development of curves that represent trends in …development of curves that represent trends in...

DEVELOPMENT OF CURVES THAT REPRESENT TRENDS IN

SELECTED HYDRAULIC VARIABLES FOR THE SACRAMENTO RIVER AT

BUTTE CITY, CALIFORNIA

by D. E. Burkham and Richard Quay

U.S. GEOLOGICAL SURVEY

OPEN-FILE REPORT 81-693

o I

Menlo Park, California November 1981

UNITED STATES DEPARTMENT OF THE INTERIOR

JAMES G. WATT, Secretary

GEOLOGICAL SURVEY

Dallas L. Peck, Director

For additional information write to:

District Chief Water Resources Division U.S. Geological Survey 345 Middlefield Road Menlo Park, Calif. 94025

CONTENTS

PageAbstract - - - 1Introduction - - - - 2Trends in discharge-- --------'-- ------- - - ---- ------------ 3Temporal shifts in the stage-discharge relation - 7Trends in stage 12Trends in velocity -------------------------------------------------- 18Summary - ~ - - - 22References cited - 22

FIGURES

Page Figures 1-9 Graphs showing

1. Trend curves for Q95, Q90, Q75, Q50, and Q25 42. Flow-duration curves - - - 63. Relations of stage to measured and computed

4. Relation of shifts to stage - 95. Relation of shift, obtained as the difference

between GH and GH, to time 106. Relation of residual, obtained as the difference

between GHA and GH, to time - 147. Trend curves for GH95, GH90, GH75, GH50, and

G H2 5 168. Relations of discharge to measured and computed

velo cities - - - 199. Trend curves for V95, V90, V75, V50, and V25 20

TABLE

Page Table 1. SAS statements for equations representing shifts in

relations of stage to discharge, and discharge to velocity 13

III

CONVERSION FACTORS

For readers who may prefer to use metric units rather than inch-pound units, the conversion factors for the terms used in this report are listed below:

Multiply By To obtain

ft (feet) 0.3048 m (meters)ft/s (feet per second) 0.3048 m/s (meters per second)ft 3 /s (cubic feet per second) 0.02832 m 3 /s (cubic meters per second)mi (miles) 1.609 km (kilometers)

National Geodetic Vertical Datum of 1929 (NGVD of 1929) t A geodetic datum derived from a general adjustment of the first-order level nets of both the United States and Canada, formerly called mean sea level. In this report, NGVD of 1929 is referred to as sea level.

The use of the Statistical Analysis System (SAS) in this report does not imply endorsement of the system by the U.S. Geological Survey.

IV

DEVELOPMENT OF CURVES THAT REPRESENT TRENDS

IN SELECTED HYDRAULIC VARIABLES FOR THE

SACRAMENTO RIVER AT BUTTE CITY, CALIFORNIA

By D. E. Burkham and Richard Quay

ABSTRACT

Streamflow records for the Sacramento River at Butte City, California, are used to develop curves that represent trends in discharges, stages, and velocities that are equaled or exceeded 95, 90, 75, 50, and 25 percent of the time.

TRENDS IN VARIABLES, SACRAMENTO RIVER, CALIFORNIA

INTRODUCTION

The U.S. Bureau of Reclamation has asked the U.S. Geological Survey to supply them with curves that represent trends, or lack of trends, in values of selected hydraulic variables for the Sacramento River at streamflow gage sites. Specifically, for each of the sites, they requested curves that repre sent trends in discharges, stages, and mean velocities that are equaled or exceeded 95, 90, 75, 50, and 25 percent of the time. The gage sites on the Sacramento River are as follows: Above Bend Bridge near Red Bluff, at Vina Bridge, at Hamilton City, at Ord Ferry, at Butte City, at Colusa, below Wilkins Slough, at Knights Landing, and at Verona.

The purpose of this report is to present a brief description of the procedure used to develop the requested curves for the Sacramento River at Butte City, Calif., (U.S. Geological Survey gaging station 11389000). Neces sary for this description are brief discussions concerned with the development of equations that represent average stage-discharge and discharge-velocity relations, and concerned with the development of curves and equations that represent temporal shifts in these relations. Real data are used to develop the curves and equations. The data and curves are not analyzed for trends. However, a few cursory remarks are given that are concerned with the prob able reasons for or amounts of changes in the different hydraulic variables. The procedure described herein is similar to that used to develop trend curves for discharges, stages, and mean velocities for the other gage sites for the Sacramento River.

