Soil Science Society of America Journal 64:1004-1008 (2000)
© 2000 Soil Science Society of America
DIVISION S-6-SOIL & WATER MANAGEMENT & CONSERVATION
The Effect of Slope Length on Sediment Concentrations Associated with Side-Slope Erosion
P.I.A. Kinnell
Centre for Resource and Environmental Studies, The Australian National Univ., Canberra ACT 0200, Australia
pkinnell{at}cres.anu.edu.au
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ABSTRACT
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Data from experiments where artificial rainfall was applied on side slopes associated with ridge-tillage in the field and short inclined surfaces in the laboratory were analyzed with respect to the effect of rainfall intensity and slope length on sediment concentrations associated with the flows from the side slopes. In both the field and laboratory experiments, sediment concentrations associated with side-slope erosion were linearly related to the intensity of the rain produced by the rainfall simulator over the range of slope length (150–600 mm) and gradient (5–30%) used in this study once the surface condition stabilized. In addition, sediment concentrations associated with flows from the side slopes were found to increase not only with slope gradient but also with slope length, particularly when side-slope gradients exceed 10%. Increases in side-slope erosion rate with slope length on these higher side-slope gradients have, in the past, been associated with the development of small rills. However, increases in sediment concentrations with slope length also occurred on the higher slope gradients when rilling did not take place. In this latter case, the effect may be the result of a change from erosion dominated by raindrop detachment and raindrop-induced flow transport (RD-RIFT) to erosion dominated by RD and flow transport (RD-FT).
Abbreviations: FT, flow transport • RD, raindrop detachment • RIFT, raindrop induced flow transport • ST, splash transport • WEPP, Water Erosion Prediction Project
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INTRODUCTION
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IN THE MAJORITY of rainfall erosion experiments, soil material transported across the down-slope boundary by splash contributes little to the soil loss. In most cases, most of soil loss results from the discharge of sediment (qs, mass of sediment per unit width of flow per unit time) that varies with flow discharge (qw, volume of water per unit width of flow per unit time) and sediment concentration (mass of sediment per unit volume of water) according to the equation
 | (1) |
Under these conditions, the erosion rate (Ar, mass-1 area-1 time-1) can be assumed to be given by
 | (2) |
where Q is the runoff rate (volume-1 area-1 time-1).
In ridge-tillage systems, surface-water flow caused by rain falling on the side slopes discharges into the furrows and then passes down the furrows until it is discharged across a down-slope boundary. In this system, rill erosion may occur in the furrows and interrill erosion on the side slopes. It is quite clear from Eq. [2] that runoff is a primary independent factor in relation to water erosion no matter whether the sediment is being discharged with sheet flow, interrill flow or rill flow. Q is dependent on the rainfall intensity, the soil infiltration rate, and the soil surface conditions that influence the manner in which water flows across the surface to the discharge point, while c depends on the reaction of the soil surface to the erosive stress applied to it by either raindrop impact, or surface-water flow, or both.
In the Water Erosion Prediction Project (WEPP) cropland model (Elliot et al., 1989), detachment caused by rill flow (Df) at a point x in a rill is given by
 | (3) |
where Kfs is a soil factor, t is the hydraulic shear of flowing water, tc is the hydraulic shear below which there is no detachment, and Tc is the transport capacity expressed as a sediment discharge. Energy is used in transporting detached particles so that, as indicated by the use of the term (1 - [qs(x) / Tc(x)]) in Eq. [3], some of the flow energy is not available for detaching particles from the soil matrix. Consequently, in situations where flow from the side slopes passes into the furrow and no significant change of water volume subsequently occurs in the furrow, it follows that the sediment concentration associated with the furrow discharge (cF) is given by
 | (4) |
where css is the sediment concentration in the flow discharged from the side slopes, and cff is the contribution to cF resulting from detachment by flow in the furrow, and
if cF > css, then detachment has taken place within the furrow,
if cF = css, the flow has the capacity to transport all the material being eroded from the contributing side slope,
but
if cF < css then this is not so and deposition has occurred in the furrow.
Thus, variations in css can have a major impact on the form of erosion that is dominant in ridge-tillage systems. When the WEPP cropland model is applied to ridge-tillage systems, it is assumed that side-slope length does not influence the erosion rate on the side slopes. Here, in this paper, the effects of slope length on side-slope erosion are examined through values of css obtained in the field and laboratory experiments of Meyer and Harmon (1984, 1989).
