Recently, differentiable modeling techniques have emerged as a promising approach to bidirectionally integrating neural networks and hydrologic models, achieving performance levels close to deep learning models while preserving the ability to output physical states and fluxes. However, there remains a lack of systematic exploration into the performance and physical interpretability of hybrid models that use neural networks to replace the runoff generation and routing processes in regionalized modeling. This research developed 12 regionalized hybrid models based on a differentiable parameter learning (DPL) framework, utilizing the Hydrologiska Byråns Vattenbalansavdelning (HBV) model as the foundational backbone. These hybrid models incorporate neural networks to replace the various physical processes within the runoff generation and routing modules. The publicly available CAMELS dataset is employed to evaluate the performance and interpretability of these hybrid models. The results show that while the median Nash-Sutcliffe efficiency (NSE) and Kling-Gupta efficiency (KGE) coefficients for all hybrid models are lower than those of the purely data-driven regionalized long short-term memory neural network (LSTM) model (median NSE: 0.742, median KGE: 0.762), the best-performing hybrid model (median NSE: 0.731, median KGE: 0.761) approaches the LSTM model and has better physical interpretability. Embedding neural networks does not inherently guarantee improved performance and may, in some cases, even result in reduced performance. The degree of performance enhancement is not significantly correlated with the number of embedded neural networks. Compared to replacing the runoff generation process, substituting the routing process with neural networks yields more substantial performance improvements and enables the learning of different routing patterns based on the catchment’s static attributes. This study underscores the importance of reasonably balancing the location, complexity, and quantity of embedded neural networks to achieve a trade-off between model performance and interpretability in hybrid modeling. These insights contribute to advancing regionalized hybrid modeling development.

中文翻译：

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探索耦合物理机制和深度学习的混合水文模型的性能和可解释性


最近，可微建模技术已成为一种很有前途的方法，可以双向集成神经网络和水文模型，实现接近深度学习模型的性能水平，同时保留输出物理状态和通量的能力。然而，对于使用神经网络取代区域化建模中的径流生成和路由过程的混合模型的性能和物理可解释性，仍然缺乏系统的探索。本研究基于可微分参数学习 （DPL） 框架开发了 12 个区域化混合模型，利用 Hydrologiska Byråns Vattenbalansavdelning （HBV） 模型作为基础支柱。这些混合模型结合了神经网络，以取代径流生成和路由模块中的各种物理过程。公开可用的 CAMELS 数据集用于评估这些混合模型的性能和可解释性。结果表明，虽然所有混合模型的中位 Nash-Sutcliffe 效率 （NSE） 和 Kling-Gupta 效率 （KGE） 系数均低于纯数据驱动的区域化长短期记忆神经网络 （LSTM） 模型（中位数 NSE：0.742，中位数 KGE：0.762），但表现最好的混合模型（中位数 NSE：0.731，中位数 KGE：0.761）接近 LSTM 模型，并且具有更好的物理可解释性。嵌入神经网络本身并不能保证提高性能，在某些情况下，甚至可能导致性能降低。性能增强的程度与嵌入式神经网络的数量没有显著相关性。 与替换径流生成过程相比，用神经网络替换路径过程可以产生更实质性的性能改进，并支持根据汇流的静态属性学习不同的路径模式。本研究强调了合理平衡嵌入式神经网络的位置、复杂性和数量的重要性，以便在混合建模中实现模型性能和可解释性之间的权衡。这些见解有助于推进区域化混合建模开发。