GRAPHICAL METHOD FOR ESTIMATING OCCURRENCE AND DURATION - OF A CRITICAL LOW FLOW 'I ‘9'.“ IN THE SACRAMENTO RIVER U.S.GEOLOGICAL SURVEY ‘ Water-Resources Investigations PM W 6649/ 9% Prepared in cooperation with the SACRAMENTO COUNTY DEPARTMENT OF PUBLIC WORKS GRAPHICAL METHOD FOR ESTIMATING OCCURRENCE AND DURATION OF A CRITICAL LOW FLOW IN THE SACRAMENTO RIVER AT FREEPORT, CALIFORNIA By Jerry G. Harmon U.S. GEOLOGICAL SURVEY Water-Resources Investigations Report 82—4001 Prepared in cooperation with SACRAMENTO COUNTY DEPARTMENT OF PUBLIC WORKS 6215-25 May 1983 UNITED STATES DEPARTMENT OF THE INTERIOR JAMES G. WATT, Secretary GEOLOGICAL SURVEY Dallas L. Peck, Director [fig 3?: L12 Lma // 6 c}- \" s 0‘»? « For additional information, Copies of this report can be purchased write to: from: District Chief Open—File Services Section Water Resources Division Western Distribution Branch U.S. Geological Survey U.S. Geological Survey 2800 Cottage Way, Room W-2235 Box 25425, Federal Center Sacramento, Calif. 95825 Denver, Colo. 80225 Telephone: 303 234—5888 /T W75 """ CONTENTS I ,1 .: gi9~f L F 4 f7 T Page Abstract——---———-——————-————_—————--________-__-_--________;_;__; __________ 1 Introduction _______________________________________________________________ 2 Acoustic streamflow—measuring system _______________________________________ 5 Sources of data used to develop the graphical method _______________________ 5 Deve10pment of the graphical method ________________________________________ 6 Method to estimate duration of a critical low flow -------------------- 6 Method to estimate occurrence of a critical low flow __________________ 6 Verification of the duration graph _________________________________________ 13 Application of the graphical method ________________________________________ 13 Sources of error ___________________________________________________________ 15 Summary ____________________________________________________________________ 15 References cited ___________________________________________________________ 16 ILLUSTRATIONS Page Figure 1. Map Showing Sacramento River study area ————————————————————————— 3 2—4. Graphs showing: 2. Flow-duration curve for the Sacramento River at ‘ Sacramento, 1949-79 --------------------------------------- 4 3. Flow and stage of the Sacramento River at Freeport, January 14, 1977 ------------------------------------------ 7 4. Plotted data used to develop a relation of daily mean flow and stage index to duration of flow equal to and less than 4,000 cubic feet per second, Sacramento River at Freeport ----------------------------------------- 8 5. Duration graph for flows equal to and less than 4,000 cubic feet per second, Sacramento River at Freeport ----------------- 10 6. Graph showing relation of time when flow reaches 4,000 cubic feet per second to time when stage peak occurs ---------------- 12 TABLE Page Table 1. Comparison of computed and estimated durations of flow equal to and less than 4,000 cubic feet per second, Sacramento River at Freeport ------------------------------------- 14 III CONVERSION FACTORS The inch-pound system of units is used in this report. For readers who prefer to use metric units, the conversion factors for the terms used in this report are listed below. Multiply EX To obtain ft (feet) 0.3048 m (meters) ft3/s (cubic feet per second) 0.02832 m3/s (cubic meters per second) mi (miles) 1.609 km (kilometers) mi/h (miles per hour) 1.609 km/h (kilometers per hour) mi2 (square miles) 2.590 km2 (square kilometers) Mgal/d (million gallons per day) 3785 m3/d (cubic meters per day) IV GRAPHICAL METHOD FOR ESTIMATING OCCURRENCE AND DURATION OF A CRITICAL LOW FLOW IN THE SACRAMENTO RIVER AT FREEPORT, CALIFORNIA By Jerry G. Harmon ABSTRACT Sacramento County expected to begin operation of the Sacramento Regional Wastewater Treatment