TEMPORAL VARIATION OF SEDIMENT YIELD FROM SMALL CATCHMENTS

Abstract

Estimates of sediment yield are needed for studies of reservoir sedimentation, river morphology, soil and water conservation planning etc. Methods are already in vogue for determination of sediment yield from catchments. As the largest storm produce largest soil loss, it is also necessary to estimate the variation of sediment yield with time, during a storm or for a series of storms. In the present study, methods are developed for prediction of temporal variation of the sediment yield during a storm. Here a simplified view of the complicated process of erosion is considered. The components of catchment erosion such as rill erosion, interrill erosion, gully erosion and channel scour and deposition are not considered separately. Therefore, temporal variation of sediment yield essentially means temporal variation of sediment load carried by the stream during the storm. Various models are available for estimation of these components, they can be grouped as (i) lumped models and (ii) physically based models. The lumped models combine the erosion from all processes over a catchment into one equation. Rainfall characteristics, soil properties and ground surface conditions are represented by empirical constants in these models. Following methods can be termed as the lumped models for catchment erosion, viz. (i) Universal Soil Loss Equation, USLE (ii) Modified Universal Soil Loss Equation, MUSLE (iii) USLE + Delivery Ratio (iv) Kling's methods (v) Revised Universal Soil Loss Equation, RUSLE etc. The lumped models are universally used for computation of sediment yield. However, they cannot be used in their original form for iv estimation of temporal variation of sediment yield. The physically based models separate the ground surface Into rill and Interrill areas to consider the rill and interrill erosion separately. Because of shallow depth of flow, detachment over interrill areas is considered to be by the impact of raindrop, while the runoff is considered to be the dominant factor in rill detachment and in sediment transport, over both rill and interrill areas. The governing equations for these can be solved analytically for simplified cases. Numerical solutions are obtained when these governing equation are solved for actual conditions. These models require co-ordinated use of various sub-models related to meteorology, hydrology, hydraulics, and soil etc. As a result, the number of Input parameter for these may be very high as in the case of CREAMS model.Thus practical application of these models is limited. It is in this background that the present investigation was taken up. Data on temporal variation of sediment yield resulting from storm events was compiled for the study from twelve catchments having varying climates. In three of these catchments measurements have been made by the author for collection of precise data on temporal variation of sediment yield during different storms in 1993. The rainfall was measured using self recording raingauge. Automatic water level recorders were used to measure stream stage and the runoff was derived using the rating curve. Sediment yield was measured by collecting sediment samples using bottle samplers. For the remaining catchments the above data was compiled from various publications. The data on catchment characteristics such as area, slope, soil type and land use etc. were also collected from publications, for these catchments. In all, data for 28 storms were collected for the 12 catchments. The commonly used methods for prediction of sediment yield from storm events were verified first for their accuracy. The method selected for this purpose were the USLE, the USLE + Delivery Ratio (DR) the MUSLE and Kling's method. It was found that the USLE, the MUSLE and Kling's methods mostly over predict the sediment yield whereas, the USLE + Delivery Ratio method underpredicts the sediment yields. Analysis has been carried out using the following two approaches: (i) Sediment Delivery Ratio Method, (ii) Numerical Solution of Governing Equations for Flow and Sediment. SEDIMENT DELIVERY RATIO METHOD Kling's approach for prediction of sediment yield seems to be a rational one. However, it requires sub-division of the catchment into arbitrarily selected cells, which has no basis. Also difficulty comes in computations, when an individual cell is to drain into more than one adjacent cell. An attractive alternative method to overcome this difficulty is to discretize the catchment on the basis of time-area diagram. The total catchment area can be divided into number of sub-areas (referred as time-area segments) by isochrones. The surface erosion within each time-area segment is computed using the USLE for a specific storm. The eroded sediment is then routed through each time-area segment to catchment outlet, using the delivery ratio (D ) concept. The following relationship is assumed to hold good for the D of a time- area segment K VI D = C Ai ♦ r sl ♦ r _AL W 1 *.._, C2 T—• + C3 -FT Ai-1 si-1 a rAi-l Where subscript i denotes serial number of the time-area segments increasing to the upstream from the catchment outlet. C , C and C3 are the coefficients which are assumed to be invariant in a catchment during different storms. AA is the area, L is the land slope, and FA is the area covered by forest with in any time-area segment. Considering that an isolated rain occurs over the catchment constantly for a duration of T hours . Here T is small enough, so that the assumption of constant intensity is valid. The catchment was divided into n (n = 1,2,3...) number of time-area segments in such a way that travel time for surface runoff within each segment is T hours. Let A Ei '* *• 2,..,nJ be the surface erosion caused by rainfall and the surface runoff (A£i can be computed using any lumped method such as the USLE) in any segment. Let DR1 D^. .. D^ ,be the sediment delivery ratios for the corresponding time-area segments. Then the total sediment yield AE due to this isolated storm is given as, AE =DR1AE1 +DR2AE2+ DR1DR2'" 'DRnAEn Where DR value for each segment is computed as per the earlier equation. In case of complex storms (i.e. rainfall of different magnitudes occurring successively), the rainfall can be separated into several successive events, each occurring for T hours with a constant intensity. The total sediment yield resulting from each event can be computed using the above equation. Algebraic sum of computed sediment yield for all the events is the total sediment yield during the complex storm event. VII It is well known that the temporal variation of effect of an input to be felt at the catchment outlet i.e. the storage effects can be obtained using the time-area curve. This method can also account for the time intensity variation and the areal distribution of the rainfall i.e. the input. By combining this notion with the concept of sediment delivery, one can obtain the temporal variation of the sediment yield. NUMERICAL SOLUTION OF THE GOVERNING EQUATIONS The scheme for routing of eroded sediment through the time-area segments showed promise in an erosion prediction model. Therefore, it was thought worthwhile to discretize a catchment into time-area segments and then to obtain numerical solution of the governing equations for flow of water and sediment along such a spatial grid. Continuity equation for one dimensional flow assuming uniform conditions over width of catchments is given as, aoyax + w (ah/at) = w. i e Where Q is the discharge, h is the depth, w is the catchment width at distance x from the beginning of the channel, t is the time and i is the lateral inflow rate (i.e. rainfall excess). If A is the area of cross-section of flow then, A = « (/ Where « and /3 are kinematic wave parameters, value of which is determined by roughness, hydraulic radius and bed slope. Here it is assumed that all changes in momentum flux and pressure are negligible so that s = s , where s_ is the friction slope and s is the bed slope. Assuming A =w.h above equation can be written as, 3Q 3x ♦ a 0 QP_1 f aQ 1 vm i e The equation can be solved along a non-uniform spatial grid formed by time-area segments, where kinematic wave friction relationship parameter a was allowed to vary from one time-area segment to another in the catchment geometry. Newton's iterative procedure was used for solution of the above nonlinear equation. Values of the flow velocity and the discharge were obtained at each grid point through such a solution. The continuity equation for soil erosion in a plane can be expressed as, 9qs 3(qs/V) 3WxZ + TaTt " D-F + DTI Where q^ is the mass of eroded soil per unit width, V the flow velocity, D the detachment due to raindrop impact and D„ is the 1 F detachment due to flow. D was taken as the function of rainfall intensity, soil and vegetation characteristics, while D,, as a function F of unit discharge, segment slope and the soil type. The value of q determined through the above equation was limited by transport capacity of the flow. The flow transport capacity was considered as a function of unit discharge, slope and soil characteristics. The equation was solved using a four point implicit scheme. Simultaneous solution of the two continuity equations produced temporal variation of sediment yield for a catchment. The above two approaches were found to produce satisfactory results.