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Experimental procedures
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In the field experiments on side-slope erosion (Meyer and Harmon, 1984), 0.9-m2 plots with a ridge-furrow form were used. The area between the ridges was formed into two sloping planes meeting each other at the center of the furrow. A metal channel was used in the furrow to prevent rill erosion contributing to the sediment discharge. Flow lengths down the side slopes were of the order of 480 mm with side-slope gradients of about 20%. In these field experiments, the soil surfaces were subjected to a series of artificial rain storms produced by a rainfall simulator that uses oscillating nozzles to produce selected time-averaged rainfall rates (Meyer and Harmon, 1979). The simulator used Veejet 80150 nozzles generating impact energies of 275 kJ ha-1 per mm of rainfall (Meyer and Harmon, 1979). The general procedure adopted was to subject the surface to a 60-min storm of about 71 mm h-1 and then, on the following day, apply a 30-min storm at the same intensity followed by a series of 15-min storms with very low (e.g., 11 mm h-1), low (e.g., 26 mm h-1), medium (e.g., 71 mm h-1) and high (e.g., 107 mm h-1) application rates, although not necessarily in that order. Samples of runoff and sediment load were collected during the latter part of each 15-min storm and at various times during the 60- and 30-min storms. Further details of the procedures used can be found in Meyer and Harmon (1984). The field experiments on side-slope erosion were undertaken on about 20 different soils.
In the laboratory experiments (Meyer and Harmon, 1989), air-dried soil was placed in erosion pans in which two test areas sitting side-by-side were surrounded by a buffer strip that was at least 230 mm wide. Each test area had a width of 300 mm and was a duplicate of the other. Four slope lengths (150, 300, 450, 600 mm) and four slope gradients (5, 10, 20, and 30%) were used with each soil. Runoff and the sediment discharged with it were collected via a 25-mm wide slot at the down-slope end of each test area. The surfaces were subjected to a similar sequence of rainfalls as used in the field experiments using the same type of rainfall simulator. However, during the laboratory experiments, slightly different intensities (about 14, 27, 76, 115 mm h-1) were used and all runoff and sediment discharges were collected from each test area throughout the event at about 5-min intervals. Further details of the experimental procedures can be obtained from Meyer and Harmon (1989). The laboratory experiments were undertaken on four soils (Atwood, Brooksville, Dubbs, and Loring).
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Results
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Modern theory for erosion by raindrop-impacted flow (Kinnell, 1993, 1994) indicates that cri, the sediment concentration resulting from raindrops impacting the soil surface on the side slopes, may, in some circumstances, be given by an equation of the form
 | (5) |
where Krs is a soil factor, I is the rainfall intensity, EB is the kinetic energy per unit quantity of rain, L is slope length and S is slope gradient. Figure 1
shows two examples of how the sediment concentrations varied with rainfall intensity during experiments on side slopes undertaken in the field.
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Fig. 1 Sediment concentrations for field experiments on side slopes on (A) Brooksville and (B) Loring soils
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In some soils, sediment concentration tended to increase during the first 60-min run (e.g., vertical line at about 75 mm h-1 in Fig. 1A [Brooksville soil]) as a result of the susceptibility of the soil to erosion by rain-impacted flow increasing with time during that first 60 min of exposure to rain. In some soils, the sediment concentration and the susceptibility of the soil remained relatively constant during the first 60 min, while in other soils, sediment concentration fell as the susceptibility of the soil to erosion by rain-impacted flow decreased during the first 60 min (e.g., vertical line at about 75 mm h-1 in Fig. 1B [Loring soil]). In all cases, linear sediment concentration–rainfall intensity relationships were observed for the experiments that followed the 60-min run. In the context of the general linear equation between the sediment concentration of flow from a side slope and rainfall intensity,
 | (6) |
when EB is held constant, a value of a significantly different from zero will result if Krs varies with I during the experiments. In the majority of experiments, often small but statistically significant positive values of a were observed. Consequently, in most cases, I had an impact on Krs but it was small.
In the laboratory experiments, slope length (L) and gradient (S) were varied in addition to rainfall intensity. In order to compare the behavior of the various soils, the sediment concentrations were divided by the rainfall intensity:
 | (7) |
Since, from Eq. [5],
 | (8) |
c'ss provides an indicator of how the susceptibility of the soil on the side slopes to erosion varies when erosion by rain-impacted flow is the dominant form of erosion on the side slope and, as they do in the experiments being considered, EB, S, and L remain constant during a rainstorm or a series of rainstorms.
As a general rule, the c'ss values observed for the 60-min storm differed considerably from all other c'ss values observed for any given soil–slope length–slope gradient combination. Often, the c'ss value for the 30-min storm that was the first of the series performed the following day also differed considerably from the value obtained later at the same intensity. If the 60- and 30- min data were omitted, then, as a general rule, the sediment concentration–rainfall intensity relationships were, as in the case of the field experiments, well represented by Eq. [6]. Also, for some soils (e.g., Atwood), the deviation of a from zero was not only small but nonsignificant. A zero value of a is associated with c'ss, and hence Krs, varying independently of rainfall intensity. Usually, there was no significant difference between duplicates. However, repeating experiments on the same soils some months later did, on occasions, deliver significantly different results (e.g., Fig. 2)
. The reasons for this difference in behavior have yet to be identified.
