20. Flood frequency studies using regional methods

J.V. Sutcliffe Heath Barton, Manor Road, Goring on Thames, RGS 9EH, UK

F.A.K. Farquharson Institute of Hydrology, Wallingford, 0X10 8BB, UK

Abstract

The paper describes a number of regional flood frequency studies which have been carried out at the Institute of Hydrology during and following the investigations leading to the Flood Studies Report. These studies have been based on flood records from a number of countries throughout the world. Because the results of these studies have been published in various forms as they progressed, the opportunity has been taken to summarise some of the results of earlier studies and to bring them together in a form which enables comparisons to be made with recent findings. The estimation of floods may require the use of relations between mean annual flood and basin characteristics while the use of regional dimensionless frequency curves provides a means of extrapolation beyond the period of a single record. Examples show that the form of these curves varies widely between different climates, and it is suggested that the date of occurrence of annual maxima could be a useful index. The role of historical evidence is discussed briefly.

Résumé

Cet article décrit un certain nombre d’études régionales de fréquence de crues qui ont été effectuées par l’Institut d’Hydrologie pendant et après les études menées pour le UK Flood Studies Report. Ces études se sont basées sur les archives des crues pour un certain nombre de pays à travers le monde. Comme les résultats de ces études ont été publiés au fur et à mesure sous des formes variées, c’est ici l’occasion de réunir certains des résultats des premières études et de les présenter sous une forme permettant la comparaison avec de plus récentes. L’estimation des crues demande l’utilisation de relations entre la moyenne des crues annuelles et les caractéristiques du bassin versant, tandis que l’utilisation de courbes de fréquence non dimensionnées permet l’extrapolation au-delà de la période couverte sur le site par un simple enregistrement. Des exemples montrent que la forme de ces courbes varie énormément d’un climat à l’autre, et on suggère que la date d’occurrence des maxima annuels peut être un indice explicatif utile. Le rôle de l’information historique est discute brièvement.

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20.1. Introduction

This paper describes a series of flood frequency studies which have been canied out using regional methods of analysis, with not only the practical aim of suggesting methods of estimating flood magnitudes but also the wider ambition of leading towards an understanding of the ways in which floods vary with climate and other factors between different regions of the world. A number of the regional studies on which the paper is based have been published in various forms, and the basic data have either been included or summarised in these publications. In general the flood records were instantaneous peak flows derived from various sources, but daily flows have been included where the size of the basin allowed the assumption of equivalence. The statistical assumptions and findings are in general also confined to these publications, but some key references are included in this paper.

20.2. Need for flood estimation

In most cases efficient flood risk management requires a knowledge of relations between flood magnitude and frequency of occurrence. Although the estimated maximum flood is usually required for dam spillway design where heavy loss of life is threatened by underdesign, the flood flow expected to be exceeded with a given frequency may be specified by codes of practice for small dams in sparsely populated areas. In other engineering examples the appropriate design frequency may be deduced by optimising the balance between expected damage and the cost of damage reduction by flood control. This requires estimates of the flood frequency relation and the extent of potential damage.

The benefits of flood control may be assessed from analyses of potential damage as a function of river level or flow (Penning-Rowsell & Chatterton, 1977). These studies of damage may be based on sampling the types of buildings present on the floodplain and relating damage to flooding level, and on similar studies of agricultural land within the floodplain. Financial estimates of damage provide one side of the cost : benefit analysis once the river levels have been related to frequency through flood assessments.

Having set out the context in which flood estimates are required, this paper concentrates on the role of statistical hydrology in providing these estimates. The relation between flood magnitude and frequency of occurrence is required at the project site which may have a long period of flow records but often has a short or no record nearby. In order to take account of a11 available information it is desirable to make use of relations between floods and basin characteristics and to combine regional sources of information, including historical flood records, with any records at the site (Dalrymple, 1960).

20.3. Flood studies of the British Isles

The application of these principles to flood frequency estimation in the British Isles was illustrated by the studies leading to the Flood Studies Report (NERC, 1975). These studies included the collation of flood records, paying attention to the reliability of the calibration curve at high flows, the extraction of both annual maximum (AM) flows and peaks over threshold (POT) series from microfilmed records, and the derivation of estimates of the mean annual flood from both AM and POT series. It was shown by Bernier (1967) that the combination of a Poisson process for the incidence of flood events and an exponential distribution for their magnitude was equivalent to an extreme value Type 1 (EVl) distribution of the AM series, and thus the mean annual flood (MAF) may readily be derived from either the AM or POT series, with a relative precision which depends on the number of years of record (Cunnane, 1973).

