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Considering that water flow energy affects the detachment of soil particles, the transport and deposit of the detached particles, the flow velocity is a key variable governing the soil erosion processes at the hillslope scale. The simple dye-tracer technique for measuring mean flow velocity can be applied in non-controlled field applications for which some measurement difficulties (e.g. due to sediment transport, and shallow flows) can occur. The correction factor is usually obtained as the ratio between the mean velocity, deriving from measurements of flow discharge and water depth, and surface velocity. Alternatively, the possibility of using the velocity profile in a given vertical to determine a suitable correction factor has not yet been explored. In this article, the flow velocity measurements were carried out in five verticals having a different distance from the wall of a flume whose bed was covered by hemispheres with different concentrations (9%–64%) and organized in two arrangements (square, staggered). Fifteen runs, characterized by different Reynolds and Froude numbers, were performed and the correction factor αvv was calculated for each vertical. For the axial vertical αvv was independent of the arrangement, decreased with the hemisphere concentration, and increased with both the Froude and Reynolds numbers. Furthermore, αvv decreased from the bank to the flume axis as a result of the varying shape of the velocity profile. The analysis showed that the frequency distributions of the ratio between αvv and its mean value αm were overlaid and αm was used to represent the correction factor, accordingly. A relation of αm with the distance from the flume wall was detected. For the measured velocity profiles having a power shape, the analysis also demonstrated that the αvv values, obtained by fitting the power law to the measurements, were close to both those calculated as the ratio between the mean velocity along the vertical and the surface velocity and their averaged values across the hydraulic section. These three methods give comparable average values of the correction factor, in the range of 0.72–0.75, which are close to the commonly applied value of 0.8. Finally, this investigation demonstrated that a single survey of a power velocity profile allows for obtaining the correction factor accounting for different verticals across the entire hydraulic section.

Purpose In this paper, a deduced flow resistance equation for open-channel flow was tested using measurements carried out in mobile bed rills with sediment-laden flows and fixed bed rills. The main aims were to (i) assess the effect of sediment transport on rill flow resistance, and (ii) test the slope-flow velocity relationship in fixed bed rills. Methods The following analysis was developed: (i) a relationship between the Γ function of the velocity profile, the rill slope and the Froude number was calibrated using measurements carried out on fixed bed rills; (ii) the component of Darcy-Weisbach friction factor due to sediment transport was deduced using the corresponding measurements carried out on mobile bed rills (grain resistance and sediment transport) and the values estimated by flow resistance equation (grain resistance) for fixed bed rills in the same slope and hydraulic conditions; (iii) the Γ function relationship was calibrated using measurements carried out on mobile bed rills and the data of Jiang et al. (2018). Results This analysis demonstrated that the effect of sediment transport on rill flow resistance law is appreciable only for 7.7% of the examined cases and that the theoretical approach allows for an accurate estimate of the Darcy-Weisbach friction factor. Furthermore, for both fixed and mobile beds, the mean flow velocity was independent of channel slope, as suggested by Govers (1992) for mobile bed rills. Conclusions The investigation highlighted that the effect of sediment transport on rill flow resistance is almost negligible for most of the cases and that the experimental procedure for fixing rills caused the unexpected slope independence of flow velocity.

Rills caused by runoff concentration on erodible hillslopes generally have very irregular longitudinal profiles and cross-section shapes. Rill erosion directly depends on the hydraulics of flow within the rills which may differ greatly from that in larger and regular channels like streams or rivers. At first, in this paper, a review of the two different approaches to estimate rill flow velocity, based on flow regime and flow resistance laws, is presented. Recent advances in measurements of rill geometry by the three-dimensional photo-reconstruction (3D-PR) technique, which allows one to obtain a Digital Terrain Model (DTM) by low-altitude aerial and terrestrial photogrammetry, are also discussed. Indeed, information on rill geometry is also necessary to estimate flow velocity and depth using flow resistance equations. Then, the results of related laboratory and field investigations carried out from 1984 to 2022 are reported. In particular, the review was developed considering the studies conducted investigating the different components of rill flow resistance due to grain resistance, morphological resistance (step-pool), and sediment transport. Moreover, a brief mention of the slope threshold, equal to 18%, determining differences in hydraulic and sediment transport variables, is done. Also, an analysis is developed to demonstrate that a theoretical rill flow resistance law has been erroneously presented as an example of spurious correlation. Finally, some research needs on rill flow hydraulics are highlighted.

The main purpose of this article is to give a general idea of the scientific activity that was carried out starting from the 2000s on the basis of the data collected in the plots installed at the Sparacia experimental station for soil erosion measurement in Sicily, South Italy. The paper includes a presentation of the experimental site, a description of the methods and procedures for measuring soil erosion processes both available in the literature and applied at the Sparacia station (sediment sampling and water level reading in the storage tanks for total erosion measurements; profilometer, and Structure from Motion technique for rill erosion measurements), and the main results obtained in the monitoring period in the experimental site. The latter concern the effects of plot size and steepness on soil loss, the measurement variability, the frequency analysis of soil loss, the rill erosion characterization, and the comparison between rill and interrill erosion rates. Each of these topics is addressed with multi-temporal analyses performed with increasing size of the available database, which allowed to draw robust conclusions. Soil loss did not vary appreciably with plot length in contrast with the assumption made in the USLE/RUSLE. The variability of the measurements of soil loss, runoff volume, and sediment concentration at the event scale in replicated plots decreased as the mean measured value increased. The normalized event soil loss was distributed according to a two-component distribution. A power relationship between rill volumes and lengths was established. The measurements also confirmed the morphological similarity between the channels of the rills and ephemeral gullies described by a power dimensionless relationship. Rill erodibility of the sampled clay soil varied over time, maintaining relatively low values. Finally, rill erosion was dominant relative to interrill erosion, and a more efficient sediment transport system through the rill network occurred as plot steepness increased.

This is the closure to the discussions on the paper "Testing the Stage-Discharge Relationship in Sloping SMBF Flumes".

In this paper, for the first time, the effect of the longitudinal profile shape of the rill (uniform, concave, and convex) on flow resistance law was studied. The first part of the paper is based on a theoretical equation to estimate the Darcy–Weisbach friction factor f, deduced from the power velocity distribution and rill measurements performed on a plot. At first, the equation to estimate the Γ parameter of the velocity profile was calibrated using all available measurements. Then an analysis of the hydraulic characteristics at reach scale, for comparable values of discharge, was carried out, comparing the different profile shapes. To assess the influence of the rill profile shape on flow resistance law, this calibration was also carried out using the data categorized by profile. In the second part of the paper, an analysis of the scour depth and eroded rill volume was developed for four rills of each configuration. The results showed that an accurate estimate of f can be obtained by calibrating the flow resistance equation for each profile shape. The component of the Darcy–Weisbach friction factor that is due to the profile shape varied from 0.68 to 14.6% of the overall friction factor for the concave profile, and from 3.4 to 26.9% for the convex profile. The analysis also showed that, for the convex profile, the scour was concentrated downstream of the slope change, while for the uniform and concave profiles, it was uniformly distributed. Furthermore, the scour depth measured in correspondence of the rill thalweg had a generally increasing trend, with discharge for all the investigated profile shapes. Total eroded rill volume of the concave profile was lower than those detected for the uniform and convex profiles and was characterized by a reduction of 57.9%, as compared to the uniform profile.

