HYDROLOGICAL PROCESSES, VOL. 8, 567-572 (1994)

MODELLING SEDIMENT TRANSPORT IN STREAM CHANNELS IN THE ARID ZONE OF INDIA

IS. D. SHARMA AND J. S . R. MURTHY* Central Arid Zone Research Institute, Jodhpur-342003, India

ABSTRACT

Ephemeral channels in arid regions convey larger amounts of sediment than perennial channels in humid regions. Sedi- ment graphs at the outlet of channels have been derived by the standard sediment rating curve technique and by a lumped model based on the instantaneous unit sediment graph (IUSG) concept. The IUSG gives estimates of sediment transport that are better than those derived with the sediment rating curve as it takes into account the availability of erodible material within the channel bed.

KEY WORDS Ephemeral channels Suspended sediments Transport Rating curves IUSG Arid zones

INTRODUCTION

There is some evidence that the pattern of sediment transport recorded in ephemeral streams in arid regions may differ significantly from that of perennial channels in more humid environments. Arid zones produce high suspended sediment concentrations (Jones, 198 1). A compilation of river suspended sediment yields for moderately sized drainage basins suggests that arid basins export 36 times more material than humid temperate basins and 21 times more material than humid tropical basins. (Reid and Frostick, 1987).

In an arid environment various sources of sediment supply have to be taken into account (Hadley, 1977). As flood flows traverse coarse, unsaturated sediments in ephemeral channels, the sediment transport capac- ity is reduced progressively by transmission losses and this results in the deposition of sediments (Sharma et al., 1984a; Sharma, 1992). The turbulent wave front that constitutes the sharply rising stage acts as a broom on the channel bed, removing some of the sediments deposited during the preceding floods (Sharma et al., 1984b; Reid and Frostick, 1987). As the resultant sediment transport is so large, and because the rarity of flash floods makes gauging uncertain, there is a considerable need for predictive models of river sediment transport in arid regions to aid in the development of water resources.

Sediment transport data were collected for nine years (1979-87) from 15 channel reaches in the Luni Basin in the arid zone of north-west India (Sharma et al., 1994). Each channel reach was sampled at a mini- mum of two stations, one in the headwater region and the other down valley. In the headwater region the mean depth, width and gradient of the channels are 1.2 m, 158 m and 0.00245, respectively, whereas in the down valley region these channel parameters are 3.6 m, 1960 m and 0.0012, respectively. The weighted mean diameter of the bed material varies from 1.267 to 1.680mm in the headwater region and from 0.160 to 0.550 mm in the down valley region. These channels drain an area of 104-950 km2 in the headwater region and an area of 1449-5492 km2 in the down valley region. Hourly sediment concentrations were determined from samples collected using 3-5 US DH-48 depth-integrating suspended sediment wading-type hand samplers simultaneously, using the equal transit rate method as recommended by Jones (1981) for arid

* Present address: Indian Institute of Technology, Bombay-400 076, India.

CCC 0895-6087/94/060567-06 8 1994 by John Wiley & Sons, Ltd

Received 8 February 1993 Accepted 7 October 1993

568 K. D. SHARMA AND J . S. R. MURPHY

regions. Discharge was measured by the current meter and velocity area method according to standard United States Geological Survey practice.

METHODS

Two simple methods of analyses were used. The first was a sediment rating curve, which when applied to a long-term flow duration curve gave the sediment yield. The second method was a conceptual model o f the instantaneous unit sediment graph (IUSG) generated by routing mobilized sediments through a series of linear reservoirs.

Sediment rating curve The expression

Qs = f ( Q ) (1) where Q, (kg s-I) is the sediment transport rate and Q (m3 s-') is the water-sediment discharge, is a sedi- ment rating curve that expresses the mean instantaneous value of sediment discharge in a given cross-sec- tion for any water discharge.

