Flow Detachment by Concentrated Flow on Smooth and Irregular Beds

Transcription

1 Flow Detachment by Concentrated Flow on Smooth and Irregular Beds Rafael Giménez* and Gerard Govers ABSTRACT points. Whereas on smooth beds, the total shear stress Historically, soil detachment by overland flow has mainly been is equal to the grain shear stress. A considerable amount studied using small samples with smooth surfaces. It may be questioned of form shear stress is generated on such irregular rill to what extent information from such experiments can be ap- beds, thereby reducing the flow velocity and increasing plied to predict flow detachment in actively eroding rills which are flow depth. characterized by rough irregular bed surfaces. To evaluate how flow It may therefore be questioned whether information detachment on rough and smooth beds are related, two types of la- on soil detachment derived from flat bed experiments boratory experiments were carried out: natural rill experiments, where can directly be applied to actively eroding rills with a a rill could freely develop; and small sample experiments, where small rough, irregular bed geometry. There are only a few boxes with smooth surface were used. Soil conditions in both types of experiments were kept as constant as possible. Flow hydraulics and studies on rill detachment under realistic conditions. sediment load were recorded in detail during each experiment. Our Brown and Norton (1994) carried out studies in field experiments show that unit length shear force and shear stress are plots to evaluate the effect of crop residues on interrill the most universal detachment predictor in rills (i.e., the relationship and rill (ridge) erosion. Similar studies were done in between these variables and soil detachment is independent of bed the field by Van Liew and Saxton (1983) to assess both geometry). Other hydraulic variables can also be successfully related the slope steepness and incorporated residue effects on to flow detachment on a given bed type (smooth or rough), but they rill erosion rates. Nearing et al. (1999) evaluated soil cannot accommodate for the effect of changing bed geometry. The detachment rate as a function of shear stress, stream fact that total shear stress controls flow detachment rather than grain power, and hydraulic friction in artificial rills created shear stress or unit stream power implies that the coupling between sediment detachment and sediment transport is more complex than is on the field in a stony soil. Field experiments were con- presently assumed. A detachment prediction approach using hydraulic ducted on a loam and a silt loam soil by Franti et al. parameters based on unit length may allow a more accurate and simpler (1999) to determine the effect of tillage on soil detach- way to estimate sediment detachment in rills than a predictor, ment in concentrated flow channels and to define a which needs an a priori calculation of flow width. shear stress-based detachment model including a soil strength index. I In these papers no attempt was made to relate the n overland flow, the main hydraulic variables controlling sediment detachment and transport are tion obtained on small soil samples with a smooth sur- results for natural rills with flow detachment informaslope, flow velocity, and flow depth. These variables can face. Nearing et al. (1997) attempted to combine data be combined in different ways to form composite pre- obtained from natural rills with data obtained from dictor variables with a physical basis for sediment de- small soil samples with a smooth surface. However, the tachment and transport such as hydraulic shear stress data obtained were not directly comparable as the soil (i.e., the drag exerted by the flow on the bed; e.g., Near- types used and the slopes and discharges applied in both ing et al., 1997), stream power (i.e., the energy of the types of experiments were different. Lei et al. (1998) flow dissipated to the bed by flow; e.g., Hairsine and took a different approach and developed a dynamic Rose, 1992a,b; Bagnold, 1966; Nearing, 1997), unit stream finite-element model for rill development model based power (i.e., the amount of energy dissipated per unit on the relationships of Nearing et al. (1997) for sediment time and per unit weight of the flow; e.g., Moore and transport and detachment derived from smooth bed ex- Burch, 1986; Yang, 1972), and effective stream power periments. Experiments showed that the model was ca- (Govers, 1992a). pable of simulating observed patterns of rill erosion. Soil detachment has mainly been studied using rela- However, the application of such a model on a routine tively small soil samples with fixed geometry and a basis is not possible because of the required input data smooth surface (e.g., Poesen et al., 1999; Nearing et al., and computer processing power. 