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Macroscopic modelling of floods over urban areas

Lhomme Julien

Owing to the complexity and variability of the urban geometry, the amount of data needed to build reliable models of urban flooding processes is considerable. In addition, data processing and model construction remain extremely time-consuming when a detailed analysis of the flow is needed.
An alternative approach to the classical, refined modelling of the flow is proposed, whereby the flow patterns over a given urban area are accounted for by so-called "macroscopic" properties. The geometric and hydraulic properties of the urban fabric are represented at a large scale by the means of a porosity and a specific head loss formulation. The porosity accounts for the reduction in storage and flow section due to the presence of the buildings and other structures. The specific head loss term accounts for the energy dissipation caused by the multiple wave reflections against the urban singularities and the transitions in the flow regime near crossroads, roundabouts, squares, etc. The head loss parameters can be derived to a large extent from the geometric properties of the urban zone.
The macroscopic approach has been validated against scale model experiments, where typical building and street patterns have been implemented. The comparison of the modelled flow fields with the measurements indicates that (i) the macroscopic model allows the general flow pattern in the neighbourhood of the urban area to be represented with a good accuracy, (ii) the average flow pattern inside the urban area is represented acceptably, (iii) the quality of the simulation results given by the macroscopic model is not significantly different from that given by a classical shallow-water model with a much more finer grid and (iv) the computations by the macroscopic model may be 2 to 10 times faster than a classical shallow water model for a similar accuracy, depending on the fraction of the model area covered by the urban zone.