2.1 ASPECTOS GENERALES DEL SECTOR TEXTIL ALPAQUERO DE
2.1.1 FIBRA DE ALPACA
Doys after 31 Moy, 1959—88 adjusted
Figure 4.2b ABOVE 0.65 0.60 -- 0.65
Hi
0.55 -- 0.60 0.50 -- 0.55 BUS 0.45 -- 0.50 mi 0.40 -- 0.45 M 0.35 -- 0.40 fWi 0.30 -- 0.35 0.25 -- 0.30 0.20 -- 0.25 o BELOW 0.20r VALUES
1959-88 adjusted 92of data from the database must be weighed carefully against the loss of detail which this would involve. With this in mind, it was decided that mean day, r and any other statistics used should be standardised to a 30 year period, and 1959 - 88 was selected as the 30 year period for which there was the greatest number of stations in the database with a complete record. For these stations, statistics were calculated for this 30 year period only. For stations without this complete record, it was necessary to adjust the statistics for the period of record available to values which might be expected for the standard period.
The method employed to make this adjustment was based on the assumption that any shift in seasonality (characterised by whatever statistics) between the period of record held at a station and the standard period would be matched at neighbouring stations. Further, it was assumed that the similarities between neighbouring stations in such shifts would become weaker with increasing distance between them, eg in attempting to adjust the seasonality statistics of a short record to those for the 30 year standard period, a neighbour 20 km distant would give a better indication of the shift in seasonality than would one at a distance of 200 km. Finally, it was also assumed that a greater length of overlap period between a station and a neighbour would increase the accuracy with which seasonality statistics could be adjusted; this overlap period need not necessarily be within the standard period. Use of two neighbouring stations, preferably in opposite directions from the station of interest (‘target’ station), would further enhance the accuracy of the method by providing more information on which estimates could be based. Similar assumptions are made and similar methods employed in the artificial extension of records and in the prediction of other hydrological statistics (eg Vogel and Kroll 1991).
In order to evaluate the applicability of this method, a test was devised whereby all complete 1959 - 88 records were used in all possible combinations of periods of record and pairs of neighbours, to predict 30 year statistics for all of the stations within this group. Each prediction of mean day and r was based on estimates from two neighbours (i = 1, 2) at distances di and d2 from the target station, the weightings assigned to each neighbour being calculated as
_1_
di
W/"J_ JL’ di + d2
The predicted statistics were then compared with the known values, and from these results a confidence limit was produced to define the minimum record overlap length and maximum neighbour distance combinations within which mean day of flood and r could be predicted with 95% confidence to be within an error of 15 days and 0.15 respectively. Weighting of estimates by an inverse distance squared method rather than by inverse distance resulted in no improvement in performance, the latter therefore being employed.
Within this confidence limit, standardised mean day of flood and r values were calculated for all stations lacking a complete 1959-88 POT record. For those stations to which too short an overlap period applied, or too far from any neighbour with a complete standard period record, it was deemed unsafe to attempt to predict standardised statistics; Figures 4.2.a and 4.2b are therefore constructed only on the basis of complete 1959 - 88 records and those for which adjustment could be made within the 95% confidence level. In this way 36 of the 143 stations for which threshold revision was possible were lost from the database available for the production of these maps.
4.2.3 Mean day of flood and r statistic maps
Figures 4.2a and 4.2b are choropleth maps based on mean day and r values with interpolation to show values of these statistics in areas between gauging station locations. Areas more than 40 km from any data point have been left unshaded as interpolation cannot be made with great confidence. It is important to note that the patterns shown are based on interpolation of values from only a finite number of data points; values indicated between these points are based only on values at neighbouring points and do not necessarily reflect the nature of seasonality at every point on the map. Also, in a few exceptional cases where data points close to each other have markedly different values, the choropleth shading is unable to show this; Appendix D however gives mean day of flood and r values for all stations before and after standardisation. Despite these two minor limitations, sufficient data are available to allow a number of spatial patterns of seasonality to be identified with absolute certainty.
