Hourly Regional Rainfall–Runoff Prediction Using Transformer with Water Conservation Constraints

This paper introduces MC-former, a Transformer-based rainfall-runoff model designed for hourly regional runoff prediction. Unlike the original Transformer, MC-former integrates a water-balance-guided constraint into the attention layer and enforces physical consistency through a penalty structure. Additionally, MC-former transforms the aggregated input embeddings into the frequency domain via a Fourier transform, enabling more effective modeling of long-range dependencies in hourly runoff data. We tested MC-former on two tasks: regional rainfall-runoff simulation and runoff prediction for ungauged basins with similar hydrogeological units. In the first task, MC-former outperformed baseline models in prediction accuracy. In the second, it improved performance under ungauged conditions, with a notable increase in the Nash–Sutcliffe efficiency coefficient (NSE) in the HUC03 region, surpassing the baseline by nearly 0.08. Furthermore, adopting a strategy of training MC-former with hydrological data from climatically and geologically similar regions further enhanced its predictive accuracy, as demonstrated by consistently higher NSE and Pearson-r values. The MC-former model can support sustainable water resources management and enable transferable prediction of rainfall runoff in ungauged basins.