Maps of flood statistics for regional flood frequency analysis in New Zealand

Transcription

1 Hydrological Sciences - Journal - des Sciences Hydrologiques, 35,6, 12/1990 Maps of flood statistics for regional flood frequency analysis in New Zealand A. I. McKERCHAR & G P. PEARSON Hydrology Centre, DSIR Marine and Freshwater, PO Box , Christchurch, New Zealand Abstract The two-parameter EV1 distribution adequately describes New Zealand's flood series. Contour maps of Q/A - & and <2 10 r/2 are presented, where ) is the mean annual flood, A is the basin area and Q 1Q0 is the 1% annual exceedance probability flood. The maps are based directly on measured discharge series from a large sample of river recording stations. Thus when basins are ungauged, or have just a short record, an estimate of a design flood Q T with specified annual exceedance probability (1/T) can be obtained using - map estimates of ~Q/A 0-8 and Q 100 /<2, without having first to estimate rainfall statistics for the basin, a particularly difficult task in sparsely instrumented mountainous areas. These maps succinctly summarize a great deal of hydrological information and permit improved flood frequency estimates. Cartes des caractéristiques statistiques des crues pour l'analyse régionale des fréquences des crues en Nouvelle-Zélande Résumé La distribution à deux paramètres EV1 représente les séries de crues de la Nouvelle-Zélande d'une façon adéquate. Dans les cartes avec courbes des valeurs "Q/A 0-8 et Q 1Q0 /Q, Q représente la moyenne des crues annuelles, A est la surface du bassin et <2 100 est la crue annuelle de probabilité 1% au dépassement. Les cartes sont basées directement sur des séries de débits mesurés d'un large échantillon de stations enregistreuses de débit. Ainsi, quand les stations n'ont pas été jaugées ou présentent une durée d'enregistrement limité, une estimation de la crue de projet Q T avec une probabilité spécifique au dépassement annuel (1/T) peut être obtenue en utilisant les estimations cartographiques de Q/A 0-8 et Q lq0 /Q, sans avoir à faire d'abord l'estimation des caractéristiques statistiques des précipitations pour le bassin, tâche particulèrement difficile dans les régions montagneuses où les instruments enregistreurs sont peu nombreux. Ces cartes résument succinctement une grande partie de l'information hydrologique et ont amélioré les estimations des fréquences de crues. Open for discussion until 1 June

2 A. I. McKerchar& C. P. Pearson 610 INTRODUCTION Flood estimates are needed when engineering works involve rivers. A conventional approach is to estimate a quantile Q T which has the probability 1/T of being exceeded by the annual maxima in any one year. Where sufficient data are available such that the specified return period, T, is less than, say, twice the length of record, satisfactory at-site estimates of Q T are achieved by standard extreme-value frequency analysis. Where no data are available for the site in question, flow quantiles may be estimated by combining estimates from other sites in the region, thereby obtaining a regional quantile estimate. Between these extremes, a pooled quantile estimate is based on both data from the site and data from other sites in the region. One regional scheme is described in the UK Flood Studies Report (NERC, 1975) which derived a q^-t relationship, where q T is a regional estimate of Q T /Q is the mean annual flood), by combining all flood data within a region. This method was used in a previous New Zealand study (Beable & McKerchar, 1982). For a site with no records of flow, the mean annual flood must be estimated to obtain a flood quantile. Progress with this aspect of regional flood estimation has been slow. Most previous studies have used regressions of the form: Q = aa b B c C d (1) where: A is the basin area; B, C,... are rainfall and other basin characteristics; and a, b, c, d,... are regression parameters to be estimated. For the estimation of "Q at sites where no data are available (the ungauged basin) Beable & McKerchar (1982) divided New Zealand into nine regions and derived equations of the form of equation (1), where A is the basin area; B is the mean 2 year return period 24 h duration rainfall for the basin; and C is the mean annual rainfall for the basin. Urban basins and basins containing significant lakes were excluded. Other variables considered were stream frequency, channel length, channel slope, mean basin elevation and proportion of forest cover, but none of these was important in predicting }. Factorial standard errors ranged from 1.21 to 1.47, slightly better than the UK results, and prediction errors typically were equivalent to errors when Q was estimated from one to five years of record. Stedinger & Tasker (1985) showed from Monte Carlo simulations that estimating the parameters in equation (1) by record length weighted least squares and generalized least squares improved the precision of such equations. A particular problem in New Zealand is that raingauges are sparse in hilly and mountainous regions where many rivers rise. For example, about km 2 (10%) of the South Island receives more than 4800 mm annual precipitation, but this region contains only five long-term daily read gauges. Basin mean values of rainfall intensity, in many cases, are thus subject to large uncertainties. In the Clutha basin in the southern South Island, a study for designing a major electricity-generating project concluded that mean

