Earth Surface Processes and Landforms Misrepresentation of the USLE ‘Is sediment delivery a fallacy?’ Earth Surf. Process. Landforms 33, in 1627–1629 (2008) Published online 23 January 2008 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/esp.1629
1627
ESEX Exchanges
Discussion: Misrepresentation of the USLE in ‘Is sediment delivery a fallacy?’ P. I. A. Kinnell* Institute of Applied Ecology, School of Resource, Environment and Heritage Sciences, University of Canberra, Canberra, Australia
*Correspondence to: P. I. A. Kinnell, Institute of Applied Ecology, School of Resource, Environment and Heritage Sciences, University of Canberra, Canberra ACT 2601, Australia. E-mail:
[email protected]
Received 13 June 2007; Revised 18 July 2007; Accepted 9 October 2007
Abstract The assertion that the application of the USLE to predicting soil losses within a catchment or watershed is not sound because the USLE provides an estimate of erosion that would be measured if the entire area were divided up into 22·1 m long plots, and the output from them all added together, is incorrect. The slope length factor was derived from data obtained using a wide range of plot lengths and included the 22·1 m length simply to force it to take on a value of 1·0 when the slope length is 22·1 m. The 22·1 m length has no physical significance but the USLE slope length factor has a physical basis when applied to planar and convex hillslopes. The use of sediment delivery ratios when the USLE is applied to concave areas attempts to correct for applying the USLE beyond its design criteria. It fails because, in using the sediment delivery ratios in the prediction sediment delivery, it is incorrectly assumed that sediment delivery ratios de not vary with the amount of sediment entering a zone of deposition. Copyright © 2008 John Wiley & Sons, Ltd. Keywords: hillslope soil losses; sediment delivery ratios
Although the sediment-delivery ratio, the percentage ratio between the sediment yield and erosion within a watershed or catchment, was conceived as a practical tool for estimating sediment storage within a catchment or watershed, Parsons et al. (2006) argue that it is not conceptually sound, implying that it cannot be relied upon to give useful results. Certainly there are a number of papers in the literature that support the view that using the sediment delivery ratio to predict sediment discharge from hillslopes is flawed, but Parsons et al. state that ‘most estimates of gross erosion are based on predictive equations such as the USLE or by using this (or similar equation) to give upland erosion and then estimating erosion from other sources’ even though the USLE ‘provides an estimate of the erosion that would be measured if the entire area were divided up into 22·1 m long plots and the output from them all added together’. This perception about the how the USLE and its derivates model soil loss on hillslopes is completely false. The USLE is often given as A = RKLSCP
(1)
where A is average (mean) annual soil loss (mass/area) over the long term (e.g. 20 years), R is the rainfall-runoff ‘erosivity’ factor, K is the soil ‘erodibility’ factor, L and S are the topographic factors that depend on slope length and gradient, C is the crop and crop management factor and P is the soil conservation practice factor. While Equation (1) is commonly seen in the literature, the model actually works mathematically in two steps. The reason for this is that the USLE is based on the unit plot concept, where the unit plot is defined as bare fallow area 22·1 m long on a 9% slope with cultivation up and down the plot. Only R and K have units and, for the unit plot, L = S = C = P = 1·0. As a consequence of this the USLE first predicts soil loss for the unit plot condition (A1) A1 = RK
(2)
and the result is subsequently multiplied by appropriate values of L, S, C and P to account for the difference between the area of interest and the unit plot, A = A1LSCP Copyright © 2008 John Wiley & Sons, Ltd.
(3) Earth Surf. Process. Landforms 33, 1627–1629 (2008) DOI: 10.1002/esp
1628
P. I. A. Kinnell
Contrary to the claim by Parsons et al. that the USLE is based upon regression equations derived from over 10 000 plot-years of data for plots 22·1 m long, the USLE is based on data from a wide range of plot lengths. The slope length factor that resulted from analysis of this data is calculated using the equation L = (λ/22·1)m
(4)
where λ is the slope length in metres and m is a factor that varies with slope gradient from a value of 0·2 for slopes less than 1% to 0·5 for slopes greater than 10% (Wischmeier and Smith, 1978). The length of slope upon which the calculation of L is based is defined as the distance from the onset of overland flow to the point where deposition begins or where overland flow enters a channel bigger than a rill. However, the 22·1 m length that appears in the denominator of Equation (4) has no physical significance. It is simply there to force L to take on a value of 1·0 when λ is 22·1 m. Its appearance in Equation (4) does not mean that the USLE provides an estimate of the soil loss that would be measured if the entire area were divided up into 22·1 m long plots and the output from all of them added together. In fact, the designers of the USLE could have chosen some other value for the length of the unit plot without having any impact on the amount of soil loss predicted by the model, given that the value of K (Equation (2)) would differ from the value of K used when the unit plot is 22·1 m in length. The USLE was designed to predict soil loss from areas that have uniform slope gradients. However, it can be applied to irregularly shaped hillslopes if the hillslope is broken into a number of planar segments. Under these circumstances, the L factor for each segment i is calculated using Li =
λmi +1 − λ im−1+1 ⋅ )m λi − λi−1(221
(5)
