Seasonality of flooding: a case study of North Britain

Journal of

Hydrology ELSEVIER

Journal of Hydrology 195 (1997) 1-25

Seasonality of flooding: a case study of North Britain A n d r e w R. B l a c k a'*, A l a n W e r r i t t y b "Institute of Hydrology, Alpha Centre, Innovation Park, Stirling FK9 4NF, UK bDepart~nt of Geography, University of Dundee, Dundee DDI 4HN, UK

Received 12 May 1995; revised 21 August 1996; accepted 2 September 1996

Abstract The seasonality of river flooding in North Britain displays considerable spatial variation. This paper identifies the geographical patterns of flood seasonality, using a ~t_~base of events exceeding modest flood-flow thresholds at each of 156 gauging stations, and seeks to explain them in terms of climatological and catchment characteristics. Hoods are found to occur at all times of year, but most rivers register at least 78% of events in the October-March half-year, and these generally occur later in the year with distance from west to east. However, notable exceptions are superimposed upon this general pattern and, in particular, two areas of less pronounced seasonality occur on north-facing parts of the east coast. Seasonality is characterized using three complementary methods, including a four-fold seasonal classification which summarises the patterns found. In order to explain these patterns, reference is made to the seasonality of storm rainfall, soil moisture deficits, catchment size and lake storage. Seasonality class is correctly explained by reference to these catchment characteristics in 74% of cases using discriminant analysis. The work is presented as an advance in the understanding of flood generation and, ultimately, in the assessment of flood risk.

1. I n t r o d u c t i o n This paper adds a significant new component to the existing literature on flooding in Scotland and northernmost England. No previous study in the U K has systematically considered seasonality at such a level of detail on such a number of rivers, or across such a complex geographical region. The area described includes variations in mean annual rainfall values from less than 650 m m to over 4000 m m and topography ranging from steep mountains to coastal plains, and all within a compact unit of only 75 000 km 2 in areal extent. * Corresponding author present address: Department of Geography,Universityof Dundee, Dundee DDI 4HN, UI~ 0022-1694/97/$17.00 O 1997- Elsevier Science B.V. All rights reserved PII S0022-1694(96)03264-7

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A.R. Black, A. Werritty/Journal of Hydroiosy 195 (1997) 1-25

There is much historical information which has persuaded us that such an investigation would be valuable. On the River Findhorn in northern Scotland (see Fig. 1), the three great floods of 1829, 1956 and 1970 all occurred in July and August (Green, 1958, 1971), months associated with severe flooding only in restricted areas of eastern Scotland (Werritty and Acreman, 1985; Acreman, 1989). On the upper River Spey and the River Ness, all known major floods have occurred in the winter months between November and March (Black, 1992), while on the Tay at Perth, records from 1814 show that major events have occurred in all months except March, April, July and September (Black and Anderson, 1994). Similarly, in small rivers and streams, interesting seasonal behaviour can be identified: for example, a very strong concenu'ation of floods in the White Laggan Burn (in the Galloway Hills, Fig. 1) between August and November (Black, 1994) and, by contrast, a relatively even distribution of events on the West Peffer Bum (East Lothian), with no two-month season being characterized by more than 30% of events over a standard period (see below). These contrasts and the anticipations of regional patterns form the stimulus to this study of flood seasonality. The Institute of Hydrology (IH) has recently published a set of flood seasonality summary statistics for 856 gauging stations across the UK (Bayliss and Jones, 1993). This gives a clear illustration of the general patterns of flood seasonality across the UK although, partly because of the large volumes of data involved, it does not consider the various elements contributing to these patterns in detail. Flood seasonality has formed the focus of a number of studies in northeast England, including a regional study of flood seasonallty and the development of a simple model for assessing seasonal flood risk (Archer, 1981a), and has also provided the basis of several statistical models for assessing risk on a range of timescales (Todorovic, 1978; Ettrick et al., 1987 Futter et al., 1991). In addition, a number of informal papers were written in the early 1980s at IH (e.g.A.D. Hewson, unpublished work, 1982) in which both national and regional patterns of seasonality were explored. The results of these studies are responsible for the extension of the study area from Scotland to include Northumberland, the most northerly county of England (see Fig. 1). The combined area is referred to as North Britain. By choosing this study area, it was possible to achieve a high level of comprehensible spatial resolution, while focusing on a geographical unit of sufficient size to show substantial internal variations in seasonality. Seasonality has been identified in Canada and Italy as having important implications for the specification of flood magnitude-frequency relationships. In the areas considered (Waylen and Woo, 1982; Rossi et al., 1984), annual maximum flood series are composed of a mixture of rainfall-generated and snowmelt-generated events, such that separate components for each type of event can be identified. In both countries, it has been reported that modelling these series with separate parameters for the individual components has been beneficial for design flood estimation, offering scope for application in areas such as floodplain management. In the UK however, a method has yet to be developed by which floods may be assigned to groups describing their origins. Frontal rainfall, convectional storms, snowmelt, frozen and parched ground are all known to produce floods either alone or in combination (Smith, 1992). Because the interaction of several flood generating or enhancing mechanisms is so often a feature of UK floods (e.g. Black and Werritty, 1993), meaningful classification

A.R Black, A. Werritty/Journalof Hydrology 195 (1997) 1-25

N

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Fig. !. North Britain, showing main rivers and locations referenced in text.

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A.R. Black. A. WerrittylJournal of Hydrology 195 (1997) 1-25

remains problematic. Yet if the identification of components in flood series in some countries has been beneficial in developing new methods of risk estimation, the same may nonetheless apply in countries such as the UK where the distinction between components in flood series is less clear. The direct recognition of heterogeneous components has been recommended as an area for development in flood frequency analysis by Archer (1997), who explicitly identifies the scope for progress offered by seasonality. The purpose of this paper is to document the results of an investigation of flood seasonality in the rivers of North Britain (Black, 1992), based on a database of flood peaks exceeding moderate-flow thresholds. The range of seasonalities found is related to the physical and climatological characteristics of catchments, and the findings reached are discussed in the context of improving the cmrent knowledge of heterogeneity within flood series. Such an advance will be of value in informing the development of new models of flood risk estimation. Attention is also directed to the importance of the methods chosen to characterize seasonality.

