Measurements and estimation of flow velocity in mobile bed rills

Rills are primary sediment sources and hillslope water/sediment runoff transport channels. Water flow velocities in rills are easily affected by bed condition over eroding and non-eroding slopes, which is an important hydrodynamic process in soil erosion research. This research is done to demonstrate the poorly understood “feedback mechanism” related to slope independence of flow velocity to slope gradient. A series of experiments were done on silt loam soil slopes to measure water flow velocity...     

Rill hydraulics on a semiarid hillslope,southern Arizona

Seventy field experiments were conducted in seven rills located on a semiarid rangeland hillslope underlain by gravelly soils at Walnut Gulch, Arizona. The rills, which are characterized by wide, shallow cross-sections and gravel-covered beds, have mean at-a-station hydraulic geometry exponents of b = 0·33, f = 0·34 and m = 0·33. Although the differences between these values and typical values of b = 0·30, f = 0·40 and m = 0·30 for cropland rills are not statistically significant, they are thought to be real, as cropland rills often have more rectangular cross-sections and steeper sides than the rangeland rills under study. For rills formed in silty loamy soils, Govers developed an empirical relation between mean flow velocity and discharge. Emphasizing the generality of this relation, he suggested that it may be used as a simple means of routing runoff through rills. He also noted that this relation appeared to be unaffected by either slope or soil materials. The present data represent rills underlain by coarser and somewhat more varied gravel-rich soils. These data do not conform to Govers' relation, and a multiple regression analysis reveals that slope and soil materials, either directly or indirectly through bed roughness, exert almost as much influence on flow velocity as does discharge. Three alternative methods are developed for predicting flow velocity in the rills under study. All three methods give good results with the largest root mean square deviation being 3·115 cm s⁻¹.     

Estimating flow resistance in steep slope rills

Recent research recognized that the slope of 18% can be used to distinguish between the ‘gentle slope’ case and that of ‘steep slope’ for the detected differences in hydraulic variables (flow depth, velocity, Reynolds number, Froude number) and those representatives of sediment transport (flow transport capacity, actual sediment load). In this paper, using previous measurements carried out in mobile bed rills and flume experiments characterized by steep slopes (i.e., slope greater than or equal to 18%), a theoretical rill flow resistance equation to estimate the Darcy-Weisbach friction factor is tested. The main aim is to deduce a relationship between the velocity profile parameter Γ, the channel slope, the Reynolds number, the Froude number and the textural classes using a data base characterized by a wide range of hydraulic conditions, plot or flume slope (18%–84%) and textural classes (clay ranging from 3% to 71%). The obtained relationship is also tested using 47 experimental runs carried out in the present investigation with mobile bed rills incised in a 18%—sloping plot with a clay loam soil and literature data. The analysis demonstrated that: (1) the soil texture affects the estimate of the Γ parameter and the theoretical flow resistance law (Equation 25), (2) the proposed Equation (25) fits well the independent measurements of the testing data base, (3) the estimate of the Darcy-Weisbach friction factor is affected by the soil particle detachability and transportability and (4) the Darcy-Weisbach friction factor is linearly related to the rill slope.     

