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The Bureau of Reclamation is currently (1995–2001) testing the Lower Colorado River Accounting System as a method to estimate the consumptive use of Colorado River water by diverters from Hoover Dam to Mexico. Consumptive use is estimated in the Lower Colorado River Accounting System method, in part, on the basis of the annual discharge or annual change in reservoir contents, as well as the variance of estimate of the annual discharge or the annual change in reservoir contents at several surface-water gaging stations in the lower Colorado River stream-gaging network. The standard error and the variance of estimate were determined for the annual discharge at 14 streamflow-gaging stations and for the annual change in content at 2 reservoir-content gaging stations used in the Lower Colorado River Accounting System for calendar years 1995–99. The standard error of the annual discharge was determined by using modifications to an existing method that assumes that the uncertainty in the discharge-rating shift is the main source of uncertainty in computed discharges and that the discharge-rating shift behaves as a first-order Markovian process. The method uses Kalman filtering of a first-order Markovian process as a statistical analogy to computing streamflow with a shifted discharge rating. Temporally unbiased residuals from a discharge rating are used as a surrogate for the actual shifts used to compute discharge. The standard error of the annual discharge is determined by using Kalman-filter theory and estimates of four parameters: (1) the measurement variance of the discharge measurements used to determine the discharge-rating shift, (2) the process variance of the discharge-rating residuals, (3) the serial correlation of the discharge-rating residuals, and (4) the frequency of the discharge measurements. The existing methodology was improved by estimating the measurement variance from a semivariogram of the discharge-rating residuals, rather than on the basis of empirically derived error estimates for discharge measurements. The process variance and serial correlation of the discharge-rating residuals are estimated from the semivariogram, rather than a variogram, of the discharge-rating residuals. The empirically derived estimates are based on characteristics of the discharge measurements such as number of depth and velocity observation sections, type of current meter, and bed material composition and stability. Measurement variance determined from the semivariograms was site specific and is therefore considered a better estimate than measurement variance determined from the empirically-derived estimates. The method of estimating the standard error of the annual discharge requires the assumption of unbiased discharge-rating residuals, and for this reason, the standard errors presented in this report only represent the random error in the annual discharge data. Estimates of the standard error of the annual change in reservoir content were determined on the basis of the reservoir-surface area and the standard error of reservoir-stage readings.

water-resources investigations report

Standard errors of annual discharge and change in reservoir content data from selected stations in the lower Colorado River streamflow-gaging station network, 1995-99