Stormwater runoff generates one of the most critical natural risks in urban environments: impervious surfaces and high drainage network densities lead to frequent urban flooding events, with short process times and within small urban areas. In all parts of the world, urbanisation is growing, and urban flood hazards consequently occur more and more frequently. Examples of important flood damages suffered by urban populations are numerous, especially in tropical regions where the violence and rapidity of tropical storms often lead to an overloading of the drainage system and to the flooding of adjacent built-up areas. Prediction and evaluation of these damages require the determination of some important hydraulic characteristics of the flood, such as maximum water depth or flooding duration. Currently-used models are generally limited to checking the sewer system efficiency. Therefore new models are now expected to represent with accuracy and reliability the stormwater runoff, which can result from sewer system overloading. However, this kind of modelling is hard to carry out because of the geometric complexity of the urban media and because of the rapidity of urban storms and their associated flooding. Moreover, the modelling of the behaviour of the flooded built-up areas should sometimes be integrated into complete models of urban flooding, given their important influence on the hydrodynamics of the flood. However the geometric complexity of these built-up areas prevents us from a complete and accurate description of the different obstacles and water ways encompassed in such areas. Simplified descriptions at a larger scale are consequently to be found.
This paper highlights the important physical characteristics that determine the hydraulic behaviour of every hydraulically-independent urban cell, and suggests a way to represent the exchange and storage laws of built-up areas at different scales: individual plots and blocks of plots. The study was performed in the particular case of Ouagadougou's areas. The hydraulic behaviour of every built-up area can be modelled with three important physical characteristics, the two first of which are related to the structure of the surrounding walls:
These three characteristics are functions of height. Moreover, they are essential and sufficient to describe the behaviour of every basic or global urban object (plot, block of plots...). At the "block of plots" level, the transmissivity and storativity concepts are comparable to the hydraulic roughness and urban porosity concepts that have already been proposed in scientific papers (e.g., Braschi et al. 1991). These two characteristics are sufficient for modelling the hydraulic behaviour of every open urban medium. Nevertheless, some urban media are non-transmissive because of a high connection level between the different obstacles. In these cases the perviousness property is very useful for modelling the different exchanges between the built-up areas and the adjacent flooded roads. The residential urban areas of Ouagadougou, used as an illustration for this study (Figure 1), correspond to this case of partitioned urban areas. The structure of the Ouagadougou's residential districts is standard and is organised around the individual plot, a parcel shielding one or several families: the individual plot is isolated from other plots and from the roads by a surrounding wall that constitutes one of the elementary hydraulic objects of the urban environment. The evolution of the flood water depth in a plot adjacent to a flooded road, determined by equation 1, depends on its floodable surface Sc and on its perviousness. Its perviousness is defined by the geometric characteristics of the apertures present in the wall: the type of aperture, weir or orifice; its height, hs, its length, Ls, and its opening if an orifice, a. Measures of exchanges between roads and plots made during some flood events in Ouagadougou (Hingray 1999) showed that the classical discharge laws for weirs or trough orifices can be used to model these exchanges (equations 2, 3 and 4).
We suggest a way to simulate the exchange and storage laws of these built-up areas at a larger scale: the block of plots. An aggregation approach enables us to define a structure indicator: " l'HistoSeuil " (Figure 2). It is based on the description of the lengths of weirs and apertures found in road façades, and is equivalent to an aperture density function. The exchange discharge between the block of plots and the flooded adjacent road can be computed with a simply convolution (equation 6) between this HistoSeuil and the reference discharge laws for broad-crested weirs (equations 7 and 8). The geometric relevance of the indicator is next discussed: it seems to be a relatively stable geometric characteristic of an urban area (Figure 3). This result is given by a systematic survey of the apertures observed in 24 road façades belonging to 3 different districts of Ouagadougou. The two first are traditional residential districts, more and less developed. The "Patte d'Oie" district is fairly old and was established in the 1970's (numerous well developed plots). The second one (Wemtenga 1) is a recent housing estate (1988) (numerous unfinished or empty plots). The final one (Wemtenga 2) is a very recent district of spontaneous development (disorganised built-up area structure). Furthermore, the hydraulic relevance of this indicator, its ability to reproduce the average hydraulic behaviour of a block of plots, is approached. Initial results seem to be positive. If both the hydraulic and geometric relevance of the structure indicator presented in this paper are validated by the additional work that we are carrying out at this present time, this approach may prove to be useful for the hydraulic modelling of built-up areas . Moreover the study of other types of built-up areas could lead to the determination of a hydraulic typology of urban areas. In particular, this study, performed in the case of Ouagadougou, a big city in a developing country, seems to be valid for every city where the built-up areas are highly partitioned.
Urban, flooding, hydrology, hydraulics, model, scaling, Ouagadougou, aggregation approach, perviousness, built-up areas, Burkina Faso (Africa).
B. Hingray, EPFL
DGR/IATE-HYDRAM, CH-1015 Lausanne, SUISSE