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Apportioning contributions of individual rill erosion processes and theirinteractions on loessial hillslopesChao Qina,b, Fenli Zhenga,c,⁎, Glenn V. Wilsond, Xunchang J. Zhange, Ximeng Xufa State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Soil and Water Conservation, Northwest A & F University, Yangling 712100,Shaanxi, PR Chinab State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, PR Chinac Institute of Soil and Water Conservation, CAS & MWR, Yangling 712100, Shaanxi, PR ChinadUSDA-ARS National Sedimentation Laboratory, Oxford 38655, MS, USAeUSDA-ARS Grazinglands Research Laboratory, EI Reno 73036, OK, USAf Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences,Beijing 100101, PR China
A R T I C L E I N F O
Keywords:Channel erosionHeadcut advanceBed incisionSidewall expansionLoess plateau
A B S T R A C T
Channels (rill, ephemeral gully, gully and river channel) exhibit a continuum of sizes and flow magnitudes. Rillerosion, as the initial stage of channel erosion, accounts for> 80% of total eroded sediments on sloping farminglands in many parts of the world. Previous researches often regard rill erosion as an entirety or focus on in-dividual rill erosion process separately. Few attentions have been paid to the contributions of individual pro-cesses including rill headcut advance, bed incision, sidewall expansion and their interactions to the over-all rillerosion. Thus, simulated upslope inflow experiments were designed to investigate the impacts of individualprocesses involved and their interactions in rill erosion under four inflow rates (1.0, 2.0, 3.0 and 4.0 Lmin−1)and two slope gradients (15° and 20°). Photogrammetry and manual sampling were used to measure hillslopemorphology variation and sediment delivery, repectively. The results show that headcut advance, bed incisionand sidewall expansion interact with each other and exhibit both independent and dependent features acrossspatial and temporal scales. Headcut advance interacts with bed incision and sidewall expansion before rill headadvancing to a critical slope length. Initial rill depth and width are determined by initial headcut morphology.Bed incision and sidewall expansion dominate rill erosion before and after the non-erodible layer is exposed toconcentrated flow, respectively. Headcut advance contributed the largest amount of rill erosion (44%–68%),followed by bed incision (27%–44%) and sidewall expansion (3.8%–12%). Headcut advance contributed more(63%–83%) to total rill width increment while bed incision contributed larger percentage (51%–65%) to totalrill depth increment. Prediction equations for length, width and depth of a single rill on a loessial hillslope andempirical equations of rill erosion for the individual erosion processes were fitted and validated. Quantificationand understanding of the contributions of individual rill erosion processes provides the necessary scientific basisfor the development of process-based rill erosion models, and then, for preventions of soil losses and landdegradation.
1. Introduction
1.1. Rill erosion and its impacts on land degradation
Soil erosion is a dominant force for land degradation in agriculturewatersheds as 15.1% of global land is suffering from human-induceddegradation, 83.6% of which is by soil erosion (Lal, 2002). As aeolian
deposit, soil on the Loess Plateau is highly erodible and suffers fromserious erosion. Channel erosion (concentrated flow erosion), includingrill, ephemeral gully and gully channel erosion, is the dominant meanscausing soil loss, land deterioration, and subsequent sediment deposi-tion in streams (Jia et al., 2005). Channels exhibit a continuum of sizesand concentrated flow velocities (Govindaraju and Kavvas, 1992;Simon and Rinaldi, 2006; Stefanovic and Bryan, 2007; Wells et al.,
https://doi.org/10.1016/j.catena.2019.104099Received 3 March 2019; Received in revised form 14 May 2019; Accepted 31 May 2019
⁎ Corresponding author to: F. Zheng, No. 26, Xi'nong Road, Institute of Soil and Water Conservation, Northwest A&F University, Yangling 712100, Shaanxi, PRChina.
E-mail addresses: [email protected] (C. Qin), [email protected] (F. Zheng), [email protected] (G.V. Wilson),[email protected] (X.J. Zhang), [email protected] (X. Xu).
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2013; Babazadeh et al., 2017). Rill erosion, as the initial stage of con-centrated flow erosion at a hillslope scale, facilitates accelerated runoff,and sediment and nutrient transport into larger-scale channels. Rillsaccount for 50%–70% of total eroded sediments at hillslopes where rillerosion is dominated around the world and>80% in the Loess Plateau(Zhu, 1956; Lal, 2002). Sediment yield increases significantly duringand after rill formation due to the increased concentrated flow depth,velocity and shear stress compared to inter-rill flow (Lal, 2002;Larionov et al., 2008; He et al., 2017).
