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amination of the probability plots for each station, the perlormance of each frequency analysis method was classified into a good, reasonable or poor category according to the following four criteria: (i) the frequency curve should fit the whole of the series well, but particularly the upper half of the series; (¡i) the frequency curve should not necessarily pass through the very largest items in the series, since there is a far larger sampling variation with these items; (¡¡¡) the frequency curve should appear to produce a good estimate of the 10O-year flood peak; (iv) the Chi-square value should not be abnormally high. Criterion (iii) needs some explanation. Although a method could perform well under criterion (i), it could not be automatically assumed that the method therefore gave a sensible estimate oI the 10O-year flood peak. Because of the small-sample effect with some of the samples used, a method could produce an extremely good fit to a data sample but a 100-year value that was only minimally greater (e.9., less than l-290) than the 2O-year value. One hundred years was chosen as the return period for the flood peak estimate on the basis of it being the most commonly used maximum value in bridge waterway design (MWD 1979). It follows, therefore, that the subsequent evaluations of the methods for fitting individual station data are with reference to this maximum return period and they should not be interpreted as being applicable beyond the 100-year return period. Afler the classification of the performances of the methods they were then quantified, by allotting a score of 2 for each good fit, I lor each reasonable fit and 0 for each poor fit. A.4.3 F¡rst test The first evaluation test was made midway through the data collection phase when all the annual flood peak data had been collected for the South Island stations. The results of this test were presented and discussed by Maguiness et al. (1977). Of the 50 stations for which data were available, 28 stations were selected for the test (see Table A. I for details). These stations were considered to have reasonably reliable streamflow records and each flood record was l0 or more years in length. Altogether there were 377 station years of rccord, giving an average length of 13.5 years per station. The performance of the different methods is summarised in Table 4.2, which shows the number of times each method gave a good, reasonable and poor performance. It also shows the final score for each method after the performances were quantified. The adjusted LP3 method is not included in the table, since in only one case was the record length long enough (20 years or greater) for an adjustment to be made to the coefficient of skew using Equation 4.6. As can be seen from Table 4.2 the Jenkinson method performed best, scoring 52 out of a possible 56. lt produced Table 4.1 Deta¡ls of the f low stations used in the first evaluation test. Site No. 56901 57502 60110 60114 621 03 621 05 64301 64602 64606 65104 65107 69302 69506 69614 6961 I 6962 1 71 103 71116 71129 7'l 135 93203 93204 93205 93206 93209 93211 93212 93217 Flow Station Catchmenl Record area, km' Length, Years Riwaka at Moss bush 48 10 Wairoa at Gorge 464 15 Waihopai at Craiglochart 744 16 Wairau at Dip Flat 505 25 Acheron at Clarence 997 18 Clarence at Jollies 44O 'l 3 Conway at Hundalee 47O 12 Waiau-uha at Marble Point 1980 14 Waiau-uha at Malings Pass 74-6 10 Hurunui at Mandamus 1 O7O 1 I Hurunui at Lake Sumner 342 1 5 Rangitata above Klondyke 1495 10 Orari at Silverton 52O 15 Opuha at Skipton 456 12 Opihi at Rockwood 412 12 Rocky Gully at Rockburn 22.4 10 Hakataramea at M.H. Bridge 899 13 Ahuriri at South Diadem 557 12 Forks at Balmoral 13O 'l 1 Jollie at Mt Cook Station 1 39 10 Buller at Te Kuha 6350 14 Buller at Berlins 5960 16 Buller at Woolfs 4560 11 lnangahua at Land¡ng 1000 'l 3 Maruia at Falls 980 1 1 Matakitaki at Mud Lake 857 13 Mangles at Gorge 284 16 Glenroy at Blicks 198 1 1 377 what were considered good fits on 24 occasions (or more than 8590 of the time) and, significantly, gave no poor fits. Next in order of performance were the LP3 and the Gumbel methods, scoring 4l and 39 respectively. The former method gave only slightly more good fits than the latter, and both produced only a minimal number of poor fits. At the lower end of the performance rankings were the EVl,log-Normal and GEV methods. Little distinction can be made between the EVI and log-Normal methods, with both giving on average about the same performance. In comparison, the CEV method gave fewer poor fits, but at the same time produced only three good lits - less than half the number achieved by each of the other two methods. The flood records used in this first test were relatively small samples. Although each record was at least l0 years long, this is the minimum acceptable length for a flood frequency analysis. The average record length of 13.5 years is only a marginal improvement on this and is still less than the minimum length of l5-20 years recommended by some, Table 4.2 Summary of the performance of the methods ¡n the f¡rst test. Method Performance Categories No. 1 LP3 No. 3 Log-Normal No. 4 GEV No. 5 EV1 No. 6 Gumbel No. 7 Jenkinson Good Reasonable Poor Number Score Number Score Number Score Number Score Number Score Number Score 16 32 99 30 Total Score: 4'l 27 26 Note: Score calculated as 2 for good fit, 1 for resonable, O for poor fit. Maximum possible score: 2 x 2a :56 8 'l 6 3 6 11 22 13 26 24 48 11 11 20 20 7 7 13 13 4 4 9 0 5 0 10 0 2 0 0 0 Water & soil technical publication no. 20 (1982) 89
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
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Regional flood est¡mat¡on in New
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Tables 1.1 Risk ofexceedence for sp
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