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Fig. 2 Sediment concentrations for two separate laboratory experiments on Brooksville soil inclined at 10%. Each point represents data obtained for 15 min of rain on each of the duplicated 600-mm long, 300-mm wide test areas during the variable intensity storm series used on each occasion
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In terms of the comparisons between soils with respect to the effect of slope length, only the data where a was small or nonsignificant were considered. Under these circumstances, it follows from Eq. [6] and [7] that little difference exists between c'ss (Table 1) and b. The effects of slope length and gradient on erosion rate within the laboratory experiments have been reported by Meyer and Harmon (1989). Meyer and Harmon noted that when the side-slope gradient is 20% or more, soils that have a high susceptibility to rilling (e.g., Dubbs and Loring) produce higher erosion rates when side-slope length increases. This increase in erosion rate, which was associated with the development of small rills on surfaces that had not rilled when slope lengths were less, results in c'ss increasing with slope length on the steeper slopes (Fig. 3A and 3B) . However, the increase in c'ss is not restricted to soils that rill. The Atwood soil sealed readily but also produced an increase in c'ss with slope length when slope gradients were 20% or more (Fig. 3D) even though rilling was not a feature of this soil.
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Fig. 3 Mean c'ss values for the series of 15-min storms in the laboratory experiments with four soils after they had been treated with 60-min and 30-min medium intensity (70–75 mm h-1) rainfalls
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Discussion
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Four detachment and transport systems may operate on a side slope.
1. Raindrop detachment and splash transport (RD-ST). In this system, material detached by raindrop impact is splashed aerially over the surface.
2. Raindrop detachment and raindrop induced flow transport (RD-RIFT). In this system, material detached by raindrop impact is moved across the surface by rain impacted surface flow that, if not impacted by the raindrops, would not be able to move this material. Raindrop-induced flow transport operates through the combined action of raindrops and the flow and operates only in shallow flow.
3. Raindrop detachment and flow transport (RD-FT). In this system, material detached by raindrop impact is moved across the surface without the aid of raindrop impact. For this to occur, the hydraulic shear of flowing water must be sufficient to entrain the detached particles but not sufficient to detach soil particles from the soil matrix.
4. Flow detachment and flow transport (FD-FT). In this system, material is detached and transported by the flow without any raindrop involvement. For this to occur, the hydraulic shear of flowing water must be sufficient to detach soil particles from the soil matrix.
These systems may operate singly or in combination. In the laboratory experiments reported here, all of the systems operate together on some occasions but splash transport (ST) makes no significant direct contribution to the measured soil loss because only material transported by the flow was collected and measured (Meyer and Harmon, 1989). However, ST does contribute to material transported by the RIFT and FT systems.
In the experiments reported here, neither flow depth nor flow velocity were controlled. The linear relationships between sediment concentration and rainfall intensity observed in the side-slope erosion experiments undertaken on soil with slope gradients of 10% or less in the laboratory are, in general terms, consistent with observations made in the laboratory experiments where non-cohesive beds of uniform-sized particles were eroded by rain-impacted flows under conditions where flow depth and velocity were controlled (Kinnell, 1990, 1993). However, as noted earlier, some variation in Krs during the 15-min storm series resulted in values of a that differed significantly from zero. In most cases when this happened, a was positive (e.g., Fig. 2) indicating Krs was greater when I was low. A reason for this may lie in the fact that raindrop-induced flow transport (RIFT), which dominates erosion by rain-impacted flow when flow velocities are below those where flows transport detached particles without the aid of raindrop impact, is a transport limiting process (Kinnell, 1994). This leads to the development of a layer of pre-detached particles sitting on top of the soil matrix that provides a degree of protection to the particles in the soil matrix. Consequently,
 | (9) |
where Krs.D is the value of Krs when the soil matrix is fully protected by that layer, Krs.M is the value of Krs when there are no pre-detached particles sitting on the surface, and HRg, which has values between 0 and 1, is the degree of protection provided to the soil matrix particles by the layer of pre-detached particles above them. With HRg tending to increase with decreases in flow velocity, and Krs.D > Krs.M (Kinnell, 1994), there is a potential for Krs to increase as the runoff rate decreases in response to decreases in rainfall rate on infiltrating soil surfaces when RIFT operates. However, the reason why a was significantly greater than zero for a set of experiments on a soil on one occasion and not on another (Fig. 2) is not known at this time.
