COMPUTATION OF FLUVIAL-SEDIMENT DISCHARGE

Transcription

1 Technques of Water-Resources lnvestga tons of the Unted States Geologcal Survey Chapter C3 COMPUTATON OF FLUVAL-SEDMENT DSCHARGE \ By George Porterfeld Book 3 APPLCATONS OF HYDRAULCS

2 UNTED STATES DEPARTMENT OF THE NTEROR ROGERS C. B. MORTON, Secretary GEOLOGCAL SURVEY W. A. Radlnsk, Actng Drector UNTED STATES GOVERNMENT PRNTNG OFFCE, WASHNGTON : 1972 For rde by the Superntendent of Documents, US. Government Prntng ORce, Washngton, D.C Prce 75 cents Stock Number

3 PREFACE The seres of mauals on technques descrbes procedure3 for plannng and executng specalzed work n water-resources nvestgatons. The materal s grouped under major subject hedngs called books and further snbdvded nto sectons and chapters; Secton C of Book 3 s on sedment md eroson t eclnques. The unt of publcaton, the chapter, s lmted to a 1a.rrow feld of subject matter. Ths fornst permts flexblty n revson and publcclton as the need uses. 11

4 CONTENTS Preface. Abstract. ntroducton. Types of records. Checklst for daly records. Partcle-sze analyss. Evaluaton of sze data. Tabulaton of sze data. Water. temperature. Suspended-sedment concentraton... Adequacy of data. Relaton between sngle-vertcal and cross-sectonal concentratons. Cross-secton coeffcent. Varaton wth tme... Analyss of cross-secton concentraton data... Development of a temporal concentraton graph... Plottng symbols and scales. Theoretcal consderatons. Study of past records. Relaton of water dscharge to concentraton. Estmates for perods of mssng data... Vsual comparson wth adequately defned concentraton graphs... Hydrographc comparson wth records of upstream and downstream statons. Paw Development of a temporal concentraton graph-contnued Estmates for perods of mssng data- Contnued Water-sedment relaton curves... Examples of the sedment-concentraton graph... Snowmelt dseharge and sedment concentraton... Applcaton of cross-secton coeffcent... Computaton of daly mean concentraton... Footnotes... Sgnfcant fgures. Computer programs. Format of sedment tables... Compukaton of sedment dscharge... Unts of measurement... Computaton of subdvded days... Mean-nterval method... Mdnterval method... Sedment-dscharge worksheet... Staton analyss. Staton descrpton headng... Perodc observatons. Checklst for perodc records :... Combned perodc and seasonal observatons. Transmttal of completed data. Selected references. Page FGURES 1. Graph showng mnmum number of bottles of sample requred to yeld suffcent sedment for sze analyss Form for- 2. Annual tabulaton of partcle-sze ana! yses of suspended sedment Maxmum and mnmum daly water-temperature tabulaton Tabulaton of once-daly water temperatures Sedment-concentraton notes (short form). 6. Tabulaton of sedment data n the cross secton. 7. Tabulaton of sedment data n the cross secton Graphs showng- 8. Relaton of cross-secton coeffcent to dscharge and season for San Joaqun Rver near Vernals, Calf Water dscharge, sedment concentraton, and coeffcents for correctng observer s sngle-vertcal samples to cross secton... Page V

5 v CONTENTS Page Graphs Showng- 1. Relaton of cross-secton coeffcent to gage heght Advanced concentraton durng excess runoff perods Smultaneous concentraton durng excess runoff perods Laggng concentraton durng excess runoff perods.....~ Sedment-transport curve on a storm bass wth ndcated mean concentraton Cumulatve unt relaton of total water dscharge and total sedment dscharge for typcal advanced, smultaneous, and laggng types of concentraton graphs _..._ Typcal effect of hgh-ntensty short-dur aton ranfall on dscharge and concentraton for a small-dranage-basn stream havng a very small amount of base flow or none Gage heght and sedment concentraton, Corey Creek near Manesburg, Pa. _..._..._ Effect of two dfferent flow condtons on dscharge and concentraton for the Ro Grande near Bernalllo, N. Mex.....~ Gage heght and sedment concentraton, Colorado Rver near San Saba, Tex., May 1-6, Gage heght and sedment concentraton, Colorado Rver near San Saba, Tex., August 13-17, _.._ Gage heght and sedment concentraton, Colorado Rver near San Saba, Tex., May 22-27, Gage heght and sedment concentraton, Colorado Rver near San Saba, Tex., June 11-14, Gage heght and sedment concentraton, Susquehanna Rver at Harrsburg, Pa Suspended-sedment concentraton, sedment dscharge, and water dscharge, Wllamette Rver at Portland, Oreg., December 21-3, _ Temporal relaton of sedment concentraton to water dscharge durng a snowmelt perod Relaton of water dscharge to sedment concentraton, Green Rver at Green Rver, Utah, Graphcal adjustment of concentraton Dagrams showng determnaton of mean concentraton by graphcal method...._.._.._ Form showng format table , suspended-sedment dscharge _..._._ ~ , suspended-sedment dscharge for selected days , suspended-sedment dscharge measurements , suspended-sedment dscharge durng perods of hgh flow , total sedment dscharge , partcle-sze dstrbuton of suspended sedment , partcle-sze dstrbuton of surface bed materal. _.._..._..._.._ Graph showng gude to subdvson, assumng accuracy about 5 percent Dagram showng gage heght and sedment concentraton for a subdvded day.._...._ Worksheet for annual suspended-sedment dscharge Graph showng relaton between daly suspe nded-sedment dscharge and water dscharge, Thomas Creek at Paskenta, Calf., water years Format and content for- 4. Staton analyses of water, sedment, temperature, and ranfall Staton analyses of chemcal qualty and sedment..._ _ Staton analyses of sedment Headng and chemcal-qualty tabulaton n annual water-qualty-data report._...._ Updated staton headng......_ Tabulaton of perodc sedment data 63 TABLES Temperature converson table to nearest.5 degree Converson factors, C, for sedment concentraton : parts per mllon to mllgrams per lter... Computaton of subdvded day, mean-nterval method... Computaton of subdvded day, mdnterval m~hod... Page

