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Stacked 1D Convolutional LSTM (sConvLSTM1D) Model for Effective Prediction of Sunspot Time Series

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Abstract

A multi-layer, deep-learning (DL) architecture consisting of stacked Convolutional Long Short Term Memory (sConvLSTM1D) layers is proposed to forecast the sunspot number (SSN) more effectively. The proposed model with optimized hyper-parameters performs efficiently on four kinds of sunspot data with different frequencies of time that are yearly, monthly, daily, and 13-month smoothed provided by the World Data Center-Sunspot Index and Long Term Solar Observation (WDC-SILSO), the Royal Observatory of Belgium (SILSO World Data Center). The model was contrasted with other traditional DL models on different performance metrics, namely root-mean-square error (RMSE), mean-absolute error (MAE), mean-absolute-percentage error (MAPE), and mean-absolute-scaled error (MASE). A non-parametric statistical test has also been carried out to confirm the model’s effectiveness. The prediction of the highest yearly mean of total sunspot number (SSN) in Solar Cycle 25 (SC25) has also been performed. The proposed sConvLSTM1D model suggests that the solar cycle exhibits the characteristics of a weak cycle. However, it is anticipated to be stronger than the preceding Solar Cycle 24 (SC24). The year of peak sunspot number will be 2024, as per the prediction, with the peak value of yearly mean sunspot number as 140.84, which is 24.3% higher than the peak value of the yearly mean of total sunspot number, which was 113.3 in the Solar Cycle 24 in the year 2014.

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Acknowledgments

The authors thank the WDC-SILSO, Royal Observatory of Belgium, Brussels, for the sunspot-number data.

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Authors and Affiliations

  1. Department of Computer Science and Information Technology, Mahatma Gandhi Central University, Motihari, Bihar, India

    Abhijeet Kumar & Vipin Kumar

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  1. Abhijeet Kumar
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  2. Vipin Kumar
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Contributions

Abhijeet Kumar developed the methodology, performed the experimental analysis for the article and prepared the original draft. Vipin Kumar did the conceptualisation of the article, and methodology, supervised, reviewed and validated the work, formal analysis.

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Correspondence to Vipin Kumar.

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Appendix: Loss Plots of Different Models for Different Datasets

Appendix: Loss Plots of Different Models for Different Datasets

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Forecast of SC25 based on the proposed stacked ConvLSTM1D model over yearly mean of sunspot number.

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Training loss of all models on the yearly mean of SSN.

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Validation loss of all models on the yearly mean of SSN.

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Training loss of all models on the monthly mean of total SSN.

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Validation loss of all models on the monthly mean of total SSN.

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Training loss of all models on the 13-month smooth of total SSN.

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Validation loss of all models on the 13-month smooth of total SSN.

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Training loss of all models on the daily SSN.

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Validation loss of all models on the daily SSN.

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Kumar, A., Kumar, V. Stacked 1D Convolutional LSTM (sConvLSTM1D) Model for Effective Prediction of Sunspot Time Series. Sol Phys 298, 121 (2023). https://doi.org/10.1007/s11207-023-02209-3

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