用小波分解+ARIMA+Transformer预测印度东北部月降雨量,精度显著提升。
Wavelet-SARIMA-Transformer: A Hybrid Model for Rainfall Forecasting
- 先用小波变换分解降雨序列,再分用SARIMA和Transformer处理线性与非线性部分。
- 基于哈尔小波的混合模型在所有分区均实现最低误差,且无系统偏差。
- 适合需高精度气候预测的缺数据地区,尤其对防洪与水资源规划有实用价值。
本研究构建并评估了一种新型混合模型WST(Wavelet-SARIMA-Transformer),用于预测1971至2023年间印度东北部五个气象区的月降雨量。该方法采用最大重叠离散小波变换(MODWT)结合哈尔、达布奇斯、对称小波、柯伊夫莱特等四类小波,实现降雨序列的平移不变、多分辨率分解。线性与季节成分由季节自回归积分滑动平均模型(SARIMA)建模,非线性成分由Transformer网络捕捉,最终通过逆MODWT重构预测结果。基于80:20训练测试划分及多项指标(RMSE、MAE、SMAPE、Willmott's d、技能得分、百分比偏差、解释方差、Legates-McCabe E1)的综合验证表明,基于哈尔小波的混合模型WHST在所有分区均表现最优,误差更低、与实测值一致性更强、预测无偏。残差经Ljung-Box检验确认充分性,泰勒图进一步证实其相关性、方差保真度和均方根误差均优。结果表明,融合多分辨率分解与互补模型可有效提升水文气候预测性能。该框架可推广至复杂环境时间序列预测,在数据稀疏、气候敏感区域对洪水风险管理、水资源规划与气候适应具有直接意义。
原文摘要 · Abstract (English)
This study develops and evaluates a novel hybridWavelet SARIMA Transformer, WST framework to forecast using monthly rainfall across five meteorological subdivisions of Northeast India over the 1971 to 2023 period. The approach employs the Maximal Overlap Discrete Wavelet Transform, MODWT with four wavelet families such as, Haar, Daubechies, Symlet, Coiflet etc. to achieve shift invariant, multiresolution decomposition of the rainfall series. Linear and seasonal components are modeled using Seasonal ARIMA, SARIMA, while nonlinear components are modeled by a Transformer network, and forecasts are reconstructed via inverse MODWT. Comprehensive validation using an 80 is to 20 train test split and multiple performance indices such as, RMSE, MAE, SMAPE, Willmotts d, Skill Score, Percent Bias, Explained Variance, and Legates McCabes E1 demonstrates the superiority of the Haar-based hybrid model, WHST. Across all subdivisions, WHST 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 WST framework offers a scalable methodology for forecasting complex environmental time series, with direct implications for flood risk management, water resources planning, and climate adaptation strategies in data-sparse and climate-sensitive regions.
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