As noted earlier, c'ss changed little with slope length when slope gradients were at or below 10% in the laboratory experiments but increased with slope length at high slope gradients. For some of these soils, this increase in sediment concentration was associated with the development of small rills in surfaces that had not rilled when slope lengths were short. It follows from this that, for the flows discharged from side slopes on the rilling soils,
 | (10) |
applies for the shorter slope lengths on the higher gradients and all the slope lengths on the lower gradients, whereas, for the longer slope lengths on the higher gradients,
 | (11) |
where cfs is the contribution to css resulting from detachment by flow in the rills on the side slopes, applies. However, the rilling of these longer surfaces when inclined at the higher gradients also indicates that RIFT may not be operating over the whole of the surface for the longer surfaces inclined at the higher gradients even if they do not rill. For example, given a soil that readily crusts, the critical shear stress associated with the crusted surface (tc.M) may exceed the flow shear stress (t) over the whole of the surface but at some point down the plane, t may exceed tc.D, the critical shear stress required to entrain loose particles that have been pre-detached by raindrop impact. If this is the case, then RIFT operates upstream of the point where
, while raindrop detachment–flow transport (RD-FT) operates downstream of that point. Since RD-FT is a more efficient transport process than RIFT (Kinnell, 1994), sediment concentration to slope length relationships can vary between soils and with slope gradient even when differences in rilling susceptibility do not feature in the comparison. When particles detached by raindrop impact move with the flow, qs varies with the distance particles travel after being disturbed by a drop impact (Kinnell, 1990). When RIFT controls sediment discharge, travel distances vary with flow velocity. However, when RD-FT operates, particle travel distances equal the distance between the point of drop impact and the end of the eroding surface. Thus cri tends to increase as L increases and the dominance changes from RD-RIFT to RD-FT.
The results reported above conflict with the conclusion of Meyer and Harmon (1984) that soils that do not rill on side slopes do not produce higher erosion rates as slope length increases. The Meyer and Harmon analysis was restricted to data obtained during the 30-min "wet" experiments performed before the variable intensity storm series. Had they used the data for the variable intensity storm series (e.g., Fig. 4)
, their conclusion would have been different.
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Summary and conclusions
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In these experiments, the effect of rainfall intensity on side-slope erosion was investigated using artificial rainfall under both laboratory and field conditions. In both the field and laboratory experiments, sediment concentrations associated with side-slope erosion were linearly related to the intensity of the rain produced by the rainfall simulator over the range of slope length (150–600 mm) and gradient (5–30%) used in this study once the surface condition stabilized. In the majority of cases, 1 h of about 70 mm h-1 rain was sufficient for the stabilized condition to be achieved. In some cases, 1.5 h of rain was required.
In addition to the effect of rainfall intensity on side-slope erosion, the laboratory experiments produced data on the effect of slope length and gradient on sediment concentrations in flows from side slopes. These data indicate that the sediment concentrations associated with flows from the side slopes increase not only with slope gradient but also with slope length, particularly when slope gradients exceed 10%. Increases in side-slope erosion rate with slope length on these higher slope gradients have, in the past, been associated with the development of small rills. However, increases in sediment concentrations with slope length also occur on the higher slope gradients when rilling does not occur. In this latter case, the effect may result from a change from erosion dominated by raindrop-induced flow transport (RIFT) to erosion dominated by raindrop detachment–flow transport (RD-FT).
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ACKNOWLEDGMENTS
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The author would like to acknowledge L.D. Meyer and W.C. Harmon for providing access to the data on which this paper is based.
Received for publication January 4, 1999.
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REFERENCES
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- Elliot, W.J., A.M. Liebenow, J.M. Laflen, and K.R. Kohl. 1989. A compendium of soil erodibility data from WEPP cropland soil field erodibility experiments 1987 & 88. NSERL Rep. 3. The Ohio State University & USDA Agricultural Research Service, National Soil Erosion Res. Lab., Purdue Univ., West Lafayette, IN.
- Kinnell P.I.A. The mechanics of raindrop-induced flow transport. Aust. J. Soil Res. 1990;28:497-516.
- Kinnell P.I.A. Sediment concentrations resulting from flow depth/drop size interactions in shallow overland flow. Trans. ASAE 1993;36:1099-1103.
- Kinnell P.I.A. The effect of pre-detached particles on erosion by shallow rain-impacted flow. Aust. J. Soil Res. 1994;31:127-142.
- Meyer L.D., Harmon W.C. Multiple intensity rain-fall simulator for erosion research on row side slopes. Trans. ASAE 1979;22:100-103.
- Meyer L.D., Harmon W.C. Susceptibility of agricultural soils to interrill erosion. Soil Sci. Soc. Am. J. 1984;48:1152-1157.[Abstract/Free Full Text]
- Meyer L.D., Harmon W.C. How row-sideslope length and steepness affect sideslope erosion. Trans. ASAE 1989;32:639-644.
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