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U.S. GEOLOGICAL SURVEY
Water-Resources Investigations Report 01–4240

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

This report is available online in pdf format (1 MB): USGS WRIR 01–4240 ()

Prepared in cooperation with THE BUREAU OF RECLAMATION

By D.W. Anning

ABSTRACT

The Bureau of Reclamation is currently (1995�01) 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�.

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.

The standard error of the annual discharge, as a percentage, ranged from 0.11 percent for the All-American Canal near Imperial Dam in 1998 to 12.3 percent for the Colorado River below Imperial Dam in 1996. The standard error of the annual discharge was less than 2 percent for all 5 years for 11 of the 14 streamflow-gaging stations. In terms of flow volume, the standard error of the annual discharge ranged from 97 acre-feet for the Mittry Lake Diversions in 1995 to 77,000 acre-feet for the Colorado River at the northerly international boundary with Mexico in 1998. In general, the standard error of the annual discharge, as a percentage, was smallest at streamflow-gaging stations on the main stem of the Colorado River; however, the standard error of the annual discharge in acre-feet was largest at these stations because of the large annual discharge on the main stem. The standard error of the annual change in content for the two reservoirs ranged from 1,590 acre-feet for Lake Havasu in 1996 to 2,790 acre-feet for Lake Mohave in 1995.

The variance of estimate of the annual discharge for a streamflow-gaging station can be reduced by making additional discharge measurements; either by increasing the number of discharge measurements made per site visit, or by increasing the frequency of site visits. Measurement error can be reduced by using the average shift for two or more discharge measurements made during a site visit. For a streamflow-gaging station where measurement error is much greater than process error and the serial correlation of the discharge-rating residuals is high, an improved gaging strategy would involve making multiple discharge measurements per site visit. In contrast, for a streamflow-gaging station where process error is much greater than measurement error and the serial correlation of discharge-rating residuals is low, the gaging strategy would consist of several single discharge-measurement site visits. For a given operating cost or for a given variance of estimate of the annual discharge at a streamflow-gaging station, the optimal site-visit and discharge-measurement strategy can be determined, providing that the travel costs as well as the measurement variance, process variance, and serial correlation of discharge-rating residuals are known.

CONTENTS

Abstract

Introduction

Streamflow-gaging techniques

Previous error-estimation studies

Methods of estimating the standard error of the annual discharge

Methods of estimating the standard error of the annual discharge in reservoir content

Application of the methods for streamflow-gaging stations

Application of methods for reservoir-content gaging stations

Summary of the uncertainty in the annual discharge and in the annual change in reservoir content

Uncertainty-reducing stream-gaging strategies

Improvements for standard-error estimates

Summary

Selected references

This report is available online in Portable Document Format (PDF). To view the PDF document, you need the Adobe Acrobat® Reader installed on your computer. (A free copy of the Acrobat® Reader may be downloaded from Adobe Systems Incorporated.)

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