Discussion: Misrepresentation of the USLE in ‘Is sediment delivery a fallacy?’

The assertion that the application of the USLE to predicting soil losses within a catchment or watershed is not sound because the USLE provides an estimate of erosion that would be measured if the entire area were divided up into 22·1 m long plots, and the output from them all added together, is incorrect. The slope length factor was derived from data obtained using a wide range of plot lengths and included the 22·1 m length simply to force it to take on a value of 1·0 when the slope length is 22·1 m. The 22·1 m length has no physical significance but the USLE slope length factor has a physical basis when applied to planar and convex hillslopes. The use of sediment delivery ratios when the USLE is applied to concave areas attempts to correct for applying the USLE beyond its design criteria. It fails because, in using the sediment delivery ratios in the prediction sediment delivery, it is incorrectly assumed that sediment delivery ratios de not vary with the amount of sediment entering a zone of deposition.     

Enhancing RUSLE to include runoff‐driven phenomena

RUSLE2 (Revised Universal Soil Loss Equation) is the most recent in the family of Universal Soil Loss Equation (USLE)/RUSLE/RUSLE2 models proven to provide robust estimates of average annual sheet and rill erosion from a wide range of land use, soil, and climatic conditions. RUSLE2's capabilities have been expanded over earlier versions using methods of estimating time‐varying runoff and process‐based sediment transport routines so that it can estimate sediment transport/deposition/delivery on complex hillslopes. In this report we propose and evaluate a method of predicting a series of representative runoff events whose sizes, durations, and timings are estimated from information already in the RUSLE2 database. The methods were derived from analysis of 30‐year simulations using a widely accepted climate generator and runoff model and were validated against additional independent simulations not used in developing the index events, as well as against long‐term measured monthly rainfall/runoff sets. Comparison of measured and RUSLE2‐predicted monthly runoff suggested that the procedures outlined may underestimate plot‐scale runoff during periods of the year with greater than average rainfall intensity, and a modification to improve predictions was developed. In order to illustrate the potential of coupling RUSLE2 with a process‐based channel erosion model, the resulting set of representative storms was used as an input to the channel routines used in Chemicals, Runoff, and Erosion from Agricultural Management Systems (CREAMS) to calculate ephemeral gully erosion. The method was applied to a hypothetical 5‐ha field cropped to cotton in Marshall County, MS, bisected by a potential ephemeral gully having channel slopes ranging from 0·5 to 5% and with hillslopes on both sides of the channel with 5% steepness and 22·1 m length. Results showed the representative storm sequence produced reasonable results in CREAMS indicating that ephemeral gully erosion may be of the same order of magnitude as sheet and rill erosion. Copyright © 2010 John Wiley & Sons, Ltd.     

Runoff dependent erosivity and slope length factors suitable for modelling annual erosion using the Universal Soil Loss Equation

Despite revisions and refinements, the Revised Universal Soil Loss Equation (RUSLE), which is the revised version of the Universal Soil Loss Equation (USLE), over predicts small annual soil losses and under predicts large annual soil losses. To some large extent, this results from the equation over estimating small event soil losses and under estimating large event soil losses. Replacing the USLE/RUSLE event erosivity index (EI₃₀) by the product of EI₃₀ and the runoff ratio (Q_R) significantly reduces the errors in estimating event erosion when runoff is measured, but the USLE‐M, the USLE variant that uses the Q_REI₃₀ index, requires crop and support practice factors that differ from those used in the RUSLE. The theory which enables the Q_REI₃₀ index to be used in association with the RUSLE crop and support practice factors is presented. In addition, the USLE/RUSLE approach was developed for conditions where runoff is produced uniformly over a hill slope. A runoff dependent slope length factor that takes account of runoff variations over a hill slope is presented and demonstrated for the situation where runoff from a low runoff producing area passes onto an area where runoff is produced more readily. Copyright © 2007 John Wiley & Sons, Ltd.     

