•GOVERNMENT Of THE REPUBLIC Of INOONESIA

MINISTRV Of PUBLIC WORKS

OIRECTORATE GENERAL Of WATER RESOURCES OEVElOPMENT

PROGRAMME Of ASSISTANCE fOR THE IMPROVEMENT

Of HYDROLOGIC DATA COLLECTION, PROCESSING

AND EVALUATION IN INDONESIA

COMPUTATION OF FLUVIAL SUSPENDED SED IMENT OISCHARGE

b y

M. Fr o v o qli o ,

~. SOCIETE CENTRALE

~~ POUR L" EQUIPEMENTDU TERRITOIRE

ftlERUlIONAI. INTERNATIONAL

Bandung, May 1981

COMPUTATION OF FLUVIAL SUSPENDED SEDIMENT DISCHARGE

by

M. Travaglio

Bandung, May 1981

Table of Contents

Paqe

Introduction . . . . . 1

4. Computation of Daily Sediment Discharge

5. Rating Curve Technique • • • • • • • • • •

Annex - Drawing and Extension of the Rangkasbi tung Rating Curve

1. Relation between Single-Vertical and

Cross-Sectional Concentrations • 3

8

11

22

• . . 28

35

Temporal Concentration Graph • •

Examples of the Sediment-Concentration Graph •

2.

3.

..

1

INTRODUCTION

Given a gauging station in a stream, let us assume that at a given

time bath the mean concentration, c,and the water discharge, Q , are avail­

able, then the suspended sediment discharge, in weight of material per unit

time denoted Qsi' is determined by multiplying these two quantities, so we have:

(1)

where k is a factor depending on the units employed and the_index i indicates

that the instantaneous sediment discharge is calculated.

'ro calculate the sediment load over a given period of time, T ,

we have to integrate over this period, so we have •

= S: kCQ dt (2)

(mg/l)

Usually

and Q

Q . is in tons per day (tons/day), C in milligrams per literS1 . 3

in cubic meters per second (m /s) and consequently k is

equal to 0.0864.

In fact, in most cases no continuous records of concentration are

available and one has to deal with individual values of concentration. Ob­

viously to define adequately the changes in c~ncentrationwith time a suffi­

cient number of samples should have been obtained which is the only way to

integrate the many variables which intervene in the highly involved process

of erosion and movement of sediment in streams. The following quotation from

COLBY shows the complexi ty of the phenomenums.

"Relationships of sediment discharge to characteristics ofsediment, drainage basin, and streamflow are complex becauseof the large number of variables involved, the problems ofexpressing some variables simply, and the complicated rela­tionships among the variables. At a cross section of a stream,the sediment discharge may be considered to depend: on depth,width, velocity, energy gradient, temperature, and turbulenceof the flowing wateri on size, density, shape, and cohesive­ness of particles in the banks and bed at the cross section

and in upstream channels 1 and on the geology, meterology,topography, soils, subsoils and vegetal cover of thedrainage area. Obviously, simple and satisfactory mathe­matical expressions for such factors as turbulence, sizeand shape of the sediment particles in the streambed,topography of the drainage basin, and rate, amount, anddistribution of precipitation are very difficult, if notimpossible, te obtain."

Prior to any computation basic data should be collected, as pointed

out by the U.N. Sediment Specialist, "compilation of data for daily records

takes a long time to complete so the water discharge record for these sta­

tions should be given a high priority and supplied to the Hydrochemistry

Branch at an early date and so should be the following items":

Copy of the water level strip chart for the entire'year

Listing of aIl discharge measurements

Copy of aIl rating tables (or/and curves) used during

the year

Description of the cross-section (station analysis)

Copy of daily water discharge and water level.

An efficient way to evaluate the adequacy of sampling is to plot

the concentrations values on the gauge-height record as soon as possible

after the data are available.

In the following paragraphs we draw heavily on George Poterfield's

"Computation of Fluvial Sediment Discharge" - Techniques of water­

Resources Investigations of the U.S. Geological SUrvey, Book C3

Chapter C3.

2 .

3

1. RELATION BETWEEN SIN:iLE-VERTICAL AND CROSS-SECTIONAL CONCENTRATIONS

If sediment samples are Obtained routinely at a single vertical in

a cross section, the relation of -the concentration of the single-vertical

sample to the mean concentration in the cross section must be determined prior

to computation of sediment discharge.- This relation, in the form of a coeffi­

cient, is determined by comparison of the results of cross-section samplings

carried out by teams of the Hydrochemistry Branch with concentrations of sam­

pIes taken at the same time by the observer.

The so-called cross-section coefficient defined as the ratio of the

real mean concentration ta the concentration at a single vertical may vary with

the season and/or the gauge height. In figure l, cross section coefficient is

plotted versus discharge and time of the year, it can readily be seen that the

correlation with discharge is poor; however the correlation with season indi­

cates a possible trend •

. 1.41 1 1 1 1 1 1 1 1 1 1 1

1.2 1- .-~

00 0z 0III 0U 1.0() 0

~ 0...III0 0 0CJ

0.8 ~0 0 -

0.61 1 1 1 1 1 1 1 1 1 1

0 2 4 6 8 10 12DISCHARGE. IN THOUSANDS OF CU81C FEET PER SECOND

12~ J 1 1 1 1 1 1 1 1

1.1 -~

00z 0 0lOI

Ü 1.0 0 ~ ~ 0 0~... 0 '"' '"' -0III 00CJ 0 0

0.9 1-.00 -

0.8 1 1 1 1 1 1 1 1 1 1 1 1 10 N D J F M A M J J A S

TIME. IN MONTHS

figure l.--Ielotion of crou-MCfion coeflici.nt to dilCho'lI. ond MOlOn for Son Jooctuin Ri"•• IlHr Ve...olls. CaIU.

4

In figure 2 a reasonable correlation with stage is indicated and

J.2

. Ran ••• ,..t Correction

<18 1.018.5-19.5 1.01

0- 19.5-20.5 1.02z 20.5-23.5 1.04... 1.1 23.5-24.5 1.05Ü~ 24.5-25.5 1.01

'"" 25.5-26.5 1.09...0 26.5-27.5 1.10u 27.5-28.5 1.11z 28.5-29.5 1.120;: 30.0- 1.13u...1/1,n1/1 1.00a::o

10

0.9 """"- --l. ---'L- .l...- "- ~

5

Fi"ur. 2 -R.lotion of crou·section coefficl.nt ta "0". heI"ht.

thus the values may he used to correct concentration Obtained at a single

vertical.

Tc evaluate the quality of a cross-section coefficient the following

procedure developped by GUY may be used. Two groups of data are involved for

adjusting the concentration of single-vertical sample, namely, a list of the

concentrations of the single-vertical samples and a list of the concentration

of the cross-section samples.

An example is presented in table 1 with the purpose of testing the

quality of the mean of a single group, first the data are converted to a base643 x 100

of 100 (the percentage each observation is of the mean), i.e. 104 = 618 •

then the sum of the squared deviations from the base 100, i.e. 16 = (104-l02}2,

is determined, and these data are entered on the alinement chart given in

figure 3.

