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<br />used to compute weights for the regression performed for this report. The <br />resulting weighting factors for some stations deviate significantly from <br />unity, apparently because of different basin characteristics and other <br />unexplained factors that affect the standard deviation of the logarithms of <br />the annual peaks. Thus, the reciprocal of the number of years of station <br />record was normalized and averaged with the variance to define the final <br />station weights; <br /> <br />Si - (VAR(QlOi) + a/Ni) , <br /> <br />where VAR(QlOi) is the variance of the 10-year estimate, a is a normalizing <br />factor, chosen to give equal weight to the variance and years of record, and <br />Ni is the number of years of record for the station. The final station weight <br />is the reciprocal of the sum of the variance and the reciprocal number of <br />years of record; <br /> <br />w - - b/S - , <br />~ ~ <br /> <br />where W is the final station weight and b is chosen so that the sum of the <br />weights equals the number of stations used in the regression analysis. <br /> <br />Re2ional Analvsis <br /> <br />( <br /> <br />Hydrologic regions shown on figure 3 were defined by several techniques <br />of regional analysis _ Preliminary residual analysis indicated within the <br />state five loosely defined regions _ Subsequent analysis of residuals of <br />equations obtained for each region indicated that only minor boundary <br />adjustments were necessary to reduce regional bias that was not indicated by <br />the analysis of clusters. The regression equations from two of the original <br />regions were very similar and were joined into one group. <br /> <br />Intraregional comparisons of the regression equations shows differences <br />which may help understand factors that affect flood magnitudes in each region. <br />For example, the coefficients in the equations for region G are all similar <br />except for slope. This implies tha~ slope is the major determining factor, in <br />region C, for the differences between streams for the various T-year flood <br />magnitudes. Compare this to region A, where only the coefficient for area is <br />roughly constant. <br /> <br />Equations derived by further subdivision of these regions did not vary <br />significantly from those for the region as a whole. For example, region D was <br />divided into 5 subregions and regression analysis performed on the data with <br />different subregions deleted. The results from those regression analyses did <br />not vary significantly from the regression on the whole dataset_ <br /> <br />\ <br /> <br />Regional boundaries outlined on figure 3 generally follow basin divides_ <br />The single exception is the boundary between regions Band C where the <br />boundary crosses the watershed of the St. Louis River. Headwaters of the <br />St. Louis River are in a flat region, but the tributaries to Lake Superior <br />are very steep, similar to region C_ Based on these topographic and geologic <br />features, the boundary between regions Band G crosses the St. Louis River <br />below Thompson Reservoir. <br /> <br />6 <br />