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Limited information is currently available on how sediment transport affects rill flow resistance and the influence of hydraulic variables, as stream power, on sediment transport capacity for rill flows. In this paper, the available measurements of hydraulic variables (flow depth, channel slope, mean flow velocity, Reynolds number, Froude number, and Darcy–Weisbach friction factor) carried out by Ban et al. (Measurement of rill and ephemeral gully flow velocities and their model expression affected by flow rate and slope gradient. Journal of Hydrology, 589, 125172) and Ban (Measurements and estimation of flow velocity in mobile bed rills. International Journal of Sediment Research, 38(1), 97–104) for fixed and mobile bed rills are used to test the applicability of a theoretically deduced rill flow resistance equation based on a power‐velocity profile. The results allowed for stating that (i) the theoretical flow resistance approach can predict Darcy–Weisbach friction factor for flows over fixed and mobile beds, (ii) the stream power, dependent on flow discharge and slope, determines different flow behaviour, and (iii) the data are supportive of the slope independence hypothesis of rill velocity, for the mobile bed condition, only for the highest investigated discharge values (greater than 0.133 L s−1). [ABSTRACT FROM AUTHOR]

The authors also described methods and procedures for quantify soil erosion processes (sediment sampling and water level reading in the storage tanks for total erosion measurements; profilometer, and structure from motion technique for rill erosion measurements). Merlo et al. [[11]], in turn, evaluated the relationship between soil properties (microbial biomass carbon, basal soil respiration, and metabolic quotient) and erosion in areas managed with different cropping system practices under no-tillage in the Brazilian Cerrado. Soil erosion is a process in which soil particles are first detached from the soil surface and then transported by erosive agents such as rainfall, overland flow and channelized flows in rills, ephemeral gullies and gullies [[1], [3]]. 10.3390/w15132378 15 Todisco F., Vergni L., Ortenzi S., Di Matteo L. Soil Loss Estimation Coupling a Modified USLE Model with a Runoff Correction Factor Based on Rainfall and Satellite Soil Moisture Data. [Extracted from the article]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, the applicability of a theoretical flow resistance law to sediment-laden flow in pipes is tested. At first, the incomplete self-similarity (ISS) theory is applied to deduce the velocity profile and the corresponding flow resistance law. Then the available database of measurements carried out by clear water and sediment-laden flows with sediments having a quasi-uniform sediment size and three different values of the mean particle diameter Dm (0.88 mm, 0.41 mm and 0.30 mm) are used to calibrate the Γ parameter of the power-velocity profile. The fitting of the measured local velocity to the power distribution demonstrates that (i) for clear flow the exponent δ can be estimated by the equation of Castaing et al. and (ii) for the sediment-laden flows δ is related to the diameter Dm. A relationship for estimating the parameter Гv obtained by the power-velocity profile and that Гf of the flow resistance law is theoretically deduced. The relationship between the parameter Гv, the head loss per unit length and the pipe flow Froude number is also obtained by the available sediment-laden pipe flow data. Finally, the procedure to estimate the Darcy-Weisbach friction factor is tested by the available measurements. [ABSTRACT FROM AUTHOR]

Badlands are extremely fragmented landforms characterized by soil erosion processes at a short-time scale. In this paper, the annual evolution of hillslope morphological characteristics and erosion/deposition processes in a Sicilian badland area, surveyed on May 2021 and April 2022 by Unmanned Aerial Vehicles (UAVs), was investigated. Three-dimensional (3D) and planimetric (2D) approaches were applied to determine the badland morphometric characteristics. UAV surveys and photogrammetric 3D-model generation allowed for obtaining the digital terrain model and identifying the badland unit. The convergence index method was applied to evaluate the drainage network and its variation due to the erosion processes. The analysis highlighted a decrease of the morphometric indexes with increasing slope, which can be explained by the fact that the drainage network tends to be less tortuous and branched as slopes become steeper. The geomorphic change analysis showed that the soil erosion is evenly distributed along the badland slopes, while it is negligible along the drainage networks. The geomorphic changes due to slope collapses and soil erosion and deposition phenomena lead to a modification of the morphological characteristics of the badland unit, sub-units and the corresponding drainage networks. The results confirmed that badlands are intense erosion spots, with soil loss (approximately 348 t ha−1 y−1) much higher than the soil loss tolerance. Finally, the morphometric indexes were positively related to the sediment yield values, suggesting that in more extended and branched drainage networks sediment transport is more efficient. • Soil erosion is evenly distributed along the badland slopes. • Soil erosion is negligible along the drainage network. • Extended and branched drainage networks promote the sediment transport. • Badland areas are confirmed to be intense erosion spots. [ABSTRACT FROM AUTHOR]