Table 1

B... otl00

MS 10& 11118 100 0103 ll8 11M9 1. •llB7 ll8 21

5

1Ium••••••••••••••••••••••••••Mean•••••••••••••••••••••.•••

lIOllO •••••••••••••• 1:1118 .

, -ClOt' 10 chAn•• f ••"" tG .......Numbeor. o, umpl.. Iif'v.l 0' .,p.hcance

ln nw.~uremif'nt 9!» ao 70 50

1 101 0.49 o.ll Q.16l 1 41 ..~ "7 .284 • as .70 .~l .U~ • JO J2 .!i6 .n6 • 28 .7l .tI .J68 1 2~ .14 ~lI .JI

ro l.2l .76 .60 dtI~ 1.22 .77 .60 dt

,20 t.ll.77 .61 ..0JO .... l!J .71 .6. .«)

10.1Y.IQ1000I000Osoœ0000

1000

8 2000..0z 1000c 100..

l>OOJz !>OO

0 ~

0 JOlI....~C

Il..Z 1002 !lOc eosë ~

400 JO•s 200..~ III

Z8

:> 6.. ~

4

'.

JO

"20::J~ I~eZ 10

.. 8~ ~... ~

{••'''P~ ~----- '" .:sIr

:D::1::JZ

• 2olE•...~z::: 4

"'-_----------~ !tr 6

g 7

'" ." lia10..

40

sa60

JO

Fi9ur~ 3 ,-Alinemenl cheri 10 determine Ih~ quality of themean for a 'fl'OUP of samples given the lum of Iqùoreddevielions Qt' th 9O.percent level of lignificance. Thequelily of Ihe "'COli 'or other levell il oblained by ule 01Ihe faclors shown. Alter Guy (1968, p. 8166).

6

In the example the number of samples if 5 the sum of the square

deviations is S2 and the resulting quality of the mean for the group, that

is, 6lS, expressed in percent error is + 4.5\ at the 90 percent level of

significance. For the 95 percent level of significance we should multiply

the result by 1.30 and for the SO percent level by 0.72 obtaining :!:. 6.0~and 3.0\ respectively.

In table 2 an example ispresented ta test the quality of the cross­

section coefficient. Two cross-section concentrations and four single-vertical

concentrations are used, the same procedure as for testing the Mean of a715 . 2

group is followed for each group, for instance 99 =720 x 100 and 1 = (100-99)

600 2likewise 104 =624 x 100 and 16 = (104 -100) ; however, it is the sum of the

square deviations for the two groups which is calculated and entered on the

alinernent chart given in fig. 4.

Buaple l"1li1'1

Cross seetlon _

Single vertical. _

Bue 01 100J,f~_- Mean

eentrll&1OalI Coneen&raUonl 8umof~ared(m«/I) dn

{7l"} 720 {Igr 1725 1r r 16606 600 lOI 1600 100 0570 95 25

44 (total)

Table 2

In the example the number of samples are 2 and 4 and are represented

in the center scale by, .4 , (the dot stands for the number 2) the sum of the

square deviations is 44 and the resulting quality of the cross-section coef­

ficient expressed in percent error is ~ 6\ at the 90 percent level of signi­

ficance. For a different level of significance the terms "degreesof freedan"

is defined as two less than the total number of samples in bath groups, in

the foregoing example the total number of samples is 6 sa the degrees of

freedOOl is 4 ( 6 - 2 ) and the corresponding result for the 95 percent level

of significance will be + 6 x 1.30 = ~ 7.S percent likewise for the SO percent

level of significance one obtains + 6 x 0.72 = + 4'.

7

2000

1000

100

400

f .ctal ta ch.nll. lelult to ctve"

0.""'011.....1at l'inifle.ne.

".edam '5 80 70 50----1 2.02 0.4' 0.31 016

2 1.47 .65 .47 .le3 1.35 .70 .53 .32." 1.30 .72 .56 .35

5 1.21 .73 .57 .166 1.26 74 !II .37.·1 1.24 .75 .59 ..JI

10 1.23 .76 .60 .JI15 1.22 .77 .60 .JI 2JO 1.21. .77 .61 40

)(l

620

i~15~15~20

e~15 4

itr-6 llI:0llI:

• 1llI: 5

8--4 w.....!.-6 ...o. Z 6w

03_------- ullI:

.4 w6-

05Il... 1

• 3Zw

o. Ü 9ii:... 10...

• 20u

o ~ ...0

l=:j0(~

0

20

o 2

...ollI:wIII

~r

llI:o...0(z::EoZwooz0(

6

5

•10

)(l

10

100

60[ .."",,,. -----~

~------- iw::1~

z

!CIlwC::E~

... - 20oIII::E~CIl

oW..Jo~

~... 200oIIIZ0(w::EzoowIII0(CD

IIIZo;::0(

swoowllI:0(~s

3.

2

EXPLANATION rOR SMAllERNUMBER or SAM PlES

(CENTER SCAlEl

o =1 o =3 60

• =2 70

Figure 4-Alinement chart tci de(ine the quality af a coefficient for a given sampling de.ign and pooledlum' of .quared deviation. at the 9O.percent level of ligni(icance. The quality fOr other level. isobtained by ule of the facton .hown. The expIanation und on the center scale indicales theImaller number of the two grouP' of semples used.

8

2. TEMPORAL CONCENTRATION GRAFH

The drawing of a temporal concentration curve fram individual values

of concentration is the first ste,p in the computation of sediment discharge.

It is not only useful to study the variations of concentration with time but

to estimate concentration graphs for missing periods or for inadequately sam­

pIed periods. For a given watershed, though the absolute values of concentra­

tion may vary considerably from event to event, the shape of the concentration

graph presents characteristics which are likely to be the same for runoff

events of the same order. Each station should be sampled in detail during suf­

ficient runoff events to provide a catalog of the shape and magnitude of the

sediment curves pertinent to the station.

The following is drawn fram Porterfield:

Oevelopment of a temporal concentration graph may hedifficult if tao few samples were obtained. Preparationof the concentration graph will require application oftheoretical and practical principals of sedimentation.Inadequate sampling results in a less accurate graph, andmuch more time is required to prepare the graph. Becauseof the extra time, in addition to loss in accuracy, it isusually less expensive to collect additional samples thanto estimate the concentration graph.

A sampling program for each station should be designedto obtain optimum results when the desired accuracy ofrecord is balanced against the many physical and economicconditions. A few samples properly spaced with time mayadequately define the concentration of a flood event atcertain stations, providing that the personnel computin~

sediment discharge have detailed knowledge of seasonalsediment trends for the complete range of flow conditionsexperienced. Lack of knowledge of these trends, such asat a new station or a station with a large number of vari­able conditions affecting sediment erosion and transport,requires an intensive sampling program. Successful stationoperation requires continuous modification of the samplingprogram to obtain the best accuracy pos~ible with a rea­sonable expenditure of time and effort.