Hydrodynamic characteristics of rill flow on steep slopes

Rill erosion is a dominant sediment source on sloping lands. However, the amount of soil loss from rills on steep slopes is vastly more than that on gentle slopes because of differences in rill shape and hydraulic patterns. The aims of this paper are to determine the hydrodynamic characteristics of rills and the friction coefficients in steep slope conditions and to propose modifications of some hydraulic parameters used in soil loss prediction models. A series of inflow experiments was conducted on loess slopes. The results show that the geometric and hydraulic properties of rill on the steep loess slopes, which are characterized by the mean width of cross sections, mean velocity and mean depth of flow, are related to discharge and slope gradient in power functions. However, the related exponents to discharge are 0.26, 0.48 and 0.26, respectively, which are different from the exponents derived in previous studies, which were conducted on gentle slopes. The Manning roughness coefficient ranged from 0.035 to 0.071, with an average of 0.0536, and the Darcy–Weisbach friction coefficients varied from 0.4 to 1.9. The roughness coefficients are closely related to the Reynolds numbers and flow volumes; however, the correlations vary with slope gradient. The roughness coefficients are directly proportional to the Reynolds number and the flow volume on steep slopes, in contrast with the roughness coefficients found on gentle slopes, which decrease as the Reynolds number and flow volume increase. This difference is caused by the interactions among the hydraulics of the flow, the shape of the rills and the sediment concentrations on steep slopes. The results indicate that parameters used in models to predict rill erosion have to be modified according to slope gradient. Copyright © 2015 John Wiley & Sons, Ltd.     

Comparing flow resistance law for fixed and mobile bed rills

Rills caused by run‐off concentration on erodible hillslopes have very irregular profiles and cross‐section shapes. Rill erosion directly depends on the hydraulics of flow in the rills, which may differ greatly from hydraulics of flow in larger and regular channels. In this paper, a recently theoretically deduced rill flow resistance equation, based on a power–velocity profile, was tested experimentally on plots of varying slopes (ranging from 9% to 26%) in which mobile and fixed bed rills were incised. Initially, measurements of flow velocity, water depth, cross‐section area, wetted perimeter, and bed slope, carried out in 320 reaches of mobile bed rills and in 165 reaches of fixed rills, were used for calibrating the theoretical flow resistance equation. Then the relationship between the velocity profile parameter Γ, the channel slope, and the flow Froude number was separately calibrated for the mobile bed rills and for the fixed ones. The measurements carried out in both conditions (fixed and mobile bed rills) confirmed that the Darcy–Weisbach friction factor can be accurately estimated using the proposed theoretical approach. For mobile bed rills, the data were supportive of the slope independence hypothesis of velocity, due to the feedback mechanism, stated by Govers. The feedback mechanism was able to produce quasicritical flow conditions. For fixed bed rills, obtained by fixing the rill channel, by a glue, at the end of the experimental run with a mobile bed rill, the slope independence of the flow velocity measurements was also detected. Therefore, an experimental run carried out by a rill bed fixed after modelling flow action is useful to detect the feedback mechanism. Finally, the analysis showed that, for the investigated conditions, the effect of sediment transport on the flow resistance law can be considered negligible respect to the grain roughness effect.     

Testing slope effect on flow resistance equation for mobile bed rills

In this paper, a recently theoretically deduced rill flow resistance equation, based on a power‐velocity profile, is tested experimentally on plots of varying slopes in which mobile bed rills are incised. Initially, measurements of flow velocity, water depth, cross‐sectional area, wetted perimeter and bed slope conducted in 106 reaches of rills incised on an experimental plot having a slope of 14% were used to calibrate the flow resistance equation. Then, the relationship between the velocity profile parameter Γ, the channel slope, and the flow Froude number, which was calibrated using the 106 rill reach data, was tested using measurements carried out in plots having slopes of 22% and 9%. The measurements carried out in the latter slope conditions confirmed that (a) the Darcy–Weisbach friction factor can be accurately estimated using the proposed theoretical approach, and (b) the data were supportive of the slope independence hypothesis of rill velocity stated by Govers.     

Time-dependency of runoff velocity and erosion the effect of the initial soil moisture profile

The paper reports on experiments carried out to evaluate the effect of the initial soil moisture profile on temporal variations in runoff erosion rate. The moisture profile was varied by applying infrared heating to the soil sample surface over various time periods, while runoff erosivity was varied by varying the slope of the flume. The experiment confirms that dry loamy soils are very erodible: on a slope length of only 4.3 m long sediment concentrations are near transporting capacity in case of a dry soil sample. It appears that temporal variations in sediment concentrations can be well simulated using a simple relationship between runoff erosion resistance and initial soil moisture content, thereby implicitly assuming that the effect of initial moisture content is persistent over the whole duration of the experiment. The implications of these findings with respect to the modelling of sediment output from larger catchments and the design of experiments on rill erodibility are discussed. The experiments also show that, under the present circumstances, mean velocities in the rills appear to be independent of slope. This finding may be of importance with respect to overland flow routing and deterministic erosion modelling.     

