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In the first test the GEV method was often affected in
this manner, producing many curves that fitted the data
very well but giving 100-year flood peak estimates that were
not always sensible. For example, the trend in the lower
half of the series would cause the GEV curve to flatten off
at the top end, impþing that there was a limit to flood
peaks of about twice the mean annual flood. While there
may be an upper limit to flood magnitude, it is certainly
more than the figure implied (see Tables 3.3 and 3.6).
In comparison, the straight-line fits of the Gumbel and
EVI methods were often a good approximation to the data
and gave more sensible 100-year flood peak estimates.
However, this better performance by the t$'o-pa¡ameter
methods can be attributed to the small samples used
(NERC 1975; pp. 159-60). The fact that the Gumbel
method still performed better than the GEV method in the
second test suggests that the samples in this test may also
have been small. However, it is also likely that the leastsquÍues
fitting technique of the Gumbel method influenced
the evaluation test in the method's favour.
The two-parameter log-Normal method also gave good
approximations to the data at times, producing a reasonable
proportion of good fits. However, the method assumes
that there is no skew in the logarithms of the series, an
assumption which was rarely true. Hence the method did
not perform as well as others in the test, including its parent
method, the three-parameter LP3.
A.4.5 Gonclusions
The evaluations in the two tests involved a good deal of
subjective judgement, but this typifies the present situation,
with the objective goodness-of-fit indices not providing rigorous
enough criteria for discriminating between different
frequency analysis methods.
From the findings of the tests, the following conclusions
were reached:
(¡) the Jenkinson method was the superior method in both
tests and should be used in flood frequency analysis,
especially when the sample is small;
(iÐ the Gumbel method improved in performance with increase
in sample size, and should be a satisfactory alternative
to the Jenkinson method on the larger sam-
Ples;
(ii¡) the GEV and LP3 methods were more flexible than the
two-parameter methods, with their frequency curves
geneially following the trend in the data extremeiy
well;
(iv) on small samples, in particular, the straight-line fits
from the two-parameter methods can give good approximations
to the data and sometimes more sensible
results than those obtained from their parent threeparameter
methods;
(v) on small samples the LP3 method appears to perform
better than the GEV method, being influenced less by
the trend in the lower part of a series;
(vi) on larger samples the GEV and LP3 methods can produce
similar shaped curves and give a comparable performance.
These conclusions apply for individual records and up to
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Water & soil technical publication no. 20 (1982)
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