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alysis of the country's rainfall intensity data. As this revision used data for twice the number of stations used by Robertson, more accurate estimates of 1024 for individual catchments should be possible using Tomlinson's results. Note that an areal reduction factor should not be applied to an 1224 estimate. Further, the rainfall stations used in the estimation of 1224 should not necessarily be the nearest but should be the ones that record weather patterns that are of most relevance to the catchment. In the Southern Alps, Tomlinson's (1980) maps of rainfall intensity assume that the intensity increases with altitude. This increase was not considered in the estimates of 1224 used to obtain the regional mean annual flood equations. Thus the use of the estimates of rainfall intensity in the equations may lead to overestimates of Q for catchments running into the Southern Alps. Therefore, when calculating 1224, poinr estimates of intensity should be averaged for the raingauges which receive rainfall typical of that for the middle and lower parts of the catchment. MARAIN The mean annual rainfall for a catchment may be estimated directly from rainfall records for stations within, or near to, the catchment. Where only short rainfall records exist, or where there are none, estimates of MARAIN should be obtained from the l:500 000 isohyetal maps of l94l-1970 annual rainfall normals published by the NZ Meteorological Service. When there is at least one year of flood record available, we suggest that both the available record and the regional equation be used to obtain separate estimates of Q. These estimates can then be combined to form a weighted average estimate of Q , with the weighting of the Q value estimated from the record being based on the length ofthe record relative to Nr. Hence, for example, if N : 3 and N, : 4' the weighting factors for the estimates taken from the record and regional equation should be 3/'7 lì.e. (ii) N > Nu NN N+Nu N*N, When the flood record length exceeds N' Q may be estimated as the arithmetic mean of the annual series. It could also be estimated f¡om a partial duration series (NERC 1975, pp. 185-213) when N is less than l0 years. In the case where an outlier or historical flood peak Q."* occurs in an annual series such that Q*"*/Q.e¿ ) 3, it is suggested that Q be estimated graphically from a probability plot of the annual series as the flood peak with return period T : 2.33 years. more flexible frequency curves, it was found in the evaluation tests (Appendix A) that a two-parameter distribution gives a good approximation to a three-parameter one up to T : 100 and that it can give more sensible results, even though it may not produce quite as good a fit to the annual senes. (iii) N > 20 V/ith a flood record of 20 or more years in length, both two- and three-parameter distributions should be fitted to tbe annual series for the estimation of Qr ' A visual inspection of the goodness-of-fit of the distributions to the series should then be made and a distribution chosen for estimating Qr . When it is difficult to decide between two or more fitted distributions, the Q.¡ estimate should be determined by averaging the estimates given by these distributions. In applying frequency analysis methods to estimate a design flood peak Qt, care should be taken to ensure that they are not grossly extrapolated. For example, if N < 20 and the two-parameter EVI distribution is fitted to the annual series, its extrapolation past T : 100 years for catchments in some of the eastern regions, e.g' South Canterbury, may lead to an under-estimation of Q1. It is recommended that the fitted distribution should not be extrapolated beyond a return period T : 5N' This limit is less stringent than those often recommended in other tests (e.g. a limit of T : 2N is suggested (ICE 1975) for the NERC (1975) study) and extrapolation beyond it is unwise on the basis of present evidence. The safest