Apparent Hack’s law in river deltas

Authors

• Tian Y. Dong, The University of Texas Rio Grande ValleyFollow
• Lawrence Vulis, University of California, Irvine
• Hongbo Ma, University of Illinois at Urbana-Champaign
• Alejandro Tejedor, Universidad de Zaragoza
• Timothy A. Goudge, University of Texas at Austin

Document Type

Article

Publication Date

4-30-2026

Abstract

River deltas are densely populated, ecologically vital landscapes threatened by rising sea levels. Distributary channel networks disperse sediment to build deltaic land, yet the relationship between the network organization and land building remains elusive. Inspired by Hack’s law, which shows that watershed drainage area scales with channel length in tributary networks, we analyzed a global dataset of distributary networks and found a nearly identical scaling relationship between distributary channel length and nourishment area, the land-building counterpart to drainage area. Despite this apparent global scaling, we further identified two distinct local land-building patterns: uniform delta networks consistently follow Hack’s law, whereas composite delta networks exhibit a scale break, transitioning from space-filling growth around the delta apex to quasi-linear growth near the coast. The unexpected growth patterns suggest that global simplicity and local variability coexist in how river deltas grow and organize.

Comments

https://www.science.org/eprint/PKQDEBMRRRAXWXCFHTQH/full?activationRedirect=/doi/full/10.1126/science.ady6805

Recommended Citation

Dong, Tian Y., Lawrence Vulis, Hongbo Ma, Alejandro Tejedor, and Timothy A. Goudge. "Apparent Hack’s law in river deltas." Science 392, no. 6797 (2026): 493-498. https://doi.org/10.1126/science.ady6805

Publication Title

Science

DOI

10.1126/science.ady6805