Pertanika 12(3), 367-376 (1989)

The Use of Suspended Sediment Rating Curves In MalaysiaSome Preliminary Considerations

G. BAlAMURUGAt"lInstitute oj Advanced Studies

University MalayaLernbah Pantai, 59100 Kuala Lumpur

Key words : Suspended sediment, rating curves, regression analysis

ABSTRAKKelok kadar endapan ampaian masih rnerupakan kaedah yang paling biasa digunakan untuk rnenentukanbeban endajJan arnpaian di sungai-sungai di Malaysia. Dengan demikian, walaupun kaedah ini kasar danmernpunyai banyak kelemahan, prosedur-prosedur yang betul peTiu dipatuhi. Tiga kesilapan yang selalu di­lakukan semasa menggunakan kaedah ini telah dikaji dan dibandingkan dengan keputusan yang diperolehidengan menggunakan kaedah yang betul. Hasil kajian rnenunjukkan bahawa kaedah yang salah telah me­nyebabkan kejJUtusan beban endapan amjJaian tahunan disalahtaJsirkan iaitu lebih daripada 50%. FaktorjJernbetulan untuk mengambil kim pengunaan data kadar alir tidak berterusan juga diperolehi dalarn kajian1.nz.

ABSTRACTThe suspended sediment mting cume technique is the most common method oj estimating river susjJendedsedirnent loads in Malaysia. Thus, despite its crudeness, adherence to the conec! jJ1"Ocedures oj this techniqueis very imp01tant. Three oj the most common incorrect procedures in the suspended sediment rating cumetechnique were studied and compCl1ed to the results obtained Jrom using correct procedures. Results oj analysisshowed that incorrect practices oj this technique underestimate the annual susjJended sedirnent load by morethan 50 %. A correction Jactor to compensate Jor the use oj non-continuous discharge data is also derived in

this study.

INTRODUCTIONAs soil erosion and conservation is currentlythe subject of a great research effort, methodsof estimating soil losses are being widely ex­plored. The most common method in Malaysiain this respect is the use of river suspendedsediment load to indicate the magnitude of soilerosion although such measures do not takeinto account the retention of eroded materialon land, but in turn do include channel ero­sion.

River suspended sediment load can bedetermined by a number of methods. The useof theoretical and semi-theoretical equations,although quite common in more developedcountries, is hardly used in Malaysia. The morepopular method here is determining the sus­pended sediment concentration and multiply-

ing it with river discharge value. The sedimentconcentration is obtained by laboratory analy­sis of water samples and river discharge valuesobtained by velocity-area measurements or byinterpretation of stage readings. This method,although adequate for measurements of instan­taneous sediment loads, is of little help in thecomputation of annual suspended sedimentloads. In the typical Malaysian situation ofinadequate manpower, funds and automaticsampling equipment, it is almost impossible toobtain daily sediment concentrations in therivers for long periods of time. Considering theabove mentiorkd factors, many researchers inMalaysia (Peh 1981; Lai & Samsuddin 1985;Mohammad oor 1987; Balamurugan 1987;Wan Ruslan 1989) utilize the suspended sedi­ment rating curve technique to estimate long-

'G. BAlAMURUGAN

term suspended sediment loads of rivers vis-a­vis soil losses.

This paper investigates the use of thesuspended' sediment rating curve technique,some of the common mistakes made by usersand the correspending consequences on theprocess of estimating suspended sediment loadsin Malaysian' rivers.

SUSPENDED SEDIMENT RATING CURVEThe suspended sediment rating curve (orequation) is basically a relationship betweenriver discharge and suspended sediment con­centration or load. Instantaneous suspendedsediment concentration or load and river dis­charge values are plotted together to derive aline of best-fit. The best-fit line equation is thenused together with river discharge data toestimate suspended sediment transport rates orto analyze other sediment-related processes.