1991, 1997; Shainberg et al., 1994; Glass and Smerdon, A comparison of flow detachment data obtained from 1967; Ghebreiyessus et al., 1994; Van Klaveren and smooth bed experiments with those obtained from natu- McCool, 1998; and Ciampalini and Torri, 1998). Under ral rills is useful for several purposes. First, it is worthsuch circumstances, flow detachment rates can be suc- while to investigate if a flow detachment parameter exists cessfully related to hydraulic parameters such as shear that can be used to predict detachment on surfaces with stress (e.g., Ghebreiyessus et al., 1994). However, real varying bed geometry. On rough surfaces a large amount rills have a rough irregular bed with headcuts and knick- of the flow s energy is dissipated on form roughness, so that form shear stress is often more important than grain Rafael Giménez and Gerard Govers, Lab. for Experimental Geomorphology, shear stress. Govers and Rauws (1986) and Govers (1992a) Catholic Univ. of Leuven, Redingenstraat 16, Leu- showed that the sediment transporting capacity of over- ven, Belgium. Received 3 Sept *Corresponding author (rafael. land flow on irregular beds is not determined by the gimenez@geo.kuleuven.ac.be). total shear stress, as an important part of the shear stress Published in Soil Sci. Soc. Am. J. 66: (2002). is dissipated on macroroughness elements and therefore 1475

2 1476 SOIL SCI. SOC. AM. J., VOL. 66, SEPTEMBER OCTOBER 2002 not effective for sediment transport. For fine sediments, transporting capacity on irregular beds was therefore much better related to grain shear stress and unit stream power. Whether this also holds for sediment detachment remains unclear. Second, if a relationship between flow detachment and flow hydraulics can be established that is valid both on smooth and irregular beds, it becomes much easier to transfer the results from experiments with small soil samples to real rills. This is important, as experiments with small soil samples are much easier to carry out and to replicate than simulations of natural rills. Govers (1992b), Takken et al. (1998), and Nearing et al. (1997) showed that flow velocities in rills eroding loose materials are well related to the total rill discharge. The power relationships they proposed are similar to the ones used in studies of river geometry (e.g., Langbein, 1964) and recognize that flow velocity is determined by the geometry of the whole cross-section. The finding that flow velocity in rills can be well predicted from total discharge may also have some implications for the prediction of flow detachment in rills. Usually, sediment detachment is related to parameters that are calculated on a unit width or unit surface basis (e.g., flow shear stress, stream power). This requires that rill width and, in some cases, also average flow velocity have to be predicted first, before rill detachment can be calculated. This may result in a loss of accuracy. We may therefore be more successful in predicting rill detachment using hydraulic parameters based on total discharge or on a unit length basis. An example of a parameter based on total discharge is the total stream power ( T ) that can be defined as: T gqs [1] Natural Rill Experiments The natural rill experiments were carried out in a 4.30-m long, 0.4-m wide, and 0.45-m deep flume using a set-up similar to the one described by Giménez and Govers (2001). The up- stream part of the flume was filled with soil and then covered with a 1.5-m long plastic sheet over which the water was led to the entrance of the 2.80-m long test section without causing any erosion. The bottom 0.2 m of the test section was filled with a silt loam soil which was manually compacted to simulate a subsoil. This soil was left in place for all experiments. Before each experiment, the top 0.25 m of the test section was filled with soil that was air-dried and sieved at 0.02 m to simulate fine seedbed conditions. The surface was smoothed with a rake, creating a flat-bottomed longitudinal depression of around 0.15 m wide and around 0.05 m deep to avoid water flowing down along the flume wall. Before each experiment, the soil s topography was deter- mined with a 1-mm resolution in the transverse direction and a 2-mm resolution in the longitudinal direction using a laser microreliefmeter driven by computer controlled stepping mo- tors, similar to the system described by Huang et al. (1988). The accuracy of the height measurements is around 0.1 mm. A detailed topographic map with a horizontal resolution of 1 mm was constructed from the raw data by kriging using the Surfer software (Golden Software, 1999). Soil moisture, bulk density, and vane shear strength were also measured (Table 1). At the start of the experiment, the flume was set at the de- sired slope and a preset discharge was applied at the upper end. During the experiments, flow velocity was measured