Velocities of shallow overland flow on semiarid hillslopes

A series of 188 rainfall plot simulations was conducted on grass, shrub, oak savanna, and juniper sites in Arizona and Nevada. A total of 897 flow velocity measurements were obtained on 3.6% to 39.6% slopes with values ranging from 0.007 m s^‐1 to 0.115 m s^‐1. The experimental data showed that shallow flow velocity on rangelands was related to discharge and ground litter cover and was largely independent of slope gradient or soil characteristics. A power model was proposed to express this relationship. These findings support the slope–velocity equilibrium hypothesis. Namely, eroding soil surfaces evolve such that steeper areas develop greater hydraulic roughness. As a result overland flow velocity becomes independent of the slope gradient over time. Our findings have implications for soil erosion modeling suggesting that hydraulic friction is a dynamic, slope and discharge dependent property. Copyright © 2018 John Wiley & Sons, Ltd.     

Flow resistance equation for rills

In this paper, a new flow resistance equation for rill flow was deduced applying dimensional analysis and self‐similarity theory. At first, the incomplete self‐similarity hypothesis was used for establishing the flow velocity distribution whose integration gives the theoretical expression of the Darcy–Weisbach friction factor. Then the deduced theoretical resistance equation was tested by some measurements of flow velocity, water depth, cross section area, wetted perimeter, and bed slope carried out in 106 reaches of some rills shaped on an experimental plot. A relationship between the velocity profile, the channel slope, and the flow Froude number was also established. The analysis showed that the Darcy–Weisbach friction factor can be accurately estimated by the proposed theoretical approach based on a power–velocity profile.     

Depth distribution of interrill overland flow and the formation of rills

A Gumbel distribution for maxima is proposed as a model for the depths of interrill overland flow. The model is tested against three sets of field measurements of interrill overland flow depths obtained on shrubland and grassland hillslopes at Walnut Gulch Experimental Watershed, southern Arizona. The model is found to be a satisfactory fit to 81 of the 90 measured distributions. The shape δ and location λ parameters of all fitted distributions are strongly correlated with discharge. However, whereas a common relationship exists between discharge and δ for all depth distributions, the relationships with λ vary systematically downslope. Using the Gumbel distribution as a model for the distribution of overland flow depths, a probabilistic model for the initiation of rills is developed, drawing upon the previous work of Nearing. As an illustration of this approach, we apply this model to the shrubland and grassland hillslopes at Walnut Gulch. It is concluded that the presence of rills on the shrubland, but not on the grassland, is due to the greater runoff coefficient for the shrubland and/or the greater propensity of the shrubland for soil disturbance compared with the grassland. Finally, a generalized conceptual model for rill initiation is proposed. This model takes account of the depth distribution of overland flow, the probability of flow shear stress in excess of local soil shear strength, the spatial variability in soil shear strength and the diffusive effect of soil detachment by raindrops. Copyright © 2005 John Wiley & Sons, Ltd.     

Soil erosion by surface water flow on a stony,semiarid hillslope

Soil erosion on hillslopes occurs by processes of soil splash from raindrop impacts and sediment entrainment by surface water flows. This study investigates the process of soil erosion by surface water flow on a stony soil in a semiarid environment. A field experimental method was developed whereby erosion by concentrated flow could be measured in predefined flow areas without disturbing the soil surface. The method allowed for measurements in this study of flow erosion at a much wider range of slopes (2·6 to 30·1 per cent) and unit discharge rates (0·0007 to 0·007 m2 s−1) than have been previously feasible. Flow velocities were correlated to discharge and hydraulic radius, but not to slope. The lack of correlation between velocity and slope might have been due to the greater rock cover on the steeper slopes which caused the surface to be hydraulically rougher and thus counteract the expected effect of slope on flow velocity. The detachment data illustrated limitations in applying a linear hydraulic shear stress model over the entire range of the data collected. Flow detachment rates were better correlated to a power function of either shear stress (r2 = 0·51) or stream power (r2 = 0·59). Published in 1999 by John Wiley & Sons, Ltd.     

