regional flood frequency analysis for small new zealand basins 1.

for homogeneous groupings of catchments, (Kuczera, 1982; Hosking et al., 1985;Wallis and Wood, 1985; Cunnane, 1989). These qualities of Watlis'(1980) regionalflood frequency procedure are preserved even when there is significant correlationpresent amongst annual series of a region's drainage basins (Hosking and Wallis,1988) or when the region is heterogeneous (Lettenmaier et al., 1987). Hoskingand WaÌlis (1991) have developed statistical tests based on L-moments toinvestigate the homogeneity of a given group of drainage basins. These tests,based on the L-moment ratios L-CV, L-skewness and L-kurtosis, may be usedto monitor the homogeneity of selected groups.The initial problem is to choose candidate homogeneous groups of basins.Traditionally regional groupings have been used (e.g. Natural EnvironmentResearch Council, 1975; Beable and McKerchar, 1982). Acreman and Wiltshire(1989) review all approaches, incÌuding the use of groups of physically similarbasins not necessarily in the same geographic regions. Homogeneous groupingsof small basins are sought in this paper using a method proposed by Wiltshire(1985) which monitors the effect on flood frequency of splitting basins intophysically similar groupings. Wiltshire's method is advanced by using L-moments(Hosking, 1990) of flood series to monitor the flood frequency behaviour. L-moments have been shown to be reliable statistics for discerning differencesand confirming similarities in flood frequency groupings and regions (Wallis,1988, 1989; Hosking, 1990; Hosking and \üallis, 1990; Chowdhtry et al., l99l:'Pearson, this issue).METHODWiltshire (1985) groups basins first by splitting a set of basins into two groupsusing a single partitioning value of a physical characteristic, for example, intowet and dry basin groups on the basis of average rainfall. Measures of floodfrequency variability are then derived for each group, and aggregated into onemeasure, corresponding to the group partitioning value. (Wiltshire used fourflood frequency variability measures based on fitting the generalised extremevalue (GEV) distribution to each group.) This procedure is repeated using arange of partition values. The optimum grouping is achieved at the basincharacteristic value where the group variability statistic for flood frequency isminimum. This process can be repeated with other basin characteristics, andfor multiple partitions of the basins.This study used ll7 small New Zealand basins (i.e. area less than 100 km2),each with n = l0 or more years of annual maximum flood peaks (see Appendix).The longest annual series has 29 flood peaks. (fhis flood-set is the subset ofMcKerchar's (this issue) set of basins with l0 or more years of record.)Basin characteristics investigated were basin area (A), and areally averagedrainfall, soil, hydrogeology and slope statistics. The rainfall statistic (Izo) is the24-hotr rainfall total of5-year return period (207oan¡tal exceedance probability(AEP) event) derived from Tomlinson's (1980) maps. Iz¿ ranges from 45 mmto 440 mm for the small basins used in this study. The soil property is depthweighted-macro-porosity(DWP) estimated from soil survey information by M.J. Duncan (pers. comm., l99l): it ranges from 1% for impermeable basins to29/61or porots basins. The hydrogeology index (H) was developed by Hutchinson(1990) using a national land resources inventory. H ranges from I for low to78Ø 0.3.t)oL 0.2VI-J o.lL-SkewnessFIG' l-L-kurtosis and L-skewness for I 17 small New Zealand basins. The GEV distributioncurve to the left of the EVI point is EV3, and to the right of the EVI pointis EV2.8 for high bedrock infiltration capacity and transmissibility. A slope measure(S) used by Hutchinson (1990) was also used. It is the areally-weighted mean- slope extracted from the national land resources inventory and ranges from2" to 35" for basins in this study. More detailed information on these basincharacteristics is given in McKerchar (this issue).The flood frequency variability measure proposed in this paper for use inwiltshire's basin grouping procedure is based on L-moments of ànnual maximumflood peak data. This avoids fitting a statistical distribution to the flood data(at this stage) and takes advantage of the superior properties of L-moments(Hosking, 1990). The Lskewness-L-kurtosis plane serves as a useful tool fordiscerning heterogeneous regions (Wallis, 1988, 1989) and is the basis of theflood frequency variability measure required for basin grouping. L-skewness andL-kurtosis are the L-moment ratios À¡/Àz and Àq/Àz respectively, where À. isthe r-th population L-moment (see Hosking 1990, for definitions). Àr is themean and Àz is a measure of scale.Unbiased estimators (l) of À., that are linear combinations of the flood data,areusedinthispaper(Hosking'rt-tJ"i*31:î".'r'i'ö'P"iK:i¿:iîîåîlåxi:record-length-weighted average ([l:/ b]*,fh I lzl*) = (0.242,L-moment ratio estimates for each basin are given in79