Beneath city streets, sewer systems direct the flow of wastewater toward treatment plants. Sewer pipe networks also drain storm water to prevent urban flooding. These urban networks perform a landscape drainage function similar to that of natural river networks. Now a new study by Yang et al. demonstrates for the first time that the two network types also evolve similarly over time.
A community’s unique needs and setting often drive the careful engineering of its urban drainage network. However, few studies have investigated these networks from the standpoint of network scaling theory, a mathematical approach that is increasingly used to better understand urban infrastructure.
In the new study, the researchers used network theory to explore whether urban drainage networks evolve according to the same mathematical relationships that govern river systems. These mathematical patterns are universally found in all rivers on Earth and even on other planets. The authors focused on sanitary sewers in the Hawaiian cities of Wahiawa and Honouliuli, as well as a sanitary sewer in a large Asian city whose water utility authority provided data under the condition that the city’s name remain anonymous.
In line with typical network scaling analysis, the scientists organized each city’s urban sanitary drainage system into a network of nodes (pipe connections) and links (pipe segments). By incorporating pipe installation dates and other information, they investigated how the networks evolved and expanded over several decades as the cities grew.
The analysis revealed that as they expand, urban drainage networks do indeed develop topological features that are increasingly similar to those of rivers. River networks are known to be self-similar or fractal, meaning that their shape at larger scales is similar to their shape at smaller scales. The researchers found that growing sanitary networks become increasingly self-similar, following scaling relationships similar to those seen for river networks.
In this study, urban drainage networks didn’t perfectly resemble river networks because of engineering constraints and differences in their formation processes. Nonetheless, the findings suggest that the extensive literature that exists for river networks could potentially be applied to better understand and predict water flow in urban drainage networks. (Water Resources Research, https://doi.org/10.1002/2017WR021555, 2017)
—Sarah Stanley, Freelance Writer