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<br /> <br />1'\.") <br />o <br />I-~ <br />"l <br /> <br />nonconstant and is estimated by &2/W., where W. is the weighting factor <br />1 1 <br />applied to the ith observation. In the present study, observations were <br />classified by month; therefore, the residual variance within a particular <br />month is &2/W , where W is the weighting factor for the month. When this <br />m m <br />residual variance is used in the bias correction factor, equation 7 can be <br />rewritten: <br /> <br />BC = exp(&2/2W ), <br />m m <br /> <br />where BC = the bias-correction factor for month m, <br /> m <br /> &2 = the mean square error of the calibrated model, and <br /> W = the weighting factor applied to observations within month m. <br /> m <br /> <br />The <br /> <br />detransformed model with bias correction is then: <br /> <br />. [ . . ( 2ron) <br />C = exp ao + a1 sin ~ <br /> <br />. (2nm)] b [^2 ] <br />+ a2 cos ~ Q exp IT /2Wm . <br /> <br />The procedure, in this study, for record extension using weighted <br />regression was: <br /> <br />1. Calibrate the linearized model, including a time-variable intercept <br />(eq. 5), using simple least-squares regression. <br />2. Compute monthly weighting factors based on the inverse of the monthly <br />residual variance. <br />3. Recalibrate the model using weighted least-squares regression. <br />4. Compute dissolved-solids concentrations during the extension period <br />using the detransformed model with the bias correction (eq. 9). <br /> <br /> <br />(8) <br /> <br />(9 ) <br /> <br />The dissolved-solids concentrations used for model calibration were flow- <br />weighted monthly values. Streamflows in the models were monthly values at the <br />record-extension site, if a complete record was available for the extension <br />period. Otherwise, monthly streamflows at a base-station site were used. <br /> <br />Regression on Dissolved Solids at a Base-Station Site <br /> <br />An alternative technique used for extension of dissolved-solids records <br />required the availability of water-quality data at a base-station site. This <br />technique involved simple regression on dissolved-solids concentration at the <br />base-station site. The model was: <br /> <br />Ce = a + b Cb, <br /> <br />10 <br /> <br />(10) <br />