Eigen time series modeling: a breakthrough approach to spatio-temporal rainfall forecasting in basins

Rainfall is crucial for understanding local climate systems and their distribution patterns in watersheds. Accurate regional rainfall forecasting is vital for flood and drought mitigation efforts. However, understanding the deterministic and stochastic properties of rainfall data is essential before using it in prediction models due to its chaotic nature. This study introduces the use of eigen time series to provide a compact and comprehensive representation of rainfall data across all stations within a watershed. By identifying key patterns, extracting relevant features, and reducing dimensionality, the eigen time series method enables the entire basin to be effectively modeled with a single dataset. Additionally, the prediction models in this approach utilize a dual-layer stacking ensemble framework, which enhances both the precision and reliability of the rainfall predictions. The study presents an innovative methodology by both deriving the eigen time series representation and integrating the prediction models based on these eigen time series into a stacking ensemble model. The results of this study are evaluated based on diagnostic metrics mean squared error (MSE), Nash–Sutcliffe efficiency coefficient (CE), Wilmott's refined index (WI), and mean absolute error (MAE). The introduced methodological approach exhibits exceptional performance in forecasting rainfall data for 40 stations solely based on eigen rainfall time series, surpassing a CE value of 0.95. The utilization of the eigen time series methodology alongside the stacking ensemble prediction model highlights their capacity as robust instruments, not only for addressing rainfall-related challenges but also for prospective applications within the engineering and scientific domains. These approaches exhibit promising capabilities in predicting future spatial–temporal patterns without being reliant on a priori assumptions.