DOWNSLOPE EROSION PROCESS UNDER UPSLOPE RUNOFF AND SEDIMENT USING A DUAL-BOX SYSTEM

1 INTRODUCTION Soil erosion at the hilly-gully region of the Loess Plateau has obvious vertical erosion zones from watershed boundary to gully edge, i.e., sheet erosion-dominated zone, rill erosion-dominated zone and shallow gully erosion-dominated zone, from top to bottom (Chen et al., 1988). Meanwhile, upslope runoff and sediment have a significant impact on the downslope erosion process. But with the limits of research methods,there is not much data to quantify upslope runoff and sedi…     

Applying the QREI30 index within the USLE modelling environment

The USLE/RUSLE model was designed to predict long‐term (~20 years) average annual soil loss by accounting for the effects of climate, soil, topography and crops. The USLE/RUSLE model operates mathematically in two steps. The first step involves the prediction of soil loss from the ‘unit’ plot, a bare fallow area 22.1 m long on a 9% slope gradient with cultivation up and down the slope. Appropriate values of the factors accounting for slope length, gradient, crops and crop management and soil conservation practice are then used to adjust that soil loss to predict soil loss from areas that have conditions that are different from the unit plot. Replacing EI₃₀, the USLE/RUSLE event erosivity index, by the product of the runoff ratio (Q_R) and EI₃₀, can enhance the capacity of the model to predict short‐term soil loss from the unit plot if appropriate data on runoff is available. Replacing the EI₃₀ index by another index has consequences on other factors in the model. The USLE/RUSLE soil erodibility factor cannot be used when the erosivity factor is based on Q_REI₃₀. Also, the USLE/RUSLE factors for slope length, slope gradient crops and crop management, and soil conservation practice cannot be used when runoff from other than the unit plot is used to calculate Q_R. Here, equations are provided to convert the USLE/RUSLE factors to values suitable for use when the erosivity factor is based on the Q_REI₃₀ index under these circumstances. At some geographic locations, non linear relationships exist between soil loss from bare fallow areas and the Q_REI₃₀ index. The effect of this on the slope length factor associated with the Q_REI₃₀ index is demonstrated using data from runoff and soil loss plots located at the Sparacia site, Sicily. Copyright © 2012 John Wiley & Sons, Ltd.     

Evaluation of a dynamic multi‐class sediment transport model in a catchment under soil‐conservation agriculture

Soil erosion models are essential tools for the successful implementation of effective and adapted soil conservation measures on agricultural land. Therefore, models are needed that predict sediment delivery and quality, give a good spatial representation of erosion and deposition and allow us to account for various soil conservation measures. Here, we evaluate how well a modified version of the spatially distributed multi‐class sediment transport model (MCST) simulates the effectiveness of control measures for different event sizes. We use 8 year runoff and sediment delivery data from two small agricultural watersheds (0·7 and 3·7 ha) under optimized soil conservation. The modified MCST model successfully simulates surface runoff and sediment delivery from both watersheds; one of which was dominated by sheet and the other was partly affected by rill erosion. Moreover, first results of modelling enrichment of clay in sediment delivery are promising, showing the potential of MCST to model sediment enrichment and nutrient transport. In general, our results and those of an earlier modelling exercise in the Belgian Loess Belt indicate the potential of the MCST model to evaluate soil erosion and deposition under different agricultural land uses. As the model explicitly takes into account the dominant effects of soil‐conservation agriculture, it should be successfully applicable for soil‐conservation planning/evaluation in other environments. Copyright © 2008 John Wiley & Sons, Ltd.     

