Sediment yield estimation in small watersheds based on streamflow and suspended sediment discharge measurements

SOIL TECHNOLOGY ELSEVIER

Soil Technology 11 (1997) 57-65

Sediment yield estimation in small watersheds based on streamflow and suspended sediment discharge measurements J.R. Cbrdova *, M. Gonzalez Departamento

de Procesos

y Sistemas,

Universidad

Simbn Boliuar,

Caracas,

Venezuela

Abstract In the past, the watershed sediment yield estimation, in rivers where hydrometric information is available, has been done using the sediment rating curve, which is obtained fitting theoretical functions to the water and sediment discharge relationship. Once this relationship is defined, it can be used along with the flow duration curve of a given year (or runoff-frequency data) to obtain the annual sediment yield prediction. Sometimes, specially in recent years, a better estimation has been developed using the same procedure but replacing the flow duration curve for the daily flow series, transforming each daily flow in suspended sediment discharge, by means of the sediment rating curve, and accumulating this information to monthly and annual levels. This procedure is judged adequate for large watersheds, where the differences among the mean daily flow and the maximum and minimum streamflow during the day are not very large. Generally the equations that fit best the sediment rating curves are highly nonlinear, therefore, in small watersheds where the differences among mean daily flows and the extreme instantaneous flows during the day are important, working with mean daily flows (and even worse with flow duration curves) introduces large errors in sediment yield estimations. In addition to this. there also exists other problems related to the previous procedure, namely the extrapolation errors, that can be very important. Also the quality of the basic information is of paramount importance in this type of analysis. This paper discusses all the above problems analyzing case studies related to two important Venezuelans reservoirs: DOS Cerritos in the Tocuyo River and Cumaripa in the Yaracuy river. An evaluation is made of the effects of these sources of errors in the sediment yield estimation of both cases. Keywords: errors

Suspended

* Corresponding +58-2-9621362;

sediment;

Watershed

author. Apartado fax: +58-2-9621084;

00933-3630,/97/$17.00 PIZ SO933-3630(96)00115-8

Copyright

sediment

yield:

Sediment

Postal 88236, M&it110 e-mail: [email protected]. 0 1997 Elsevier

Science

rating

de1 Club

curve;

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Sediment

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B.V. All rights reserved.

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1. Introduction

In the reference C6rdova and Gonzalez (199 I), a detailed analysis is presented of the problems related with estimation of sediment yields in watersheds, with a description of the different methodologies of analysis contained in the literature and also emphasizing their main advantages and disadvantages. In this paper, reference is made to analyses performed by Parra and Rodriguez (1989) and the Venezuelan Ministry of Environment and Natural Renewable Resources (MARNR) in four reservoirs. Through the use of reservoir sediment surveys, it has been confirmed that the estimates of sediment yield made in the past, have been underestimated with errors varying between 100 and 2800%. Recently, MARNR made new sediment surveys in two of these reservoirs, Cumaripa on the Yaracuy river and DOS Cerritos on the Tocuyo river, confirming once again the errors of underestimation of sediment yields in the tributary basins of these reservoirs. C6rdova and Gonzalez (1991) emphasize that these underestimations have been caused by the methodology used for data processing and analysis of suspended sediments, as well as by the changes of patterns of land use by anthropological intervention of the basins. It is important to stress that MARNR is presently developing conservation programs on the tributary basins of these reservoirs trying to reduce the negative effects of this manmade intervention. We consider that one of the most important source of error in these underestimations is the way in which the basic data, regarding the joint gauging of water flow and concentration of suspended sediment load, has been analyzed and processed. For this reason, the main objective of the present work is to make a detailed analysis of the manner in which the data of streamflow and suspended sediment rating curves has been traditionally processed, evaluating the different sources of error that may be present, both in the quality of the basic data and the processing and treatment of this data. In order to illustrate the magnitude of these errors, two case studies of the reservoirs DOS Cerritos and Cumaripa located on the Tocuyo and Yaracuy rivers, respectively, are used. 2. Curve fitting to the water discharge and suspended sediment concentration relationship.