using the dye tracing technique. Potassium permanganate solution was used as a dye, a small amount of which was injected 0.3- to 0.4-m upslope of the measuring section. Flow velocities were then measured by recording the travel time of the dye cloud over a distance of 1 m. Travel time was taken as the mean of 10 measurements. The point where the dye cloud reached 80 to 90% of its maximum width was taken as a benchmark for timing the cloud. To avoid an overestimation in the velocity measurements using the dye tracing technique, a correction factor of 0.94 was used (Govers, 1992b). Flow widths were mea- sured using a ruler. At regular time intervals, sediment and water samples were collected at the flume outlet from which discharge and sediment concentration were determined. The downslope wall of the flume was lowered regularly to avoid grsw p gas [2] important deposition in the test section. However, care was taken to avoid excessive erosion because of a too rapid decrease of the baselevel; thus, the downslope wall of the flume Where, equals density of the fluid, g equals gravitational acceleration, Q equals total discharge, and S equals slope. An example of a hydraulic parameter calculated on a unit length basis is the unit length shear force MATERIALS AND METHODS Two types of experiments were carried out: natural rill experiments, whereby a rill could freely develop in a simulated plough layer; and small sample experiments, where soil detachment from a smooth soil surface with limited dimensions was measured. Where, W p represents wetted perimeter, R equals hy- draulic radius, and A equals wetted cross section. A series of laboratory experiments was set up to address these issues. Our objectives are therefore (i) to evaluate to what extent the relationship between flow detachment and flow hydraulics is affected by bed geometry and to investigate whether there exists a hydraulic parameter that may be used to predict flow detachment independent of bed geometry, and (ii) to evaluate the potential of flow hydraulic parameters calculated on a total discharge or unit length basis to predict sediment detachment in rills. was never lowered below the rill bed level. This assured that no regressive erosion within the rill was initiated because of baselevel lowering. Experiments were continued as long as necessary to reach equilibrium flow conditions, i.e., flow velocities no longer changed significantly over time. Such conditions were achieved much quicker when the flow was more erosive. Experiments therefore lasted anywhere between 5 and 60 min. After the experiments, soil moisture, bulk density, and vane shear strength were again determined (Table 1). The flume was then replaced in a horizontal position and a new laser scan of the surface was made. Experiments were conducted at four slopes (3, 5, 8, and 12 ) and five inflow rates (0.2, 0.4, 1, 2.2, and 3.6 m 3 h 1 ). Experiments were carried out with two different topsoils (Table 2). In total, 20 experiments were carried out with a silt loam loess-derived topsoil, while 17 experiments were carried out with a loamy sand topsoil. The topographic data obtained by the laser scanner were used to (i) determine the longitudinal profile of the rill, and

3 GIMENEZ & GOVERS: FLOW DETACHMENT BY CONCENTRATED FLOW ON TWO BEDS 1477 Table 1. Soil physical parameters of the two soils before and after running the natural rill experiments. The three repetitions are averaged. Slope, degrees Disch m 3 h 1 Before After Before After Before After Before After Silt loam soil 0.2 Moisture, g 100 g Bulk density, Mg m v.s.s., kpa Moisture, g 100 g Bulk density, Mg m v.s.s., kpa Moisture, g 100 g Bulk density, Mg m v.s.s., kpa Moisture, g 100 g Bulk density, Mg m v.s.s., kpa Moisture, g 100 g Bulk density, Mg m v.s.s., kpa Loamy sand soil 0.2 Moisture, g 100 g Bulk density, Mg m v.s.s., kpa Moisture, g 100 g Bulk density, Mg m v.s.s., kpa Moisture, g 100 g Bulk density, Mg m v.s.s., kpa Moisture, g 100 g Bulk density, Mg m v.s.s., kpa Moisture, g 100 g Bulk density, Mg m v.s.s., kpa Discharge. Vane shear strength. to (ii) estimate the hydraulic characteristics of the rill flow. It contains a plot box (0.39-m long, m wide, and 0.09-m To obtain the longitudinal rill profile, a line was digitized deep) in its bottom. along the rill s central axis; the slope of the regression line of The soil box was filled with air-dried soil sieved at 0.02 m. height versus distance (S reg ) was used to determine the final Before the experiment the soil sample was saturated by capil- bed slope of the rill (S cor ), which was slightly different from larity and then drained to field capacity. The soil box was the slope of the flume (S f ). then inserted in the flume, making sure that the soil surface Next, estimates of flow depth, wetted perimeter, and hy- was at the same level as the bottom of the flume. The