The applicability of a theoretical rill flow resistance equation, based on the integration of a power velocity distribution, was tested using measurements carried out in mobile and fixed bed rills, shaped on plots having different slopes (9, 14, 15, 18, 22, 24, 25 and 26%) and soil textures (clay fractions ranging from 32.7% to 73% and silt of 19.9–30.9%), and flume measurements available in the literature. The Darcy–Weisbach friction factor resulted dependent on the slope, Froude number, Reynolds number and clay and silt percentages, used as variables representative of soil transportability and detachability, respectively. This theoretical approach was applied to two different databases distinguished by the slope threshold of 18%. The results showed that for both steep (≥18%) and gentle (

The Universal Soil Loss Equation (USLE) is still widely used to predict soil loss by water erosion and to establish soil conservation measures. In this model, the soil erodibility factor K accounts for the susceptibility of the soil to be eroded due to the detachment and transport processes operated by the erosive agents. According to the USLE scheme, the K factor should be measured on unit plots, i.e., bare plots of given length (22 m) and steepness (9%) tilled along the maximum slope direction, but there is little evidence that there ever existed an actual unit plot between the plots used to develop the USLE. Given the difficulty in collecting sufficient data to adequately measure K, the nomograph method was early developed to allow estimation of K based on standard soil properties. First, in this investigation the soil erodibility factor was experimentally determined for the clay soil of the Sparacia (Sicily) experimental station, based on the available measurements collected in two unit plots. Although a limited database was available for this analysis, a very low value (0.0038 t ha h ha-1 MJ-1 mm-1) was determined, which was an order of magnitude lower than the nomograph value. Then, the values of the plot steepness factor S were determined using soil loss measurements collected on plots varying in steepness from 9 to 26% and resulted higher than the estimated values by a well-known literature expression. Finally, the plot length factor L resulted independent of the plot length and equal to one. The former result was explained by the different flow transport capacity in the unit plot and plot with increased steepness, while the result of a constant length factor was supported by other experimental investigations.

Recent research on rill flows recognised that an 18% slope can be used to distinguish between ‘gentle’ and ‘steep’ slope cases for the detected differences in hydraulic (flow depth and velocity) and sediment transport variables (flow transport capacity, actual sediment load). The effects of slope on flow velocity, friction factor and transport capacity and their interactions affect process-based erosion modelling. The main aim of this paper is to investigate, for the first time, how slope affects the overland flow resistance on sandy soils, which are characterised by loose particles readily available to be transported and deposited. Using literature measurements carried out in sandy soils for both gentle and steep slopes, a theoretical overland flow resistance equation, based on the integration of the power velocity distribution, is tested. The relationship between the velocity profile parameter Γ, the channel slope, the Reynolds and Froude number is calibrated using measurements characterized by a wide range of hydraulic conditions and distinguishing between gentle (5.2%–13.2%) and steep (17.4%–42.3%) slope conditions. The analysis demonstrated that: (1) the parameter Γ can be accurately estimated by Equation (15) in which the exponents are independent of slope condition; (2) the coefficient a of Equation (15) is equal to 0.8750 and 0.8984 for the gentle and steep slope condition, respectively; (3) the estimations of the Darcy–Weisbach friction factor f (Equation 19) are accurate and characterised by errors less than or equal to ±5% for 97.2% of cases; and (4) in the range of steep slopes, the flow resistance law calibrated for the gentle slope condition (Equation (19) with a=0.8750) systematically overestimates the f value. In conclusion, this study allowed the recognition, for an unlimited soil detachment condition and an overland flow, of how the energy dissipation processes and the estimate of the friction factor are affected by slope. Highlights: A theoretical overland flow resistance law is tested by data obtained on sandy soils. Differences between gentle and steep slope conditions are investigated. The Darcy–Weisbach friction factor estimate by the flow resistance law is accurate. The law calibrated for gentle slopes overestimates f in the range of steep slopes.

Flow velocity is one of the most important hydrodynamic variables for both channelized (rill and gullies) and interrill erosive phenomena. The dye tracer technique to measure surface flow velocity Vs is based on the measurement of the travel time of a tracer needed to cover a known distance. The measured Vs must be corrected to obtain the mean flow velocity V using a factor αv=V/Vs which is generally empirically deduced. The Vs measurement can be influenced by the method applied to time the travel of the dye-tracer and αv can vary in different flow conditions. Experiments were performed by a fixed bed small flume simulating a rill channel for two roughness conditions (sieved soil, gravel). The comparison between a chronometer-based (CB) and video-based (VB) technique to measure Vs was carried out. For each slope-discharge combination, 20 measurements of Vs, characterized by a sample mean Vm, were carried out. For both techniques, the frequency distributions of Vs/Vm resulted independent of slope and discharge. For a given technique, all measurements resulted normally distributed, with a mean equal to one, and featured by a low variability. Therefore, Vm was considered representative of surface flow velocity. Regardless of roughness, the Vm values obtained by the two techniques were very close and characterized by a good measurement precision. The developed analysis on αv highlighted that it is not correlated with Reynolds number for turbulent flow regime. Moreover, αv is correlated neither with the Froude number nor with channel slope. However, the analysis of the empirical frequency distributions of the correction factor demonstrated a slope effect. For each technique (CB, VB)-roughness (soil, gravel) combination, a constant correction factor was statistically representative even if resulted in less accurate V estimations compared to those yielded by the slope-specific correction factor.

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.

In this paper, a recently deduced flow resistance equation for open channel flow was tested under equilibrium bed-load transport conditions in a rill. First, the flow resistance equation was deduced applying dimensional analysis and the incomplete self-similarity condition for the flow velocity distribution. Then, the following steps were carried out for developing the analysis: (a) a relationship (Equation) between the Γ function of the velocity profile, the rill slope, and the Froude number was calibrated by the available measurements by Jiang et al.; (b) a relationship (Equation) between the Γ function, the rill slope, the Shields number, and the Froude number was calibrated by the same measurements; and (c) the Darcy–Weisbach friction factor values measured by Jiang et al. were compared with those calculated by the rill flow resistance equation with Γ estimated by Equations and. This last comparison demonstrated that the rill flow resistance equation, in which slope and Shields number, representative of sediment transport effects, are introduced, is characterized by the lowest values of the estimate errors.