Testing alternative erosivity indices to predict event soil loss from bare plots in Southern Italy

Methods for predicting unit plot soil loss for the ‘Sparacia’ Sicilian (Southern Italy) site were developed using 316 simultaneous measurements of runoff and soil loss from individual bare plots varying in length from 11 to 44 m. The event unit plot soil loss was directly proportional to an erosivity index equal to (Q_REI₃₀)^1·47, being Q_REI₃₀ the runoff ratio (Q_R) times the single storm erosion index (EI₃₀). The developed relationship represents a modified version of the USLE‐M, and therefore it was named USLE‐MM. By the USLE‐MM, a constant erodibility coefficient was deduced for plots of different lengths, suggesting that in this case the calculated erodibility factor is representative of an intrinsic soil property. Testing the USLE‐M and USLE‐MM schemes for other soils and developing simple procedures for estimating the plot runoff ratio has practical importance to develop a simple method to predict soil loss from bare plots at the erosive event temporal scale. Copyright © 2009 John Wiley & Sons, Ltd.     

Inherent relationship of the USLE,RUSLE topographic factor algorithms and its impact on soil erosion modelling

ABSTRACT

The accurate representation of the Earth’s surface plays a vital role in soil erosion modelling. Topography is parameterized in the Universal Soil Loss Equation (USLE) and Revised USLE (RUSLE) by the topographic (LS) factor. For slope gradients of < 20%, soil loss values are similar for both models, but when the gradient is increased, RUSLE estimates are only half of those of USLE. The study aims to assess the validity of this statement for complex hillslope profiles. To that end, both models were applied at eight diverse mountainous sub-watersheds. The USLE and RUSLE indices were estimated utilizing the SEAGIS model and a European dataset, respectively. LS factors were in a 3:1 ratio (i.e. USLE:RUSLE) considering the entire basin area. For areas with slopes <20%, gross erosion estimates of both models converged. Sites of strong relief (>20%) USLE yielded significantly higher values than RUSLE.     

Physically based modelling of sheet erosion (detachment and deposition processes) in complex hillslopes

A one‐dimensional uncoupled model governed by this research is a physics‐based modelling of the rainfall‐runoff induced erosion process. The presented model is composed of three parts of a three‐dimensional (3D) hillslope geometry, a nonlinear storage (kinematic wave) model for hillslope hydrological response, and an unsteady physically based surface erosion model. The 3D hillslope geometry model allows describing of the hillslope morphology by defining their plan shape and profile curvature. By changing these two topographic parameters, nine basic hillslope types are derived. The modelling of hillslope hydrological response is based on a flow continuity equation as the relation of discharge and flow depth is passed on kinematic wave approximation. The erosion model is based on a mass conservation equation for unsteady flow. The model assumes that suspended sediment does not affect flow dynamics. The model also accounts for the effect of flow depth plus loose soil depth on soil detachment. The presented model was run for two different precipitations, slope content, and length, and results were plotted for sediment detachment/deposition rate. Based on the obtained results, in hillslopes with convex and straight profile curvatures, sediment detachment only occurred in the whole length of the hillslope. However, in concave ones, sediment detachment and deposition only occurred together in hillslope. The hillslopes with straight profiles and convergent plans have the highest rate of detachment. Also, results show that most detachment rates occur in convex profile curvatures, which are about 15 times more than in straight profiles. Copyright © 2015 John Wiley & Sons, Ltd.     

Influence of thawed soil depth on rainfall erosion of frozen bare meadow soil in the Qinghai–Tibet Plateau

