A Daubechies Wavelet–ARIMA Hybrid Model for Long-Term Monthly Rainfall Forecasting: Outperforming Machine-Learning Benchmarks in a Monsoon-Dominated Urban Watershed

Abstract

Accurate monthly rainfall prediction is essential for water-resource planning, agricultural management, and flood-hazard mitigation, particularly in rapidly urbanizing tropical cities. This study presents a hybrid wavelet-based ARIMA model (HWAM) that couples discrete wavelet decomposition with individually optimized autoregressive integrated moving average (ARIMA) models to forecast monthly rainfall in Bangalore, India. The Daubechies wavelet of order 6 at decomposition level 4 is applied to a 123-year record (1901–2023) to separate the signal into one approximation subseries and four detail subseries, each of which is independently modeled by an appropriate ARIMA process. Forecasts are reconstructed by summing the component predictions. The HWAM is trained on 80% of the data (1901–1998) and validated on the remaining 20% (1999–2023). On the validation set, the HWAM achieves a mean absolute error (MAE) of 0.221 mm, a root-mean-square error (RMSE) of 0.662 mm, a mean absolute percentage error (MAPE) of 1.121%, and a coefficient of determination ( R 2 ) of 0.998. To demonstrate the comparative performance of the HWAM, its results are benchmarked against four state-of-the-art machine-learning and deep learning models: Transformer, bidirectional long short-term memory (BiLSTM), convolutional neural network–bidirectional LSTM (CNN-BiLSTM), and extreme gradient boosting (XGBoost). The HWAM achieves the lowest MAPE (1.121%) and highest R 2 (0.998) among all five models, outperforming the standalone ARIMA baseline by approximately 85–95% and surpassing all machine-learning benchmarks across every error metric under the same univariate forecasting setting. The novelty of this work lies in the systematic selection and optimization of wavelet parameters for long-record monthly rainfall prediction in a monsoon-dominated urban watershed, comprehensive benchmarking against contemporary deep-learning models, and the generation of reliable 3-year-ahead monthly forecasts that can directly support urban infrastructure planning and climate-adaptation decisions in Bangalore.