A set of computer programs called SAS (Statistical Analysis System) was used to analyze and process data (Helwig and Council, 1979). Computer related acronyms are fully described in this report or in the report by Helwig and Council (1979).

The gaging station at Butte City is about 115 mi upstream and north of Sacramento, Calif. Datum of the gage is 2.92 ft below sea level. Records of daily streamflow for the site have been continuous since September 1938. From April 1921 to September 1938, records were obtained only during low- flow periods, usually in April through September. Streamflow records for April 1931 to February 1980 were used in the study.

The Sacramento River at the Butte City gage is tentatively characterized as a sand-bed river, but gravel is interbedded with the sand (Kresch, 1970, table 3). The clay-to-gravel banks of the river are unstable for long reaches in the vicinity of the gage (Brice, 1977). Changes in the river can occur rapidly in unstable reaches or slowly in reaches that are relatively stable.

The Sacramento River, which rises in the Cascade Range about 50 mi south of the northern boundary of California, flows through the Sacramento Valley, a structural trough filled with fluvial and marine sediments. The river's flow is affected by upstream reservoirs, power development, bypasses for flood control, diversion for irrigation, and return flow from irrigation. The largest deviations from natural flow probably have been due to regulation at Shasta Dam, beginning in December 1943, and to transbasin diversions from the Trinity River, beginning in April 1963. These developments have caused changes in the dominant rate of flow that is carried by the main channel.


TRENDS IN DISCHARGE

Curves representing trends in discharge for the Butte City site are developed by steps as follows:

1. Data values are developed for use in SAS. The terms QMEAS and DURQ are arbitrarily assigned to groups of data, called data sets.

2. Data sets QMEAS and DURQ are combined to give the set, QMDUR.

3. Using QMDUR and SAS procedure PLOT (Helwig and Council, 1979), a plot of instantaneous discharge versus time overlaid with plots of Q95, Q90, Q75, 050, and Q25 versus time is developed (fig. 1).

4. Trend curves for Q95, Q90, Q75, Q50, and Q25 are constructed by connecting appropriate points in figure 1.

The data set QMEAS contains station number, measurement number, date and starting time of measurement, gage height of water surface, meas ured discharge, width of water surface, cross-sectional area of flow, accuracy of measurement, type of measurement boat, bridge, wading, cable maximum depth, and distance of measurement site from gaging station. Some of these data, which were obtained directly from measurement notes in files of the U.S. Geological Survey, were used only for screening purposes. Only discharges less than 60,000 ft3 /s (bankful discharge) were used in the analyses.

The data set DURQ contains values of daily discharge that are equaled or exceeded 95, 90, 75, 50, and 25 percent of the time for 10-year periods. These values, called, respectively, Q95, Q90, Q75, Q50, and Q25, are ob tained using the National Water Data Storage and Retrieval System WATSTORE, Program A969 (Meeks, 1975) and Program G490 (Williams, 1975). Thirty values each for Q95, Q90, Q75, Q50, and Q25 for overlapping 10-year (progressive) periods were obtained for the study station. As previously in dicated, these 150 values of data were used to develop the curves shown in figure 1. The first 10-year period is water years 1939-48 and the final period is water years 1968-77. Dates are represented by the "date of the midpoint of the 10-year period.

The curves shown in figure 1 can be used to study trends in daily discharges for the Sacramento River in the vicinity of Butte City that are equaled or exceeded 95, 90, 75, 50, and 25 percent of the time. The instantaneous discharges that are shown in figure 1 can be used to study trends in discharge that is directly determined by measurement. The changes in trends in discharge that occurred after regulation began at Shasta Lake in 1943 and that occurred after the transbasin diversion from the Trinity River in 1964, can readily be seen in figure 1. The downward trend that began after 1970 is due to the drought in 1976 and 1977.

The daily discharge that is equaled or exceeded 95 percent of the time increased from about-2,400 ft3 /s in 1939-48 to about 7,200 ft3 /s in 1966-75, a 200-percent increase (fig. 2). The discharges that were equaled or exceeded 90, 75, 50, and 25 percent of the time also increased but the rate of increase was smaller. The flow-duration curves for 1939-48, 1954-63, and 1966-75, shown in figure 2, were developed directly from data produced in step 2.