Concentration data should be interpreted and the graphdrawn by personnel with a knowledge of the sampling pro­gram, the physical and cultural environments affecting thestream regimen and s~diment sources, and the fundamentalsof sediment transport. After the graph is drawn, it shouldhe reviewed and modified as required prior to computationof daily mean concentration values and sediment discharges.Changes in the graph are made easily at this point andmayeliminate possible future recamputation.

Difficulties may be encountered while drawing :the conti­nuou~ graph because of paucity of samples, unusual stormevents, or periods of missing records. Valuable guidancemay he available from past records of sediment dischargeat the site and at nearby sites. A study of these recordshefore plotting the data and drawing the graph should be'a required part of the computation procedure. Sorne of the .factors that should be considered prior to drawing the con­centration graph and examples of concentration graphs areincluded in the following section.

Concentration values are plotted on a gage-heiqht chartor a copy of the chart. If an analog record of stream stageis not available hecause of the use of digital recorders, aplot of gage height or discharges from the digital recordmust be made for the important periods of changing stage andconcentration, such as during storm runoff.

If possible a scale should he chosen so that concentra­tion values can be plotted to three significant figures.

Study of past records

9

A study of the variation and range of suspended-sedimentconcentration with time at a given point, or sampling station,reveals many similarities among different flood events. Aplot of concentration values with time and with flood stagewill define graphs that can he used to estimate concentrationgraphs for missing periods or for inadequately sampled periods.The absolute values and durationof these values may vary con­siderably from event to event; however, the shape of the tempo­ral graph may he similar among the ~everal events. Thus, thefirst step in drawing the concentration graph is to study theplotte~ points for trends, sketch in the parts of the graphweIl defined previously - for the entire historical record ifnecessary.

A file of historical concentration graphs that are charac­teristic of the variation and range of suspended-sediment con­centration should be assembled to facilitate the use of thesegraphs during development of the temporal concentration graphand to reduce the number of past records stored in currentfiles. Characteristic graphs may be different for differentbasins, and many characteristic graphs may exist for each sta­tion.

Estimates for periods of missing data

The shape and magnitude of the'temporal concentration graphfor individual rises have characteristics based on the princi­pIes previously discussed. A knowledge of the typical patternsfram past reoords is helpful when interpreting the concentra­tion data and constructing the concentration graph for periodeof inadequate concentration data.

Concentration ddta are considered inadequate when asignificant part of a record cannot be defined withinprobable limits of 5 or la percent. The efficient andreasonably accurate development of a continuous concen­tration graph or determination of sediment dischargeduring the period of missing data requires carefui study, .in which experience and ability to make sound estimatesbased on concentration data collected during other periodsare most helpful. The length of the inadequately definedperiod may range from 20 minutes to several days. Theshort period usually occurs on streams having rapid changesof water discharge and concentration, and very frequentlyoccurs at the beginning of arise resulting from intenserainfall. This situation is particularly critical onstreams with small drainage areas. Long periods of missingdata may occur because the samplingsite is inaccessableduring floods or because of loss of equipmentor samples.

An estimated concentration graph is preferable to directestimates of sediment discharge. During short periods ofmissing data, a continuous concentration graph may be esti­mated accurately and used to compute daily mean concentra­tion and sediment discharge. During long periods of missingdata, an accurate estimate of concentration may not be pos­sible, and daily values of sediment discharge must be esti­mated directly from the historical relation between waterand sediment discharge by interstation correlation or bycomparison with records obtained at an upstream or downstreamstation. A complete record of daily values facilitates inter­pretation or statistical evaluation of the data by computertechniques; therefore, if possible, estimates of both sedimentconcentration and discharge should he made. During periodsthat sediment discharge was estimated directly, daily concen­tration values must be estimated independently of sedimentdischarge if the period includes rapid or large changes inconcentration or water discharge. An independent estimate ofdaily mean concentration is necessary because published valuesof concentration are time weighted, and daily time-weightedvalues of concentration cannot be computed from daily valuesof water and sediment discharge that represent periods ofchanging streamflow and concentration. If an acceptable esti­mate of concentration is impossible, no daily concentrati.onwill be published, and a leader ( •• ) will he placed in theconcentration column.

The methods or combination of methods used to estimatemissing data may vary from station to station and seasonallyfor the same station. Each period of missing data, therefore,must be studied, ar.d the best estimate made on the basis ofexisting data and circumstances; regardless of the methodchosen the estimate should be verified by a second method.

la

• EXAMPLES OF THE SEDINENT-CONCENTRATION GRAPH

The preceding sections discuss many reasons for the va­riation of sediment concentration with time and discharge.This section presents examples of (1) the relation betweenconcentration and discharge (or gage height) for basins ofvarious size, climatic conditions, geology, and land useand (2) variations of this relation that may occur in alarge basin.

Figure 5 is an example of the typical, sharp dischargepeak and concentration graph produced when high-intensityrainfall of short duration occurs over a small basin andthe stream channel is dry or has only low flow prior to thestorm. The typical concentration graph will rise rapidlyand peak at or slightly before the discharge peak, afterwhich it decreases rapidly, generally at a faster rate thanthe recession in water discharge. The shape of the recessioncurve usually is parabolic. At the discharge peak, the con­centration may fluctuate rapidly for a short period beforestarting to recede. The duration of the concentration peakis seldom greater than that of the water-discharge peak. Notethat the concentration did not start to increase prior tothe increase in water discharge.

An example of a concentration graph of a stream in asmall basin, Corey Creek near Mainesburg, Pa., (31.6 krn2) whenthe runoff increased at a slower rate is shown in figure 6.Thi.s basin generally has better vegetal cover, less intenseprecipitation, a more humid climate, and a higher base flowthan the basin illustrated in figure 5.

11

...ClctoC:ru

'"s

l\\\\\\\\\,\\\ ,

f-----I -,---~ . .......

'S.chmenl concenl'.'_ "--

liME. IN HOURS

zo;::oCct0­ZloiUz80­Zloi2sloiCIl

Figur. 5- Tl'picol ."ed 01 high-lnfen,1ty .h«t-cfuratlonrainloll on di.charg. and co...,en'ration for a ......11­drainog..b...ln ,".om havln" a ft." ,_" a_t ofba.e flow or none.

12

..IIIIII...!..:

4 XCI~X'

50 50

'\CI: 1 \III 1 \..~ 1 \CI: 40 400 %III 1 1 \CL \CIl 1 1 \:1

1 y....mM.œ~M"_oCCI:

.1 qCI 1:;::! 30 III lOIf -

1 \ ~30:1 CI èz 1 ~! -e , \ \x xZ o ,

<:> \o

Q III , lAI \..J 1 \ ..J..~ \-e .~ •cr:

1 \ i.... 20 VI 200 VI 20 \z 1lAI 1 \ \uz 1 1 \0 \u1 1 \ "...

z~oo 1 \ 10 "'" 10 "' ........

:1ë 1 \... ---____d ........-CIl --

0JANUAAY 24 JANUAAY 25 JANUARY 26

Figure 6 --Goge heillht and ••dim.nt conc.ntratlan. Cor.y Cr.... n.ar Moinnbu'll. '0.