The estimates of MAF at a11 gauged sites (532 in all, with average duration of 13.5 years) were compared with basin characteristics in a multivariate regression analysis in order to provide estimates at ungauged sites. The characteristics selected for this comparison were intended to

342

sample all the factors which give rise to flood events :

“basin size giving scale (AREA, kn?),

‘net daily rainfall (gross rainfall less mean soi1 moisture deficit) of an arbitrary .5-year retum period to index runoff volume (RSMD, mm),

“soi1 index of rapid runoff under standard conditions (SOIL),

Ochannel slope and stream frequency to indicate response time and tbus hydrograph shape (SlOSS, m.km-l and STMFRQ), and

“indices of lake control and urban development (LAKE and URBAN) . The variability of conditions within the British Isles meant that although the equation linking

MAF (in m?s-1) to these characteristics, eg :

MAF=0.0201 AREAO~~4STh4FRQO~~?U0850~1~SOIL1~2~RSMDl~O~ (l+LAKE)-“.85 (20.1)

explained 92% of the variante, the factorial standard error of estimate (fsee) of the prediction was 0.168 in (base 10) logarithmic terms or times 1.47 or 0.679 in multiplicative terms. Comparisons of results obtained from sets of records of different durations suggest that about half the residual error is accounted for by sampling error (NERC, 1975, p.I.327). It was encouraging to note that as further flood-producing factors were included in the regression, the exponents of the two factors area and short-term net rainfall tended towards the physically reasonable values of unity. Nevertheless the predictive power of the equation was worth only about one year’s actual record at the site, SO that the preferred method of estimating MAF was from either AM or POT series of measured flows.

The fitting of a curve to a set of flood records implies the choice of a suitable statistical distribution. Gumbel (1940, 1941) first applied the extreme value distribution, for which there is some theoretical justification, to flood records while working in France. Bernier (Morlat et al., 1956; Bernier, 1956) pointed out that other forms of the extreme value distribution may be used for floods, and applied the Fréchet distribution which is related to the Gumbel distribution by a logarithmic transformation. Jenkinson (1955) combined the three forms of the extreme value distribution into the General Extreme Value (GEV) distribution, defined by :

F(x) = exp {-[1 -k(x-U)t@]-llk}. (20.2)

This distribution was chosen for the Flood Studies Report because of its flexibility and its ability to fit the records of storm rainfall and flood peaks in practice.

Flood frequency may be related to the estimated MAF by a dimensionless frequency curve. This may be based on the records at a single site but as individual records are generally too short to sample the full variability of storms and floods it should be more reliable to use a11 the records of a reasonably homogeneous region to increase the sample. A separate exercise led to regional grouping of flood records and the derivation of regional dimensionless flood frequency curves. Although the initial groups were selected geographically by major basin boundaries for convenience of definition, it was realised that the reasons for differences between regions were largely climatic. The slope and curvature of the regional frequency curves based on these samples were both found to increase as the rainfall decreased. It was noted during the study that the growth curves of the different regions were consistent with the regional growth curves of the net rainfall, which were deduced from the growth curve corresponding to the average rainfall of each region by subtracting the effective mean soi1 moisture deficit, which was found to be independent of return period (Beran & Sutcliffe, 1972).

As historical records of major floods cari extend the sampling period where these exist, a

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search was made for such information during the course of the study (NERC, 1975, pp.IV.73-88). Where physical flood marks could be related to the calibration curve at a nearby flow station, or where newspaper accounts gave sufficient information to deduce the flows on specific dates, these records were used to extend the effective record period. Techniques were developed to include such records in single station analysis by maximum likelihood methods, but in order to include them in the regional frequency curves graphical methods of curve extension were used.