The Qinghai–Tibet Plateau has a vast area of approximately 70×10⁴ km² of alpine meadow under the impacts of soil freezing and thawing, thereby inducing intensive water erosion. Quantifying the rainfall erosion process of partially thawed soil provides the basis for model simulation of soil erosion on cold-region hillslopes. In this study, we conducted a laboratory experiment on rainfall-induced erosion of partially thawed soil slope under four slope gradients (5, 10, 15, and 20°), three rainfall intensities (30, 60, and 90 mm h⁻¹), and three thawed soil depths (1, 2, and 10 cm). The results indicated that shallow thawed soil depth aggravated soil erosion of partially thawed soil slopes under low hydrodynamic conditions (rainfall intensity of 30 mm h⁻¹ and slope gradient ≤ 15°), whereas it inhibited erosion under high hydrodynamic conditions (rainfall intensity ≥ 60 mm h⁻¹ or slope gradient > 15°). Soil erosion was controlled by the thawed soil depth and runoff hydrodynamic conditions. When the sediment supply was sufficient, the shallow thawed soil depth had a higher erosion potential and a larger sediment concentration. On the contrary, when the sediment supply was insufficient, the shallow thawed soil depth resulted in lower sediment erosion and a smaller sediment concentration. The hydrodynamic runoff conditions determined whether the sediment supply was sufficient. We propose a model to predict sediment delivery under different slope gradients, rainfall intensities, and thawed soil depths. The model, with a Nash–Sutcliffe efficiency of 0.95, accurately predicted the sediment delivery under different conditions, which was helpful for quantification of the complex feedback of sediment delivery to the factors influencing rainfall erosion of partially thawed soil. This study provides valuable insights into the rainfall erosion mechanism of partially thawed soil slopes in the Qinghai–Tibet Plateau and provides a basis for further studies on soil erosion under different hydrodynamic conditions.     

Spatial discretization of large watersheds and its influence on the estimation of hillslope sediment yield

The combined use of water erosion models and geographic information systems has facilitated soil loss estimation at the watershed scale. Tools such as the Geo‐spatial interface for the Water Erosion Prediction Project (GeoWEPP) model provide a convenient spatially distributed soil loss estimate but require discretization to identify hillslopes and channels. In GeoWEPP, the TOpographic PArameteriZation (TOPAZ) model is used as an automated procedure to extract a watershed boundary, hillslopes and channels from a digital elevation model (DEM). Previous studies in small watersheds have shown that the size of the hillslopes and the channel distribution affect the model estimates, but in large watersheds, the effects on the soil loss estimates have yet to be tested. Therefore, the objective of this study was to evaluate the effect of discretization on the hillslope sediment yield estimates using GeoWEPP in two large watersheds (>10 km²). The watersheds were selected and discretized varying the TOPAZ parameters [critical source area (CSA) and minimum source channel length (MSCL)] in a 30‐m resolution digital elevation model. The drainage networks built with TOPAZ were compared with each other using the drainage density index. The results showed that the discretization affected hillslope sediment yield estimates and their spatial distribution more than the total runoff. The drainage density index and the hillslope sediment yield were proportional but inversely related; thus, soil loss estimates were highly affected by the spatial discretization. As a result of this analysis, a method to choose the CSA and MSCL values that generates the greatest fraction of hillslopes having profile lengths less than 200 m was developed. This slope length condition is particularly crucial when using the WEPP and GeoWEPP models, in order for them to produce realistic estimates of sheet and rill erosion. Finally, and as a result of this analysis, a more reliable method was developed for selecting the TOPAZ channel network parameters (CSA and MSCL). Copyright © 2015 John Wiley & Sons, Ltd.     

Plot‐scale measurement of soil erosion at the experimental area of Sparacia (southern Italy)

Obtaining good quality soil loss data from plots requires knowledge of the factors that affect natural and measurement data variability and of the erosion processes that occur on plots of different sizes. Data variability was investigated in southern Italy by collecting runoff and soil loss from four universal soil‐loss equation (USLE) plots of 176 m², 20 ‘large’ microplots (0·16 m²) and 40 ‘small’ microplots (0·04 m²). For the four most erosive events (event erosivity index, R_e ≥ 139 MJ mm ha^?1 h^?1), mean soil loss from the USLE plots was significantly correlated with R_e. Variability of soil loss measurements from microplots was five to ten times greater than that of runoff measurements. Doubling the linear size of the microplots reduced mean runoff and soil loss measurements by a factor of 2·6–2·8 and increased data variability. Using sieved soil instead of natural soil increased runoff and soil loss by a factor of 1·3–1·5. Interrill erosion was a minor part (0·1–7·1%) of rill plus interrill erosion. The developed analysis showed that the USLE scheme was usable to predict mean soil loss at plot scale in Mediterranean areas. A microplot of 0·04 m² could be used in practice to obtain field measurements of interrill soil erodibility in areas having steep slopes. Copyright © 2003 John Wiley & Sons, Ltd.     

