Flood routing

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 5-10 m. 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.

The second use is to provide flood forecasts at a downstream site in real time, given some estimates of flows or water levels at an upstream site. The upstream levels might come directly from observations of water levels or might come from predictions from a rainfall-runoff model, but the routing of the flood wave downstream will affect both the magnitude and timing of the peak. Accurate predictions of the arrival of the flood peak ahead of time can then be important in issuing flood warnings to the public or deploying temporary flood defences.

A flood hydrograph is modified in two ways as the storm water flows downstream. Firstly, and obviously, the time of the peak rate of flow occurs later at downstream points. This is known as translation. Secondly, if there are no major inputs to the channel, the magnitude of the peak discharge is diminished at downstream points, the shape of the hydrograph flattens out, and the volume of flood water takes longer to pass a lower section. This modification to the hydrograph is called attenuation (Fig. 14.1).

Flood Hydrograph
Fig. 14.1 Modification of a flood wave showing translation and attenuation of the hydrograph from an upstream to a downstream site.

A further consideration that can be important in determining the magnitude and shape of the downstream hydrograph is the volume of lateral inflows to the channel between the two sites, particularly if there are significant inputs from tributary streams.

The derivation of downstream hydrographs like B in Fig. 14.1 from an upstream known flood pattern A is essential for river managers concerned with forecasting floods in the lower parts of a river basin. The design engineer also needs to be able to route flood hydrographs in assessing the capacity of reservoir spillways, in designing flood protection schemes or in evaluating the span and height of bridges or other river structures. In any situation where it is planned to modify the channel of a river, it is necessary to know the likely effect on the shape of the flood hydrograph in addition to that on the peak stage, i.e. the whole hydrograph of water passing through a section, not just the peak instantaneous rate.

Flood routing methods may be divided into two main categories differing in their fundamental approaches to the problem. One category of methods uses the principle of continuity, and a relationship between discharge and the temporary storage of excess volumes of water during the flood period. The calculations are relatively simple and reasonably accurate and often give satisfactory results. The second category of methods, favoured by hydraulic engineers, adopts the more rigorous equations of motion for unsteady flow in open channels, but in the complex calculations, assumptions and approximations are often necessary, and some of the terms of the dynamic equation might be omitted in certain circumstances to obtain solutions.

The choice of method depends very much on the nature of the problem and the data available. Flood routing computations are more easily carried out for a single reach of river that has no tributaries joining it between the two ends of the reach. According to the length of reach and the magnitude of the flood event being considered, it may be necessary to assess contributions to the river from lateral inflow, i.e. seepage or overland flow draining from, and distributed along, the banks. Further, river networks can be very complex systems, and in routing a flood down a main channel, the calculations must be done for separate reaches with additional hydrographs being introduced for major tributaries. In order to develop an operational flood routing procedure for a major river system, detailed knowledge of the main stream and the various feeder channels is necessary. In addition, the experience of several major flood events with discharge measurements made at strategic points on the drainage network will be useful to both calibrate and evaluate model predictions, especially if information on the extent of inundation is available from surveys after past events.

In this chapter, a selection of flood routing methods will be presented, beginning with the simplest using the minimum of information and progressing through to the more complex methods requiring significant computer power for their application.

14.1 Simple non-storage routing

It has been said that 'engineering is the solution of practical problems with insufficient data'. If, in an application to a particular river, there are no gauging station data available and therefore no measurements of discharge, the engineer may have to make do with stage measurements. In such circumstances, it is usually the flood peaks that have been recorded, and indeed it is common to find the people living alongside a river have marked on a wall or bridge pier the heights reached by notable floods. Hence the derivation of a relationship between peak stages at upstream and downstream points on a single river reach may be made (Fig. 14.2) when it is known that the floods are caused by similar notable conditions.

This is a very approximate method, and should not be used if there are major tributaries or significant lateral inflows between the points with the stage measurements, which would cause the relationship to change between events. However, with enough stage records it may be possible to fit a curve to the relationship to give satisfactory forecasts of the downstream peak stage from an upstream peak stage measurement.

Fig. 14.2 Peak stage relationship between upstream and downstream sites.

Downstream stage at Prome (m)

Fig. 14.3 Peak stage relationship for two sites on the River Irrawaddy, Burma.

Downstream stage at Prome (m)

Fig. 14.3 Peak stage relationship for two sites on the River Irrawaddy, Burma.

For example, on the River Irrawaddy in Burma a linear relationship exists between the peak stages of an upstream gauging station at Nyaung Oo and a station at Prome, 345 km downstream. Thirty-five comparable stages (m) for irregular flood events over 5 years (1965-69) are shown in Fig. 14.3. An equation HD = 1.3Hj +1.4 relating HD, the downstream stage to Hj, the upstream stage, can then give forecast values of Hd from Hj.

The time of travel of the hydrograph crest (peak flow) also needs to be determined; curves of upstream stage plotted against time of travel to the required downstream point can be compiled from the experience of several flood events. (The time of travel of the flood peaks between Nyaung Oo and Prome on the Irrawaddy ranged from 1 to 4 days.)

A typical stage-time of travel plot in Fig. 14.4 shows the time of travel at a minimum within the stage range; this occurs when the bankfull capacity of the river channel is reached. After reaching a minimum at this bankfull stage, the time of travel tends to increase again as the flood peak spreads over the flood plain and its downstream progress is retarded owing to storage effects on the flood plain.

The complexities of rainfall-runoff relationships are such that these simple methods allow only for average conditions. Flood events can have very many different causes, and spatial distributions of runoff production, that will produce flood hydro-graphs of different shapes. Flood hydrographs at an upstream point, with peaks of the same magnitude but containing different flood volumes, in travelling downstream will produce different peaks at a downstream point. Modifications to the flow by the channel conditions will differ between steep, peaky flood hydrographs and gentle fat hydrographs with the same peak discharges.

The principal advantages of these simple regression methods are that they can be developed for stations with only stage measurements and no rating curve, and they are quick and easy to apply, especially for warning of impending flood inundations when the required answers are immediately given in stage heights. The advantages of

Fig. 14.4 Expected relationship between water levels (stage) and travel time for in-bank and out of bank flows.

speed and simplicity are less important now that fast computers are available, and more accurate and comprehensive real-time techniques can be used.

14.2 Storage routing

When a storm event occurs, an increased amount of water flows down the river channel and, in any one short reach of the channel, there is a greater volume of water than usual contained in temporary storage. If, at the beginning of the reach, the flood hydrograph (above a normal flow) is given as I, the inflow (Fig. 14.5), then during the period of the flood, Tj, the channel reach has received the flood volume given by the area under the I hydrograph. Similarly, at the lower end of the reach, with an outflow hydrograph O, the flood volume is again given by the area under the curve. In a flood situation, relative quantities may be such that lateral and tributary inflows can be neglected, and thus, by the principle of continuity, the volume of inflow equals the volume of outflow,

v = /T idt = t odt, i.e. the flood volume J^1 Idt has entered the reach and an amount /TT3 Odt has left the reach. The difference must be stored within the reach, so the amount of storage, St, within the reach at time t = T is given by:

r Tt

0 -1

Responses

  • Violanda
    Why does a hydrograph attenuate downstream?
    9 months ago
  • susanne freytag
    Does flood hydrograph routing use to evaluate span and height of bridge?
    22 days ago

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