6 COMPUTATON OF FLUVAL-SEDMENT DJSCHARGE George Porterfeld Abstract Ths report s one of a seres concernng the concepts, measurement, laboratory procedures, and computaton of fluval-sedment dscharge. Materal n ths report ncludes procedures and forms used to comple and evaluate partcle-sze and concentraton data, to compute fluval-sedment dscharge, and to prepare sedment records for publcaton. ntroducton Collecton, computaton, and publcaton of fluval-sedment and related envronmental data are part of a natonal program to evaluate effects of sedmentaton on the lfe and economcs of projects related to navgaton, flood control, transportaton, reclamaton, water supply, recreaton, polluton, and fsheres. Fluval-sedment nvestgatons may nclude determnaton of the sedment dscharge of rvers, surveys of reservors, studes of channel morphology, research n basc processes, and nterpretaton of sedment data. The purpose of ths chapter s to combne nto a sngle handbook the necessary nformaton to evaluate sedment data, compute sedment dscharge, and tabulate the data for publcaton. The content s based not only on the author's experence but ncludes nformaton from the volumnous lterature accumulated durng the past two or three decades as well as the deas of many experenced coworkers. Although ths chapter s lmted to methods of complaton, computaton, and edtoral format, t also ncludes reference to samplng technques, laboratory procedures, prncples of sedment transport, and qualty control, because knowledge of these s f undamental to computaton of sedment records. The entre operaton, from the collecton of the sample n the feld to the laboratory analyss and the computaton and publcaton of the records, requres a hgh degree of coordnaton. Mnor duplcaton of materal n other chapters of the manual s necessary and ntentonal to allow use of the chapter as separate enttes. Ths manual was prepared by the Calforna dstrct, Water Resources Dvson, U.S. Geologcal Survey, Menlo Park, Calf., under the general supervson of R. Stanley Lord, Dstrct Chef. Techncal advce and assstance were gven by Geologcal Survey personnel n Calforna, Texas, New Mexco, and Pennsylvana dstrcts and by 3'. C. Ames, H. P. Guy, and J. K. Culbertson. Types of Records Two basc types of sedment recordsdaly and perodc-are publshed by the Geologcal Survey. Daly records are prepared for stes where suffcent determnatons of sedment concentraton and water dscharge are obtaned to justfy computaton of daly sedment dscharge. The end product s a tabulaton of daly mean concentraton, suspended-sedment dscharge, and perodc determnatons of partcle-sze dstrbuton of suspended sedment and bed materal. These are combned wth other qualty-of-water data and released, usually by water year (October through followng September) and on an annual bass, by the Geologcal Survey n basc-data reports coverng a specfc State

7 2 TECHNQUES OF WATER-RESOURCES NVESTGATONS or n the water-supply-paper seres Qualty of Surface Waters of the Unted States. Perodc records are prepared for stes where determnatons of concentraton and water dscharge are not suffcent to justfy computaton of daly sedment dscharges or where only mscellaneous samples are obtaned. n addton to publcaton of the records, the data and computatons are mantaned on fle n the dstrct offces of the Water Resources Dvson and are avalable for examnaton or for use n nterpretatve reports or research. Checklst for Daly Records Steps n the procedure for the computaton of daly records of fluval-sedment dscharge are gven n the followng checklst. A checklst for perodc and mxed records s gven n the secton Perodc Observaton of ths report. Data on stream stage and dscharge needed n the daly sedment computaton may be obtaned from an A-35-analog-recorder chart or a plot of bhourly gage heghts or dscharge and from data forms 9-192, 9-21, and The checklst tems are as follows: Partcle-sze analyses : Compute from laboratory analyses Tabulate Apply nstantaneous water dscharge Tabulate water temperature Sedment concentraton : Compute from laboratory analyses Lst sedment measurements Copy sze-concentraton values on concentraton notes Compute coeffcents Chart computatons : Plot concentraton Draw concentraton graph Revew concentraton graph Compute concentraton Apply concentraton coeffcent Compute subdvded days Check subdvded days Sedment-dscharge worksheet : COPY water dscharge Copy concentraton Compute sedment dscharge Compute totals Check totals Sedment-dscharge worksheet-contnued Compute maxmum and mnmum nsert footnotes Plot sedment-transport curve Plot hydrograph Wrte or update staton descrpton Wrte staton analyss Revew entre record Prepare copes for records-processng center Partcle-Sze Analyss Samples of suspended sedment from each samplng ste taken at specfc or selected tmes of the year are analyzed for partclesze dstrbuton. These samples ndcate the average partcle-sze dstrbuton of the materal transported and should be obtaned at varous seasons of the year and at suffcent ncrements of dscharge to cover the complete range n seasonal flow. Samples of bed materal also are obtaned to defne the sze dstrbuton of bed materal at varous ncrements of flow and to defne the physcal propertes of the materal avalable for transport. The type and purpose of the sample dctates to some degree the samplng procedure, the methods used to analyze the sample, and the methods and forms used to present the data. Samplng procedures are dscussed n detal n the manual on feld methods for fluval-sedment measurements (Guy and Norman, 197) and by the U.S. nter-agency Commttee on Water Resources (1963). Laboratory procedures and methods of analyses are dscussed n detal n the manual on laboratory theory and methods for sedment analyses (Guy, 1969). Evaluaton of sze data Partcle-sze analyses should be evaluated durng the revew and tabulaton process for- 1. Correct method of analyss, 2. Total number of analyses, 3. Range of water dscharge, 4. Agreement of concentraton and water dscharge on the partcle-sze tabulaton wth those on the sedment-dscharge sheet and publshed records of water dscharge, and [ 1 1! \ ~ /!

