Comparison of the performance of flow‐routing algorithms used in GIS‐based hydrologic analysis

Flow direction and specific catchment area were calculated for different flow‐routing algorithms using TAPES‐G and TauDEM. A fuzzy classification was used along with eight topo–climatic attributes to delineate six landscape classes from a 10‐m USGS DEM. A series of maps and tabular outputs were produced to compare flow‐routing predictions in different parts of the study area in the Santa Monica Mountains of southern California. The matched pair t‐test was used to compare the performance of pairs of specific catchment area grids across six user‐defined fuzzy landscape classes. The results show that (1) the ‘source’ cells predicted with the D∞, DEMON, and FD8 algorithms were confined to hilltops; (2) two single flow‐routing algorithms (Rho8, D8) produced poor results; and (3) the choice of flow‐routing algorithm has potentially important consequences for the calculation of upslope contributing areas, sediment transport capacity, topographic wetness, and several other topographic indices. Copyright © 2007 John Wiley & Sons, Ltd.     

Hydrological controls of erosion and sediment transport in volcanic torrents

Abstract

Sediment is transported in the form of debris flows in major gullies dissecting permeable volcanic slopes as exemplified by the Kami-kamihori Valley in the northern Japan Alps. Four years of hydrological observations in the headwater area of the gully showed that the surface runoff which triggers debris flows is related to peak 10- to 20-minute rainfall. Sediment production in such a short time is not sufficient to prepare a debris flow. Therefore, debris must have been accumulated at a particular section by repeated sediment discharge due to minor rainstorms. The volume of the debris produced in the headwaters was evaluated and correlated to an effective rainfall. The quantity of sediment transport at seven sections along the gully by debris flows in three periods was evaluated through the measurement of the topographic changes. It was compared with the total effective rainfall for the pertinent period, and the mean “sediment concentration” in the debris flow was calculated for each section and for each period. It was shown that the change in the sediment concentration along the gully reflects the entrainment of debris from the gully floor in the acceleration zone and the deposition in the deceleration zone. It was also demonstrated that the sediment delivery of a debris flow depends on the time distribution of rainfall, because rainfall time bases appropriate to prediction of the sediment transport at different reaches vary.     

A non‐equilibrium sediment transport model for rill erosion

Sediment transport in rill flows exhibits the characteristics of non‐equilibrium transport, and the sediment transport rate of rill flow gradually recovers along the flow direction by erosion. By employing the concept of partial equilibrium sediment transport from open channel hydraulics, a dynamic model of rill erosion on hillslopes was developed. In the model, a parameter, called the restoration coefficient of sediment transport capacity, was used to express the recovery process of sediment transport rate, which was analysed by dimensional analysis and determined from laboratory experimental data. The values of soil loss simulated by the model were in agreement with observed values. The model results showed that the length and gradient of the hillslope and rainfall intensity had different influences on rill erosion. Copyright © 2006 John Wiley & Sons, Ltd.     

Sediment production and yield from an alluvial gully in northern Queensland,Australia

Sediment production, transport and yield were quantified over various timescales in response to rainfall and runoff within an alluvial gully (7 · 8 ha), which erodes into dispersible sodic soils of a small floodplain catchment (33 ha) along the Mitchell River, northern Australia. Historical air photographs and recent global positioning system (GPS) surveys and LiDAR data documented linear increases in gully area and volume, indicating that sediment supply has been relatively consistent over the historic period. Daily time lapse photography of scarp retreat rates and internal erosion processes also demonstrated that erosion from rainfall and runoff consistently supplied fine washload (< 63 µm) sediment in addition to coarse lags of sand bed material. Empirical measurements of suspended sediment concentrations (10 000 to >100 000 mg/L) and sediment yields (89 to 363 t/ha/yr) were high for both Australian and world data. Total sediment yield estimated from empirical washload and theoretical bed material load was dominated by fine washload (< 63 µm). A lack of hysteresis in suspended sediment rating curves, scarp retreat and sediment yield correlated to rainfall input, and an equilibrium channel outlet slope supported the hypothesis that partially or fully transport‐limited conditions predominated along the alluvial gully outlet channel. This is in contrast to sediment supply‐limited conditions on uneroded floodplains above gully head scarps. While empirical data presented here can support future modelling efforts to predict suspended sediment concentration and yield under the transport limiting situations, additional field data will also be needed to better quantify sediment erosion and transport rates and processes in alluvial gullies at a variety of spatial and temporal scales. Copyright © 2013 John Wiley & Sons, Ltd.     