2. Data preparation and presentation 2.1. Data extraction and compilation The database assembled for this study is drawn largely from the river gauging station records of the statutory national hydrometric authorities for Scotland and England, reorganized in 1996 as the Scottish Environment Protection Agency and the Environment Agency respectively. Some 260 primary ganging stations are currently operated across the study area (see Institute of Hydrology/British Geological Survey, 1993), and a further 150 secondary or decommissioned stations are known. This latter group includes several stations in remote areas of Scotland operated for purposes distinct from those applying to most hydrometric authority stations, and by other organisations, e.g. hydro-power generators. While the national networks include gauges on all main rivers and many smaller watercourses in their areas, knowledge of records held by non-statutory measuring authorities was valuable in identifying all sources available for the creation of a comprehensive database for the study. A database comprising records from all parts of the study area and with lengths of at least 10 years each was sought. A further objective was to avoid using records from rivers heavily influenced by reservoir storage, since it is felt that the seasonal variation of storage may often distort natural patterns of flood seasonality. An early decision to use peaks-over-threshold (or partial-duration) flood series was made, in preference to the alternative annual maximum data, in order to provide a greater amount of seasonal information. A peaks-over-threshold database gives the date and peak flow of each event exceeding a given flow threshold, whereas an annual maximum series gives information concerning only the largest event each year (Shaw, 1993). The peaks-over-threshold method of flood extraction, with thresholds giving approximately four to five peaks per year on average, as used in the UK Flood Studies Report

A.R. Black, A. Werriny/Joumal of Hydrology 195 (1997) 1-25

5

(Natural Environment Research Council, 1975), offers three advantages over the annual maximum method. It is more objective, comprising floods exceeding a consistent threshold only, rather than including small events for years in which no higher flows occurred. All floods ahove the threshold are included in the series, rather than just the largest in each year. Finally, more information is included in a peaks-over-threshold series, by virtue of the larger number of events included. The overall result is that a more detailed description of seasonality is allowed, and based on a more consistent definition of floods than would otherwise be possible. Of great benefit to the assembly of the database was the existence of previously collated data. Records to ca. 1971 were available from Natural Environment Research Council (1975), and subsequent work by Acreman (1985a. b) extended many of these records to ca. 1982. Using microfilmed water level charts and rating equations supplied by measuring authorities, a further 682 station-years of peaks-over-threshold series were added to the existing database up to 1989/1990, to give a total of 3458 station-years available for analysis from 156 gauging stations. Flood Studies Report independence rules were applied in the extraction of new data to ensure compatibility with existing records. Where an event occurred with more than one peak in the flow hydrograph, these rules required that: 1. the flow must drop to two-thirds of the value of one peak before rising to the next, and 2. the interval between peaks must be at least three times the mean time to peak before individual peaks could be included as implicitly independent events in the peaks-overthreshold series (Natural Environment Research Council, 1975). 2.2. Threshold adjustment After the database was compiled, a process of threshold standardisation was embarked upon, in order to moderate the effects of annual variations in event frequencies. This allowed objective comparison of seasonality to be made between stations, and was based on the adoption of a common frequency threshold. The most commonly occurring 1O-year period in the database, 197% 1988, was adopted for this purpose and flow thresholds at each station were raised to a value which resulted in a peaks-over-threshold series comprising exactly 45 events over the period; Where records lacked some of these 10 years, neighbouring stations with overlapping records were used to guide threshold adjustment and, where records contained fewer than 45 peaks or equivalent over this period, these were excluded from subsequent analysis. The number of events (45 over the 10 years) was chosen subjectively in order to achieve. an acceptable compromise between loss of spatial coverage within the database on the one hand and the loss of detail within individual records on the other, each of which would result from applying small or large increases to threshold values respectively. Only 13 stations were, thus, excluded from the database and, of these, just one was more than 15 km from another station which was retained. The result was a comprehensive peaks-over-threshold database, rich in seasonal information, and comprising records which could be fairly compared as a result of achieving equivalence in threshold values.

A.R Slac& a. Werrmy/Joumaloftlydroiosy 195 (1997) 1-25

6

2.3. Methods of characterizing flood seasonallty In order to effectively present the seasonal information contained in the database, it is important to employ the most appropriate statistics. Three methods are used in this paper to characterize flood seasonality, and are outlined here. 2.3.1. Directional statistics For each event in a flood series, time of year is translated into location on the circuraference of a circle, with mathematical convention dictating that the start of year is shown at its most easterly point and that the seasons proceed in a counter-clockwise sense (Manila, 1972; Fisher, 1993). The use of a 31 May start-of-year avoids a discontinuity in numerical date values during the main seasons of flooding. By joining each point to the centre by a vector, the central tendency can be found by resolving each of these into perpendicular x and y components, the means of which define a mean vector (Fig. 2). The angle of'the mean vector can be readily translated into a mean day value (by multiplication by 365/360), giving a measure of central tendency based on all the data points. Beyond its angle, the length of the mean vector is of interest also, indicating the degree of seasonal clustering about the mean, with values ranging from 0 (balanced distribution of events around the year) to 1 (all events on the same day). Indexed as I",

Based on

Batsr.lmlet (1981), Fig. 1.3.3.

Oburva~on (flood), location on circle repreeenting time of year. Vectors join each cl~NvaUco to origin; dashed lines show x and y components for selected obsermUon.

Fig. 2. Application of directional statistics to flood season data (Based on Batschelet (1981) Fig. 1.3.3.).