3 611 Maps forfloodfrequency analysis in New Zealand annual runoff measured for sub-basins, plus an allowance of 700 mm for annual evaporation and transpiration, were better estimates of mean annual basin rainfall than values derived from maps of isohyets of mean annual rainfall. A similar conclusion would apply to many basins draining hilly and mountainous country. Hence equations using intensity and mean annual rainfall are not expected to offer much potential beyond that achieved by Beable & McKerchar (1982). The geographic regions used in these studies were defined somewhat arbitrarily and inevitably raise problems about where boundaries should be placed. Recent studies have alleviated this problem by developing approaches to regional flood frequency analysis based on catchments grouped by similarity in physical characteristics rather than on geographic groupings (see e.g. Wiltshire, 1985; Acreman & Sinclair, 1986; Acreman & Wiltshire, 1989; Burn, 1990). Mosley (1981) successfully grouped catchments according to similarity in the South Island of New Zealand, but not in the North Island. Study of New Zealand Q T (Q values for given T suggests smooth trends over the country, rather than regions of constant values. This suggests the possibility of using contour maps of flood statistics for regional flood frequency analysis. However, the concept of isolines on a map implies that there is a more or less constant change of the variable with distance. Variables such as drainage density, soil and rock type, slope, topography, land use, and basin geometry, which are all probably important in a small way (e.g. Acreman & Wiltshire, 1989, show that soil storage capacity influences flood frequency), do not necessarily change linearly with distance. Furthermore, points used to draw isolines would represent catchments, and not points, and so it might be expected that flood statistic isolines would change suddenly as tributary junctions are reached. However, on a larger scale, rainfall does vary smoothly with distance, and Beable & McKerchar (1982) found rainfall variables the most useful in assisting basin area explain Q (equation (1)). This paper reports an alternative approach of mapping flood statistics. The general extreme value (GEV) distribution is fitted to 275 records of annual maxima of 10 or more years of length. Most (228) records are adequately represented by the two-parameter EV1 (extreme value type 1 or Gumbel) distribution. Thirty-two of the remainder appear to be EV2 and 15 to be EV3. For the EV2-like records, a biennial, instead of annual, time partition eliminates many of the years with only minor floods and the EV1 distribution then fits 28 of the 32 series acceptably well. The EV1 distribution is adopted as the parent frequency distribution with the quantities Q 100 /<2 and Q used to specify the distribution for each series. Contour maps drawn for the quantities Q/A 0-8 and <2 100 /<2 > <2 100 i n m 3 s" 1 ; A in km 2 ) show trends consistent with broad rainfall patterns. From these maps, floods can be estimated for basins with little or no record. Use of the maps is illustrated with an example. DATA COMPILATION Annual maximum discharge series assembled for 343 stations had an average