20.4. Choice of regions

The regional approach depends on dimensionless frequency curves derived from a number of basins which may be regarded as reasonably homogeneous. Problems associated with the regional approach are on the one hand those of basin heterogeneity and on the other hand those of regional dependence (Hosking & Wallis, 1988). Because the basis of the regional approach is that frequency curves reflect floods which might occur at a given site but may not have been sampled in the relatively short measured record, a degree of variability of record is desirable SO that, for example, severe convective storms which have been observed at some sites are reflected in the distribution at other sites. On the other hand, it is desirable that single widespread floods should not have undue influence (Reed & Stewart, 1991). A variety of approaches have been advocated in selecting regions. In some cases, like those leading to the Flood Studies Report, geographical regions were selected using groups of river basins, and differences in regional curves were noted to correspond with climatic and topographie factors.

Other studies (eg Wiltshire, 1986b) have used site flood statistics to test these groupings and shown that the groups were heterogeneous. When alternative groupings are derived directly from the records by linking those sites with similar specific floods (MAFIAREA) and coefficients of variation (CV), the groups are naturally found to be more homogeneous and the regional curves more distinct. However, this approach makes it more difficult to allocate an ungauged site to a specific group, and it is necessary to relate the groupings to basin characteristics and derive the probabilities of the ungauged site being in one of the groups defined by records. It could be argued that this is not dissimilar to using geographical regions. It appears desirable to test the effect of grouping sites by basin characteristics other than position, but this requires the availability of the relevant characteristics for a11 sites.

In most of the studies described in this paper, a more empirical approach has been used. It has generally been found that the variability of floods, whether expressed as CV or as a regional curve, is related mainly to climate factors, as measured by short-term rainfall and soi1 moisture deficit or even by mean annual rainfall. Although there was no apparent link between basin size and variability in the British Isles, it could be argued that size is important, because extreme convective storms are more effective on small basins while large basins are less liable to extreme storms over their whole extent. Other basin characteristics are more likely to affect the whole range of storms and floods in a similar way, SO are less likely to be significant in regionalisation. In fact basin size and average rainfall are in many cases the only characteristics which are generally available. It is hoped that the evidence from a very wide range of conditions Will provide a contribution to the debate on effective regionalisation.

20.5. Extension of studies

Since the publication of the Flood Studies Report, the techniques developed have been applied to flow records from a number of other countries. In some cases the flood rating curves were checked during the investigations but in other cases the records were accepted as published. The main features of these studies have been the use of annual maximum series, the general extreme value (GEV) distribution for the regional growth curve and the estimation of its parameters using the method of probability weighted moments (PWM) (Hosking et af., 1984). Regressions between MAF estimates and basin characteristics were also carried out but the range of characteristics was often limited by the need to derive these for all the records from available maps.

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The results of these studies have been published in a variety of forms but the purpose of this paper is to attempt to draw more general conclusions, particularly on the form of the regional growth curves.

20.6. Studies in western Europe

In the context of collaborative studies of flow regimes in northwestern Europe (Gustard et af., 1989), annual maximum flood records from some 1600 stations with an average record of 17 years were analysed. The dominant dates of occurrence of these floods were used to classify flood regimes into glacier and mountain regimes, with summer maxima derived largely from snowmelt, maritime regimes with high winter floods from frontal rain, and inland regions with lower average floods but with occasional heavy storms increasing variability. Regional growth curves were derived for each of the 12 countries contributing data, and show growth curves which are flat in Ireland and the Scandinavian countries and rise towards the centre of Europe. However, these groups were found to be highly heterogeneous using tests for regional homogeneity suggested by Wiltshire (1986a). When all the stations were regrouped from their records according to their specific floods and the CVs of annual maxima, the results were naturally more homogeneous and more distinctive in terms of growth curves, but the distribution of the basins was less clearcut, with one of the flatter groups associated with hilly areas near western toasts and a group with steep distributions mostly in lowland areas in the east and south with their highest floods from summer storms. An attempt to group stations over the whole area according to selected basin characteristics (Acreman & Sinclair, 1986) failed to produce distinct regional subsets. This study illustrates the choice between geographical regions which are distinct but not homogeneous and regions defined by flow data or by basin characteristics, which tend to be more homogeneous but less easy to define in terms of ungauged basins.