Hillslope sediment fence catch efficiencies and particle sorting for post-fire rain storms

Sediment fences are often used to monitor hillslope erosion, but these can underestimate sediment yields due to overtopping of runoff and associated sediment. We modified four sediment fences to collect and measure the runoff and sediment that overtopped the fence in addition to the sediment deposited behind the fence. Specific objectives were to: (1) determine the catch efficiency of sediment fences measuring post-fire hillslope erosion; (2) assess particle sorting of sand, silt/clay, and organic matter from each hillslope through the sediment fence and subsequent runoff collection barrels; (3) evaluate how catch efficiency and particle size sorting relate to site and rainfall-runoff event characteristics; and (4) use runoff simulations to estimate sediment fence volumes for future post-fire monitoring. Catch efficiency ranged from 28 to 100% for events and 38 to 94% per site for the entire sampling season, indicating a relatively large underestimation of sediment yields by sediment fences. Most of the eroded sediment had similar proportions of sand and silt/clay as the hillslope soils, but the sediment behind the fence was significantly enriched in sand while the sediment that overtopped the fence was more strongly enriched in silt/clay. The sediment fences had capacities of 3 m³ for hillslopes of 0.19–0.43 ha, but simulations of runoff for 2- to 100-year storms indicate that the sediment fences would need a capacity of up to 240 m³ to store all of the runoff and associated sediment. More accurate measurements of sediment yields with sediment fences require either increasing the storage capacity of the sediment fence(s) to accommodate the expected volume of runoff and sediment, reducing the size of the contributing area, or directly measuring the runoff and sediment that overtop the fence. © 2020 John Wiley & Sons, Ltd.     

Connectivity of post-fire runoff and sediment from nested hillslopes and watersheds

Wildfire increases the potential connectivity of runoff and sediment throughout watersheds due to greater bare soil, runoff and erosion as compared to pre-fire conditions. This research examines the connectivity of post-fire runoff and sediment from hillslopes (< 1.5 ha; n = 31) and catchments (< 1000 ha; n = 10) within two watersheds (< 1500 ha) burned by the 2012 High Park Fire in northcentral Colorado, USA. Our objectives were to: (1) identify sources and quantify magnitudes of post-fire runoff and erosion at nested hillslopes and watersheds for two rain storms with varied duration, intensity and antecedent precipitation; and (2) assess the factors affecting the magnitude and connectivity of runoff and sediment across spatial scales for these two rain storms. The two summer storms that are the focus of this research occurred during the third summer after burning. The first storm had low intensity rainfall over 11 hours (return interval <1–2 years), whereas the second event had high intensity rainfall over 1 hour (return interval <1–10 years). The lower intensity storm was preceded by high antecedent rainfall and led to low hillslope sediment yields and channel incision at most locations, whereas the high intensity storm led to infiltration-excess overland flow, high sediment yields, in-stream sediment deposition and channel substrate fining. For both storms, hillslope-to-stream sediment delivery ratios and area-normalised cross-sectional channel change increased with the percent of catchment that burned at high severity. For the high intensity storm, hillslope-to-stream sediment delivery ratios decreased with unconfined channel length (%). The findings quantify post-fire connectivity and sediment delivery from hillslopes and streams, and highlight how different types of storms can cause varying magnitues and spatial patterns of sediment transport and deposition from hillslopes through stream channel networks.     