A.R. Black, A. Werritty/Journalof Hydrology 195 (1997) 1-25

7

this seasonal clustering index complements the mean day value, and serves a similar function to the standard deviation in non-circular based statistics.

2.3.2. Seasonal frequencies This method is based on counting the number of events in each of a number of seasons and, to allow comparison between records, expressing these counts as a percentage of the total number of events in each record. In North Britain, where most floods occur between October and January, Black (1992) found that this method could be usefully employed by the creation of six seasons, of two months each. This method provides more specific information than the directional statistics method, the six seasons.offering a good compromise between detail and the maintaining of numbers in each season.

2.3.3. Classification analysis This final method uses all the date information in a peaks-over-threshold series and condenses it by assigning each record to one seasonality class. The method is considerably more complex than the others described above and is well established in hydrology, e.g, the grouping of catchments for regional flood frequency analysis according to their physical characteristics (Acreman and Wiltshire, 1989; Burn, 1989) and grouping for the estimation of unit hydrograph parameters (Burn and Boorman, 1992). Classification analysis involves the successive allocation of cases (in this case peaksover-threshold records) to clusters according to their location in a multivariate space. Here the six two-monthly percentage peaks-over-threshold frequency values for each gauging station provide the input for the classification analysis. Mean day and r values could be taken as an alternative input but provide less detail and their use is therefore avoided. Great freedom exists both in the algorithms selected for the classification analysis and the final number of clusters to be produced. Implementation of this analysis is highly dependent on the availability of a suitable computer software package, CLUSTAN (Wishart, 1987) being used in this investigation. Clustering begins with the two cases closest in n-dimensional space merging to form the nucleus of a cluster and, according to their relative proximity, continues with further cases joining this nucleus or one of the remaining single cases to form another nucleus. The process continues until all cases have been allocated to the desired number of clusters. Merging may proceed either by hierarchical fusion of clusters, iterative relocation of individual cases, or by a combination of the two methods (Gordon, 1981; Wishart, 1987; Jain and Dnhes, 1988). If the hierarchical fusion algorithm is used, cases cannot be relocated once assigned to a cluster. However, the iterative relocation algorithm does transfer cases between clusters where this reduces n-dimensional distances within clusters and increases n-dimensional distances between them. The commonly recommended strategy of proceeding first by hierarchical fusion, and then by iterative relocation to enhance the distinction between clusters, was adopted (Wishart, 1987) in this study, and the results of its application are presented below. The method is able to condense the detailed descriptions provided by seasonal frequencies into a classification with a small number of physically meaningful seasonal types. Experience working with the data suggested that each of these three methods was

8

A.R. Black, A. Werritty/Journalof Hydrolo#y 195 (1997) 1-25

complementary to the others: specific tasks demand differing levels of generalisation in the seasonal characterization. All three methods are drawn upon in the descriptions and analyses below. 2.4. Period of record standardisation

Both the mean day/r and seasonal frequency sets of statistics were modified to compensate for the considerable range in periods of record obtained from each gauging station. While year-to-year variability of flood behaviour may detract only slightly from the validity of seasonal comparisons between stations if each record exceeds, say, 30 years in length, some records used here are as short as 10 years and may not be representative of long-term flood seasonality at a site. A standard period of 30 years, from 1959 to 1988 (the most frequently occurring such period in the database), was selected for this purpose. Where a record extended fully through the standard period, statistics were calculated simply for that period alone. In those cases where the full 30 years were not available, neighbouring stations with overlapping records including the standard period were used as the basis of adjustment. However, this was undertaken only where neighbour stations were sufficiently close and had adequate overlapping records to make this worthwhile. Relationships were developed (Black, 1992) on the basis of available long records to define those combinations of neighbour proximity and overlap length which would allow standard period values of: 1. mean day and rto be predicted with 95% confidence to an accuracy of 15 days and 0.15 respectively, and 2. seasonal frequencies to be predicted with 90% confidence to an accuracy of 12%. Seasonality statistics for periods of overlap were transformed to 1959-1988 equivalent values through scaling by the ratio of standard period to overlap period seasonality values. Where two or more neighbouring stations were used, estimates of the standard period value were weighted according to an inverse distance method before summation. The method was applied to mean day, r and seasonal frequency data sets. In the next section, which describes patterns of flood seasonality across the study area, all statistics relate to the standard 30-year period. The classification analysis described above was based on seasonal frequency data which had been adjusted by this process. The database resulting from these processes of data collection and transformation forms the basis for the descriptive and analytical parts of the paper. The use of modest flow thresholds (based on a fixed event frequency over a 10-year period) in the peak flow series provides a high level of seasonal detail, and the inclusion of records from rivers across a geographically complex study-area ensures the scope for representing a wide range of flood seasonalities.

3. Patterns of seasonality

The overall spatial pattern of flood seasonality across North Britain is depicted in Fig. 3(a) in which the orientation and length of each arrow represent the mean day of flood and

A.R. Black, A. Werritty/Journal of Hydrology 195 (1997) 1-25

seasonal clustering index (r) respectively. The mean day of flood typically occurs in late November or December (mean day values 175-214), and the degree of seasonal clustering around these values is relatively high (more than 0.5) for many stations. More detailed examination, however, reveals some notable departures from this general pattern. The location of the rivers and geographical regions noted below can be found by reference to

