Hybrid principal component analysis and singular value decomposition based fuzzy models for multi-step daily rainfall forecasting

Reliable rainfall forecasting is crucial for hydropower production, reservoir management, agricultural planning, and flood preparedness. Yet, accurate prediction remains challenging because rainfall time series are highly nonlinear, intermittent, and stochastic. To address this problem, this study develops two hybrid forecasting models, PCA-Fuzzy and SVD-Fuzzy, which combine fuzzy inference with preprocessing based on principal component analysis (PCA) and singular value decomposition (SVD). In these frameworks, the original rainfall series is decomposed into energy-ranked components prior to forecasting in order to better represent the underlying structure of the signal. The proposed models are compared with a Wavelet-Fuzzy model and a stand-alone Fuzzy model using daily rainfall records from three meteorological stations in the Upper Euphrates Basin, Turkey, for forecast horizons ranging from 1 to 7 days. Model performance is evaluated using mean squared error (MSE) and the Nash–Sutcliffe efficiency coefficient (CE). Results indicate that preprocessing substantially improves forecasting accuracy relative to the stand-alone Fuzzy model for all stations and lead times. Overall, the PCA-Fuzzy model achieves the best predictive performance, followed by the SVD-Fuzzy model, and both outperform the Wavelet-Fuzzy benchmark in most cases. The performance gains are strongest at short lead times and diminish as the forecast horizon increases, reflecting the inherent complexity and reduced predictability of rainfall dynamics at longer horizons. The study shows that PCA- and SVD-based decomposition provides effective and computationally simple alternatives to wavelet preprocessing for hybrid rainfall forecasting models.