Interpreting rainfall‐runoff erosivity by a process‐oriented scheme allows to conjugate the physical approach to soil loss estimate with the empirical one. Including the effect of runoff in the model permits to distinguish between detachment and transport in the soil erosion process. In this paper, at first, a general definition of the rainfall‐runoff erosivity factor REFe including the power of both event runoff coefficient QR and event rainfall erosivity index EI30 of the Universal Soil Loss Equation (USLE) is proposed. The REFe factor is applicable to all USLE‐based models (USLE, Modified USLE [USLE‐M] and Modified USLE‐M [USLE‐MM]) and it allows to distinguish between purely empirical models (e.g., Modified USLE‐M [USLE‐MM]) and those supported by applying theoretical dimensional analysis and self‐similarity to Wischmeier and Smith scheme. This last model category includes USLE, USLE‐M, and a new model, named USLE‐M based (USLE‐MB), that uses a rainfall‐runoff erosivity factor in which a power of runoff coefficient multiplies EI30. Using the database of Sparacia experimental site, the USLE‐MB is parameterized and a comparison with soil loss data is carried out. The developed analysis shows that USLE‐MB (characterized by a Nash–Sutcliffe Efficiency Index NSEI equal to 0.73 and a root mean square error RMSE = 11.7 Mg ha−1) has very similar soil loss estimate performances as compared with the USLE‐M (NSEI = 0.72 and RMSE = 12.0 Mg ha−1). However, the USLE‐MB yields a maximum discrepancy factor between predicted and measured soil loss values (176) that is much lower than that of USLE‐M (291). In conclusion, the USLE‐MB should be preferred in the context of theoretically supported USLE type models.

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.

The Samani, Magallanez, Baiamonte, Ferro (SMBF) flume is a simple and inexpensive instrument for indirect discharge measurement that was originally proposed for use in a horizontal channel and then also applied in sloping channels. The contraction of the flow cross section, aimed at establishing a critical flow condition, is simply obtained by applying two half cylinders to the walls of a rectangular cross section. In this paper a theoretical approach previously proposed for a horizontal SMBF flume is first extended to a sloping SMBF flume and a new stage-discharge relationship is deduced. Then, this equation is experimentally tested using laboratory measurements from literature for different values of the contraction ratio and flume slope, and its reliability is compared to the reliability of the equation originally proposed in the literature.

Rill erosion is considered one of the most important soil processes because of the large amount of soil loss due to the development of a rill network able to promote an efficient transport of both rill flow-detached particles and those delivered from the inter-rill areas. Rill flow experiments are useful to overcome the gap in rill hydraulics knowledge and to test the reliability of currently applied uniform open channel flow equations for mobile bed rills. In this paper the applicability of a theoretical flow resistance equation, based on a power-velocity profile, to rill channels shaped on soils having different textures was investigated. The measurements (437 runs) of water depth, cross-section area, wetted perimeter, bed slope and flow velocity carried out in rill reaches shaped on experimental plots, having different slope values (9–26%) and soil texture (clay fraction range of 32.7–73%), were carried out. These measurements were jointly examined with 35 experimental runs carried out by other authors in a rill flume having a slope range of 18–84% and a clay content of 3%. The main aim of this paper is to deduce a relationship between the velocity profile parameter Γ, the channel slope and the flow Froude number using a database characterized by a wide range of slope (9–84%) and textural classes (clay ranging from 3 to 73%). The obtained relationship was also verified using 117 experimental runs carried out in this investigation by sloping plots (slope equal to 9 and 15%) with a soil having a clay content of 32.7%. The analysis demonstrated that the applicability of the theoretical flow resistance law is experimentally supported and that the effect of soil grain-size distribution is represented by silt and clay fractions which take into account the influence of the detachability and transportability properties of the soil particles. Highlights: Rill flow resistance is affected by interaction between flow, bed morphology and sediment transport. A new theoretical flow resistance law is tested for rills shaped on different textured soils. The velocity profile is related to the channel slope, the flow Froude number and the soil texture. The Darcy-Weisbach friction factor can be accurately estimated by the proposed theoretical approach.

In this paper, the morphology of step–pool features is analysed using rill measurements and literature data for streams. Close-range photogrammetry was used to carry out ground measurements on rills with step–pool units, shaped on a plot having slope equal to 14, 15, 22, 24 and 26%. Data were used to compare the relationships between H/L, in which H is the step height and L is the step length, and the mean gradient of the step–pool sequence, Sm, for streams or the slope of the step–pool unit, S, for rills. The relationship of H/L against Sm is widely used to test the occurrence of the maximum flow resistance condition in streams, which is associated with the range 1 ≤ (H/L)/Sm ≤ 2. Further analyses were carried out to compare both the formation process and the profile of the pool in rills with those related to streams. Moreover, for a single rill channel, an analysis of flow characteristics expressed in terms of Darcy–Weisbach friction factor and Froude number was developed. The results allowed us to state: (i) the relationships of H/L versus Sm and S are quite similar and the steepness ratio for streams, (H/L)/Sm, and for rills, (H/L)/S, generally ranges from 1 to 2; (ii) the formation process and the profile of the pool in rills are not consistent with those occurring in streams; (iii) in the rills, the longitudinal size of the pool is dominant with respect to the maximum scour depth; (iv) the presence of a sequence of step–pool units within a rill segment noticeably increases flow resistance compared to segments with a flat bed; (v) the Froude number of the flow over the sequence of step–pool units in rills is slightly below the range of 0.8–1 corresponding to the maximum flow resistance in step–pool units.

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 and soil texture in which mobile bed rills are incised. Measurements of flow velocity, water depth, cross section area, wetted perimeter and bed slope conducted in rill reaches incised on experimental plots, having different slope values (9, 14, 22, 24 and 26%) and soil texture (clay fraction ranging from 42 to 73%), and literature data were used to calibrate the flow resistance equation. In particular, the relationship between the velocity profile parameter Γ, the channel slope, the flow Froude number and texture fractions was firstly calibrated using 147 rill reach data. Then this relationship was tested using 126 measurements carried out with soils having different texture (percentage of clay ranging from 9.6 to 73%) and slopes (6.9%–26%). The measurements allowed to establish that a) the Darcy-Weisbach friction factor can be accurately estimated using the proposed theoretical approach, and b) the data were supportive of the soil texture influence on rill velocity and flow resistance.

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.