where λ i is the slope length to the bottom of segment i, λi–1 is the slope length to the bottom of the previous segment and m is determined by the slope gradient of segment i. Equation (5) results from an equation for sediment yield for the ith segment developed by Foster and Wischmeier (1974) and adopted in the Revised Universal Soil Loss Equation (RUSLE). The RUSLE maintains the same mathematical structure as the USLE but uses different methodology to determine some of the factor values (Renard et al., 1997). In reality, surface water flows converge and diverge in two dimensions on hillslopes because slopes usually have both a vertical and a lateral direction. Grid cell representations of landscapes in catchments provide a common vehicle for modelling spatial variations in soil loss given that each grid cell is considered to be uniform in terms of soil, slope length and gradient, and vegetation and management. In the L factor equation for grid cell i, j, contributing area ( χ) divided by the width of the contour (w) over which the overflow from that area flows replaces λ. This approach gives Li, j =
( χ i, j.in + D2 )m+1 − χ im, j+.in1 Dm+2 χ im, j (221 ⋅ )m
(6)
where χi,j.in is the contributing area for overland flow into the cell, D is the size of the cell (length of the sides of the cell) and x is a factor that accounts for variations in flow width that depend on the direction of flow relative to cell orientation (Desmet and Govers, 1996). Equations (5) and (6) account for not just segment length or grid cell size but also the position of the segment or cell in the landscape and, as noted above, the use of 22·1 m in the denominator of these equations does not mean that, in effect, the USLE provides an estimate of the soil loss that would be measured if the entire area were divided up into 22·1 m long plots and the output from all of them added together. It simply arises from the fact that the USLE works mathematically in two steps as indicted by Equations (2) and (3). It should also be noted that the neither the USLE, nor the RUSLE predict erosion as defined by Trimble (1975). They predict the soil lost from an area that results from the discharge of sediment across a downslope boundary, and the official documentation for the RUSLE discusses the effect of topography in terms of sediment yield (Renard et al., 1997), not erosion. It has long been recognized that the movement of soil material over the land surface is restricted by either detachment or transport processes (Figure 1). In reality, the USLE predicts sediment yield where transport limiting conditions do not cause significant deposition and, under these circumstances, the topographic factors in the USLE have a physical basis (Moore and Burch, 1986). Consequently, in a gross sense, the USLE works correctly within the scheme shown in Figure 1 on planar and convex hillslopes. However, given the definition of slope length in the USLE, its ability to take account of the effect of transport capacity on sediment delivery does not extend to situations where the transport capacity decreases in the downslope direction such as in the case of convex hillslopes. Thus, in many circumstances, the role of the sediment-delivery ratio in the prediction of sediment delivery from hillslopes has simply been as a correction factor for extending the USLE beyond its design criteria. Even so, the Copyright © 2008 John Wiley & Sons, Ltd.
Earth Surf. Process. Landforms 33, 1627–1629 (2008) DOI: 10.1002/esp
Misrepresentation of the USLE in ‘Is sediment delivery a fallacy?’
1629
Figure 1. Approach used by Meyer and Wischmeier (1969) to simulate the processes associated with the downslope movement of soil by water.
capacity to do this is questionable because the approach is based on the assumption that the sediment-delivery ratio does not vary with the amount of soil material entering a segment or cell when it has been shown that this is not the case (Kinnell, 2004). It should be noted that RUSLE2 (Yoder and Lown, 1995; Foster et al., 2003), a derivative of the USLE, uses a sediment transport capacity approach to deal with deposition on concave hillslopes and the impact of this deposition on the size characteristics of the sediment discharge from hillslopes. However, all models are likely to fail if their assumptions and approximations are not valid for the situations to which they are applied.
References Desmet PJJ, Govers G. 1996. A GIS procedure for automatically calculating the USLE LS factor on topographically complex landscape units. Journal of Soil and Water Conservation 51: 427– 433. Foster GR, Toy TE, Renard KG. 2003. Comparison of the USLE, RUSLE1.06 and RUSLE2 for application to highly disturbed lands. In First Interagency Conference on Research in Watersheds, 2003, Renard KG, McIlroy SA, Gburek WJ, Cranfield HE, Scott RL (eds). US Department of Agriculture, Agricultural Research Service: Washington, DC. Foster GR, Wischmeier WH. 1974. Evaluating irregular slopes for soil loss prediction. Transactions of the ASAE 17: 305–309. Kinnell PIA. 2004. Invited commentary: ‘Sediment delivery ratios: a misaligned approach to determining sediment delivery from hillslopes’. Hydrological Processes 18: 3191–3194. Meyer LD, Wischmeier WH. 1969. Mathematical simulation of the process of soil erosion by water. Transactions American Society Agricultural Engineers 12: 754–758, 762. Moore ID, Burch GJ. 1986. Physical basis of the length–slope factor in the Universal Soil Loss Equation. Soil Science Society of America Journal 50: 1294–1298. Parsons AJ, Wainwright J, Brazier RE, Powell DM. 2006. Is sediment delivery a fallacy? Earth Surface Processes 31: 1325–1328. Renard KG, Foster GR, Weesies GA, McCool DK, Yoder DC. 1997. Predicting soil erosion by water: a guide to conservation planning with the Revised Universal Soil Loss Equation (RUSLE). Agricultural Handbook No. 703. US Department of Agriculture: Washington, DC. Trimble SW. 1975. A volumetric estimate of man-induced soil erosion on the southern Piedmont Plateau. In Present and Prospective Technology for Predicting Sediment Yields and Sources, US Department of Agriculture Publication ARS-S-40; 142–154. Wischmeier WC, Smith DD. 1978. Predicting rainfall erosion losses – a guide to conservation planning. Agricultural Handbook No. 537. US Department of Agriculture: Washington, DC. Yoder DC, Lown JB. 1995. The future of RUSLE: inside the new Revised Universal Soil Loss Equation. Journal of Soil and Water Conservation 50: 484–489. Copyright © 2008 John Wiley & Sons, Ltd.
Earth Surf. Process. Landforms 33, 1627–1629 (2008) DOI: 10.1002/esp
