Daily Predictions of F10.7 and F30 Solar Indices with Deep Learning
Authors: Zhenduo Wang, Yasser Abduallah, Jason T. L. Wang, Haimin Wang, Yan Xu, Vasyl Yurchyshyn, Vincent Oria, Khalid A. Alobaid, Xiaoli Bai
Organizations: Institute for Space Weather Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA · Department of Computer Science, New Jersey Institute of Technology, Newark, NJ 07102, USA · Center for Solar-Terrestrial Research, New Jersey Institute of Technology, Newark, NJ 07102, USA · Big Bear Solar Observatory, New Jersey Institute of Technology, Big Bear City, CA 92314, USA · College of Applied Computer Sciences, King Saud University, Riyadh 11451, Saudi Arabia · Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08854, USA
The F10.7 and F30 solar indices are the solar radio fluxes measured at wavelengths of 10.7 cm and 30 cm, respectively, which are key indicators of solar activity. F10.7 is valuable for explaining the impact of solar ultraviolet (UV) radiation on the upper atmosphere of Earth, while F30 is more sensitive and could improve the reaction of thermospheric density to solar stimulation. In this study, we present a new deep learning model, named the Solar Index Network, or SINet for short, to predict daily values of the F10.7 and F30 solar indices. The SINet model is designed to make medium-term predictions of the index values (1-60 days in advance). The observed data used for SINet training were taken from the National Oceanic and Atmospheric Administration (NOAA) as well as Toyokawa and Nobeyama facilities. Our experimental results show that SINet performs better than five closely related statistical and deep learning methods for the prediction of F10.7. Furthermore, to our knowledge, this is the first time deep learning has been used to predict the F30 solar index.
Figures & tables
Figure 1: Illustration of the time series data sets for F10.7 (top) and F30 (bottom) used in our study.
Figure 2: Illustration of the two prediction approaches employed by SINet. (a) The fixed prediction approach uses the historical F10.7 values of the previous 30 days, d−30+1 , d−30+2 , … , d−1 , d . represented by orange rectangles, to predict the F10.7 values on days d+1 , d+2 , … , d+59 , d+60 , represented by gray rectangles. (b) The rolling prediction approach uses a sliding window method, where each predicted value is appended iteratively to generate new predictions one day at a time, ultimately achieving a 60-day ahead forecast. Orange rectangles represent true historical F10.7 values, while yellow rectangles represent predicted synthetic F10.7 values that are used subsequently to make new predictions. See text for detailed descriptions of the rolling prediction approach.
Figure 3: Illustration of the SINet model architecture. (a) Overall architecture of SINet, which contains two TimesBlocks. (b) Architecture of a TimesBlock, which contains a dual-inception model structure with two inception blocks. (c) Architecture of the dual-inception model structure, in which the two inception blocks are connected by a Gelu layer. See text for detailed descriptions of the components of SINet.
Layer
Input Dimension
Kernel Size
Output Dimension
InConvBlock 1
30×32
1×1
30×64
InConvBlock 2
30×32
3×3
30×64
InConvBlock 3
30×32
5×5
30×64
InConvBlock 4
30×32
7×7
30×64
InConvBlock 5
30×32
9×9
30×64
InConvBlock 6
30×32
11×11
30×64
Table 1: Configuration Details of the Dual-Inception Model Structure in SINet
Loss Function
Optimizer
Learning Rate
Dropout Rate
Batch Size
Epoch
MSE
Adam
0.001
0.3
32
10
Table 2: Model Training Conditions of SINet
Forecast
SINet \mboxf
SINet \mboxr
ARIMA
LSTM
CNN
LSTM+
TCN
1st Day
2.3 ±0.1
2.3 ±0.1
2.4 ±0.0
2.8 ±0.1
3.0 ±0.2
2.5 ±0.1
2.4 ±0.1
27th Day
8.0 ±0.1
8.8 ±0.2
9.1 ±0.1
8.9 ±0.2
8.5 ±0.2
8.7 ±0.1
8.6 ±0.1
45th Day
9.1 ±0.1
9.3 ±0.1
11.3 ±0.1
11.0 ±0.4
9.6 ±0.1
9.6 ±0.2
9.4 ±0.1
60th Day
10.1 ±0.1
10.9 ±0.3
11.6 ±0.0
11.1 ±0.5
10.7 ±0.5
10.4 ±0.1
10.4 ±0.3
Table 3: Average and Standard Deviation of MAPE (%) Obtained by SINet and Related Methods on F10.7 Prediction in the 5-Fold Validation Experiment
Figure 4: Comparison of three forecasting methods: SINet \mboxf , TCN and SINet \mboxr , on the 60-day ahead prediction of F10.7 in the period between 2009 and 2021. The figure shows the annual comparison results and the overall comparison results in this period.