In Malaysia, the most common form ofrelationship assumed to exist between riverdischarge and sediment concentration or load(Sieh & Sivapakianathan 1977; Peh 1981) is

c = a Qb (1)or

(2)

where C = suspended sediment concentrationin mg/l

L = suspended sediment load in tonnes/day

Q= river discharge in cumecsa = coefficientb = exponent

Due to scarcity of relevant data, multipleregression analysis to derive different forms ofrelationships involving variables other than theabove two have seldom been tested in Malaysia.

The most important assumption madewhen applying the suspended sediment ratingcurve technique is that the sediment concen­tration is dependent and only dependent onriver discharge, which is quite clearly untrue(Geary 1981; Walling 1974). Sediment trans­port rates have been shown to be governed bycomplex relationships involving sediment para­meters such as size, density and shape, flowparameters such as velocity, Reynolds numberand Froude number and channel parameters

like bed configuration channel slope andhydraulic radius (Lawson & O'Neil 1975; Ken­nedy & Brooks 1965). In addition to thesefactors, the availability of sediment, a majorfactor effecting the transport rates, is governedby many hydro-geomorphological factors suchas rainfall intensity-duration, topography andland use.

The assumption that suspended sedimentconcentration or load is dependent on riverdischarge or in other words the fact that sedi­ment content increases with discharge can beexplained by the following:

(a) Higher discharge means the occurrence ofheavier rainfall. Heavier rainfall normallyhas higher erosivity, thus the cause forhigher sediment production.

(b) Higher discharge normally is accompaniedby higher velocity and increased sedimentcarrying capacity of the river.

Although discharge is not the only ex­planatory variable, it has been reported as themost important. one in explaining sedimentconcentration variations (Imeson 1971). Stu­dies by Walling (1974) showed that dischargewas the most important single variable com­pared to many other variables including timerelation of sample to hydrograph peak, flowlevel preceding storm and index of flood inten­sity. However, several studies have shown thatother parameters such as rainfall, basin mor­phometry and land use may have a strongerinfluence on annual sediment yield (fansen &Painter 1974;Dunne 1979;Ogunkoya&jeje1987)

The above assumption also ignores thesedimen t exhaustion effect. In areas whereexhaustion effects constitute an importantcharacteristic of the suspended sediment res­ponse, the use of suspended sediment ratingcurves to calculate loads from streamflowrecords could give rise to significant errors(Golterman et at. 1983). Furthermore, it is aninherent assumption of the rating curve thatthe water and sediment concentration peaksare synchronous (Walling 1978) which in realtime is usually not true, in that the suspendedsediment concentration - discharge curves usu­ally exhibit either clock-wise or anti clockwisehysterisis (Loughran et al. 1986; Lootens &

368 PERTAN1KA VOL. 12 NO.3, 19t19

THE USE OF SUSPENDED SEDIMENT RATING CURVES IN MAlAYSIA

Lumbu 1986; Grimshaw & Lewin 1980; Klein1984). Furthermore, the lead or lag effects ofpeak sediment concentration with respect topeak discharge is also ignored (Grimshaw &

Lewin 1980) .

DATA LIMITATIONDue to the tediousness and large volume ofcomputations involved in using continuousdischarge data, it is common practice to incor­porate daily mean, weekly mean or monthlymean discharge values into the rating curves tocalculate annual sediment loads. These databeing averages of certain time series, have thepeakedness of flow smoothened. A T-day meanflow is the average flow over T-days. Thus it willonly represent the actual flow in a arithmeticrelationship, unlike in the case of the suspendedsediment rating curve where the relationship isgeometric. Thus the computed annual sedimentloads are actually underestimates when usedtogether with rating curves with 'b' values otherthan unity. In this respect, the use of any set ofdischarge data other than continuous valueswill underestimate the long-term sedimentloads. This effect will be more pronounced forsmall streams as compared to large rivers.' Inlarge rivers, the maximum instantaneous flowon a particular day may only be slightly higherthan the daily mean flow but in small streams,the maximum values is usually very much higherthan the mean flow. Thus, the underestimationof sediment loads will be much greater in smallstreams compared to larger rivers.