Physical rill development includes three sub-processes: headcutadvance, bed incision (downward scouring) and sidewall expansion(widening); and each individual process dominates at different phasesof rill development (Bingner et al., 2016; Qin et al., 2018b). These threeprocesses occur consecutively or concurrently and interact with eachother through feedbacks (Bryan and Poesen, 1989; Bennett et al., 2000;Mancilla et al., 2005; Qin et al., 2018b). Mass collapsing throughchannel sidewall, headwall slumping and plunge pool erosion are mainsediment processes of channel evolution based on long-term observa-tions (Nichols et al., 2016). Rill evolution, which is relatively easy tosimulate with indoor experiments, can be extended to larger-scalechannel erosion process to some degree (Govindaraju and Kavvas,1992).
1.2. Headcut advance
A headcut is a small abrupt change in channel elevation that ad-vances the channel upslope and results in accelerated erosion (SoilScience Society of America, 2008; Babazadeh et al., 2017). Soil loss dueto headcut erosion remains a critical concern in agricultural regions,since these processes can lead to landscape degradation (Gordon et al.,2011). Headcut advance, as a highly turbulent and three-dimensionalerosional system (Jia et al., 2005), is the initial phase of rill develop-ment (Han et al., 2002). The occurrence and migration of headcutscauses the sediment concentration to become greater than the sedimenttransport capacity which leads to deposition (Wirtz et al., 2012).Headcuts play a critical role in rill formation and drainage systemevolution (Bryan and Poesen, 1989; Bennett et al., 2000).
Researches regarding rill headcut advance processes, migrationrate, sediment contributions, impact factors and identification of po-tential headcut locations have attracted wide attention (Bennett, 1999;Bennett et al., 2000; Bennett and Casalí, 2001; Gordon et al., 2007a;Bingner et al., 2016). Headcut advance distance is linearly correlated totime series of headcut advancing and is affected by particle size dis-tribution, upslope contributing area, topography (slope length andgradient), sediment concentration, scour hole depth and soil layering(Alonso and Bennett, 2002; Vandekerckhove et al., 2003; Gordon et al.,2007b; Wells et al., 2010). Bennett et al. (2000) indicated that headcutsmaintain a constant geometry while migrating and exhibit a behavior ofself-similar propagating phenomenon when the soil layer eroded ishomogeneous, and the slope gradient and upslope inflow are constant.Headcut geometry tends to become vertical when soil clay content in-creases (Wilcox et al., 2001; Wells et al., 2009; Babazadeh et al., 2017).
Small scale channel headcut models were built on hillslopes to in-vestigate the headcut advance mechanisms including the plunge poolerosion and the rate of headcut migration based on approximations tothe laws governing mass, momentum, and energy transfer (Alonso andBennett, 2002). Models combined with SWAT hydrologic flow routinesand numerical models were also developed for headcut advance andmorphology simulation, and the verification of field observations andphysical experimental results (Jia et al., 2005; Zhu et al., 2008; Allenet al., 2018). However, it is hard for current soil erosion models toaccurately predict soil erosion immediately below and above the knickpoint in a rill due to the complicated changes in scour morphologiesand flow regimes. Simplifying assumptions have been applied in somemodels (Foster et al., 1977; Alonso and Bennett, 2002; Gordon et al.,2007a; Gordon et al., 2007b). Researches on scour hole morphology,
secondary headcut formation and advance, and interactions betweengravitational erosion and concentrated flow shear stress erosion are stillunclear. Effects of headcut advance on subsequent downward bed in-cision and sidewall expansion need to be studied.
1.3. Bed incision
Channels, no matter the scale of the incised channels from rills (cmscale) to canyons (km scale), are part of a drainage-network that con-tribute to landscape evolution (Simon and Rinaldi, 2006). As such, thiscontinuum of channels from rills to canyons experience the same inci-sion processes, but to differing magnitudes and interactions. The inci-sion process is a response to excess amounts of flow energy or streampower relative to the sediment as a result of concentrated flow. Chan-nelization starts when concentrated flow tractive forces exceed soilentrainment resistance. Sufficient runoff volume and flow velocity wereprerequisites for producing flows that lead to bed incision (Evans andBoardman, 2003). Initial drop-pits, or micro-plunge pools, develop onsmooth surfaces caused by surface seal failure, facilitate the formationof rills and determines the initial rill depth and width. Secondaryheadcuts, which develop only in well-established rills, determine bedroughness to a great extent (Bryan and Poesen, 1989; Qin et al., 2018a).Due to the significant difference in erodibility between topsoil andsubsoil, and the alternation of relatively narrow and deep rills and wideand shallow rills, rill depth usually does not increase uniformly withslope length (Bryan and Poesen, 1989; Qin et al., 2018a).
