Physical & Numerical Model

Once the flows entering a river network during flood are known, a way of predicting how the flood event will propagate is needed. River catchments taken as a whole is a complex system. The main system of channels may simply flow together or, as is often case in developed areas, have interconnecting channels joining various limbs of the network together. The flow within a given channel is affected by the way the water level is controlled, by variations in channel roughness, the channel cross-sections and bed levels, and the location and shape of bridge openings and other structures.

Hydraulic models are an essential tool in the design of flood alleviation works, assessing levels of service and estimation of residual flooding (John, 1991). The models are used to understand past flood events and predict possible behaviour of future events. There are broadly two types of model namely physical model and mathematical model.

The Physical Model

Physical modelling involves studying the behaviour of water in a scaled physical model of the relevant part of the catchments. Flow velocities and depths of the water in the model are assumed to be proportional to that in the prototype according to an appropriate scaling law such as Froude Number. Water levels and discharges are controlled at appropriate points in the model and the resulting flow conditions measured at points of interest. Such models have been used in the past on extensive sections river. However, because of the high cost of large physical models, the considerable space which they occupy, and the subsequent need to break them up to release that space, such models are now most often confined to specific areas of the catchments to investigate local flow patterns or calibrate control structures.

The Mathematical (Numerical) Models

The numerical models are more appropriate to the modelling of extensive reaches of river and large areas of floodplain. In a mathematical hydraulic model the equations most nearly representing conditions in the river under investigation and on the floodplain are identified and expressed in a form amenable to solution on a computer. The river characteristics and floodplain topography are given in the form of data appropriate to the model. These will comprise channel cross-section data at intervals along channels, bank and floodplain levels, details of flow controls, inflow hydrographs and observed flood levels. Example – HEC-RAS, Mike 11, EXTRAN, EXTRAN-XP and others.