In order to obtain the actual annualsediment loads, a correction factor K(b, T)corresponding to the values of 'b' and 'T' hasto be multiplied to the computed value. This isto compensate for the effect of smoothening offlow due to the use of mean flows. T representsthe number of days from which the mean flowvalues were computed; ego for weekly mean flow,T = 7.

Actual load = K (b,T) x Computed load (3)

LINEAR REGRESSIONThe suspended sediment rating curve is usuallya line fitted to the logarithmic transformationof a set of river discharge and sediment concen­tration measurements. Most researchers use the

classical (least-squares) regression to derive thebest-fit line for the rating curve which actuallymay not be the proper type of regression to beused in this case. The classical regressionrequires at least one of the variables to besubjected to no or minimal errors in its mea­surement (Poole & O'Farrell 1971) where asin the case of suspended sediment rating curves,both the variables are prone to errors inmeasurement (Loughran 1976; Walling 1977).Probably due to the abundance of publicationsand computer software on the classical regres­sion, this fact has been frequently over-looked.

. The least-squares regression of Y on Xassumes that X is the independent variable,and Y, the dependent one. In a given set ofdata, one should be able to demonstrate a cleardependence of one variable on the other. Forexample, the weight of a chicken depends onits age and not vice-versa (Till 1973). In theexample above, the age of the chicken in dayscan be determined without errors, thus theclassical regression can be applied in this case.In the case of the suspended sediment ratingcurve, both variables are subjected to errors ofmeasurement, thus the classical regression isinapplicable. Till (1973) has commented thatdespite such implications, most researchers havepersisted in using the classical regression, whenthe reduced major axis line is in fact the correctsort of linear fit to apply to such data.

The reduced major axis line (R.M.A.L) isused to obtain best-fit line between two vari­ables in cases where both are known to be withmeasurement errors. The R.M.A.L. sums theareas of the triangles between the set of dataand the line to a minimum (CDE in Fig. 1)whereas the classical regression sums the verti­cal distances of a point from the line to aminimum (AB in Fig.I). The computationprocedures of both the classical and the re­duced m~or axis line are shown in Tabl.e 1.

Besides the above, many researches havealso evaluated the rating curve in terms ofrelationship between sediment load (L) andriver discharge (Q) when the C-Q relationshipwill be more meaningful (Walling 1977). A highcorrelation between sediment load and riverdischarge is inevitable due to the spuriouscorrelation effects, in that the relationship

PERTAN1KA VOL. 12 NO.3, 1989 369

G. BALAMURUGAN

y

F-----rG

A

E

B

l--------------------~x

Fig. 1 Different ways ojfitting a stmight line to a set oj data (Till, 1973)

TABLE 1Linear regression computation procedures

370

Equation

Slope, b

Intercept, a

Coefficient ofcorrelation, r

where

Sxy

Sx

Sy

Classicalregression

y=ax+b

Sxyb=­

Sxa = y - bi{

Sxyr= --~-

.jSxSy

L(x - x) . Cy - y)N

L(x- X)2

NLCy _y)2

PERTANlKA VOL. 12 NO.3, 1989

R.M.A.L.

y=ax+b

b=_SySx

a=y-bX

Sxyr =-_:........-

.jSxSy

THE USE OF SUSPENDED SEDIMENT RATING CURVES IN MALAYSIA

involves one variable (discharge) and theproduct of that same variable and a secondvariable (discharge x concentration). This couldlead to an incorrect significance of correlation,in that the L-Q relationship could be signifi­cant when the proper C-Q one might not be so.

EFFECTS OF ASSUMPTIONS AND DATAUMITATIONS ON COMPUTED

SEDIMENT LOADAn analysis was performed to study the effectsof the use of incorrect regression analysis andnon-continuous discharge data on the annualsuspended sediment loads calculated usingrating curves. The main aim of this study wasto obtain a general idea on the above effects,and thus only a small set of data was used. Thefollowing three effects were studied:

(a) Use of non-continuous streamflow recordssuch as daily mean and weekly mean flows.

(b) Use of classical regression instead of re­duced major axis line.

(c) Use of Load (L) - Discharge (Q) regres­sion instead of Concentration (C) - Dis­charge regression.

