A Spatiotemporal Network Model for Global Ionospheric TEC Forecasting
<p>The distribution of global IGS stations, the orange dots indicate IGS observatories at various locations around the world.</p> "> Figure 2
<p>A standard global ionospheric TEC map. Shown here is the global distribution of ionospheric TEC at hour 8 on 3 January 2013.</p> "> Figure 3
<p>The ST-LSTM unit’s internal structure. Superscript l indicates the number layer of the ST-LSTM unit in the stack, and subscript t indicates the current moment. Different letters indicate different parameters in the ST-LSTM unit.</p> "> Figure 4
<p>Spatiotemporal Network Model structure. Letters without the ~ symbol indicate the output of the global spatiotemporal characteristics extraction part, and letters with the ~ symbol indicate the output of the regional spatiotemporal characteristics correction part. The red arrow shows the ionospheric global spatiotemporal characteristics extraction module. The blue arrow shows the ionospheric regional spatiotemporal characteristics correction module.</p> "> Figure 5
<p>Structure of the ST-LSTM unit for the modified region spatiotemporal properties module. Different letters indicate different parameters in the ST-LSTM unit, superscript l indicates the number layer of the ST-LSTM unit in the stack and subscript t indicates the current moment.</p> "> Figure 6
<p>The convergence performance of the spatiotemporal network model using Huber loss function, L1 loss function, and L2 loss function trained for 200 epochs, respectively.</p> "> Figure 7
<p>Global ionospheric TEC map error distribution statistics for the maximum and minimum solar activity period forecasts. (<b>a</b>,<b>b</b>) are the error distribution statistics of the CODE and PredRNN models’ prediction results for the maximum and minimum solar activity periods, respectively. (<b>c</b>,<b>d</b>) are the error distribution statistics of the convLSTM and our models’ prediction results for the maximum and minimum solar activity periods, respectively. (<b>e</b>,<b>f</b>) are the error distribution statistics of the PredRNN models’ and our models’ prediction results for the maximum and minimum solar activity periods, respectively.</p> "> Figure 8
<p>Normal distribution of errors in global ionospheric TEC maps for the maximum and minimum solar activity period forecasts. (<b>a</b>) is a plot of the normal distribution of errors in the results of four algorithms for forecasting periods of maximum solar activity. (<b>b</b>) is a plot of the normal distribution of errors in the results of four algorithms for forecasting periods of minimum solar activity.</p> "> Figure 9
<p>Global ionospheric TEC map during periods of maximum solar activity. (<b>a</b>–<b>d</b>) are the global ionospheric TEC maps forecast by CODE, the convLSTM model, the PredRNN model, and our spatiotemporal network model, respectively. (<b>e</b>) is the final global ionospheric TEC map from the IGS.</p> "> Figure 10
<p>Global ionospheric TEC map residuals during periods of maximum solar activity. (<b>a</b>) is the residual of the global ionospheric TEC map forecast by CODE. (<b>b</b>) is the residual of the global ionospheric TEC map forecast by convLSTM model. (<b>c</b>) is the residual of the global ionospheric TEC map forecast by PredRNN model. (<b>d</b>) is the residual of the global ionospheric TEC map forecast by our spatiotemporal network model.</p> "> Figure 11
<p>Global ionospheric TEC map during periods of minimum solar activity. (<b>a</b>–<b>d</b>) are the global ionospheric TEC maps forecast by CODE, the convLSTM model, the PredRNN model, and our spatiotemporal network model, respectively. (<b>e</b>) is the final global ionospheric TEC map from the IGS.</p> "> Figure 12
<p>Global ionospheric TEC map residuals during periods of minimum solar activity. (<b>a</b>) is the residual of the global ionospheric TEC map forecast by CODE. (<b>b</b>) is the residual of the global ionospheric TEC map forecast by convLSTM model. (<b>c</b>) is the residual of the global ionospheric TEC map forecast by PredRNN model. (<b>d</b>) is the residual of the global ionospheric TEC map forecast by our spatiotemporal network model.</p> "> Figure 12 Cont.
<p>Global ionospheric TEC map residuals during periods of minimum solar activity. (<b>a</b>) is the residual of the global ionospheric TEC map forecast by CODE. (<b>b</b>) is the residual of the global ionospheric TEC map forecast by convLSTM model. (<b>c</b>) is the residual of the global ionospheric TEC map forecast by PredRNN model. (<b>d</b>) is the residual of the global ionospheric TEC map forecast by our spatiotemporal network model.</p> "> Figure 13
<p>Accuracy assessment for each moment of the day during the maximum and minimum periods of solar activity. (<b>a</b>) is the average PSNR of the four algorithms during periods of maximum solar activity. (<b>b</b>) is the average PSNR of the four algorithms during periods of minimum solar activity. (<b>c</b>) is the average MAE of the four algorithms during periods of maximum solar activity. (<b>d</b>) is the average MAE of the four algorithms during periods of minimum solar activity. (<b>e</b>) is the average PSNR of the four algorithms during periods of maximum solar activity. (<b>f</b>) is the average PSNR of the four algorithms during periods of minimum solar activity.</p> "> Figure 13 Cont.
