In addition to the period 1954-92, extensive analysis was carried out on records covering the interval 1964-92, in the hope of gaining a better understanding of how temporal variability within flood frequency and magnitude series are spatially related. Fifty-one records (Table 3.1 (Appendix One); Map 5.7) contain data for this period and, although there is still a noticeable bias towards the south and east, the spatial coverage is more extensive than with the longer subsets of records. The greatest drawback is that no records from the north-west are included in this group but additional data from Scottish Hydro-Electric (SHE) has provided some insight into flow variability (Section 5.11).
Within this group of records, a wide range of hydrological regime and catchment
. . 2
characteristics are represented. Catchment areas, for example, range from 4587.1km (Tay at Ballathie (15006)) to just 43.8km2 (Almond at Almond Weir (19002); NERC, 1993). Other catchment characteristics such as land use, soil characteristics and channel features also vary, but such features tend to vary locally and it is therefore difficult to make generalised statements. Hydrological characteristics are also highly
variable, and tend to be associated with the nature of the physical environment. Mean annual rainfall values, for example, are typically highest in north and west Scotland although these areas are poorly represented in the data set. Of those records analysed, rainfall values are highest in the west and south-west; the Gryfe at Craigend catchment (84011) has a mean annual precipitation of 1795mm in contrast to lower values in the east, such as the Esk at Musselburgh catchment (19007) where a mean of 847mm is recorded (NERC, 1993). Peak flow events also vary between records, although they are likely to be a function of catchment size and geographical location. The Tay at Ballathie (15006) has a large catchment area and relatively high mean annual rainfall (1904mm); consequently the mean annual flood is high (955.6m s a
Smaller catchments with lower precipitation inputs, such as the Esk at Musselburgh
3 -1
(19007) have lower mean annual flood values (71.1 m s ).
5.10.1 FLOOD FREQUENCY SERIES
First impressions of the temporal variability within the frequency series, using time series and running mean plots (Figures 5.19(a)-5.69(a)), indicate highly variable series although some general patterns can be identified, particularly within the RPB regions:
• Highland RPB: the Findhorn at Shenachie record (07001) shows a possible increase in frequencies although no clear pattern appears downstream at Forres (07002); this may be related to the incidence of thunderstorms which are common in this region (McEwen, 1993);
• North-East RPB: a number of series clearly show a 'flood-poor' period in the 1970s;
• lay RPB: the majority of records show no discernible pattern although records from the Tay at Pitnacree (15007) and Ruchill Water at Cultybraggan (16003) indicate a possible increase in frequencies over recent years;
• Forth RPB: all records show a clear 'flood-poor' period in the late 1960s and early 1970s;
• Tweed RPB: few records show any clear pattern, although the 'flood-poor' period of the early 1970s is evident in the Tweed at Peebles (21003) and Gala Water at Galashiels (21013) records;
• Solway RPB\ the Cree at Newton Stewart (81002) series shows a distinct increase in frequencies during the second half of the record;
• Clyde RPB\ few series show any clear pattern of frequencies.
Although it is apparent that some distinct changes in flood frequency behaviour have been detected using these plots, it is often difficult to draw out any finer details on any changes (the exact timing, the significance, etc.). The value of the additional time series statistics are clearly evident under such circumstances. Within these raw data series, a number of years are associated with extreme flood frequencies. A large proportion of these extremes are confined to the period since 1980, and in particular 1982 and 1990 are often associated with high frequencies. Whether this period signifies a general increase (and possible trend) in the occurrence of floods or whether these events are isolated occurrences has yet to be determined.
5.10.1.1 CLUSTER ANALYSIS
Having generated time series statistics from each of the fifty-one flood frequency records, it was again clear that many records appeared to display similar characteristics. In an attempt to group together those records which share a broadly
similar pattern of temporal variability, cluster (or classification) analysis was used. This classification was based upon the Mann’s trend plots (the sequence of the test statistics u(i) derived from the Mann's test for trend in the mean) derived from each of the fifty-one flood frequency series, since this provides a good measure of year-to- year temporal variability. This analysis was undertaken for two reasons. Firstly, it provided an overall temporal variability pattern for groups of stations and secondly, to provide a means of ascertaining how temporal variability is spatially coherent.
For those series included in subset D, similar trend signatures have previously been grouped together using simple correlation techniques. This was feasible since there were only fourteen series included in the subset. With over fifty series a correlation matrix would, in fact, be too complex to retrieve any clear groupings. Hence the cluster analysis technique was favoured.
Classification analysis is a way of grouping objects which display similar characteristics using a set of computer-based algorithms (Wishart, 1987). Clustering begins with the two objects (in this case the u(i) plots for two gauging stations) closest in ^-dimensional space merging to form the nucleus of a cluster. The process continues with further objects (i.e. plots for gauging stations which have not yet merged into a cluster) either joining this nucleus or one of the remaining single objects to form a new nucleus. The process continues until all the objects have been allocated to the desired number of clusters. Merging may proceed either by hierarchical fusion of clusters, iterative relocation of individual objects, or by a combination of the two methods (Gordon, 1981). A sequential application of Ward's method, hierarchical fusion and then iterative location to these data series was carried out, based upon recommended guidelines (Wishart, 1987), with the resultant outputs producing three optimum clusters for the flood frequency database (Clusters A-C). The size of these optimum clusters was determined on the basis of the maximum rate of change in the D2 statistic at each successive fusion, where D2 represents the square of the average inter-group distance. The characteristic trend patterns of each cluster are presented below. However, the results of all time series techniques carried out on the fifty-one flood frequency series are presented with reference to the clusters or groups identified in the classification process.
Mean flood frequencies calculated for five-year sub-periods of a record can be useful in identifying periods of extreme (high or low) values and gradual changes in the mean. Table 5.6 identifies the sub-periods displaying the maximum and minimum mean flood frequencies for the fifty-one time series covering the period 1964-92. Although it is clear from this table that within the frequency cluster groupings there is a degree of variation on the timing of maximum and minimum sub-period means, a general theme is evident, with high sub-period means being recorded in the 1980s and 1990s and low means in the late 1960s and the first half of the 1970s. This theme is apparent in all three cluster groupings, which suggests that one over-riding factor which has influenced a large proportion of the flood frequency series.
Table 5.6: Five-year sub-periods recording the highest and lowest mean flood frequencies, 1964-92
CLUSTER STATION NUMBERS PERIOD OF
HIGH MEAN