A Multi-Site Probabilistic Water Quality Prediction Method Coupling Learnable Frequency-Domain Filtering and Multi-Residual Ensemble

Abstract

Multi-site water quality sequences are jointly affected by seasonal periodicity, meteorological disturbances, and inter-site differences in the Jianghuai Watershed region. Conventional quality prediction models struggle to simultaneously achieve multi-scale feature extraction, spatial heterogeneity characterization, and prediction uncertainty expression. This study used daily-scale monitoring data on dissolved oxygen (DO), pH, and ammonia nitrogen (NH3N) from 32 monitoring stations within the region in 2025 and proposed the FT-TransONet (Fourier-enhanced Temporal Transformer Operator Network) multi-site probabilistic water quality prediction model. Within a Transformer framework, the model employed a FourierTime learnable frequency-domain filtering module, a GeoBias (Geographic Bias) attention bias mechanism, and a multi-residual ensemble strategy composed of a multilayer perceptron (MLP), a gated recurrent unit (GRU), and a temporal convolutional network (TCN) combined with a mass conservation constraint, thereby achieving both point and interval prediction of key water quality indicators. The results showed that FT-TransONet achieved the lowest Macro_RMSE among all compared methods on the multi-site water quality prediction task. At a prediction horizon of three days, its Macro_RMSE reached 0.2255, which was 21.89% lower than that of the long short-term memory network and 5.57% lower than that of the strongest baseline MC-Dropout. For the three individual indicators, the model attained coefficients of determination of 0.9135, 0.9338, and 0.8660 for dissolved oxygen, pH, and ammonia nitrogen, with corresponding root-mean-square errors of 0.5145, 0.1098, and 0.0523, confirming its potential to characterize the temporal variation in the main water quality indicators. Under multi-step prediction, the error grew gently, with the Macro_RMSE rising only from 0.2255 to 0.2384 as the horizon extended from three to seven days, and the ablation experiments, together with the probabilistic prediction results, further supported the effectiveness of the proposed structural design. Validated on 32 water quality monitoring stations in the Jianghuai Watershed, the method improved multi-site prediction accuracy while accounting for stability and uncertainty quantification, providing a preliminary reference for regional water quality early warning and management.