The main aim of this paper was to test a recently theoretically deduced flow resistance equation, based on a power-velocity profile, using a wide database of available measurements carried out in laboratory and field experimental runs with overland flow under simulated rainfall. In comparison with previous calibrations and validations of this theoretically deduced flow resistance equation, the used database by Emmett is characterized by a wide range of rainfall intensities (from 79.2 to 303.5 mm h−1 for laboratory runs and from 178.3 to 215.9 mm h−1 for field investigations) and bed slopes (from 0.33 to 17% for laboratory runs and from 2.9 to 33.2% for field investigations). For the first time, the wide Emmett’s database of laboratory runs carried out by an overland flow subjected to rainfall in a rough-bed-flume was used for testing the theoretical resistance law. Furthermore, the seven investigated field vegetated plots allowed to broaden the range of examined subcritical flows and rainfall intensity. Laboratory data were divided into two datasets (calibration and testing), and the overland flow measurements on a smooth bed by Yoon and Wenzel were added to the testing dataset to assess the applicability of the calibrated equation for different bed roughness conditions. The available laboratory measurements of flow velocity, water depth, hydraulic cross-section area, wetted perimeter and bed slope allowed both to calibrate and test the relationship between the velocity profile parameter Γ, the bed slope, the flow Froude number, and the rainfall Reynolds number, which is a dimensionless group representing the effect of rainfall intensity on flow resistance. The field data were used to calibrate the same flow resistance law and evaluate the effect of different types of vegetation, adapting the relationship obtained by Nicosia et al. The developed analysis showed that: i) the theoretical flow resistance equation gave an accurate estimate of the Darcy–Weisbach friction factor for overland flow under simulated rainfall on rough bed both in laboratory and in field condition; ii) the flow resistance increased with rainfall intensity for the investigated laminar overland flow; iii) the flow resistance relationship is able to take into account different vegetation types characterized by different roughness.

In this paper the results of a plot experiment on rill erosion are reported. The rill network, manually incised on the soil and further shaped by a clear inflow discharge, was surveyed using the three-dimensional photo-reconstruction (3D-PR) technique which allows to obtain a digital terrain model (DTM) by a large series of oblique images of the channel from consumer un-calibrated and non-metric cameras. The three-dimensional (3D) DTM and the quasi-tridimensional (2.5D) model were generated by Agisoft Photoscan software. For a single rill channel, the reliability of the 3D image-based ground measurements of morphological and hydraulic variables was positively tested by the corresponding measurements carried out on the rill gypsum cast. Moreover, the morphological and hydraulic variables were measured at 11 transects of the plot by a profilometer P, the 2.5D and 3D models. Using the 3D model as reference, the analysis showed that the reliability of the measurements by P and 2.5D methods was comparable and the error was generally lower than 15%. The rill measurements carried out by the three methods agreed with the available literature measurements and supported the applicability of both the empirical relationship between rill length and its eroded volume and the theoretical dimensionless relationship among the morphological variables describing the channelized erosion process. The analysis also showed that the effect of the distance between two consecutive cross sections on the rill volume measurement by 3D model is negligible. Finally, the shaping effect of different flow discharges on three straight rills incised into the plot was tested. In particular, three increasing flow discharges (0.15, 0.35 and 0.5 l s − 1 ) were used sequentially in two rills while the maximum discharge of the sequence (0.5 l s − 1 ) was used into the third rill. Both the grain-size distribution of the eroded sediment and the total amount of soil loss were affected by the discharge sequence.

Previous experimental investigations showed that a large proportion of total plot soil erosion over a long time period is generally due to relatively few, large storms. Consequently, erosion models able to accurately predict the highest plot soil loss values have practical importance since they could allow to improve the design of soil conservation practices in an area of interest. At present USLE-based models are attractive from a practical point of view, since the input data are generally easy to obtain. The USLE was developed with specific reference to the mean annual temporal scale but it was also applied at the event scale. Other models, such as the USLE-M and the USLE-MM, appear in principle more suitable to predict soil loss at this last temporal scale, because they include event plot runoff as an additional variable. At first in this investigation, carried out by using plot data collected at the experimental station of Sparacia, in Sicily (length, λ = 11–44 m, slope steepness, s = 14.9–26.0%), the circumstance that a single event in the year was responsible of approximately the 75% of total erosion during that year was recognized. Then the suitability of the USLE-derived models to predict maximum annual values of event soil loss was tested by measured events in all experimental plots (570 soil loss values for the complete data set, and 57 values for the data set of the maximum annual soil loss), in the period January 2002–March 2015, at Sparacia experimental area. This analysis showed the best model performance of USLE-MM schemes (Nash and Sutcliffe index, NSEI > 0.70) to determine the annual maxima of event soil, compared with the classical parameterization of USLE ( NSEI = 0.32). The development of methodologies widely applicable for estimating both the soil erodibility factor and the plot runoff coefficient will represent a step towards a diffuse application of this model.

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.

Many field investigations have clearly shown that rare and severe events control total soil erosion occurring over a long time period with up to 92% of total soil erosion over a 7‐year period resulting from just three daily events. Therefore, soil conservation strategies should be developed taking into account large events rather than long‐term average erosion. From an engineering point of view, establishing the soil loss of a given return period is needed. This can be obtained by the frequency analysis of soil loss measurements or by suitable soil erosion models. The USLE‐M modified and USLE‐M based are two empirical Universal Soil Loss Equation‐Modified (USLE‐M) type models which were developed using runoff and soil loss measurements collected at the Sparacia (South Italy) station. According to USLE‐M type models, the return period of the estimated soil loss coincides with that of the rainfall‐runoff erosivity index. In this investigation, using the maximum annual values of event soil loss measured on bare plots at Sparacia, this hypothesis was recognized to be not valid. To overcame this limit, a parameterization method which imposes the coincidence of the two return periods was applied. The models, which were parameterized by the maximum annual values of event soil loss, produced only moderate improvements in the prediction of the soil loss of given return period as compared with their previously published versions, which were parameterized by all available measurements. This result induced to hypothesize that parameterization of the USLE‐MM and the USLE‐MB models useful to estimate the soil loss of given return period in other sites can be also performed with all available data, not only with the maximum annual event soil losses which would require a larger number of recording years to obtain a suitable sample size. However, the developed database should span a wide soil loss measurement range. In general, at Sparacia both USLE‐MM and USLE‐MB were able to yield accurate predictions for return period ranging from 4 to 20 years.

Overland flow, sediments, and nutrients transported in runoff are important processes involved in soil erosion and water pollution. Modelling transport of sediments and chemicals requires accurate estimates of hydraulic resistance, which is one of the key variables characterizing runoff water depth and velocity. In this paper, a new theoretical power–velocity profile, originally deduced neglecting the impact effect of rainfall, was initially modified for taking into account the effect of rainfall intensity. Then a theoretical flow resistance law was obtained by integration of the new flow velocity distribution. This flow resistance law was tested using field measurements by Nearing for the condition of overland flow under simulated rainfall. Measurements of the Darcy–Weisbach friction factor, corresponding to flow Reynolds number ranging from 48 to 194, were obtained for simulated rainfall with two different rainfall intensity values (59 and 178 mm hr⁻¹). The database, including measurements of flow velocity, water depth, cross‐sectional area, wetted perimeter, and bed slope, allowed for calibration of the relationship between the velocity profile parameter Γ, the slope steepness s, and the flow Froude number F, taking also into account the influence of rainfall intensity i. Results yielded the following conclusions: (a) The proposed theoretical flow resistance equation accurately estimated the Darcy–Weisbach friction factor for overland flow under simulated rainfall, (b) the flow resistance increased with rainfall intensity for laminar overland flow, and (c) the mean flow velocity was quasi‐independent of the slope gradient.