Fig. 1. In southwest Scotland there is a striking tendency for the mean day Of food to occur earlier in the autumn, notably throughout the western Southern Uplands and for some of the north-bank tributaries of the River Clyde. There is a tendency also for the arrow to rotate counter-clockwise as one moves from west to east indicating a progressively later mean day of flood, with late Dem=.mber-January values occurring at stations on the lower courses of major rivers in northeast Scotland (e.g. Spey or Don) and some smaller rivers in East Lothian. This p a l m , however, is not sustained along the south Moray Firth Coast wbere the Rivers Findhorn and Lossie revert to a late November mean day value, substantially earlier than all the stations on the adjacent River Spey. Locally there are interesting anomalies such the Dean Water (a small lowland catchmerit north of Dundee) which records a January mean day of flood in contrast to its immediate neighbour the River Isla (draining from the Grampian Mountains) which is 30 days earlier. Similar anomalies occur in Northumberland with the Rivers Blyth and Wansbeck both registering mid-late January mean days. The earliest mean day value is to be found in southwest Scotland where the White Laggan Bum has a mean day in mid-September, two to three months earlier than most other stations (Black, 1994). However, because of a short record length, no standard period equivalent value could be produced. In terms of the seasonal clustering around these mean day values, the majority of inland stations show a moderate to high level of clustering (r > 0.55) implying that one particular season is dominant. By contrast low r values (lower than 0.35) indicative of a wide distribution of events throughout the year and a weaker seasonal signal are to be fotmd on the south Moray Firth Coast, in East Lothian, parts of the Tweed basin and in Northumberland. Another anomalously low r value is the Allt Uaine (a small, high altitude and mountainous catchment), 55 km northwest of Glasgow. The vectors of Fig. 3(a) show that there is general agreement between seasonality statistics based on the standard period and those for periods of record (used where standard period values could not be produced). A more precise characterization of the seasonal signal can be obtained from maps showing the percentage of floods recorded in six two-monthly seasons (Fig. 4). These maps reveal an interesting symmetry with April-May and June-July both registering low flood frequencies and October-November and December-January high flood frequencies. The spatial patterns for the low frequency months (April-July) show high values on the east coast (though rarely over 10%). By contrast in the next two months (AugustSeptember) the highest frequencies (over 30%) are in the southwest with some high values also in the nc41heast. High values continue to be present in the southwest through OctoberNovember but generally decline to the east, with some local contrasts (e.g. around Fort William in the West Highlands). The pattern for December-January is dominated by high frequencies (over 30%) across much of Scotland, particularly the north and east, with local exceptions south of the Moray F'h-th. Part of this pattern continues into February-March

A.R. Black. A. Werritty/.lournal of Hydrology 195 (1997) 1-25

10

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A.R. Black, A. Werri~/Journal of Hydrology 195 (1997) 1-25

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A.R. Black,A. Werriny/Journalof Hydrology 195 (1997) 1-25

13

where virtually the whole of the study area registers i0--20% of floods with locally higher values in the southeast and extreme northwest. It is clear from the above that there is a strong spatial patterning to flood seasonality across Scotland, and this can be summarized concisely with the results of a classification analysis. Using the procedure described above, flood records were allocated to four seasonality classes which were felt to represent physically meaningful seasonality types. The classes are described in Fig. 5, and the geographical distribution of class members in shown in Fig. 6. The rivers with strong winter seasonality (Class A) occur mostly in inland areas and on rivers with large catchments, e.g. Rivers Spey, Dee, Tweed and Clyde. Late winter (Class B) rivers are most concentrated in Northumberland, although isolated examples also occur across most of Scotland. Rivers with weak seasonaiity (Class C) occur in two distinct geographical areas, in Lothian and in NE Scotland, while rivers having autumn/winter seasonality (Class D) are equally concentrated in southwest Scotland.

4. Physical determinants of seasonality Having described the seasonality of flooding in the rivers of Scotland and Northumberland, the physical factors responsible for the production of these patterns are now examined. A number of controlling factors are identified on the basis of the literature, and methods of indexing them described. Discriminant analysis is then used to assess the extent to which these otherwise diverse factors explain the observed patterns. 4.1. Controlling factors 4.1.1. Rainfall seasonality (mean day, r) Most, though not all, floods in North Britain are produced entirely by rainfall of either frontal or convective origins, the exceptions being those generated by snowmelt and which occasionally occur without any significant rainfall (Archer, 1981b, 1992). It therefore follows that an explanation of the seasonality of flooding must take account of the time of year of peak rainfalls. A critical storm duration of 24 h is typical of many North British catchments (see Natural Environment Research Council, 1975), and allows use of the extensive Meteorological Office database of daily rainfall totals for an analysis of seasonality. Raingauges located within, or near to, the catchments of the 143 streamflow gauging stations satisfying the threshold adjustment requirements were identified, and peaks-overthreshold series extracted from each rainfall record for as much of the period 1961-1990, as was available. Up to four raingauges were used for larger catchments, using simple daily means to crudely represent areal rainfall. Thresholds giving an average of 10 rainfall events per year were set, giving approximately twice as many events per year as in the flood series. Mean day, r and seasonal frequency values were then obtained in a manner directly analogous to that applied to the flood data. The patterns of peak rainfall seasonality are shown in Fig. 3(b). Surprisingly, mean day of peak rainfall shows a geographical gradient roughly opposite

A.R. Black, A. Werritty/Journal of Hydrology 195 (1997) 1-25

14

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to that for mean day of flood (Fig. 3(a)). Although November mean day values are common for both peak rainfall and floods in the west, peak rainfall seasonality becomes generally earlier with distance east while mean day of flood becomes later. It is noticeable that peak rainfalls have a lower seasonal concentration in the east (Fig. 3('o)). This is explained by eastern areas having higher rainfall event frequencies between April and July than western areas (typically 21 and 15% of total, respectively) and lower frequencies than in the west between October and January (43 and 49% respectively; Black, 1992). Other factors must, therefore, be considered in order to achieve an understanding of this unexpected contrast between the seasonal patterns of floods and peak rainfall.

