Morphometric properties and hydrological responses of sewer networks: cases studies from France.

Catchment morphology and river network structure greatly condition hydrological response to flooding. While scaling laws have been established for natural catchments and Optimal Channel Networks (OCNs) (Rinaldo and Rodriguez-Iturbe, 1997; Moussa, 2003 & 2009), fewer works have looked into artificial urban water networks, namely stormwater and sewer networks. Optimal Channel Networks (OCNs) are defined based on a generative geomorphological mechanism minimizing the total energy dissipation. However, man-made networks are conceived based on engineering efficiency taking governed by local optimizations, both in time and space, for minimal costs. Hence questions arise regarding the applicability of OCN scaling laws to sewer networks and their potential impact on the shape of the Geomorphological Instantaneous Unit Hydrograph (GIUH).

This work addresses these issues through a case study on twelve nested subcatchments of the Greater Paris combined sewer system (France). A two-step methodology is used. First, the morphometric properties are analysed using the reference Horton-Strahler, Rodríguez-Iturbe and Moussa-Bocquillon scaling laws. They are used in the second step to calculate four GIUHs: the reference Width Function (GWF), the Nash unit hydrograph (GN) using Horton-Strahler ratios, the Nash Unit Hydrograph equivalent (GNe) using Moussa- Bocquillon descriptors, and the Hayami function (GH) solution of the diffusive wave equation (Achour et al., 2023).

In an effort to generalize the methodology to smaller catchments and Separate Sewer System (SSS), a case study is presented on a sub-network of the city of Montpellier (Southern France). The preliminary results show the need to adapt catchment delimitation methods. Indeed, while hillslopes are the main contributing areas to water flow in natural rivers, the flow in sewer networks is generated by individual production units such as residential, industrial and commercial units. Hence the methods traditionally used to automatically extract hydrographic networks from digital terrain models (DTMs) and delimit catchment boundaries lead to an overestimation of contributing areas. Thus, the geomorphological properties of Moussa and the power law of Rodriguez-Iturbe were not verified.