13

rial contained in, 01' plcked up by, the re­leased water. Figure 7B illustrutes the ef­fect of initial channel storage on concentra­tion. Because of hijrh initial flow, the changein sta~c' and velocity is less, and there ls lit­tle or no additional erosion of sediment fromthe hed and banks of UlC' stream by theinitial increase in flow. The concentrationpattern for the released water, however, isthe same as that for figure 7A. The inter­face between the water iuitlally in the riverand the released water is defined not onlvby the channes in suspended sediment butalso hy a change in temperature and con­ductivity. In other words, the water repre­sented by the hvdronraph peak precedingthe sediment-concentration zraph is waterthat was in the channel prier to the releaseand moved downstream ahead of the rel case.

The exnrnplcs shown in fi~llres 8-11 il-'lustrate for the Colorado River near SanSaba, Tex., the range of concentration peaksand the variation of concentration with tirnewhich can OCCIll' in a river that drains alarge basin of diverse geologie, topographie,climattc, and land-lise eharacteristics.

The graphs for the period May 1-6, 1952(fig. 8 ), illustrate a typical water-dischargepeak and sedimcnt-coneentrntion g-raph fora large stream when the flow was caused bythunderstorm activity in a small a rea of thebasin. The graphs differ from those shownfor a small basin (fig. 5 ) in that (1) theincrease in discharze from 0400 and 1700hours May 1 is wnter previously in thechannel and (2) the rate of increase of dis­charge was atteuuated bv the distance fromthe source to the station. Thèse two differen­ces cause the signiûcunt risc in concentra­tion to be delayed.

Several srenerùl conclusions regarding thesediment chaructcristics of this station canbe inferred from figure 8 and illustrate thetype of analysis thnt should he applied toeach station record. First, the concentrationfrom 0400 to ]700 hours on May 1 is onlyslightly lnrger thau the concentration on theprecedinz day and illustrates a general rulethat the concentration I!'raph seldorn willshow a large increase before the actual storm

Fig. 7A. Law INITIAL FLOW

Il:0 loi..Z :::;00 Il:

:li loiL

Il: VIloi ::1L •.. Il:loi "loi :::;... ...0 si::l !0

i! 0loi ;:::e :Il: ..• z:r loi

~ 0zQ 00

Il:0 loi..Z :::;00 Il:loi loiVI LIl: VIloi ::1L •.. Il:loi eloi :::;...0

::!i ::1

::l !0

! i0

. loi ;:::e •Il:Il: ..• z:r loi

~ 0zQ 00

Figu,e 7 -EfI.ct of two difl.renl flow condilion" on dilcho,geond concentrolion for th. Rio Grand. .....r lIernalillo. N.Me/(.

nalillo, N. Mex., of two separate releasesof water from a tributary reservoir over 160km. upstream. In both instances, the l'e­leaso is at the Rame rate of discharge : themajor ditTerence is in the quantity of waterin the stream at the time of release (theinitial flow). The shape of the hvdrogruphis sirnilar in both cases, but there is amarked difference in the sediment-concentra­tion graph owinjr to the initial flow condi­tions, Figure 7A illustrates low initial flowconditions. The released ' ...·ater erodes sedi­ment from the bed and the banks of thestream and causes an initial sedimentpeak,followed by the usual recession, si mila r tothat illustrnted in flgure 5 After the initialrecession another rise in concentration oc­curs which represents the suspended mate-

Fig. 7 B HIGH INitIAL FLOW

TIMf,lN DAYS

Figure 7 shows the etrect on sedimentconcentration in the Rio Grande near Ber-

-~".~? ; :,

......~

4b.[n"n_', Mm"..

Ob'.FYe,·, ..mpl.

EXPLANATION

o

........................

......­--. ---r-_E.t1m.t.d reco ••ion coneontrotton!' ---

'rom Inlti.1 pe.k

4116

Agu,. 8 -Gogo heIvh' ..... Ndi....nt conCMItration, C%raclo 11ft, n_ San Saba, T.... lMrt 1-6, 1952.

o1 1 l , 1 Y 1 UI· 1 1 1 l "IV 1 1 l , 1 1 1 1 1 1 l , , 1 1

........~ • ..a .... _ a .. aa.... "aa... • ...~ _ .aa.a

2000

*lb

20.000 j i 1 i , _ J__ i Iii i 1 i :>< i i i 1 i 1 i i ( i i Ils

18.000

16.000

•w14.000~

:::;•w..":1c 12.000 7 7 3 3 ti•s 101... ......j !!: ..:z' 10.000 %

Cl0 Wï=c %

•~ 101Z ~wu 1000 8 8 2 Clz0u~

zw:1

6000 ~ l 1 '"'t 1 1ëi .•:li

15

20,000 r-----,----,.---"T--,----,---r::-r--r-....,.---:J;'Ir--....-...,--,--...- ....-,--...---,r----,--, 6

5

AUGUST 17

6ln......,·•••mple

EXPL.ANATION

o011__', ••mple

o[..,n..,'. crou-'- aamole.

AUGUST 16

•

AUGUST 15AUGUST 14

9 v."icel c'o••••ction

AUGUST 13

12,000 • 4~loi...!~

0.900 %~III%loi

lIOOO 3 ~,,"6000 """""" 2

"'"2000

11.000

16.000

14.000

figure 9 -<Oog. h.ighl and Mdim_nl concen',olion. Colo,ado Rive, neo, San Saba. T.... Â"llult 13-17. 1951.

16

4

3

MAY 26MA'" 25

'-'1 ~, \, \

1 \11,,,

1,

c

MAY 23

EXPLANATION

oOb..",..·......D..

6

4

3

- 5 7

io4AY 22

Figur. 10-G01l. h';lIht and MdillMftt co~ntratian, Colorado Rjy., "'0' So" Soba, Tu.. May 22·21, 1951.

17

2

• tilAI

""!..:3iiiz:MI

J ~

•

II:MI !IOO sooot:~ "'0,II: 1r , ,CIl «10 «100 c)9 11' .~

1 "'0,~ s.dIment concentrationi 1 1~

xœ! 1 '0.~ 11 JOO 1 1 ~,! z ,1 u

Z loi 1,

s , ~,

c 200 2000~ Ô 10 12 "II: ........ 1-0. ....... ,z 1 ,MI '0~ 1 , 10 '-JU 100..ZMI~sMIIII 0

JUNE 11

Fillure11-Galle height and sediment concentration, Colo,acIo Ri"e, n_' San Saba, Tex., June 11·14, 1951.

water reaches the station-i-in this instance.at about 1630 hours. Second, the water peakoccurred about 24 hours after the ûrst stormwater reached the station, althouzh the con­centration peak occurred about 7 hours afterthe first storm water reached the station.