4.1.2. Soil moisture deficit (SMD) Soil moisture deficits normally attenuate the runoff response of North British catchrnents to rainfall, except where parched or frozen ground is involved, and must therefore also be considered as a physical determinant of flood seasonality. MORECS data (Meteorologicai Office Rainfall and Evaporation Calculation System, Thompson et al., 1981) are available from 1961 for a grid of 40 km squares which covers the UK, and 30 years of end-of-month SMD values were extracted for each square covering the study area. Each catchment was associated with one or more grid squares. In order to index the length of season during which runoff response might be substantially

A.R. Black, A. Werritty/Journal of Hydrology 195 (1997) 1-2.5

15

Seasonality class

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Fig. 6. Geographical distribution of scasonality class members. reduced, it was decided to focus on the length of time between SMD values first exceeding 10 mm and subsequently returning below that value. The 30 years of data were, therefore, used to calculate a mean SMD season length for each catchment. Start and end of season dates were calculated using linear interpolation between end-of-month values immediately above and below 10 mm. Where more than one grid square was used for a catchment, end-of-month values were based on the calculation of means.

16

A.R. Black, A. Werritty/Journalof Hydrology 195 (1997) 1-25

The data obtained show a strong gradient in values from west to east coasts, with mean SMD season lengths of less than 60 days in the far northwest contrasting sharply with some values of more than 220 days on the east coast (Fig. 7). Use of this simple index clearly illustrates the presence of a significant spatial pattern in SMD values, which must exert a strong influence on the patterns of flood seasonality obtained from the peaks-overthreshold database. The distribution of these values appears to explain the observed mismatch between flood and peak rainfall seasonality maps. Further factors, however, need to be identified before assessing their combined effects. 4.1.3. Catchment size (AREA)

Catchment size is expected to exercise substantial control over flood seasonality because of its influence on the type of rainstorm producing floods. With catchment size acting as a control on hydrograph time to peak (Natural Environment Research Council, 1975), size will, in turn, control the response to rainfall and, if there is some seasonal variation in storm types, then size will affect flood seasonality. It is expected that small catchments will be more responsive to localized rainfall of high intensity, particularly thunderstorms, while large catchments will produce floods in response to regional rainfall of generally lower intensities (Werritty and Acreman, 1985). Flood seasonality characteristics for the six smallest catchments with standard period event frequencies are shown in Table 1, and it can be seen that most exhibit quite early flood seasonalities, although, within the group, there is still considerable variation. The catchments range from mountainous to lowland settings, with the one eastern, lowland catchment in East Lothian (the West Peffer Burn) having a much later seasonality than the others shown. The nine-year record for the White Laggan Burn in the Galloway Hills also shows exceptionally early flood seasonality, and it has been demonstrated that this is due to a strong, late-summer dominance of short duration, high-intensity rainstorms in that area combined with a small catchment size (Black, 1994). By contrast, details for the six largest catchments used are shown also in Table 1, with winter-strong seasonality characterizing the records of the Rivers Dee, Tweed and Clyde, while the Ness shows a late-winter seasonality, and the Spey and Don exhibit weak flood seasonalities. It was noted above that Class A (strong winter) seasonality characterizes many large catchment flood records, so the variability reported here seems surprising. However, snowmelt is recognized as an important contributor to many floods on the Ness, Spey, Don and Dee (e.g. McEwen, 1987), particularly in late winter and spring, and summer flooding on the Spey is often attributable to localized runoff generation in its lower tributaries (Green, 1958; Werritty and Acreman, 1985), so much of the observed variation can be explained. Fig. 8 shows the scatter of mean day of flood values with catchment size. It can be seen that while large catchments (over 1000 km 2) all have values in the relatively narrow range 186-214 (3-31 December), extreme values are found only in smaller catchments. Nine of the 12 highest values occur in catchments of less than 500 km 2 and, including records for which no standardized data were available, two of the lowest-three values occur in catchments of less than 6 km 2. The broadly average seasonality for rivers draining large catchments is explained by the integration of flows from smaller, more physically diverse catchments nested within them, producing broadly similar flood seasonalities. Catchment

17

A.R. Black, A. Werritty/Jottrnalof Hydrology 195 (1997) 1-25

Length of SMD season (values exceeding lOmm) MORECS data

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3.1 6.5 23.7 26,2 30.8 31.0 1273 1839 1844 1903 2640 4390

Allt Uaine Allt Leachdach Fruid Water West Peffer Little Eachaig Tima Water Don at Parkhill Ness at Ness-side Dee at Fedc Clyde at Daldowie Spey at Aberlour Tweed at Norham

13.9+ 7.7+ 3.4 6.0+ 1.0 3.2 8.1+ 1.4 0.01.0 6.1+ 1.7

28.9+ 11.6 12.8 8.228.2+ 35.8+ 8.28.711.3 13.4 16.2 10.9

AugustSeptember

June-

July (%)

October-

21.541.3+ 49.9+ 28.5 34.8+ 28. l 19.625.627.8 32.3 21.9-26.2-

November 24.525.020.1 27.0 18.6! 9.536.2+ 31.0 34.8+ 35.6+ 31.4 37.0+

8.99.79.1 18.6 10.4-13.3 20.1+ 33.2+ 18.4 15.7 19.4 21.7+

FebruaryMarch (%)

December-

January(%) 2.4 4.7 5.1 11.7+ 6.9+ 0.07.6+ 0.07.7+ 2.0 5.0 2.5

April-May (%)

148.7170.6186.8* 207.0+ 150.816 ! .3213,6+ 196.9 198,0 186.7 207.9+ 201.4+

Mean day

0.3630,4180.485 * 0.3800.443-0.459 0.4240.547 0.478 0.634+ 0.3470.535

r

Values greater than all-stations upper quartile value shown by +, less than lower quartile by -. All values are for 1959-88 standard period unless shown by * (period of available record).

Area (km2)

Station

Table 1 Flood seesonality of six smallest and six largest catchments

~"

-~

~.