The most striking feature of the mean day of flood map is an east - west gradient, with the highest values (latest mean day of flood) on the east of the map and the lowest (earliest) in the west. 21 east-draining catchments record adjusted mean day
of flood values greater than or equal to 200 days after 31 May; only one west draining catchment exceeds this value (84018 Clyde @ Tulliford Mill: adjusted mean day = 200.2). Of catchments with adjusted mean day values less than 170 days, 4 drain east and 16 drain west. In some parts of the map, this gradient shows itself very well, but the pattern is by no means uniform.
Furthermore, the map of r values shows significant information which should be considered in conjunction with these patterns: higher r values (>0.55) suggesting dominance of one particular season tend to be found in inland areas but are associated with a considerable range of mean day values; low r values (<0.35) indicating a wide distribution of events throughout the year are found on the south Moray Firth coast and in East Lothian, with other low values also being found in parts of the Tweed basin and Northumberland. Few stations on the west coast show low r values (only 87801 Allt Uaine @ Loch Sloy Intake has a value of less than 0.4); this indicates that the generally earlier flooding found on the west coast exerts a greater dominance in the year as a whole, whereas lower r and higher mean day values in the east suggest a wider distribution of events throughout the year with a general tendency for events to occur slightly later in the annual cycle.
The south coast of the Moray Firth is perhaps the single most outstanding anomaly on the mean day map. The two stations on the River Findhorn (07001/07002) record very low mean day values, while on the adjacent River Spey, a significant gradient in mean day values can be observed, with the mean day of flood becoming progressively earlier up-river. The low Findhorn and high Spey mean day values are associated with a considerable scatter of events through the seasons and are further discussed in Section 4.4. In Angus, station 15008 Dean Water @ Cookston records a mean day of flood value (224.0) 30 days greater than its neighbour 15010 Isla @ Wester Cardean draining an adjacent catchment area. In the Tweed basin, clusters of data points on the map show an uneven pattern; again adjacent catchments do not always have similar mean day statistics.
In the west of Scotland, while it has already been stated that the mean day statistic shows that flooding generally occurs earlier in the year than in the east, there are some notable values to be mentioned. The most exceptional of these is station 80003 White Laggan @ Loch Dee: while its record is too short to allow standardised statistics to be calculated, the mean day of flood value for its nine years of record is 108, with a not insignificant r value of 0.560. This is a remarkably early mean, two or three months earlier than most other stations, but
also in south-west Scotland stations 83002, 83005 and 83006 all show early mean day values at moderate to high r values: while these are all based on short records, they are over different periods of time so it would seem that some rivers in this area are normally characterised by very early flooding. At a lower r value, the longest POT record in Scotland, 83802 Irvine @ Glenfield, shows a low mean day value of 165.3, reduced to 152.4 for the standard period. Further north, these low west coast mean day values are complemented by values of 154.1 and 152.0 at stations 86001 and 87801 respectively: although r values here are low, the early mean day statistics do reflect significant concentrations of flood events in the autumn months. Finally on the west coast, a noticeable feature in the map of mean day values is a clustering of low values in the Kelvin basin: values on the nearby mainstream Clyde and on its other tributaries are clearly much later in the year by a margin of 20 - 30 days.
The values of these statistics are the result of varying distributions of events through the seasons at individual stations. Section 4.3 examines the frequency of occurrence of events in 2-monthly periods in order to gain further detail on this, while Section 4.4 considers in addition discharge values of events. However, the east - west gradient of mean day values identified here, along with anomalies within this pattern should be taken to be significant in their own right, as should the map of r values, distinguishing those areas with flood events widely distributed through the year (especially the Moray-Naim and Lothian areas) from those where flooding is more concentrated in particular seasons (upland and more generally west coast areas). Nevertheless, it must be noted that drainage basins in close proximity to each other do not necessarily exhibit similar seasonal characteristics; the reasons for this will become the focus of attention in later chapters.