Urban climate research has surged in the past decades due to its unique position in addressing the concomitant issues of the rapid global urbanization and emergent climate changes. Nevertheless, there is still a lack of holistic and system-based toolkit for investigating complex dynamics of urban climate systems, especially those of hydroclimate extremes. Here we propose a novel framework based on complex networks for analyzing the topological structure of the urban climate in the contiguous United States (CONUS). In addition, we simulate CONUS urban networks using Kuramoto model and the master stability function formalism, which sheds new light on the occurrence and evolution of heat waves as dynamic synchronization processes. It is found that the CONUS urban climate networks are highly modular with spatial hierarchical (hub-periphery) organization. The small-world effect is also manifest in these networks with the characteristic path length between any pair of nodes no more than 5. For globally connected urban networks, as the sparsity of connections increases (with threshold of correlation coefficient), the path length decreases roughly linearly, whereas the synchronizability reduces exponentially.

城市气候研究因其在解决全球快速城市化和突发气候变化的伴随问题方面的独特地位而在过去几十年中激增。尽管如此，仍然缺乏用于研究城市气候系统复杂动态的整体和基于系统的工具包，尤其是极端水文气候系统。在这里，我们提出了一个基于复杂网络的新框架，用于分析美国本土（CONUS）城市气候的拓扑结构。此外，我们使用 Kuramoto 模型和主稳定函数形式来模拟 CONUS 城市网络，这为热浪的发生和演变作为动态同步过程提供了新的视角。发现 CONUS 城市气候网络是高度模块化的，具有空间层次（枢纽-外围）组织。小世界效应也体现在这些网络中，任意一对节点之间的特征路径长度不超过5。对于全局连接的城市网络，随着连接稀疏度的增加（相关系数阈值），路径长度减小大致呈线性，而同步性呈指数下降。