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<br /> <br />interval of interest is selected, a weighted estimate of <br />the peak discharge can be computed for a site using <br />the regression equation for the appropriate region and <br />the peak-discharge value from the flood-frequency <br />curve. <br /> <br />\, <br /> <br />. <br /> <br />Weighted estimates are used for unregulated <br />streams to reduce the time-sampling error that may <br />occur in a station flood-frequency estimate. This time- <br />sampling error is associated with the length of record <br />for a gaging station. A station with a short period of <br />record may have a large time-sampling error because <br />its record may not be representative of the actual flood <br />history of the site based on a large number of years. <br />The observed period of record has the possibility <br />of falling within a wet or dry climatic cycle. The <br />weighted estimate of flood frequency should be a <br />better indicator of the bUe value because the regres- <br />sion estimate is an average of the flood histories of <br />many gaging stations over a long period of time <br />(Thomas and Lindskov, 1983). <br /> <br />. <br /> <br />I <br /> <br />I <br /> <br />I <br /> <br />I <br /> <br />I <br /> <br />Table 2. Basin characteristics and the range of values used <br />in the analysis <br /> <br />B811n characteristics <br />Drainage-basin area. in square miles <br />Mean annual precipitation. in inches <br />Mean drainage-basin elevation. in feet <br />Mean drainage-basin s'ope. in foot per foot <br /> <br />Range of values <br />5,5 to 988.0 <br />1,0 to 49,0 <br />2.805 to 12.200 <br />0,081\00,562 <br /> <br />Sites near Gaging Stations on the Same <br />Stream <br /> <br />Peak discharges for sites near gaging stations on <br />the same stream can be estimated by using a ratio of <br />drainage area for the sites near the un gaged sites and <br />the gaged sites, This method is considered to be reli- <br />able when the drainage-area ratio is between about <br />0.5 and 1.5 and when the two sites have similar <br />drainage-basin and climatic characteristics, If the sites <br />of interest have similar basin and climatic characteris- <br />tics and meet the drainage-area-ratio requirement, <br />peak discharges can be computed by the following <br />equation: <br /> <br />QT(u) = QT(g)(A/ Ag)x, <br /> <br />10 Analyala 01 the Magnitude and FraquollC'/ 01 Floodaln CoIOf8<Io <br /> <br />where <br /> <br />QT(u) <br /> <br />is the peak discharge, in cubic feet per <br />second, at the ungaged site for T-year <br />recurrence interval; <br />is the weighted peak discharge, in cubic feet <br />per second, at the gaged site for T-year <br />recurrence interval; <br />is the drainage area, in square miles, at the <br />ungaged site; <br />is the drainage area, in square miles, at the <br />gaged site; and <br />is the average exponent for drainage area for <br />each flood region as follows: <br /> <br />QT(g) <br /> <br />Au <br /> <br />Ag <br /> <br />x <br /> <br />Flood raglon <br />Mountains <br />Rio Grande <br />Southwest <br />Northwest <br />Plains <br /> <br />E>ponant <br />0.69 <br />0.88 <br />0.11 <br />0.64 <br />0,40 <br /> <br />The following is an example calculation to <br />detennine the lOO-year peak discharge for an ungaged <br />site near a gaged site on the same stream in the moun- <br />tain region. The drainage area at the ungaged site is <br />given as 350 mi2 and at the gaged site is 450 mi2. The <br />weighted discharge for the 100-year peak at the gaged <br />site is given as 1J,500 ft3/s. <br /> <br />I. Check that the drainage area ratio AjAg is between <br />0.5 and 1.5. That ratio is as follows: <br /> <br />A/ Ag = 350/450 = 0.78 <br /> <br />which meets the ratio requirement. <br /> <br />2. Compute the discharge at the ungaged site using the <br />specified values in equation 3: <br /> <br />QlOO(u) = 11,500(350/450)0,69 = 9,670 ffls. <br /> <br />Ungaged Sites <br /> <br />(3) <br /> <br />Peak discharges at ungaged sites can be <br />computed using the appropriate regional equation <br />shown in table 1. For sites on streams that cross <br />regional boundaries, results from more than one of the <br />regional equations need to be weighted as described <br />below. <br />