The role of one- and two-dimensional mathematical models for flood risk simulation

With regard to the aspects of river basin management, mathematical flood modelling can be a valuable tool in order to simulate hazardous effects both in rural as well as in urban river basins. In a strict mathematical sense there is no need to work with momentum equations in two plane dimensions, and it may be sufficient to assume that the flow occurs along pre-defined directions in space, resulting in the so-called pseudo two-dimensional model, also known as the flow cell model. Generally, in most rural areas, one-dimensional models give good results as the river flow can be considered to occur in a preferential space direction. In this case, the river is assumed to flow in a straight way only at each sub-reach and the flooding levels are extrapolated to the floodplains without significant errors. However, when studying urban and some particularly flat rural areas, one may notice that frequently the one-dimensional approach may lack the flood pattern meanings. In such cases, a pseudo two-dimensional mathematical model should be employed, in which flooding waters follow different ways and common features of the urban landscape begin to act hydraulically. It must be noted that in this case, where the landscape dictates flow patterns, the use of true two-dimensional modelling is not recommended, as independent flows from one place to another may occur outside the main drainage net, and the water surface is not continuous. In this paper, we briefly present the hydrological and hydraulic concepts involved, and we show the application results for three case studies: flood flow simulation in a Brazilian rural river by a kinematic wave model, flood flow simulation in a rural river basin using both a simplified hydrodynamic and a full dynamic one-dimensional mathematical model and flood flow simulation in a large Brazilian rural marsh through pseudo two-dimensional mathematical modelling.