In this paper a recently theoretically deduced flow resistance equation, based on a power-velocity profile, was tested using laboratory measurements by Yoon and Wenzel for an overland flow on a smooth bed under rainfall. These measurements of the Darcy-Weisbach friction factor, corresponding to a wide range of the flow Reynolds number (191–5700), were carried out for an overland flow under a simulated rainfall characterized by different intensity values ranging from 13 to 381 mm h−1. At first, the available measured values of flow velocity, water depth, cross sectional area, wetted perimeter and bed slope were used to calibrate the relationship between the velocity profile parameter Γ, the slope steepness s and the flow Froude number F. Then the theoretical approach and the measurements in the investigated conditions allowed to state that the coefficients of the relationship (Eq. (8)) between Γ, s and F vary with rainfall intensity. Furthermore, the theoretical flow resistance equation (Eq. (9)) allowed an accurate estimate of the Darcy-Weisbach friction factor, which is characterized by errors less than or equal to ±10% for 91.3% of cases and less than or equal to ±5% for 84.8% of cases. Finally, the developed analysis stated that the effect of rainfall intensity on flow resistance is always negligible for turbulent conditions while for Re < 2000 the effect of rainfall impact becomes negligible for rainfall intensities greater than a critical value occurring in the range 31.75–95.25 mm h−1.

In this paper a recently theoretically deduced flow resistance equation, based on a power-velocity profile, was tested using data collected for overland flow under simulated rainfall carried out in plots with vegetation. The available data were obtained exploring a wide range of rainfall intensities (from 60 to 181 mm h−1) and slopes (from 3.6 to 39.6%), and with four different types of vegetation. The database, including measurements of flow velocity, water depth, cross sectional flow area, wetted perimeter and bed slope, was divided in four datasets (one for each vegetation type), which allowed the calibration of the relationship between the velocity profile parameter Γ, the slope steepness, the flow Froude number, and the rainfall Reynolds number. The effect of rainfall intensity and different types of vegetation on flow resistance was investigated. The results showed that the theoretically deduced flow resistance equation allowed an accurate estimate of the Darcy-Weisbach friction factor for overland flow under simulated rainfall and in presence of vegetation. The developed analysis also suggested that flow resistance increases with rainfall intensity for laminar overland flow. The available data demonstrated that a quasi-independence between slope and mean velocity occurred. Finally, a single flow resistance equation resulted applicable to all investigated vegetation types and this equation was affected by flow regime represented by flow Reynolds number.

At first, in this paper a general definition of the event rainfall-runoff erosivity factor for the USLE-based models, REFe = (QR)b1(EI30)b2, in which QR is the event runoff coefficient, EI30 is the single-storm erosion index and b1 and b2 are coefficients, was introduced. The rainfall-runoff erosivity factors of the USLE (b1 = 0, b2 = 1), USLE-M (b1 = b2 = 1), USLE-MB (b1 ≠ 1, b2 = 1), USLE-MR (b1 = 1, b2 ≠ 1), USLE-MM (b1 = b2 ≠ 1) and USLE-M2 (b1 ≠ b2 ≠ 1) can be defined using REFe. Then, the different expressions of REFe were simultaneously tested against a dataset of normalized bare plot soil losses, AeN, collected at the Sparacia (south Italy) site. As expected, the poorest AeN predictions were obtained with the USLE. A distinction was made among the four power-type models since the fitting to the data was poor with the USLE-MR as compared with the other three models. Estimating two distinct exponents (one for EI30 and another for QR, USLE-M2) instead of a single exponent (USLE-MB, USLE-MR, USLE-MM) did not appreciably improve soil loss prediction. The USLE-MB and the USLE-MM were the best performing models.

Improving Universal Soil Loss Equation (USLE)‐based models has large interest because simple and reliable analytical tools are necessary in the perspective of a sustainable land management. At first, in this paper, a general definition of the event rainfall‐ runoff erosivity factor for the USLE‐based models, REFₑ = (QR)ᵇ¹(EI₃₀)ᵇ², in which QR is the event runoff coefficient, EI₃₀ is the single‐storm erosion index, and b₁ and b₂ are coefficients, was introduced. The rainfall‐runoff erosivity factors of the USLE (b₁ = 0 and b₂ = 1), USLE‐M (b₁ = b₂ = 1), USLE‐MB (b₁ ≠ 1 and b₂ = 1), USLE‐MR (b₁ = 1 and b₂ ≠ 1), USLE‐MM (b₁ = b₂ ≠ 1), and USLE‐M2 (b₁ ≠ b₂ ≠ 1) can be defined using REFₑ. Then the different expressions of REFₑ were simultaneously tested against a data set of normalized bare plot soil losses, AₑN, collected at the Sparacia (south Italy) site. As expected, the poorest AₑN predictions were obtained with the USLE. The observed tendency of this model to overestimate small AₑN values and underestimate high AₑN values was reduced by introducing in the soil loss prediction model both QR and an exponent for the erosivity term. The fitting to the data was poor with the USLE‐MR as compared with the USLE‐MB and the USLE‐MM. Estimating two distinct exponents (USLE‐M2) instead of a single exponent (USLE‐MB, USLE‐MR, and USLE‐MM) did not appreciably improve soil loss prediction. The USLE‐MB and the USLE‐MM were recognized to be the best performing models among the possible alternatives, and they performed similarly with reference to both the complete data set and different sub‐data sets, only including small, intermediate, and severe erosion events. In conclusion, including the runoff coefficient in the soil loss prediction model is important to improve the quality of the predictions, but a great importance has to be paid to the mathematical structure of the model.

For an erosion event (October 2016) occurred at the Sparacia experimental area (Southern Italy), both terrestrial and low-altitude aerial surveys were carried out by consumer grade camera and quadcopter (low-cost unmanned aerial vehicle [UAV]) to measure rill erosion on two plots with steepness of 22% and 26%. Applying the structure from motion (SfM) technique, the three-dimensional digital terrain models (3D-DTMs) and the quasi three-dimensional models (2.5D-digital elevation model [DEM]) were obtained by the two surveys. Furthermore, 3D-DTM and DEM were built using the available aerial photographs (166) and adding 40 terrestrial photographs. For the first time, the convergence index was applied to high-resolution rill data for extracting the rill network, and a subsequent separation into contributing and non-contributing rills was carried out. The comparison among the three surveys (terrestrial, UAV, and UAV+terrestrial) was developed using two morphometric parameters of the rill network (drainage density and drainage frequency). Moreover, using as reference the weight of sediment stored on the tanks located downstream of the plots, the reliability of soil loss measurement by 3D models was tested. For both contributing and non-contributing rills, the morphometric parameters were higher for the terrestrial than for UAV and UAV+terrestrial surveys. For both plots, SfM always provided reliable soil loss measurements, which were affected by errors ranging from −8% to 13%. Although the applied technique used a low-cost UAV and a consumer grade camera, the obtained results demonstrated that a reliable estimate of rill erosion can be obtained in an area of interest.

