Algal bloom forecasting leveraging signal processing: A novel perspective from ensemble learning

Accurate forecasting of algal blooms is essential for implementing timely control measures. However, given their inherent complex time-frequency characteristics, capturing the dynamics of algal blooms remains an ongoing challenge in standalone models. Targeting this challenge, this study demonstrates an ensemble framework that combines signal processing with machine learning (ML) techniques to collectively forecast algal dynamics. This method utilizes an efficient signal processing algorithm, namely the compete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), to decompose the highly non-stationary patterns of algal dynamics, while leveraging the complementary strengths of four distinct ML models to optimize the learning of the decomposed components. Our results demonstrated that CEEMDAN can largely improve the forecasting performance of standalone ML models (e.g., long short-term memory), achieving an average increase in validation R² by 63 %. Moreover, by incorporating the ensemble effects that leverage model-specific strengths, this performance gain was further amplified, resulting in an average increase of 75 % in validation R² compared to standalone ML models. The developed method, termed CEEMDAN-Hybrid-Ensemble (CHES) model, consistently delivered accurate forecasting of algal dynamics across multiple time resolutions (hourly, daily, and biweekly) in both rivers (River Enborne and The Cut) and lakes (Blelham Tarn and Lake Lillinonah), as suggested by high validation R² values of 0.955, 0.878, 0.824, and 0.957, respectively. In addition, the CHES model achieved stable multi-step forecasting of algal dynamics with gaps ranging from 1 to 7 steps, as indicated by an average validation R² of 0.72 $\pm$ 0.17 (S.D.) and an average validation root-mean-square-error (RMSE) of 0.32 $\pm$ 0.11 RFU. This study highlighted the ensemble effect achieved by integrating signal processing and ML techniques, presenting a novel perspective that enhances forecasting robustness to support the early warning of algal blooms.