Elsevier

CATENA

Volume 101, February 2013, Pages 197-204
CATENA

A unit stream power based sediment transport function for overland flow

https://doi.org/10.1016/j.catena.2012.09.006Get rights and content

Abstract

Soil erosion is a serious global problem requiring effective modeling for accurate assessment of sensitive areas and related erosion rates. The outcome of soil erosion models depends strongly on the estimation of sediment transport capacity. In most of the existing spatially distributed soil erosion models sediment transport capacity of overland flow is often estimated using stream flow transport capacity functions. The applicability of stream flow functions to overland flow conditions is questionable because hydraulic conditions like flow depth, slope steepness and surface roughness under overland flow are substantially different from stream flow conditions. Hence, the main objectives of this study were i) to check the suitability of five existing well known and widely used transport capacity functions (Yalin, 1963, Low, 1989, Govers, 1990; modified Engelund and Hansen (Smith et al., 1995); and Abrahams et al., 2001) for use under overland flow conditions, and ii) to derive a new function based on unit stream power by dimensional analysis to quantify transport capacity for overland flow. To accomplish the objectives, experiments in a 3.0 m long and 0.5 m wide flume were carried out using four different sands (0.230, 0.536, 0.719, and 1.022 mm). The unit discharges used for experimentation ranged from 0.07 to 2.07 × 10 3 m2 s 1 and slopes ranged from 5.2 to 17.6%. In this study, none of the predictions with the existing functions was in good agreement with measured results over the whole range of experimental conditions, especially at low flow intensities. The percentages of observations in which the discrepancy ratio ranged between 0.5 and 2.0 were: 65% (Yalin 1963), 74% (Low, 1989), 57% (Govers, 1990), 54% (modified Engelund and Hansen (Smith et al., 1995)), and 25% (Abrahams et al., 2001). The results showed that the selected functions reasonably estimate transport capacities only under those ranges of conditions for which they were formulated. Although the excess shear stress concept based function (i.e. Low's function) produced excellent results, the degree of accuracy of the results varied substantially with grain size (P.O.0.5–2.0: 53–100%). In contrast, the performance of the Govers' function, which is based on the unit stream power concept, was quite similar for all the selected sands (P.O.0.5–2.0: 50–63%). Based on the unit stream power concept, a new function for low flow intensities was derived by dimensional analysis using the data gained from the flume experiments.

Highlights

► Precise estimation of sediment transport capacity (Tc) is essential for modeling. ► Results revealed that each Tc function is only applicable to certain conditions. ► Tested Tc functions were unable to precisely estimate transport capacities. ► A new Tc function was derived by using dimensional analysis.

Introduction

Soil erosion is one of the world's biggest environmental problems with both on-site and off-site effects in cultivated watersheds (Vigiak et al., 2005). In particularly, it is a serious problem in hilly and mountainous terrain. Several spatially distributed soil erosion models (e.g. KINEROS2, Smith et al., 1995; LISEM, De Roo et al., 1996; EUROSEM, Morgan et al., 1998; WEPP, Flanagan et al., 2001) are being widely used to assess the rate of erosion at catchment scale, and also to discover the areas in a catchment which are more susceptible to erosion. Accurate identification of susceptible areas in a catchment is necessary for the planning of mitigation measures.

Erosion models distinguish between sediment detachment, which is the loosening of the soil material, and sediment transport, which is the removal of the detached sediment by the flow (Foster and Meyer, 1972). During the last three decades, a number of efforts have been made to better understand the processes entailed in sediment transport (Abrahams et al., 2001, Ali et al., 2012a, Everaert, 1991, Govers, 1990, Govers, 1992, Govers and Rauws, 1986, Jayawardena and Bhuiyan, 1999, Julien and Simons, 1985, Prosser and Rustomji, 2000, Zhang et al., 2009).

The precise estimation of sediment transport capacity plays a vital role in the outcome of each soil erosion model because both the rate of sediment detachment and deposition depend strongly on it (Foster and Meyer, 1972). Sediment transport capacity is the maximum amount of a specific sediment type which can be transported at a certain discharge rate and slope (Merten et al., 2001). Many transport capacity functions have been derived for stream flow conditions that are often used in soil erosion models (e.g. Engelund and Hansen, 1967, Low, 1989, Smart, 1984, Yalin, 1963). However the application of stream flow functions to overland flow conditions is questionable because the hydraulic conditions in overland flow are entirely different from the conditions in stream flow. For example, flow depth and slope gradient under overland flow conditions are considerably different than under stream flow conditions (Hessel and Jetten, 2007). Overland flow is much shallower as compared to stream flow and flow conditions in shallow flows are changing continuously due to surface roughness (Alonso et al., 1981). Under overland flow, slopes are generally steeper than under stream flow, and soil erosion properties on steep slopes are entirely different from soil erosion on low slopes (Govers, 1992). Furthermore, hillslope surfaces are normally rougher than stream beds. In view of the differences between stream flow and overland flow conditions, several researchers have derived empirical functions to quantify the transport capacity for overland flow by regression analysis of their experimental results (Everaert, 1991, Govers, 1990, Govers, 1992, Govers and Rauws, 1986, Smith et al., 1995). Only Abrahams et al. (2001) developed a transport capacity function by dimensional analysis for overland flow conditions using a limited range of flume experimental results.