flume draulic radius were obtained for each experiment using a series was then set at the desired slope and a preset discharge was of 10 to 12 rill cross-sections obtained with the laser scanner applied. Flow velocities were measured by recording the travel and spaced 0.1 m apart. From the measured values of discharge time of the dye cloud over a distance of 0.4 m. As the flow and flow velocity the water height in a cross-section was esti- velocities in these experiments were rather high, the movement mated by matching the calculated discharge (using the assumed of the dye cloud was recorded on a video tape that was water height and the measured flow velocity) with the analyzed later. The same benchmark within the dye cloud and measured discharge using an iterative procedure. The values velocity correction factor as those in natural rill experiments of flow depth, hydraulic radius, and cross-sectional area were were used. Again, runoff samples were taken at regular time calculated for each cross-section and then averaged. Such an intervals to determine sediment load and detachment rates. estimation procedure neglects local variations in flow velocity Because of the small size of the soil sample, it was not possible as well as the fact that the water surface in a cross-section to determine soil moisture and bulk density on the samples is not horizontal. Therefore, the estimated values should be used for the experiments. Therefore, two to three sample treated with caution. For example, it was noticed that estimates boxes were prepared with each soil using exactly the same hydraulic mean depth showed a coefficient of variation of 10 procedure as the one applied to the sample boxes used in the to 35% for different cross-sections obtained after one experiment, so that the coefficient of variation of the average value Table 2. Soil characteristics. The granulometric analysis was done for 10 to 12 cross-sections varied between 3 and 10%. The by laser diffractometry (Beuselinck et al., 1998). true uncertainty is probably even greater, as flow velocity is Grain-size classes, % not constant along the rill. D 50 Organic matter 2 m 50 m 2 50 m m % Small Sample Experiments The flume used was similar to that described previously by Ciampalini and Torri (1998) and Poesen et al. (1999). It is made of Plexiglass and measures 2-m long by m wide. Silt loam Loamy sand

4 1478 SOIL SCI. SOC. AM. J., VOL. 66, SEPTEMBER OCTOBER 2002 experiments. From these boxes, two to three subsamples were RESULTS AND DISCUSSION taken to determine soil moisture and bulk density. Experiments were run at three slopes (5, 8, and 12 ) and Flow Hydraulics four inflow rates (0.4, 1, 2.2, and 3.6 m 3 h 1 ) for both soils. In the natural rill experiments, flow Reynolds s num- Each experiment lasted 5 min. Experiments were carried out bers ranged from approximately 280 to 8000 while the with the same two soils used in the natural rill experiments Froude numbers ranged from approximately 0.4 to 1.8. (Table 2). In total, 10 experiments were carried out with each soil. In experiments where rills formed, the Froude number Flow depth was estimated by dividing the total discharge tended towards a constant value for a given soil type by the product of measured flow velocity and flume width (Giménez and Govers, 2001). Flow width ranged from (0.098 m) while the hydraulic radius was calculated by the to m and flow depth from to m, estimated flow cross-section by the estimated wetted perime- respectively. ter ( w 2d, where w the flume width and d the Reynolds s numbers in the small sample experiments flow depth). were similar to those in the natural rill experiments, that is between 1000 and However, in the small Flow Detachment flume experiments much higher flow velocities were For each experiment in both flumes, sediment concentraand hydraulic radius. Consequently, Froude numbers obtained and therefore much lower values of flow depth tion measurements over the first 5 min were averaged and the net detachment was calculated as the amount of sediment were much higher and ranged between 2.4 and 5.7. Flow leaving the flume per unit time and per unit of rill length, D L, width was constant at m while flow depth ranged or per unit of rill bed area, D A. The rill bed surface area was from to 0.01 m. calculated as the product of rill length and flow width. Thus, Soil Conditions D L Q s /L (kg s 1 m 1 ) [3] The results of the measurements of characteristics of D A Q s /A x (kg s 1 m 2 ) [4] the two soils before and after the natural rill experiments Where Q s is solid discharge (kg s 1 ) and L (m) and A x (m 2 ), are the rill length and the rill surface area, respectively. are presented in Table 1. Some variation in initial conditions occurred between experiments, despite the efforts to keep soil conditions as constant as possible. Initial Hydraulic Parameters soil