FLOOD FREQUENCY SERIES

The pattern of annual flood frequencies for each of the fourteen records are depicted in Figures 5.5(a)-5.18(a) (Appendix Two). Although a general pattern of high flood frequencies in the 1950s, low frequencies in the 1970s and a return to higher values into the 1980s, is clearly displayed in many records, it is not universal to all records. Some frequency series, such as the Tay at Pitnacree (15007) and Dean Water at Cookston (15008) records, show no obvious pattern on first inspection. The Avon at Delnashaugh flood frequency series (08004) appears to display a unique pattern, with annual values showing an almost continual decline from the mid 1950s. This is where the value of the time series program lies (WMO, 1988), as it should be possible to

extract more detailed information on the significance of variability which is not readily apparent from observing raw data and running mean series.

A number of years within the period 1954-92 are associated with extreme flood frequency values:

• 1954 is recognised as an extreme value (by Minitab) in records from the Spey at Grantown (08010), Tay at Caputh (15003), Tay at Ballathie (15006), Tay at Pitnacree (15007) and the Tweed at Peebles (21003);

• 1962 and 1990 also record extreme frequencies in the Tweed at Peebles (21003) record;

• 1982 is classified as an extreme in the Dee at Woodend (12001) series.

When examining how mean flood frequencies vary through time, the analysis of sub­ period statistics within the time series program (WMO, 1988) reveal four general scenarios:

• Similarly high mean frequencies in the early and latter sub-periods of the record, with the 1970s associated with the lowest sub-period means:

Spey at Boat of Brig (08006), Tay at Caputh (15003), Earn at Kinkell (16001) and the Tweed at Peebles (21003);

• The most recent sub-period, 1988-92, recording the highest mean flood frequency whilst the lowest mean is reached in the late 1960s:

Spey at Invertruim (08007), Dulnain at Balnaan (08009), and the Tay at Ballathie (15006) and Pitnacree (15007);

• A peak in the mean flood frequency occurring in either sub-period 1978-82 or 1983-87, following the lowest mean recorded in the late 1960s and early 1970s: Spey at Boat of Garten (08005) and Invertruim (08010), the Dee at Woodend (12001), Dean Water at Cookston (15008) and the Kelvin at Killermont (84001)); • The highest mean frequency associated with the earliest sub-period and a general

decline thereafter:

The equality of these sub-period means was tested using the Kruskall-Wallis test. Using division of ten years (1963-72 etc.) and six years (1954-59 etc.), statistical inequality was detected in eight of the flood frequency series, at either the 10% or 5% confidence levels. In addition to detecting this equality, it is also important to understand why it has occurred. Very often inequality may be associated with one period recording an extreme mean frequency.

• the Dee at Woodend (12001) and Tay at Pitnacree (15007) both record very low mean frequencies in the period 1963-72;

• a very high mean frequency for the 1983-92 sub-period is evident in the Tay at Ballathie (15006) record.

However, inequality may also result from an extreme range of mean values, as evident in the following records:

• the Spey at Boat of Brig (08006), Dulnain at Balnaan Bridge (08009), Earn at Kinkell Bridge (16001), Tweed at Peebles (21003) and the Kelvin at Killermont (84001).

Runs tests carried out on each series detected just four series which could be classified as non-random. Three of these series (Spey at Invertruim (08007) and the Tay at Ballathie (15006) and Pitnacree (15007)) had previously been identified as displaying a high mean flood frequency in the final sub-period of record (1988-92). The fourth series is the Kelvin at Killermont (84001). The number of runs observed in each of these series was statistically less than expected from a random series (at the

10% confidence interval) which indicates the presence of a possible trend.

The graphical output from the Mann's test for trend in the mean, applied to each series, is given in Figures 5.5(b)-5.18(b) (Appendix Two). The key points and general patterns of these plots are described in Table 5.4 for groups of records which display similar trend patterns, rather than for individual series. These similarities between series were detected by correlating all of the individual Mann’s trend plots (depicted by the sequence of the test statistic u(i)). The groups are based upon flood frequency series linked by high ( +0.80 and above) correlation coefficients (Table 5.4).

Table 5.4: Characteristics of the Mann's Test for Trend in the Mean 1954-92: Flood Frequency Series

Avon at Delnashaugli (08004)

Spey at Boat of Brig (08006)

Random series until late 1960s. Frequencies decline thereafter until

(a) 1992 (08004)

(b) 1980 (08006) when an increase occurs:

u(i): varies around zero

(a) u(i): downward trend (5% conf level) by 1977 (1% conf.level) by 1988 (b) u(i):downward trend (1% conf.level) by 1977 Figure 5.5(b) and 5.7(b) respectively

Spey at Boat of Garten (08005)

Spey at Gran town (08010)

Variable series, no significant trends recorded:

u(i): negative during 1960s/1970; positive after 1982

Figures 5.6(b) and 5.10(b) Spey at Invertruim (08007)

Kelvin at Killermont (84001) Dulnain at Balnaan Bridge (08009)

Random series until 1978 when frequencies increase to 1992:

u(i): upward trend (5% conf.level) by late 1980s Figures 5.8(b), 5.18(b) and 5.9(b) respectively Dee at Woodend (12001)

Tay at Pitnacree (15007) Dean Water at Cookston (15008)

Frequencies decrease from late 1950s to late 1960s; an increase follows to early 1980s and random behaviour follows:

u(i): downward trend (5% conf.level) late 1960s u(i): returns to zero level by 1982

Figures 5.11(b), 5.14(b) and 5.15(b) respectively Tay at Caputh (15003)

Tay at Ballathie (15006) Tweed at Peebles (21003) Earn at Kinkell Bridge (16001)

Random series until late 1960s; frequencies decline during 1970s but increase from the early 1980s:

u(i):downward trend (5% conf.level) late 1970s u(i): reaches zero level by 1992