Generally the mathematical functions that best fit sediment rating curves are not linear and among the ones mostly used are the quadratic and cubic polynomials, as well as functions of the exponential and potential type. To illustrate this, Fig. 1 shows this relationship for the gauging station of the Tocuyo river at La Guaya (with a tributary basin of 532 km2> where 393 joint measurements of water discharge and suspended sediment concentration, for the period 1967-1970, are available. The best fit of a theoretical function to this data can be obtained with equations of the potential type or with quadratic polynomials. Both fittings were made separating the region in two curves, one for the upper part of the data and the other for the lower part, using as a breaking point the value of 19 m3/s. The expressions of these functions are presented in Eqs. (l)-(4).

J.R. C&dom,

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I1111 10 Water

n

59

Measurements

100 discharge,

-Tbeoretieal

m’ls curve

Fig. 1. Sediment rating curve for the Tocuyo River at La Guaya.

Quadratic polynomiaLFor Q,=21.69-

Q I 19 m3/s

1.12Q+0.33Q2=fi,(Q).

(1)

For Q > 19 m3/s Q, = 96.30 - 10.52Q + 1.15Q2 =fi2( Q).

(4

Equation of potential type:For Q I 19 m3/s Q, = 2.987Q’,“’

=fsl( Q).

(3)

For Q > 19 m3/s Q, = 0.065Q2.555 =fs2( Q),

(4) where Q is the water flow in m3/s, while Q, represents the suspended sediment discharge in t/day. The most important region of this relation, from the point of view of estimating sediment yield, corresponds to the upper part of the curve 19 m3/s) where, in both cases, a correlation coefficient greater than 0.91 was obtained. Fig. 1 shows the fitting of the potential function (Eqs. (3) and (4)).

3. Estimation of sediment yield through the use of the flow duration curve

In the literature (AXE, 1977; Perez, 1991, etc.) thorough descriptions exist as to obtain an estimation of sediment yield by using the flow duration curve. This paper

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Table 1 Suspended sediment load computation for the flow duration-sediment River at La Guaya. Climate year: 1967-1968. Area: 532.0 km*

rating

57-65

curve method.

Cumulative duration, as a percentage

Duration, as a percentage

Duration midpoint

Flow at midpoint Cm3 /s)

Sediment rate (t/day)

Q,Col. 100

(1)

(2)

(3)

(4)

(5)

6)

(7)

0.00-0.02 0.02-O. 10 0.10-0.50 0.50-1.50 1.50-5.00 5.00-15.0 15.0-25.0 25.0-35.0 35.0-45.0 45.0-55.0 55.0-65.0 65.0-75.0 75.0-85.0 85.0-95.0 95.0-98.5 98.5-99.5 99.5-99.9 99.9-99.98 99.98-100.

0.02 0.08 0.40 1 .oo 3.50 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 3.50 1.00 0.40 0.08 0.02

0.01 0.06 0.30 1.00 3.25 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 96.75 99.00 99.70 99.94 99.99

45.20 39.50 37.00 33.00 22.00 13.25 9.50 7.50 6.10 5.10 4.50 3.90 3.30 2.60 1.49 -

2,100.o 1.420.0 1,150.o 850.0 280.0 84.0 45.0 28.0 21.0 15.5 13.0 10.5 8.8 6.5 3.6 -

0.009 0.032 0.148 0.330 0.770 1.330 0.950 0.750 0.610 0.510 0.450 0.390 0.330 0.260 0.052 -

0.42 1.14 4.60 8.50 9.80 8.40 4.50 2.80 2.10 1.55 1.30 1.05 0.88 0.65 0.13 -

Total

-

2 X Col. 4 /

S,Col. 100

Station:

Tocuyo

2 X Col. 5 /

6.92

47.82

Q, is the mean daily streamflow: 6.92 m3/s. .S, is the mean daily suspended sediment discharge: 47.82 t/day. N is the number of days: 366. V, is the total water volume: (86,400.O. Q; N)/106 = 218.8 hm3/year. Sr, is the total sediment in suspension: (5; N) = 17,500.O t/year.

presents an applied example of this methodology, which is illustrated in Table 1. The table contends original data provided by MARNR for the gauging station Tocuyo river at La Guaya, for the calendar year April 1967 to March of 1968. As can be observed in this table, during this period, all the flow distribution of the Tocuyo river, at the gauging station of La Guaya, was discretisized in 15 values that go from 45.2 m3/s to 1.49 m3/s. For each of these values the corresponding suspended sediment discharge was estimated, using a curve similar to the one described in the previous section and then, weighting these data by the time or duration associated to each water flow, thus it is estimated that the sediment yield in that climatic year is in the order of 17,500.O t.

