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<br /> <br />residual variance is used in the bias-correction factor, equation 17 can be <br />rewritten: <br /> <br />'" BC = exp(&2/2W ) (18) <br />~... m m , <br />I,,'" <br />-...1 where BC the bias-correction factor for month m, <br /> = <br /> m <br /> &2 = the mean square error of the fitted model, and <br /> W = the weighting factor applied to observations within month m, <br /> m <br /> <br />The detransformed model with bias correction is then: <br /> <br />DN = exp(ao + al sin(t) + a2 cos(t)) QNb exp(&2/2Wm), (19) <br /> <br />Because the bias-correction factor and the periodic coefficient are both <br />functions of month, they can be incorporated for convenience and equation 19 <br />can be rewritten: <br /> <br /> DN . Q b <br /> = a <br /> m N <br />where a varies m6nthly and is defined: <br />m <br /> . exp(aa + . sin(t) + . cos(t) + &2/2W ) <br /> a = al a2 <br /> m m <br /> <br />(20) <br /> <br />(21 ) <br /> <br />Outline of the Statistical Method <br /> <br />Equations 18 and 19 define the model used to compute natural dissolved- <br />solids discharge for the 16 selected sites in the Upper Colorado River Basin. <br />The regression coefficients (aa, ai, a2, and b), monthly weighting factors <br />(W ), and mean square error (&2) were determined for each site using the <br />m <br />following method: <br /> <br />1. Compute the mean annual (water years 1914-57) natural dissolved-solids <br />discharge at the site, using information reported by Iorns and others <br />(1965), <br />2, Select the independent variables representing water-resources <br />development using step-wise regression, <br />3, Calibrate the exponential model (eq, 14) using historical data for the <br />site and ordinary least-squares regression, <br /> <br />28 <br />