Plant in 1982. The California State Water Resources Control Board has ruled that the plant will not be allowed to release effluent into the Sacramento River when flow in the river is 4,000 cubic feet per second or less. Depending on tide condition, flows less than 4,000 cubic feet per second may occur either once or twice during each 24—hour 50—minute tide cycle when the daily mean flow is less than about 12,000 cubic feet per second. Daily mean flows less than 12,000 cubic feet per second occur about 28 percent of the time. Riverflow at the plant outfall is monitored by an acoustic streamflow— measuring system. Regulation of effluent released from the plant will normally be based on real—time flow data computed by the acoustic system. A graphical method for determining the occurrence and duration of flows of 4,000 cubic feet per second and less was developed as a backup system to be used if a temporary failure in the acoustic system occurs. INTRODUCTION Sacramento County expected to begin operation of the Sacramento Regional Wastewater Treatment Plant in 1982. Effluent from the plant will be released into the Sacramento River at Freeport, Calif. (fig. 1). The California State Water Resources Control Board has ruled that the plant will not be allowed to release effluent into the river when flow in the river is 4,000 ft3/s or less. Flow in the Sacramento River at Freeport is affected by tides when the flow is less than about 45,000 ft3/s. Depending on tide condition, flows at Freeport can be less than 4,000 ft3/s during one or two periods per day when the daily mean flow is less than about 12,000 ft3/s. Based on the flow—duration curve (fig. 2) for the Sacramento River at Sacramento (1949—79), flows less than 12,000 ft3/s occur about 28 percent of the time (daily mean flow of the Sacramento River at Freeport is considered equivalent to that of the Sacramento River at Sacramento, 10.8 miles upstream). The Sacramento River at Freeport has a drainage area of 23,510 miz. Mean annual flow, based on 31 years of record at Sacramento, is 23,590 ft3/s. Flow in the Sacramento River at the plant outfall has been monitored on a real—time1 basis since 1978 by an acoustic streamflow—measuring system installed by Sacramento County. The county will use data from the acoustic system to regulate effluent release from the plant. Because failure or malfunction in the acoustic system eliminates real—time flow data at the plant, a backup system is needed to prevent possible effluent-release violations. In October 1980, the U.S. Geological Survey, in cooperation with the Sacramento County Department of Public Works, began a study to develop an independent method to determine when flow at the plant outfall is 4,000 ft /s or less. Three methods were considered: (1) Installation of another acoustic streamflow—measuring system, (2) conversion of the Sacramento—to—Hood transient—flow model (Oltmann, 1980) to a real—time system, and (3) development of a graphical method. The graphical method was chosen because it was considered the most practical. This report describes the development, verification, and application of the graphical method. 1For the purpose of this report, real—time system is defined as a system which can produce the present streamflow value when the system is interrogated. 121°37'30" 121°30' 121°22'30" 121°15' ' q. 393730" —- ‘V- / — \ \ VA / d <9 C A N /A/ ./ SACRAMENTO RIVER §$ I R I ‘ AT SACRAMENTO “iamyflf\ M b // STAGE GAGE (D /l:~.'l"lll /‘ / / ‘.:'i/I'l'" ¥ 1, / ~.'l/'l:ll\ / // I 7 , \\__// o SACRAMENTO E 0 <1: 2 l ‘3» ® 2 A E as 38030 — I Z .— S 1) c ‘3» V‘ ’1‘ STUDY AREA 0 SACRAMENTO RIVER NEAR FREEPORT STAGE GAGE " SAN FRANCISCO , SACRAMENTO RIVER AT FREEPORT BRIDGE SACRAMENTO REGIONAL , STAGE GAGE WASTEWATER TREATMENT - (TEMPORARY) PLANT OUTFALL LOS ANGELES _ CD 38°22'30" — SACRAMENTO O HOOD RIVER AT HOOD . STAGE GAGE W MIles A" 4CR/1MENT0 O 1 2 3 4 5 6 7 Kilometers FIGURE 1.