regional flood frequency analysis for small new zealand basins 1.

Analysis with subsets of the data is proposed, \,ith the subsets defined as:a) arbitrary splits of the data, e.g. into four sets with high rainfalt P and highminimum porosity MP, high P and low MP, low P and high MP, low P andlow MP; with the high/low splits for P and MP taken as the median value.b) Clusters of data using the algorithm K-means of SYSTAT (Wilkinson, I986),which splits data into groups such that between-group variation is maximisedand within-group variation minimised. Variation is measured as the Euclideandistance between data for a basin and the group mean. These methods avoidsplits based on loose geographic regions.RESULTSData statisticsThe compiled data statistics (Table l) reflect the very large range of hydrologicalconditions encountered across the country.For example, mean annual rainfalls range from 550 to 11700 mm/yr, meanbasin slopes from 1.5 to 35 degrees, depth-weighted macroporosity ranges froml.2Vo to 29.3V0, and minimum porosity ranges from ÙVo to 26.6%.Hydrogeology and drainage, both measures ofinfiltration, are near their upperbounds for volcanic ash-covered Central North Island basins where Q./Au'oare low. For example for Mangakara (site number 1043434), hydrogeology H= 7.5, soil drainage D = 6.2, and the porosity measures (DWP = 26.lEo, MP= 16.870) are amongst the highest for all the 140 basins, and Q./A'o is 0.36(Q* in m3/s, A in km2) . In contrast, for two basins in Northland (Pukewaenga,46662 and. Pukeiti, 46663) intensity lz+= 155 mm is almost identical to Mangakara(Iz+ = 150 mm), but Q./Ao' = 5.0 and 5.4 respectively, and for both basinshydrogeology H = 4.0, soil drainage D = 1.0, depth-weighted macroporosìtyDWP = 2.1/s and, minimum porosity MP = o.lTa. The low values of the latterthree parameters reflect the poor drainage and low porosities of the heavy clayeysoils in these basins.Another basin with unusually low values for Q-/40'8 is Maryburn (71122)in the central South Island. Here Q./N8 = 0.17, and the intensity estimateis Iz¿ = 80 mm. Hydrogeology H = 8.0, soil drainage D = 5.0, depth weightedmacroporosity DWP = 20.Wa and minimum porosity MP = 15.5Va, are all greaterthan the respective means across all basins (Table I ). This basin has been discardedas an outlier in previous studies.For many basins at the extremes of the dataset, there is an inverse correlationbetween the flood parameter Q-/Ao't, and the Land Resource Inventoryderived quantities, soil drainage D, depth-weighted macroporosity DWP and -minimum porosity MP. This study seeks to verify this correlation across a largesample of data, and to use it to provide better estimates of Q. for ungaugedbasins.CorrelationsFor logarithms (base l0) of data, correlation coefficients (Table 2) are generallypositive. Correlation of log (Q.) with area is notable, but otherwise its correlationsare weak. Correlations between the three rainfall parameters and between thethree soil parameters are also notable. These suggest that just one rainfall andone soil parameter may be sufficient as independent variables.70TABLE 2-Correlation matrix for logarithms of basin characteristics.Q,a. l.0ooA 0.879P 0.500\ 0.3720Á41lzqH -0.131s 0.082D 0.064DWP 0.116MP 0.1451.0000.262 1.0000.062 0.7540.160 0.804-0.006 0.0600.1l0 0.0540.219 0.1510.287 0.2040.298 0.155lrIzq H S D DWPMPl.0000.883 1.0000.076 0.094 1.0004.052 -0.032 -0.431 1.000-0.011 0.057 -0.017 0.248 1.0000-025 0.103 0.064 0.209 0.876 1.0000.032 0.109 -0.001 0.245 0.895 0.884 1.000Regression analysisTable 3 gives a selection of regression results using all the data. The resultsgiven are the best result, in terms of minimum standard error, for l, 2, 3, and4 variables. The standard errors and factorial standard errors, ofsimilar magnitudeto those reported for country-wide equations in Beable and McKerchar (1982),are too large for the results to be used for design flood estimation.TABLE 3-Multiplication regression results for prediction of Q. using all 140basins. "t" is Student's statistic; "Rz" is coefficient of determination;and "s.e." is standard error-No.VariableVariables NameI2AAlzoAIztHAII¿HDWPCoef.s.e.tRR2b,c,d ofcoef0.856 0.0400.808 0.031r 559 0.1600.805 0.028l.ó35 0.r464.422 0.0170.848 0.0261.679 0.t3t{.397 0.069{.606 0.102217 0.879 0.713 0.4n26.2 0.930 0.866 0.3t79.7281 0.9M 0.890 0.2881.2-5.5325129-58-60s.e . Factorial Const Multþliers.e. log a a2.572.071.940.956 0.913 0.257 r.8r0.279 r.90-3.029 9.35*10-a-2.961 10.9"10 a-2.449 35.ó"10-¡The data set \üas partitioned in a number of ways, including splitting the datainto one of four groups depending on whether mean rainfall P and minimumporosity MP were above or below their median values. The most promisingwas to split between "high infiltration" and "Iow filtration" with low infiltrationbasins arbitrarily defrned as having hydrogeology H ( 7 and soil porosity DWP'11