20.7. Studies in other parts of the world

Following initial trials and a suggestion that more studies could prove fruitful (Sutcliffe, 1980), regional statistical studies have been carried out in different parts of the world, some by national bodies and others as part of a continuing research programme at the Institute of Hydrology, largely funded by the Overseas Development Administration. These studies have covered a wide variety of countries and climates, for which the necessary flood data were readily available. Sources of records included a number of areas for which investigations had been carried out. Other records were deduced from national yearbooks or from international publications such as UNESCO (1976) and IAHS (Rodier & Roche, 1984) which provided annual maximum series for selected stations from a number of countries. In these studies the estimation of MAF from basin characteristics has been to a large extent limited by the lack of available detailed maps, particularly for characteristics whose estimation requires thematic maps like soi1 type which proved to be an important variable in the British Isles. The lack of large scale mapping made consistent derivation of such variables as stream frequency or even channel slope impossible in most cases, SO that the two variables generally available for comparison were limited to basin area and mean annual rainfall (AAR).

Fortunately these are the two variables which appear to be most important in controlling the regional growth curve, SO that it is the dimensionless frequency curves which provide the most useful comparisons within and between areas of study. It is in these curves that the effect of climate has been most clearly evident, and it is to a large extent the seasonal distribution of the rainfall which has proved to be as important as its annual total. For example, the limited records readily available (Farquharson et al., 1987) from areas where snowmelt is the dominant cause of flooding show that regional growth curves are extremely flat and unskewed; examples of such records include NW USA and Canada and N Russia where very similar examples of growth curves are listed in table (20.1) and illustrated in figure (20.1).

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Table 20.1. Summary of snowmelt region frequency curves

Retum period (T), years No. of Stns u a k 5 10 25 50 100 200 500

Region Q( T)IMAF

NW USA & Canada 15 ,857 .254 .016 1.23 1.42 1.65 1.82 1.98 2.15 2.36

N Russia 12 ,849 .254 -.018 1.24 1.43 1.69 1.88 2.07 2.26 2.52

After : Farquharson et aL(1987)

3 T N Russia

Gumbel reduced tariate. v

Fig. 20.1. Regional growth curves for sample snowmelt areas

At the other extreme, analysis of 162 stations from arid areas (AAR < 6OOmm) provide (Farquharson et ai., 1992) very steep and skewed curves deriving from areas as far apart as SW USA, Saudi Arabia, Botswana and South Africa, and SW Queensland. Although relations between MAF and basin characteristics :

MAF = 0.172 AREA0.572 AARO.416 (R2 = 0.57) (20.3)

are imprecise and variable in these areas, partly because of the problems of measurement and extreme sampling errors, the regional growth curves are in several cases indistinguishable from each other or from the curve derived from the total set (table (20.2) and figure (20.2)).

Table 20.2. Summary of arid region frequency curves

Region Return period (T), years

No. of u a k 5 10 25 50 100 200 500 Stns

Q(T)IMAF S Africa & Botswana 42 .450 .429 -.422 1.35 2.06 3.36 4.70 6.51 8.95 13.4

Ensland 24 30 .586 .426 .396 .492 -.326 -.378 1.35 1.42 2.17 1.90 2.82 3.49 4.82 3.70 4.81 6.53 6.21 8.77 8.57 12.8 Saudi Arabia & Yemen 30 .428 .460 -.408 1.38 2.12 3.46 4.84 6.66 9.10 13.5

Total region 162 .476 .428 -.400 1.36 2.04 3.25 4.51 6.15 8.32 12.3 After : Farquharson et a1.(1992)

Fig. 20.2. Regional growth curvesfor sample arid areas

Another area where a large body of data had been published and which could be used for detailed analysis (Farquharson et al., 1993) was West Africa, where a number of yearbooks provide annual maximum flows for 224 stations in 12 countries. Basin areas ranged from 56 to 400,000 km2 and AAR from 740 to 3600 mm. Although relations betwen MAF and AREA and AAR were derived for different ranges of area and rainfall, it was found that the most reasonable groupings were by ranges of latitude and longitude. For deriving growth curves, however, it was found by tria1 and error that grouping by rainfall provided the most consistent criterion; the wetter areas provided the flatter curves, with the exception of the driest group, which was dominated by the largest rivers like the lower Senegal stations. There was also some tendency for smaller basins to have steeper curves and large basins the flatter curves. Examples of these curves are given in table (20.3) and illustrated in figure (20.3).