~,

~. '~

.~

.~ ~e

OO

A.R. Black, A. Werritty/Journal of Hydrology 195 (1997) 1-25

19

250-

Jan ee

~

o o

•

:':.-, •

Q

Dec

e

•

e| I 0

g

Nov

P,.* ee

•

•

150

g~e~as days~

3~ May

~(km~ Fig. 8. Variation of mean day of floodwith catchmentsize. size is, therefore, thought to be important, in combination with other factors, in an overall explanation of flood seasonality.

4.1.4. Lake storage (LAKE) Scotland is renowned for its large number of lakes (or lochs), and both these and storage reservoirs are known to attenuate flood peaks (Ward, 1981). Flood records dominated by storage reservoir effects have been excluded from this study, but there remains a requiremerit to represent such effects in those catchments used. The catchment characteristic L A KE w as adopted in Natural En viro nmen t Research Council ( 1975 ) to index the proportion of a catchment draining through one or more lakes or reservoirs, each with surface areas at least 1% of their respective catchment sizes, and it was chosen to serve the same purpose in this study. The distribution of LAKE values was found to be severely positive-skewed, with only 17 catchments having LAKE values greater than 0.3. Of these, 12 are characterized by Class A seasonality, and a further four (all with LAKE values of more than 0.7) represented by Class B seasonality. The lack of any high-LAKE catchments having early flood seasonalities is consistent with expectations. Early seasonalities in small catchments experiencing short-duration, intense storms will be tempered by the presence of a lake, which would attenuate the resultant floods, while longer-duration events would be less heavily affected. Some of the late flood seasonalities in high-LAKE catchments can be explained indirectly, in that some of these rivers drain large and snowy tracts of the Scottish Highlands (e.g. Rivers Ness, Ewe and Lochy). The results presented, therefore, suggest that, in combination with other factors, LAKE is effective in determining flood seasonality. Accordingly, it is taken forward with rainfall seasonality, SMD and catchment size into the discriminant analysis in order to explain the observed patterns of flood seasonality. Snowmelt has been referred to as a further controlling variable but has not, however, been indexed as a separate catchment characteristic because of a lack of suitable data at the time of the study. A new method of deriving

20

A.K Black, A. Werritty/Journalof Hydrology 195 (1997) 1-25

snowmelt estimates from altitude and latitude data (Hough and Hollis, 1995) may be helpful in the future. 4.2. Discriminant analysis

Of all the indices available to characterize flood seasonality (see above), it was decided to use the results of the classification analysis (i.e. class membership) as the single best characterization. Only classification analysis was felt to provide the opportunity of condensing all the seasonal detail of a peaks-over-threshold series into a single index. Having chosen class membership for this purpose, linear regression could not be used to attempt explanation because seasonality and catchment characteristics are described on different types of measurement scale: nominal and interval data, respectively. The equivalent method based on the general linear model is discriminant analysis and this was, therefore, adopted for use. In order to encompass a wide range of catchment types, all records satisfying the threshold adjustment requirement were used for this part of the analysis. Seasonal patterns derived from the classification analysis were thus to be explained using discriminant analysis based on the climatological and catchment characteristics discussed above. Values of all controlling factor variables were transformed using log10 to reduce the effects of skewed distributions. Each was then standardized, and principal components were taken to eliminate the unwanted effects of interdependence amongst the predictor variables. Five principal components were thus produced from the five original variables (peak rainfall mean day, r, SMD, AREA and LAKE). Discriminant analysis was then used with these five principal components to explain flood seasonality, indexed by class membership, and resulted in 62% of catchments being assigned to their correct class. It was noticeable that the discriminant analysis identified the true class as the second most probable assignment at 65% of the incorrectly assigned stations. It therefore follows that a more suitable classification method might be employed. This seems especially pertinent in view of the fact that the classes do not have distinct boundaries. The plots of Fig. 5 show that some stations could arguably be allocated to another class. Following the initial application of the recommended classification procedure (see above), a variety of alternative similarity measures were, therefore, tried. The greatest improvement in discrimination was achieved by classifying with a "shape" measure which calculates distance' 'as the variance of the differences between variable values of two cases or cluster centres" in all dimensions (Wishart, 1987, p. 197), and with a discriminant analysis based on principal components of just four variables (mean day of peak rainfall became redundant and was therefore excluded). By this means, 74% of stations' class membership could now be explained. Table 2 characterizes the membership of the four new Classes E - H produced by this revised classification, which again seems physically reasonable. While Classes A, C and D change little in their transformation to new Classes F, G and H, respectively, Class B (late seasonality, 18 members) is lost and is replaced by Class E, comprising just two members and characterized by very early seasonality. The distribution of incorrectly assigned catchments among these new classes is shown in Table 3. This more successful level of explanation clearly indicates that the physical characteristics used here are important determinants of seasonality, notwithstanding the limitations of the data used (i.e. rainfall seasonality based on one-day peak totals irrespective of

A.R. Black, A. WerrittylJournal of Hydrology 195 (1997) 1-25

21

Table 2 Catchinent characteristics of seasonality groups E-H Catchment characteristic

Seasonality group E* Very early

POT rainfall mean day

POT rainfall clustering (r)

SMD season

F strong winter

G Weak

H autunm/winter

UQ

181.2

184.2

162.0

170.0.