This paper focuses on the dissipative similarity of step-pool units at rill, flume and stream scale. This investigation is carried out using recent advances in open channel flow resistance, applications of close-range photogrammetry to rill erosion, available published data on step-pool features in flumes and streams and a new dataset of measurements in fixed bed step-pool rills. A theoretically-based equation for calculating the Darcy-Weisbach friction factor obtained by integration of a power velocity profile is presented. The scale factor Γ of this power velocity profile, which is included in the flow resistance equation, was previously calibrated (Eq. 10) for mobile bed rills with step-pool units. At first, in this investigation an additional test of this flow resistance equation is developed using measurements carried out in fixed bed rills with step-pool features. In particular, the proposed Γ function is tested using the measurements carried out in 63 fixed bed rill reaches incised on a 24 and 26% sloped plot. This test shows that the effect of sediment transport on the flow resistance law can be considered negligible as compared to the effect of the form-induced dissipative mechanisms due to the presence of step-pools structures. Then, using measurements carried out in 61 flume experimental runs and 109 reaches of step-pool streams, this investigation demonstrates that the Γ function for flume and stream conditions can be obtained scaling that (Eq. 10) determined for step-pool rills. The Darcy-Weisbach friction factor values measured in flumes and streams are, on average, higher than those related to rills. Finally, the application of the theoretical equation for calculating the Darcy-Weisbach friction factor for flume and stream conditions requires Γ, estimated by Eq. (10), to be multiplied by a specific scale factor.

Flow velocity controls hillslope soil erosion and is a key hydrodynamic variable involved in sediment transport and deposition processes. The dye-tracer technique is one of the most applied methods for measuring velocity of shallow interrill and rill flow. The technique is based on the injection of a tracer in a specific point and the measurement of its speed to travel the known distance from the injection point to a given channel section. The dye-tracer technique requires that the measured surface flow velocity has to be corrected to obtain the mean flow velocity using a correction factor which is generally empirically deduced. The technique has two sources of uncertainties: i) the method applied for measuring the travel time of the dye-tracer and ii) the estimate of the correction factor, which is the ratio between the mean flow velocity and the surface velocity, in different flow conditions. In this paper the results of a wide experimental investigation, carried out using a fixed bed small flume simulating a rill channel, are presented. At first, the comparison between a chronometer-based (CB) and video-based (VB) technique was carried out for establishing the influence of the travel time measuring technique. For each experimental run, which was characterized by a sample of 20 measurements carried out with the same values of slope and discharge, the developed analysis showed that the empirical frequency distribution of the ratio between the single measurement and the sample mean (i.e., the average of 20 measurements) is more uniform for the VB technique than for the CB one. In any case, this sample mean was representative of surface flow velocity for both the CB and the VB technique. Furthermore, the mean value obtained by the CB measurements lightly underestimated (−1.7%) the corresponding mean obtained by the VB technique. Finally, the effects of slope (0.1–8.7%), flow Reynolds number (3462–10040), Froude number (1.44–5.17) on the correction factor are presented. The analysis demonstrated that the correction factor is independent of flow Reynolds number while a relationship with a Froude number, obtained by surface velocity measurement, or channel slope can be established.

Soil erosion is a key process to understand the land degradation, and modelling of soil erosion will help to understand the process and to foresee its impacts. The applicability of the Universal Soil Loss Equation (USLE) at event scale is affected by the fact that USLE rainfall erosivity factor does not take into account runoff explicitly. USLE-M and USLE-MM, including the effect of runoff in the event rainfall– runoff erosivity factor, are characterized by a better capacity to predict event soil loss. The specific objectives of this paper were (i) to determine the suitable parameterization of USLE, USLE-M and USLE-MM by using the dataseries of Sparacia experimental site and (ii) to evaluate their performances at both event and annual scale. The measurements allowed to establish the relationships for calculating the factors of USLE, USLE-M and USLE-MM usable at the Sparacia experimental area. At first, for slope-length values greater than 33 m, the calibration of USLE model at event scale pointed out that sediment delivery processes, that is processes involving deposition of the transported eroded soil particles, occur. The analysis showed that USLE and USLE-M tend to overestimate low event soil losses, while for USLE-MM, this tendency is less pronounced. However, the USLE-MM performed better than USLE and USLE-M and was able to reproduce better than other two models the highest soil loss values that are the most interesting from a practical point of view. The results obtained at annual scale were generally consistent with those obtained at event scale.

The first part of this investigation was aimed at testing the use of a three-dimensional (3D) Digital Terrain Model (DTM) and a quasi-tridimensional (2.5D) Digital Elevation Model (DEM) obtained by a large series of oblique images of eroded channels taken from consumer un-calibrated and non-metric cameras. For two closed earth channels having a different sinuosity the ground measurement of some cross-sections by a profilometer (P) was carried out. The real volume of each channel was also measured by waterproofing it by a plastic film and filling it with a known volume of water. The comparison among the three methods (3D, 2.5D and P) pointed out that a limited underestimation of the total volume always occurs and that the 3D method is characterized by the minimum difference between measured and real volume.This preliminary analysis allowed to conclude that 3D model can be used as benchmark and the 2.5D model is accurate enough to describe the investigated earth channels. In the subsequent part of the investigation the three ground measurement methods were applied for surveying of an ephemeral gully (EG) channel at the Sparacia area. Using the 3D model as benchmark, the morphological and hydraulic variable values of the 24 surveyed cross-sections determined by both 2.5D model and profilometer were compared. This comparison showed that the estimate error is generally less than ±10%. The EG measurements carried out by the three methods agreed with the available literature measurements and supported the applicability both of the empirical relationship between EG length and its eroded volume and the theoretical dimensionless relationship among the morphological variables describing the channelized erosion process. Finally, it was demonstrated that the effect of the distance interval on the EG volume measurement by 3D and 2.5D models is negligible for the investigated EG.

