<p>The existing ionospheric Total Electron Content (TEC) spatiotemporal prediction models, such as Convolutional Gated Recurrent Unit (ConvGRU), Convolutional Long Short-Term Memory (ConvLSTM) and Prediction Recurrent Neural Networks (PredRNN) are all convolution-based models, which will encounter difficulties in extracting low-frequency features using large convolution kernels due to over parametrization. One solution is to replace convolution with the recently proposed wavelet transform convolution (WTConv), which convolves in the wavelet transform domain. However, there is a noise band in wavelet transform domain, and WTConv did not consider its adverse effects. To address this issue, this article proposed denoising wavelet transform convolution (DWTConv) by removing the noise from WTConv. Then, we proposed DWTConvLSTM by replacing the convolution in ConvLSTM with DWTConv. In addition, an attention module called Channel and Spatial Attention (CSA) was proposed to focus on important features. Based on DWTConvLSTM and CSA, this paper proposed a spatiotemporal model CSA-DWTConvLSTM for TEC prediction. Finally, the proposed CSA-DWTConvLSTM was compared with 4 state-of-the-art models in TEC prediction, including C1PG, ConvGRU, ConvLSTM and PredRNN on a 6-year Global Ionospheric Maps (GIMs), with 4&#xa0;years as the training set and 2&#xa0;years as the test set. The experimental results indicate that compared to C1PG, ConvGRU, ConvLSTM, and PredRNN, CSA-DWTConvLSTM’s <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10291_2025_1891_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="60" /> </InlineMediaObject> <EquationSource Format="TEX">\(RMSE\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">RMSE</mi> </mrow> </math></EquationSource> </InlineEquation> decreased by 21.22%, 17.08%, 14.26%, and 11.57% in high solar activity years, and by 24.53%, 21.61%, 17.32%, and 13.28% in low solar activity years. Additionally, the superiority of CSA-DWTConvLSTM was further validated from both spatial and temporal perspectives, as well as in extreme situations.</p>

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Spatiotemporal prediction of ionospheric TEC based on denoising wavelet transform convolution

  • Rui Zhou,
  • Yanxiong Wu,
  • Jianxian Cai,
  • Haijun Liu,
  • Huijun Le,
  • Jian Xiao,
  • Yan Ma

摘要

The existing ionospheric Total Electron Content (TEC) spatiotemporal prediction models, such as Convolutional Gated Recurrent Unit (ConvGRU), Convolutional Long Short-Term Memory (ConvLSTM) and Prediction Recurrent Neural Networks (PredRNN) are all convolution-based models, which will encounter difficulties in extracting low-frequency features using large convolution kernels due to over parametrization. One solution is to replace convolution with the recently proposed wavelet transform convolution (WTConv), which convolves in the wavelet transform domain. However, there is a noise band in wavelet transform domain, and WTConv did not consider its adverse effects. To address this issue, this article proposed denoising wavelet transform convolution (DWTConv) by removing the noise from WTConv. Then, we proposed DWTConvLSTM by replacing the convolution in ConvLSTM with DWTConv. In addition, an attention module called Channel and Spatial Attention (CSA) was proposed to focus on important features. Based on DWTConvLSTM and CSA, this paper proposed a spatiotemporal model CSA-DWTConvLSTM for TEC prediction. Finally, the proposed CSA-DWTConvLSTM was compared with 4 state-of-the-art models in TEC prediction, including C1PG, ConvGRU, ConvLSTM and PredRNN on a 6-year Global Ionospheric Maps (GIMs), with 4 years as the training set and 2 years as the test set. The experimental results indicate that compared to C1PG, ConvGRU, ConvLSTM, and PredRNN, CSA-DWTConvLSTM’s \(RMSE\) RMSE decreased by 21.22%, 17.08%, 14.26%, and 11.57% in high solar activity years, and by 24.53%, 21.61%, 17.32%, and 13.28% in low solar activity years. Additionally, the superiority of CSA-DWTConvLSTM was further validated from both spatial and temporal perspectives, as well as in extreme situations.