Table 20.3. Summary of West African frequency curves

1 , ye=- m (mm) No. of u a k 5 10 25 50 100 200 500

Stns Q(T)IMAF

<lOOO 23 .84 1 .370 .174 1.33 1.53 1.75 1.89 2.01 2.12 2.25 1001-1250 53 .806 .424 .136 1.38 1.63 1.91 2.09 2.26 2.41 2.59 1251-1500 51 .813 .390 .llO 1.35 1.59 1.87 2.05 2.22 2.38 2.57 1501-1750 70 .881 .234 .076 1.21 1.37 1.55 1.67 1.79 1.90 2.04 >- 1750 27 .908 .219 .183 1.20 1.31 1.44 1.52 1.59 1.65 1.72 After : Farquharson et al. (1993)

347

Gum bel reduced variate, y

Fig. 20.3. Regional growth cuves for rainfall zones in West Africa

The peculiarity of this area is that in general floods are derived from the accumulated volume of surplus rainfall over a single monsoon season, and in this sense it appears that this area has similarities to the snowmelt region. It has been shown (Sutcliffe & Piper, 1986) that annual runoff cari be estimated from seasonal net rainfall, or accumulated rainfall less potential transpiration, after soi1 moisture recharge has refilled the soi1 storage at the beginning of the rainfall season. Thus, by comparison with most other areas, the regional growth curves in a11 cases are extremely flat and the k values are positive, implying a finite maximum flood.

20.8. Evidence from other areas

There appear to be at least three distinct areas with contrasting growth curves :

%nowmelt areas where the curves are flat;

“arid regions where the growth curves are extremely steep and concave upwards and where they are very similar in areas as far apart as Botswana, Saudi Arabia and Queensland;

“areas covering wide parts of tropical Africa from Senegal to the Blue Nile basin where the curves are not only flat but concave downwards.

These three sets of curves may be compared with the three types of Gumbel curve which are respectively linear, concave upwards and concave downwards. Before attempting to speculate on the features which might cause these contrasts, it is appropriate to review the evidence from other areas.

The flood curves derived for NW Europe (Gustard et al., 1989) cari be extended towards the east by considering the less complete information available for a number of countries of eastern Europe (Farquharson et al., 1987). These data, taken from UNESCO and IAHS publications, are included in table (20.4) and suggest that the increases in slope and curvature which were a feature of NW Europe continue farther east as illustrated by the curves of figure (20.4) from different countries (the small selection of stations from Belgium is considered atypical.) The grouping by countries is arbitray but illustrates the apparent increase in flood vatiability as the climate becomes less maritime and more continental.

- .--

i 2 3 4 5 6 I

Gum bel reduced varlate. Y

Fig. 20.4. Regional growth curvesfor selected European countries

Table 20.4. Summary of European frequency curves

Country Return period (T), years

No. of u a k 5 10 25 50 100 200 500 Stns

Q(T)IMAF UK 401 .796 .320 -.058 1.30 1.57 1.92 2.20 2.49 2.78 3.19 Ireland 71 .868 .230 .OOl 1.21 1.38 1.60 1.76 1.92 2.08 2.29 France 266 .794 .346 -.017 1.32 1.59 1.93 2.19 2.45 2.71 3.06 FR Germany 326 .755 .372 -.077 1.35 1.67 2.10 2.45 2.81 3.19 3.72 Belgium II .710 .357 -.194 1.33 1.72 2.29 2.79 3.36 4.02 5.01 Netherlands 3 .795 .368 .022 1.34 1.60 1.93 2.17 2.40 2.64 2.93 Switzerland 83 .786 .297 -.127 1.28 1.56 1.96 2.29 2.64 3.03 3.59 Norway 89 .833 .281 -.015 1.26 1.48 1.75 1.96 2.17 2.38 2.66 Sweden 36 .817 .319 .OOl 1.29 1.53 1.84 2.06 2.28 2.50 2.79 Finland 36 .787 .337 -.053 1.31 1.59 1.96 2.25 2.54 2.85 3.27 Bulgaria 5 .667 .390 -.220 1.36 1.80 2.48 3.08 3.78 4.58 5.84 Czechoslovakia 16 .717 .356 -.182 1.33 1.71 2.26 2.74 3.28 3.89 4.82 Denmark 62 .814 .302 -.037 1.28 1.52 1.84 2.08 2.33 2.58 2.92 Hungary/Yugo. 12 .793 .281 -.139 1.26 1.54 1.93 2.25 2.61 2.99 3.56 Poland 11 .734 .373 -. 120 1.35 1.70 2.19 2.59 3.03 3.50 4.17 Romania 13 .669 .336 -.296 1.30 1.74 2.46 3.14 3.97 4.98 6.67