8 COMPUTATON OF FLUVAL-SEDMENT DSCHARGE 5. Valdty of percentage-fner values. The number of samples analyzed, methods of sample collecton, and method of analyss depend partly on the purpose and scope of the sedment project or data program ; results of analyses should be revewed to determne f the number of samples and method used for analyss fulflls the goals of the samplng program. Accuracy of the analyss s dependent, among other factors, on the quantty and physcal characterstcs of the sedment analyzed; an nspecton of the data sheet wll ndcate f a suffcent quantty of materal was collected for analyss. Analyss made on samples contanng nsuffcent materal may be n error. Partcle-sze dstrbuton of these samples should be carefully evaluated for accuracy, and f suspect they should not be publshed. n general, the quantty of sedment needed for analyss s as follows: Quantty of sedment, n grams Method Mnmum Dry seve. 5. Wet seve.5 VA tube..5 Ppet..8 BW tube..5 3 Optmum The mnmum number of bottles of sample requred to provde suffcent sedment for sze analyss may be determned from the curves n fgure 1. The range of concentraton values and percentage fner than 62 mcrons needed to use fgure 1 are avalable n the staton records for the precedng year. Fgure 1.-Mnmum number of bottles of sample requred to yeld sugcent sedment for sze analyss. Explanaton: Estmate sedment concentraton and percentage fner than 62 mcrons by referrng to analyss of samples obtaned prevously or by vsual examnaton of the sedment sample. The number of bottles requred s the value ndcated by rhe lne to the left of the ntersecton of the ordnate and abscssa. nterpolaton of number of bottles s made along the abscssa. Values of the number of bottles requred were computed on fhe assumpton that each sample bottle contans 35 grams of woter-sedment mxture and that a mnmum of.2 gram of sand for a seve or vsual-accumulathn-tube analyss and.8 gram of slt and clay for a ppet analyss n 4-mlllter suspenson are needed for analyss. The number d bottles requred to yeld suffcent slt and clay for a bottam-wthdrawal-tube analyss s fve-eghths of the number ndcated

9 Tabuluton of sze dutu Partcle-sze analyses of suspended sedment are tabulated on form D, shown n fgure 2. Ths form s also used to tabulate perodc or mscellaneous concentraton and partcle-sze data. Partcle-sze analyses of bed materal are tabulated on form (not llustrated). Examples of off set copy furnshed by computer for publcaton are llustrated n the secton on "Format of Sedment Tables." nstantaneous water dscharge at the tme of samplng and concentraton of the sample analyzed for partcle-sze dstrbuton are determned and tabulated for each sample. These values must be compared for valdty wth the daly values publshed for water dscharge n the surface-water records and on the sedment-dscharge sheet. Water-dscharge values may be computed and lsted n the space provded on the partcle-sze forms or may be lsted on the multple-purpose form descrbed n the secton on "Analyss of Cross-Secton Concentraton Data." Data from the partcle-sze analyses should be transcrbed neatly on the form shown n fgure 2. The data are arranged on the form as follows: Date of collecton.-tabulate year, month, and day. January 1, 197, for example, s 711. Tme (24 hour).-tme s reported n 24- hour local standard tme. The hours and mnutes are always wrtten to four places and wthout punctuaton. Do not use a.m. or p.m. For example: 1 hours s 1 mnute after mdnght; 1 hours s 1 a.m. ; 148 hours s 1:48 a.m.; 12 hours s 12 m. (noon) ; 143 hours s 2:3 p.m.; and 24 hours s 12 p.m. (mdnght). Water temperature ("C).-Water-temper- Fgure l.-annual fabulaton of partcle-sze analyses of suspended sedment. t 1

10 COMPUTATON OF FLUVAL-SEDMENT DSCHARGE 5 ature data are reported to the nearest.5 degree Celsus. Number of samplng ponts.-use when reportng bed-materal analyses. Ths s the number of samples obtaned n the stream cross secton. The laboratory may report ndvdual analyss for each sample to show varaton of bed-materal sze dstrbuton n the cross secton and to provde necessary data for computaton of total sedment dscharge by the procedure descrbed by Colby and Hembree (1955). Generally the average sze dstrbuton n the cross secton s publshed; however, ndvdual analyss may be publshed f there s a large varaton of medan dameter among vertcals or f there s a need for more detaled nformaton. Dscharge (cfs).-the dscharge s usually reported for the tme of samplng; however, f no measurment s made or the ratng does not justfy reportng the nstantaneous dscharge, the daly mean dscharge s reported. f mean dscharge s used, change headng to Mean dscharge (cfs) or use footnote D as explaned n the secton on LFootnotes. Concentraton (mg/l).-a11 sedment concentratons wl be reported n mllgrams per lter although they wl be determned n the laboratory as parts per mllon. The supervsor must determne that all concentratons have been properly converted pror to tabulatng concentratons or computng sedment dscharge. Sedment dscharge (tons per day).- Values for tons per day should be determned as dscussed n the secton on Computaton of Sedment Dscharge. Records tabulated for computer processng do not requre computaton of sedment dscharge because values n ths column are computed and lsted by computer. Partcle sxes, percent fner than sze (n mllmeters) ndcated-the szes for suspended sedment are.2,.4,.8,.16,.31,.62,.125,.25,.5, 1., 2. mm. The snes for bed-materal analyses are.4,.62,.125,.25,.5, 1., 2., 4., 8., 16., and 32. mm. Method of analyss.-n the method of analyss column, the symbols should be recorded n the same order that the methods were used for the analyss. For example: SBWC VPWC SPWC VPN SV The symbols are explaned n the headnotes and are standard. Water Temperature Temperature s an mportant physcal characterstc of water, and nformaton on water temperature s a necessary part of any study of water qualty. t s also an mportant parameter needed to compute total-sedment dscharge. A temperature observaton should be obtaned wth each chemcal-qualty or sedment sample. A temperature record may consst of a tabulaton of maxmum and mnmum observatons, once-daly observatons, or observatons obtaned durng perodc vsts to a staton. A contnuous temperature record may be obtaned from one of the many devces that sense and record fluctuatons of water temperature on a contnuous chart. Maxmum and mnmum temperatures for each day are computed from the chart and lsted as llustrated n fgure 3. A tabulaton of once-daly temperature observatons obtaned by feld personnel or contract observers s llustrated n fgure 4. The form shown n fgure 4 s a modfed 9-211C. Those observatons taken daly or more frequently wl be ncluded r? the tables of annual reports ; observatons obtaned at nfrequent vsts to the staton wl be publshed n conjuncton wth other data, such as the tabulaton of partcle-sze data on form 9-265b (fg. 2) or perodc sedment data (fg. 45). The completed tabulatons (fg. 3 or 4) ncludng maxmum and mnmum values are sent to the records-processng center where they are prepared for publcaton. The tabular data must be complete, that s wth an entry n each space. f no