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EXPLANATION

DISCHARGE THAT IS EQUALED OR EXCEEDED 90 PERCENT OF THE TIME FOR 10-YEAR (PROGRESSIVE) PERIODS. DISCHARGE IS PLOTTED AT MIDPOINT OF THE 10-YEAR PERIOD

INSTANTANEOUS DISCHARGE

Q25

Q50

Q75

SEPT. 30, 1943 1945

SEPT. 30, 1950

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TIME IN

FIGURE 1.--Trend curves for

TRENDS IN DISCHARGE

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PERCENTAGE OF TIME FLOW IS EQUALED OR EXCEEDED

FIGURE 2. Flow-duration curves.


TEMPORAL SHIFTS IN THE STAGE-DISCHARGE RELATION

A curve representing temporal shifts in the stage-discharge relation for the study site is developed by steps as follows:

1. Using QMEAS and the SAS procedure NLIN (Helwig and Council, 1979), an equation is developed that represents the average stage- discharge relation for the period 1931-77 (fig. 3).

2. Shifts in the stage-discharge relation developed in step 1 are deter mined.

3. Shifts determined in step 2 are plotted against stage (fig. 4) and against time (fig. 5).

4. A curve representing average trend is drawn on figure 5.

The model required in the SAS procedure NLIN is represented asQQM=A(GH-B) , in which QM is discharge, A is a coefficient, GH is gage

height or stage of water surface, B is a parameter, and C is an exponent. The NLIN procedure (Helwig and Council, 1979) uses iteration and least- square regression analyses to develop estimates for A, B, and C. The equation representing the average stage-discharge relation for the study station is:

QM = 704.3(GH-66.48) 1 * 47 (1)

in which

QM = computed discharge, in cubic feet per second; and GH = gage height or stage, in feet.

The number 66.48 represents, on an average, the apparent stage below which flow ceases. The standard error of estimate for equation 1 is 767 ft 3 /s, which is about 8 percent of the mean of measured discharges in the QMEAS data set. Equation 1 is applicable to stages greater than 66.48 ft and less than bankful stage (fig. 3). All measurements of discharge less than 60,000 ft3 /s were used to develop equation 1.

Shifts in the stage-discharge relation (step 2) are determined by trans posing equation 1 to give an equation for GH (equation 2), computing values for GH using equation 2 and measured values of discharge from QMEAS, and determining shifts, in feet, as the difference between GH and GH. Equation 2 is:

A Z Q

GH = 0.0116(QMr*° +66.48. (2)

Shift, in feet, is represented as:

Shift = GH-GH. (3)

The standard error of estimate for equation 2 is 0.55 ft.

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* SHIFT

CSHIFT

SHIFT = G_H- GHwhere GH= Measured stage of river, in feet

GH = 0.0116(QM) 0-68 +66.48

in which GH = Computed stage of river, in feetQM= Measured discharge, m cubic feet per second

CSHIFT is shift correction, in feet, determined by use of linear equations shown in table 1

SE/T. 30, 1935

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SEPT. 30, 1945

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TIME IN

FIGURE 5.--Relation of shift, obtained as the

TEMPORAL SHIFTS IN THE STAGE-DISCHARGE RELATION 11

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difference between GH and GH (equation 3), to time.


The graph showing the relation of shift to stage (step 3), or a graph showing the relation of (QM-QM) to stage, is needed in order to verify that

Qthe model "QM=A(GH-B) " and equation 1 adequately represent the average stage-discharge relation for the study site. A need to modify the model would be indicated if the plotted shifts, shown in figure 4, were not approx imately isometrically grouped around a shift of zero for the full range of stage being studied.

The trend curve, which was developed in steps 3 and 4, and shown in figure 5, can be used as a "tool" in investigations concerned with changes in the stage-discharge relation for the study site. Changes in the stage- discharge relation for the site apparently occurred in 1935, 1941, 1943, 1950, 1957, 1965, 1971, 1972, 1974, and 1977. An investigation to determine why these changes occurred is beyond the scope of this report. Changes such as those indicated, however, often coincide with or follow the occurrences of major floods.

QThe model, QM = A(GH-B) , can be used to represent the stage- discharge relation for many streams. It probably would have to be modified, however, for streams where two or more controlling conditions affect the stage-discharge relations. The model should be used only with caution, if ever, to represent the stage-discharge relation for sand-bed streams.

