Exemples d'utilisation du modèle mathématique HYDROG-LIGNEAU sur les bassins versants urbains et semi-ruraux

Examples of the use of the HYDROG-LIGNEAU mathematical model on urban and semi-rural catchments

¹ Safege, Nanterre
² Société Lyonnaise des Eaux et de l'Éclairage, Paris
³ Direction Départementalede L'Équipement du Val-de-Marne

Abstract

The Hydrog-Ligneau model was compiled by Safege in 1972, since when it has been continually improved for new problems arising in its applications. It is a simplified model for calculating hydrographs and level gradients in a ramified system. 1. General description The Hydrog-Ligneau model comprises two modules which can be used separately : the Hydrog module and the Ligneau module. 1.1. Hydrog module This module processes the rainfall/runoff relationship, i.e. it calculates hydrographs resulting from rainfall in the catchment area for any point of the ramified system draining that area. The hydrographs are calculated in the two following stages : Stage 1 : Rainfall-to-runoff transformation at the outlets from subsidiary catchment basins by solving the Muskingum and continuity equations. Stage 2 : Propagation and summing of hydrographs from the upstream heads of the ramified system to its outlet by solving the "single reservoir" equation (Muskingum with x = 0) and the continuity equation. The main setting parameters for the module are as follows : - Runoff coefficients C, which can be assumed to vary with time (allowance for initial saturation state of soil) - Coefficients Km for transformation of rainfall hyetographs into hydrographs at the sub-catchment outlets. -Hydrograph propagation coefficients Kp 1.2. Ligneau module This module calculates outfall level gradients at considered times of the flood flow, from which observed level diagrams can be reconstructed or the dimensions of planned structures checked. Water level gradients are calculated on the assumption that successive permanent flow conditions are established in the ramified system, which is justified where discharge shows little variation between two consecutive time steps (i.e. hydrograph maxima and minima). The calculations are effected by solving the standard Bernoulli equation from the downstream to the upstream limits of the ramified system, assuming streaming flow conditions. Thus, systems with a steep gradient, i.e. generalized shooting flow, are excluded. The Ligneau module also automatically calculates the local head losses (on which the upstream levels depend) at sills, sharp expansions, syphons and other singularities. Accurate definition of the system geometry is essential for calculating its level gradients. The setting parameters for this are as follows : - Manning Strickler coefficients K, which can be varied with head. - Singular head loss coefficients. 2. Use of model The Hydrog-Ligneau model is being used at present for forecasting purposes as a means of optimizing drainage system dimensions for predictable soil use conditions. It can also be applied to urban and semi-rural catchments with small or very extensive canalized systems. Before the model can be used for forecasting it must be adjusted on the basis of a few observed rainfall-runoff events (e.g. Ruisseau d'Ars and Val de Marne catchments discussed in Author's paper). A further possible use of the model is for system management applications, for which it runs through the calculations in a matter of seconds.