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<br />~ <br />~. <br />~~ <br />C) <br /> <br />Although the extrapolated estimates of natural dissolved-solids discharge <br />varied among the models, the standard errors for estimating historical dis- <br />charge generally were similar. The extrapolation differences were the result <br />of differences in incorporation of the development terms in the models. For <br />example, the irrigated area was included as a development variable in all the <br />tested models. It was an annual value that generally varied little from year <br />to year; therefore, it was virtually constant. In the power and exponential <br />models, this variable was a multiplicative factor, which could modify the <br />coefficient for streamflow to such an extent that, when irrigated area was set <br />to zero, the computed natural dissolved-solids discharge was drastically <br />underestimated, The effect of this underestimation is apparent in the power- <br />model results for site 3, and the power-model and the exponential-model <br />results for site 9 (table 6). The additive model produced more reasonable <br />extrapolation estimates of natural dissolved-solids discharge, particularly <br />for site 9 (table 6). <br /> <br />To decrease the problems associated with extrapolation, estimates of <br />predevelopment dissolved-solids discharge and streamflow were introduced into <br />the calibration data set. These estimates were made by separating the annual <br />mass-balance estimates into monthly values and pairing them with the monthly <br />mean natural streamflows for water years 1914-57, This pairing resulted in 12 <br />estimates of mean monthly dissolved-solids discharge and streamflow that <br />possibly would have occurred if there had been no development in the basin <br />during 1914-57, <br /> <br />Separation of the annual mass-balance estimate of natural dissolved- <br />solids discharge was based on the monthly distribution of predicted natural <br />discharges given by the initial model calibration. For example, at site 1, <br />the initial calibration of the exponential model produced an estimate of mean <br />natural dissolved-solids discharge of approximately 709,000 tons per year for <br />water years 1914-57, The estimated mean natural dissolved-solids discharges <br />for individual months ranged from 4.5 to 17.5 percent of the total, The <br />monthly predevelopment discharge estimates used in model recalibration were <br />computed based on these monthly percentages and the mass-balance value of <br />approximately 549,000 tons for mean annual natural dissolved-solids discharge. <br />Separate predevelopment discharge estimates were computed for each model. The <br />predevelopment discharge and streamflow estimates were added to the data set <br />and the model was recalibrated, The predevelopment estimates were then <br />adjusted, based on the new distribution of mean monthly natural discharge, and <br />the model was recalibrated once more. <br /> <br />The results of recalibration of the models with predevelopment discharge <br />and streamflow estimates included in the data sets are reported for the three <br />test sites in table 6. The standard errors and R2 values were virtually <br />unchanged; however, differences between the model and mass-balance values of <br />natural dissolved-solids discharge were greatly decreased, particularly for <br />the exponential model. Substantial differences in standard errors and R2 <br />among the models for a specific site occurred only for site 3, and the expo- <br />nential model yielded the best results, <br /> <br />Differences in regression coefficient values between models calibrated <br />with and without the predevelopment estimates are listed in table 7. The <br />intercept term (ao) of the seasonally variable coefficient (eqs, 9 and 11) <br /> <br />21 <br /> <br />, <br /> <br />