The uniform flow resistance equation, in the form due to Manning or Darcy-Weisbach, is widely applied to establish the stage-discharge relationship of a river cross-section. The application of this equation, namely the slope-area method, allows to indirectly measure the corresponding river discharge by measurements of bed slope, water level, cross-section area, wetted perimeter and an estimate of channel roughness. In this paper, a recently deduced flow resistance equation for open channel flow was tested during conditions of suspended sediment-laden flow. First, the flow resistance equation was determined by dimensional analysis and by applying the condition of incomplete self-similarity for the flow velocity profile. Then the analysis was developed by the following steps: (i) for sediment-laden flows characterized by known values of mean diameter and concentration of suspended sediments, a relationship (Eq. (28)) between the Γ function of the velocity profile, the channel slope and the Froude number was calibrated by the available measurements; and (ii) a relationship for estimating the Γ function (Eq. (29)) which also takes into account the mean concentration of suspended particles was also established. The theoretical flow resistance law (Eq. (26)) coupled with the relationship for estimating the Γ function (Eq. (28) or Eq. (29)), which is characterized by the applicability of a wide range of flow conditions, allowed to estimate the Darcy-Weisbach friction factor for flows with suspended-load. The analysis showed that for large-size mixtures the Darcy-Weisbach friction factor can be accurately estimated neglecting the effect of mean concentration of suspended sediments while for small-size mixtures the friction factor decreases when the mean sediment concentration increases.

In this paper the dissipative similarity of step-pool units at different spatial scales ranging from rills to streams is analyzed. This investigation benefits from the latest theoretical advances in open channel flow resistance, high-resolution topography from close-range photogrammetry applied to rill erosion and the availability of published data from literature on step-pool streams. At first, the integration of a power velocity distribution allowed to obtain a theoretically-based expression of Darcy-Weisbach friction factor, in which Γ function and δ exponent of the velocity profile are included. Then this theoretically-deduced flow resistance relationship is calibrated and tested by flow measurements carried out in rill reaches where the step-pool units occurred. In particular, the proposed Γ function is calibrated using the measurements corresponding to 88 rill reaches shaped on a plot having a slope equal to 14, 22 and 24% and the calibrated equation is also positively tested with measurements carried out in 48 rill reaches shaped on a 26% sloping plot. For the rill flow the developed analysis stated that the friction factor is characterized by estimate errors which are less than or equal to ±15% for 86% of cases and less than or equal to ±10% for 70% of cases. Using measurements of flow velocity, water depth, width and bed slope measurements carried out in 109 reaches of step-pool streams, this investigation demonstrates that the theoretical flow resistance equation can be applicable to step-pool streams carrying out a specific calibration of the Γ function. The comparison between the Darcy-Weisbach friction factor values measured in streams and step-pool rills demonstrates that in the stream features the friction factor values are, on average, higher than those related to rills with step-pool sequences. In conclusion, the comparison between rills and streams with step-pool units highlights that the same theoretical flow resistance equation can be applied even if a scale effect between the two features is detected.

Planning soil conservation strategies requires predictive techniques at event scale because a large percentage of soil loss over a long-time period is due to relatively few large storms. Considering runoff is expected to improve soil loss predictions and allows relation of the process-oriented approach with the empirical one, furthermore, the effects of detachment and transport on soil erosion processes can be distinguished by a runoff component. In this paper, the empirical model USLE-MB (USLE-M based), including a rainfall-runoff erosivity factor in which the event rainfall erosivity index EI30 of the Universal Soil Loss Equation (USLE) multiplies the runoff coefficient QR raised to an exponent b1>1 is tested by the measurements carried out for the Masse (10 plots) and Sparacia (22 plots) experimental stations in Italy. For the Masse experimental station, an exponent b1>1 was also estimated by tests carried out by a nozzle-type rainfall simulator. For each experimental site in fallow conditions, the effect of the sample size of the plot soil loss measurements on the estimate of the b1 coefficient was also studied by the extraction of a fixed number N of randomly obtained pairs of the normalized soil loss and runoff coefficient. The analysis showed that the variability of b1 with N is low and that 350 pairs are sufficient to obtain a stable estimate of b1. A total of 1,262 soil loss data were used to parameterize the model both locally and considering the two sites simultaneously. The b1 exponent varied between the two sites (1.298–1.520), but using a common exponent (1.386) was possible. Using a common b1 exponent for the two experimental areas increases the practical interest for the model and allows the estimation of a baseline component of the soil erodibility factor, which is representative of the at-site soil intrinsic and quasi-static properties. Development of a single USLE-MB model appears possible, and sampling other sites is advisable to develop a single USLE-MB model for general use.

Este artículo contiene 16 páginas, 6 figuras, 2 tablas., Soil degradation by water is a serious environmental problem worldwide, with specific climatic factors being the major causes. We investigated the relationships between synoptic atmospheric patterns (i.e. weather types, WTs) and runoff, erosion and sediment yield throughout the Mediterranean basin by analyzing a large database of natural rainfall events at 68 research sites in 9 countries. Principal Component Analysis (PCA) was used to identify spatial relationships of the different WTs including three hydro-sedimentary variables: rainfall, runoff, and sediment yield (SY, used to refer to both soil erosion measured at plot scale and sediment yield registered at catchment scale). The results indicated 4 spatial classes of rainfall and runoff: (a) northern sites dependent on North (N) and North West (NW) flows; (b) eastern sites dependent on E and NE flows; (c) southern sites dependent on S and SE flows; and, finally, (d) western sites dependent on W and SW flows. Conversely, three spatial classes are identified for SY characterized by: (a) N and NE flows in northern sites (b) E flows in eastern sites, and (c) Wand SW flows in western sites. Most of the rainfall, runoff and SY occurred during a small number of daily events, and just a few WTs accounted for large percentages of the total. Our results confirm that characterization by WT improves understanding of the general conditions under which runoff and SY occur, and provides useful information for understanding the spatial variability of runoff, and SY throughout the Mediterranean basin. The approach used here could be useful to aid of the design of regional water management and soil conservation measures., This research was supported by projects funded by the MINECOFEDER: CGL2014-52135-C3-3-R, CGL2014-59946-R, CGL2015-65569- R, CGL2015-64284-C2-2-R, and PCIN-2017-061/AEI. When this manuscript was first submitted Estela Nadal-Romero and Damià Vericat received a “Ramón y Cajal” postdoctoral contract (RYC-2013-14371 and RYC‐2010‐06264, Spanish Ministry of Economy and Competitiveness, MEC). Damià Vericat is now a Serra Húnter Fellow at the University of Lleida. María Fernández-Raga received a “José Castillejo” postdoctoral grant (Spanish Ministry of Education, Culture and Sports). Carla Ferreira was supported by a post-doctoral research grant from the Portuguese Science and Technology Foundation (SFRH/ BPD/120093/2016). Mariano Moreno-de las Heras received a Juan de la Cierva postdoctoral contract (IJCI-2015-26463) from the MEC. José Andrés López-Tarazón received a Vicenç Mut postdoctoral fellowship from the Autonomous Balearic Government (CAIB PD/038/2016). José Andrés López-Tarazón and Ramon Batalla also acknowledge the Secretariat for Universities and Research of the Department of the Economy and Knowledge of the Autonomous Government of Catalonia for supporting the Consolidated Research Group 2014 SGR 645 (RIUSFluvial Dynamics Research Group), and the CERCA Programme. This paper has benefited from the Lab and Field Data Pool created within the framework of the COST action CONNECTEUR (ES1306).

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.