Jones (1981) and Jansson (1982) reported that the best grouping and linear trend of the Q, versus Q data was produced by a bilogarithmic plot. The equation that defines a linear regression on bilogarithamic paper takes the form

Qs = aQh where a and b are derived empirically.

outlet. The sediment rating curve in combination with the hydrograph gives the sediment graph at the channel

IUSG model

a linear storage law. For time interval At, these can be written as Sediment transport in a stream channel can be represented by a spatially lumped continuity equation and

where f s ( t ) is the sediment input (kgs-I), Q,( t ) is the sediment discharge (kgs-I), S s ( t ) is the sediment storage (kg), K, is the sediment storage coefficient (s) and t is time since the beginning of sediment discharge (s). For an instantaneous sediment inflow to the channel, the outflow from the first linear reservoir is

where K is the mobilized sediment (kg). By successively routing through n reservoirs, the sediment outflow from the nth reservoir is

where n, is a dimensionless shape parementer and I? is the gamma function. Differentiating Equation (6) with respect to time and using the condition dQ,/dt = 0 at t = tp, where tp is the time to peak sediment discharge (s)

t , = ( n , - 1)K, (7 )

MODELLING SEDIMENT TRANSPORT IN ARID ZONES 569

On substituting the value of K, from Equation (7) to Equation (6), the sediment impulse response, Us, becomes

where lJs(07t) s-' is the IUSG ordinate at time t . The IUSG convoluted with the mobilized sediment generates the sediment graph at the channel outlet. V , in the present study was calculated by a regression model:

v, = a + bV, + c[ VUP(X, w ) - V(X, w ) ] (9)

where VI is inflow sediment (kg); Vus is inflow runoff (m3), V is the outflow runoff (m3) both in a channel reach of length X(m) and average width W(m); and a, b and c are derived by least-squares analysis.

RESULTS AND DISCUSSION

A test was made to verify and validate the equivalence between the stream channel performance and that of the models. Observed sediment graphs for four representative channels covering the dominant lithologies encountered in the Luni Basin were compared with the corresponding sediment graphs obtained from the models. For these stream channels the peak runoff rate and the maximum sediment transport rate coincided for individual storms. At each gauging station three flow events covering the range of sediment transport rates from the lowest to the highest were analysed in this study.

A plot of Q, versus Q shows a large scatter of the data points, usually of the order of one log cycle (Figure 1). Jones (1981) and Reid and Frostick (1987) also observed a large scatter in Q, versus Q diagrams

I0 b

. o

a . .

I 10 too 1000

WATER DISCHARGE ( m3 <' )

Figure 1 . Suspended sediment transport versus water discharge for four representative stream channels in the Luni Basin. (0) Jawdi; (0) Luni; (0 ) Jojri; and (A) Mitri

570 K . D. SHARMA AND J. S. R. MURPHY

1800,

a

a a v) z

I-

k E a I

W

TOO,

- OBSERVED

RATING CURVE --- _ - - IUSG

JOJRl

20/25-07-81

_ - - IUSG

20/25-07-81

0-

2 6/ 31- 07-83

0

2 8 / 2 9 - 0 7 - 8 6

0 20 40 60 80 100 120 140 160

JAWAl

18-07-84

2 4 0

20 0

160'

I20

8 0

4 0

0

\ \

15-07-87

I 0 20 30 40

MODELLING SEDIMENT TRANSPORT IN ARID ZONES 57 1

Table I . Parameters of sediment rating curves, Q, = aQb for four representative streams in the Luni Basin

Stream channel a b r2 * Number of observations

Luni 8.08 1-12 0.60 26 Jojri 0.24 1.54 0.90 17 Mitri 4.26 1.16 0.80 32 Jawai 5.07 1.20 0.82 44

* Significance level p < 0.01

Table 11. Time and shape parameters of test flood hydrographs

Drainage Basin Date Time parameters Shape parameter, n,

Time to peak, Storage coefficent, t , (hours) K, (hours)

~ ~~

Jasnager 10 July 1981 24 July 1982

22 August 1983

Binawas 20 July 1981 26 July 1983 28 July 1986

Bhuti 10 July 1981 14 July 1982 25 July 1982

Nawakhera 18 July 1984 12 August 1984

15 July 1987

1 .oo 2.00 7.00

2.00 2.00 0.50

1.80 0.83 4.50

2.00 1.83 2.00

32 23 6

4 12 20

10 17 6

19 16 13

1.03 1.09 2.17

1.50 1.17 1.03

1.18 1.05 1.75

1.11 1.1 1 1.15

for ephemeral channels in Saudi Arabia and Kenya. However, their scatter is less than in this study, imply- ing a diversity in hydrological characteristics within different arid regions. The probable differences within the arid regions are the types of runoff-producing storms, the relative relief and climatological differences (Pilgrim et al., 1988). The parameter values (a and b) of the sediment rating curve [Equation (2)] for the study channel reaches are given in Table I. Coefficient a has no particular range of values and is propor- tional to the width of the channel. On the other hand, coefficient b lies between 1.12 and 1.54, i.e. greater than unity, thereby implying that the sediment concentration increases with discharge. For a given channel the turbulence which creates the forces for the suspension of the particles also increases with Q. This implies that b must be greater than unity. In practice b lies between 1-10 and 2.80 (Oltman, 1962).