moisture content was rather high, so that the soil was relatively resistant to runoff erosion (Govers et al., Using the measured or estimated data of flow depth and 1990; Bennett et al., 2000). This was considered to be an velocity, the following flow hydraulic parameters were cal- advantage as rill evolution was relatively slow, so that culated: changes could well be monitored even on steep slopes. Hydraulic shear stress (Nearing, 1997) Bulk density and vane shear strength of the silt loam grs [5] soil did not show a systematic evolution during the experiment, while they increased slightly in the loamy sand Unit length shear force soil. The initial average bulk density for the silt loam W p gas [2] and loamy sand soils in the natural rill experiments were and Mg m 3, respectively. Stream power (Bagnold, 1966) The soil moisture before the small sample experiments v [6] (0.26 g g 1 ) was somewhat higher (p 0.01) than that before the natural rill experiments (0.23 g g 1 ). Unit stream power (Yang, 1972; Moore and Burch, 1986) Although the erosion resistance of soils is known to Sv [7] vary with the moisture content prior to the erosion event (Govers et al., 1990; Bennett et al., 2000; Bryan, 2000), Effective stream power (Bagnold, 1980; Govers, 1992a) the relative dependency of the runoff erosion resistance eff ( v) 1.5 /d 2/3 [8] is considered to be rather small for initial moisture contents exceeding 20% for the soil types used in our experi- The grain shear stress ments (Govers, 1991). g f g v 2 /8 [9] Initial bulk densities in the small sample experiments were similar to those measured in the natural rill experi- Where, equals the water density (kg m 3 ), g corresponds ments. The average bulk density for the silt loam and to the gravitational acceleration (m s 2 ), W p is the wetted loamy sand soil were and Mg perimeter (m), A represents the wetted cross-section area (m m 3, respectively. ), R equals the hydraulic radius (m) A/W p, S corresponds to the slope (sin), v is the average flow velocity (m s 1 ), d equals the flow depth (m), and f g represents the grain roughness Evolution of Sediment Concentration friction factor (-). Over Time The variable g was estimated following the approach of Govers and Rauws (1986): f g is estimated from the unit distion did not show a clear, systematic evolution over In the natural rill experiments, sediment concentracharge, the slope, the grain roughness (D 90 ), and the water temperature using the algorithm of Savat (1980). Next, the time. However, in most experiments an initial peak in grain shear stress can be calculated using Eq. [9]. sediment load was measured just after the start of the

5 GIMENEZ & GOVERS: FLOW DETACHMENT BY CONCENTRATED FLOW ON TWO BEDS 1479 load but in a way not fully explained by current detachment-transport coupling theory. The fact that our results are different from those of Merten et al. may be because of several factors, one of which is the difference in exper- imental set-up (a concatenation of soil boxes versus a continuous rill). It is also important to realize that sediment loads in our experiments were always well below the flow s transporting capacity (see below), so that any effect of sediment load on detachment rates may have been quite small. However, the absence of a sediment load effect on rill development in our experiments cannot be considered as an artifact because of the baselevel in our experiments was periodically lowered; the level of the the downslope wall of the flume was always kept slightly above the rill bed level, so that no regressive erosion could occur. experiment. This is thought to be because of the washing out of readily detachable soil material from the top of the soil surface. After this initial peak has passed, the variation in sediment yield remains considerable. This is probably due to local sediment production events, such as the generation of a headcut or a scour hole (Poesen et al., 1999; Bennett et al., 2000), as well as the slumping of the rill walls. The fact that the variation of sediment load over time is to some extent determined by random events implies that there is some experimental uncertainty associated with the 5 min average values that were used throughout the analysis. Therefore, a perfect correlation between flow detachment and average hydraulic parameter values cannot be expected. Prediction of Sediment Detachment The flow detachment rate (i.e., detachment per unit length and detachment per unit area) was modelled as a linear function of different hydraulic parameters (Table 3). The best relationship between flow detach- ment rate and hydraulic parameters for the two soils and both types of experiments was obtained by using unit length shear force,, as the independent variable and detachment per unit length, D L, as the dependent one (Table 3). The performance of the shear stress, which