Water flux and sediment transport within a forested landscape: the role of connectivity,subsurface flow,and slope length scale on transport mechanism

The connectivity and upscaling of overland runoff and sediment transport are important issues in hillslope hydrology to identify water flux and sediment transport within landscape. These processes are highly variable in time and space with regard to their interactions with vegetation and soil surface conditions. The generation of overland runoff and its spatial connectivity were examined along a slope to determine the variations in the transport mechanism of runoff and soil particles by rain splash and overland runoff. Field experiments were conducted by erosion plots on a steep hillslope at lengths of 5, 10, and 15 m. The overland runoff connectivity and flow transport distance decreased with the slope length, while spatial variability of infiltration increased significantly with the slope length. Observation of subsurface flow revealed that surface soil and litter layer could have important role in water transport. However, the surface soil water content and water flux transport along the slope was highly variable for different storm events; the variability was related to the complexity of the system, mainly by way of the initial wetness conditions and infiltration characteristics. Only net rain‐splashed soil was measurable, but examination of the water flux, overland runoff and sediment transport connectivity, characteristics of sheetwash, and the variability in spatial infiltration indicated an increase in the contribution of the rain splash transport mechanism along the slope. Copyright © 2013 John Wiley & Sons, Ltd.     

Gullying and erosion control at archaeological sites in Grand Canyon,Arizona

Gully erosion of cultural sites in Grand Canyon National Park is an urgent management problem that has intensified in recent decades, potentially related to the effects of Glen Canyon Dam. We studied 25 gullies at nine sites in Grand Canyon over the 2002 monsoon–erosion season to better understand the geomorphology of the gully erosion and the effectiveness of erosion‐control structures (ECS) installed by the park under the direction of the Zuni Conservation Program. Field results indicate that Hortonian overland flow leads to concentrated flow in gullies and erosion focused at knickpoints along channels as well as at gully heads. Though groundcover type, soil shear strength and permeability vary systemat‐ically across catchments, gradient and, to a lesser degree, contributing drainage area seem to be the first‐order controls on gully extent, location of new knickpoints, and ECS damage. The installed ECS do reduce erosion relative to reaches without them and initial data suggest woody checkdams are preferable to rock linings, but maintenance is essential because damaged structures can exacerbate erosion. Topographic data from intensive field surveys and detailed photogrammetry provide slope–contributing area data for gully heads that have a trend consistent with previous empirical and theoretical formulations from a variety of landscapes. The same scaling holds below gully heads for knickpoint and ECS topographic data, with threshold coefficients the lowest for gully heads, slightly higher for knickpoints, and notably higher for damaged ECS. These topographic thresholds were used with 10‐cm digital elevation models to create simple predictive models for gully extent and structure damage. The model predictions accounted for the observed gullies but there are also many false‐positives. Purely topographical models are probably inadequate at this scale and application, but models that also parameterize the variable soil properties across sites would be useful for predicting erosion problems and ECS failure. Copyright © 2006 John Wiley & Sons, Ltd.     

Deriving formulas for an unsteady virtual velocity of bedload tracers

In a flume experiment with steady flow conditions, H. A. Einstein recognised the transport of bedload particles as consisting of steps of rolling, sliding, or saltation with intermittent rest periods, and introduced the concept of an average, ‘virtual’ transport velocity. This virtual velocity then has also been derived from tracer studies in the field by dividing the travelled distance of a tracer by the duration of competent flow. As a consequence, the virtual velocity in the field is represented by one single value only, despite the unsteady flow variables. Tracer measurements in a river have not been yet used to express transport velocity as a direct function of these actual variables, and insights from tracer measurements into the processes of sediment transport remain limited. In particular, the unsteady conditions for bedload in the field have impeded the derivation of sediment transport characteristics as determined from laboratory experiments, as well as the transfer of laboratory insights to a field setting. We introduce a method of data regression for the derivation of an ‘unsteady’ virtual velocity from repeated surveys of tracer positions. The regression program called graVel (provided as supplementary material) relates the integral of an excess flow variable term to measured travel distances, yielding the most probable threshold value for entrainment and the coefficient of linear and non‐linear formulas. An extended regression allows additional fitting of the exponent in non‐linear formulas. Application to published tracer data from the Mameyes River, Puerto Rico, shows that the unsteady virtual velocity is more likely governed by non‐linear relations to excess Shields stress, similar to bedload transport, than by relations linking the particle velocity linearly to excess shear velocity. Partial agreements with non‐dimensional results derived from the larger, non‐wadeable Mur River encourage the establishment of a generalised formula for the unsteady virtual velocity. Copyright © 2017 John Wiley & Sons, Ltd.     

