Methods of flood estimation

The purpose of this section is to introduce the reader to some of the background to flood estimation, since this is the wider context within which this study arises. From the objectives set out in Chapter 1 it can be seen that this study is in part simply an exploratory one, but it has also been explained that it could be of significance in the wider field of flood frequency analysis. The various approaches to flood estimation are therefore outlined here, giving an indication of the historical development of ideas and presently accepted methods.

The justification for flood estimation has always lain in the need to estimate the magnitude of floods for the design of structures. These include bridges, culverts, spillways, flood protection works and any other structures which might lie within reach of a flooding river. Either the probable maximum flood, the magnitude of a given recurrence interval flood or the recurrence interval of a given flood magnitude may be required. Generally, the peak instantaneous discharge of the flood is the quantity of interest, but peak stage may alternatively be sought, derived from a

stage-discharge relation at the site of interest, or occasionally, perhaps when storage reservoirs are involved, a flood volume may be required. Attention in this study will be focused exclusively on peak discharge values.

In a review of work from the early part of the present century and the latter part of the 19th, Wolf (1966) explains that early approaches to flood estimation were based on surveys of the largest known floods in many parts of the world, and aimed to estimate the maximum possible flood to be expected for any given site on a river,

Qmax. Empirical formulae were used, with catchment area being the prime determinant, but Wolf also lists catchment length and width, rainfall, runoff volume and various indices to represent catchment soils, geology, drainage pattern, etc as having been proposed for use. Amongst these relations is the well-known ‘rational method’ originally due to Kuichling (1889), given by

Qmax — CAi

where C is a coefficient of runoff, A is catchment area and i represents a mean intensity of precipitation.

A major advance in the UK was the publication in 1933 of the Interim Report of the Institution of Civil Engineers' Committee on Floods in Relation to Reservoir Practice (Institution of Civil Engineers 1933). This gave envelope curves showing highest recorded specific discharge values against catchment area, and made numerous design recommendations for practising engineers. The concept of return periods was not in use at this stage; ‘normal maximum flood’ and ‘catastrophic flood’ magnitudes were the focus of concern for engineers at this time. In 1960, following the receipt of many further flood observations from throughout the UK, a subsequent report, Floods in the British Isles, was issued (Institution of Civil Engineers 1960) to improve upon the Interim Report's inability “to put forward any rules for arriving at the probable maximum flood discharge”. However, despite envelope curves again being produced as in the 1933 report, reference is made to the potential use of gauged records, and the concept of recurrence interval is introduced, although the desirability of defining ‘normal maximum’ and ‘catastrophic’ flood values still appears to be of paramount importance. Return period-based analyses are now much more important than previously, but envelope curves showing the variation of maximum recorded specific flood discharges with return period are still useful; Werritty and Acreman (1985) provide such a curve specifically for Scotland.

An alternative approach to flood estimation has been to work from a maximum estimated rainfall over a catchment (probable maximum precipitation (PMPn in order to derive a maximum flood value. Perfect application of this method requires that the processes by which rainfall is converted to runoff are understood in every detail, and that their highly complex behaviour can be represented in a model. Unit hydrograph theory, initially developed by Sherman (1932) and Bernard (1935), provides a useful approximation to this, hydrograph ordinates being taken to be directly proportional to storm rainfall. This method can be used for the calculation of design floods by the input of a maximum calculated storm rainfall, and in practice can be used for comparison with the results of flood frequency methods, the discussion of which forms the basis of the remainder of this section.

In present-day hydrology, there are two broad approaches to design flood estimation, rainfall-runoff methods represent one approach and flood frequency analyses the other. The latter involve the definition of flood magnitude-frequency relationships for application at any given site of interest, such that a flood peak magnitude can be related to a specific return period.

One of the earliest publications to outline the application of this method is Dalrymple's Flood-Frequency Analyses (Dalrymple 1960), being a manual of methods used by the United States Geological Survey. An index flood, the mean annual flood, O, was derived from a curve showing its relation with basin area (and possibly other catchment characteristics), and the magnitude, Qt, of a flood of a greater, T-year, return period was then found from a second curve relating Qp/Q to recurrence interval. While Dalrymple's method may appear somewhat simple in comparison with later developments, the basic approach of calculating an index flood and then applying a scaling factor to obtain a flood of higher return period still lies firmly at the heart of current flood frequency analysis.

In Britain, the publication of the five-volume Flood Studies Report (NERC 1975) after much research at the then recently-established Institute of Hydrology represented a further major step in this direction for design flood estimation. The

Flood Studies Report has already been referred to on a number of occasions in the preceding sections; this is indicative not only of the great amount of work presented in it, but also of the importance with which its recommendations have been viewed in subsequent years (a useful guide to its recommendations is given by Sutcliffe (1978)).

A number of methods were presented for the estimation of the mean annual flood, both for gauged and ungauged sites (Figure 2.1). Where data from a gauging station were available, several methods could be used, the preferred choice depending on record length. Methods for both annual maximum and partial duration series data were described, though use of the former type dominated the recommendations, largely reflecting the development of the statistical theories underlying their analysis. For ungauged sites, the index flood was to be estimated by reference to catchment characteristics using a six-term regression equation:

Q = m AREA0-94 STMFRQ0-27 S10850-16 SOIL1-23 RSMD1-03 (l+LAKE)-°-85

where m = a regional multiplier AREA = catchment area (km2)

STMFRQ = stream frequency (junctions km-2) S1085 = 10-85% mainstream slope (mknr1)

SOIL is a catchment soil index representing its winter rainfall acceptance potential

RSMD = maximum one-day rainfall of five year return period minus SMD (mm)

LAKE = proportion of the catchment draining through a significant loch or reservoir.

The estimation of high return period flood magnitudes was in most cases to be made using a regional growth curve relating Qt/Q to return period. Ten significant geographical regions were identified for this purpose; the appropriate map and growth curves are shown in Figure 2.2. Where more than 25 years of annual maximum series were available, however, it was recommended that magnitudes could be estimated by fitting a general extreme value distribution without the need to calculate mean annual flood first.

The selection of statistical distributions for flood series is a key issue in flood frequency analysis, since the distribution chosen will determine the value of a design flood estimate, and this applies equally to empirically derived regional growth curves and to curves derived directly from extreme value theory for application at an individual site. The appropriate choice might be made on the basis of graphical inspection of the fit of points from any one station; alternatively the

Flood Studies Report suggests goodness-of-fit tests which might be applied. The

Figure 2.1