The variation of soil erosion across scales remains a controversial issue. A theoretical framework, coupling the normalized Green-Ampt equation for infiltration, 1D kinematic wave model for overland flow, and WEPP erosion modeling approaches for soil erosion, was used to explain and quantify the direct effect of scale on the soil erosion process. The results show that the relation between interrill erosion and slope length accords with a power-law decreasing trend, while the relation of rill erosion versus slope length shows a power-law increasing trend. Moreover, the power-law scaling of interrill erosion becomes more prominent with an increase of rainfall duration and intensity but is nearly independent of the interrill erodibility factor. The rainfall duration, soil type, soil critical shear stress, sediment transport coefficient, and rill erodibility factor substantially influence the magnitude of scale effect on rill erosion, while rainfall intensity, slope gradient, and Manning's roughness have minor effects. It suggests that the scale effect on soil erosion is variable and dynamic for different erosion types, rainfall and soil characteristics, which can explain why the controversial scaling relationships of soil erosion exist in previous studies. The physically based soil erosion model WEPP is compared to the empirical models USLE and RUSLE at various scales. Only when rill erosion plays a dominant role in soil loss do all these models exhibit consistent scale effect on erosion. These results provide insights into the essence of scaling in the hillslope soil erosion process, which are expected to benefit the development of upscaling techniques for the large-scale hydrological, geomorphological, and ecological processes.

Variable scale effects on hillslope soil erosion during rainfall-runoff processes

Effect of varying wheatgrass density on resistance to overland flow

Effects of raindrop impact on the resistance characteristics of sheet flow

The frequent occurrence of roll waves in overland flow can increase the water depth and accelerate sheet erosion. To investigate the variation laws and hydrodynamic characteristics of roll waves, indoor artificial experiments with five roughness types, seventeen flow discharges, and five slope gradients were conducted in a hydraulic flume. The results showed that the evolution process of roll waves is divided into three phases: monochromatic, quasi-sine, and mature wave regions. In addition, the parameter roll-wave velocity increased in terms of its power function with the unit discharges, while the slopes showed that a positive line was related to this increase. An empirical formula of the wave velocity was obtained by conducting a regression analysis after synthesizing the influencing factors. The wavelength varied at a single peak with increasing unit discharges, showing a negative linear correlation with the test slope. Additionally, an empirical formula of the wavelength was derived using regression methods. The correction coefficients in the laminar flow instability zone varied from 0.27 to 0.39, while the Reynolds number was approximately 100. The critical average Freud number Fr and the Onsager value Z were 0.6 and 3.33 × 10−3, respectively. In addition, the correction coefficients in the turbulent flow instability zone varied within 0.412–0.730, while the Reynolds number fluctuated between 900 and 3300. The range of the critical Fr value was 1.59–2.20, and the critical average Z was 1.88 × 10−3. These results are vital for understanding the hydrodynamic characteristics and evolution laws of roll waves in overland flow.

Hydrodynamic characteristics and evolution law of roll waves in overland flow

Combined effects of rainfall and flow depth on the resistance characteristics of sheet flow on gentle slopes

\n Overland flow is the initial driver of slope surface erosion. To discover resistance characteristics of overland flow influenced by rainfall intensity and roughness, indoor simulated rainfall experiments with six kinds of roughness, five flow discharges, and five rainfall intensities were investigated. Results showed that overland flow over rough surfaces could be considered as laminar and turbulent flow when using flow Reynolds number. According to roll waves observed, flow regimes belonged to the laminar transitional zone based on the viscosity-to-depth ratio. A critical water depth formula for overland flow was re-derived, and it showed that this test water flow consisted of supercritical flow in most cases, and subcritical flow in only a few cases. The flow resistance coefficient increased with increasing roughness, whereas it decreased as rainfall intensity increased. Considering the ‘increasing resistance’ phenomenon, this study focused on frictional resistance, thickness of the viscous sublayer, pressure drag and roll waves. Finally, a formula for sheet flow resistance was proposed based on resistance segmentation and multi-element linear regression. These findings are of significance both for understanding the characteristics and development of overland flow and overland flow dynamics.

The effect of roughness and rainfall on hydrodynamic properties of overland flow

Indoor experiments consisting of 15 flow discharges, six kinds of roughness, and five different gradients were systematically investigated to discover the evolution laws of rolling waves, f...

Unsteady-State Hydraulic Characteristics of Overland Flow

Soil erosion is a major contributor to land degradation in the Loess Plateau in China. To clarify the sediment transport capacity of overland flow influenced by hydraulic parameters, such as shear stress, sand shear stress (hydraulic gradient partition method and hydraulic radius partition method), mean flow velocity, Froude number, stream power, and unit stream power, indoor experiments with eight‐unit‐width flow discharges from 0.0667 × 10⁻³ to 0.3333 × 10⁻³ m²·s⁻¹, six slope gradients from 3.49 to 20.79%, and two kinds of sand soils (d₅₀ = 0.17 and 0.53 mm) were systematically investigated. A nondimensional method was adopted in data processing. Results showed that there was a partition phenomenon of relation curves because of the different median grain diameters. The correlation between the nondimensional stream power and nondimensional sediment transport capacity was the highest, followed by the correlation between the nondimensional unit stream power and nondimensional sediment transport capacity. However, there was a poor correlation between the flow intensity indices of velocity category and nondimensional sediment transport capacity. Nondimensional stream power, nondimensional unit stream power, and nondimensional shear stress could predict sediment transport capacity well. Ignoring the partition phenomenon of the relation curves, stream power could be used to predict sediment transport capacity, with a coefficient of determination of .85. Furthermore, a general flow intensity index was obtained to predict sediment transport capacity of overland flow. Finally, an empirical formula for predicting sediment transport capacity with a coefficient of determination of .90 was established by multiple regression analyses based on the general flow intensity index. During the analysis between measured sediment transport capacities in present study and predicted values based on Zhang model, Mahmoodabadi model, and Wu model, it was found that these three models could not accurately predict sediment transport capacities of this study because different models are estimated on the basis of different experimental conditions.

Pu Li

Papers

The effect of roughness and rainfall on hydrodynamic properties of overland flow

Unsteady-State Hydraulic Characteristics of Overland Flow

Hydrodynamic characteristics and evolution law of roll waves in overland flow

Nondimensional sediment transport capacity of sand soils and its response to parameter in the Loess Plateau of China

Response of interrill erosion to flow parameters of sand loess in regions with high and coarse sediment yields