Functional Topology of Evolving Urban Drainage Networks

Soohyun Yang, Kyungrock Paik, Gavan S. McGrath, Christian Urich, Elisabeth Krueger, Praveen Kumar, P. Suresh C. Rao

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)


We investigated the scaling and topology of engineered urban drainage networks (UDNs) in two cities, and further examined UDN evolution over decades. UDN scaling was analyzed using two power law scaling characteristics widely employed for river networks: (1) Hack's law of length (L)-area (A) [L α Ah] and (2) exceedance probability distribution of upstream contributing area (δ) [P(A≥δ)~aδ]. For the smallest UDNs (<2 km2), length-area scales linearly (h ∼ 1), but power law scaling (h ∼ 0.6) emerges as the UDNs grow. While P(A≥δ) plots for river networks are abruptly truncated, those for UDNs display exponential tempering [P(A≥δ)=aδ exp (-cδ)]. The tempering parameter c decreases as the UDNs grow, implying that the distribution evolves in time to resemble those for river networks. However, the power law exponent ɛ for large UDNs tends to be greater than the range reported for river networks. Differences in generative processes and engineering design constraints contribute to observed differences in the evolution of UDNs and river networks, including subnet heterogeneity and nonrandom branching.

Original languageEnglish
Pages (from-to)8966-8979
Number of pages14
JournalWater Resources Research
Issue number11
Publication statusPublished - 2017 Nov

Bibliographical note

Publisher Copyright:
© 2017. American Geophysical Union. All Rights Reserved.


  • fractal
  • infrastructure
  • river network
  • self-organization
  • self-similarity
  • urban drainage network

ASJC Scopus subject areas

  • Water Science and Technology


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