 13. Based on these figures, it can be seen that the TEC prediction map of the proposed model is closer to the true map, and the difference is relatively small compared with other models. For ease of comparison, the corresponding absolute error contour maps on these two days are shown in Figure 14 and Figure 15, respectively. In addition, we labeled the $RMSE$ of each model on each map, with the best highlighted in red. Based on Figure 14 and Figure 15, all models exhibit $RMSE$ anomalies in the EIA region. In most cases, C1PG consistently shows the largest anomaly regions, whereas CASA-BiDWTConvLSTM produces relatively smaller anomaly areas. In addition, in the mid or high latitudes of the southern hemisphere, especially near the Antarctic region, various models also exhibit $RMSE$ anomaly areas, with C1PG being the most obvious and our model being the least obvious. While no model completely eliminates errors in highly disturbed regions, CASA-BiDWTConvLSTM achieves consistently lower $RMSE$ across different times and solar activity conditions. This reflects its stronger ability to generalize under both high and low-activity scenarios.

4.2.5. Comparison of Geomagnetic Storm Periods

As shown in

Table 3. Descriptions of DOYs and minimum $\mathrm{D}\mathrm{s}\mathrm{t}$ for the selected four geomagnetic storm events.

Storm Event	DOYs	${\mathbf{D}\mathbf{s}\mathbf{t}}_{\mathit{m}\mathit{i}\mathit{n}}\left(\mathbf{n}\mathbf{T}\right)$
Case1	76–77	−234
Case2	173–174	−198
Case3	280–281	−130
Case4	354–355	−166

and Figure 16, in order to verify the effectiveness of CASA-BiDWTConvLSTM under extreme conditions, four geomagnetic storm events in 2015 were selected. For each geomagnetic storm, we choose the two days with the smallest $\mathrm{D}\mathrm{s}\mathrm{t}$ as extreme events.

Each geomagnetic storm event consists of 2 days and 24 TEC maps. For a given geomagnetic storm event, we calculate the $RMSE$ and $MAPE$ of each model on each TEC map and display their boxplots, as shown in Figure 17, with the left for $RMSE$ and the right for $MAPE$. In the boxplots, the top, bottom, and center lines of the rectangular box correspond to the upper quartile, lower quartile, and median of the indicator, respectively.

From the left column of Figure 17, we can see that for all four geomagnetic storm events, the median, upper quartile, and lower quartile of the $RMSE$ of our model are lower than those of the comparative models, indicating the superiority of our model under extreme situations. From the perspective of $MAPE$ (the right column of Figure 17), our model performs best in three cases except for Case 1. Our model has the lowest median $RMSE$ in case 1, while our median $MAPE$ is not the lowest, because $MAPE$ is a relative error metric. When a model has a large prediction error in areas with smaller TEC values, the $MAPE$ will be large. In Case 1, the median $MAPE$ of our model is slightly higher than that of PredRNN, and in all other cases, our model is the best.

Overall, the prediction results of the four geomagnetic storm events indicate that our model is also effective in extreme situations.

5. Conclusions

The recently proposed DWTConvLSTM model incorporates wavelet transformation to effectively capture multi-scale features from low to high frequencies while significantly suppressing noise interference. However, a notable limitation of this model lies in its unidirectional temporal structure, which relies solely on historical information for prediction, thereby making it inefficient for comprehensively characterizing the complex dynamic variations in ionospheric TEC. This article improves it by adopting a bidirectional structure to organize DWTConvLSTM and proposes BiDWTConvLSTM to solve the problem of its inability to accommodate bidirectional dependencies. In addition, we integrate a recently proposed CASA attention mechanism to focus on critical spatiotemporal features.

To validate the effectiveness of the bidirectional structure and CASA, ablation studies are first conducted. Following this, the proposed CASA-BiDWTConvLSTM model is benchmarked against C1PG, ConvGRU, ConvLSTM, and PredRNN on an 11-year GIM dataset (2009–2019). The overall quantitative comparison revealed that during the high solar activity year, our model outperformed competitors with $RMSE$ reductions of 26.11%, 16.83%, 11.68%, and 7.04%, accompanied by $MAPE$ decreases of 31.74%, 20.64%, 14.05%, and 9.41%, respectively; during the low solar activity year, our model’s $RMSE$ decreased by 26.11%, 16.83%, 11.68%, and 7.04%, and $MAPE$ decreased by 37.26%, 33.25%, 17.43%, and 9.48%. In addition, this article further compares various models from the perspectives of space and time in a more specific way, and these experimental results also confirmed the superiority of our proposed CASA-BiDWTConvLSTM. Finally, the comparative results on four geomagnetic storm events indicated that our model outperformed the comparative models under extreme situations.

However, there are also shortcomings in this study. The spatiotemporal resolution of the GIMs used in this article is not currently the highest. This is because using high-precision GIMs means expensive computing resources, which exceed what our devices can afford. Future research will concentrate on developing computationally efficient architectures tailored for high-resolution ionospheric TEC spatiotemporal forecasting. In addition, how to effectively integrate this model into actual GNSS service systems is also our future work.