Testing a new rill flow resistance approach using the Water Erosion Prediction Project experimental database

In this paper, a recently theoretically deduced rill flow resistance equation, based on a power‐velocity profile, was tested using the Water Erosion Prediction Project database. This database includes measurements of flow velocity, water depth, cross section area, wetted perimeter, and bed slope that were made in rills shaped on experimental sites distributed across the continental United States. In particular, three different experimental conditions (only rainfall, only flow, and rain with flow) were examined, and for each condition, the theoretically based relationship for estimating the Γ function of the power velocity profile was calibrated. The results established that (a) the Darcy‐Weisbach friction factor can be accurately estimated using the proposed theoretical approach, and (b) the flow resistance increases with the effect of rainfall impact.     

In-situ assessment of the spatial arrangement of step–pool units on eroded rills

Rills are generated on homogeneous hillslopes by the action of different discharges and evolve morphologically over short timescales due to a strong interaction between the flow and bed morphology. Such an interaction generates a reconfiguration of the bed geometry. Previous works suggest that bed geometry is often characterized by alternation between pools and flat reaches (steps). Each step–pool unit may contribute to hydraulic resistance and affects flow behaviour. The objectives of this work are (i) to assess different (innovative) techniques for the in-situ assessment of rill bed geometry, (ii) to use these techniques to assess the geometry of eroded rills in situ in order to determine the spatial arrangement in the bed macro-scale roughness and (iii) finally to analyse the role of slope and discharge as driving factors associated with the development of these macroforms. Roughly rectilinear, long rills were formed in the field as a result of combining different slope and discharges. Photogrammetry provided detailed digital elevation models (DEMs) before and after the experiments. The rills were morphologically characterized from the DEMs. In each rill, the presence of step–pools was identified from long profiles according mainly to morphological criteria published elsewhere, but with ad hoc critical threshold values more appropriate for small eroded channels. The minimum slope required for the development of step–pool units seems to be somewhere between 5 and 15%. Discharge seems to affect pool size or roughness amplitude. There does not seem to be a clear step–pool periodicity. However, external factors could have affected the normal growth and alternation of these structures. Identification of steps and pools from longitudinal elevation profiles can be objectively accomplished using a series of geometric rules originally proposed for rivers and large channels, and adapted to rills. © 2019 John Wiley & Sons, Ltd.     

Sediment delivery on rill and interrill areas

Equations which relate sediment delivery to a power function of flow rate and slope gradient were evaluated in this study. The data used to parameterize the equations were obtained from sites where crop residues had been removed, and moldboard plowing and disking had occurred. Measurements of sediment delivery resulting from simulated rainfall were obtained from preformed rills and interrill areas. The equations provided reliable sediment delivery estimates for selected soils located throughout the United States. To use the sediment delivery equations, soil-related parameter values must be identified. Multiple regression analyses were performed to relate parameter values used in the equations to selected soil properties. Equations were also developed for estimating rill sediment delivery under rainfall conditions from rill soil loss and discharge data collected without the addition of rainfall. The equations identified in this study, and appropriate soils information, can be used to predict sediment delivery on both rill and interrill areas.     

