Using Fractal Geometries to Understand Urban Drainage Networks and Green Stormwater Infrastructure Development

Abstract

Human development significantly alters the hydrologic cycle. This change is most apparent in urban environments where infrastructure in many ways has replaced the natural ecosystem. In particular to cities, construction with impervious surfaces greatly increases runoff in the water budget. One contemporary way to manage urban runoff is through the use of green stormwater infrastructure (GSI). The impact of GSI on the urban hydrologic response can be assessed through modeling the drainage network based on the sewer layout, pipe diameter, inverts, catchment properties, and other physically based parameters. Developing physically based models can often be difficult given the limited availability of sewer plans and the time required to make a full resolution model. As a result, municipal drainage modelers often resort to simplifications that have (in certain circumstances) been shown to be less accurate than higher resolution models. Artificial sewer networks, based on fractal geometries typical of natural river basins, can help improve simplified models with accuracy similar to physically based models. This point is developed in three logical steps: 1) establish that fractal geometries exist in urban drainage networks in order to build confidence that they could be modeled as such, 2) develop artificial models to simulate urban drainage networks and compare the results to traditional physically based models in reproducing observed flow measurements, and 3) demonstrate applications of artificial models to address contemporary urban hydrologic challenges related to GSI. While previous research has, to a limited degree, revealed fractal geometries in urban drainage networks, there has been little attempt to apply fractal scaling laws developed in natural river basins to urban sewer systems. Additionally, artificial models incorporating fractal geometries have not been validated against hydrologic observations. This research addresses this knowledge gap and shows that 1) fractal geometries exist in urban drainage networks as defined by Hack's Law and Horton order in three study locations in East Boston, Massachusetts and the Bronx, New York, 2) in a 54 ha study catchment in East Boston, Massachusetts, over a one month duration of observed sewer flow both the artificial fractal based and physically based models when calibrated produced strong Nash-Sutcliffe model efficiency coefficients of 0.85, and 3) GSI when simulated with artificial models produces hydrologic simulations comparable to their physically based counterparts and can be used to address questions related to the practice such as effective levels of implementation, spatial layout of the systems throughout the catchment, and adaptation to increasing rainfall patterns associated with climate change.%%%%Ph.D., Environmental Engineering – Drexel University, 2017