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Technology

4. Evaluation of errors carried out in the estimation suspended sediments measurements 4.1. Errors

due to the discretization

and use

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of sediment yield using data of

of the flow?

duration curve

To illustrate this type of error, the same example described in the previous section is used, where it was obtained a sediment yield estimation of 17,500.O t, during the climatic year of 1967-1968, in the gauging station La Guaya at the Tocuyo river. In the first place it is important to stress the following: the data available at this gauging station shows that on April 30, 1967, a water flow of 132 m3/s (the highest of the 393 values) and a suspended sediment discharge of 18,203.O t/day were recorded. Thus, if this flow was maintained as average during that day, the sediment yield was higher than the one estimated for the whole year according to the method of the flow duration curve. The reason for this contradiction is simple; the method is applied in such a manner that the discretization of the distribution of flows practically eliminates those values higher than the 45.2 m3/s (upper limit), and due to the non linear behavior of the sediment rating curve, the major flows, specifically floods, are the ones that really define the sediment yield in this type of basins. The error carried out by this type of discretization increases in importance the smaller the size of the basin, since its response is quicker. As an example, an alternative solution could be the utilization of the series of daily average flows in substitution of the flow duration curve. However, this alternative solution would also lead to serious errors in the case of a basin the size of the Tocuyo river (532 km’). To illustrate this, the following example is analyzed (Rodrfguez-Iturbe (1992)). According to historical data, the hydrometric station at La Guaya, on June 22, 1985, recorded an instantaneous maximum flow of 1032 m3/s and a daily average flow of 172 m3/s, while in the days before and after this date, the mean daily flow was about 30 m3/s. This great variation in the discharges (from 30 to 1032 m3/s) during the day is characteristic of the way that floods occur in small basins. The large range of variation, together with the non linear behavior of the equations that transform the water discharge into sediment concentration introduce a big error when this transformation is estimated from daily mean flows. To evaluate what could be the magnitude of the error, a Gamma distribution was fitted to the flows that occurred that day, representing analytically the hydrograph of this flood. The fitted equation is the following: Q(t) K=

= [RV(t/K)“-‘exP(-t/K)]/(KT(n)) [RV(n-

l)n-l

exp(-(n-l))]/(QIr(n)),

(6)

where K and n are parameters of the gamma distribution, RV the runoff volume, QI the maximum instantaneous flow, T(n) the gamma function evaluated at n and Q(t) the flow hydrograph. With Eqs. (1) and (2) (selecting the quadratic polynomial to represent the sediment rating curve), Eqs. (3) and (4) one can estimate the sediment yield during that day in a

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more detailed manner. If the sediment volume is defined as SV, the volume corresponding to the day 6-22-85 can be calculated as

Q(t)) dt, sv=J ’ (day)fS( 0

(7)

where

$(Q(t>)

=.f$(Q(t>)

fi( Q(t)) =fi2( Q(t))

for Ql 19m3/s for Q > 19 m3/s.

The integral was solved numerically using a time interval of fifteen minutes and the Simpson 3/8 method. The result was the following: sv = 120,000.0 t. On the other hand, if instead of using all the hydrograph we use the daily mean flow, the result is obtained through Eq. (2) for Q = 172 m3/s, giving a result of 30,588.46 t. As may be observed, the error in the estimation can be around 250%. However, it is important to consider that in both estimates an additional error will be present due to the extrapolation which is being made on the sediment rating curve. This will be analyzed in the following section. At this point it is convenient to stress the following. According to the historical record of the La Guaya station, the data of sediment yield processed by MARNR gives an average, for the period 1963-1973, of about 50,OOO.Ot annually, which, divided by the area of the basin brings about a modulus of 93,8 t/krr?/year. Rodriguez-Iturbe (1992) describes the results of a sediment survey made that same year in the reservoir of the Tocuyo river at DOS Cerritos (located downstream of the station of La Guaya), according to which in 20 years of operation 22 hm3 of sediments had been accumulated. This is equivalent to an average of 1.102 hm3 per year. Using a specific weight of submerged sediment equal to the one adopted by the MARNR (1.12 t/m3 and an area of the basin up to the DOS Cerritos reservoir (894.8 km2>>, the modulus is of 1,232.0 m3/km2/year, that is, 1,380.O t/km2/year. Thus, if you add the modulus obtained through the data of suspended sediments published by MARNR for the La Guaya station the estimates corresponding to the bed load, the total modulus would barely represent a 10% of the value estimated through the reservoir sediment survey, meaning that the error carried out could exceed a 1000%. 4.2. Extrapolation