Water flow on hillslope soil surface supplies energy which is required to detach soil particles, to transport and deposit sediments, therefore flow velocity is a key variable related to hillslope hydrodinamics of soil erosion processes. Among the different methods available for measuring velocity of shallow interrill and rill flow, the trace technique is widely used. Trace technique is applied by adding a material (salt, magnetic material, water isotope, floating object) and then measuring the speed of the material to travel a known distance from the injection point. When flow velocity is measured using a dye-tracing method, the mean velocity is calculated by multiplying the measured surface velocity of the leading edge of the tracer plume by a correction factor which was generally empirically deduced. The main uncertainty of the dye-tracing technique stands in the estimate of this correction factor, which is the ratio between the mean flow velocity and the surface velocity. The main goal of this paper is establishing a theoretical relationship for calculating the correction factor by using a power velocity profile. At first, the developed analysis demonstrated that the correction factor only depends on the exponent of the power velocity distribution (Eq. (5) ). Then, this theoretical expression of the correction factor was applied using the velocity profiles measured by Baiamonte and Ferro for the condition of sediment-free flow in motion on a rough bed and by Coleman for a sediment-laden flow moving on a smooth flume. Using the correction factor values calculated by the velocity measurements carried out for the sediment-free flow in motion on a rough bed, the relationship between the correction factor and roughness height was established. In agreement with a previous study by Ali et al., for a sediment-free flow the correction factor increases with roughness height. Finally, the velocity profile measurements carried out for a sediment-laden flow in motion on a smooth bed were used to state the effect of sediment load on the correction factor. This last analysis allowed to conclude, in agreement with Li and Abrahams and Zhang et al., that the correction factor decreases when the sediment load increases.

Many process-oriented erosion prediction models reproduce rill erosion as affected by site-specific parameters, as for example, rill erodibility, and thus, their practical application requires the measurement of these parameters or their estimate. The aim of this paper was establishing a method for indirectly measuring field rill erodibility. A simple mathematical approach based on a known soil detachment equation and accounting for the rill erosion dynamic process is applied. Field measurements carried out for seven natural rainfall events occurring at the plots of the Sparacia experimental station, southern Italy, are used for indirectly measuring the rill erodibility of the investigated soil. This method needs only the knowledge of the geometric characteristics of the rills at the end of the erosion event and the event duration. The method was also tested by using the Water Erosion Prediction Project database, and this analysis showed that a reliable value of rill erodibility can be obtained by the proposed Equation (18). The proposed method has the following advantages: (i) to be applicable at field scale, being more realistic than the laboratory scale because the soil structure is not destroyed, and (ii) to avoid the disadvantages of field experiments such as the cumbersome experimental set-up and the large volume of water inflow needed. Copyright © 2015 John Wiley & Sons, Ltd.

Improving empirical prediction of plot soil erosion at the event temporal scale has both scientific and practical importance. In this investigation, 492 runoff and soil loss data from plots of different lengths, λ (11 ≤ λ ≤ 44 m), and steepness, s (14.9 ≤ s ≤ 26.0%), established at the Sparacia experimental station, in Sicily, South Italy, were used to derive a new version of Universal Soil Loss Equation (USLE)-MM model, by only assuming a value of one for the topographic length, L, and steepness, S, factors for λ = 22 m and s = 9%, respectively. An erosivity index equal to (QREI30)b1, QR and EI30 being the runoff coefficient and the event rainfall erosivity index, respectively, with b1 > 1 was found to be an appropriate choice for the Sparacia area. The specifically developed functions for L and S did not differ appreciably from other, more widely accepted relationships (maximum differences by a factor of 1.22 for L and 1.09 for S). The new version of the USLE-MM performed particularly well for highly erosive events, because predicted soil loss differed by not more than a factor of 1.19 from the measured soil loss for measured values of more than 100 Mg ha−1. The choice of the relationships to predict topographic effects on plot soil loss should not represent a point of particular concern in the application of the USLE-MM in other environments. However, tests of the empirical approach should be carried out in other experimental areas in an attempt to develop analytical tools, usable at the event temporal scale, reasonably simple and of wide validity. Copyright © 2015 John Wiley & Sons, Ltd.

The traditional direct method (i.e. metric ruler and rillmeter) of monitoring rill erosion at plot scale is time consuming and invasive because it modifies the surface of the rilled area. Measuring rill features using a drone-based technology is considered a non-invasive method allowing a fast field relief. In the experimental Sparacia area a survey by a quadricopter Microdrones md4-200 was carried out, and this relief allowed the generation of a Digital Elevation Model (DEM), with a mesh size of 1 cm and a resolution elevation equal to 2 mm, for three plots (L, G and C) affected by rill erosion. At first for the experimental L plot, which is 44 m long, the rill features were surveyed by a ‘manual’ method which was carried out by drawing on the PC screen the rill paths obtained by a visual orthophoto interpretation. This manual method was not applicable for the plots in which rills of limited depth occurred and were not detectable. Then, for both L plot and the other experimental plots having a length ranging from 22 to 44 m, an ‘automatic’ extraction method of rills from DEM was applied. Using an appropriate calculation routine, a vector coverage of transects orthogonal to the main flow direction (i.e. the maximum slope steepness path) was generated. The intersection of each plot DEM with the transect coverage allowed to obtain both the cross sections and the main rill morphological features. For the L plot the comparison between the rill morphological features obtained by the two different methods (manual, automatic) was carried out. Finally, the length–volume relationship and a dimensionless relationship proposed in literature were tested for all studied experimental plots. Copyright © 2015 John Wiley & Sons, Ltd.

Purpose: The USLE-MM estimates event normalized plot soil loss, Ae,N, by an erosivity term given by the runoff coefficient, QR, times the single-storm erosion index, EI30, raised to an exponent b1> 1. This modeling scheme is based on an expected power relationship, with an exponent greater than one, between event sediment concentration, Ce, and the EI30/Pe(Pe= rainfall depth) term. In this investigation, carried out at the three experimental sites of Bagnara, Masse, and Sparacia, in Italy; the soundness of the USLE-MM scheme was tested. Materials and methods: A total of 1192 (Ae,N, QREI30) data pairs were used to parameterize the model both locally and considering all sites simultaneously. The performances of the fitted models were established by considering all erosive events and also by distinguishing between events of different severity. Results and discussion: The b1exponent varied widely among the three sites (1.05–1.44) but using a common exponent (1.18) for these sites was possible. The Ae,Nprediction accuracy increased in the passage from the smallest erosion events (Ae,N≤ 1 Mg ha−1, median error = 3.35) to the largest ones (Ae,N> 10 Mg ha−1, median error = 1.72). The QREI30term was found to be usable to predict both Ae,Nand the expected maximum uncertainty of this prediction. Soil erodibility was found to be mainly controlled by the largest erosion events. Conclusions: Development of a single USLE-MM model appears possible. Sampling other sites is advisable to develop a single USLE-MM model for a general use.