Since the 1980s, several scientists checked the suitability of many stream flow and overland flow transport capacity functions for overland flow conditions (Ahmadi et al., 2006, Alonso et al., 1981, Govers, 1992, Guy et al., 1992, Hessel and Jetten, 2007, Low, 1989, Nord and Esteves, 2007). In these studies, researchers evaluated the performance of selected transport capacity functions under different ranges of hydraulic (slopes varied from 0.08 to 250%) and sediment conditions (median grain diameter ranged from 0.004 to 3.5 mm), and each study came to somewhat different conclusions. Govers (1992) reported that when a large number of transport capacity functions are tested on a limited range of hydraulic and sediment conditions, at least one function will show good agreement between measured and predicted transport capacities. Usually, the bed-load functions derived for stream flow and functions developed under overland flow conditions exhibited potential to quantify the transport capacity for shallow flows (Alonso et al., 1981, Govers, 1992, Hessel and Jetten, 2007, Low, 1989, Nord and Esteves, 2007). The reason for the bed load stream flow functions to perform well is probably that the transport of sand particles under overland flow is mainly by rolling, sliding and saltating movement (Lu et al., 1989), similar to bed load transport of sand in streams.

A majority of the available overland flow transport capacity functions were derived using concepts of shear stress (i.e. the drag force exerted by the flowing water on soil particles per unit bed area) and unit stream power (i.e. the amount of energy expenditure per unit time and per unit weight of water). Many researchers have found that unit stream power theory showed the best relationship with the measured sediment transport capacity for overland flow under erodible beds (Ali et al., 2012a, Govers, 1990, Govers, 1992, Govers and Rauws, 1986). Hence, the unit stream power theory is probably better in dimensional analysis to derive a physically based transport capacity function for overland flow conditions. According to Govers (1990), stream power and effective stream power theories are not recommended for predicting transport capacity under overland flow.

Sediment transport functions based on the shear stress concept are usually recommended for non-erodible beds, in which changes in morphology like headcuts, knickpoints, scourhole and slumping of rill walls do not occur (Guy et al., 1992, Low, 1989). This is due to the fact that both form shear stress (the part of shear stress which is absorbed by bed irregularities) and grain shear stress (the part of shear stress consumed on soil grains) are preferentially utilized to transport sediment particles under non-erodible beds (Ali et al., 2012a, Govers and Rauws, 1986). The function based on the shear stress concept by Yalin (1963), Low (1989), and Abrahams et al. (2001) were only considered in this study, because the Yalin (1963) function is used in the WEPP model (Flanagan et al., 2001), the Low (1989) function is recommended by Govers (1992), and the Abrahams et al. (2001) function was specifically developed for overland flow conditions.

On the other hand, the functions recommended either for natural hillslopes or for small erodible laboratory plots are often based on the unit stream power concept (Govers, 1992, Hessel and Jetten, 2007, Nord and Esteves, 2007). Govers’ (1990) and a modified version of the Engelund and Hansen (Smith et al., 1995) unit stream power concept based functions were only considered in this study, since the Govers (1990) function is recommended by Govers (1992) and Hessel and Jetten (2007), and the revised version of Engelund and Hansen function is used in the KINEROS2 model (Smith et al., 1995). In order to corroborate the findings of previous studies, there is a need to evaluate the performance of the most often recommended shear stress and unit stream power concept based functions for erodible beds.

Therefore, the aims of the present paper were (i) to check the suitability of the most well known and widely used shear stress and unit stream power concept based transport capacity functions for overland flow under erodible bed conditions, and (ii) to derive a new dimensionless function to quantify the sediment transport capacity of overland flow. For this purpose, flume experiments were performed to test selected sediment transport capacity functions, and to derive a new sediment transport capacity function (Ali et al., 2012a).

Section snippets

Sediment transport capacity functions

In order to have the study results be of broad value it was decided that, from all the available functions, only the best-known and widely used functions for soil erosion modeling would be considered. Therefore, in this study, the performance of three stream flow (Low, 1989, Yalin, 1963; Modified Engelund and Hansen, Smith et al., 1995) and two overland flow (Abrahams et al., 2001, Govers, 1990) functions was evaluated for shallow flows. The selected functions are based on both shear stress and

Experiment set-up

Experiments on sediment transport in overland flow using erodible bed conditions were carried out in a flume (3.0 m long and 0.5 m wide) with a smooth wooden floor and a Plexiglas wall on one side. The details of the experimental setup have already been described in a previous research paper (Ali et al., 2012a), and therefore are only briefly described here. A sketch of the setup is shown in Fig. 1.

The flume consisted of a 2.7 m long test section, with a sandy bed, and 0.2 and 0.1 m long pieces of

Performance of selected transport capacity functions

Fig. 2 shows the measured versus predicted sediment transport capacities obtained using the functions tested. Fig. 2a shows that the agreement between measured and predicted transport capacities is reasonable for the Yalin (1963) function. There were large discrepancies between measured and predicted values for low transport capacities (0.001 to 0.01 kg m 1 s 1), but relatively good results for transport capacities measured between 0.01 and 0.1 kg m 1 s 1 (Fig. 2a). The calculated value of P.O.0.5–2.0

Summary and conclusions

The suitability of five sediment transport capacity functions was evaluated for overland flow conditions using graphical and statistical analysis. The results show that the application of these functions is limited to the range of hydraulic and sediment conditions for which each was formulated. The selected functions do not adequately predict transport capacities, particularly at low flow rates (i.e. transport capacity below 0.01 kg m 1 s 1). This implies that there is still a need to improve the

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