4 A. I. McKerchar & C. P. Pearson 612 length of 18.4 years, similar to the average length of records used in Beable & McKerchar (1982), but using more than double their number of stations. Of the 343 series, 275 with 10 or more years of record were used to study flood frequency. The remainder, with six to nine years of record, were used to assist with mapping of the mean annual flood. Details about the selection of stations, sources of data, checks applied, calculation of lake inflows, and reasons for exclusion of historical data are given in McKerchar & Pearson (1989), which includes lists of all the data. FLOOD FREQUENCY ANALYSIS Method For at-site estimation in New Zealand, the Gumbel or extreme value type 1 (EV1) distribution has been widely used. The EV1 distribution function is defined as: F(0 = exp{-exp[-(<2-«)/«]} (2) where u and a are location and scale parameters respectively. The EV1 is a special case of the general extreme value distribution (GEV; Jenkinson, 1955). The GEV distribution function is: F(Q) = exp {-[1 - k(q - u)l a] 1 '*} (3) where k is the shape parameter which specifies one of the three asymptotic extreme-value distribution types: EV1 (k = 0), EV2 (k < 0) or EV3 (k > 0). In contrast to other candidate frequency distributions, there is some theoretical justification to support use of the EV1. It is both the limiting distribution for the maxima of exponential tail statistical events and the distribution for the maxima of a Poisson process with exponential magnitudes. The bulk of the flood frequency data sets have record lengths between 10 (an arbitrary minimum allowed for at-site frequency analysis) and 20 years. Therefore a two-parameter EV1 was more appropriate since it has lower standard errors for parameter (and hence quantile) estimates for shorter records. The method of probability weighted moments (PWM) (Greenwood et al., 1979) was used to estimate the parameters of the EV1 distribution. PWM estimation gives parameter estimates that are unbiassed and have standard errors which rival those of the method of maximum likelihood (e.g. Hosking et al., 1985). The PWMs themselves also have the added advantage of linearity and simplicity. Phien (1987) gives an EVl/PWM at-site algorithm including an estimator for vai(q T ). The EVl/PWM procedure has been shown to be statistically robust (Kuczera, 1982), which means that it will provide reasonable results in the face of mild departures from the EV1 distribution. A statistical test derived by Hosking et al. (1985) was used to test whether the EV1 is acceptable against the GEV alternative. The test statistic z = fc(n/0.5633) a5 is asymptotically distributed standard normal. If z,

5 613 Maps forfloodfrequencyanalysis in New Zealand and hence k, is significantly positive (negative), the EV1 is rejected in favour of the EV3 (EV2). If k is not significantly different from zero, the EV1 distribution is acceptable. In the at-site flood frequency analysis, 275 sites with 10 or more years of record were used. In general, the EV1 distribution fitted the flood data very well. There were a some sites which did not conform to the EV1 distribution according to the two-sided Hosking et al. (1985) test. Of the 275 sites used, 47 appeared to be either EV2 (32) or EV3 (15) at the 5% significance level, whereas if the EV1 was the parent distribution for all the flood records, one would expect about 7 EV2 and 7 EV3 distributions to be indicated by this test. For the EV2-, EV3-like annual flood series, it is assumed that the EV1 is the true distribution, but that the number of flood events in one year at these sites does not satisfy the asymptotic requirements of extreme value theory. Bardsley & Manly (1987) give arguments to support this assumption. Analyses at these sites were therefore extended by examining biennial and triennal flood series. Note that to assume the EV2-, EV3-like sites are indeed EV2, EV3, and then to expect biennial etc. series to be EV1 would be flawed, since in theory k remains the same as the time interval is extended. EV2-like sites tended to cluster in the dry centre-east of the South Island, and in the absorbent volcanic ash area of the central North Island. In the drier areas the records showed some years with only a few minor episodes of flows exceeding baseflows and it seemed that the asymptotic condition required by the extreme value theory (Kendall & Stuart, 1977) was not attained. Hence for the EV2-like records the time interval was extended from one year to two and the biennial maxima series examined using the EV1/PWM procedure, and so on until the EV1 was accepted. This procedure was satisfactory for all but one of the EV2-like sites: 28 were accepted as EV1 with biennial series, and three with triennial series. For the 15 EV3-like sites, some of which grouped on the South Island's West Coast, the EV1 annual results were not as biassed as the EV1 annual results for the EV2-like sites. These analyses confirmed that it was reasonable to use the EV1 distribution. This distribution is summarized for each record by <2 and j For predicting flood frequency for any basin, the quantities Q/A - and q im = Q WQ /Q are calculated, and contour maps prepared. For the EV2-like sites handled with the biennial and triennial analyses, the maps introduce biases. For these sites q 1QQ is defined as the biennial or triennial Q m estimate divided by <2 annual. For up to 100 years this will overestimate the design flood peak, and for over 100 years it will underestimate e.g. the mean q m was 4 and the mean S biennial /S annua i ratio was 1.4, so that the negative bias for T = 200 years was less than 1%, and the positive biases for the 50 and 20 year events were 1.5% and 2.6% respectively. For EV3-like sites, one is only likely to be overestimating the design flood peaks. All of these biases are much less than the uncertainties in measuring flood peaks.