After : Gustard et ai. (1989) and Farquharson et al. (1987)

There are anomalous areas where monsoon climates apparently not dissimilar to West Africa give rise to relatively steep and skewed growth curves. These include Kenya, and particularly Sri Lanka, where the growth curves are extremely steep in spite of the heavy rainfall. A detailed study of the flood regimes of Sri Lanka was carried out as part of a review of dam safety, and the flood records of a11 72 stations with adequate periods of record and calibration were collated. The correlation of MAF with AREA and AAR gave an equation:

MAF = 7.17.5”10-3 AREAO.7176 AARO.8215 (R2 = 0.82) (20.4)

This equation explained 82% of the variante but still had a fsee of 1.45 in multiplicative terms. However, the growth curves gave valuable evidence of the variability of annual floods by comparison with the variability of the climate. Table (20.5) and figure (20.5) show the curves derived from grouping the stations into regions N, SW and SE of the central massif (C).

Table 20.5. Summary offrequency curves for Sri Lanka

Region

North South west South east

Central Al1 data

Return period (T), years No. of u a k 5 10 25 50 100 200 500 Stns

Q(T)IMAF 18 .540 .374 -.403 1.31 1.91 2.98 4.08 5.53 7.44 11.0 32 .773 .319 -.121 1.30 1.60 2.02 2.36 2.73 3.14 3.73 7 .670 .445 -.143 1.41 1.85 2.48 3.00 3.57 4.20 5.12 15 .686 .322 -.290 1.29 1.71 2.38 3.02 3.79 4.73 6.30 72 .687 .343 -.257 1.31 1.73 2.39 2.99 3.70 4.55 5.94

10 /

9

8 i

7 Ï

Fig. 20.5. Regional growth cuves for Sri Lanka

The steepness of the curves generally reflects the relative wetness of the different areas, where the average annual rainfall for the different groups ranges from 1720 to 3400 mm. However, the curves are extremely steep by comparison with say the West African set. The likely cause of this is the seasonal variability of the climate, which is dominated by the SW and NE monsoons providing rainfall during the periods May-September and December-February, with smaller amounts of rainfall of either convective or cyclonic origin during the inter-monsoon periods. Although the high and steep central massif divides the island into areas of dominant rainfall in different seasons, an inspection of the dates of the annual maximum floods shows that in most

different seasons, an inspection of the dates of the annual maximum floods shows that in most cases there is a wide variety of dates of occurrence over the periods of record. This is illustrated by figure (20.6), where the recorded dates of annual maxima for typical rivers in central Sri Lanka, West Africa and NW Canada are compared. Whereas in West Africa there is a dominant date when the flood is caused by accumulated rainfall over the concentrated season giving rise to saturated conditions, the floods in Sri Lanka are liable to occur over a wide range of dates. This hypothesis is supported by evidence from Kenya, where the growth curves are steeper than would be expected from rainfall alone; there are two distinct wet seasons and there is evidence that although the main rain season is in April/June, the second season in November/December has been responsible for exceptional floods as in 1961. This contrast is mirrored by the examples of a snowmelt river in NW Canada, where the flood date varies little, and an arid wadi in Jordan where a range of dates is found.