is the most frequently used predictor of flow de- tachment is also good. The relationships found for the unit length shear force and shear stress appear to be valid both for rough and smooth beds (Table 3, Fig. 2b). The other hydraulic parameters tested, with the ex- ception of the grain shear stress, also show a reasonable to good relationship with flow detachment if the natural rill and the small sample experiments are considered separately (Table 3). However, there is a clear, statisti- cally significant difference between the relationships obtained for the two types of experiment; measured flow detachment is much higher for the same value of the hydraulic parameter on a rough, natural rill bed than on a smooth bed (Table 3, Fig. 2a). Thus, these flow parameters do not accommodate for the differences in hydraulic conditions on smooth and rough surfaces. This finding is somewhat surprising: for a given dis- charge and slope flow detachment rates are relatively high on a rough rill bed where flow velocities are low. On a smooth bed where flow velocities are high flow Effect of Sediment Load on Detachment A problem that may arise in evaluating flow detachment is the effect that sediment load may have on flow detachment: Foster and Meyer (1972) proposed that the flow detachment capacity is a linear function of the difference between the sediment load (Qs) and the transporting capacity (Tc): Dr (Tc Qs) [10] Where equals rate control constant. If the presence of sediment affected flow detachment significantly in our experiments one would expect that the final rill cross sections would decrease with increasing distance downslope. To investigate this, the eroded volumes of the rills were plotted against the downslope distance in the rill (Fig. 1). The rill cross-sections show a considerable variation but there is no systematic decrease of the rill s cross-section with increasing distance downslope. This suggests that, at least for our experiments, the effect of sediment load on flow detachment is not important. This is in agreement with the findings of Huang et al. (1996); they found that in most of their experiments sediment export from natural rills increased linearly with rill length. Sediment detachment in the rills appeared to be independent of actual sediment load and they concluded from their experiments that rill detachment and transport should not be considered as coupled processes. On the other hand, Merten et al. (2001) working with small soil boxes connected to each other to form a narrow long canal, found that, in general, detachment decreased with increasing sediment Fig. 1. Eroded rill cavity volumes against downslope distance. Example of three rills formed in the loamy sand soil. Q discharge (m 3 h 1 ), S slope (degree).

6 1480 SOIL SCI. SOC. AM. J., VOL. 66, SEPTEMBER OCTOBER 2002 Table 3. Rill erosion as a linear function of different hydraulic parameters. D L, D A equals detachment per unit of rill length and per unit of rill bed area, respectively; equals unit length shear force; equals hydraulic shear stress; g equals grain shear stress; equals stream power; eff equals effective stream power; T equals total stream power; Sv equals unit stream power. Loamy sand Natural rill experiments Silt loam D L r ; p D L r ; p D A r ; p D A g r ; p D A r ; p D A r ; p D A g r ; p D L eff r ; p D A r ; p D L T r ; p D L eff r ; p D L 0.108Sv r ; p D L T r ; p D L 0.531Sv r ; p Loamy sand Small sample experiments Silt loam D L r ; p D L r ; p D A r ; p D A r ; p D A g r ; p D A g r ; p D A r ; p D A r ; p D L eff r ; p D L eff r ; p D L T r ; p D L T r ; p D L 0.091Sv r ; p D L 0.080Sv r ; p 0.03 Fig. 2. Detachment rate per unit of rill length as a function of (a) unit stream power and (b) unit length shear force both in natural rill and small sample experiments for the silt loam and loamy sand soils.

7 GIMENEZ & GOVERS: FLOW DETACHMENT BY CONCENTRATED FLOW ON TWO BEDS 1481 detachment rates are relatively low. The absolute magcapacity Table 4. Average values for the two soils of the transporting (Tc) and the soil s sensitivity to runoff erosion detach- nitude of the effect of different bed geometries on flow detachment is accounted for when the unit length shear ment ( ) for both natural rill and small flume experiments. A 95% level of confidence was used. force or the total shear stress are used as predictor variables. This result is different from what was found Experiment type Soil Tc with respect to the transporting capacity of overland kg s 1 m 1 flow. The transporting capacity of overland flow for Natural rill Silt loam fine-grained sediment can be predicted using the unit Small sample Silt loam Natural rill Loamy sand stream power or the grain shear stress, that is, the part Small sample Loamy sand of the shear stress absorbed by individual grains. Total shear stress is a poor predictor of