--Sacramento River study area. . .mNIQNGF .OHCwEMLUMW #0 Lw>_.~_ OHCGEMLUMM 0:3. 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VN mm mm pm ON 09 m: t m: m: #1 mF NF : 0— m. m N. 0 m v I A _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ # .I .0 .l I O C on O F .. T .00 O T I on _I DO. .0... ll 0.. .. O .I O 0 .0. l I F _ _ _ _ _ _ _ _ _ _ b _ _ P _ _ _ NF m— w— m— m: t m— mp ON FN mm mm VN SHnOH NI 'CINOOES 83d L333 DIEGO 000'? SBHOVSH MO‘H NEHM 3WLL 12 VERIFICATION OF THE DURATION GRAPH Data from low-flow periods in 1980-81 were used to verify the duration graph (fig. 5) developed from 1976—77 data. The 1980—81 flow data for Freeport were computed by the transient—flow model because records from the acoustic streamflow- measuring system were not complete during the 1980—81 low-flow periods. The gage at the Freeport bridge was discontinued in 1977; stage indices for the 1980-81 low-flow periods were computed from stage data recorded 2 miles upstream from Freeport. A plus 0.12-foot stage-index correction was used based on comparison of synchronized stage data recorded at the two sites in 1976-77. Estimated durations from the graph, based on computed stage indices and daily mean flows, were compared with computed durations in table 1. 0f the 49 estimated durations, 29 are less than computed durations, 15 are more than computed dura— tions, and 5 are the same. More than half the estimated durations are within 15 minutes of the computed durations. The average difference is 26 minutes. APPLICATION OF THE GRAPHICAL METHOD At Freeport a daily mean flow of 12,000 ft3/s or less in the Sacramento River indicates the probable occurrence of one or two critical low-flow periods (flow less than 4,000 ft3/s) during the 24—hour 50-minute tide cycle. Projected values of stage index and daily mean flow are required to use the graph to estimate the duration of a critical low—flow period. Projected time of a stage peak is required to predict the occurrence (time) of a critical low-flow period. Projected times of stage peaks and projected stage indices are obtained from a Freeport stage recorder operating independently of‘the acoustic streamflow- measuring system. Projected daily mean flow is available by telephone from the California Department of Water Resources in Sacramento. The projected daily mean flow is based on stage-discharge relations at upstream gages and seasonal consumptive—use factors. The occurrence and duration of critical low flows are estimated as follows: Step 1. Project the time of the next stage peak by adding 24 hours 50 minutes to the time of the recorded corresponding stage peak of the previous day. This will be the estimated time of the end of the critical low—flow period. Step 2. From the corresponding events recorded the previous day, compute the stage index by subtracting trough stage from peak stage as shown in figure 3. Step 3. Obtain the projected daily mean flow from California Department of Water Resources. Step 4. Plot stage index and daily mean flow on the duration graph (fig. 5). From the band where the point plots, read the duration. Step 5. Subtract the duration from the time projected in step 1. The result is the estimated beginning time of the critical low-flow period. 13 TABLE l.-—Comparison of computed and estimated durations of flow equal to and less than 4,000 cubic feet per second, Sacramento River at Freeport - ' . 