Median LQ

174.9

170.4 157.7

119.7 93.1

156.7 147.8

UQ

0.381

0.381

0.227

0.363

Median LQ

0.345

0.313 0.223

0.145 0.103

0.319 0.297

UQ

130.8

161.7

220.5

161.7

Median LQ

125.1

132.4 121.2

214.3 177.7

1.56.5 135.4

UQ

5.7

990.0

472.0

246.0

Median LQ

3.1

367.0 167.0

216.0 100.0

142.0 56.2

len~h (days)

Catchment

area 0an 2)

LAKE

UQ Median LQ

Number of members

0.000 0.000 2

0.275 0.066 0.017 61

0.087 0.001 0.000 33

0.060 0.000 0.000 47

UQ, upper quartile; LQ, lower quartile; *, values shown for higher and lower values in group of two.

critical storm duration of catchments, and the relatively small number of physical factors used). Finally, two particular aspects of the discriminant analysis are considered in relation to the remaining 26% of stations which were incorrectly assigned. The first of these is the continuing dependence of the discriminant analysis upon the classification method chosen. The most appropriate choice of classification algorithm for any particular application must always be open to question (see lain and Dubes, 1988). While the use of a shape similarity measure has resulted in an increase in the proportion of stations correctly assigned by this discriminant analysis, the problem of stations being classified into one class while they might relatively easily be classified into another remains, and total success of the discriminant analysis is therefore unlikely. Of the 37 stations (26% of total) incorrectly assigned in the final analysis, 23 (16% of total) belonged to the class identified as second most probable by the discrirninant analysis. The second important aspect is the proportion of incorrectly assigned records belonging to each class. It is striking that the class with most members, Class F (strong winter seasonality) with 61 members, also has the greatest proportion (33%) of its members incorrectly assigned (see Table 3). Of these 20 stations, 13 were assigned to Class H

22

A.R Black, A. Werritty/Journalof Hydrology 195 (1997) 1-25

Table 3 Results of final discriminant analysis Put into group

E F G H Total number Number correct % correct

True group E

F

G

H

2 0 0 0 2 2 100.0

0 41 7 13 61 41 67.2

1 4 24 4 33 24 72.7

1 5 2 39 47 39 83.0

(autumn/winter seasonality) while the other seven were assigned to Class G (weak seasonality). One possible reason for the underestimation of winter flood frequencies by this discriminant analysis may be the failure to take account of the snowmelt contribution to winter flood generation. Most Class F stations are found in inland areas and, as winter snow accumulations will be relatively high in such areas, this does seem physically sensible, although such an explanation is unlikely to account for all the incorrectly assigned members of this class. High base-flow indices (Institute of Hydrology, 1980) may account for the misallocation of some other catchments. These will have a higher propensity to flood in late winter and spring than in autumn owing to a strong runoff lagging effect, but such data are not available for all catchments in the study and did not, therefore, contribute to the discriminant analysis. Despite the identification of these factors as being likely to detract from the success of the method, we suggest that the combination of information on peak rainfall seasonality, SMDs, catchment size and lake storage has achieved a useful and convincing level of explanation of the observed patterns of flood seasonality, and should provide a useful basis for future work to build upon. The importance of snowmelt in this context may be more clearly established through the application of new methods of estimating melt rates.

5. Discussion and conclusions The preceding sections have presented the results of a study of flood seasonality, using floods defined for each gauging station by a modest flood-flow threshold. Clear spatial patterns in the seasonality of flooding across North Britain have been identified, with southwest Scotland registering the earliest flooding as a result of relatively high flood frequencies between August and November. The east coast (notably the Tweed and Northumberland catchments) is characterized by later flood seasonality with particularly high frequencies in February-March. In Lothian, and also across northeast Scotland, the seasonal signal is weak with floods being more evenly distributed throughout the year. Winter-dominated flooding is characteristic of large basins and inland areas across the whole of Scotland except in the southwest. These patterns have been illustrated in varying levels of detail through the

A.R. Black, A. Werritty/Journalof Hydrology 195 (1997) 1-25

23

complementary use of directional statistics, seasonal frequencies and classification analysis. Seasonal class membership has been successfully explained in terms of four physical factors (peak rainfall seasonality, soil moisture deficits, catchment size and lake or reservoir storage) by discriminant analysis, with the correct prediction of seasonal flood regime in 74% of cases. The future development of new methods to fully assess the contribution of snowmelt to flood generation in North Britain and beyond may help to increase the level of prediction further. It is recognized that a high degree of interdependence exists between some of the physical characteristics of catchments; nevertheless, the methods developed in this paper have allowed an objective and successful explanation to he made of the patterns of flood seasonality across North Britain. Despite its regional focus, the paper provides a robust method for identifying and explaining the seasonal incidence of floods based upon a peaks-over-threshold database. The patterns of seasonality in North Britain have been explored in detail, with a matching advance in our understanding of flood regimes. The key significance of this work lies in demonstrating the seasonal heterogeneity within and amongst the flood series studied. This is already recognized in existing methods of assessing seasonal flood risk for construction projects. However, by linking differences in flood seasonality to physical and climatic factors which are known to vary widely between catchments, it is possible to attach a more fundamental importznce to the observed patterns. A seasonal analysis allows the identification of distinct components within a flood series, and these will individually be able to form the basis of distinct flood frequency analyses. In the same way that two-component extreme value models have shown their value in flood risk assessment in Canada and Italy, it is anticipated that the explicit identification of seasonal components in the flood series of North Britain will enable more physically reasonable risk estimates to be made. The development of these ideas will form the basis of future research papers.

Acknowledgements We thank staff at the Scottish Environment Protection Agency and the Environment Agency for valuable co-operation in the collection and interpretation of data, and for many useful discussions. ARB acknowledges the support of a Natural Environment Research Council CASE studentship held jointly at St Andrews University and at the NERC Institute of Hydrology. Frank Law, Mike Acreman, Duncan Reed and Adrian Bayliss (all at IH) have kindly offered helpful advice and comments at various stages in the work, and three referees have provided further useful comments on an earlier version of the paper. Graeme Sandeman, Rob Flavin and Jim Ford are thanked for preparing the figures. References Acreman, M.C., 1985a. Estimating flood statistics from basin characteristics in Scotland. Ph.D. thesis, University of St Andrews, 317 pp. Acreman, M.C., 1985b. Predicting the mean annual flood from basin characteristics in Scotland. Hydrol. Sci. J., 30: 37-49.