TRENDS IN STAGE

Curves showing trends in stage are developed by steps as follows:

1. Linear equations are developed for lines representing average trends in shifts that are shown in figure 5 (table 1).

2. Equation 2 is adjusted, using the shift-correction relations from step 1 above. The adjusted equation 4 represents an adjusted GH, which is shown as GHA.

3. A graph is developed that shows the relation between residuals, obtained by using the formula "residual = GHA-GH," and time (fig. 6)

4. Values for stages that are equaled or exceeded 95, 90, 75, 50, and 25 percent of the time are determined on the basis of 10-year (progressive) periods. These values are called, respectively, GH95, GH90, GH75, GH50, and GH25.

5. A data set composed of QMEAS and values of GH95, GH90, GH75, GH50, and GH25 is developed.

6. The data set from step 5 is used to develop a graph showing a plot of stage versus time overlaid with plots of GH95, GH90, GH75, GH50, and GH25 versus time (fig. 7).

7. Trend curves for GH95, GH90, GH75, GH50, and GH25 are developed by connecting appropriate points in figure 7.

In step 1, equations representing shift (CSHIFT) were developed for 18 increments of time (table 1). These equations were used to determine a value for CSHIFT for each measurement in QMEAS.

Equation 4, referred to in step 2, is:o Afl

GHA = 0.0116(QM) U * °The standard error of estimate for equation 4 is 0.24 ft.

f) Aft GHA = 0.0116(QM) + 66.48-CSHIFT. (4)

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-1.2

-2.2

EXPLANATION* RESIDUAL

ZERO RESIDUAL

RESIDUAL = GHA-GH

where G H = Measured stage of river, in feet

GHA =0.0116(QM)0 '68 + 66.48- CSHIFT

in which GHA = Computed stage of river, in feet,with shift correction

QM = Measured discharge, in cubic feet per secondCSHIFT = Shift correction, in feet, determined by use of linear

equations shown in table 1

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SEPT. :1935 7940

SEPT. 30, 1945

SEPT. 30, 1950

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TIME IN

FIGURE 6.--Relation of residual, obtained

TRENDS IN STAGE 15

4

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SEPT. 30, SEPT.1955

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SEPT. JO, SEPT". 30,1970

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7575

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DAYS FROM OCTOBER 1, 1930

as the difference between GHA and GH, to time.


75 *~ + » » » » * » » * * » » » » + + + » « 4 + +

73

72

71

70

68

GH25

GH50

GH75

67 SEPT. 30, 1935

SEPT. 30, 1943 1945

Sfpr. 30,1950

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TIME IN


TRENDS IN STAGE 17

EXPLANATION

,GH90 STAGE THAT IS EQUALED OR EXCEEDED 90 PERCENT OF THE TIME FOR 10-YEAR (PROGRESSIVE) PERIODS. STAGE IS PLOTTED AT MIDPOINT OF THE 10-YEAR PERIOD

INSTANTANEOUS STAGE, OBTAINED FROM DISCHARGE MEASUREMENT NOTES

SEPT. 30, 1955

SEPT. 30, I960

SEPT. 30, 1965

SEPT. 30, 1970

SEPT. 30, 1975

DAYS FROM OCTOBER 1,1930

GH95, GH90, GH75, GH50, and GH25.


The graph given in figure 6 (step 3) is needed as a check to insure that equation 4 will not give biased results.

Equation 4 was used to directly estimate values of GH95, GH90, GH75, GH50, and GH25 from values of Q95, Q90, Q75, Q50, and Q25. An average value of CSHIFT was used to represent shift for each 10-year period. Aver age values of CSHIFT were determined from a table containing CSHIFTS and entered in the DURQ data set.

The curves shown in figure 7 can be used to study trends in stage of the Sacramento River in the vicinity of the Butte City gage. From 1939-48 to 1967-76, GH95, GH90, GH75, GH50, and GH25 apparently increased 1.5, 1.4, 1.1, 1.0, and 1.3 ft, respectively. Presumably, these increases, which average 1.3 ft, resulted mostly from regulation of flow.