Use of Non-continuous Discharge DataAs explained earlier, the use of daily mean orweekly mean discharge records will under­estimate the annual suspended sediment loads.Thus, a correction factor (Eq. 3) has to beiI].corporated.

In order to obtain a preliminary set ofcorrection factors K(b,T), 3 years of dischargedata from the Drainage and IrrigationDepartment's (DID) river stations in the Kelangriver basin were analyzed. The stations and yearsused were

(a) Sg. Kelang @ Jambatan Sulaiman 1978(b) Sg. Kelang @ Lrg. Yap Kwan Seng 1982(c) Sg. Batu @ Sentul 1982

Hypothetical rating curve equations(Equation 2) with exponent 'b' values of 1.5,2.0, 2.5 and 3.0 were used to evaluate thereduction in annual suspended sediment loadscomputed with daily mean, 2-day mean, 7-day,la-day, 30-day, 50-day and annual mean dis­charge. The 'b' values were chosen to representthe typical exponent values, which usually rangefrom 1.0 - 3.0. The 'a' value was taken LO be 1.0because being the linear component of theequation, it will not effect the relative sedimentloads computed using the rating curves.

As expected, the computed annual sus­pended sediment loads decreased with theincreases in 'b' and 'T' values. Computationusing weekly mean discharge resulted in an­nualloads being 3% - 47% lower compared tothose computed using daily mean discharge.The use of monthly mean discharge producedannual loads which were 6% - 62% lower whilethe use of annual mean discharge resulted inannual loads being 11 % - 80% lower than thosecomputed using daily mean discharge records.The computed annual suspended sedimentloads are shown in Table 2.

As neither the continuous nor hourly datawere available to the author, the above findingswere used to derive a relationship to enablesediment load reductions to be predicted basedon 'b' and 'T' values. There was poor correla­tion between T and reduction factors (RF), soregression analysis were performed between thelogarithmic transformation of'T' and RF. Theresulting equations are as shown below. L(T) isannual sediment load derived using T-day meandischarge data.

Using the regression equations above, itwas possible to calculate the reductions insuspended sediment loads due to changes in'b' values and discharge data interval. Thecorrection factor K(b,T), which is the ratio

b

1.52.02.53.0

RF = L(T) / L(1)

Equation

RF = 1.0046 - 0.0568 log TRF = 1.0020 - 0.1340 log TRF = 0.9863 - 0.2112 log TRF = 0.9577 - 0.2740 log T

r

0.9150.9220.9180.908

K(b,T) = RF(1-hour) / RF(T)

Significance

0.010.010.010.01

PERTANIKA VOL. 12 NO.3, 1989 371

between actual sediment load and the com­puted value may be obtained through interpo­lation for various values of band T. However,from the above equations, it is obvious thatthere will not be a K vallie for T = 0 (continuousdischarge data) and the values for t ~ 0 willbe very high. In this respect, T = 1 hour isassumed to represent continuous discharge. TheK values are shown in Table 3.

The K(b,T) values shown in Table 3 werederived using just 3 years of data and are thustentative and by no means universal. Further­more, no efforts were made to distinguish thedifferences in catchment sizes. More detailedstudies, involving catchments of varying sizesare required in order to establish applicablevalues. However, these results show that sus­pended sediment loads computed using daily

TABLE 3Correction factor K (b, T)

Discharge Data

b Daily Weekly Monthly Annual

1.5 1.078 1.132 1.176 1.261

2.0 1.185 1.335 1.476 1.8022.5 1.300 1.582 1.895 2.871

3.0 1.395 1.840 2.416 5.226

372 PERTANlKA VOL. 12 NO.3, 1989

THE USE OF SUSPENDED SEDIMENT RATING CURVES IN MALAYSIA

mean and weekly mean discharge data can be40% and 84% respectively less than the actualloads. This is comparable with studies byLoughran (1976), where loads calculated usinghourly discharge data were 28% - 47% higherthan those calculated with daily mean data.

