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<br />generally changed significantly following recalibration. Changes in the time <br />terms (a1 and a2) were not significant, except for the additive model at sites <br />ru 1 and 3, There was a significant change in the exponent (b) for the additive <br />~ model at sites 1 and 3 and for the power model at site 1. The exponential <br />~ model was the most stable, The time terms (a1 and a2) and exponent (b) <br />~J remained essentially unchanged for all the test sites. The primary effect of <br />adding the predevelopment estimates was a shift in the intercept (ao). This <br />shift caused the change in the estimates of natural dissolved-solids discharge <br />reported in table 6. Overall, the exponential model was found to equal or <br />exceed the additive and power models in terms of fit, accuracy, and stability. <br />Therefore, the additive and power models were disregarded in subsequent <br />analyses. <br /> <br />Selected Model <br /> <br />The linearized exponential model with a periodic coefficient and constant <br />exponent was selected for estimation of natural dissolved-solids discharge at <br />all sites. The true model relating historical discharge to streamflow and <br />development was assumed to be: <br /> <br />In (DH) <br /> <br />= ao + a1 sin(t) + a2 cos(t) + bln(QH) + Le.X. + E , <br />I I <br /> <br />(13) <br /> <br />where <br /> <br />E = random error, which is assumed to be normally distri- <br />buted with a mean of zero. <br /> <br />The parameters in equation 13 were estimated using the method of least <br />squares. The fitted model was: <br /> <br />In (DH) = ao + a1 sin(t) + a2 cos(t) + bln(QH) + L ciXi ' (14) <br /> <br />where <br /> <br />In(8H) = the predicted value of In(DH), and <br /> <br />ao, ai, a2. b, and c. = regression coefficients. <br />1 <br /> <br />For any particular observation, the residual was defined as the difference <br />between the actual value of In(DH) and the corresponding prediction from <br />equation 14. <br /> <br />Sensitivity to Mass-Balance Estimates <br /> <br />Addition .of the estimates of predevelopment streamflow and dissolved- <br />solids discharge introduced into the data set 12 observations that had a <br />disproportionate influence on the fitted regression model. Recalibration of <br />the exponential model using these data resulted in estimates of natural <br />dissolved-soli.ds discharge that were approximately the same as the mass- <br />balance estimates. Because the predevelopment data were derived from the <br /> <br />23 <br /> <br />