@article{14374dc7-25b3-4e4b-a72c-d5bc8f8ccfab,
  abstract     = {{Climate warming profoundly alters cryospheric hydrological cycles, exacerbating the challenge of simulating the poorly understood processes, particularly in complex, glacier- and permafrost-dominated headwater basins. This difficulty centers on accurately representing the compound runoff regimes generated by the complex, overlapping interactions between rainfall and multiple cryospheric melt processes. These overlapping processes yield highly nonlinear and state-shifting runoff responses, making cold-region hydrological simulation particularly challenging. To address this, we introduce Hybrid-Cryo, a modular data-physics hybrid framework for cryospheric runoff simulation, guided by a “skeleton-and-muscles” design philosophy. The framework’s physical “skeleton” reformulates process-based models (PBMs) into a differentiable architecture to enforce physical consistency and generate key hydrological states. Its adaptive “muscles”, comprising deep learning components, then learn the complex runoff dynamics from these states while correcting for the skeleton’s inherent biases. We evaluated the proposed framework in two major headwater basins on the Tibetan Plateau: the source regions of the Yangtze River (SRYZ) and the Yellow River (SRYE), benchmarking it against a suite of conventional PBMs, a standalone Long Short-Term Memory (LSTM), and other physics-guided deep learning (PGDL) approaches. Results show that the proposed approach outperformed all benchmark models, with test Kling-Gupta Efficiency (KGE) of 0.925 (SRYE) and 0.883 (SRYZ). The proposed framework also showed promising transferability to data-scarce upstream sub-basins with local fine-tuning. Analysis using Gradient-weighted Class Activation Mapping (Grad-CAM) uncovered the proposed framework’s internal problem-solving strategy, revealing that it learns to dynamically down-weight the contributions of poorly performing physical modules.}},
  author       = {{Tang, Zijie and Zhang, Jianyun and Hu, Mengliu and Hashemi, Hossein and Yuan, Feifei and Xie, Kang and Ning, Zhongrui and Liu, Cuishan and Xie, Mingming and Zhang, Jiangjiang and Wang, Guoqing}},
  issn         = {{0022-1694}},
  language     = {{eng}},
  month        = {{04}},
  publisher    = {{Elsevier}},
  series       = {{Journal of Hydrology}},
  title        = {{Hybrid-cryo: a modular data-physics hybrid framework for cryospheric runoff simulation}},
  url          = {{http://dx.doi.org/10.1016/j.jhydrol.2026.135575}},
  doi          = {{10.1016/j.jhydrol.2026.135575}},
  volume       = {{675}},
  year         = {{2026}},
}