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A.R. Black, A. Werriny/Journalof Hydrology 19.5 (1997) 1-25

Acreman, M.C., 1989. Extreme historical UK floods and maximum flood estimation. J. Inst. Water Environ. Manage., 3: 404--412. Aereman, M.C. and Wiltshire, S., 1989. The regions are dead; long live the regions. Methods of identifying and dispensing with regions for flood frequency analysis. In: L. Roald, K. Nordseth and K.A. Hassel (Editors), FRIENDS in Hydrology. International Association of Hydrological Sciences Pubfication 187. IAHS, Wallingford, UK, pp. 175-188. Archer, D.R., 1981a. Seasonality of flooding and the assessment of seasonal flood risk. Proc. Inst. Civ. Eng., 71(2): 1023-1035. Archer, D.R., 1981b. Severe snowmelt runoff in north east England and its implications. Prnc. Inst. Civ. Eng., 71(2): 1049-1060. Archer, D.R., 1992. Land of Singing Waters: Rivers and Great Floods of Northumbria. The Spredden Press, Stocksfleld, UK, pp. 138-141. Archer, D.R., 1997. Flood frequency analysis. In: R. Herschy (Editor), Encyclopaedia of Hydrology and Water Resources. Chapman and Hall, London, (in press). Batschelet, E., 1981. Circular Statistics in Biology. Academic Press, London, pp. 7-15. Bayliss, A.C. and Jones, R.C., 1993. Peaks-over-threshold flood database: Sullmlar'y statistics and seasonality. Institute of Hydrology Report No. 121. Institute of Hydrology, Wallingford, UK, 61 pp. Black, A.R., 1992. Seasonality of flooding in Scottish rivers. Phi) thesis, University of St Andrews, UK, 463 pp. Black, A.R., 1994. Seasonality of flooding in the White Laggan Burn, Kirkcudbfightshire. Scott. Geogr. Mag., 110: 162-167. Black, A.R. and Anderson, J.L., 1994. The Great Tay Flood of January 1993. Hydrological Data UK: 1993 Yearbook. Institute of Hydrology, Wallingfc/d, UK, pp. 25-34. Black, A.R. and Werritty, A., 1993. Seasouality and the generation of peak flows in small, Scottish upland catchments. Proceedings of British Hydrological Society Fourth National Hydrology Symposium 1993, Cardiff. British Hydrological Society, Wallingford, UK, pp. 4.7-4.12. Bum, D.H., 1989. Cluster analysis as applied to regional flood frequency. J. Water Resour. Plann. Manage., 115: 567-582. Bum, D.H. and Boorman, D.B., 1992. Catchment classification applied to the estimation of hydrological parameters at ungauged catchments. Institute of Hydrology Report No. 118. Institute of Hydrology, Wallingford, UK, 71 pp. Ettrick, T.M., Mawdsley, J.A. and Metcalfe, A.V., 1987. The influence of antecedent catchment conditions on seasonal flood risk. Water Resour. Res., 23: 481--488. Fisher, N.I., 1993. Statistical Analysis of Circular Data. Cambridge University Press, Cambridge, UK. Futter, M.R., Mawdsley, J.A. and Metcalfe, A.V., 1991. Short term flood risk prediction: a comparison of the Cox regression model and a conditional distribution model. Water Resour. Res., 27: 1649-1656. Gordon, A., 1981. Classification: Methods for the Exploratory Analysis of Multivariate Data. Chapman andHall, London, 250 pp. Green, F.H.W., 1958. The Moray floods of July and August 1956. Scott. C-eogr. Meg., 74: 48-50. Green, F.H.W., 1971. History repeats itself--flooding in Moray in August 1970. Scott. Geogr. Mag., 87: 150152. Hough, M.N. and HoUis, D., 1995. Rare snowmelt estimation in the United Kingdom. Report to UK Department of Environment, Metstar Consultants, Bracknell (February 1995 revision), 65 pp. Institute of Hydrology, 1980. Low Flow Studies: Research Report. Institute of Hydrology, Wallingford, UK, 42 PP. Institute of Hydrology/British Geological Survey, 1993. Hydrological Data United Kingdom: Hydrometric Register and Statistics 1986-90. Institute of Hydrology, Wailingford, UK, 190 pp. Jain, A.K. and Dubes, R.C., 1988. Algorithms for Clustering Data. Prentice-Hall, Englewood Cliffs, 320 pp. Mardia, K.V., 1972. Statistics of Directional Data. Academic Press, London, pp. 1-38. McEwen, LJ., 1987. The use of long-term rainfall records for augmenting historic flood series: a case study on the upper Dee, Aberdcenshire, Scotland. Trans. R. Soc. Edinburgh: Earth Sci., 78: 275-285. Natural Environment Research Council, 1975. Flood Studies Report. London, NERC. Rossi, F., Fiorentino, M. and Versace, p., 1984. Two-component extreme value distribution for flcod-frequency analysis. Water Resour. Res., 20: 847-856.

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Smith, K., 1992. Environmental Hazards: Assessing Risk sod Reducing Disaster. Routledge, London, pp. 220245. Thompson, N., Barrie. LA. and Ayles, M., 1981. The Meteorological Oftice rainfall sod evaporation calculation system: MORBCS. Hydrological Memorandum 45. Meteorological Office, Bracknell, UK, 72 pp. Todorovic, P., 1978:Stochastic models for floods. Water Resour. Res., 14: 345-356. Ward, R-C., 1981. River systems and river regimes. In: J. Lewin (Editor), British Rivers..George Allen and Unwin, London, pp. l-33. Waylen, P. sod Woo. M.-K., 1982.Prediction of annual floods geoerated by mixed processes. Water Resour. Res., 1s: 1283-1286. Wenitty, A. and &reman, M.C., 1985. Tbe flood hazard in Scotland. In: S.J. Harrison (Editor), Climatic Hazards in Scotland. Geo Books, Norwich. UK, pp. 25-40. Wishart, D., 1987. CLUSTAN User Manual.4th edition, University of St Andrews Computing Laboratory, St ArKhews, VK, 250 pp.