6 A. I. McKerchar& C. P. Pearson 614 MAPPING FLOOD STATISTICS Mean annual flood The quantities Q/A 0-8 calculated for each record were plotted on the basin maps and the pattern of values was examined. The maps were prepared at scale 1: , and for most basins the Q/A - & statistic was written at the centroid of the basin. Exceptions were large basins in the South Island which drain south and east and receive most flood-producing rainfall in their headwaters near the main divide (McKerchar & Pearson, 1989). Contours of ~Q,IA Q& drawn by hand on these maps are reproduced in Fig. 1. These contours generally follow the pattern of annual rainfall (NZ Met. Ser., 1985) and rainfall intensity (Tomlinson, 1980) over the country, with high values along the main mountain ranges and around the North Island volcanoes and low values in rain-shadow areas. In addition, low values occurring in the central North Island are attributed to absorbent volcanic ash in that area. Q/A - 8 is essentially an index of all the physical characteristics of the catchment other than drainage area which influence Q. It was difficult to contour the northern end of the North Island satisfactorily. Although the contours shown are tentative, the general trend for increasing values from west to east is supported by Tomlinson's (1980) Fig. 1 Maps of Q/A - s for (a) South Island and (b) North Island; dots show the locations of recorder stations used in the study.

7 615 Maps forfloodfrequency analysis in New Zealand map of 5 year return period 24 h rainfalls. To assess the fit of the contours to the data, Rvalues estimated from the maps (Fig. 1) for each basin were compared with the at-site sample values. Summary statistics for the differences between the estimates were calculated. The percentage difference was defined by E = 100(2^ - J2 sit )/Ù site > and for all sites the mean of was 8.6% (i.e. the bias) and the root mean square error (RMSE) of E was 55%. Values of E range from -69% to +578%. Errors in the range -70% < E < +70% appeared to be normally distributed. Of the 19 sites for which E exceeded +70% (that is, sites for which the maps appeared to overestimate Q grossly), 10 had weirs or flumes installed. For such sites the stage-discharge ratings for flood flows were usually the theoretical ratings with field discharge measurements to verify the ratings only in the low flow section. The theoretical ratings require specific upstream flow conditions, for example negligible approach velocity in the case of vee notch weirs. It is postulated that for most of the 10 sites the theoretical ratings underestimate the actual flood discharges because the conditions in floods are not as theory requires. In particular it is postulated that approach velocity is significant in floods and that some weirs may have been overtopped. Furthermore, Potter & Walker (1985) show that sites with low maximum gauged flow to maximum rated flow ratios are associated with larger flood measurement errors and more variable annual maximum flood series statistics. These factors, as well as model/mapping error, may account for the apparent overestimation by the maps for 10 of the 19 sites. The remaining nine sites have natural channel controls, and six of the nine have high stage rating curves that are well defined by gaugings. No particular reason could be advanced for Q m exceeding D.. by such large /ncip sas amounts except, of course, model/mapping error. Three of these sites also were reported as not conforming in the Beable & McKerchar (1982) study. The nine sites appear to be randomly distributed throughout the country and are anomalies to the general patterns given by the maps. Setting aside these 19 sites where E exceeds 70%, the bias and RMSE of E for the remaining 324 sites were -0.9% and 22% respectively. Two points concerning E should be noted. First, E is treated as a measure of the error in 'Q m as an estimator of the population mean annual flood, but it is an overestimate since E also contains a contribution due to the error in the sample mean (Q she). However, when using > for flood frequency analysis, the EV1 model assumption introduces another source of error, which can be assumed to compensate for the overestimation inherent in JE. The second point is that E could have been reduced to zero by al choosing contours sufficiently elaborate that Q mad = Q S i te every site. Thus E could be viewed as a reflection of how smooth the contours were restrained to be. A split-sample test was conducted to check the credibility of the E results: 20 sites were randomly chosen and held back while the contours of Q/A os were redrawn using the remaining 323 sites. These adjusted maps provided Q m estimates for each of the 20 sites, and 20 E statistics: bias = -6% and RMSE = 33%, after 2 outliers were discarded. This confirmed that the original map and E statistics are valid. Considering these two points, the assumption was made that contour map