Former studies revealed that soil erodibility, bed slope, upslopeinflow rate, sediment concentration and near-surface hydraulic gra-dient were dominant factors affecting channel incision (Bryan andPoesen, 1989; Slattery and Bryan, 1992; Bennett et al., 2000; Alonsoand Bennett, 2002; Liu et al., 2015; Qin et al., 2018a). Numericalmodels were applied in predicting rill incision (Zhu et al., 1995; Favis-Mortlock, 1998; Casalí et al., 2003; Jia et al., 2005), which had thepotential to be verified by some physical models (Bryan and Poesen,1989; Bennett et al., 2000).
Woodward (1999) and Liu et al. (2015) emphasized that rill depthinformation could significantly increase the accuracy of rill erosionestimation. Soil erosion predicting models such as WEPP (Water Ero-sion Prediction Project) might be improved by clarifying the processesand interactions of headcut advance and bed scour (Nearing et al.,1990; Zhu et al., 1995), in which only bed incision is simulated.However, due to the rapid development of rills and complicated rillmorphologies, measurement accuracy of rill depth variation and hy-drodynamic characteristics near headcuts is not easily accomplished(Römkens et al., 1990; Slattery and Bryan, 1992), which limits thedevelopment of soil erosion models for bed incision. Therefore, researchon rill depth dynamics is of great importance to rill erosion modeling,e.g. loessial rill erosion modeling on the Loess Plateau of China (Shenet al., 2015).
1.4. Sidewall expansion
Rill sidewall expansion, initially determined by headcut advanceprocess, has been confirmed to be a main process following headcutadvance in overall rill evolution and overall erosion on hillslopes.Sidewall expansion processes of channels include subaerial erosion ofthe banks, fluvial erosion of the toe of the channel bank, seepage ero-sion of channel banks that undercut sidewalls, internal erosion of soilpipes that exit the bank, and mass failure of the bank generally in re-sponse to undercutting of the banks by fluvial erosion and seepageerosion, as well as to geotechnical instability factors (Lawler et al.,1997; Rinaldi and Darby, 2007; Fox and Wilson, 2010; Midgley et al.,2013; Masoodi et al., 2018). These processes of channel sidewall ex-pansion are complex and have attracted much attention for largechannels such as gullies and streams but to a lesser extent for rills(Martinez-Casasnovas et al., 2004; Chaplot et al., 2011; Chen et al.,
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2013; Wells et al., 2013; Bingner et al., 2016).Larionov et al. (2008) stated the importance of flow direction re-
lative to the rill sidewall and quantified erosion rate of sidewalls underseveral flow angles. Rill sidewall failure could be attributed to a com-bination of water erosion (fluvial shearing process) and gravity erosioneffects (gravitational mass failure process) (Istanbulluoglu, 2005).Erosion due to gravity, began with sidewall toe scour and ended withhigh and unstable sidewall failures (Stefanovic and Bryan, 2007; Chenet al., 2013). Such sidewall failures contributed 80%–89% of sedimentdelivery when a simulation of channel sidewall expansion was appliedto upland concentrated flows (Qin et al., 2018b). Previous researcheson river bank failure processes and mechanisms have laid a foundationfor rill sidewall expansion research. The scopes of these studies includebank erosion process monitoring (Wells et al., 2013; Qin et al., 2019),bank failure affecting factors (Wang et al., 2016), tension crack devel-opment mechanisms (Hossain et al., 2011), gravity erosion mechanisms(Darby et al., 2002; El Kadi Abderrezzak et al., 2014) and bank stabilitysimulation (Darby et al., 2002).
Researches related to sand-bed channels of varied bank resistanceverify that flow energy and the rate of energy dissipation determinesthe channel's ultimate stable geometries (Simon and Rinaldi, 2006).However, depth limitation was not taken into account in some algo-rithms that have been developed to determine channel width, whichmay significantly impact the channel width estimation when channelbed incises to a less erodible layer (Gordon et al., 2007a; Grigor'Ev,2007; Wells et al., 2013; El Kadi Abderrezzak et al., 2014; Bingner et al.,2016). Water erosion prediction models including WEPP, EphGEE(Ephemeral Gully Erosion Estimator) and AnnAGNPS (AnnualizedAgricultural Non-Point Source Pollution Model) can be improved byclarifying mechanisms of channel widening processes and its interac-tions with headcut advance and bed incision (Wells et al., 2013; Dabneyet al., 2014; Bingner et al., 2016).
