摘要：质量守恒感知器（Mass-Conserving Perceptron，MCP）建立了一种建模范式，可将概念水文模型重构为具有物理约束、且在概念层面可解释的神经网络。本文开发了一套雪—水 MCP 网络框架，并在 513 个 CAMELS-US 流域中对其进行了评估。我们首先将耦合的双状态 SOIL-MCP 和 SNOWMCP 概念模型重构为质量守恒神经网络，并表明水文模型与神经网络两种表述可实现相当的预测性能。随后，我们考察了双状态 HYDROMCP 架构中跨节点的状态信息共享，并评估了由三类可解释 MCP 单元构建的、更广泛的单层网络；这些单元包含一至五个状态。在美国本土（CONUS）范围内，KGEss 中位数从单状态网络的 0.82 提升至双状态网络的 0.89，并在五状态网络中达到 0.90，这表明状态数超过两个后，整体性能提升趋于递减。针对每个流域在 MCP 和 LSTM 之间进行选择，得到的 KGEss 中位数同为 0.90，但所选 MCP 网络平均使用的参数更少。结合 AIC 和 KGE 的选择方法识别出紧凑的、流域特定的定向图表征，能够在预测精度与模型复杂度之间取得平衡。这些分析为识别水文表征所需状态的数量、类型及其相互作用提供了实证基础。未来研究应测试针对多种水文响应的联合训练，例如径流、雪水当量和地下水储量。

Abstract:The Mass-Conserving Perceptron (MCP) establishes a modeling paradigm in which conceptual hydrologic models can be reformulated as physically constrained, conceptually interpretable neural networks. Here, we develop a snow-water MCP network framework and evaluate it across 513 CAMELS-US basins. We first recast a coupled two-state SOIL-MCP and SNOWMCP conceptual model as a mass-conserving neural network and show that the hydrologic-model and neural-network formulations achieve comparable predictive performance. We then examine cross-node state-information sharing within two-state HYDROMCP architectures and evaluate broader single-layer networks constructed from three types of interpretable MCP units with one to five states. Across CONUS, the median KGEss increases from 0.82 for one-state networks to 0.89 for two-state networks and 0.90 for five-state networks, suggesting diminishing aggregate gains beyond two states. Basin-specific MCP and LSTM selection yields the same median KGEss of 0.90, while the selected MCP networks use fewer parameters on average. Complementary AIC- and KGE-based selection identifies compact, basin-specific directed-graph representations that balance predictive accuracy and model complexity. These analyses provide an empirical basis for identifying the numbers, types, and interactions of states needed for hydrologic representation. Future studies should test joint training against multiple hydrologic responses, such as streamflow, snow water equivalent, and groundwater storage.