8 A. I. McKerchar & C. P. Pearson 616 prediction error for 324/343 = 95% of the basins in the country was ±22%. In Beable & McKerchar (1982) factorial errors for prediction of ) ranged from 1.21 to 1.47 for the different regions. A weighted mean gave a single value of Further, these results were based on 148 basins, after 12 of the original 160 were excluded as outliers. Hence, disregarding the unquantified error associated with regionalizing, the Beable & McKerchar (1982) ~Q prediction factorial error for 148/160 = 93% of the basins in the country was 1.35 (i.e. +35%, -26%). Clearly the contouring method outperformed this approach. No constraint was placed on basin area in this study. Examination of the results suggested that errors for basins with area exceeding about 10 km 2 in area will generally be less in magnitude than errors for basins less than about 10 km. Omitting the 19 E values exceeding 70%, gave the following statistics for E: for A > 10 km 2, bias was -0.9% and RMSE was ±19% (281 sites); and for A 10 km 2, bias was -0.7% and RMSE was ±34% (43 sites). Because the biases are small, the RMSE is a satisfactory approximation for the standard error of E. For A > 10 km 2, the RMSE is only marginally less than the overall RMSE, but is significantly larger for A $ 10 km 2. This, however, can be attributed to some extent to the tendency for small basins to have short records and hence more variable Q site values. Further, the northern North Island area contained 12 of the 43 stations with A 10 km 2, which is consistent with the poorer predictions in that area. Dimensionless 100 year flood Figure 2 shows the hand-drawn contours of equal q 100 for the North and South Islands. Low q 10Q values occur along the western sides of the main mountains where the rainfall is high and frequent. High q 1QQ values occur where rainfall is low and infrequent (e.g. centre-east South Island). A notable feature is that the range of variation in the North Island (2.0 to 3.0) is much less than in the South Island (less than 1.8 to more than 5.0). Another feature is the clear trend for increasing values from west to east across the South Island and, to a lesser extent, from southwest to northeast in the North Island. To assess the fit of the contours to the q 1QQ at-site results, q 1QQ values for each basin estimated from the maps (Fig. 2) were compared with the at-site values. Summary statistics for the differences between the estimates were calculated. The percentage difference is defined as E = W0(q mmap - <7 10(UVe )/<7 100 * For all sites the mean (i.e. bias) and RMSE of E were 0.3% and 17% respectively. Values of E ranged from -58% to +69% and E appeared to be normally distributed. As previously for Q, it was assumed that the overestimation in E due to the sampling error in? 10 o wte sampling error is compensated by the EV1 model error. Likewise, a split-sample test was conducted to check the validity of the E statistics: another 20 sites were randomly chosen and held back while the contours of q lqq were redrawn using the remaining 255 sites. For these 20 sites the revised E statistics gave: bias = 3% and RMSE = 17%,

9 617 Maps forfloodfrequencyanalysis in New Zealand Fig. 2 Maps of q 1Q0 = <2 100 /Q/or (a) South Island and (b) North Island; dots show the locations of recorder stations used in the study. after one outlier was discarded. From the above error analysis it was assumed that the standard error for predicting q m at any basin in the country using the contour maps (Fig. 2) was ± 17%. Estimation of J2 r and its prediction error The map estimate for the 100 year flood peak, Q m, for any basin is obtained by multiplying the contour 2 and q lqq estimates from the maps (Figs 1 and 2) i.e.: 0100 = 2^100 < 4 > The prediction standard errors of > an d q 10Q are assumed to be ±22% and ± 17% respectively. Therefore the prediction variance of Q WQ is approximately (Kendall & Stuart, 1977, p. 261): var(q 100 ) = q m 2 (0.22Q) 2 + Q 2 (0.17^100 ) 2 + (0.22g) 2 (0.17ç 100 ) 2 = [0.280 q m f (5)