Concentrated-flow erosion, a major component of hillslope erosion,is responsible for channel formation and evolution on cropland (Zhuet al., 1995; Thomas et al., 2009). Up to date, previous studies mainlyconcentrated on rill erosion as an entirety or focused on individualprocesses separately. But as the above mentioned, few attempts havebeen made to understand the comprehensive interactions amongheadcut advance, bed incision and sidewall expansion, and to clarifytheir contributions to over-all rill erosion. Thus, the specific objectivesof this study were: 1) to discriminate individual rill erosion processes atdifferent rill development stages, 2) to explore interactions amongheadcut advance, bed incision, sidewall expansion and their
contributions to total rill erosion, and 3) to establish empirical equa-tions of rill erosion for loessial hillslopes.
2. Materials and methods
2.1. Experimental setup of rill headcut advance, bed incision and sidewallexpansion tests
Rill channel flumes were formed to investigate headcut advance,bed incision and sidewall expansion under a set of slope gradients andinflow rate combinations with the existence of a non-erodible layer.High precision DEMs obtained from photogrammetry were used forhillslope morphology analysis.
2.1.1. Experimental materials and facilitiesThe soil used in this study was loess (fine-silty, mixed), which can be
classified as a Calcic Cambisol (USDA NRCS, 1999). The soil texture was28.3% sand (> 50 μm), 58.1% silt (50–2 μm), 13.6% clay (< 2 μm),and contained 5.9 g kg−1 soil organic matter.
A soil bed inside a flume measuring 200 cm-long, 30 cm-wide and50 cm-deep (Fig. 1), containing drainage holes (1 cm diameter in gridspacing) in the bottom, was used in this study. The soil bed and flumedesign changed according to the process studied (headcut advance, bedincision and sidewall expansion) in order to isolate the individual rillerosion processes (Fig. 2). Upslope inflow was controlled by a constant-head water tank fixed 2.5 m above the flume bottom of the lower end(Fig. 1).
2.1.2. Experimental designAccording to the field investigations and previous studies of rill
evolution (Govindaraju and Kavvas, 1992; Stefanovic and Bryan, 2007;Shen et al., 2015; Bingner et al., 2016), rill development processes canbe briefly outlined as follows: 1) headcuts firstly advance to criticalslope lengths and then stop advancing, forming initial rill channels; 2)overland flow concentrates within the formed rill channel, which leadsto bed incision until less- or non-erodible layer exposes to concentratedflow; 3) concentrated flow begins to scour rill toe and contributes tosidewall expansion.
To maximize the simulation of natural rill evolution, three groups oftests were conducted to quantify the individual rill erosion processes ofheadcut advance, bed incision and sidewall expansion (Fig. 2 andTable 1). Headcut advance tests were firstly applied to form an initialrill channel (Fig. 2a). Initial rill width and depth were determined.
Fig. 1. Experimental facilities including a soil bed inside a flume, upslope inflow system and photogrammetric monitoring of rills.
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Then, two steel plates were inserted at the two sidewalls of the well-formed rill channel to confine rill widening and to simulate bed incision(Fig. 2b). Due to the generation of many rill widths after headcut ad-vance test (Table 2), only one rill width (8 cm) was selected for bedincision test. Lastly, steel plates were removed, and non-erodible layerwas established at the bottom of rill bed to simulate the followingsidewall expansion process (Fig. 2c). Similar to the simulation of bedincision, two initial rill widths (4 and 8 cm) were selected for sidewallexpansion test. For the rill width of 8 cm, only one slope gradient wastested (Table 1). In order to better establish the three models, threeindividual flumes were used to consecutively simulate the processes ofheadcut advance, bed incision and sidewall expansion.
Four upslope inflow rates (1.0, 2.0, 3.0, 4.0 Lmin−1), two slopegradients (15° and 20°) and two initial rill widths (4 and 8 cm) wereconsidered (Table 1). The designing of inflow rates was according to: 1)
The erosive rainfall standards of the Loess Plateau ranges from 16 to150mmh−1 (Zhou and Wang, 1987). 2) The observed runoff coeffi-cient for bare and fallow treatment is 0.8 when I30 (the maximum30min rainfall intensity) is> 30mmh−1. The designing of slope gra-dient was according to: 1) Rill erosion widely occurs on hillslopes withslope gradients from 10° to 25° on the Loess Plateau (Zheng, 1989). 2)The critical slope length of rill headcut initiation is 2.5 m on loessialhillslope when slope gradient is 20° (Zheng, 1989). 3) 25° slope gra-dient was the upper limit of “Grain for Green” Project of the LoessPlateau.
