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<p>Rainfall forecasting in monsoon-dominated regions is challenging due to the nonlinear, nonstationary, and scale-dependent nature of precipitation dynamics. This study develops and evaluates a novel hybrid Wavelet–SARIMA–Transformer (W-ST) framework to forecast using monthly rainfall across five meteorological subdivisions of Northeast India over the 1971–2023 period. The approach employs the Maximal Overlap Discrete Wavelet Transform (MODWT) with four wavelet families (Haar, Daubechies, Symlet, Coiflet) to achieve shift-invariant, multiresolution decomposition of the rainfall series. Linear and seasonal components are modeled using the Seasonal Autoregressive Moving Average (SARIMA) model, while a Transformer network models nonlinear components, and forecasts are reconstructed via the inverse MODWT. Comprehensive validation using an 80:20 train–test split and multiple performance indices (Root Mean Square Error[RMSE], Mean Absolute Error(MAE), Symmetric Mean Absolute Percentage Error(SMAPE), Willmott’s <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varvec{d}\)</EquationSource> </InlineEquation>, Skill Score, Percent Bias, Explained Variance, and Legates–McCabe’s <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\varvec{E}_{\varvec{1}}\)</EquationSource> </InlineEquation>) demonstrates the superiority of the Haar-based Wavelet-SARIMA-Transformer [(W(H)-ST)]. Across all subdivisions, W(H)-ST consistently achieved lower forecast errors, stronger agreement with observed rainfall, and unbiased predictions compared with stand-alone SARIMA, stand-alone Transformer, and two-stage wavelet hybrids. Residual adequacy was confirmed through the Ljung–Box test, while Taylor diagrams provided an integrated assessment of correlation, variance fidelity, and RMSE, further reinforcing the robustness of the proposed approach. The results highlight the effectiveness of integrating multiresolution signal decomposition with complementary linear and deep learning models for hydroclimatic forecasting. Beyond rainfall, the proposed W-ST framework offers a scalable methodology to forecast complex environmental time series, with direct implications for flood risk management, water resource planning, and climate adaptation strategies in data-sparse and climate-sensitive regions.</p>

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Wavelet-SARIMA-Transformer: a hybrid model for rainfall forecasting

  • 期刊论文

  • 发表日期：

    2026年2月2日

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  • Junmoni Saikia,
  • Kuldeep Goswami,
  • Sarat C. Kakaty

摘要

Rainfall forecasting in monsoon-dominated regions is challenging due to the nonlinear, nonstationary, and scale-dependent nature of precipitation dynamics. This study develops and evaluates a novel hybrid Wavelet–SARIMA–Transformer (W-ST) framework to forecast using monthly rainfall across five meteorological subdivisions of Northeast India over the 1971–2023 period. The approach employs the Maximal Overlap Discrete Wavelet Transform (MODWT) with four wavelet families (Haar, Daubechies, Symlet, Coiflet) to achieve shift-invariant, multiresolution decomposition of the rainfall series. Linear and seasonal components are modeled using the Seasonal Autoregressive Moving Average (SARIMA) model, while a Transformer network models nonlinear components, and forecasts are reconstructed via the inverse MODWT. Comprehensive validation using an 80:20 train–test split and multiple performance indices (Root Mean Square Error[RMSE], Mean Absolute Error(MAE), Symmetric Mean Absolute Percentage Error(SMAPE), Willmott’s \(\varvec{d}\) , Skill Score, Percent Bias, Explained Variance, and Legates–McCabe’s \(\varvec{E}_{\varvec{1}}\) ) demonstrates the superiority of the Haar-based Wavelet-SARIMA-Transformer [(W(H)-ST)]. Across all subdivisions, W(H)-ST consistently achieved lower forecast errors, stronger agreement with observed rainfall, and unbiased predictions compared with stand-alone SARIMA, stand-alone Transformer, and two-stage wavelet hybrids. Residual adequacy was confirmed through the Ljung–Box test, while Taylor diagrams provided an integrated assessment of correlation, variance fidelity, and RMSE, further reinforcing the robustness of the proposed approach. The results highlight the effectiveness of integrating multiresolution signal decomposition with complementary linear and deep learning models for hydroclimatic forecasting. Beyond rainfall, the proposed W-ST framework offers a scalable methodology to forecast complex environmental time series, with direct implications for flood risk management, water resource planning, and climate adaptation strategies in data-sparse and climate-sensitive regions.