These graphs illustrate that, for this sta­tion, the concentration peak usually precedesthe water peak and indicate that, by a com­parison of the initial peaks in fi~ures 8-11,the longer the Ume period between the firstarrivaI of storm water and the storm peak,the longer the time interval between the con­centration peak and water peak. Or, con-

versely, the concentration peak occurredabout 7 hours after the initial storm waterreached the station, even though the timeinterval between the initial storm waterreaching the station ami the water peak in­creases. Alt hough this time interval (7hours) should not he considered a lirm ruleat this station, it could be used in coniunc­tion with the general shape of the concen­tration curve shown in fiJ\'lll"e 19 to describeadequately the curves in fiJ\'ures 8-11 eventhouzh only two samples bad been collectedeach day.

The May 1-6 rise (fiK. 8 ) has a near

classic hydrograph recession; however, theconcentration gruph fuils to follow the clas­sic pattern. The sediment recession seernsnormal until 1800 hours May 2, after whichthe concentration increnses and is somewhatabove the normal recession eurve until about1200 hours May 5. For purposes of illustra­tion, a normal concentration recession linewas estimated for Muy 2-.1) And is repre­sented by a dashed Iine. The sediment rep­resented by the difTercnce in the estimatedgraph and the s:rraph based on sarnples proh­ably was introduced into the main stern hyinflow from a small storm on one or moretributaries in the lower part of the basin.The tributary flow contained a hizher con­centration of suspended sediment than theriver, but the water discharze was insuffi­cicnt to be noticed on the stage record. ThE.'efîect of various sediment sources superim­posed on one hydrozraph is more pronouncedin the exarnples to follow.

The period August 13-17, 1951 (fig. 9),has a hydrozraph similar to thut previouslydiscussed (fig. 8), and runoff apparentlvcame from one source. Correspondingly, thesediment-concentration graph would he ex­pected to have a single rise and characteris­tic recession, The sediment samples indicate,however, that possiblv three major sourcesof water and suspended material comhinedto form the single water peak. The initialconcentration peak occurred about 4 hoursprior to the water peak. Then a tributarvflow of higher concentration combined withthe initial flow and caused a secondary, andhigher, concentration peak. Evidence of athird source of rnaterinl il' indicated hy thechanze in recession rate of concentrationabout 0~OO-0800 hours August 1G, F'inally.on A ugust ] 6 the Red imcnt concentrationdropned abrupt lv to a level that mav haveoccurred AlIJ!URt ]5 had the flood peak con­tained water and sediment from only onel'ource.

The graphs for May 22-27, 1951 (fiJ!.lO),indicate the effect of ReveraI peaks pro­duced from severa! rainstorms or fromdrainage of Reverai Rubbasins, or from Loth.The first increase in discharge was rapid,

18

und the initial concentration peak was con­veutional, althouzh the peak concentrationWIIR not 8S high as that previously experi­enced (fi~. 9). The difference hetween thisgraph and those in the previous exarnplesmay he the result of different antecedentconditions in the basin or sediment from adifferent subbnsin. The second concentrationpeak superimposed on the orhrinal sedimentrecession could not he predicted from thegage-height trace. The third concentrationpeak may he anticipated because of theabrupt deerease in rate cf recession about2200 hours May 23. The fourth concentra­tion peak, that of May 25, apparently fol­lows the eharacteristic pattern, The fifthpeak (May 27) could not be anticipated fromstudy of the hvdrozraph and may have beencaused by small downstream tributary flowor more Iikely lI,v bank slouzhing which fol­lowed the extensive period of high flow.

The per'iod June 11-14 (fiJ!.ll), has ahigher water discharge than the precedingexamples and Il longer delay time betweenarrival of the first floodwater and the peakdischarge, as usually charaeterized by longperiods of general low-intensity rainfall. Thesediment concentrations are lower than inthe preceding exnrnples. The low concentra­tion may he attributed to antecedent condi­tions caused by the May storms or, morelikely, to the IE.'sS intense rainfall but longerduration of the June storms,

The examples discussed previously demon­strate sorne of the variations in concentra­tion zraphs that may be expected in a largebasin when the runoff events are producedin upstream tributnries of diverse character­istics br isolated rainfall of short durationand high intensitv. Figure 12 illustrates 8.

storm event on a larjre stream, SusquehannaRiver at Harrisburg, Pa. (drainage area,62,400 square km ), th nt drains a basinconsisting of three major physiographicprovinces with J{enerally $:!'ood vegetal cover.The March ::J-14 flood was caused by inter­mittent raillfllll t hat occlIrred March 2-10thl'OlIJ:"hollt the State. The R<'diment concen­tration started to increase with the increasein water discharge, unlike the example in

19

22

20.

II

II

~loi

1• loi...!

12~x2loiX

10 III

!1

1

•2

015714J

II:loi..~

11: 100loiL

fil2!1OO~

!=4002

!iJOOo5II:; 2OO1--_~loiUz8 100~

Zloi:1 ol-.-=::::C::="'-l.__L-_-L_--l__...L.-_...J.._~L---:-...l-",",:":,""""__L-,:"":,,,""""-~"""

aloilit

F1vu•• 12--Gog. h.;ght _cl Mdi......t concentration. Susquehonna Il.,.. CIt "o.,W..",. '0.figure 8 • because the source area of thewater and sediment was local as weIl as up­stream and the concentration continued toincrease until the discharge started to de­crease. Even 50, there was a small secondaryconcentration peak March 8. The secondwater-discharge peak on March 11-12, ul­though hizher than the first peak, had alower concentration' because less soil wasrendily available for erosion afterthe ürstfew days of rain, . ,:

The hydrograph of the discharge and sus­pendod-sediment concentrations of the Wil­lamette River at Portland. Ore., durinz therecordbreaking floods of December 1964 (fig.13) is a good example of the relation be­tween discharge and concentration for alarge flood on a large river. The dischargecontinued 10 increase for 4 days until itreached a peak. Sediment concentration, 1

however, reached the maximum value the

second day following the beginning of therise and decreased over 50 percent by thetime the water discharge reached a maximumvalue. Several common characteristic trendsmay he noted here: (1) The large increase indischarge nt the outset caused a minor in­crease in concentration, (2) the dischargeincreased 1I10wly for several days to reacha maximum value whereas the concentrationincreased rapidly and reached a maximumvalue. in less tirne, and (3) the water dis­charge receded slowly, beine sustained byadditional rainf'all and contributions frombank and channel storage, whereas the con­centration receded rapidly after reaching themaximum value, .

20

Figure 14 presents bath the hydrograph and the concentration graph

concerning the Ciujung river at Rangkasbitung for the 20th, 21st and 22nd

of December 1978. Though no data are avai1ab1e about concentrations during

the rising stage on the 20th it can readi1y be seen that for the same range

of water 1eve1s, concentrations can be cornp1ete1y different. The second water

discharge peak on Decernber 22 is in fact partly dependent on the first peak

which occured on the 21st so concentrations are lower for the same range of

water discharges, the sarne can be said about the peak on the 23rd. 50 the

shape of the concentration graph for cornp1ex flood is comp1etely different

fram the single peak flood concentration graph.

500 r-----r---,----..,.-'---r----r-...,......--,------.----!--.-------r--.......---. 2.5

'.