- 1

Fig. 20.6. Month of occurrence of annual maxima for selected stations

Thus there appears to be a distinction between those tropical areas where two monsoon seasons, and perhaps other storm regimes, give rise to variable flood dates, and those areas where a single monsoon season results in predictable flood dates; in the latter case it is to an extent the accumulation of rainfall over the season that gives rise to floods, as illustrated by a typical annual hydrograph. The same reasoning explains the relatively flat curves for snowmelt flooding and even the winter flooding of maritime basins in Europe, where the date of flood events has been found to be predictable near the western toasts and more variable as the variety of flood events increases to

351

-~ .~- -

the east. Other influences clearly play a part, for instance the basin size. In West Afiica, as noted, the slope of the growth curve has been found to decrease on average as the basin size increases. Indeed, if the group of ver-y large basins from a11 parts of the world is considered, the growth curves are extremely flat (Acreman & Farquharson, 1992). Nevertheless, the climate appears to be the dominant factor in determining the shape of the regional frequency curve. The extreme contrast between different climate zones is illustrated by figure (20.7), where the British curve is included for reference.

12

11

10

9

8

i

1

Arid zone

UK

0 1 2 3 4 5 6 f

Gumbel reduced variate, y

Fig. 20.7. Regional growth curves for varions regions

20.9. Historical flood evidence

Historical flood evidence is a potentially useful source of information on regional flood frequencies. In many areas there is evidence of the levels of floods before the start of scient& river flow measurement. This may take the form of flood marks in ancient city sites or along well-populated river valleys. Examples (Sutcliffe, 1987) are flood marks in York or Nottingham in B&ain, which cari provide evidence of floods spanning several centuries, or the rock-tut marks along the Yangtze which provide evidence of high floods as far back as the 12th century. In some cases the stability of the rating curve may make it difficult to interpret early evidence in terms of flow. Although the Yangtze gorge is relatively stable, SO that recent flood frequency curves may be adjusted using early evidence, it is difficult to use the long Roda Nilometer record in Cairo, where annual maximum and minimum levels have been recorded more or less continuously since 622 AD, since the site has been subject to aggradation. Even longer periods of floods may be covered by

prehistoric or geological evidence. For example, there is evidence from a cave near the outfall of Lake Victoria that the recent highest lake level following the rise of 1961-64 had not been exceeded over nearly 4000 years. Palaeoflood evidence (Baker, 1987) from sediments deposited by past floods may provide further evidence of the potential of a river basin.

The incorporation of historical evidence in single station analyses has been developed by maximum likelihood methods (NERC, 1975, p.I.215), where the historic evidence may be treated as a period of censored record, on the assumption that all floods above a threshold indicated by the existing flood marks would have been recorded. This evidence has also been included in regional analysis in Britain by graphical methods, using appropriate plotting positions for each flood. Studies have shown (Tasker & Stedinger, 1987) that the inclusion of historical information cari significantly improve estimates of regional regression mode1 parameters. There is a need to extend the PWM approach to provide formal ways of incorporating historical flood evidence in regional growth curves, taking note that the ubiquity of large floods might be exaggerated by assuming that those sites with such records are typical.

20.10. Discussion and conclusions

It is recommended that the estimation of the flood frequency relation at a site be approached in two stages. The mean annual flood may be estimated from records at or near the site from the arithmetic mean of annual maxima if the record is adequate, or from the POT series using the Bemier hypothesis where the record is short. When no flood records are available at the site, it may be necessary initially to estimate the mean annual flood from basin characteristics. Although regional relations between mean annual flood and generally available factors like basin area and rainfall cari give a preliminary estimate, it is desirable to include other basin factors like soi1 permeability, channel slope and network, and perhaps land use, in a more detailed study of flood records. An example of such a study where local knowledge cari be incorporated is that of Rodier (1993) for West Africa.

Because the length of record at a single project site is insufficient to estimate the shape of the frequency curve, in particular the slope and skewness, the dimensionless regional frequency curve presents a valuable method of converting the estimated mean annual flood to estimates for other return periods (Cunnane, 1988). The derivation of these frequency curves for reasonably homogeneous regions is a method of overcoming the problem of limited lengths of record at individual sites. There is also need for methods of incorporating historical evidence in regional frequency curves. The intelligent use of geographical areas to delimit appropriate regions should take account of the apparent dominante of rainfall depth and its seasonal distribution in determining the shape of frequency curves in a wide variety of climates. Because the purpose of combining records from a variety of sites is to sample as far as possible the different storm events which could occur over any one basin, the evidence of position and basin characteristics with an emphasis on rainfall incidence is preferable in delimiting boundaries than an emphasis on short flow records at individual sites.

353

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