errors

Following with the example of the Tocuyo river at La Guaya, it is important to outline that the difference existing between the maximum joint observation of streamflow (132 m3/s) and sediment concentration, and the maximum instantaneous flow recorded at this station (1032 m3/s), is practically an order of magnitude. This introduces an additional estimation error, which is due to the extrapolation that is necessarily made to transform, those water discharges that exceed the 132 m3/s, to suspended sediment discharges.

J.R. Cbrdoua,

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M. Gonz&ez/Soil

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w Measurements

Fig. 2. Sediment

Technology

400

500

600

Water

dkcharge,

m’ls

-

Theoretkal

rating curve for the Tocuyo

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000

63

900

1,000

c.~~rve River at La Guaya.

As an example, Fig. 2 shows the same measurements shown in Fig. 1, but changing the scale of the abscissa, in order to include the maximum value of water discharge recorded. As it may be observed in this figure, this extrapolation allows for an enormous ground for error in the most important region of this relationship which is the upper part of the curve. To illustrate this type of error, if in Eq. (7) we use Eqs. (3) and (4) (function of the potential type) instead of the Eqs. (1) and (2) (quadratic polynomials), the volume of sediment obtained would result in more than the double of the 120800.0 t previously mentioned. All this in spite of the fact that in both cases a similar coefficient of correlation was obtained (superior to 0.91 in the upper part). In addition, the extrapolated water and sediment discharge relationship has physical limitations that will depend on the transport capacity of the river and of the availability of sediment volumes to be dragged, which have not been reflected in the theoretical equations when an extrapolation is made. The only way to eliminate this type of error is to carry out measurements in the upper part of the curve (gauges of high flows) that cover the major part of the registered flows. 4.3. Quality of basic data

To illustrate this aspect of the analysis, reference is made to the data on sediment rating curves available at the Yaracuy river station at Cumaripa Bridge (330 gauges). Table 2 shows the maximum gauged values at the station (taken from Matute, 1992). As described in this reference, taking into account the variability of the series of streamflows and sediment concentrations in the rivers with small basins, it is practically

64 Table 2 Suspended

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measurements

Year of survey

Water discharge

1957-1958 1969-1960 1957-1958 1959-1960 1955-1956 1957-1958 1959-1960 1959-1960

14.0 14.0 9.2 9.2 7.8 7.8 7.8 7.8

(m3/s)

Suspended

sediment

discharge

(t/day)

1,149.l 1,149.l 3,020.5 3,020.5 2,291.3 2,291.3 2,291.3 2,291.3

impossible that in different measurements, not only the same water discharge, but also the same suspended sediment discharge are observed. All this leads us to conclude that these values were repeated without having taken the measurements. Situations such as this one introduce a great uncertainty about the rest of the data. Finally, it is important to clarify that in the case of the Cumaripa Reservoir, the modulus of sediment yield used in the project of the dam was of 165.0 m3/km2/year (Parra and Rodriguez, 1989), while the results obtained through an analysis of the last sediment survey of the reservoir (Rodriguez-Iturbe, 1992) was of 3,939.0 m3/km2/year, that is, an error exceeding 2200%.

