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turn period. A plotting position formula merely gives the
position at which the item should be plotted in order to
assess the goodness-of-fit of the frequency distribution.
The actual return period of the item should be inferred
from the fitted distribution.
TP N + 0.12
i-0.4
Equation 3.20 also gives a reasonable approximation of
the unbiased plotting positions for a GEV distribution displaying
small or moderate curvature. It was therefore used
in this study for the calculation of plotting positions for the
methods involving EV distributions. It is possible to calculate
exact plotting positions for the EVI distribution for
small values of N but in practice, for N ) 35, the calculation
is overwhelmed by ro
a
,N
" a' iD=, 321
320
S).
(section
where Q¡ an individual annual flood peak, and
N the length, in years, of the annual series.
A dimensionless probability plot was then obtained for
The annual flood
3.2.1) for each flow s ¡sionless
form by dividing through by the corresponding mean annual
flood Q, defined as the arithmetic mean of the annual
series. Thus
mean annual flood Q standardises the series, permitting a
direct comparison of the plot of one series with anothèr.
Significant differences between plots are interpreted to
mean that the corresponding ftow stations belong to different
flood frequency regions.
volved, namely whether
(D the historical floods occurred outside the annual series;
or
(ii) tne historical floods occurred inside the annual series.
Dealing first with the type (i) series, consider an annual
period of J years,
to have occurred,
seri
dur
givi
fN+Jyears.In
this
nnual seiies were
based on a record length of N years, as before, while the
plotting positions of the historical floods were based on the
th of N + J years. Hence, for exorical
flood had a return period plotby
TP :(N + J) + 0.12 =
i-o.4
(N+J) + 0.t2 322
0.56
For the type (ii) series, consider the largest flood peak in
the annual series, of length N years, which also is known to
be the largest over a longer period of N + J years. Here the
t8
plotting position of the largest peak was based on the length
of the historical series N + J years, giving a return period
as indicated by Equation 3.22. The other flood peaks in the
annual series were then treated as the 2nd, 3rd largest etc. in
N years.
In the special case where there were two historical floods,
one outside and one inside the annual series of length N
years, the plotting positions of these two floods were based
on N + J years. Again the ordinary annual flood peaks
were considered as the 2nd, 3rd largest etc. in N years.
3. 1.7 Computer programs
In this study flood frequency analyses were performed
analytically using a computer program called FRAN
(Maguiness et al. in prep.). The methods included in the
program are outlined in Appendix A. Another program
called FRANCES (Appendix A) was developed ro analyse
the historical series data, which typically comprised an annual
series and an additional period of unknown record in
which one or more large, notable, and hence historical
floods, occurred. The program FRANCES performs a frequency
analysis of a censored sample, which may be defined
as a sample which contains unknown flood peaks that
all lie on one side of a given threshold value or censoring
point. An historical series may often be regarded as a censored
sample, where the unknown peaks are those which
occurred outside the annual series and which were less than
the known historical flood peaks. In using the program, it
is necessary to specify the historical flood peaks and to
assume that none of the unknown peaks exceeded the censoring
point, which must be set at a value less than the historical
peaks.
same method.
3.2 Flood frequency data
3.2.1 Data collect¡on
The collection of annual series data was restricted to
thosè flow stations which satisfied the following conditions:
(i) the catchment land use had not changed significantly
over the period of record;
(ii) the annual flood peaks were not substantially regulated
or affected by impoundments, swamps or diversions
within the catchment;
(iii) there were eight or more annual flood peaks available;
(iv) when historicat flood peak information was available,
there were also at least five annual flood peaks;
(v) the catchment was rural, or predominantly so;
(vl) the catchment area was greater than 20 kmr.
The first two conditions are consistent with the normal
requirements for data samples (section 3.1.4). The third
condition of only 8 or more years of record is slightly less
than the l0 years that is generally recommended as the
minimum sample length required for a typical flood frequency
analysis. However, this study was concerned, not so
much with flood frequency analyses for individual stations,
as with the derivation of regional curves from mass plots of
all the data for the regions (section 3.1.5). The reduction in
this study of the minimum sample length to 8 years allowed
the data for an extra 25 ftow stations to be used. It appeared
that these extra data would reinforce the definition
of the lower end of the regional curves.
The fourth condition, specifying five or more annual
flood peaks, was needed so that the mean annual flood Q
could be calculated, thus permitting the station,s historical
peaks Q to be expressed in the form of Q/Q and included
in the mass data plot for the region. Unless there were eight
Water & soil technical publication no. 20 (1982)