ASIA

4.1 Introduction

This chapter is a spatial description of the seasonality of flooding throughout the study area. Overall patterns of general applicability are identified, along with exceptions to them. The data used are the POT series described in the previous chapter, having been standardised to a discharge threshold of 45 events in the 10 years 1979-88 or equivalent. Details of the data are given in Appendix A while threshold adjustments are shown in Appendix B.

In order to fully describe the spatial patterns of seasonality, three methods of data presentation were selected for use. In order of decreasing generalisation, the first is a pair of maps showing mean day of flood and an associated clustering statistic, r, for gauging stations in the study area (Section 4.2; Figures 4.2a, 4.2b). These maps give a broad indication of the annual distribution of events at individual stations and allow comparisons to be made between regions. The second method uses a set of maps to show relative frequencies of events in two-monthly periods by displaying at each gauging station location the number of events in each two month period as a proportion of the total number of events at the station (Section 4.3; Figures 4.3a - 4.3f). This presentation therefore shows the seasonal distribution of events in greater detail than the mean day of flood and r statistic maps, allowing the importance of individual ‘seasons’ in the overall seasonal regime of a catchment to

be evaluated. In Section 4.4, the description of seasonality is extended to include a consideration of discharge in the seasonal distribution of events, with the seasonality of only the larger peaks in each record being compared with that of each record as a whole. During the course of the chapter, records which show anomalous seasonalities are highlighted and possible reasons for these are suggested. Finally, in Section 4.5, a classification method is described which allows these patterns to be condensed into a readily understandable form, the seasonality of flooding at any station being represented simply by its class membership. This allows a general summary of the spatial patterns of seasonality across the study area to be made.

4.2 Mean day of flood and r statistics

Figures 4.2a and 4.2b show values of mean day of flood and r statistics for all gauging stations meeting the threshold frequency requirement referred to above. Values are plotted at the gauging station locations themselves as opposed to the centre of their respective catchments, since the values refer to the seasonality of flooding at those points rather than being representative of flooding behaviour at all points upstream of them. It will be shown that seasonal behaviour does vary within catchments.

4.2.1 Directional Statistics

The statistics presented are directional statistics, used to overcome the circular nature of the data (Mardia 1972, Batschelet 1981). Linear techniques would lead to misleading representation of the data, eg the arithmetic mean day of occurrence of two flood events occurring on day 1 and day 365 of a year is day 183, whereas a value of day 0.5 is much more helpful in such a context. In order to derive a mean day of flood value which would give a measure of central tendency for the season of occurrence of all events at each station, the date of each event must be considered as an observation on the circumference of a circle of unit radius: direction from the centre of the circle relative to a fixed axis therefore represents season relative to a fixed start of year date (Figure 4.1). Events are treated as unit vectors which can be resolved into components with respect to x and y axes; a mean vector 0

Figure 4.1

Mean vector to represent season of occurrence of flood events

Based on Batschelet (1981), Fig. 1.33.

(expressed in degrees relative to the x axis) to represent the mean day of flood can then be found by

a _ f arc tan (y/x) if x < 0

V ~ 1 180° + arc tan (y/x) if x > 0 ' (Batschelet 1981 plO)

(p can then be translated to a mean day of flood statistic, which is plotted in Figure 4.2a showing spatial variations in the overall annual distribution of flood events. The index has been computed as a number of days after 31 May, this date being chosen as a convenient one at the time of year when fewest events are found in the POT database.

A second statistic, r, the length of the mean vector (Figure 4.1), can be computed to indicate the amount of clustering of points about the mean vector. As the individual events are represented as unit vectors, the value of r must range from a minimum of 0, representing no clustering (equal distribution of vectors in all directions) to 1, representing total clustering, ie all vectors in the same direction from the centre, r is calculated as r = (x2 + y2)1/2 (Batschelet 1981 plO). POT records with low r

values must therefore have events widely distributed throughout the year with little clustering around the time of year indicated by the mean day of flood statistic, while those with high r values have a strong concentration of events about the mean day of flood, r values can therefore be used as a means of qualifying the information provided by the mean day of flood statistic: a high r value indicates that the season indicated by the mean day of flood is a dominant season of flooding, while a low r

value indicates that the mean day of flood does not represent a dominant time of year in the flood record. In such cases, events may be distributed widely throughout the year, or a bimodal distribution with two modes separated by six months may apply, r values for the stations used in this study are shown in Figure 4.2b and discussed in detail in Section 4.2.3.

4.2.2 Period of record standardisation

In Section 3.8, it was demonstrated that the period of record used could influence seasonality statistics as the seasonality of flooding on any river may vary significantly through time; this was thought to be a particular problem in the use of short records. To make a useful description of spatial patterns of seasonality it is therefore important to suppress this period of record sampling error as much as possible, although the advantages offered by any measures which involve exclusion

ABOVE 220 210 - 220 200 - 210 190 - 200 180 - 190 170 - 180 160 - 170 BELOW 160 Figure 4.2a