Testing assumptions and procedures to empirically predict bare plot soil loss in a Mediterranean environment

Empirical prediction of soil erosion has both scientific and practical importance. This investigation tested USLE and USLE‐based procedures to predict bare plot soil loss at the Sparacia area, in Sicily. Event soil loss per unit area, A_e, did not vary appreciably with plot length, λ, because the decrease in runoff with λ was offset by an increase in sediment concentration. Slope steepness, s, had a positive effective on A_e, and this result was associated with a runoff coefficient that did not vary appreciably with s and a sediment concentration generally increasing with s. Plot steepness did not have a statistically detectable effect on the calculations of the soil erodibility factor of both the USLE, K, and the USLE‐M, K_UM, models, but a soil‐independent relationship between K_UM and K was not found. The erosivity index of the USLE‐MM model performed better than the erosivity index of the Central and Southern Italy model. In conclusion, the importance of an approach allowing soil loss predictions that do not necessarily increase with λ was confirmed together with the usability of already established and largely applied relationships to predict steepness effects. Soil erodibility has to be determined with reference to the specific mathematical scheme and conversion between different schemes seems to need taking into account the soil characteristics. The USLE‐MM shows promise for further developments. The evolutionary concept applied in the development of the USLE should probably be rediscovered to improve development of soil erosion prediction tools. Copyright © 2014 John Wiley & Sons, Ltd.     

Modelling event soil losses using the QREI30 index within RUSLE2

Recently, a USDA Curve Number‐based method for obtaining estimates of event runoff has been developed for use in enhancing the capacity of Revised Universal Soil Loss Equation (RUSLE2) to deal with runoff‐driven phenomena. However, RUSLE2 still uses the EI₃₀ index as the basis for determining the erosivity of the rainfall for sets of runoff producing storms at a location even though the product of the runoff ratio (Q_R) and EI₃₀ index is better at prediction event erosion when runoff is known or predicted well. This paper reports the results of applying the Q_REI₃₀ index using data available from tables within RUSLE2 to predict storm event soil losses from bare fallow areas and areas with continuous corn at Holly Springs, MS, and Morris, MN. In RUSLE2, all rainfall during a calendar year is considered to detach soil material that is flushed from the area if and when runoff occurs. However, the Q_REI₃₀ index is calculated using the EI₃₀ value for the amount of rain in the storm that produces runoff. Consequently, changes were made to the timing of events during the calendar year in order to meet the criteria for using the Q_REI₃₀ index. As a general rule, the peak event soil loss produced using the Q_REI₃₀ index were higher than produced by RUSLE2, and the peak event soil loss for the bare fallow occurred later than for the continuous corn. The results of the work reported here show that the Q_REI₃₀ index may be used to model event erosion produced by a set of storms within RUSLE2 provided that the appropriate mathematical rules upon which the USLE was developed are adhered to. Copyright © 2013 John Wiley & Sons, Ltd.     

Runoff and road erosion at the plot and road segment scales,St John,US Virgin Islands

Previous studies have identified unpaved roads as the primary source of erosion on St John in the US Virgin Islands, but these studies estimated road erosion rates only as annual averages based primarily on road rill measurements. The goal of this project was to quantify the effect of unpaved roads on runoff and sediment production on St John, and to better understand the key controlling factors. To this end runoff and sediment yields were measured from July 1996 to March 1997 from three plots on naturally vegetated hillslopes, four plots on unpaved road surfaces and two cutslope plots. Sediment yields were also measured from seven road segments with contributing areas ranging from 90 to 700 m². With respect to the vegetated plots, only the two largest storm events generated runoff and there was no measurable sediment yield. Runoff from the road surface plots generally occurred when storm precipitation exceeded 6 mm. Sediment yields from the four road surface plots ranged from 0·9 to 15 kg m⁻² a⁻¹, and sediment concentrations were typically 20–80 kg m⁻³. Differences in runoff between the two cutslope plots were consistent with the difference in upslope contributing area. A sprinkler experiment confirmed that cross‐slope roads intercept shallow subsurface stormflow and convert this into surface runoff. At the road segment scale the estimated sediment yields were 0·1 to 7·4 kg m⁻² a⁻¹. Road surface runoff was best predicted by storm precipitation, while sediment yields for at least three of the four road surface plots were significantly correlated with storm rainfall, storm intensity and storm runoff. Sediment yields at the road segment scale were best predicted by road surface area, and sediment yields per unit area were most strongly correlated with road segment slope. The one road segment subjected to heavy traffic and more frequent regrading produced more than twice as much sediment per unit area than comparable segments with no truck traffic. Particle‐size analyses indicate a preferential erosion of fine particles from the road surface and a rapid surface coarsening of new roads. Published in 2001 by John Wiley & Sons, Ltd.     

