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e.9., Linsley et ol. (1915); lrish and Ashkanasy (1977).
There was, in fact, only one station with more than 20 years
of record. However, these relatively small samples reflect
the situation the design engineer is often faced with
- having
to estimate design figures from records of barely adequate
length.
Most of the findings of the test could only be regarded as
preliminary ones pending further investigation with larger
samples and covering a great'Jr part of the country. The
findings are a guide to the design engineer using a small
sample in flood frequency analysis, but the test itself was
not very helpful in the choosing of a distribution for the regional
curves. A second test was therefore carried out at the
end of the data collection phase using larger data samples.
4.4.4 Second test
The second evaluation test used annual series data from
14 stations with 20 or more years of record. Details of these
stations are listed in Table 4.3. As shown in the table, there
was a total of 366 station years of record, giving an average
record length of 26.1 years per station, almost double the
figure for the first test.
The performances of the different methods on the second
set of data were evaluated in exactly the same manner
as tbr the first test. The results of the evaluation are summarised
in Table A.4.
Table A.4 shows that the Jenkinson method again performed
best, but this time the Cumbel method gave a pertbrmance
that was almost as good. Notably, neither
method gave any poor fits to the data. At the second level
of performance were the GEV and LP3 (unadjusted and
adjusted) methods, all with the same score of 22. The performances
of the unadjusted and adjusted LP3 methods
were indistinguishable and the two methods are collectively
referred to as the LP3 method. Last were the log-Normal
and EVI methods. Both methods gave good fits at least
5090 of the time, but also a noticeable percentage (2190) of
poor fits.
As in the lirst test, the Jenkinson method performed the
best ot'the methods, and in this second test could rarely be
faulted. ln the one instance where it gave other than a good
performance, its frequency curve still fitted the data well
and produced a realistic 100-year flood peak estimate.
However, its performance was reduced because of its Chisquare
value, which was high and more than twice that for
any of the other methods. Some allowance was always
made for a higher Chi-si¡uare value with the Jenkinson
method, but in this particular case the value was excessively
high. The higher values for the method are caused by the
fact that the frequency curve does not always fit the lowest
four items in a series, since these items clo not form part of
the generated 5-year maxima to which the method fits the
EVI curve.
The Cumbel method improved on its first test ranking
giving an overall performance almost the same as the Jenkinson
method. However, a surprising aspect in both tests
Tabþ 4.3 Details of the flow stations used in the second evaluation
test.
Site No.
Flow Station
Catchment Record
area, km' Length,
yeafs
14614 Kaituna at Te Matai 958 21
1551 1 Waimana at Waimana Gorge 44O 25
1 5514 Whakatane at Whakatane 1 557 20
29201 Ruamahanga at Wardells 637 22
29202 Ruamahanga at Waihenga 2340 21
29224 Waiohine at Gorge 183 22
32502 Manawatu at Fitzherbert 3916 48
32503 Manawatu at Weber Road 713 22
32514 Oroua at Almadale 312 24
32526 Mangahao at Ballance 266 24
32529 Tiraumea at Ngaturi 734 24
601 14 Wairau at Dip Flat 5O5 25
92216 Buller at Lake Rotoiti 195 26
93213 Gowan at Lake Rotoroa 368 42
366
was the difference in performance between the Gumbel and
EVI methods. Both fit the same distribution (EVl) to a
series yet the EVI method did not perform as well, presumably
because the ML fitting technique, in comparison with
the least-squares technique, puts relatively greater weight
on the smaller items in a data series (Gumbel 1966). Consequently,
if the upper half of a series exhibited a different
trend. to that for the lower half, the EVI method, especially,
did not always produce a good fit to the upper half
and its performance suffered accordingly. In addition, the
visual inspection of the goodness-of-fit of the frequency
curves may have given the Gumbel method an unfair advantage
over the EVI method, since curve-fitting by eye can
be considered as a least-squares fit (Chernoff and Lieberman
1954, 1956). Thus, although the results may indicate
that the Gumbel method may be a worthy substitute for the
Jenkinson method when a computer is unavailable, the
evaluation may have been weighted unfairly in favour of
the Gumbel method.
The methods using three-parameter distributions, i.e.,
the LP3 and the GEV methods, displayed their greater flexibility
over the two-parameter methods by always producing
a curve that fitted the data particularly well. However,
occasionally this was to their detriment, because the
resulting 100-year flood peak estimate was sometimes not
very realistic. For example, in the case where the LP3
method gave a poor performance, the curve fitted the data
very well; so well in fact that it was almost horizontal at the
high return periods. The difference between the 20 and
10O-year flood peaks estimated from the curve was less than
0.690, indicating an implausible 10O-year flood peak estimate.
Table A.4 Summary of the performance of the methods in the second test.
Method
Performance
Categories
No. 1
LP3
No. 2
Adjusted
LP3
No. 3
Log-Normal
No. 4
GEV
No.5
EV1
No. 6
Gumbel
No. 7
Jenkinson
No Score No. Score No, Score No. Score No. Score No. Score No. Score
Good
Reasonable
Poor
9 18 I 18 9 18 8 16 7 ',t4 12 24 13 26
44442266442211
10103000300000
Total Score
22
22 20 ?2 18 26
27
Note: Maximum possible score = 28
Water & soil technical publication no. 20 (1982)
90