Prepared in cooperation with the BUREAU OF RECLAMATION Uncertainty in Annual Streamflow and Change in Reservoir Content Data from Selected Surface-Water Gaging Stations on the Lower River

116° 115° 114° U T A H 113° 37° A R I Z O N A

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N he lower is an im- estimated the standard error of the annual

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D A portant water resource for metropolitan discharge for calendar years 1995–99

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A populations, agriculture, and industry at 14 streamflow-gaging stations and Lake Las Vegas Mead C er o iv in , , and . The the standard error of the change lo R r Bureau of Reclamation (BOR) manages in reservoir content at 2 reservoir- 36° a Hoover d o the river, releasing water stored in Lakes content gaging stations (table 1 and NE CA VA Mead, Mohave, and Havasu, and in other fig.1; Anning, 2002). These standard LIFO DA Lake smaller reservoirs as needed so that it can error estimates provide a measure of the RN Mohave IA be used by diverters. To help guide river random uncertainty for the annual data. 1 Laughlin management, streamflow and reservoir 2 35° r content are monitored at strategically ve i located gaging stations along the lower Why Quantify Uncertainty? Needles Lake R Havasu ams lli Colorado River, its tributaries, and its Lake City i W diversions. The data obtained from these In the United States, water from the Havasu 4 l l 3 i B gaging stations, however, contain uncer- main stem in the lower Colorado River A 5 I tainty and are only estimates of the ‘‘true’’ is apportioned among the States of N Parker A R 34° N

O streamflow and reservoir content. As part California, Arizona, and Nevada by the

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L R of a cooperative project with the BOR, Boulder Canyon Project Act of December

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C A Blythe the U.S. Geological Survey (USGS) 21, 1928, and confirmed by the U.S. Supreme Court decree, 1964, Arizona v. California, in terms of consumptive ive r Table 1. Site numbers and names. use (U.S. Congress, 1948). The decree 33° R la Laguna Dam Gi 1. at Davis Dam is specific about the responsibility of the Secretary of the Interior to account 2. Colorado River below Davis Dam Yuma for consumptive use of water from the 0 25 MILES UN 3. Bill Williams River below Alamo Dam ITED mainstem. Accounting for the use of STAT 4. near Parker Dam 0 25 KILOMETERS ME ES Colorado River water is required by XICO 32° 5. Colorado River below Parker Dam the 1964 decree (U.S. Supreme Court, 115° 45' 30' 114°15' 6. 1964); a report that contains records of 33° Colorado River above Imperial Dam 7. Colorado River below Imperial Dam diversions, returns, and consumptive 6 7 use of water is published annually 15 Imperial Dam 8. near Dome Laguna Dam 11, 12 by the BOR (Bureau of Reclamation, 10 9. 16 GilaDome Colorado River at the northerly interna 45' River R 1965–2000). 8 i xxxxxxtional boundary Morelos ver The USGS, in cooperation with the Dam o 9 13, 14 d 10. Diversions at Imperial Dam a Yuma BOR, developed the Lower Colorado r o 11. l Gila Gravity Main Canal at Imperial River Accounting System (LCRAS; o

C xxxxxxDam (stilling well gage operated by Owen-Joyce and Raymond, 1996) 32°30' UN ITED xxxxxxthe USGS) as a method to determine the annual 0 2 MILES ST MEXI ATES 12. Gila Gravity Main Canal at Imperial consumptive use of Colorado River CO 0 2 KILOMETERS xxxxxxDam (acoustic velocity meter gage water by diverters from to EXPLANATION xxxxxxoperated by the BOR) Mexico. The LCRAS is being tested by 1 CONTINUOUS-RECORD RESERVOIR- 13. Welton-Mohawk Canal (radial-gates the BOR to calculate the consumptive CONTENTS GAGING STATION— xxxxxxgage operated by the USGS) use of Colorado River water. The Number corresponds to site number in table 1 14. Welton-Mohawk Canal (acoustic LCRAS is based on a water balance that 6 CONTINUOUS-RECORD STREAMFLOW- xxxxxxvelocity meter gage operated by is applied to four reaches of the lower GAGING STATION — Number corre- xxxxxxthe BOR) Colorado River: Hoover Dam to Davis sponds to site number in table 1 15. All-American Canal near Imperial Dam Dam, Davis Dam to Parker Dam, Parker Figure 1. Location of streamflow and 16. All-American Canal below Pilot Knob Dam to Imperial Dam, and Imperial Dam reservoir-contents gaging stations. xxxxxxwasteway to Morelos Dam (fig. 1).