11 6,

12 7 f a + e a f + L + (u $ -.- x a" Q Y E a P ( 7 E m L-

13 ~ 8 TECHNQUES OF WATER-RESOURCES NVESTGATONS value s avalable, a leader (. ) should be placed n the blank space. Although temperature data have been publshed by the Geologcal Survey n degrees Celsus snce October 1967, many temperature measurements are made wth a Fahrenhet thermometer and converted to Celsus when recorded on the permanent laboratory and feld sheets. Thermograph records may be converted drectly to Celsus by template, or the values may be tabulated n Fahrenhet (fgs. 3, 4) and the converson to Celsus made by dgtal computer. Values recorded on dgtal tape by temperature montors also may be converted by computer. All other temperature values, ncludng the extremes values for the perod of record, should be converted to Celsus (table 1) n Table 1.-Temperature converson table to nearest.5 degree [The numbers n the center columns refer to temperatures, ether n Celsus or Fahrenhet, whch are to be converted to the other scale. f convertng Fahrenhet to Celsus, the equvalent temperature wll be found n the left columns. f convertng Celsus to Fahrenhet, the equvalent temperature wll be found n the rght columns] to to to to ~ ~ 29. ~ ~ ~ O , f

14 1 the feld. Temperature data are to be observed, reported, and publshed to the nearest.5 degree Celsus. COMPUTATON OF FLUVAL-SEDMENT DSCHARGE 9 Suspended-Sedment Concentraton Sedment concentraton may be determned as the rato of the weght of the sedment to the (1) weght of the water-sedment samplse, (2) weght of the water n the water-sedment sample, or (3) weght of the pure water equal n volume to the volume of the sample. Dscharge-weghted concentraton s usually determned by the frst method and s the concentraton determned by the laboratory and referred to n ths manual. Because of convenence n the laboratory, t s determned n parts per mllon and s defned as the dry weght of sedment dvded by the weght of the watersedment mxture multpled by 1 mllon. As the concentraton s publshed n mlgrams per lter, however, the values determned n the laboratory must be converted to mllgrams per lter pror to computaton of sedment dscharge or publcaton. The dscharge-weghted mean concentraton n the vertcal generally s obtaned from depth-ntegrated samples obtaned wth standard velocty-weghtng samplers. The mean concentraton n the vertcal also may be obtaned from pont samples, whch represent equal unts of depth by (1) weghtng each sample by the velocty at each samplng depth or (2) recordng the samplng tme for each sample and usng the weght of the sample collected per second n leu of pont velocty to weght each sample. A dscharge-weghted mean n the vertcal also may be obtaned from a composte of pont sarnples f all sarnples n the vertcal are taken for an equal perod of samplng tme (U.S. nter-agency Commttee on Water Resources, 1963, p. 46-5). The dscharge-weghted mean concentraton n the cross secton may be computed from the mesm concentratons of the several sampled vertcals. f the sampled vertcals represent centrods of equal dscharge (ED1 method) (Guy, 197), the mean concentraton s the average of the several vertcals or s the mean of the composted samples, provded all samples are of the same volume. Thus, samples obtaned by the ED1 method that are to be composted for partcle-sze analyss must be the same volume. Samples collected at centrods to defne lateral dstrbuton of sedment n the cross secton should be analyzed ndvdually and, therefore, do not requre an equal volume of water n each sample. f the sampled vertcals are unformly spaced and the same transt rate s used for all vertcals (ETR method) (U.S. nter-agency Commttee on Resources, 1963, p. 41), the mean concentraton s the rato of the total weght of sedment to the total weght of the water-sedment mxture n all samples. Hence, samples collected by the ETR method must be composted ether n the laboratory or arthmetcally, because the concentraton of any ndvdual sample s relatvely meanngless. Concentraton data obtaned to compute sedment dscharge should defne the vertcal and lateral dstrbuton of concentraton n the cross secton and the varaton of the mean concentraton wth tme. Each sample obtaned at daly and perodc statons s analyzed for concentraton, and the results are lsted n the concentraton notes (fg. 5). Concentraton notes also nclude the date and tme and dentfy the samplng and laboratory procedures. Samples may be composted for analyss or analyzed ndvdually. Compostng, as used here, s the practce of combnng the water-sedment mxture of all samples nto one contaner to determne the concentraton or partcle-sze dstrbuton. The mean concentraton of a composte sample s the rato of the total weght of the sedment to the total weght of watersedment mxture. Samples usually composted are those collected only to defne the average Concentraton n the cross secton, those collected for analyss of partcle-sze dstrbuton, and those collected by the ETR method. Samples analyzed ndvdually are those collected to defne the vertcal or lateral dstrbuton of concentraton n the stream