course of action when T exceeds the extrapolation limit is to use the regional curve, or the appropriate generalised curve when T exceeds the upper limit of the regional curve. Finally, when the record length N is sufficiently great to warrant the performing of a frequency analysis, the resulting Q1 estimates should be compared with that using the regional (or generalised) curve, with Q being calculated from the annual series. A, decision must subsequently be made as to which estimate to accept for design. This may involve taking a weighted average of the estimate from the frequency analyses of the site data and the estimate obtained using the regional curve, and this procedure is suggested when T > 2N. In making this decision on the final Q1 value it should be lemembered that variations are inherent in all flood records, especially small ones, so that the trend in the probability plot should not be over-emphasised, even though it may depart significantly from the regional one. Instead, the emphasis should be placed on the regional curve, for it represents the trend of all the flood peak data for the region and its construction involved the averaging out of the variations in the individual flood records. 5.3.3 Estimation of 01 (i) N
Year 1958 1959 1960 l96r t962 1963 t9& r 965 1966 1967 1968 Pe¡k (m¡ls) 2238 562 1506 702 1552 1644 2201 2859 2689 I 802 1082 Year t969 t970 t91l 1972 1913 1974 1975 t976 1977 1978 Peak (m3ls) 6t3 2387 20t9 t9u t094 1357 1690 l3l I 865 2875 The following four examples estimate the 100_year flood peak Q,oo and the corresponding 68,3g0 confidence limits lor the site, assuming that: (¡) no flood record is available; (ii) only the first 3 years of record, from l95g to 1960, are available; (¡iD l¿ years of record from 1958 to l97l are available; (iv) the full length of record from I 95g to I 97g is available. 5.4.1 Example 1: N:e e estimated from the regional Figure 4. 10, the catchment lies ellEast Cape flood region and a = 2. 18 x l0-? AREA o ó1 MARAIN ,3! Substituting the values for AREA and MARAIN as given above produces: a = 2.18 x l0-? X 13930 64 X 2550, 13 = l94O m'/s (b) The regional curve ordinate should now be obtained. The site is in the North Island East Coast flood frequency region, i.e, Region 3 in Figure 3.6, and hence, lrom Table 3.4, the regional curve ordinate is: Q'oo/Q = 2.89 . Alte^rnatively, Q,oolQ can be computed from the equa_ tion of the regional curve in Table 3.4: Q/Q = 0.762+0.469y For T = 100, y given by Equation 3.16 is y : -ln(-ln(l- I ) ) = 4.60 100 (This result could also have been obtained irom Table 3.1.) Substituting for y in the regional curve equation gives Q'oo/Q : 0.726 + 0.469 x 4.60 : 2.88 (The difference of 0.01 is due to rounding effecrs.) (c) Combining the estimates for Q and e,oole produces Q'oo. Thus Q,oo = 1944. x 2.89 = 5607 m3,/s (d) The corresponding standard error of estimate is ob_ tained from Equation 3.25, namely var(Qr) = E(Q),. var(ea/Q) + E(er/Q),. var(e) The RHS terms of this equation are estimated as follows: E(Q) -- l9¿lo From Equation 3.26 var (Q1/Q) : (Cr . Qt )' o where, from Table 3.9 CF (_t.zs + 5.74 tnT)/100 = 0.25 Thus var (Qr/Q) = @.25 x 2.89), = 0.522 Also E(Q'/Q) = 2.89 ]tr9.ti1a! term var (Q) is obtained from rhe p estimates in Table 4.12. lf p is assumed to be 0.5, Cp : b.¡Of for the Northland,/Coromandel,/East Cape flood- region. Since, by definition, cË = uar (Q)/Q' .'. var(Q)= C'..Q, : (0.301 x t940)' = 3.410 x l0' Reverting to Equation 3.25 var (Q'oo) = 1940'z x 0.522 + 2.89, x 3.410 x 105 = 4.813 x 10. Therefore the standard error of estimate of e,oo is Se (Q'oo) = (4.813 * 1gc¡t/z = 2194 m,/s, which is 39Vo of e,on Figure 5.2 Location of the Motu catchment above Houpoto. 1435 ml/s Water & soil technical publication no. 20 (1982) 80 5.4.2 Exampte 2: N:3 (l) W¡th N = 3 = Nu, Q should be estimated from both the flood record and the regional equation. Using the flood record: Qobs %Q238 + 562 + 1506)
