F10.7 Index Prediction: A Multiscale Decomposition Strategy with Wavelet Transform for Performance Optimization

TL;DR

A novel F10.7 index forecasting method using wavelet decomposition, which feeds F10.7 together with its decomposed approximate and detail signals into the iTransformer model, which demonstrates superior generalization and prediction capability over the method of H. Ye et al. (2024) across all forecast horizons.

Abstract

In this study, we construct Dataset A for training, validation, and testing, and Dataset B to evaluate generalization. We propose a novel F10.7 index forecasting method using wavelet decomposition, which feeds F10.7 together with its decomposed approximate and detail signals into the iTransformer model. We also incorporate the International Sunspot Number (ISN) and its wavelet-decomposed signals to assess their influence on prediction performance. Our optimal method is then compared with the latest method from S. Yan et al. (2025) and three operational models (SWPC, BGS, CLS). Additionally, we transfer our method to the PatchTST model used in H. Ye et al. (2024) and compare our method with theirs on Dataset B. Key findings include: (1) The wavelet-based combination methods overall outperform the baseline using only F10.7 index. The prediction performance improves as higher-level approximate and detail signals are incrementally added. The Combination 6 method integrating F10.7 with its first to fifth level approximate and detail signals outperforms methods using only approximate or detail signals. (2) Incorporating ISN and its wavelet-decomposed signals does not enhance prediction performance. (3) The Combination 6 method significantly surpasses S. Yan et al. (2025) and three operational models, with RMSE, MAE, and MAPE reduced by 18.22%, 15.09%, and 8.57%, respectively, against the former method. It also excels across four different conditions of solar activity. (4) Our method demonstrates superior generalization and prediction capability over the method of H. Ye et al. (2024) across all forecast horizons. To our knowledge, this is the first application of wavelet decomposition in F10.7 prediction, substantially improving forecast performance.

Figures (23)

• Figure 1: Daily F10.7 index of DRAO data from 1957 to 2020. The training set, validation set and testing set are divided according to solar cycles. The blue part in the data is used for model training, the green part for model validation, and the yellow part for model testing.
• Figure 2: Comparison of Langfang data and DRAO data for the time period 2024-2025.
• Figure 3: Wavelet multi-level decomposition. X$^\mathrm{AL}$ and X$^\mathrm{DL}$ respectively represent the approximate signals and the detail signals of the L-th level.
• Figure 4: The prediction scheme of the F10.7 index for future periods based on the iTransformer model.
• Figure 5: The schematic diagram for F10.7 prediction method based on the iTransformer model and wavelet decomposition. The lower section of the diagram displays the integrated inputs to the model, which include the F10.7 index, ISN, their respective approximate signals and detail signals derived from wavelet decomposition, along with the original data. The upper section presents the iTransformer model architecture, which primarily consists of an embedding layer, a projection layer, and multiple inverted Transformer Blocks.