Linxi Fu ^1,2* Ping Zhang ^1,2* Lixia Niu ^1,2 Xiaohe Zhang ^1,2 Jianliang Lin ^1,2* Huayang Cai ^1,2 Qingshu Yang ^1,2*

• ¹ Institute of Estuarine and Coastal Research/State and Local Joint Engineering Laboratory of Estuarine Hydraulic Technology, School of Ocean Engineering and Technology, Sun Yat-sen University, Guangzhou, China
• ² Guangdong Provincial Engineering Research Center of Coasts, Islands and Reefs/Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai, China

Shoals and troughs are the fundamental geomorphological units of estuarine systems. However, their definition and morphodynamic characteristics in an estuary, influenced by the complex dynamic environment, remain a critical challenge. This work introduces a depth–area spatial function as a quantitative criterion for the definition of shoals and troughs, while simultaneously elucidating their geodynamic implications. The Lingdingyang Bay (LDB) of the Pearl River Estuary serves as a case study. The depth–area curve reveals the critical morphodynamic features, such as pronounced peaks corresponding to geomorphologic units with substantial areas, as well as a transitional segment that connects the gently sloping sections at the extremities of the cumulative frequency curve. This transitional segment marks the threshold depth that distinguishes between stable shoal states and trough states. From 1901 to 2018, the LDB consisted of the West Shoal, Middle Shoal, and East Shoal and the West Trough and East Trough. The threshold depth of the LDB shifted from −5.75 m in 1901 to −4.75 m between 1964 and 2018. The shoal–trough area ratio in the LDB, relative to the threshold depths, increased from 1901 to 1998, followed by a decline between 2008 and 2018, and culminated in a restoration to the level seen in 1901 (65% shoals and 35% troughs). Furthermore, the dominant forces influencing shoal formation and evolution showed distinct regional variations. The West Shoal is river dominated, the East Shoal is tide dominated, and the Middle Shoal reflects an interaction between riverine inflows and tides. A depth–area spatial function is useful for identifying shoals and troughs within various estuaries, which also provides a geomorphological framework for understanding the estuarine evolution and sediment dynamics.