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WATER & SOIL TECHNICAL PUBLICATION
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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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Preface Water & soil technical publ
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annual flood Q (the mean of the ann
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Water & soil technical publication
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Doto ovoiloble on TIDEDA Figure 2'1
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P=45 O= 15 x4 (l) '= o o t.25 2'.O
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Êv2 ( ko) Reduced Voriote y I'O t1
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turn period. A plotting position fo
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'o ,l\, I zl l- I Water & soil tech
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Table 3.2 Flow stat¡ons used. SITE
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e process of examining the simtrend
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Iì_ t_ I I I I I I I t-. I I tñ I
Page 29 and 30: Þ I"IEST COFST 0 o I E 6o o o 25 3
Page 31 and 32: SOUTHEBN REDUCEO Y VRBIßTE NETURN
Page 33 and 34: SOUTH ISLFND HEST COFST I]ÊTR èo
Page 35 and 36: SOUTH CÊNTERBURY DRTÊ NEOUCEO Y V
Page 37 and 38: COMB I NED ,,IE5T CORST DRTR o rt
Page 39 and 40: BÊY OF PLENTY DRTF o o o NEOUCEO Y
Page 41 and 42: NOBTH ISLRND ßEGIONÊL CUBVES 1.50
Page 43 and 44: data for this area are required bef
Page 45 and 46: NELSON REGIONFL CURVE BEOUCEO Y VRR
Page 47 and 48: 46 EÊSTEFìN NEI,,I ZEFLÊND DÊTI
Page 49 and 50: Table 3.9 The grouping and the grou
Page 51 and 52: allowing curves rather than just st
Page 53 and 54: 3.5.5 Extension method The NERC (19
Page 55 and 56: Table 4.1 South lsland catchment ch
Page 57 and 58: I 2 t l¡ 5 5 7 I 9 l0 t1 ,12 I5 1{
Page 59 and 60: decided instead to use estimates of
Page 61 and 62: \Í l{ I t, ìj( Fþurc 4.4 Distrib
Page 63 and 64: 62 Fþurc 4,6 Logarithmic rcsidual
Page 65 and 66: Table 4.6 Final equations for South
Page 67 and 68: I ++ ++ * E 4.6 Analysis of North l
Page 69 and 70: Non Pumice = õ = 3-24xto'6 AREA'7
Page 71 and 72: Northlond f C"ro^ondel f Eost Cope
Page 73 and 74: Table 4.11 Comparable equations for
Page 75 and 76: Poo led cv Pooled o.40 F¡guro 4.12
Page 77 and 78: mates of Cp typically range between
Page 79: -J æ 'll o Eo !¡ Assemble llood p
Page 83 and 84: The estimate of Q from the regional
Page 85 and 86: Water & soil technical publication
Page 87 and 88: Maguiness, J.A.; Blackwood, P.L.; B
Page 89 and 90: The liequency factor K is a functio
Page 91 and 92: e.9., Linsley et ol. (1915); lrish
Page 93 and 94: Maguiness, J.A.; Blackwood, P.L.; B
Page 95 and 96: sltt 930 t [rûltRÀict ¡ l? s;¡t
Page 97 and 98: 3950't flrlÀRt R tr îlt¡Ît ;tP
Page 99 and 100: S ITI 29202 RuNttiltcl I ¡t tllEtt
Page 101 and 102: ïI-'_____ ::19: lt¡IPt0r n À1 i
Page 103 and 104: 9100r GNE? R ¡T DOBSO| s¡18 93207
Page 105 and 106: 6800 1 sBlrri R tT SrITEC¡,tttS 6I
Page 107 and 108: APPENDIX C Summary of tho data for
Page 109 and 110: oæ ON LAT. STATION NA ATION LAT. N
Page 111 and 112: o NUI,IBER HHAKAIIARU 854801 38 L7'
Page 113 and 114: l9 AT NU¡IB ËR AR',tËtlANA ÂRAI
Page 115 and 116: A ON LAT. STATION NA NUMBER AHUNA 5
Page 117 and 118: â NUI,IBER Lü{G.E ON NU14EER I,IU
Page 119 and 120: æ TATI ¡rouNT sor.tERS 7L740? 43
Page 121 and 122: N) o STATIoN NAr{gmLfï3---ffij NUI
Page 123 and 124: APPENDIX E Compadson of Regional Fl
Page 125 and 126: Table F.2 Flood peak data. NEW OTAG
Page 127 and 128: F.3 Analysis and results tatively p
Page 129 and 130: ét êt REOUCEO VßFIHTE 2. 33 5 l0
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SOLITH I EA l') COAST soUTH CANTERB
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0tiftflt a itÉitut5 ü¡. il/5 tg?
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Water & soil technical publication
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