transporting capacity on irregular beds (Govers and Rauws, 1986; Govers, dict detachment in rills would therefore lead to a considerable 1992b). On the other hand, grain shear stress appears underestimation of flow detachment in rills. to be a poor predictor of sediment detachment in natural The above calculations are only illustrating that the rills (Table 3). This may be qualitatively explained as value of is dependent on bed geometry and do not follows. A large part of the form shear stress in natural imply that sediment load does not affect flow detachment. rills is dissipated on knickpoints, headcuts, and other The presence of a sediment load may indeed rerills bed irregularities; these are indeed the locations where duce the flow s ability to detach sediment. However, a most of the sediment detachment occurs. However, the different modelling concept than that proposed by Fos- presence of these bed irregularities slows down the wa- ter and Meyer is necessary to describe this interaction; ter flow and reduces locally the slope gradient, thereby the relationship between transporting capacity and de- reducing the flow s transporting capacity. Thus, for a tachment capacity cannot be described using a simple given slope and discharge, the transporting capacity of rate control constant ( ). A possible approach is to model flow over a rough, natural rill bed will be lower than detachment rate (Dr) as a function of both detachment the transporting capacity over a smooth bed while its detachment capacity will be higher. As long as the whole rill bed consists of erodible soil, the form shear stress contributes effectively to sediment detachment while it does not contribute to sediment capacity (Dc) and transporting capacity, using different hydraulic parameters to predict detachment capacity and transporting capacity: Dr Dc 1 Q s [14] Tc ent hydraulic parameters. The relationship between the flow s detachment capacity and the flow s transporting capacity is therefore dependent on bed roughness. This can be illustrated by comparing values of (see Eq. [10]) for both types of experiments. Govers (1992a) proposed the following equation for the calculation of the transporting capacity of overland flow on smooth and rough beds: transport. The implication of this is that a simple coupled modelling of sediment detachment and transport, as proposed by Foster and Meyer (1972) and implemented whereby: in various erosion models, is not possible because sedi- Dc ae v [15] ment detachment and transport are controlled by differa equals constant, E v represents explanatory variable such as or and Tc may be calculated using Eq. [11]. Our data also indicate that predicting flow detach- ment rate on a per unit length basis using unit length shear force as a predictor gives somewhat better results than prediction on a unit surface area basis using shear stress. This is interesting as former research has shown that flow velocity, and therefore also the wetted cross- section in rills can be quite well predicted from total rill discharge, using equations of the form: 86.7(Sv 0.005) Tc Q [11] D V aq b [16] Where, D equals the grain size (m) and Tc represents the and transporting capacity (kg s 1 ). Assuming that sediment load has no effect on sediment detachment and considering A cq d [17] flow detachment per unit length rather than per where, V equals the flow velocity (m s 1 ), A is the unit surface, Eq. [10] can be rewritten as: cross-section area (m 2 ) and a, b, c, d represents the D L T c [12] constant values. can then be calculated as: Using over 400 datapoints, Govers (1992b) obtained values of 3.52 and for a and b and 0.34 and for c and d, respectively for rills eroding loose homogeneous D L [13] materials. Further research has shown that, for rills developing in a homogeneous substrate, the effect of soil Tc Table 4 shows that the average values of for the type or soil conditions on rill flow velocities is rather natural rill experiments are almost 10 times higher than limited (Takken et al., 1998). However, flow velocities those for the small sample experiments. The use of the appear to be lower when rock fragments are present -value derived from small sample experiments to pre- (Takken et al., 1998; Nearing, 1999; Govers et al., 2000)

