One of the most common problems facing a practising hydrologist or hydraulic engineer is the estimation of the hydrograph of the rise and fall of a river at any given point on the river during the course of a flood event. The problem is solved by the technique of flood routing, which is the process of following the behaviour of a flood water upstream or downstream along the river and over the flood plain. There are two primary uses of flood routing models. The first is to provide maps of areas at risk of inundation for design events with a chosen probability of exceedance. In the UK, as required under Section 105 of the Water Resources Act, 1995 and by the EU Floods Directive (see Chapter 16), there are national maps of the area at risk of inundation. It is possible to examine such maps on the web site of the Environment Agency for any postcode in England and Wales.1 The Scottish Environmental Protection Agency (SEPA) has a similar site for flood risk areas in Scotland2 and, in the USA, the Federal Emergency Management Agency (FEMA) is developing similar tools.3 These are ‘indicative’ flood maps, produced by approximate estimates of the 1 in 100 year annual peak discharge for each reach of river using hydraulic models based on a relatively fine topographic model of the flood plain with a resolution of 5-10m. In recent flood-plain inundation studies, the Environment Agency has required additional model predictions that make an allowance for potential climate change. There are estimates of the area at risk of inundation from the 0.001 probability (1 in 1000 year) event, although it should be remembered from Section 11.7 that the uncertainty in estimating the discharge for such a low probability of exceedance can be rather high.