Functional Topology of Evolving Urban Drainage Networks

Abstract

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∝Ah] and (2) exceedance probability distribution of upstream contributing area (δ) [ P(A≥δ)∼aδ−ɛ]. 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−ɛexp⁡(−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.

Paradoxical impact of sprawling intra-Urban Heat Islets: Reducing mean surface temperatures while enhancing local extremes

“…Similar effects of urban expansion and densification on the power-law node degree observed is observed in several urban infrastructure systems such as roads and sewage networks (Mohajeri et al, 2015;Yang et al, 2017;Klinkhamer et al, 2017). Note that we don't refer to the spatial organization of urban assets such as buildings or impervious areas.…”

Centrality and shortest path length measures for the functional analysis of urban drainage networks

“…In rivers, such pathways are generally determined based on the Horton-Strahler Order, a numerical measure of the networks branching complexity (Strahler 1957). Several studies have applied this ordering scheme in real and virtual sewer systems (Cantone and Schmidt 2011a; Cantone and Schmidt 2011b; Sitzenfrei et al 2013;Yang et al 2017). However, this measure was developed for branching networks (rivers), where only one main flow path exists.…”

“…drinking water supply and drainage systems, have been however limited, due to lack of data or difficulty of accessing information. In the case of water supply networks, studies have focused on the usage of metrics derived from complex network analysis for the assessment of topological robustness and vulnerability (Yazdani and Jeffrey 2012;Agathokleous et al 2017;Hwang and Lansey 2017;Zeng and Li 2017;Krueger et al 2017;Yang et al 2017;Nazempour et al 2018;Ulusoy et al 2018;Zischg et al 2018). On the other hand, studies related to graphtheory based analysis of Urban Drainage Networks (UDNs) have focused mainly on the evolution and topological characteristics of both virtual (Ghosh et al 2006;Möderl et al 2009;Urich et al 2010) and real sewer systems (Zischg et al 2017;Krueger et al 2017), and on the application of graph-theory based methodologies for determining critical elements in the network (e.g.…”

Spatial Organization of Human Population and Wastewater Treatment Plants in Urbanized River Basins

“…Conceptualizing engineered urban drainage networks as analogs of river networks has improved our understanding of the hydrologic responses of urban areas discharging storm flow and wastewater to rivers (Seo & Schmidt, , ; Yang et al, ). Alterations to hydrological, chemical, and ecological status of receiving rivers and increasing risks to public health are all interconnected manifestations of diverse anthropogenic pressures in urbanized river basins.…”

“…Motivated by previous findings for Horton scaling relationships of human‐related variables (Fang et al, ; Miyamoto et al, ), we investigated whether POP distributions in German urbanized basins follow globally consistent patterns of human settlements (Fang et al, ). Knowing that sanitary sewer networks exhibit self‐similar topology like river networks (Yang et al, ), we hypothesized that total PE, the aggregation of POP over multiple sanitary sewer networks, also involves scale‐invariance over H‐S orders. Spatial distribution of WWTPs by H‐S orders reflects not only the total PE‐size distribution over H‐S orders but also the aggregation of PE for multiple WWTPs discharging to a given H‐S order.…”