Classical Regression vs. Reduced Major Axis LineSediment concentration data from 2 DID

stations for the period 1980 - 1984 were usedto analyze the discrepancies between sedimentloads computed with rating curves derived usingthe classical regression and the reduced majoraxis line. The two stations were Sg.Kelang @

Lrg. Yap Kwan Seng and Sg. Batu @ Sentul. Therating curves are shown in Fig. 2 and Fig. 3. Thesuspended sediment rating curve equations thatwere obtained are as follows:

C = 164.63 Q0854

Sg. Batu

ClassicalregressionR.M.A.L. C = 87.48 Ql~IJ

Coefficient

of correlation 0.705

Significance 0.01

40

c:

~ 2·5ou

cQ)

E 20

Sg. Kelang

C = 64.34 Q0894

0.641

0.01

The above equations were substituted intoequations 4 to derive equations to compute thesuspended sediment loads,

L = 0.0864 x C x Q (4)

where 0.0864 is the factor for converting theconcentration and discharge units into tonnes/day. The subsequent equations to computesediment loads and the computed annual sedi­ment loads are as follows :

Sg. Batu Sg.Kelang

Classical L = 14.22 Q1854 L = 5.56 Q1894

regression

Sediment load 228698 89006(tonnes)

R.M.A.L. L = 7.56 Q2~11 L = 2.75 Q~39"

Sediment load 302778 163759(tonnes)

In both cases, it was observed that thesediment loads computed using R.M.A.L. rat­ing curves were higher than those computedusing classical regression rating curves. At Sg.Batu, the sediment load calculated usingR.MAL. was 32.8% higher while at Sg. Kelang,

n : 19

:lr : 0·705p : 001

I

00 02 04 06 08 10 12 14 16

Log dischorge (m 3/s )

Fig. 2 Suspended sediment rating curve JOT Sg. Batu at Sentul

PERTANlKA VOL. 12 NO.3, 1989 373

G. BALAMURUGAl

4-0

=35........

'"E~ 30~c:CI>

g 25o<.>

c:CI>

.§ 20-0

CI>

'"c>

.3 I 5

•

•

•

••

R·MA-L-~

1Clossicol regression

n = 28r = 0 ·641

p = 00 I

1·614I· 206 0·8 10

Log discharge (m 3/s )

0402OL------'----'----'--_l--_---L__i-_--l__---l

00

Fig. 3 Suspended sediment mting CU11Je JOT Sg. Kelang at Lrg. Yap Kwan Seng

the increase was 84.0%. The R.M.A.L. producedhigher 'b' values in the best-fit line, thus ex­plaining the increase in the computed annualloads. The higher 'a' values in the classicalregression equations do not compensate forthe lower 'b' values, thus resulting in lowerannual sediment loads.

GQ regression vs. L-Q regressionRegression analyses using R.M.A.L. were per­formed between sediment load (L) and riverdischarge (Q) for both the stations. R.MAL.was used because the classical regression willproduce equations similar to those derived usingEq. 4. The regression equations obtained fromthe above exercise as compared to those de­rived using Eq. 4 and the resulting annualsediment loads are as follows:

As expected, the coefficients of correla­tion were higher for the L - Q regression, in­creasing from 0.705 and 0.641 to 0.907 and0.871 respectively. Although in this study, allregression were significant at p = 0.01, in othercases, the use of L - G regression may overlookthe fact that the proper C - Q regression migh tnot be significant. At Sg. Batu, the use ofsediment load rating curves derived from L - Qregression produced an annual load of 263009tonnes compared to 302778 tonnes obtainedfrom using equations derived from C - Q re­gression or a reduction of 13%. At Sg. Kelang,it resulted in a reduction from 163759 tonnesto 124046 tonnes only, or 24%. Thus the useof L - Q regression instead of C - Q regressionunder-estimated the annual sediment load atboth stations.

