Retrieval of Missing Data in Urban Stormwater Networks Based on Graph Theory

Urban stormwater networks (USNs) are essential in safeguarding urban areas from pluvial flooding. To better understand USNs’ performance and manage them effectively, these infrastructures often undergo various simulations and analyses. However, a significant challenge arises from the quality and availability of data required for such simulations, particularly network data such as sewer slopes and diameters. Due to inconsistent and incomplete documentation, network data are often missing or of poor quality, especially in USNs constructed decades ago. Thus, reliable methods for retrieving these data are crucial to ensure a solid foundation for hydrodynamic analyses in USNs.

This study proposes a data retrieval model to reconstruct missing sewer diameter and slope information. The model is built on graph theory, leveraging the topological and connectivity patterns of USN components. Unlike other retrieval approaches, it is fully automated, computationally efficient, and does not require detailed information. The model comprises four modules: uniformity, hierarchy, elevation, and hydrodynamic, explained as follows: 1) Uniformity Module: In this module, missing data between sewers with identical diameters connected along a directed path are filled with the same diameter information using the shortest path metric, retrieving part of the missing sewer diameter. 2) Hierarchy Module: This module employs a modified centrality metric called runoff edge betweenness centrality to reproduce transition patterns in USNs, where sewer diameters progressively increase from upstream to downstream and accordingly fill the gaps in sewer diameter data. 3) Elevation Module: Missing sewer slope information (invert elevations) is retrieved in this module by considering available slopes of neighbouring sewers and incorporating minimum slope requirements derived from the retrieved diameters. This allows for the approximation of the so-called underground slope surface. 4) Hydrodynamic Module: After filling the data gaps, a hydrodynamic model of the USN is assembled by converting the graph of the network to a Stormwater Management Model (SWMM). The aim here is to ensure that the reconstructed USN can meet actual operational conditions (e.g., by investigating capacity discrepancies in terms of the flow depth-to-diameter ratio in reconstructed USNs). In case of any flow discrepancies, the reconstruction procedure is repeated for specific sewers with the flow depth-to-diameter ratio exceeding a specified threshold.

The proposed model was validated using two real-world USNs. Data gaps were artificially generated by randomly eliminating sewer diameter and slope information, ranging from 10% to 90%, and repeating each data gap scenario 100 times, resulting in 1,800 incomplete USN scenarios. The model was applied to these incomplete networks, and the retrieved USNs were compared to those with complete datasets in terms of hydrodynamic properties (e.g., flow rates, flooded nodes, and flood volumes) and physical characteristics (e.g., diameters and invert elevations). The results demonstrate that the model provides highly promising outcomes, successfully retrieving missing sewer diameter and slope information even with up to 90% data gaps while preserving the hydrodynamic behaviour of the original networks. This graph-theory-based model can be used as a practical tool for water utilities, offering a reliable method for retrieving missing or unavailable data.