Response of soil detachment rate to the hydraulic parameters of concentrated flow on steep loessial slopes on the Loess Plateau of China

Using hydraulic parameters is essential for describing soil detachment and developing physically based erosion prediction models. Many hydraulic parameters have been used, but the one that performs the best for describing soil detachment on steep slopes when the lateral expansion (widening) of rills is not limited has not been identified. An indoor concentrated flow scouring experiment was performed on steep loessial slopes to investigate soil detachment rates for different flow rates and slope gradients. The experiments were conducted on a slope‐adjustable plot (5 m length, 1 m width, 0.5 m depth). Sixteen combinations of 4 flow rates (10, 15, 20, and 25 L/min) and 4 slope gradients (17.6%, 26.8%, 36.4%, and 46.6%) were investigated. The individual and combined effects of slope gradient and flow hydraulic parameters on soil detachment rate were analysed. The results indicated that soil detachment rate increased with flow rate and slope gradient. Soil detachment rate varied linearly and exponentially with flow rate and slope gradient, respectively. Multivariate, nonlinear regression analysis indicated that flow depth exerted the greatest influence on the soil detachment rate, followed by unit discharge per unit width, slope gradient, and flow rate in this study. Shear stress and stream power could efficiently describe the soil detachment rate using a power equation. However, the unit stream power and unit energy of the water‐carrying section changed linearly with soil detachment rate. Stream power was an optimal hydraulic parameter for describing soil detachment. These findings improve our understanding of concentrated flow erosion on steep loessial slopes.     

The differential impact of some soil loss factors on flow,runoff creep and rainwash

The Hortonian model of runoff flow which had been thought to be applicable in arid areas has previously been shown not to be valid, notably in Israel, where inverse relations have been observed between slope angle, and runoff discharge and slope erosion. The paper discusses laboratory experiments on simulated slope conditions in a rather arid environment. It is shown by rain simulation on granite grus that infiltration capacity is a function of rainfall intensity, slope angle and runoff discharge. The infiltration capacity f can equal the rainfall intensity beyond a critical distance x(m) so that discharge becomes constant. Debris covers affect runoff hydraulics, especially on poorly cohesive soils, and both slow downslope and upslope movements which correspond to the process of so-called runoff creep can occur. Coarse debris and grass covers, as roughness factors, induce hydraulic discontinuities and activate local turbulent flow and slope erosion. Instead of being merely protective elements these factors tend to catalyze the slope wash, in comparison with naked surfaces, if the Reynolds number of the flow exceeds a certain critical value.     

Rill erosion processes on a constantly saturated slope

Rill erosion processes on saturated soil slopes are important for understanding erosion hydrodynamics and determining the parameters of rill erosion models. Saturated soil slopes were innovatively created to investigate the rill erosion processes. Rill erosion processes on saturated soil slopes were modelled by using the sediment concentrations determined by sediment transport capacities (STCs) measurement and the sediment concentrations at different rill lengths. Laboratory experiments were performed under varying slope gradients (5°, 10°, 15°, and 20°) and unit-width flow rates (0.33, 0.67, and 1.33 × 10⁻³ m³ s⁻¹ m⁻¹) to measure sediment concentrations at different rill lengths (1, 2, 4, and 8 m) on saturated soil slopes. The measured sediment concentrations along saturated rills ranged from 134.54 to 1,064.47 kg/m³, and also increased exponentially with rill length similar to non-saturated rills. The model of the rill erosion process in non-saturated soil rills was applicable to that in saturated soil rills. However, the sediment concentration of the rill flow increased much faster, with the increase in rill length, to considerably higher levels at STCs. The saturated soil rills produced 120–560% more sediments than the non-saturated ones. Moreover, the former eroded remarkably faster in the beginning section of the rills, as compared with that on the non-saturated soil slopes. This dataset serves as the basis for determining the erosion parameters in the process-based erosion models on saturated soil slopes.     