Sg.Batu Sg.Kelang

C - Q regression

L - Q Equation 4

Coefficient of correlation

Sediment load (tonnes)

C = 87.48 QL2l1

L = 7.56 Q2211

0.705

302778

C = 31.70 QL~96

L = 2.75 Q2~9ti

0.641

163759

L - Q regression

Coefficient of correlation

Sediment load (tonnes)

L = 10.17 Q204~

0.907

263009

L = 3.74 Q2180

0.871

124046

374 PERTANIKA VOL. 12 NO.3, 1989

THE USE OF SUSPENDED SEDIMENT RATING CURVES IN MALAYSIA

CONCLUSIONThe analyses using 3 years of discharge dataand sediment concentration data from 2 sta­tions permit several conclusions. The use ofdaily mean discharge or weekly mean dischargecan underestimate the annual sediment loadsby as much as 40% to 84% respectively. Thedifference is expected to be greater with the

As expected, the combination of all threefactors produced annual sediment loads thatgrossly underestimated the actual sediment load.The use of R.A.M.L. and C-Q regression re­sulted in the computed annual sediment loadsat Sg. Batu and Sg. Kelang being 32.3% and84.0% higher respectively. The incorporationof the correction factors resulted in furtherincreases of 22.9% and 27.1 %. The overallincrease in the computed sediment loads forSg. Batu and Sg. Kelang due to the use of correctprocedures were 62.7% and 133.8% respectively.

Cumulative ErrorsThe study of three aspects of the suspendedsediment rating curve, namely the use of clas­sical regression instead of R.M.A.L., the use ofnon-continuous discharge data without correc­tion and the use of L-Q regression instead ofC-Q regression has shown that all three prac­tices underestimate the annual sediment loads.In order to evaluate the cumulative errors dueto the combined effects of the three practices,annual loads were calculated for both the sta­tions using both correct and incorrect proce­dures. The results are as shown below:

Incorrect method(no correction, use

of classical regression

Correct method

Load computed usingC-Q & R.M.A.L.Correction factor K(b,T)Corrected load

% differenceCorrect/Incorrect

Sg. Batu(tonnes)

228698

302778

1.229372114

62.7%

Sg. Kelang(tonnes)

89006

163759

1.271208138

133.8%

increase in 'b' values and decrease in catch­ment area. The use of rating curves derivedusing the improper classical regression canunderestimate the annual loads by 33% to 84%while the use of rating curves derived from L­Q regression instead of C-Q regression canunderestimate the annual loads by 13% - 24%.When all the three incorrect practices arecombined, the actual sediment load can be62.7% -133.8% higher than the computed ones.

Among the three incorrect proceduresstudied, the use of classical regression and theuse of L-Q regression can be easily rectified.However, the use of daily or weekly mean dis­charge data poses a bigger problem. To obtaincontinuous data is almost impossible and hourlydata difficult for an average practitioner inMalaysia, and therefore the use of daily meandischarge data will continue in the future. Thus,it is important that the calculated sediment loadsbe corrected in this respect. Much more re­search is required before the correction factorsderived in this study can be used in real-time.Although this study was based on only twostations, the findings require serious considera­tions as they indicate that previous publicationsof sediment yield data may be only half theactual value.

Despite all the above improvements, itmust be reiterated here that the suspendedsediment rating curve is still a crude method ofestimating sediment loads. Scarce samplingduring flood events and inadequate overallsampling will only produce rating curves whichare suspicious in terms of reliability of thecomputed loads. Furthermore, laboratoryprocedures and methods of sampling can alsoinfluence the final results. However. it must beemphasized that the rating curve is still themost important tool in Malaysia in terms ofestimating sediment yield. Until better me­thods are adopted, hydrologists and engineersshould adhere to the correct methods whenusing the suspended sediment rating curvetechnique.

ACKNOWLEDGEMENTThe author wishes to thank Prof. Ian Douglasfrom University of Manchester and Assoc. Prof.Low Kwai Sim from University of Malaya forcorrecting and commenting on an earlier draft

PERTANlKA VOL. 12 NO.3, 1989 375

G. BAU\i\1URUGAN

of this paper. The valuable comments offeredby two anonymous referees are also sincerelyappreciated.

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376 PERTAN1KA VOL. 12 0.3, 1989