Figure 5: Comparison of three forecasting methods: SINet \mboxf , TCN and SINet \mboxr , on the 60-day ahead prediction of F10.7 in the solar maximum (2014). The figure shows the quarterly comparison results and the overall comparison results in 2014.
Figure 6: Daily predictions of the F10.7 solar index made by our SINet \mboxf method with four forecast horizons: 1, 27, 45, and 60 days, respectively, in the period between 2009 and 2021.
Forecast
SINet \mboxf
SINet \mboxr
ARIMA
LSTM
CNN
LSTM+
TCN
1st Day
2.0 ±0.0
2.0 ±0.0
2.1 ±0.0
2.6 ±0.2
3.4 ±0.2
2.4 ±0.2
2.4 ±0.2
27th Day
7.1 ±0.1
7.9 ±0.1
7.6 ±0.1
8.5 ±0.1
8.2 ±0.1
7.6 ±0.1
7.5 ±0.2
45th Day
8.7 ±0.1
8.9 ±0.2
10.5 ±0.1
10.6 ±0.1
9.0 ±0.3
9.9 ±0.2
9.2 ±0.3
60th Day
9.5 ±0.1
10.2 ±0.3
10.7 ±0.0
10.3 ±0.1
10.2 ±0.1
9.6 ±0.1
9.6 ±0.1
Table 4: Average and Standard Deviation of MAPE (%) Obtained by SINet and Related Methods on F30 Prediction in the 5-Fold Validation Experiment
Figure 7: Comparison of three forecasting methods: SINet \mboxf , TCN and SINet \mboxr , on the 60-day ahead prediction of F30 in the period between 2009 and 2021. The figure shows the annual comparison results and the overall comparison results in this period.
Figure 8: Comparison of three forecasting methods: SINet \mboxf , TCN and SINet \mboxr , on the 60-day ahead prediction of F30 in the solar maximum (2014). The figure shows the quarterly comparison results and the overall comparison results in 2014.
Figure 9: Daily predictions of the F30 solar index made by our SINet \mboxf method with four forecast horizons: 1, 27, 45, and 60 days, respectively, in the period between 2009 and 2021.
Figure 10: Prediction errors made by SINet \mboxf for the F10.7 and F30 solar indices in the period between September 1, 2017 and October 30, 2017 (that is, between day 1 and day 60 on the X-axis).
Figure 11: Comparison of autocorrelation effects among seven forecasting methods on the 1-day ahead prediction of F10.7 in the period between 2009 and 2021.
Figure 12: Comparison of autocorrelation effects among seven forecasting methods on the 1-day ahead prediction of F30 in the period between 2009 and 2021.
Appendix figures & tables8 assets
Supplementary material from the paper’s appendix.
Appendix
SINet \mboxf
SINet \mboxr
ARIMA
LSTM
CNN
LSTM+
TCN
Fold 1
2.2
2.2
2.4
2.8
2.4
2.4
2.3
p -value
—
2.9E-2
8.3E-70
1.3E-31
7.1E-26
1.7E-39
Fold 2
2.3
2.3
2.4
3.1
2.4
2.6
2.4
p -value
—
9.5E-2
1.5E-83
9.6E-10
1.7E-62
5.9E-15
Fold 3
2.3
2.3
2.4
2.6
2.8
2.6
2.4
p -value
—
1.3E-1
2.3E-50
1.9E-90
7.8E-47
3.9E-16
Appendix
Table 5: MAPE (%) of SINet and Related Methods on F10.7 Prediction (at 1st Day of Forecast)
SINet \mboxf
SINet \mboxr
ARIMA
LSTM
CNN
LSTM+
TCN
Fold 1
8.1
8.7
9.2
8.7
8.7
8.8
8.7
p -value
4.6E-25
2.8E-10
2.7E-15
9.8E-30
1.8E-51
7.7E-105
Fold 2
8.0
8.8
9.1
8.8
8.5
8.7
8.7
p -value
1.6E-23
1.6E-11
3.8E-19
2.4E-44
7.7E-27
3.1E-21
Fold 3
8.1
9.0
9.1
8.9
8.4
8.8
8.5
p -value
2.6E-18