10 A. I. McKerchar & C. P. Pearson 618 and so the prediction standard error of estimate for Q 1QQ is ±28%. By expressing the EV1 parameters, u and a, in terms of Q and q 100, a map estimate for the T year flood peak, Q T for any basin in New Zealand is obtained using the contour ) and q m estimates from the maps (Figs 1 and 2): where: X T = (Vioo-J'r> / G'ioo-7> (? ) y T is the Gumbel reduced variate {-ln[-ln(l - 1/2")]} and y is Euler's constant, From equations (5) and (6) the prediction variance for Q T is: var^ = x 2 var(q) + (1 - x T ) 2 var(q 100 ) (8) and when () is estimated from the contour maps this becomes: vaxiqj = x T 2 (0.22Q) 2 + (1 - xf (0.28Q q m f (9) The percentage standard error of Q T estimated from the maps alone ranges from 17% to 19% for T = 5 and 29% to 30% for T = 200. EXAMPLE OF APPLICATION The Fraser River (station number 75259) is a tributary of the Clutha River in the southern South Island. The basin area is 118 km 2 and elevation ranges from 600 m to 1600 m a.m.s.l Precipitation, some of it snow, averages about 1000 mm year" 1. Discharge data for the station for the period were not used in preparing the flood estimation contour maps. The annual discharge maxima are given in Table 1. Two scenarios for estimating 50-year return period loods are used to illustrate the application Table 1 Annual discharge maxima Year Peak discharge Year Peak discharge 3-1? -1 rrt s 1 m s

11 619 Maps forfloodfrequencyanalysis in New Zealand of the results derived in the previous sections: (a) no data for the station; and (b) full record of 18 years , with 1978 omitted. No data The following information is compiled: Symbol A Q/A 0-8 ^100 X 50 fia/b var(q 50 ) Source Walter (1987) Fig. 1 Fig. 2 equation (7) equation (6) equation (9) Estimate 118 km From these data Q map = 25.0 m 3 s" 1 with var(^ap ) = 30.3 and hence Q, 77 m 3 s^with standard error ±26%. Full record , omitting 1978 For the 18 years of record Q sitg = 34.0 m 3 s" 1, and var( K te ) = 19.7, representing a standard error of ±13%. Frequency analysis of the annual maxima provides an excellent EV1 fit (Fig. 3). The shape parameter k for the GEV/PWM fit is k = and z = , compared with standard normal z 5% = ±1.96. The EV1 is thus adopted giving Q 50site = 83 m 3 s" 1 with var(g 50 sj J = 148 and so the standard error of Q 5Q u is ± 15%. In summary, the results show good agreement: Q 50 differing from Q 50 site (from 18 years of record) by 6 m 3 s" 1 (7%), which' is not significantly différent. The map estimate of the flood frequency is also shown in Fig. 3. Pooling of map and site estimates is detailed in McKerchar & Pearson (1989). CONCLUSIONS The EV1 distribution adequately describes New Zealand at-site flood frequency distributions, usually on an annual basis, but also for biennial or longer time intervals when the annual series includes years without floods. An asset of this distribution is its simplicity and the uncomplicated and uncontroversial manner in which extrapolations to high return period floods can be made.