Predicting sediment transport by interrill overland flow on rough surfaces

Modelling soil erosion requires an equation for predicting the sediment transport capacity by interrill overland flow on rough surfaces. The conventional practice of partitioning total shear stress into grain and form shear stress and predicting transport capacity using grain shear stress lacks rigour and is prone to underestimation. This study therefore explores the possibility that inasmuch as surface roughness affects flow hydraulic variables which, in turn, determine transport capacity, there may be one or more hydraulic variables which capture the effect of surface roughness on transport capacity suffciently well for good predictions of transport capacity to be achieved from data on these variables alone. To investigate this possibility, regression analyses were performed on data from 1506 flume experiments in which discharge, slope, water temperature, rainfall intensity, and roughness size, shape and concentration were varied. The analyses reveal that 89·8 per cent of the variance in transport capacity can be accounted for by excess flow power and flow depth. Including roughness size and concentration in the regression improves that explained variance by only 3·5 per cent. Evidently, flow depth, when used in combination with excess flow power, largely captures the effect of surface roughness on transport capacity. This finding promises to simplify greatly the task of developing a general sediment equation for interrill overland flow on rough surfaces. Copyright © 1998 John Wiley & Sons, Ltd.     

Experimental study of the response of a gravel streambed to increased sediment supply

If increased sediment supply to a river channel exceeds its transport capacity, deposition necessarily occurs as the bed adjusts to accommodate the increased supply. Both the mean and spatial patterns in bed elevation and grain size may change and an ability to understand their relative importance is needed to predict bed response. We report on an experiment in a field‐scale flume in which sediment supply is increased to a gravel bed with alternate bars. Sediment was recirculated in the experiments, but augmented in two steps, after which the bed was allowed to reach a new steady state. The transport rate at the end of the experiment was three times larger than at the start. High‐resolution sediment flux and topographic measurements, grain size derived from photographs, and hydrodynamic modeling allow us to document the topographic and textural response of the bed to increased sediment supply. The spatial patterns of bed topography and texture were forced by the flume setup and the initial and final steady states included long stationary alternate bars with associated grain size sorting. The transient bed contained several scales of shorter wavelength migrating bedforms superimposed on, and temporarily replacing the stationary alternate bars. Bed topography and textural patterns adjusted to increased sediment supply over different timescales. Bed slope and mean stress increased directly with sediment supply rate to produce a new transport steady state in a time about 2.5 times the minimum needed to deposit the required sediment wedge, indicating a trap efficiency of about 40% for the aggrading wedge. Adjustments in local topography and sorting, primarily in the form of smaller, migrating bars, continued for a period approximately equal to that required to initially reach transport steady state. Copyright © 2013 John Wiley & Sons, Ltd.     

Modelling suspended sediment concentration and load in a transport‐limited alluvial gully in northern Queensland,Australia

Alluvial gullies are often formed in dispersible sodic soils along steep banks of incised river channels. Field data collected by Shellberg et al. (Earth Surface Processes and Landforms 38: 1765–1778, 2013) from a gully outlet in northern Australia showed little hysteresis between water discharge and fine (<63 µm) and coarse (>63 µm) suspended sediment, indicating transport‐limited rather than source‐limited conditions. The major source of the fine (silt/clay) component was the sodic soils of upstream gully scarps, and the coarser (sand) component was sourced locally from channel bed material. In this companion paper at the same study site, a new method was developed for combining the settling velocity characteristics of these two sediment source components to estimate the average settling velocity of the total suspended sediment. This was compared to the analysis of limited sediment samples collected during flood conditions. These settling velocity data were used in the steady‐state transport limit theory of Hairsine and Rose (Water Resources Research 28: 237–243, 245–250, 1992) that successfully predicted field data of concentrations and loads at a cross‐section, regardless of the complexity of transport‐limited upstream sources (sheet erosion, scalds, rills, gullies, mass failure, bank and bed erosion, other disturbed areas). The analysis required calibration of a key model parameter, the fraction of total stream power (F ≈ 0.025) that is effective in re‐entraining sediment. Practical recommendations are provided for the prediction of sediment loads from other alluvial gullies in the region with similar hydrogeomorphic conditions, using average stream power efficiency factors for suspended silt/clay (F_w ≈ 0.016) and sand (F_s ≈ 0.038) respectively, but with no requirement for field data on sediment concentrations. Only basic field data on settling velocity characteristics from soil samples, channel geometry measurements, estimates of water velocity and discharge, and associated error margins are needed for transport limit theory predictions of concentration and load. This theory is simpler than that required in source‐limited situations. Copyright © 2015 John Wiley & Sons, Ltd.     