8 1482 SOIL SCI. SOC. AM. J., VOL. 66, SEPTEMBER OCTOBER 2002 tachment on a unit length basis may have some advantages compared with prediction on a unit area basis because rill flow velocity and wet cross-section can easily be predicted from total discharge. Using this approach may lead to simpler, yet more performant models of rill erosion. ACKNOWLEDGMENTS Financial support of the work presented in this paper from the European Union (through project grant FAIR CT ) and K.U. Leuven (project grant OT95/15) is gratefully acknowledged. Ingrid Takken provided invaluable advice on programming the laser scanner and solving various experimental problems. Fig. 3. Detachment rate per unit of rill length as a function of predicted unit length shear force by using Eq. [18]. REFERENCES Bagnold, R.A An approach to the sediment transport problem and can be very strongly reduced by the presence of from general physics. U.S. Geological Survey Professional Paper vegetation cover (Takken et al., 1998). 422-I. U.S. Gov. Print. Office, Washington, DC. Thus, for rills developing on bare soils without rock Bagnold, R.A An empirical correlation of bedload transport fragments, the unit length shear force can be written as: rates in flumes and natural rivers. Proc. Royal Society Series A372: gas [2] Bennett, S.J., J. Casali, K.M. Robinson, and K.C. Kadavy Charor: acteristics of actively eroding ephemeral gullies in an experimental channel. Trans. ASAE 43: g(0.34q ) S [18] Beuselinck, L., G. Govers, J. Poesen, G. Degraer, and L. Froyen Grain-size analysis by laser diffractometry: Comparison with the sieve-pipette method. Catena 32: Therefore, flow detachment can be predicted directly Brown, L.C., and L.D. Norton Surface residue effects on soilfrom the knowledge of total discharge and slope. Fig- erosion from ridges of different soils and formation. Trans. 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These re- ware, Colorado, USA, available at sults are different from what was obtained for trans- [verified 15 Apr. 2002]. porting capacity for which the relationships with grain Govers, G Time-dependency of runoff velocity and erosion: shear stress and unit stream power are independent of The effect of the initial soil moisture profile. Earth Surf. Processes Landforms 16: bed geometry. In short, this is explained by the fact that Govers, G. 1992a. Evaluation of transport capacity formulae for form shear stress, which is dissipated on bed irregularit- overland flow. p In A.J. Parsons and A.D. Abrahams ies, does contribute to soil detachment but does not (ed.) Overland flow: hydraulics and erosion mechanics. UCL contribute to sediment transport. Press, London. Govers, G. 1992b. Relationship between discharge, velocity and flow The fact that different hydraulic variables control sedarea for rills eroding loose, non-layered materials. Earth Surf. 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9 GIMENEZ & GOVERS: FLOW DETACHMENT BY CONCENTRATED FLOW ON TWO BEDS 1483 Govers, G., I. Takken, and K. Helming Soil roughness and Nearing, M.A., L.D. Norton, D.A. Bulgakov, and G.A. Larionov. overland flow. Agronomie 20: Hydraulics and erosion in eroding rills. Water Resour. Res. Hairsine, P.B., and C.W. Rose. 1992a. Modeling water erosion due 33: to overland flow using physical principles. 1. Sheet flow. Water Nearing, M.A., J.R. Simanton, L.D. Norton, S.J. Bulygin, and J. Stone. Resour. Res. 28: Soil erosion by surface water flow on a stony, semiarid hillslope. Hairsine, P.B., and C.W. Rose. 1992b. Modeling water erosion due Earth Surf. Processes Landforms 24: to overland flow using physical principles. 1. Rill flow. Water Re- Nearing, M.A., J.M. Bradford, and S.C. Parker Soil detachment sour. Res. 28: by shallow flow at low slopes. Soil Sci. Soc. Am. J. 55: Huang, C., E.G. White, E.G. Thwaite, and A. Bendeli A noncon- Poesen, J., E. De Luna, A. Franca, J. Nachtergaele, and G. Govers. tact laser system for measuring soil surface topography. Soil Sci Concentrated flow erosion rates as affected by rock fragment Soc. Am. J. 52: cover and initial soil moisture content. Catena 36: Huang, C.H., J.M. Bradford, and J.M. Laflen Evaluation of the Savat, J Resistance to flow in rough supercritical sheet flow. detachment-transport coupling concept in the WEPP rill erosion Earth Surf. Processes Landforms 5: equation. Soil Sci. Soc. Am. J. 60: Shainberg, I., J.M. Laflen, J.M. Bradford, and L.D. Norton Langbein, W.B Geometry of river channels. J. Hydraulics Div. Hydraulic flow and water-quality characteristics in rill erosion. Soil 90: Sci. Soc. Am. J. 58: Lei, T.W., M.A. Nearing, K. Haghighi, and V.F. Bralts Rill Takken, I., G. Govers, C.A.A. Ciesiolka, D.M. Silburn, and R.J. Loch. erosion and morphological evolution: A simulation model. Water Factors influencing the velocity-discharge relationship in rills. Resour. Res. 34: IAHS Publ. 249: Merten, G.H., M.A. Nearing, and A.L.O. Borges Effect of Van Klaveren, R.W., and D.K. McCool Erodibility and critical sediment load on soil detachment and deposition in rills. Soil Sci. shear of a previously frozen soil. Trans. ASAE 41: Soc. Am. J. 65: Van Liew, M.W., and K.E. Saxton Slope steepness and incorpar- Moore, I.D., and G.J. Burch Sediment transport capacity of ated residue effects on rills erosion. Trans. ASAE 26: sheet and rill flow: Application to unit stream power theory. Water Yang, C.T Unit stream power and sediment transport. J. Hy- Resour. Res. 22: draulics Div. Am. Soc. Civil Eng. 98: