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tv 10-'. ~,... t.n winter baseflow, December through February. Therefore, the inverse of the monthly residual variance was considered an appropriate weighting factor. For site 3, Gunnison River near Grand Junction, Colo., an additional weighting factor was given to the predevelopment estimates in order to equal- ize their weighted predictions with the remainder of the data set, Prede- velopment dissolved-solids discharge at this site was small for every month, Eight of the 12 monthly estimates were smaller than the minimum historical discharge. Therefore, the predevelopment values were considered to be sepa- rate from the monthly classification used to determine weighting factors for the historical data. No other site required this type of weighting, because no other predevelopment estimates were so small compared to historical values, Plots of weighted residuals for the three test sites are shown in figure 3. In all three plots, the variance of weighted residuals is'approxi- mately equal throughout the range of predicted values, Therefore, the weighted regression had the d~sired effect. Detransformation and Bias Correction To predict natural dissolved-solids discharge, the independent variables representing water-resources development in the exponential model (eq. 14) are set to zero. The prediction equation then becomes: In (DN) = ao + al sin(t) + a2 cos(t) + bln(QN) , (15) where natural streamflow (QN) is used as the independent variable to predict natural dissolved-solids discharge (DN) , When equation 15 is detransformed it becomes: b DN = exp(ao + al sin(t) + a2 cos(t))QN ' (16) Miller (1984) reported that detransformation of a calibrated model can produce a biased estimator of the mean response. Therefore, a bias-correction factor needs to be included in the detransformed equation. For a model fitted to natural logarithms and with normally distributed residuals, Miller (1984) recommended the bias-correction factor (BC) as: BC = exp (\;&2) (17) where &2 is the mean square error, which is an estimator of the residual variance. Miller's (1984) formulation was based on ordinary least-squares regression and needs to be modified for use with weighted least-squares regression. In a weighted least-squares solution, the residual variance is assumed to be nonconstant and is estimated by &2/W" where W, is the weighting factor applied to the ith observation. In the pr~sent stud~, observations were classified by month; therefore, the residual variance within a particular month is &2/W , where W is the weighting factor for the month. When this m m 26