>ca20

-II:101

Z Il.o en>= zc 0II: .... ...~li: 0

15 ~ ~ eno -' ~ua: ~.. 101 ....Z Il. :;101 en ~

:1:1 za: .li: C) ..;

10 a z ~101 - Ca 1:z U101 CIl

~ a:;, ..CIl Z

101:1

0.5 a101CIl

le)2928

W.t.r d'Kh.r••

2724 25 26

DECEMBER 1964

'\""\\\

. \ \

\ "\ \ ./SedIment d'.ch.r••

\ '(' .

\ '- .\ "

\ ", \-, -," , .

SU.llended.sedlment"/'~ .concentr.lion " ....~

. .... ....-:::--- .......................... ---­....... ... - .... _-

r-'1 \

f \,l1 ,-,"f:,11

1:J:1:Ill',:,/J:

1//--'.1'

"20

azou101CIl

II: 400101Il...101101li.

Uiii:;,u 300...oenac~:;,o~200

!,.;eII:C1:

:1la 100

II:101..cJ

Figure 13 -Su.pended.•ediment concentration. .ediment discharge. and water.di.charge, Willamette Ri.,., of Port.

·Iond, Oreg .• December 21·30. 1964. (Alter Waanone" and othe". 1971, p. 116.)

CIUJUNG (RANGKASBITU~) f'IG. 14 21

lydrograph and concentration graph - From 20/12/78 to 23/12/78

Gauge Height vers~s time

• • Concentration versus time

sca1e changes to the concentration graph so as to enab1e to read thegraph with sufficient accuracy (at 1east 2 significant figures)

22

4. COMPUTATION OF DAILY SEDIMENT DISCHARGE

At a given time the instantaneous sediment discharge is defined as

the product of the concentration and the ,water discharge, namely,

Qsi = k c Q ( 1)

as mentioned previously when concentrations are expressed in milligrams per

liter (mg/l) and water discharges in cubic meters per second (m3/s) the con­

version factor, k , is equal to 0.0864 and sediment discharges are reported

in metric tons per day (ton/day).

Let us assume that for a given time interval denoted, ~t., the mean1.

concentration and mean water discharge are known, let us denote them c. and1.

~i respectively, during that time interval, for instance, expressed in hours,

the suspended load in tons is equal to :

0.0864 ci Qi=

24(3)

Let us go further and assume that a given day is subdivided in time

i.ntervals denoted, Al' A 2' ••• , Ai' An and such that :

n~ At. == 241 1.

(hours)

:hen the suspended load for the whole day will be the sum of the loads for

!ach time interval and so we get :

n

L1

At.1.

(4)

Computation of daily sediment discharges requires subdivision of the

,ay when~ water discharges and concentrations are changing. A common

:ource of error consists in multiplying the daily mean concentration and the

aily mean water discharge to obtain the daily sediment discharge, this

23

procedure is not correct since the average of the products of two variable

quantities is not the same as the product of the averages of the quantities.

Subdivision is not required if either discharge or concentration is constant

during the day.

The daily mean watèr discharge is expressed in the form of a finite

sum by

Q1

-= 24(5)

and the daily mean concentration by

-c = 124

n

L c.1 ].

At.].

(6)

where A t i is in hours

and it is obvious that if both Qi and c. are not constant].

=n

L1

Ât.].

-is not equal to 0.0864 x Q x c.

When subdividing a day, variations of both water discharge and con­

:entration should be taken into account. Quite often a subdivision adequate

tor water discharge may not be so for sediment discharge.

Let us illustrate the foregoing with an example. On the 2lst of December

L978 at Rangkasbitung (see fig. 14) changes in concentration and water dis-·

:harges are described in the fol~owing table 1. See Annex at the end for the

;;tage-discharge rating cuzve ;

Table 1

Ciujung at Rangkasbitung

C10ck Time· Gauge Water SedimentTime Interva1 Height Discharge Concen- Q x C x At

(t) ( At) (H) (Q) tration(C)

0 0.5 280 219 (5200) 569 400.1 1.0 326 285 (7500) 2 137 500

2 1.0 366 349 (9500) 3 315 500

3 1.0 392 393 (10000) 3 930 000

4 1.0 409 423 9600 4 060 800

5 1.0 411 427 8500 3 629 500

6 1.5 402 411 6500 4 007 250

8 2.0 368 352 3300 2 323 200

10 2.0 320 276 2450 1 352 400

12 2.0 278 216 2150 928 800.14 2.0 242 170 1900 646 000

16 3.0 220 144 1700 734 400

20 2.5 197 118 1250 368 750

21 1.0 196 117 1150 134 550

22 1.0 205 127 1000 127 000

23 1.q .' 232 158 1050 165 900.24 0.5 272 208 1150 119 600

~ota1 24 28 550 550

We use to compute the sediment discharge the so-ca11ed midinterval

:thod which assumes the values of the water discharge and sediment concen­

'ation for a specifie time represent the average values for the time inter~,

1 that extends ahead and behind ha1fway to the preceding and fo110wing c10ck

mes. This amounts to using the "trapezoidal ru1e" a1so ca11ed "midsection

thod" when computing water discharges.

So we obtain for the daily sediment discharge

=0.0864

24

17

~1

Q. C. ~t.~ ~ ~

25

after rounding off to 3 significant figures

Q = 103 000 tonss ..

for the daily mean water qischarge we obtain

117-~ li,t.Q = - Qi241

l.

- 244 m3/sQ =

~nd for the daily mean concentration

17C = ..1. ~ C. At.

24 1l. l.

- 3710 mg/l.C =

If subdivision is not used, then daily sediment discharge would be

Qs. = 0.0864 x Q x C = 78200 tons

othe error caused by not subdividing is 24800 tons, that is, -24 percent.

In the following table the sarne day is subdivided in equal time inter­

aIs of 6 hours.

Clock Time Gauge Water SedimentTime Interval Height Discharge Concentra- Q x C xAt

(t) (A t) (H) (Q) tion . (C)

3 4 392 393 (10000) 3 930 000

9 4 344 313 2750 860 750

15 4 230 155 1800 279 000

21 4 196 117 1150 134 550

Total 1162 978 15700 5 204 300

26

Since time intervals are constant we obtain for the daily sediment

lischarge

=0.0864

4 = 112 000 tons

for the daily mean water discharge

-Q

1= 4 = 3

245 m /s

:or the daily mean concentration

ë 1= 43930 mg/l

Though the foregoing subdivision is quite adequate for the computation

)f the daily mean water discharge it gives rise to a 9 per cent.error in the

:omputation of the daily sediment discharge.

The matter of units is sometimes confusing, for instance, to express

.nstantaneous sediment discharges in tons per day, however this is only a

latter of habit.

When a day is subdivided, the cross-section coefficient should be ap­

)lied, if need be, prior to computing concentration values from the concentra­

:ion graph,in particular when the coefficient may change with stage.

