CDLM is developed for national-scale high-resolution streamflow simulation across China. The framework couples 3-km gridded GR4J runoff generation and 1-km Muskingum river routing as recurrent differentiable operators, while neural parameter generators infer spatially varying runoff and routing parameters from dynamic forcings and static landscape attributes. The full runoff-routing chain is optimized through streamflow errors at gauges, enabling process-embedded regionalization for ungauged basins.
CDLM 面向全国尺度高分辨率径流模拟而开发。该框架将 3 km 网格 GR4J 产流模块与 1 km Muskingum 河道汇流模块构建为递归可微算子，并通过神经网络参数生成器从动态气象驱动和静态地理属性中推断空间变化的产流与汇流参数。完整的产流-汇流链条通过水文站流量误差进行优化，从而支持面向无资料流域的过程嵌入式参数区域化。
Model Architecture模型架构
Architecture of CDLM extracted from the manuscript. National spatial discretization, dynamic forcings, static attributes, differentiable GR4J runoff generation, 1-km Muskingum routing, neural parameterization, streamflow loss, and back-propagation are integrated in one end-to-end computational graph.
图为论文中的 CDLM 模型架构。全国空间离散、动态气象驱动、静态属性、可微 GR4J 产流、1 km Muskingum 汇流、神经网络参数化、流量损失函数和反向传播被整合在同一个端到端计算图中。
Core Ideas核心思想
Physics-encoded differentiability物理过程可微化
Instead of treating runoff generation and routing as black-box predictors, CDLM implements GR4J and Muskingum equations as differentiable recurrent operators. This keeps the model interpretable while allowing gradient-based training at national scale.
CDLM 不将产流和汇流视为黑箱预测器，而是将 GR4J 和 Muskingum 方程实现为可微递归算子，在保留物理可解释性的同时支持全国尺度的梯度优化训练。
Neural regionalization神经网络区域化
Model parameters are generated from grid-cell and river-reach attributes. This shifts regionalization from donor-parameter transfer toward spatially continuous parameter learning for gauged and ungauged basins.
模型参数由网格单元和河道河段属性生成，使参数区域化从传统的相似流域参数移植，转向面向有资料和无资料流域的空间连续参数学习。
Runoff-routing coupling产汇流联合建模
Runoff from 3-km cells is mapped to a 1-km river network and routed downstream. The runoff generator and routing model are calibrated jointly rather than as isolated components.
3 km 网格产流被映射到 1 km 河网并向下游汇流。产流模块和汇流模块在同一计算链条中联合校准，而不是作为彼此独立的模块处理。
National training data全国尺度训练数据
The framework uses streamflow observations from a large set of near-natural gauges in China to learn parameter generators and evaluate spatial transfer performance.
该框架利用全国大量近自然水文站流量观测学习参数生成器，并评估模型在空间迁移和无资料流域模拟中的表现。
Spatial Distributions of Learned Parameters学习参数的空间分布
Spatial distributions of learned parameters such as X1, X2, and X3 from the manuscript, illustrating how CDLM captures regional hydrologic heterogeneity through differentiable parameter learning.
图为论文中 X1、X2、X3 等学习参数的空间分布，展示 CDLM 如何通过可微参数学习刻画不同区域的水文异质性。
Code will be provided after the manuscript is accepted.
代码将在论文接收后开放下载。