Fluvial sediment supply and pioneer woody seedlings as a control on bar‐surface topography

Plants influence river channel topography, but our understanding of the interaction among plants, flow, and sediment is limited, especially when sediment supply is variable. Using laboratory experiments in a recirculating flume with live seedlings in a mobile sand bed, we demonstrate how varying the balance between sediment supply and transport capacity shifts the relationship between plants and bar‐surface topography. Each experimental trial contrasted two sediment conditions, in which initially supply was maintained in equilibrium with transport via sediment recirculation, followed by sediment deficit, in which transport capacity exceeded supply, which was set to zero. For both sediment balances, the topographic response was sensitive to plant size, with larger plants inducing greater aggradation relative to a baseline condition. During sediment equilibrium, the positive relationship between plant size and topographic change also depended on species morphology (multi‐stemmed shrubs versus single‐stemmed plants). Plant morphology effects disappeared when the sediment balance shifted to a deficit, but the presence of plants had a greater impact on the magnitude of change compared to the topographic response under sediment equilibrium. Our results suggest that the interactions among sediment supply, plants, and topography may be strongest on rivers with a balance in sediment supply and transport capacity. Because of the large variability in fluvial sediment supply resulting from natural and anthropogenic influences, these interactions will differ spatially (e.g. longitudinally through a watershed) and at different temporal scales, from single flood events to longer time periods. Copyright © 2016 John Wiley & Sons, Ltd.     

Exploring the role of topography in small channel erosion

Erosion caused by concentrated flows in agricultural areas is responsible for important soil losses, and rapid sediment transfer through the channel network. The main factors controlling concentrated flow erosion rates include the erodibility of soil materials, soil use and management, climate and watershed topography. In this paper, two topographic indices, closely related to mathematical expressions suggested by different authors, are used to characterize the influence of watershed topography on gully erosion. The AS1 index is defined as the product of the watershed area and the partial area‐weighted average slope. The AS2 index is similar to the AS1 but uses the swale slope as the weighting factor. Formally, AS2 is the product of the watershed area and the length‐weighted average swale slope. From studies made using different ephemeral gully erosion databases, it is shown that a high correlation consistently exists between the topographic indices and the volume of eroded soil. The resulting relationships are therefore useful to assess soil losses from gully erosion, to identify the most susceptible watersheds within large areas, and to compare the susceptibility to gully erosion among different catchments. This information is also important in studying the response of natural drainage network systems to different rainfall inputs. Copyright © 2005 John Wiley & Sons, Ltd.     

PROCESSES OF HEADCUT GROWTH AND MIGRATION IN RILLS AND GULLIES

lINTRoDUCTIONHeadcuterosionwithinrills,ephemeralguIlies,classicgullies,andstreamscausesseriousenvironmentalproblems.Headcuterosionacceleratesthelossoftopsoilanddecreasestheproductivityofagriculturallands.Erodedsedimentsoftenendupinreceivingstreams,causingwaterqualityproblemsandnegativelyimpactingbioIogicalprocesses.Inadditiontolandscapedegradation,gulliesarethedominantformofdamagetoearthspillways.lfagullycanmovethroughanearthspillwayandbreachthecrestofadam,thentheimpoundedfloodwaterswiI1…     

Vegetation and topographic controls on sediment deposition and storage on gully beds in a degraded mountain area

