Morphometric properties, scaling laws and hydrologic response of the Greater Paris combined sewer system

Abstract

Morphometric properties of channel networks are useful tools to classify catchments and calculate their hydrological response. Scaling laws have been established for Optimal Channel Networks (OCNs), which are defined based on a generative geomorphological mechanism of minimizing the total energy dissipation. However, sewer networks obey engineering efficiency rules and are conceived based on local optimizations, both in time and space, for minimal costs. Not all the scaling laws have been verified for artificial sewer networks found in urban areas. This raises questions regarding the applicability of OCN scaling laws to sewer networks and their potential impact on the shape of the Geomorphological Instantaneous Unit Hydrograph (GIUH). Hence, this work aims to study the morphometric properties of the Greater Paris combined sewer system through a case study on twelve nested subcatchments. A two-step methodology is used. First, the morphometric properties are analysed using the reference Horton-Strahler, Rodríguez-Iturbe and Moussa-Bocquillon scaling laws. The results show that Horton-Strahler's laws of bifurcation are verified while the length and area laws are not always verified. Rodriguez-Iturbe and Moussa-Bocquillon laws are verified with slightly different values of the descriptors in comparison to OCNs. Second, these morphometric properties are used 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. We identified four catchments for which the scaling laws are verified and therefore all GIUHs are similar while for four other catchments the scaling laws are not verified and strongly impact the GIUHs. These morphometric descriptors and the GIUHs can be considered as ‘hydrological signatures’ of Combined Sewer Systems (CSSs) and are useful for the comparison and classification of hydrological responses.