TRENDS IN VELOCITY

The steps and procedures used to develop the stage-discharge relation, linear shift equations representing the stage-discharge relation, and trend curves for stage also were used, respectively, to develop the discharge- velocity relation (fig. 8), linear equations representing shifts in the discharge-velocity relation (table 1), and trend curves for velocity (fig. 9). Only data from discharge measurements made within 100 ft of the gage" were used to develop velocity curves. The equation representing the discharge- velocity relation, without a shift adjustment, is:

V; = 0.00612 (QM) 0 ' 644 (5)

in which _V equals computed velocity, in feet per second. With a shift correc tion, the equation is:

n VA = 0.00612 (QM) U ' +SHV (6)

in which VA equals adjusted computed velocity, in feet per second, and SHV represents an adjustment, in feet per second. The standard error of estimate is 0.23 ft/s for equation 5 and 0.18 ft/s for equation 6.

The curves shown in figure 9 can be used to study trends in velocity of the Sacramento River at the Butte City gage. The parameters V95, V90, V75, V50, and V25 represent, respectively, mean daily velocities that are equaled or exceeded 95, 90, 75, 50, and 25 percent of the time. From 1939-48 to 1967-76, V95, V90, V75, V50, and V25 apparently increased 1.09, 1.05, 0.92, 0.89, and 0.91 ft/s, respectively. Presumably, these increases in velocity, which average 0.97 ft/s, are the result of the regulation of flow.

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SEPT. 30, 1943 1945

SEPT. 30, 1950

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TIME IN


TRENDS IN VELOCITY 21

» » * » * * * + * + + » + + + » * + * * * + » * * * »

V90

EXPLANATION

VELOCITY THAT IS EQUALED OR EXCEEDED 90 PERCENT OF THE TIME FOR 10-YEAR (PROGRESSIVE) PERIODS. VELOCITY IS PLOTTED AT MIDPOINT OF THE 10-YEAR PERIOD

INSTANTANEOUS VELOCITY, OBTAINED FROM DISCHARGE MEASUREMENT NOTES

SEPT. 30,1955

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SEPT.

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30,1960

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JO,1970

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SFPr. 30,1975

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DAYS FROM OCTOBER 1, 1930

V95, V90, V75, V50, and V25.


The trend lines in figure 9 should be of special value to investigations that deal with the effects of changes in discharge on the erosion, transporta tion, and deposition of sediment in the Sacramento River. The capacity to transport sediment in a river is a function of the flow velocity raised to an exponent ranging from 3 to 6. The change in velocity for V95, V90, V75, V50, and V25, therefore, can cause changes in the capacity to transport sediment at the site on the Sacramento River by percentages ranging from 1,140 to 13,070, 875 to 7,650, 508 to 2,580, 372 to 1,383, and 270 to 728, respectively. The magnitude of these factors, however, may be misleading in regard to the total sediment yield at a site on the Sacramento River. For a given lengthy time period, a large percentage of the sediment yield at a station on the Sacramento River probably comes during floods. The sediment- carrying capacity during the peak of a major flood at the site may be larger than that for Q95 by more than 10 million percent. Thus, the changes in sediment yield resulting from alterations in Q95, Q90, Q75, Q50, and Q25 at the study site may be insignificant compared to the volume of sediment movement during floods.

SUMMARY

The procedure used to develop curves representing trends in discharge, stage, and mean velocity for the Sacramento River at Butte City, Calif., is described in this report. The curves are for discharges, stages, and mean velocities that are equaled or exceeded 95, 90, 75, 50, and 25 percent of the time.

REFERENCES CITED

Brice, James, 1977, Lateral migration of the middle Sacramento River,California: Menlo Park, Calif., U.S. Geological Survey Water-ResourcesInvestigations 77-43, 51 p.

Helwig, J. T., and Council, K. A., eds., 1979, SAS user's guide: Raleigh,N.C., SAS Institute, Inc., 475 p.

Kresch, D. L., 1970, Sediment transport in the Sacramento River in thevicinity of Colusa Weir, Sutter and Colusa Counties, California: U.S.Geological Survey open-file report, 10 p.

Meeks, W. C., 1975, WATSTORE User's guide: U.S. Geological SurveyOpen-File Report 75-426, v. 1, chap. 4, sec. G, 37 p.

Williams, O. O., 1975, WATSTORE User's guide: U.S. Geological SurveyOpen-File Report 75-426, v. 1, chap. 4, sec. B, 48 p.

development of curves that represent trends in …development of curves that represent trends in...

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