12 A. I. McKerchar & C. P. Pearson 620 y = { -ln[-ln(l - 1/T)]> Fig. 3 Frequency analysis of the annual maxima for Fraser River, , omitting 1978: the full line is the EV1 distribution fitted using probability weighted moments; the dashed line is the EV1 distribution estimated for the station using the maps in Figs 1 and 2. The choice of which statistical distribution to use for flood frequency dominates the literature, when the more difficult and critical question is how to estimate mean annual flood for sites with little or no data. The principal results of this study are the maps which show Q/A 0-8 and < The maps are based directly on measured discharge series from a large sample of river recording stations. Thus when basins are ungauged, or have just a short record, an estimate of Q T can be obtained from the maps without having first to estimate mean annual rainfall, or mean rainfall intensity of the basin, which is particularly difficult in sparsely instrumented mountainous areas. These maps provide a simple summary of much information, and the basis for flood estimation which improves on the previous regional method. Acknowledgements The assistance received from hydrological staff of the DSIR and Catchment Authorities in assembling data, preparing maps and reviewing manuscripts is appreciated. REFERENCES Acreman, M. C. & Sinclair, C. D. (1986) Classification of drainage basins according to their physical characteristics; an application for flood frequency analysis in Scotland. /. Hydrol 84, Acreman, M. C. & Wiltshire, S. E. (1989) The regions are dead. Long live the regions. Methods of identifying and dispensing with regions for flood frequency analysis. In: FRIENDS in

13 621 Maps forfloodfrequency analysis in New Zealand Hydrology (ed. Lars Roald, Kjell Nordseth & Karin Anker Hassel), IAHS Publ. no. 187, Bardsley, W. E. & Manly, B. F. J. (1987) Transformations for improved convergence of distributions of flood maxima to a Gumbel limit. /. Hydrol. 91, Beable, M. E. & McKerchar, A. I. (1982) Regional Flood Estimation in New Zealand Water & Soil Tech. Publ. no. 20, Ministry of Works and Development, Wellington, New Zealand. Burn, D. H. (1990) An appraisal of the "region of influence" approach to flood frequency analysis. Hydrol. Sci. J. 35(2), Greenwood, J. A., Landwehr, J. M., Matalas, N. C. & Wallis, J. R. (1979) Probability weighted moments: definition and relation to parameters of several distributions expressable in inverse form. Wat. Resour. Res. 15(5), Hosking, J. R. M., Wallis, J. R. & Wood, E. F. (1985) Estimation of the Generalised Extreme Value distribution by the method of probability weighted moments. Technometrics 27(3), Jenkinson, A. F. (1955) The frequency distribution of the annual maxima (or minima) values of meteorological elements. Quart. J. Roy. Met. Soc. 81, Kendall, M. & Stuart, A. (1977) The Advanced Theory of Statistics, Vol. 1, Distribution Theory (4th edn) Charles Griffin & Co. Kuczera, G. (1982) Robust flood frequency models. Wat. Resour. Res. 18(2), McKerchar, A. I. & Pearson, C. P. (1989) Flood Frequency in New Zealand Publ. no. 20, Hydrology Centre, Christchurch, New Zealand. Mosley, M. P. (1981) Delimitation of New Zealand hydrologie regions. /. Hydrol 49, NERC (1975) UK Flood Studies Report. Vol. 1. Natural Environment Research Council, London, UK. NZ Met. Ser. (1985) Climatic Map Series 1: , Part 6: Annual Rainfall Ministry of Transport, Wellington, New Zealand. Phien, H. N. (1987) A review of methods of parameter estimation for the extreme value type 1 distribution. /. Hydrol. 90, Potter, K. W. & Walker, J. F. (1985) An empirical study of flood measurement error. Wat. Resour. Res. 21(3), Stedinger, J. R. & Tasker, G. D. (1985) Regional hydrologie analysis. 1. Ordinary, weighted and generalised least squares compared. Wat. Resour. Res. 21(9), Tomlinson, A. I. (1980) The Frequency of High Intensity Rainfalls in New Zealand.' Water & Soil Tech. Publ. no. 19, Ministry of Works and Development, Wellington, New Zealand. Walter, K. M. (1987) Index to Hydrological Recording Sites in New Zealand Publ. no. 12, Hydrology Centre, Christchurch, New Zealand. Wiltshire, S. E. (1985) Grouping basins for regional flood frequency analysis. Hydrol. Sci. J. 30(1), Received 11 October 1989; accepted 24 March 1990

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