1.5E-9
1.8E-18
3.5E-24
1.1E-69
4.9E-55
Appendix
Table 6: MAPE (%) of SINet and Related Methods on F10.7 Prediction (at 27th Day of Forecast)
SINet \mboxf
SINet \mboxr
ARIMA
LSTM
CNN
LSTM+
TCN
Fold 1
9.1
9.2
11.4
11.3
9.7
9.8
9.4
p -value
1.4E-1
5.5E-16
3.7E-207
1.5E-10
3.7E-70
8.1E-45
Fold 2
9.1
9.3
11.3
10.7
9.7
9.3
9.3
p -value
8.3E-1
2.2E-18
2.4E-142
1.7E-7
1.1E-83
1.7E-36
Fold 3
9.2
9.3
11.3
11.3
9.7
9.5
9.4
p -value
4.7E-3
2.6E-16
2.4E-175
1.1E-17
1.3E-154
3.7E-50
Appendix
Table 7: MAPE (%) of SINet and Related Methods on F10.7 Prediction (at 45th Day of Forecast)
SINet \mboxf
SINet \mboxr
ARIMA
LSTM
CNN
LSTM+
TCN
Fold 1
10.2
10.4
11.6
10.6
11.6
10.6
10.8
p -value
2.3E-13
6.9E-10
1.9E-48
1.1E-7
4.8E-13
5.0E-7
Fold 2
10.0
10.7
11.6
10.8
10.5
10.6
10.5
p -value
7.9E-5
1.1E-10
2.9E-111
9.8E-9
8.1E-10
1.5E-32
Fold 3
10.1
11.0
11.6
10.9
10.6
10.4
10.0
p -value
1.3E-11
1.0E-10
2.7E-71
3.3E-8
4.6E-8
1.0E-11
Appendix
Table 8: MAPE (%) of SINet and Related Methods on F10.7 Prediction (at 60th Day of Forecast)
SINet \mboxf
SINet \mboxr
ARIMA
LSTM
CNN
LSTM+
TCN
Fold 1
2.0
2.0
2.1
2.4
3.7
2.1
2.2
p -value
—
1.2E-2
2.0E-78
1.9E-299
7.8E-26
1.6E-44
Fold 2
2.0
2.0
2.1
2.7
3.3
2.2
2.7
p -value
—
1.1E-1
2.7E-127
3.4E-235
2.5E-23
2.9E-146
Fold 3
2.0
2.0
2.1
2.7
3.4
2.5
2.1
p -value
—
2.5E-2
1.0E-149
1.1E-279
1.0E-96
5.9E-23
Appendix
Table 9: MAPE (%) of SINet and Related Methods on F30 Prediction (at 1st Day of Forecast)
SINet \mboxf
SINet \mboxr
ARIMA
LSTM
CNN
LSTM+
TCN
Fold 1
7.1
7.9
7.7
8.4
8.2
7.8
7.4
p -value
1.5E-29
2.9E-2
5.0E-43
1.4E-49
2.1E-140
5.2E-187
Fold 2
7.2
7.9
7.6
8.7
8.0
7.5
7.6
p -value
1.0E-25
3.8E-2
8.1E-65
1.2E-62
2.3E-65
1.5E-265
Fold 3
7.1
7.9
7.5
8.5
8.2
7.6
7.7
p -value
2.0E-26
5.8E-3
3.0E-53
2.3E-105
8.3E-37
1.5E-151
Appendix
Table 10: MAPE (%) of SINet and Related Methods on F30 Prediction (at 27th Day of Forecast)
SINet \mboxf
SINet \mboxr
ARIMA
LSTM
CNN
LSTM+
TCN
Fold 1
8.7
8.8
10.6
10.4
8.7
10.0
9.0
p -value
1.2E-1
6.8E-15
4.8E-67
—
1.4E-160
2.5E-219
Fold 2
8.7
9.0
10.6
10.6
9.0
10.2
9.2
p -value
1.4E-2
2.1E-17
1.5E-145
5.6E-41
1.4E-131
4.4E-28
Fold 3
8.8
8.9
10.5
10.5
8.8
10.0
9.0
p -value
1.8E-2
8.1E-16
1.9E-195
—
2.1E-172
1.4E-187
Appendix
Table 11: MAPE (%) of SINet and Related Methods on F30 Prediction (at 45th Day of Forecast)
SINet \mboxf
SINet \mboxr
ARIMA
LSTM
CNN
LSTM+
TCN
Fold 1
9.5
9.6
10.7
10.3
10.3
9.6
9.6
p -value
7.4E-32
6.1E-10
3.3E-85
9.6E-37
9.0E-25
1.4E-11
Fold 2
9.6
10.4
10.7
10.2
10.1
9.7
9.6
p -value
1.6E-9
2.5E-8
7.9E-71
2.2E-35
1.1E-20
—
Fold 3
9.5
10.2
10.7
10.2
10.2
9.6
9.4
p -value
4.8E-22
8.9E-9
1.9E-298
9.3E-46
4.2E-18
8.8E-26
Appendix
Table 12: MAPE (%) of SINet and Related Methods on F30 Prediction (at 60th Day of Forecast)
Time series forecasting predicts future values from ordered observations using statistical, neural, and probabilistic models to support decisions under uncertainty.
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