Active gully systems developed on highly weathered or loose parent material are an important source of runoff and sediment production in degraded areas. However, a decrease of land pressure may lead to a return of a partial vegetation cover, whereby gully beds are preferred recolonization spots. Although the current knowledge on the role of vegetation on reducing sediment production on slopes is well developed, few studies exist on the significance of restoring sediment transport pathways on the total sediment budget of degraded mountainous catchments. This study in the Ecuadorian Andes evaluates the potential of vegetation to stabilize active gully systems by trapping and retaining eroded sediment in the gully bed, and analyses the significance of vegetation restoration in the gully bed in reducing sediment export from degraded catchments. Field measurements on 138 gully segments located in 13 ephemeral steep gullies with different ground vegetation cover indicate that gully bed vegetation is the most important factor in promoting short‐term (1–15 years) sediment deposition and gully stabilization. In well‐vegetated gully systems ( ≥ 30% of ground vegetation cover), 0.035 m³ m^–1 of sediment is deposited yearly in the gully bed. Almost 50 per cent of the observed variance in sediment deposition volumes can be explained by the mean ground vegetation cover of the gully bed. The presence of vegetation in gully beds gives rise to the formation of vegetated buffer zones, which enhance short‐term sediment trapping even in active gully systems in mountainous environments. Vegetation buffer zones are shown to modify the connectivity of sediment fluxes, as they reduce the transport efficiency of gully systems. First calculations on data on sediment deposition patterns in our study area show that gully bed deposition in response to gully bed revegetation can represent more than 25 per cent of the volume of sediment generated within the catchment. Our findings indicate that relatively small changes in landscape connectivity have the potential to create strong (positive) feedback loops between erosion and vegetation dynamics. Copyright © 2009 John Wiley & Sons, Ltd.     

Quantifying the spatial distribution of sediment transport in an experimental gully system using the morphological method

Whilst time-series of sediment transport in gullies in both laboratory experimental and field settings can be determined through instrumentation, quantifying the spatial distribution of transport rates remains challenging. The morphological method, which was proposed for estimating bed-material transport in both one- and two-dimensions in rivers, provides an alternative. Here, we developed this method for gully systems. A laboratory catchment was used to simulate gully erosion. High-resolution topographical data were acquired by close-range digital photogrammetry. Morphological changes were determined using high-resolution topographic data and an associated level of detection. Based on measured morphological changes, one-dimensional (1D) and two-dimensional (2D) sediment transport rates were calculated via cross-section by cross-section routing (1D) and cell by cell routing (2D). The 1D application provided a general trend of longitudinal variation of sediment transport for the whole gully system, increased gradually from zones of headward extension to a zone downstream where erosion and deposition were in balance, and sediment transport rates less variable in space. For the 2D application, hydrological and blended hydrological-hydraulic routing solutions were compared. We found that the level of negative transport was insensitive to whether or not a blended hydrological-hydraulic routing was used and that results from applying the hydrological routing throughout were not significantly degraded. We also found that consideration should be given to spatial and temporal resolution of the topographic data. The 2D application provided spatial patterns of sediment transport that vary with gully evolution. The main gully remained a high transport corridor but branch transport became more important through time. The framework we report provides an additional tool for both experimental and field quantification of the spatial patterns of sediment transport in gullies; and quantification of how these patterns change under different forcing factors.     

MODELING EPHEMERAL GULLY EROSION FOR CONSERVATION PLANNING

1INTRODUCTIONEphemeral gully erosion,which is caused by concentrated flow within cultivated farm fields,is distinct from rill erosion.Ephemeral gully erosion is also distinct from gully erosion in permanent,deep,incised channels,formed by headcuts moving upstream.Ephemeral gully erosion is often overlooked.It is not estimated with rill-interrill erosion prediction technology such as the Revised Universal Soil Loss Equation(Renard et al.,1997),and it is often not measured in field survey…     

Modelling the process of soil detachment by rill flow on steep loessial hillslopes

Soil detachment by rill flow is a key process of rill erosion, modelling this process can help in understanding rill erosion mechanisms. However, many soil detachment models are established on conceptual assumptions rather than experimental data. The objectives of this study were to establish a model of soil detachment by rill flow based on flume experimental data and to quantitatively verify the model. We simulated the process of soil detachment by rill flow in flume experiments with a soil-feeding hopper using loessial soil on steep slopes. Seven flow discharges, six slopes and five sediment loads were combined. Soil detachment capacity, sediment transport capacity, and soil detachment rate by rill flow under different sediment loads were measured. The process of soil detachment by rill flow can be modelled by a dual power function based on soil detachment capacity and transport capacity deficit as variables. The established model exhibited high credibility (NSE=0.97; R²=0.97). The contributions of soil detachment capacity and transport capacity deficit to soil detachment rate by rill flow reached 60% and 36%, respectively. Soil detachment capacity exerted more influence on soil detachment rate than did transport capacity deficit. The performance of the WEPP rill erosion equation is also favourable (NSE=0.95; R²=0.97). The two power exponents in the model we established strengthen the role of soil detachment capacity in soil detachment rate and weaken that for transport capacity deficit. Soil detachment capacity and transport capacity deficit played important roles in the determination of soil detachment rate by rill flow. The results can be applied to implement the numerical modeling and prediction of rill erosion processes on steep loessial hillslopes. © 2019 John Wiley & Sons, Ltd.     

