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<br />8. The discharges computed in steps 6 and 7 above are weighted and combined <br />to yield an adjusted 10-year flood estimate. The weighting factors used <br />are the equivalent years of record for the regression estimate (step 6) <br />and the actual years of record for the estimate from the gaged site (step <br />7). The equivalent years of record for estimating a 10-year flood by <br />regression equation in region D is 6.1 from table 1. The number of years <br />of record at the gaged site is 15 from table 5. <br /> <br />Q10 (6.1xl,114+15x1,285)/(6.1+15) <br />Q10 14500/21.1 - 1,240 ft3/s (35.1 m3/s) <br /> <br />ACCURACY AND LIMITATIONS OF ESTIMATING TECHNIQUE <br /> <br />The accuracy of a statistically defined equation is measured by the <br />closeness of the estimated value to the true value. The U.S. Water Resources <br />Council (1981a, p. 48 -49) describes two elements of accuracy, variance, and <br />bias. Variance is a measure of the random variation about the mean of the <br />estimate, and bias is the deviation of the mean of the estimate from the true <br />value of the mean. <br /> <br />Random variation about the mean is caused by a combination of factors. <br />Three of the most significant factors are discussed below. Errors in predic- <br />ting flood-flow magnitudes result from short sampling records, which may not <br />be a representative sample of the population of annual peaks, and from the <br />assumptions made in procedures for defining the magnitude of flood flows. <br />Errors also result from the inability to completely describe drainage-basin <br />characteristics. No matter how complete the description of a drainage basin, <br />differences exist that contribute, in varying degrees, to the runoff <br />characteristics of a basin. As an example, morphologic features such as <br />storage may be described as a statistic (percent storage), but the impact of <br />each area of storage, its size or relative position in the drainage basin, <br />cannot be accounted for completely. The third source of random error is a <br />result of the empirical nature of the modeL The assumptions of a linear- <br />regression model may not be adequately met even though every effort is made to <br />reduce departures from the assumptions. <br /> <br />Bias of an estimate may result from bias in the dependent variable or <br />from an inadequate statistical model. Any bias in the dependent variable (the <br />T-year flood discharge) is most likely the result of time-sampling error. <br />Because most of the data used in this analysis are based on gages operated <br />between 1958 and 1983, the derived flood statistics reflect that period of <br />time and mayor may not be a representative sample of the entire population. <br />The statistical model also may be biased because the assumptions of linear <br />regression are not adequately met or because of misspecification of the <br />independent variables. The equations obtained by linear-regression techniques <br />may contain extraneous independent variables or a significant variable may <br />have been omitted. <br /> <br />16 <br />