U.S. Department of the Interior U.S.GS Fact Sheet 108-01 U.S. Geological Survey U.S. Geological Survey The water balance equation used by the BOR and its components are (Bureau of Reclamation, 2000):

Qres=Qdiff +Trm+Trum–Qex –E –CUd –ETpht –ETcrop –ΔSr–ΔSa– where

Qres=Residual (algebraic sum of xxxxxx errors); Qdiff =Qus–Qds; Qus=Flow entering the reach at the upstream boundary; Qds=Flow exiting the reach at the upstream boundary; Trm=Measured tributary inflow to the xxxxxxxx reach; T rum=Unmeasured tributary inflow to xxxxxxxx the reach; Qex=Water exported out of the basin; E=Open-water evaporation; U.S. Geological Survey hydrographer measuring discharge from a cableway at the Gila Main Canal at Imperial Dam using a vertical-axis current meter. Stage is recorded CUd =Domestic, municipal, and continuously inside the stilling well seen in the background. xxxxxxxx industrial use; ETpht=Total estimated phreatophyte evapotranspiration; The annual discharge is computed by discharge data (Moss and Gilroy, 1980). integrating the discharge record over The uncertainty of the shift changes ETcrop=Total estimated crop the year. The discharge rating changes over time; it is smallest at the time of a evapotranspiration; over time in response to changes in discharge measurement. The uncertainty ΔSr =Change in reservoir strorage; channel geometry, vegetation conditions, of the shift increases with time after and, and other factors. As a result, periodic the discharge measurement because ΔSa=Change in storage of the discharge measurements are collected channel conditions change, and the alluvial aquifer. with vertical-axis type current meters ‘‘true’’ shift may not change over time or with acoustic doppler current profile as does the shift that is estimated by The components of the water balance are meters to recalibrate the discharge interpolation. Discharge measurements measured where possible and estimated rating. The recalibration consists of provide information about the shift for otherwise. Many of the components are shifting the rating such that at the time times before and after the measurement measured by streamflow or reservoir- of a discharge measurement, the rated is collected, so the error of the shift contents gaging stations. The sum of the discharge agrees with the measured is largest midway between discharge water-balance components typically does discharge. For times in between discharge measurements (fig. 2). The uncertainty of not equal zero because each component measurements, the shift is interpolated. computed discharge data can be reduced contains some uncerainty. To force the The uncertainty of the shift is the major by decreasing the error of discharge sum of the components of the water source of uncertainty for the computed measurements or by increasing the balance to equal zero, a portion of Qres frequency of the discharge measurements. is distributed to each component on the Annual change in reservoir content is basis of the variance of estimate (squared measured as the difference between standard error) for that component. the reservoir content on December 31 Therefore, methods were established DISCHARGE of one year and the reservoir content for determining the standard error of the on December 31 of the previous year. components in the water balance that Reservoir content is determined using a ANEOUS are defined by streamflow or reservoir- stage reading and a stage-contents rating contents-gaging stations (Anning, 2002). ANT table. Assuming that the stage-contents table is without error, the major source of error for reservoir content data is the Sources of Error misrepresentation of the reservoir stage. Reservoir stage at the upstream end The techniques of computing the annual may differ from that at the downstream discharge at streamflow-gaging stations end where the gaging station is located of the lower Colorado River network because of unsteady reservoir inflows INTY OF COMPUTED INST

generally involve continuously recording TA and outflows, or from sustained winds a correlative variable as a surrogate that shift the mass of the reservoir in for discharge, such as river stage, and the direction of the wind. Other factors, UNCER then applying a discharge rating (a TIME such as drawdown from withdrawal curve relating discharge to stage) to the Figure 2. Uncertainty of computed instan- intakes for downstream releases or wind correlative data to compute a continuous taneous discharge. Dashed lines indicate generated waves, may affect the reservoir record of discharge. time of discharge measurements. stage near the recording instruments. Standard Error of the Annual small standard errors quantitatively indi- gaging stations needs to be changed so Discharge and Change in cate that much of the streamflow and that the uncertainty of the data collected reservoir content data used to estimate can be reduced. In addition, the standard Reservoir Content and distribute the consumptive use of errors can be used to distribute the Colorado River water among users are of residual of the LCRAS water balance The standard error of the annual high quality. The standard errors can be (page 2) to each of the water balance discharge and change in reservoir content used by the BOR and USGS to evaluate components. was determined for 14 streamflow- and whether the operation of individual 2 reservoir-content gaging stations,l —David W. Anning respectively (fig. 3). The methods used to estimate the standard errors were 14 developed to quantify the random component of the uncertainty and may A 12 underestimate the bias component of E

the uncertainty; therefore, the values AG for the standard errors may actually be 10 somewhat larger than those presented if

bias errors are present. PERCENT

The standard error of the annual A 8 discharge, as a percentage, was generally AS

small at most stations for calendar years OR, 6 1995–99 and ranged from 0.11 percent for the All-American Canal near Imperial ERR 4 Dam in 1998 to 12.26 percent for the ARD