In fig. 15 the concentration graph is adjusted graphically by using

:he coefficient values determined in the plot in fig. 2 • For instance, for

l gauge height of 29 feet the cross-section coefficient is 1.12 so the cor­

:esponding concentration, that is, 360 mg/l is multiplied by 1.12 and the

:esulting concentration is 403 mg/l rounded off to 400 mg/l, the same is done

'or several points and a new adjusted sediment concentration graph is drawn.

fuviously when the cross-section coefficient is constant there is no need to

:orrect individual value of concentrations but the coefficient may be applied

lirectly to the sediment discharge.

27

212019O.......--J-_-L_---.l-'-_.l..-_.....L_--1__.L..._.....L_.......JL-_.L..._.....L_--I__.L..._.....L-Jo

100 ~5

R.n•• in çoeffici.nts. EXPLANATIONhom fI.ure. 2.

600 1.13 G..e hel.ht 30'

a: -1.ïrw

1.11~ Sediment çonc:entr.tion::; ---uoa: -1.09 ---- 1.

w Adjusted çoncentr.tlonCL 500 l.lij - 25CIl ---uiS:1ca: 1.04 l-U III::; , III..J

400 -1.02 20 "":1 -1.01 " !"~..... .., .- ......

1.0 - ---, 1 %z' <, <, ~0 ......._--~ w~ %C 300 15a: III~ UZ

~w'U

Z0U~

200 10zw:1

'-sw ............... ...-. ..1/1 -100

TlME, IN HOURS

Figure lS--oraphicol adiult",ent af _·ntration.

28

5. RATING CURVE TECHNIQUE

In the absence of financial and/or labour resources sufficient to

maintain an intensive sarnpling programme, or where the rapidly fluctuating

response of a basin would make such a programme impractical, resort is often

made to the use of sediment rating curves ~

A suspended sediment rating curve is usually presented in one of

two basic forms, either as a suspended sediment concentration versus water

discharge or a suspended sediment discharge versus water discharge relation­

ship. In bath cases a logarithmic plot is commonly used with a least-squares

regression employed to fit one or several straight lines through the scatter

of points assuming a relation such as :

(7)

Figure 16 clearly demonstrates, what was to be expected, that there

apparently does not exist a.simple relationship between suspended sediment

and discharge

10,0001,00010

~..:.'

.... :-1.:..

...~ 10,000"-

1=..~

fTi j-0 ·1E 1

ë.. 1,000 :=e ·~ ·~ ·-'" ... .~ !..Co..:>

li)

100D,scharQe. ch

fi,. 16 Suspended-material-rating curve for the Powder River;{A/ur LEOPOLD~'al. {/9.5J).1

100,000 !=------+--------1l---...c..l~~.-.:._.-~

29

and that for a given level of discharge thesuspended sediment loads range

up to two orders of magnitude. The rating plot being a univariate expression

it cannot be expected to describe a complex multivariate system and that

acco~nts for the scatter of points.

An obvious explanation is that a given flow rate may be a result of

different hydrologic events which in turn could bring about different sus­

pended-sediment loads.

Although apparently simple in concept, critical evaluation of the

data, careful application of the technique and appreciation of its limita­

tions are required if the approach is to be used effectively.

A serious source of error is the use of daily mean discharges to

calculate sediment loads. We quote Colby (1956):

"an instantaneous sediment rating curve is theoreticallynot applicable to the direct computation of daily sedi­ment discharges fram daily water discharges except fordays on which the rate of water discharges is about con­stant throughout the day"

Studies carried out by Walling (1979) show that underestimation errors

of up to 50 per cent may be invo1ved by using of dai1y mean discharges instead

of using Lns tantaneous'<df scharqes ,

From a mathematica1 point of view the foregoing is obvious. If we

assume that formula (7) ho1ds true the daily mean sediment discharge is de­

fined as :

= T expressed in the proper unit (8)

and the mean dai1y water discharge as

-Q 1:. STT 0

Q dt

30

and unless Q is constant throughout the day we have the inequa1ity

1:; -

T

T -

So A Q ndt ~ A [;

Let us resume the examp1e of the Ciujung River at Rangkasbitung on the­

21st and 22nd of December 1978. Though the number of data is far too sma11

and the range of runoff events taken into account is not by far large enough

it is interesting to compare the resu1ts obtained through the rating curve

technique with those found preyious1y when using the concentration graphe

So that not to underestimate the suspended 10ad during high f10ws

two formu1ae are adopted as i11ustrated in fig. 17

for

for

H ~ 3.10 m or

H ~ 3.10 m or

Q ~ 260 m3/s c = 0.191 Q1.58

(Q in m3/s)

(c in mg/1)

Sa we obtain for Qs in tons/day

H > 3.10

=

=

0.0165 Q2.58

276 (~) 4.81100

and taking into account the functiona1 adjustment of the stage-discharge re1a­

tionship (see Annex at the end), that is :

0.40 < H ~ 1.02

1.02 <. H ~ 4.60

Q

Q

35.2 H2• 19

We can express, Qs' in the fo110wing form as a function of H

1.02 < H ~ 3.10

3.10 < H ~ 4.60

175 84• 50

2.11 H8• 37

50 on December the 21st i~ the'day is subdivided in 6 interva1s

of 4 hours each we obtain

C10ck - time Gauge height Q• • si

2 3.66 109804

6 4.02 240799

, 10 3.20 35677

14 2.42 9337

18 2.07 4623

22 2.05 4425

~ 404665

= 67000 tons

Assuming that 103000 tons in the rea1 sediment discharge the error

ls in the region of 35 per cent, however if the sediment rating curve is

lpp1ied direct1y to the mean water discharge for this day we have

= 0.0165 (244)2.58 = 24000 tons

:hat is, an error of near1y -80 per cent

Likewise on Decernber the 22nd we have

Clock - time Gauge-height Qsi

3 3.25 40621

9 2.72 9154

15 2.20 6080

21 2.30 7427

~ 63282

= = 16000 tons

The zeauLt.ant; error ·is -18 per cent and by using the daily mean wa~er

iiseharqe we have :

=

~at is, a -33 per cent error.

13000 tons

The errors are less serious on the 22nd of December sinee the vari~­

.Lons of water discharges are smaller than on the 2lst.

FIG 17

______-..0

-~~~-.

.:t.. ::~:, ...:'..-.- .

... _··t···, 'l"'i~

,-~te Although the break in slope is somewhat arbitrary in fig.17 the formula for

Q > 260 m3/s is on the eonservative side sinee thesamples were taken

during the falling stage of the flood.

Tc make the rating curve seatter less serious the data may he subdi­

.ded, for example according to season and rising or falling stage whieh are

lite- often major causes of the scatter. In sorne cases correlations may he

~eatly improved by subtracting the base flow fram the water discharqe.

~ ..'~

33

Sometimes 0 storm-by-storm analysis May he carried out, that 'is, sediment

rating ~~rves are drawn for individual storms.

