Scaling Laws and Archetypes of Urban Drainage Networks in the Megacity Seoul

Urban drainage networks (UDNs), as one of the most pivotal infrastructures, provide the public with sanitary and safe living environments, primarily by mitigating water-related diseases and hazards. The layout of UDNs and their corresponding drainage area, known as sewersheds, are inevitably linked to the geometric shape of districts in a given urban area and the distribution of people within them. This relation is evident as UDNs expand to meet the increasing demand for drainage services driven by urban expansion. Recent studies have reported remarkable findings that scaling features emerge in the most mature UDN structures, as shown from natural river networks, i.e., their analogy in nature. Such findings are fascinating as they corroborate how self-organizing human unintentionally shape engineered drainage systems over time to exhibit emerging features similar to those of naturally created ones, beyond the influences of topographic conditions and initial engineering criteria for UDN design. Given these innovative outcomes, further interesting questions naturally arise: (1) Can diverse UDNs be organized into archetypes based on the gradients of their scaling features (including cases with a lack of scaling features)? (2) If so, what factors govern the differentiation among individual archetypes? To address the questions, this study analyzed ~200 sewersheds discharging into four major tributaries of the Han River in the megacity of Seoul (~16K people/km², ~605 km²), South Korea. The analyzed UDNs represent an average of ~60% of the total UDNs length across the four tributary watersheds. We identified three archetypes of Seoul’s UDNs based on Horton’s laws, which indicate scaling features and consistent patterns in rivers for the number, the mean length, and the mean drainage area of order-by-order stream: (Archetype I) UDNs satisfying all three of Horton’s laws as found from river networks; (Archetype II) UDNs adhering to Horton’s ratios but not all three laws; (Archetype III) UDNs exhibiting at least one insignificant Horton’s ratios. Particularly, we investigated the roles of topographic (e.g., mean slope, elevation), socio-economic (e.g., population density, fiscal self-reliance), and network structure (e.g., drainage density) conditions of each sewershed. Using publicly open data, we selected ~20 descriptive indicators with low correlations to represent the independent characteristics of network structure, topography, and socio-economic factors. Multigroup analysis and post-hoc tests were employed to identify significant differences among the archetypes. Our findings are expected to not only advance the understanding of UDN structures but also serve as a cornerstone for developing a framework that connects UDN vulnerability to extreme climate conditions through their scaling features.