Sensitivity analysis of EUROSEM using Monte Carlo simulation II: the effect of rills and rock fragments

A sensitivity analysis of the surface and catchment characteristics in the European soil erosion model (EUROSEM) was carried out with special emphasis on rills and rock fragment cover. The analysis focused on the use of Monte Carlo simulation but was supplemented by a simple sensitivity analysis where input variables were increased and decreased by 10%. The study showed that rock fragments have a significant effect upon the static output parameters of total runoff, peak flow rate, total soil loss and peak sediment discharge, but with a high coefficient of variation. The same applied to the average hydrographs and sedigraphs although the peak of the graphs was associated with a low coefficient of variation. On average, however, the model was able to simulate the effect of rock fragment cover quite well. The sensitivity analysis through the Monte Carlo simulation showed that the model is particularly sensitive to changes in parameters describing rills and the length of the plane when no rock fragments are simulated but that the model also is sensitive to changes in the fraction of non‐erodible material and interrill slope when rock fragments were embedded in the topsoil. For rock fragments resting on the surface, changes in parameter values did not affect model output significantly. The simple sensitivity analysis supported the findings from the Monte Carlo simulation and illustrates the importance when choosing input parameters to describe both rills and rock fragment cover when modelling with EUROSEM. Copyright © 2000 John Wiley & Sons, Ltd.     

A simulation model for unified interrill erosion and rill erosion on hillslopes

A mathematical model was developed for simulating runoff generation and soil erosion on hillslopes. The model is comprised of three modules: one for overland flow, one for soil infiltration, and one for soil erosion including rill erosion and interrill erosion. Rainfall and slope characteristics affecting soil erosion on hillslopes were analysed. The model results show that the slope length and gradient, time distribution rainfall, and distribution of rills have varying influence on soil erosion. Erosion rate increases nonlinearly with increase in the slope length; a long slope length leads to more serious erosion. The effect of the slope gradient on soil erosion can be both positive and negative. Thus, there exists a critical slope gradient for soil erosion, which is about 45° for the rate of erosion at the end of the slope and about 25° for the accumulated erosion. Copyright © 2005 John Wiley & Sons, Ltd.     

Prediction of concentrated flow width in ephemeral gully channels

Empirical prediction equations of the form W = aQ^b have been reported for rills and rivers, but not for ephemeral gullies. In this study six experimental data sets are used to establish a relationship between channel width (W, m) and flow discharge (Q, m³ s^?1) for ephemeral gullies formed on cropland. The resulting regression equation (W = 2·51 Q^0·412; R² = 0·72; n = 67) predicts observed channel width reasonably well. Owing to logistic limitations related to the respective experimental set ups, only relatively small runoff discharges (i.e. Q < 0·02 m³s^?1) were covered. Using field data, where measured ephemeral gully channel width was attributed to a calculated peak runoff discharge on sealed cropland, the application field of the regression equation was extended towards larger discharges (i.e. 5 × 10^?4m³s^?1 < Q < 0·1 m³s^?1). Comparing W–Q relationships for concentrated flow channels revealed that the discharge exponent (b) varies from 0·3 for rills over 0·4 for gullies to 0·5 for rivers. This shift in b may be the result of: (i) differences in flow shear stress distribution over the wetted perimeter between rills, gullies and rivers, (ii) a decrease in probability of a channel formed in soil material with uniform erosion resistance from rills over gullies to rivers and (iii) a decrease in average surface slope from rills over gullies to rivers. The proposed W–Q equation for ephemeral gullies is valid for (sealed) cropland with no significant change in erosion resistance with depth. Two examples illustrate limitations of the W–Q approach. In a first example, vertical erosion is hindered by a frozen subsoil. The second example relates to a typical summer situation where the soil moisture profile of an agricultural field makes the top 0·02 m five times more erodible than the underlying soil material. For both cases observed W values are larger than those predicted by the established channel width equation for concentrated flow on cropland. For the frozen soils the equation W = 3·17 Q^0·368 (R² = 0·78; n = 617) was established, but for the summer soils no equation could be established. Copyright © 2002 John Wiley & Sons, Ltd.