15 TECHNQUES OF' WATER-RESOURCES NVESTGATONS

16 COMPUTATON OF FLUVAL-SEDMENT DSCHARGE 11 cross secton. Mean concentraton n the cross secton, or vertcal, s computed by weghtng the concentraton of each sample by the ncrement of dscharge t represents. Examples of concentraton notes are shown n fgure 5. Samples ndvdually analyzed are the sx-bottle sample of December 12 and the two-bottle sample of December 13. All other samples collected December were. composted. The samples collected from 122 to 135 hours December 12 were obtaned to determne the relaton between the mean concentraton n the cross secton and the mean concentraton at the fxed samplng statons. The average concentratons for the fxed samplng staton at 122 to 1225 hours and 13 to 1355 hours and for sx vertcals n the cross secton at 1235 to 125 hours are crcled. Adequacy of data A contnuous evaluaton of concentraton data must be mantaned to nsure that suffcent samples are obtaned and that the samples are of acceptable qualty. The stepby-step preparaton of records offers a contnung base for cross consultaton among personnel responsble for records, laboratory, and feldwork to evaluate the overall effcency of the samplng program and to determne f the quantty and qualty of the basc data meet desred standards. Errors n concentraton values usually occur because of smple mstakes n samplng procedure or because too few samples were obtaned to cover the natural random varaton n concentraton and sne gradaton of transported sedment. A descrpton of the samplng procedure s gven by Colby (1963, p. 4), by the U.S. nter-agency Commttee on Water Resources (1963), and by Guy and Norman (197). Factors that should be evaluated regularly are (1) the number of samples collected n each vertcal, (2) the number of vertcals sampled n each cross secton, (3) the number of samples wth respect to tme, and (4) the relaton of the concentraton n the sngle samplng vertcal to average concentraton n the cross secton. The number of samples requred n each vertcal and the number of vertcals whch must be sampled to determne the mean concentraton wthn acceptable lmts may vary wth locaton and tme. A study of the varaton of concentraton n sand-bed streams s gven by Hubbell (196), and a statstcal method for determnng the number of samples requred s descrbed by Guy (1968). Addtonal nformaton s avalable n Guy and Norman (197). Relaton between sngle-vertcal and cross-sectonal concentratons f sedment samples are obtaned routnely at a sngle vertcal n a cross secton, the relaton of the concentraton of the snglevertcal sample to the mean concentraton n the cross secton must be determned pror to computaton of sedment dscharge. Ths relaton, n the form of a coeffcent, s determned by an analyss of cross-secton concentraton data. deally, suffcent samples should be obtaned routnely n the cross secton to defne the mean concentraton both n tme and space, and f cost were of no concern ths procedure mght be selected for all operatons. n practce, however, we obtan a computaton of routne daly samples at from one to three vertcals plus less frequent but more comprehensve samples at suffcent vertcals n the cross secton to defne mean concentraton n the cross secton. Ths mean concentraton s used to determne the departure of the concentraton observed at the snge vertcal, or fxed-samplng vertcal, from the mean concentraton n the cross secton. Ths nformaton should be used (1) to relocate the fxed-samplng staton at a vertcal that s more representatve of the average stream concentraton or (2) to determne a coeffcent to convert the concentraton of the fxed-vertcal sample to the mean value for the stream cross secton. The adequacy of the sample at the fxed vertcal may be determned by an nspecton and analyss of the data for statons wth unform concentratons n the cross secton and by statstcal analyss at statons where varaton

17 12 TECHNQUES OF WATER-RESOURCES NVESTGATONS n sedment concentratons exceed the de- centraton n the cross secton to the consred accuracy (Hubbell, 196). centraton determned by daly samples at a fxed staton (box) s computed on the Cross-secton coeffcent forms shown n fgures 6 and 7. Ths rato The rato of the average sedment con- 1 s referred to as the cross-secton coeffcent. Fgure 6.-Tabulaton of sedment dafo n the cross secton.

18 COMPUTATON OF FLUVAL-SEDMENT DSCHARGE 13 Fgure 7.-Tabulaton of sedment data n the cross secton. The manner n whch the coeffcent s appled depends on the cause of the lateral varaton n the dstrbuton of sedment con- centraton. Ths varaton may be caused, among othser reasons, by proxmty and quantty of trbutary nflow, bed form, chan-

19 14 TECHNQUES OF WATER-RESOURCES NVESTGATONS ne1 alnement, source and type of sedment, season, and dscharge. Based on these condtons, each record should be analyzed n detal to detsrmne the most effcent and accurate manner for applcaton of the coeffcent. n addton to usng the data to adjust the current concentraton values, coeffcent analyss also may be used to reevaluate the samplng methods and the locaton of the samplng vertcal at the staton. Ths may make t possble to adjust the samplng locatons so that a coeffcent that s nearly equal to 1. wll exst for all condtons of flow. Common methods for determnng daly coeffcents nvolve the correlaton of the cross-secton coeffcent wth season and gage heght or dscharge. As an example, coeffcent values for the San Joaqun Rver near Vernals, Calf., for the 1963 water year (fg. 7) are plotted aganst dscharge and season (fg. 8). The correlaton of coeffcent wth dscharge s poor ; however, the correlaton wth season ndcates a possble trend. Ths trend was nvestgated by plottng the values of the coeffcent on the annual hydrograph of dscharge and concentraton (fg. 9). The seasonal effect ndcated on the hydrograph ndcates a coeffcent of about 1. durng the late summer and autum, less than 1. durng the frst few months of the storm season (February, March, and Aprl), and more than 1. durng the sustaned hgh dscharge durng the rrgaton season ; ths effect s verfed by the repetton of ths trend durng successve years. Sometmes coeffcents show a reasonable correlaton wth stage, as ndcated n fgure 1. The values of the coeffcent were determned for 2-percent ncrements or less for the correspondng range n stage (gage heght) and tabulated n the fgure. These c z w : s W oo O O - / DSCHARGE. N THOUSANDS OF CUBC FEET PER SECOND z W p 1. L W O - A n U o o - - Fgure 8.-Relaton of cross-secfon coeffcent to dscharge and season for San Joaqun Rver near Vernals, Calf.

20 COMPUTATON OF FLUVAL-SEDMENT DSCHARGE, San Joaqun Rver near Vernals. Calf.,1963 water year pedment concentraton Watmr dschwgo Oct26-Jan 15 1.! 5. z ln8 K W b 1.o W b. w a lo : K W!- 2 Oct OCT NOV D EC JAN MAR Water dscharge - r /. July Sedment concentraton 2. - /Coeff. engr. box/x sect 1- /JL-v--J 1. - " - v.5-3'.96 / Aug 1-Septl Junell Sept Junel "2 Sept May ; :g \;,ne May * Oct 1.96 APR MAY JUNE JULY AUG SEPT 5 1 Fgure 9.-Water dscharge, sedment concenfraton, and coeffcents for correctng observer's sngle-vertcal samples to cross secton. \ values may be used to correct daly concentraton values or concentraton values for ntervals of a subdvdred day. The average coeffcent for the Sacramento Rver at Red Bluff (fg. 6) was assumed to be 1., and no correcton was made to the daly concentraton values, even though the ratos of ndvdual measurements ranged from.83 to Ths example llustrates that the applcaton of a coeffcent, as n applyng a ratng shft to a gage-heght value, s a matter of judgment based on the data avalable. The rato of 1/9 = 1.11 ndcates a 1-percent (plus) error, and a correcton ordnarly would be made. However, the dfference of 1 mg/l (mllgram per lter) between the cross secton and the box sample may be the result of error n laboratory procedures and the result of roundng numbers ; therefore, for all practcal purposes, such coeffcents are gnored. A varaton of a few mllgrams per lter above 5 mg/l also s consdered neglgble, and a coeffcent s not appled f the ndcated correctons

21 TECHNQUES OF WATER-RESOURCES NVESTGATONS Range, feet Correcton < n U.9 GAGE HEGHT. N FEET Fgure 1.-Relaton of cross-secton coeffcent to gage heght. are random. Coeffcents should be appled, however, f all correctons are n the same drecton and f the trend perssts seasonally and s evdent n the record for precedng years. Varaton wth tme The number of samples requred to defne the varaton of concentraton wth tme may be dffcult to determne from vsual nspecton of the concentraton notes. The effectveness of the samplng schedule should be evaluated after each storm event. An effcent way to evaluate the adequacy of samplng s to plot the concentraton values on the gage-heght record as suon as possble after the data are avalable. Plottng and evaluatng the concentrton data wth respect to tme are descrbed n the secton Development of a Temporal Concentraton Graph. Analyss of cross-secton concentraton daba Concentraton values obtaned from cross-secton samples are lsted on the multple-purpose form shown n fgures 6 and 7, whch may also be used to (1) lst partclesze analyses and compute the nstantaneous dscharge requred to complete tabulaton of sze analyses (fg. 2) and (2) lst samples obtaned at perodc statons or mscellaneous stes. The tabulaton of cross-secton samples s used to compute the coeffcent needed to adjust the concentraton of samples obtaned at a sngle, or fxed, vertcal to the average concentraton determned by cross-secton samplng. The average concentraton of the cross secton determned from multple-vertcal samplng s recorded n column 4 (fg. 6) and the concentraton for the correspondng date and tme of the observer s frxed-samplng vertcal or three-vertcal set s recorded n column 5. The coeffcent used to adjust the observer s samples s the rato of a/b and s recorded n column 6. The gage heght at the tme of samplng s obtaned from the corrected gage-heght record and recorded n column 7. Any gage heght recorded on the bottle, partcularly by the observer, should be consdered as

22 COMPUTATON OF FLUVAL-SEDMENT DSCHARGE 17 uncorrected data and generally used only to fx the sample n tme, to ad n makng necessary correctons to the pen record, or to estmate mssng gage-heght records. The gage heght forms the base for computatovl of the nstantaneous water dscharge and the sedment dscharge. An evaluaton of the qualty of the coeffcent for a gven samplng desgn may be made by the method developed by Guy (1968). Samples collected by the ED1 method must have nearly equal volumes for each samplng vertcal f they are composted ; otherwse the bottles must be analyzed ndvdually, and the concentratons for each cross-sectonal set of samples averaged. f ths procedure s not followed, the qualty of the data obvously s affected. Experence has shown that suspended samples from sandbed streams occasonally wl be contamnated wth varyng quanttes of bed materal. Consderable judgment must be exercsed n the feld and laboratory to nsure that these samples are elmnated from the composte. The determnaton of sedment dscharge requres the use of water dscharge ; therefore, the accuracy of the computed value for sedment dscharge s dependent on the accuracy of measurements of both water dscharge and sedment concentraton. n many locatons, the water dscharge can be determned to a hgh degree of accuracy from the relaton of dscharge to stage. f, however, the relaton of dscharge to stage s not stable, as for most sand-bed streams, or an accurate relaton s not avalable, as for a new staton, a measurement of watar dscharge s necessary at the tme sedment concentraton s sampled n the cross secton. Dscharge measurements and dscharge ratngs at gagng statons are dscussed by Buchanan and Somers (1965,1968) and Carter and Davdan (1965, 1968). An earler detaled descrpton of stream-gagng procedures s found n U.S. Geologcal Survey Water-Supply Paper 888 (Corbett and others, 1943). The evaluaton and applcaton of daly values of the cross-secton coeffcent are dscussed n the secton Cross-Secton Coeffcent. Development of a Temporal Concentraton Graph The next step n the computaton procedure for sedment dscharge s to translate ndvdual values of concentraton nto a contnuous temporal concentraton curve. Ths step may be reasonably smple f values for water dscharge or sedment concentraton do not vary greatly and (or) f suffcent samples are obtaned to defne adequately the changes n concentraton wth tme. Accurate results are obtaned from a concentraton curve defned adequately by samples because a large number of samples successfully ntegrate the many complex nterrelatons among varables affectng the avalablty and movement of sedment n streams (Guy, 197). Development of a temporal concentraton graph may be dffcult f too few samples were obtaned. Preparaton of the rconcentraton graph wl requre applcaton of theoretcal and practcal prncpals of sedmentaton. nadequate samplng results n a less accurate graph, and much more tme s requred to prepare the graph. Because of the extra tme, n addton to loss n accuracy, t s usually less expensve to collect addtonal samples than to estmate the concentraton graph. A samplng program for each staton should be desgned to obtan optmum results when the desred accuracy of record s balanced aganst the many physcal and economc condtons. A few samples properly spaced wth tme may adequately defne the concentraton of a flood event at certan statons, provdng that the personpel computng sedment dscharge have detaled knowledge of seasonal sedment trends for the complete range of flow condtons experenced. Lack of knowledge of these trends, such as at a new staton or a staton wth a large number of varable condtons affectng sedment eroson and transport, requres

23 18 TECHNQUES OF WATER-RESOURCES NVESTGATONS an ntensve samplng program. Successful staton operaton requres contnuous modfcaton of the samplng program to obtan the best accuracy possble wth a reasonable expendture of tme and effort. Concentraton data should be nterpreted and the graph drawn by personnel wth a knowledge of the samplng program, the physcal and cultural envronments affectng the stream regmen and sedment sources, and the fundamentals of sedment transport. After the graph s drawn, t should be revewed and modfed as requred pror to computaton of daly mean concentraton values and sedment dscharges. Changes n the graph are made easly at ths pont and may elmnate possble future recomputaton. Dffcultes may be encountered whle drawng the contnuous graph because of paucty of samples, unusual storm events, or perods of mssng recordg. Valuable gudance may be avalable from past records of sedment dscharge at the ste and at nearby stes. A study of these records before plottng the data and drawng the graph should be a requred part of the computaton procedure. Some of the factors that should be consdered pror to drawng the concentraton graph and examples of concentraton graphs are ncluded n the followng secton. Plottng symbols and scales Concentraton values are plotted on a gageheght chart or a copy of the chart. f an analog record of stream stage s not avalable because of the use of dgtal recorders, a plot of gage heght or dscharges from the dgtal record must be made for the mportant perods of changng stage and concentraton, such as durng rapd snowmelt or storm runoff. The symbols and scales used for plottng should be chosen carefully and, f possble, be consstent wth those used n precedng years. Suggestons relatng to the plottng of concentraton values and the choosng of scales are summarzed as follows: 1. Adjust concentraton values from parts per mllon to mllgrams per lter pror to plottng. 2. f necessary, adjust the plottng tmes for chart-tme correctons and travel tme between samplng ste and gage. 3. Plot the average value for each set of samples. ndvdual values of each bottle should be plotted f poor agreement exsts among bottles. 4. Use plottng symbols such as the followng : Observer samples-mean value. FJ Observer samples-ndvdual samples. A Techncan sample at observer s fxed staton (box). El Techncan cross-secton samplemean value. Partcle-sze sample. Use above syrnbols and crcle f sample analyzed for partcle-sze gradaton. 5. Use of a proper plottng scale facltates computaton and checkng, ncreases accuracy of daly mean concentraton values pcked from the graph, and provdes a vsual method for comparson and study of varous flood events ; therefore, (a) Use smple scales such as 1 to 1, 1 to 2, 1 to 5, or multples of 1 thereof, wth zero at the base lne. (b) Use as few scales as possble, but do not hestate to change scale as needed. (c) Planly mark each change n scale. Use prevous year s record as gude to scales. Use the same scale for all events of smlar magntude; such a scale provdes a vsual means for comparng and evaluatng graphs and asssts n development of characterstc curves that are extremely helpful n shapng the graph when ncomplete samplng data are avalable. 6. Use a maxmum heght of the graph 5-8 nches above the base lne ( mg/l) on the gage-heght chart. As the concen-,

24 COMPUTATON OF FLUVAL-SEDMENT DSCHARGE 19 traton decreases after a storm, change the scale when the concentraton graph approaches to wthn 1 or 2 nches of the base lne. Experence ndcates that personnel drawng a graph near the base lne tend to be nfluenced by the lmtng O-mg/l base lne, and therefore values determned from a graph approachng the base lne usually are hgh. 7. Choose a scale, f possble, so that concentraton values can be plotted to three sgnfcant fgures. For example, f a stream has concentratons that range from 3, to 4, mg/l, a scale of 1 nch= 5, mg/l allolvs a maxmum heght for the graph of 6-8 nches, and concentratons above 1, mg/l (2 nches) may easly be plotted to three sgnfcant fgures. Below 1, mg/l the scale can be read only to two sgnfcant fgures and should be changed. Theoretcal consderatons Consderable nformaton s avalable on theory of sedment transport and the factors affectng the avalablty of sedment for transport. Colby (1964a, p. A3) states that Relatonshps of sedment dscharge to characterstcs of sedment, dranage basn, and streamflow are complex because of the large number of varables nvolved, the problems of expressng some varables smply, and the complcated relatonshps among the varables. At a cross secton of a stream, the sedment dscharge may be consdered to depend: on depth, wdth, velocty, energy gradent, temperature, and turbulence of the flowng water; on sze, densty, shape, and cohesveness of partcles n the banks and bed at the cross secton and n upstream channels ; and on the geology, meterology, topography, sols, subsols and vegetal cover of the dranage area. Obvously, smple and satsfactory mathematcal expressons for such factors as turbulence, sze and shape of the sedment partcles n the streambed, topography of the dranage basn, and rate, amount, and dstrbuton of precptaton are very dffcult, f not mpossble, to obtan. References that wl ad n understandng the nterrelaton of some of the above-lsted varables and sedment dscharge are cted n pertnent text sectons and are lsted at the end of ths manual. Ths lst s by no means complete, but wll serve as a startng pont for those nterested n furtherng ther understandng of sedment transport. Study of past records A study of the varaton and range of suspended-sedment concentraton wth tme at a gven pont, or samplng staton, reveals many smlartes among dfferent flood events. A plot of concentraton values wth tme and wth flood stage wll defne graphs that can be used to estmate concentraton graphs for mssng perods or for nadequately sampled perods. The absolute values and duraton of these values may vary consderably from event to event; however, the shape of the temporal graph may be smlar among the several events. Thus, the frst step n drawng the concentraton graph s to study the plotted ponts for trends, sketch n the parts of the graph well defned by samples, and study those parts defned prevously-for the entre hstorcal record f necessary. A fle of hstorcal concentraton graphs that are characterstc of the varaton and range of suspended-sedment concentraton should be assembled to facltate the use of these graphs durng development of the temporal concentraton graph and to reduce the number of past records stored n current fles. Characterstc graphs may be dfferent for dfferent basns, and many characterstc graphs may exst for each staton. Relaton of water dscharge to concentraton The relato-n of water dscharge to concentraton s an mportant aspect to consder when developng the temporal concentraton graph. The varaton of water dscharge, as depcted by the contnuous graph of stage on an analog chart or a plot of bhourly dscharges from a dgtal record, provdes a valuable clue to the tme and magntude of changes n the sedment concentraton of the stream. The relaton between water ds-

