Zhongrui Ning

This study addresses the limitations of traditional deep learning models in hydrological forecasting, which often lack physical interpretability and struggle with extreme events. We propose a hybrid framework that combines data-driven deep learning with physical constraints to enhance model accuracy and robustness. Traditional deep learning models (e.g., LSTM) have shown promise in rainfall-runoff prediction but are criticized for their "black-box" nature and poor performance under extreme conditions, while physical-based models, though interpretable, are computationally expensive and rely on detailed parameterization. To bridge this gap, we integrate physical constraints (e.g., water balance, monotonicity) into LSTM networks through three key approaches: extreme event constraints that add penalties for violating physical laws, monotonicity constraints ensuring runoff increases with rainfall intensity via ReLU-based loss functions, and hard constraints projecting outputs to strictly adhere to hydrological laws. Applied to 2683 basins globally, our physics-guided LSTM (PHY-LSTM) improved the Nash-Sutcliffe Efficiency (NSE) by 0.10 and reduced the Root Mean Square Error (RMSE) by 15% compared to standard LSTM, with a 20% enhancement in flood peak prediction using synthetic extreme samples. Additionally, we identified time-varying parameters across climate zones, revealing trends in water storage capacity (1.7mm/decade in wet regions, -0.6mm/decade in arid regions). This framework bridges data-driven efficiency and physical interpretability, enabling reliable predictions under extreme conditions and providing insights into hydrological processes, validated globally and applicable to water resource management and climate change impact assessments.

In cold regions, snow cover and seasonally frozen ground (SFG) exert a substantial influence on hydrological processes, yet their effects – especially at the scale of large basins – remain insufficiently understood due to limited observations and process-based analyses. To address this, we extended the widely used Grid Xinanjiang (GXAJ) hydrological model by developing two physically meaningful yet computationally efficient modules: (i) the GXAJ-S model, which incorporates snowmelt processes, and (ii) the GXAJ-S-SF model, which additionally accounts for freeze–thaw cycles of SFG. These modules strike a balance between physical representation and simplicity, making them applicable in data-sparse cold regions. The model performance was evaluated using multi-source remote sensing/reanalysis data and observed daily runoff, enabling a systematic investigation of how snow and SFG jointly regulate key hydrological processes. The results demonstrate that: (1) including both snowmelt and freeze–thaw processes significantly improves runoff simulation, especially during cold seasons; (2) snow dynamics directly modulates the development of soil freeze–thaw cycles, thereby altering the hydrothermal state of the vadose zone; and (3) the inclusion of the SFG module in the model variant, which already accounted for snowmelt, increased the predicted surface runoff by 39 %–77 % during cold months, reduced evapotranspiration by approximately 85 %, and substantially modified interflow processes, particularly during the early-spring thaw period. These findings provide quantitative evidence of the critical role of SFG in shaping the seasonal hydrological regime of large cold-region basins. Moreover, the modular and transferable design of the snow and SFG components allows for straightforward integration into other hydrological models, offering a valuable tool for hydro-climatic assessments and water resource management in mountainous regions under changing climate conditions.

Although of great importance for long-term, effective water resource allocation, current knowledge of monthly runoff variability, its spatio-temporal characteristics, and underlying key drivers, including their sensitivity to climate change and other human impacts, is limited. With a particular focus on 10 sub-basins along an elevation gradient (1000 to 5900 m.a.s.l.) in the hydrologically complex, seasonally cold Yalong River basin, China, this study developed an extended Budyko framework based on monthly water balances (2002–2016) to consider snow storage dynamics (∆S_snow) separately from other terrestrial water storage changes (∆S’), including those related to hydropower reservoir construction. Results showed that snow accumulation and snowmelt are main drivers of runoff seasonality in the upper sub-catchments of the Yalong River basin, with propagating impacts also on lower-elevation snow-free sub-catchments, which are increasingly under the additional influence of hydropower reservoirs. This creates a relatively strong altitudinal heterogeneity in drivers of monthly runoff, which has been hypothesized to occur also in other world regions including e.g. major European rivers of Alpine origin, although not yet quantified at similarly high spatio-temporal resolution. Furthermore, an observed decrease in runoff seasonality in the Yalong River at its Yangtze River outlet (that receives water from all 10 investigated sub-basins) was shown to be unrelated to snow storage changes and hence likely caused by trends in unfrozen precipitation seasonality and/or flow-modulating impacts of constructed reservoirs, natural lakes and groundwater, implying that further snow thinning may exacerbate such trends in the future. Implementing the variance decomposition method based on the extended Budyko framework, the intra-annual runoff variability (σ²_R) was captured by calculating the variance and covariance of influencing factors (R² values above 0.9 in most sub-basins) with the main contributors being variances of rainfall (P_r) and ∆S’. Methodologically, we have verified the substantial contribution of hydropower reservoir storage changes on total storage changes by independent analysis of reservoir storage data, supporting the applicability of the extended monthly Budyko framework for identifying dominant processes in the context of runoff generation and the rapid environmental changes that the Yalong River basin and other cold regions (not least of the Tibetan plateau) are currently experiencing.