5. Conclusions and recommendations The quality of the basic data used for the estimation of sediment yield in a watershed must be evaluated before it is processed, by verifying suspended sediment rates and discharge curves estimated for the gauging stations involved. The method of estimating suspended sediment yield that uses the sediment rating curve (taken from the measurements of streamflow and suspended sediment concentration) and the flow duration curve or a daily streamflows series, introduce gross errors by underestimating the sediment yield in small watersheds. Defining as small, a basin where the maximum discharge occurring during the day differs significantly from the daily mean flow. For example, this method applied to rivers like the Orinoco (Venezuela) or Mississippi (USA), should not have any problems of underestimation. All the historic data processed in gauging stations which represent small watersheds and has been obtained using the aforementioned methodology, for intervals of discretization in time intervals equal or greater than one day, must be discarded, as it leads to great errors of underestimation of sediment yields. At this point it is important to emphasize that in view of the importance and complexity of these hydrologic measurements and the great responsibility its validity and publication implies, it is a great burden to also ask the public entities to assume their further processing. It seems more logical to leave this to the ultimate user, who according to his needs, can benefit from the gauged data, verify its reliability, and then process it. This would also avoid the official publication of information obtained through a perhaps controversial methodology.

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The main recommendation of this paper stems from the fact that a way to obtain a reliable estimate of sediment yield in small watersheds is by measuring both streamflow and suspended sediment concentration continuously, deriving the sediment rating curve relationship for an ample range of discharges and incorporating this information for small intervals of time which are a function of the response time of the basin. It is known that there exists equipment that allows the processing of these measurements in a continuous time frame (Gregory and Walling, 1976). Another way of carrying out these estimates is through the calibration of mathematical simulation models such as MUSLE (Williams and Bemdt, 19771, with measurements of sediment accumulation in watersheds through reservoir sediment surveys. An example of this methodology of analysis is described in the research performed by Ingenierfa (1992) in the basins of the Petaquire, river in Caracas, Venezuela.

References ASCE, 1977. Sediment Sources and Sediment Yields. In: V. Vanoni (Editor), Sedimentation Engineering. Task Committee for the Preparation of the Manual on Sedimentation of the Sedimentation Committee of the Hydraulic Division. Am. Sot. Civil Eng., pp 437-493. Ingenieria, C.G.R., 1992. Evaluacidn de las Wrdidas de Suelo y de la Producci6n de Sedimentos en las Cuencas de 10s Rios Petaquire, Mamo y Topo, Distrito Federal. CA. La Electricidad de Caracas, Caracas, 255 pp. Cdrdova, J.R. and Gonzalez, M., 1991. Modelaje de la producci6n de sedimentos a nivel de cuencas hidrograficas. Proc. of the Taller sobre Metodologias de Evaluacidn e Investigation de la Erosion de1 Suelo y su Impact0 en la Productividad y en el Ambiente. CIDIAT, M&da, Venezuela, May 30-June 1 1990, pp. 3-10. Gregory, K. and Walling, D., 1976. Drainage Basin Form and Process. A Geomorphological Approach. Edward Arnold, London, 458 pp. Matute, M., 1992. Analisis de1 Azolvamiento y Rendimiento de 10s Embalses de DOS Cerritos y Cumaripa, Edos. Lara y Yaracuy. Direcci6n General de Conservaci6n y Manejo de Cuencas, Ministerio de1 Ambiente y de 10s Recursos Naturales Renovables, Caracas, 235 pp. Parra, L. and Rodriguez, M., 1989. Analisis de1 Volumen y Distribution de 10s Sedimentos Retenidos en 10s Embalses Gauremal, Los Quediches, DOS Cerritos y Cumaripa. Levantamiento Batimetrico de1 Embalse Los Quediches. Trabajo Especial de Grado, Facultad de Ingenieria, Escuela de Ingenieria Civil, Universidad Catolica And&s Bello, Caracas, 211 pp. Perez, D., 1991. Metodos y Criterios usados en el Calculo de1 Transporte de Sedimentos en rios de Venezuela. Proc. of the 4th Conf. sobre Control de la Erosibn. Ministerio de1 Ambiente y de 10s Recursos Naturales Renovables y la Embajada de la Republica de1 Japbn, 13-18 November 1991, Maracay, Venezuela, pp. 1-18. Rodriguez-Iturbe, I., 1992. Evaluaci6n de las PCrdidas de Suelo y la Production de Sedimentos en la Cuenca de1 Rio Tocuyo hasta el Embalse DOS Cerritos. Direccidn General de Conservaci6n y Manejo de Cuencas, Ministerio de1 Ambiente y de 10s Recursos Naturales Renovables, Caracas, 145 pp. Williams, J.R. and Bemdt, H.D., 1977. Sediment yield prediction based on watershed hydrology. Trans. ASAE 10(6), 1100-1104.