Colorado River below Imperial Dam in Not calculated Not calculated 1996 (fig. 3A). In general, the standard AND ST 2 error of the annual discharge, as a percentage, was smallest at streamflow- gaging stations on the main stem of the 0 Colorado River; however, the standard error, in acre-feet, was largest at these stations because of the large annual Dam discharge on the main stem. The standard error of the annual discharge was less than 2 percent with the exceptions of Bill Imperial Williams River below Alamo Dam, Gila River near Dome, and the Colorado River below Lake Havasu below Imperial Dam. The variation of Lake Mohave River radial-gates gage percent errors of the annual discharge for velocity meter gage Gila River near Dome Dam, stilling-well gage different stations reflects the differences Wellton-Mohawk Canal, Colorado River at the northerly Wellton-Mohawk Canal, acoustic in the uncertainty of the discharge Colorado River below Davis Dam Colorado River below Parker Dam Dam, acoustic velocity meter gage international boundary with Mexico Gila Gravity Main Canal at Imperial Gila Gravity Main Canal at Imperial Colorado Colorado River above Imperial Dam All-American Canal below Pilot Knob Bill Williams River below Alamo Dam measurements used to determine the Mittry Lake Diversion at Imperial Dam All-American Canal near Imperial Dam shifts, the frequency of these discharge 100,000 measurements, and the change of the B discharge rating over time in response to changes in channel geometry, vegetation conditions, and other factors. The standard error for the annual 10,000 change in content for the two reservoirs CRE-FEET ranged from 1,590 acre-feet for Lake A

Havasu in 1996 to 2,790 acre-feet for IN 1,000

Lake Mohave in 1995 (fig. 3B). The OR, standard error, in acre-feet, for the annual change in content for the two ERR

reservoir-content gaging stations was ARD smaller than the standard error for the

AND 100 annual discharge for streamflow-gaging ST stations on the main stem of the Colorado River and on the major diversions from the Colorado River; however, it was generally larger than the standard error 10 of the annual discharge for most of the EXPLANATION tributary inflows to the Colorado River. The small standard errors quanti- 1995 1996 1997 1998 1999 tatively indicate that much of the streamflow and reservoir content data Figure 3. Standard error of estimate of the annual discharge at surface-water gaging used to estimate and distribute the stations, 1995–99 (A) as a percentage, and (B) in acre-feet. Bureau of Reclamation hydrographers measuring discharge using an acoustic doppler profiler from a boat on the Gila Gravity Main Canal at Imperial Dam.

Selected References

Anning, D.W., 2002, Standard errors Moss, M.E., and Gilroy, E.J., 1980, Cost- for annual discharge and change in effective stream-gaging strategies reservoir content data from selected for the lower Colorado River basin: U.S. Geological Survey hydrographer stations in the Lower Colorado The Blythe Field Office Operations: making a wading discharge measurement at Bill Williams River below Alamo Dam River Streamflow-Gaging Station U.S. Geological Survey Open-File using a vertical-axis current meter. Network, 1995–99:U.S. Geological Report 80–1048, 112 p. Survey Water-Resources Investi- gation Report 01–4240, 81 p. Owen-Joyce, S.J., and Raymond, L.H., 1996, An accounting system for Bureau of Reclamation, 1965–2000, water and consumptive use along Compilations of records in the Colorado River, Hoover Dam accordance with Article V of the to Mexico: U.S. Geological Survey Decree of the Supreme Court of Water-Supply Paper 2407, 94 p. the United States in Arizona vs. For further information, contact: California, dated March 9, 1964, U.S. Congress, 1948, The Hoover Dam David W. Anning Calendar year 1965–99: Bureau documents: U.S. Congress, 80th, U.S. Geological Survey, WRD of Reclamation duplicated report 2nd session, House Document 520 North Park Avenue, Suite 221 Tucson, Arizona 85719-5035 (published annually). No. 717, 936 p.

Bureau of Reclamation, 2000, Lower U.S. Supreme Court, 1964, State of Colorado River Accounting System,l Arizona, plaintiff versus State Demonstration of Technology of California et. al., defendants: Calendar Year 1999: Department of Decree-March 9, 1964, no. 8, the Interior, Bureau of Reclamation,l original, 14 p. Lower Colorado River Regional E-mail: [email protected] Office, Boulder City, Nevada, 48 p. or visit home page +11 Exhibits and 90 Attachments. http://az.water.usgs.gov