A deep learning runoff prediction model based on wavelet decomposition and dynamic feature fusion – Scientific Reports

Predicting river runoff is notoriously hard: it’s stochastic, non-stationary, and driven by nonlinear dynamics across multiple time scales. A new deep learning architecture, BWDformer, tackles this head-on by fusing wavelet-based multi-scale feature extraction, a dynamic feature fusion (DFF) module, and Bayesian optimization. Built on the Informer backbone, BWDformer is designed to better capture long-term dependencies, integrate features across scales, and adaptively reweight them—delivering clear gains in accuracy and robustness for streamflow forecasting.

Why runoff prediction is getting tougher

Runoff channels rainfall and snowmelt through landscapes into rivers, lakes, and the sea—shaping water resource management, flood control, and ecosystem health. Yet climate change and intensified human activity are reshaping catchments and amplifying extremes, making runoff generation more complex and harder to forecast. As flood risks rise, pairing structural defenses with precise, timely prediction has become a practical imperative for public safety and planning.

From classical models to AI—and beyond

Traditional hydrological approaches—causal analyses and statistical models grounded in physics and observations—remain valuable, but they struggle with the nonlinearities and uncertainties embedded in modern runoff processes. Deep learning has stepped in with powerful alternatives: CNNs, RNNs (including LSTM and GRU), GANs, ResNets, and GNNs have all advanced the state of the art by learning complex temporal dependencies.

A particularly effective strategy couples signal decomposition with deep nets. Wavelet decomposition, VMD, and EMD tease signals apart across scales, improving denoising and feature clarity. Wavelet transforms, in particular, offer multi-resolution analysis that separates short-term fluctuations from seasonal patterns and long-term trends. Studies have shown this boosts predictive fidelity across hydrological tasks—from daily flood peaks to monthly trend analysis—because decomposed components are simpler, more structured, and easier for models to learn. Prior work (e.g., Moosavi et al.; Sorkhabi et al.) highlights notable accuracy gains when wavelets feed deep learning pipelines.

Inside BWDformer

BWDformer extends Informer with three synergistic innovations:

• Wavelet decomposition with adaptive windows: Extracts multi-scale features from runoff series, capturing short-term bursts, seasonal cycles, and slow trends. This helps model rapid rises and peaks typical in mountainous rivers while retaining long-horizon context.
• Dynamic Feature Fusion (DFF): An attention-driven module that dynamically reweights features across scales to optimize their combination. By adapting to changing conditions, DFF strengthens the model’s handling of complex, time-varying signals.
• Bayesian optimization: Efficiently searches hyperparameters to speed training and enhance generalization without exhaustive manual tuning.

Together, these components mitigate common pain points—computational intensity, rigid feature fusion, and weak long-term dependency modeling—leading to better accuracy, adaptability, and efficiency across time scales.

Put to the test at four hydrological stations

The team evaluated BWDformer at Hongshanhe, Manwan, Baihe, and Tangnaihai stations, benchmarking against CNN, LSTM, Transformer, and Informer using MAE, RMSE, R, NSE, and KGE.

At Hongshanhe, BWDformer’s MAE was 0.1921, beating CNN (0.2366) by 18.82%, LSTM (0.2014) by 4.65%, Transformer (0.2277) by 15.63%, and Informer (0.2086) by 7.87%. RMSE dropped by 25.46% compared to CNN. KGE reached 0.9651—an 18.51% lift over Transformer (0.8143) and 13.43% over Informer (0.8506).

At Baihe, MAE came in at 228.6971 m³/s, about 2.35% lower than CNN (243.0662). The correlation coefficient R hit 0.9998, a 4.26% increase over CNN (0.9591). NSE reached 0.9972, up 18.73% over Transformer (0.8398). KGE was 0.9934, a 9.79% improvement over Informer (0.9048).

Across all four sites, BWDformer consistently outperformed the baselines, indicating superior accuracy, robustness, and practical utility for diverse hydrological settings.

Why wavelets and dynamic fusion make the difference

Wavelet decomposition’s multi-resolution view isolates high-frequency spikes (e.g., rapid flood rises), mid-range seasonal patterns, and low-frequency climatic trends. Modeling these components separately reduces complexity and improves stability and generalization. High-frequency detail helps pinpoint surge timing and peak magnitude; low-frequency components solidify long-horizon prediction.

DFF complements this by learning to prioritize the right scales at the right moments via attention-driven weighting. This dynamic fusion is crucial for non-stationary systems where dominant drivers shift over time. Anchored by Informer’s efficient long-sequence handling, the resulting model better captures dependencies spanning hours to months.

Smarter parameter tuning for hydrology

Parameter calibration remains pivotal in hydrological modeling, where uncertainty is pervasive. Metaheuristics such as Particle Swarm Optimization, Artificial Bee Colony, and Dynamically Dimensioned Search have improved calibration quality and reduced uncertainty. Meanwhile, Bayesian methods and gradient MCMC enable time-varying parameter modeling that better reflects evolving environmental conditions. Multi-objective optimization and multi-source data (e.g., remote sensing evapotranspiration) further enhance both accuracy and physical realism. Recent work, including dynamic ensembles tuned via Bayesian optimization (e.g., Du et al.), underscores the value of probabilistic search. BWDformer adopts this by using Bayesian optimization to streamline hyperparameter search, accelerating training and boosting transferability.

The bottom line

BWDformer delivers a clear step forward for runoff forecasting by:

• Extracting and leveraging multi-scale structure with wavelet decomposition
• Adapting to changing conditions via attention-based dynamic feature fusion
• Speeding and stabilizing training with Bayesian hyperparameter optimization

Tested at four stations and benchmarked against strong deep learning baselines, the model shows consistent gains in MAE, RMSE, R, NSE, and KGE. Beyond accuracy, its design addresses real-world needs—robustness, efficiency, and adaptability—making it a compelling tool for water resource operations, flood risk mitigation, and ecosystem management.