3 Time, in hours, Duratlon of flow less than 4,000 ft /5 Date computed flow I: Corpputecil from d 1 Estér'nated from decreased to 4,000 ft3/s ”“51“” 1 9“ "‘0 9 18111133 Hours Mmutes Hours Mmutes 1980 OCt. 19 1255 2 30 2 20 1335 2 15 2 30 21 0105 2 15 2 30 21 1330 3 2 45 22 0150 2 3O 2 4S 22 1355 3 30 3 15 23 0305 2 15 3 23 1435 3 15 3 45 29 1935 2 30 3 30 1010 2 30 2 30 2115 1 45 2 31 1050 3 2 30 31 2235 1 45 1 15 Nov. 1 1135 3 2 45 1981 Jan. 15 1105 2 4S 2 15 16 1135 3 3 17 1220 3 15 3 18 1320 3 3 Apr. 17 0335 2 1 45 18 0315 3 15 2 15 18 1645 1 30 1 45 19 0130 2 45 1 45 29 0155 0 45 0 30 0200 2 2 15 30 1440 0 30 0 June 2 0315 3 2 45 0340 3 15 3 4 0425 3 30 3 15 5 0500 3 45 3 30 S 2050 2 15 2 30 6 0610 3 15 2 45 6 2110 3 15 3 15 7 0735 2 45 2 7 2220 2 30 3 11 0035 2 30 2 30 12 0125 2 15 2 15 13 0120 2 45 2 14 0155 2 15 2 15 0235 2 30 2 45 16 0235 3 15 3 17 0300 3 15 2 30 18 0325 3 45 3 15 18 1940 1 30 1 45 19 0350 3 45 3 15 19 1935 2 45 2 30 20 0435 3 45 3 15 20 2040 1 4S 2 45 l4 SOURCES OF ERROR Durations used to develop the duration graph were obtained from printouts of flows computed by the transient—flow model for 15—minute intervals. Because many of the computed flows were close to 4,000 ft3/s at a 15-minute interval, some interpolation was required. All durations used to develop the graph were calcu- lated to the nearest 15 minutes. Projected daily mean flow usually differs by less than 4 percent from the daily mean flow computed by the acoustic streamflow-measuring system. The differ— ence is rarely more than 7 percent. When daily mean flows are less than 12,000 ft3/s, day—to—day changes in the daily mean flows are gradual. Stage index from the corresponding part of the previous day's tide cycle usually differs from the current stage index by less than 0.2 feet. Projected time of a stage peak is based on an average tide cycle of 24 hours 50 minutes. From the data used to develop the duration graph, times of corre— sponding stage peaks were within 10 minutes of the average vahw 62 percent of the time and within 25 minutes 88 percent of the time. Accuracy of the relation of a stage peak to the occurrence of the critical low flow was discussed in the section ”Development of the Graphical Method." SUMMARY In order to comply with State of California regulations, Sacramento County must stop releasing effluent from the Sacramento Regional Wastewater Treatment Plant to the Sacramento River at Freeport when riverflow at the release point is 4,000 ft3/s or less. Periods of flow less than 4,000 ft3/s occur during the tide cycle when daily mean flows are less than about 12,000 ft3/s. Daily mean flows are less than 12,000 ft3/s about 28 percent of the time. Riverflow is monitored on a real—time basis at the plant outfall by an acoustic streamflow-measuring . system. Albackup system will be required if a failure in the acoustic system occurs when the daily mean flow is less than 12,000 ft3/s. A graphical method, independent of the acoustic system, was developed to estimate the occurrence and duration of periods of flow less than 4,000 ft /s. A duration graph was developed and verified, using recorded river stage and model—computed flow data. Using the graphical method, estimated duration of periods of flow less than 4,000 ft3/s is obtained by applying a projected daily mean flow and a projected stage index to the duration graph. The projected time of a stage peak indicates the end of a period of flow less than 4,000 ft3/s. Subtracting the estimated duration from the projected time of the stage peak gives the predicted beginning time of the period of flow less than 4,000 ft3/s. 15 REFERENCES CITED Oltmann, R. N., 1980, Extension of transient—flow model of the Sacramento River at Sacramento, California: U.S. Geological Survey Water-Resources Investigations 80—30, 29 p. 1 Smith, Winchell, Hubbard, L. L., and Laenen, Antonius, 1971, The acoustic streamflow—measuring system on the Columbia River at The Dalles, Oregon: U.S. Geological Survey Open-File Report, 60 p. 16 mmacmz =” 29. DmE4mm Um_u>m._._<_mz._. OT: ._.Im _Z._.mm_Om omOroQoZ. mcx ommwm Illllllllll'llll OmIOS... mcm_2mwm womfiom >zc mmmm 36 :.m. 333sz 0m Em 2:on _2fi 3w