Flow-duration curves have been widely used with sediment rating· curves

to compute the sediment load. The basis of this method is to Obtain the average

runoff rates for a series of duration incrernents and to apply these to the

rating curve to determine the associated sediment concentration or load. In

order not to underestimate the loads/&~all discharge intervals should be used

particularly at high discharges where srnall inaccuracies could lead to signi­

ficant errors, however larger incrernents can be employed where the duration

curve is near horizontal. Two standard tables of duration increments are pre­

sented in table 2 • The use of flow-duration curves shortens the computation

tirne but is less accurate that to subdivide the day and compute intantaneous

sediment discharges.

In conclusion, we may say with Porterfield that whatever the way of

:lpplying the sediment rating curve technique "Data must he available for a

1umber of adequately defined hydrographs representing a range of flow and sea­

sons to insure reasonable success wi th these methods", in particular that was

10t the case with the example of the Ciujung River at Rangkasbitung In any ','

:ase the sediment rating curve can only be expected to yield approximate annual

;ediment loads,however estimation of monthly loads are not significant, let

rl.one daily loads.

TABLE 2 Duratlon curvc intcrvals ulilized by Miller (1951) and l'icst (196.) forcalculating sedimcnt loads

~lil1cr% limits

\00 - 99.9K99.98 - 99.9099.9 - 99.599.5 0 9K.59K.5 '095.095.0 - 85.085.0 - 75.075.0 - 65.065.0 - 55.055.0 - .5.0.5.0 - 35.035.0 - 25.025.0 - \5.015.0 - 5.05.0 - 1.5

contd.

ron1:

1.5 - 0.50.5 - 0.10.1 - 0.02

0.02 - 0.00

l'iest % limils

IO() - 96.096.0 - 91.091.0 - 85.0K5.0 75.075.0 - 65.065.0 - 55.055.0 -- 45.045.0 - 35.035.0 - 25.025.0 - \9.019.0 - \3.013.0 - 9.09.0 - 7.07.0- 5.05.0 - 4.0

contd.

~0I11:

4.0 - 3.03.0 - 2.02.n - \.41.. - 1.01.0 - 0.80.8 - 0.60.6 - 0.40.4 - 0.20.2--0.10.\ - 0.08

0.08 - 0.060.06 - 0.040.04 .; 0.020.02 - 0.00

34-'

A word of caution about the least-squares method (and the use of the calculator)

It is a cornrnon pratice when using the least-squares method to give• •aIl the measurernents an equal statistical weight in spite of the fact that

most of the measurernents available for defining the relation will always

he located at the low and medium stages. Thus an extrapolation of the fornu­

la to the higher stages, where at best very few and usually no data are avail­

abl~, will be biased by the greater nurnber of "low-Iying" data points. It

follows that the least-squares method should be done carefully and checked

against other methods.

In particular, one has to plot the points prior to computing the coef­

ficients in order to decide "by eye" if one or several straight lines have

to he adjusted. Results given by a calculator must always be checked especialiè

when working with a "prograrn", especially if the line "cornputed" differs sig­

nificantly fram the line which would have been drawn by eye.

'"

35

INNEX

)rawing and Extension of the RANGKASBlTUNG RatiIlj Curv,2,

The sediment unit may have to deal with a suspended sediment problern

,n a location without a gaging station. In that case, the staff will have to

arry out net only sarnpling operations hut water discharges rneasurernents as

'eLl, and furthermore to establish the rating curve , An exarnple is presented

e re (fig. 18 to 22 )."

We ernployed the Stage-Velocity-Area rnethod which consists in dealing

eparately with cross-section area and rnean velocity as functions of gage

eight. To justify the rnethod it is supposed on hydraulical grounds that

he relation between rnean velocity and gage height is simpler than the stage/

ischarge one and therefore the drawing and extension of a line through and

eyond the scatter of points will be easier. (Fig.20 ) with the stage/velocity

arve than with the stagejdischarge rating curve ,

It is a common practice "to srnooth" the rating curve by adjusting dis­

1arge differences for equal gage height incrernents so as to obtain increasing

~ constant differences for increasing gage heights (mathernatically this

~ounts to assuming that the first derivative of the stage discharge function

an increasing or constant function of the gage height and in rnost cases it

logical to think sol. (Fig. 21)

The procedure can be surnrnarized as follow

1. Plot the discharge rneasurernents versus gage heights on

ordinary graph paper and fit a curve to the data points

by visual estimation (Fig.l8A, l8B)

2. with the drawil~ of the cross section (fig.19 ) compute

the cross section area for different gage heights and

draw the cross section area versus gage height curve

A = fct (H)

3. Divide each discharge rneasurernent by the corresponding

cross section area which is taken on the curve drawn

in step 2, so as to get the rnean veloci ty. Plot

emark

36

the velocityversus gage height points (ordinary paper)

and fit a curv~ through the points (fig.20 )~ Ü = fct (H)

4. Compute the discharge for a sufficient number of gage

heights (with equal gage height increments) by multiplying

the corresponding cross-section area (step 2) and the

mean velocity taken on the curve drawn in step 3 (fig.18A, B)

'Q = AU

5. For equal gage height increments calculate the differences

between the discharges calculated in step 4 for successive

gage heights (see Table in fig.18A, B). Plot these differences

versus gage height and fit a curve through the points

(fig. 21)

6. "Arrange" the discharges values so that differences for

equal gage height increments fit the curve drawn in step 5

7. Plot the values found in step 6 and draw the correspOnding

curve on the same sheet of paper used for step l in order

to compare with the curve drawn in step l and to make sure

that no gross error was made while performing the steps 2

to6

More detailed procedures are described in many books.

c.f. "Drawing ànd Extension of the Rating CUrves in Different

Condition of Stream Flow" by A. Muzet, DPMA Bandung.

"Stage-Discharge Relations at Stream Gaging stations" by

Osten A. TILREM - Copy of this book is available at the

Hydrometry Unit.

Through plotting on a log-log paper it was found that the

rating curve may be adequately defined by the following

relationship, see fig. 22:

0.40 <. H ~ 1.02

1.02 < H < 4.60

35.22.19

in metersQ H H

Q 36.3 Hl. 74Q in cubic meters

per second

Using the foregoing formulae give rise to errors which are in

any cases less than 3 percent for gauge heights beyond l meter.

See tables in fig. 18A and l8B.

Gauging;'.. 1 Station-

Q- Q .,. Area V Âç

(m3/s) I.li(m2) (m3/e36.3H (cm/4)

103 101 211 4919

122 1 121 232 5320

142 1 143 1 254 1 5622

164 1 167 1 276 1 5923

187 1 191 1 297 1 6325

212 1 218 319 6627

239 1 246 341 7028

267 1 275 1 363 7430

297 1 305 1 386 7732

. 329 1 337 408 8134

363 370 431 843f.-

399 405 453 88~ ~

.' J

436 1 441 476 9239

(475) 1 478 1 '500 951 41

(516) 517 523 9942

«558» 556 (546) (102)

«603» 597 1 45

2.80

3.80

4.60

4.40

4.20

3.20

3.60

3.40

2.60

2.20

2.00

3.00

2.40

4.00

1.80

(4.80)

(5.00)FLOW

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40

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41

:'.

_..•.

42

Fig.22 Rangkasbitung (Ciujung). Rating curve on log-log paper.