To verify and validate the IUSG concept the model parameter t , was taken from an S-curve relationship between the peak flow and the time to peak flow at the channel outlet and K, was approximated as the travel time of runoff crests in the trunk stream (Sharma et al., 1994). These parameters are given in Table 11. Table 111 gives the parameter values of the sediment mobilization model [Equation (9)], thereby predict- ing the sediment yield at the channel outlet.

Figure 2 compares the observed and predicted sediment graphs at the channel outlet. The sediment graphs generated by the IUSG technique have a better fit with the observed sediment graphs than the sedi- ment graphs generated using the sediment rating curves in all instances. Sediment discharge varies markedly between the rising and recession stages for the same discharge; this could not be taken into account by the

Figure 2. Comparison of observed and predicted sediment graphs

512 K. D. SHARMA AND J. S. R. MURPHY

Table 111. Parameters of the sediment mobilization model [Equation (9)]

Stream channel a b C r2 * Number of events

Luni 1119 0.6 1 -0~0001 0.99 9 Jojri 259 0.10 -20.5840 0.98 5

M i d -4998 1.29 -0.00 1 1 0.96 8 Jawai 4294 -0.03 0~0001 0.95 15

* Significance level p < 0.0 I t Disorganised stream

sediment rating curves. This also implies that in ephemeral streams sediment transport is dependent on the presence of erodible material in the channel bed. Thus in arid environments the bed sediment supply has to be taken into account in sediment transport studies.

CONCLUSIONS

A lumped model using the inflow sediment volume and channel transmission loss in combination with the instantaneous unit sediment graph technique approximates the observed sediment graphs at the channel outlet better than the sediment rating curve technique. This simple approach allows a reasonable accuracy of prediction and satisfies practical requirements in arid regions.

Sediment transport in arid ephemeral channels is hydraulically controlled and depends on the supply of erodible material.

ACKNOWLEDGEMENTS

The authors express their gratitude to Dr J . Venkateswarlu and Mr A. S. Kolarkar for granting the required permission, infrastructure and a conducive working environment during the course of this study. Help rendered by Dr R. P. Dhir and Mr N. S. Vangani at various stages is acknowledged.

REFERENCES

Hadley, R. F. 1977. ’Some concepts of erosional processes and sediment yield in a semi-arid environment’ in Toy, T. J. (Ed.), Erosion:

Jansson, M. B. 1982. ‘Land erosion by water in different climates’. UNGI Rep. No. 57, Uppsala University, Uppsala, 151 pp. Jones, K. R. 1981. Arid Zone Hydrology. Food and Agricultural Organisation of the United Nations, Rome. 272 pp. Oltman, R. E. 1962. Measurement of Sediment Concentration and Computation of Sediment Transport. Flood Control Series 22, World

Pilgrim, D. H., Chapman, T. G., and Doran, D. G. 1988. ‘Problems of rainfall-runoff modelling in arid and semi-arid regions’. Hydro/.

Reid, I. and Frostick, L. E. 1987. ‘Flow dynamics and suspended sediment properties in arid zone flash floods’. Hydro/. Process. 1,

Sharma, K. D. 1992. ‘Runoff and sediment transport in an arid zone drainage basin’, Unpublished Ph. D. Thesis, Indian Institute of

Sharma, K. D., Choudhary, J. S., and Vangani, N. S. 1984a. ‘Transmission losses and quality changes along a desert stream - the

Sharma, K. D., Vangani, N. S., and Choudhary, J . S. 1984b. ‘Sediment transport characteristics of the desert streams in India’, J .

Sharma, K. D., Murthy, J . S. R., and Dhir R. P. 1994. ‘Streamflow routing in the Indian arid zone’, Hydrol. Process., 8, 27-43.

Research Techniques, Erodibility and Sediment Delivery. Geo Books, Norwich. pp. 73-8 I .

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