<p>Accuracy assessment for each moment of the day during the maximum and minimum periods of solar activity. (<b>a</b>) is the average PSNR of the four algorithms during periods of maximum solar activity. (<b>b</b>) is the average PSNR of the four algorithms during periods of minimum solar activity. (<b>c</b>) is the average MAE of the four algorithms during periods of maximum solar activity. (<b>d</b>) is the average MAE of the four algorithms during periods of minimum solar activity. (<b>e</b>) is the average PSNR of the four algorithms during periods of maximum solar activity. (<b>f</b>) is the average PSNR of the four algorithms during periods of minimum solar activity.</p> "> Figure 14
<p>Accuracy assessment of the maximum solar activity period test set and the minimum solar activity period test set. (<b>a</b>) shows the accuracy of 546 global ionospheric TEC maps from the maximum solar activity test set. (<b>b</b>) shows the accuracy of 546 global ionospheric TEC maps on the minimum solar activity test set.</p> "> Figure 14 Cont.
<p>Accuracy assessment of the maximum solar activity period test set and the minimum solar activity period test set. (<b>a</b>) shows the accuracy of 546 global ionospheric TEC maps from the maximum solar activity test set. (<b>b</b>) shows the accuracy of 546 global ionospheric TEC maps on the minimum solar activity test set.</p> "> Figure 15
<p>The accuracy of the maximum solar activity and minimum solar activity test sets was assessed using Jason-2/3 VTEC. (<b>a</b>) is the bias between the altimeter VTEC and the forecast for the maximum solar activity. (<b>b</b>) is the STD of the difference between the altimeter VTEC and the forecast for the maximum solar activity. (<b>c</b>) is the bias between the altimeter VTEC and the forecast for the period of minimum solar activity. (<b>d</b>) is the STD of the difference between the altimeter VTEC and the forecast for the period of minimum solar activity.</p> "> Figure 16
<p>The bias of the forecast data compared to the IGS final TEC bias. (<b>a</b>) is a comparison of the bias between the altimeter VTEC and CODE with the bias between the altimeter VTEC and the IGS final TEC. (<b>b</b>) is a comparison of the bias between the altimeter VTEC and our algorithm with the bias between the altimeter VTEC and the IGS final TEC.</p> "> Figure 17
<p>Accuracy assessment under extreme magnetic storm conditions on 17 March 2015. (<b>a</b>) is the bias between the altimeter VTEC and the forecast results. (<b>b</b>) is the STD of the difference between the altimeter VTEC and the forecast results.</p> ">
Abstract
:1. Introduction
2. Database
3. Method
3.1. Spatiotemporal Network Model
3.2. Huber Loss Function
4. Results and Discussion
4.1. Accuracy Evaluation Indicators
4.2. Performance Comparison between Different Loss Functions
4.3. Performance Comparison among Different Methods
4.3.1. Comparison with IGS Final TEC Products
4.3.2. Assessment Results using Altimetry Satellite VTEC
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
ARMA | Autoregressive Moving Average |
CDDIS | Crustal Dynamics Data Information System |
CNN | Convolutional Neural Network |
CODE | Center for Orbit Determination in Europe |
convLSTM | convolutional Long Short-Term Memory |
ESA | European Space Agency |
GNSS | Global Navigation Satellite System |
IAACs | Ionospheric Associate Analysis Centers |
IGS | International GNSS Service |
IONEX | IONospheric EXchange |
IRI | International Reference Ionosphere |
LSTM | Long Short-Term Memory |
MAE | Mean Absolute Error |
RMSE | Root Mean Square Error |
PredRNN | Predictive Recurrent Neural Network |
PSNR | Peak Signal to Noise Ratio |
RNN | Recurrent Neural Network |
STD | Standard Deviation |
ST-LSTM | Spatiotemporal Long Short-Term Memory |
TEC | Total Electron Content |
UPC | Universitat Politècnica de Catalunya |
VTEC | Vertical Total Electron Content |
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CODE [20] | 4.9815 | 3.6910 | 26.1758 |
convLSTM [40,41,42] | 4.6596 | 3.2744 | 26.6119 |
PredRNN [43] | 4.3462 | 3.1449 | 27.2195 |
Ours | 3.9259 | 2.8274 | 28.2035 |
CODE | 1.9524 | 1.5073 | 24.2228 |
convLSTM | 1.9315 | 1.4048 | 24.8503 |
PredRNN | 1.3845 | 1.0126 | 27.5427 |
Ours | 1.1971 | 0.8826 | 28.7954 |
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Lin, X.; Wang, H.; Zhang, Q.; Yao, C.; Chen, C.; Cheng, L.; Li, Z. A Spatiotemporal Network Model for Global Ionospheric TEC Forecasting. Remote Sens. 2022, 14, 1717. https://doi.org/10.3390/rs14071717
Lin X, Wang H, Zhang Q, Yao C, Chen C, Cheng L, Li Z. A Spatiotemporal Network Model for Global Ionospheric TEC Forecasting. Remote Sensing. 2022; 14(7):1717. https://doi.org/10.3390/rs14071717
Chicago/Turabian StyleLin, Xu, Hongyue Wang, Qingqing Zhang, Chaolong Yao, Changxin Chen, Lin Cheng, and Zhaoxiong Li. 2022. "A Spatiotemporal Network Model for Global Ionospheric TEC Forecasting" Remote Sensing 14, no. 7: 1717. https://doi.org/10.3390/rs14071717