25 2 TECHNQUES OF WATER-RESOURCES NVESTGATONS charge and sedment concentraton s not fxed. t s affected by many varables, and the varaton and range of concentraton durng one storm perod or durng one low or medum streamflow perod may dffer from the concentratons durng other perods, even though the streamflow may be dentcal or smlar. Theref ore, nterpretaton of concentraton data and the drawng of the temporal concentraton graph always requres consderaton of the varables that affect the relaton between water dscharge and concentraton. Avalablty of sedment s a major varable affectng sedment concentraton. Factors affectng avalablty are dscussed n detal by Guy (197) and n many texts. The avalablty for a short perod may be consdered relatvely constant, and curves characterstc of the relaton of water dscharge to concentraton for dverse storm perods, trbutary nflow, and seasonal effect may be assembled for ready reference. (See prevous secton and the secton on Examples of the Sedment-Concentraton Graph. ) Changes n natural avalablty of sedment may be caused by such events as forest fres 1- channel changes, landsldes, and mass wastng assocated wth or accelerated by catastrophc floods. These changes should be noted and consdered durng development of the concentraton graph. Avalablty of sedment also s nfluenced by the actvtes of man. Actvtes whch may cause rapd and large changes n sedment avalablty nclude road constructon, dam constructon, dversons, land-use changes, loggng, urbanzaton, and gravel mnng. Basn sze may affect the correlaton of concentraton and water dscharge and the shape of the concentraton graph. n general, the smaller basn has a more predctable relaton between water dscharge and concentraton than the large basn, whch s often affected by a larger number of varables. The Colorado Rver at Grand Canyon, for example, has trbutares affected by many varables. These trbutares nclude rvers wth large flows and very low concentratons as well as streams wth small flows and large concentratons. All these water and sedment condtons, plus regulaton by upstream dams, mposed on one downstream staton cause a large range n concentraton for a gven water dscharge. Other factors affectng th,e relaton between sedment dscharge and streamflow are lsted n the secton on Theoretcal Consderatons. Estmates for perods of mssng data The shape and magntude of the temporal concentraton graph for ndvdual rses have characterstcs based on the prncples prevously dscussed. A knowledge of the typcal patterns from past records s helpful when nterpretng the concentraton data and constructng the concentraton graph for perods of nadequate concentraton data. Concentraton data are consdered nadequate when a sgnfcant part of a record cannot be defned wthn probable lmts of 5 or 1 percent. The ef cent and reasonably accurate development of a contnuous concentraton graph or determnaton of sedment dscharge durng the perod of mssng data requres careful study, n whch experence and ablty to make sound estmates based on concentraton data collected durng other perods are most helpful. The length of the nadequately defned perod may range from 2 mnutes to several days. The short perod usually occurs on streams havng rapd changes of water dscharge and concentraton and very frequently occurs at the begnnng of a rse resultng from ntense ranfall. Ths stuaton s partcularly crtcal on streams n ard regons and on streams wth small dranage areas. Long perods of mssng data may occur because the samplng ste s naccessable durng floods or because of loss of equpment or samples. An estmated concentraton graph s preferable to drect estmates of sedment dscharge. Durng short perods of mssng data, a contnuous concentraton graph may be estmated accurately and used to compute daly mean concentraton and sedment ds-,

26 COMPUTATON OF FLUVAL-SEDMENT DSCHARGE 21 charge. Durng long perods of mssng data, an accurate estmate of concentraton may not be possble, and daly values of sedment dscharge must be estmated drectly from the hstorcal relaton between water and sedment dscharge by nterstaton correlaton or by comparson wth records obtaned at an upstream or downstream staton. A complete record of daly values facltates nterpretaton or statstcal evaluaton of the data by computer technques; therefore, f possble, estmates of both sedment concentraton and dscharge should be made. Durng perods that sedment dscharge was estmated drectly, daly concentraton values must be estmated ndependently of sedment dscharge f the perod ncludes rapd or large changes n concentraton or water dscharge. An ndependent estmate of daly mean Concentraton s necessary because publshed values of concentraton are tme weghted, and daly tme-weghted values of concentraton cannot be computed from daly values of water and sedment dscharge that represent perods of changng streamflow and concentraton. f an acceptable estmate of concentraton s mpossble, no daly concentraton wl be publshed, and a leader (..) wl be placed n the concentraton column. The methods or combnaton of methods used to estmate mssng data may vary from staton to staton and seasonally for the same staton. Each perod of mssng data, therefore, must be studed, and the best estmate made on the bass of exstng data and crcumstances ; regardless of the method chosen the estmate should be verfed by a second method. A partal lst of methods commonly used to estmate sedment data follows. Vsual comparson wth adequately defned concentraton graphs The vsual procedure, when supplemented by the two succeedng methods, probably s the most common and accurate method used to construct concentraton graphs for perods when data are nsuffcent. The prncples nvolved are dscussed n more detal else- where n the manual and especally n the sectons on Study of past records and Examples of the sedment-concentraton graph. Each staton should be sampled n detal durng suffcent runoff events to provde a catalog of the shape and magntude of the sedment curves pertnent to the staton. The shape of the concentraton graph wth respect to the gage-heght graph should be carefully consdered as to the tme the rapd ncrease starts, the tme of peak concentraton, and the slope of the recesson curve. Typcal concentraton graphs of the varous types, such as advanced, smultaneous, and laggng, are llustrated n fgures 11, 12, and 13. Hydrographc comparson wth records of upstream and downstream statons Hydrographc comparson s an excellent tool to check the accuracy of the concentraton record and samplng program, as well as to estmate perods of mssng records. Each record should routnely be compared wth adjacent staton rgcords wherever possble, and consderaton should be gven to sgnfcant natural and manmade dfferences that would account for dscrepances n the computatons. Short perods of mssng concentraton data can be estmated on the bass of the concentraton curve for an adjacent staton. Longer perods of mssng sedment data can be estmated by comparng values of daly sedment dscharge plotted on hydrograph form (fg. 25). Water-sedment relaton curves The relaton between water dscharge and sedment dscharge may be expressed by an average curve. Ths curve s called a sedment-transport curve and s used frequently to estmate perods of mssng data or to extend records. The types of sedment-transport curves are numerous, and the selecton of the correct type for each use s mportant. Accordng to