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<br />(QH)' Figure 2 presents a definition sketch showing the time periods and streamflows used in the historic <br />record adjustment. <br /> <br />NBB.... <br /> <br /> <br />x' <br /> <br />QH <br /> <br /> <br />x <br /> <br />Qo <br /> <br />.... <br /> <br />I+-NHP <br /> <br />+-NHO <br /> <br />. <br /> <br />. <br />H <br /> <br />~ <br />~ <br /> <br />Figure 2. Definition sketoh showing time periods and'discharges used in historic record adjustment. <br /> <br />The Bulletin 17B historic adjustment, in effect, fills ~n the ungaged portion of the historic period with <br />an appropriate number of replications of the below-QH portion of the systematic record. This filling in is <br />accomplished by weighting the below-threshold systematic peaks in proportion to the number of the below- <br />threshold years in the historic period as illustrated in figute 2, with the following result: <br /> <br />H-NHP~NHO <br />W= <br />NS-NHO <br /> <br />(5) <br /> <br />where W is the weight to be applied to the systematic pe~s and Ns' NHP' and NHO are the numbers. of <br />systematic peaks, historic peaks, and high outliers, respe9tively. Then the effective number of peaks, N, <br />above the flood base (Qo) is <br /> <br />N = NHP+NHO+W(Ns-NHO-NBB) = H-W(NBB) <br /> <br />(6) <br /> <br />where NBB is the number of peaks below the flood base, ,including any zeros and low outliers. <br /> <br />The corresponding estimated probability of a floodiexceeding the flood base is <br /> <br />. _ N i <br />Po - - : <br />H, <br /> <br />(7) <br /> <br />Applying the historic weight W to those peaks below the historic b~se QH (and above the ~ood base Qo) <br />yields the following formulas for the historically weighted mean (M), standard deviation (8), and <br />skewness (G): <br /> <br />PEAKFQ <br /> <br />7 <br /> <br />DRAFT .1/30/98 <br />