Size characteristics of sediment in interrill overland flow on a semiarid hillslope,Southern Arizona

This study examines the size characteristics of sediment removed from a semiarid hillslope by interrill overland flow. Rainfall simulation experiments were conducted on a runoff plot 18 m wide and 35 m long established on a piedmont hillslope in southern Arizona. The top of the plot coincided with the hillslope divide, and its outlet was located within a shallow rill. Samples of runoff were obtained from two cross-sections located in the interrill portion of the plot upslope of the rill and from a calibrated flume through which was directed interrill overland flow reaching the bottom of the plot. Analyses of sediment contained in these samples showed that sediment in interrill flow is finer than the matrix soil. The fineness of the interrill sediment compared to the matrix soil appears to be due to the inability of interrill overland flow to transport the coarser fraction of the sediment supplied to it by raindrop detachment. This finding implies that the rate of soil erosion in interrill areas is not. as is commonly supposed, limited by the rate at which raindrops can detach sediment but by the rate at which they detach sediment of a size that the overland flow is competent to transport. The relative fineness of sediment eroded from this hillslope is consistent with other evidence for the recent evolution of shrub-covered hillslopes in southern Arizona.     

Effects of gradient,distance, curvature and aspect on steep burned and unburned hillslope soil erosion and deposition

Wildfire denudes vegetation and impacts chemical and physical soil properties, which can alter hillslope erosion rates. Post‐wildfire erosion can also contribute disproportionately to long‐term erosion rates and landscape evolution. Post‐fire hillslope erosion rates remain difficult to predict and document at the hillslope scale. Here we use ²¹⁰Pb_aex (lead‐210 mineral‐adsorbed excess) inventories to describe net sediment erosion on steep, convex hillslopes in three basins (unburned, moderately and severely burned) in mountainous central Idaho. We analyzed nearly 300 soil samples for ²¹⁰Pb_aex content with alpha spectrometry and related net sediment erosion to burn severity, aspect, gradient, curvature and distance from ridgetop. We also tested our data against models for advective, linear and non‐linear diffusive erosion. Statistically lower net soil losses on north‐ versus south‐facing unburned hillslopes suggest that greater vegetative cover and soil cohesion on north‐facing slopes decrease erosion. On burned hillslopes, erosion differences between aspects were less apparent and net erosion was more variable, indicating that vegetation influences erosion magnitude and fire drives erosion variability. We estimated net soil losses throughout the length of unburned hillslopes, including through a footslope transition to concave form. In contrast, on burned hillslopes, the subtle shift from convex to concave form was associated with deposition of a post‐fire erosion pulse. Such overall patterns of erosion and deposition are consistent with predictions from a non‐linear diffusion equation. This finding also suggests that concave sections of overall convex hillslopes affect post‐disturbance soil erosion and deposition. Despite these patterns, no strong relationships were evident between local net soil losses and gradient, curvature, distance from ridgetop, or erosion predicted with advection or diffusion equations. The observed relationship between gradient and erosion is therefore likely more complex or stochastic than often described theoretically, especially over relatively short timescales (60–100 years). Copyright © 2016 John Wiley & Sons, Ltd.     

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

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