Analysis of the contributions of topographic,soil, and vegetation features on the spatial distributions of surface soil moisture in a steep natural forested headwater catchment

Surface soil moisture has been extensively studied for various land uses and landforms. Although many studies have reported potential factors that control surface soil moisture over space or time, the findings have not always been consistent, indicating a need for identification of the main factors. This study focused on the static controls of topographic, soil, and vegetation features on surface soil moisture in a steep natural forested headwater catchment consisting of three hillslope units of a gully area, side slope, and valley‐head slope. Using a simple correlation analysis to investigate the effects of the static factors on surface soil moisture at depths of 0–20 cm at 470 points in 13 surveys, we addressed the characteristics of surface soil moisture and its main controlling factors. The results indicated that the mean of surface soil moisture was in the decreasing order of gully area > valley‐head slope > side slope. The relationship between the mean and standard deviation of surface soil moisture showed a convex‐upward shape in the headwater catchment, a negative curvilinear shape in the gully area, and positive curvilinear shapes at the side and valley‐head slopes. At the headwater catchment and valley‐head slope, positive contributions of soil porosity and negative contributions of slope gradient and saturated hydraulic conductivity were the main controlling factors of surface soil moisture under wetter conditions, whereas positive contributions of topographic wetness index and negative contributions of vegetation density were the main controlling factors of surface soil moisture under drier conditions. At the side slope underlain by fractured bedrocks, only saturated hydraulic conductivity and vegetation density were observed to be the controlling factors. Surface soil moisture in the gully area was mainly affected by runoff rather than were static features. Thus, using hillslope units is effective for approximately estimating the hydrological behaviours of surface moisture on a larger scale, whereas dependency between the main static factors and moisture conditions is helpful for estimating the spatial distributions of surface moisture on a smaller scale.     

NUMERICAL SIMULATION OF HEAD-CUT WITH A TWO-LAYERED BED

1INTRODUCTION The rate of gully erosion is dominated by the upstream migration of existing nick-points called headcut.Due to the shape of the headcut,the flow from the upstream channel impinges into the pool of the scour hole and forms a complex three-dimensional flow structure.The turbulent flow deepens the scour hole,transports the eroded material downstream,undercuts the headcut wall and creates gravitational slumping of the gully head material.In reality,the occurrence of a head cut i…     

How long is a hillslope?

Hillslope length is a fundamental attribute of landscapes, intrinsically linked to drainage density, landslide hazard, biogeochemical cycling and hillslope sediment transport. Existing methods to estimate catchment average hillslope lengths include inversion of drainage density or identification of a break in slope–area scaling, where the hillslope domain transitions into the fluvial domain. Here we implement a technique which models flow from point sources on hilltops across pixels in a digital elevation model (DEM), based on flow directions calculated using pixel aspect, until reaching the channel network, defined using recently developed channel extraction algorithms. Through comparisons between these measurement techniques, we show that estimating hillslope length from plots of topographic slope versus drainage area, or by inverting measures of drainage density, systematically underestimates hillslope length. In addition, hillslope lengths estimated by slope–area scaling breaks show large variations between catchments of similar morphology and area. We then use hillslope length–relief structure of landscapes to explore nature of sediment flux operating on a landscape. Distinct topographic forms are predicted for end‐member sediment flux laws which constrain sediment transport on hillslopes as being linearly or nonlinearly dependent on hillslope gradient. Because our method extracts hillslope profiles originating from every ridgetop pixel in a DEM, we show that the resulting population of hillslope length–relief measurements can be used to differentiate between linear and nonlinear sediment transport laws in soil mantled landscapes. We find that across a broad range of sites across the continental United States, topography is consistent with a sediment flux law in which transport is nonlinearly proportional to topographic gradient. © 2016 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.