The detailed design of the three groups of the tests were: headcutadvance test (two slope gradients, four inflow rates, two replications,16 runs in total), bed incision test (two slope gradients, four inflowrates, two replications, 16 runs in total), sidewall expansion test (twoslope gradients, four inflow rates, two initial rill widths, two
Fig. 2. Example of images obtained from photogrammetry during headcut advance (a), bed incision (b) and sidewall expansion (c) tests.
Table 1Experimental design and basic parameter description.
Bed slope (°) Designed inflow rate (Lmin−1) Duration (min) Individual rill erosion process
15 1 60 Headcut advance, bed incision, sidewall expansiona
2 30 Headcut advance, bed incision, sidewall expansiona
3 20 Headcut advance, bed incision, sidewall expansiona
4 15 Headcut advance, bed incision, sidewall expansiona
20 1 60 Headcut advance, bed incision, sidewall expansiona
2 30 Headcut advance, bed incision, sidewall expansiona
3 20 Headcut advance, bed incision, sidewall expansiona
4 15 Headcut advance, bed incision, sidewall expansiona
20 1 60 Sidewall expansionb
2 30 Sidewall expansionb
3 20 Sidewall expansionb
4 15 Sidewall expansionb
a Initial rill widths of sidewall expansion tests were 4 cm.b Initial rill widths of sidewall expansion tests were 8 cm.
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replications, 24 runs in total). For the inflow rates of 1.0, 2.0, 3.0,4.0 Lmin−1, the test durations were 60, 30, 20 and 15min, respec-tively. During each test, two cameras were used to capture images(Fig. 1). A summary of experimental parameters is given in Table 1.Fixed rill widths of bed incision test, fixed rill depths of sidewall ex-pansion test and fixed rill lengths of bed incision and sidewall expan-sion tests are given in Tables 2, 3 and 4, respectively.
2.1.3. Preparation of soil box2.1.3.1. Headcut advance tests. The bottom 15 cm of the soil bed wasfilled with sand to allow free drainage of excess water. A highlypermeable cloth was used to separate the sand and soil layers. Soilwas packed above the permeable cloth in 0.05m increments with a1.10 g cm−3 soil bulk density and a total depth of 20 cm (Shen et al.,2015). Then, an Al (aluminum) headcut-forming plate with 5-cmlength, 30-cm width and 5-cm height was installed at the 170 cmslope length, normal to the bed and in contact with the soil. A 5-cmlayer soil, with the same bulk density of the bottom 20-cm soil layer,was packed upstream of the plate (0–170 cm slope length), thus,producing a preformed vertical step in the bed profile (Wells et al.,
2009). A small curvature (2.5-m radius; 0.01-m elevation increase fromsoil box center to soil box edge) was cut into the soil bed from 30 to170 cm slope length to ensure the upslope inflow water concentrated atthe center of the soil bed. Then, fine soil material (passed through 0.5-mm sieve) was evenly sprayed at the slope lengths from 0 to 170 cm tofacilitate the formation of surface crust when raindrops impact the soilsurface. This thin surface crust ensured all sediments originated fromheadcut area and had no effects on headcut morphology and advancingrate. The transition section between the inlet tank and the soil wasformed and stabilized with cement (Fig. 2a).
Then, a 20-mmh−1 pre-rain was applied for 20min to the soil bedset at the 3° slope gradient. No water was allowed to pond on the soilsurface during the pre-rain. The purpose of the pre-rain was to developconsistent soil moisture, consolidate loose soil particles by raindropimpact and produce a surface seal over the treated area. After a 12 hperiod of soil water redistribution, the bed slope was adjusted to thedesigned experimental slope gradient (15° or 20°) (Wells et al., 2009).
2.1.3.2. Bed incision tests. The soil bed was modified by including twosteel plates of 2m long, fixed at the 11 and 19 cm widths of the soil bedwith an 8 cm spacing to prevent rill widening (Fig. 2b). Sand was filledoutside the steel plates in the soil bed. The bottom 20-cm depth insidethe steel plates was filled with sand while the top 20 cm was packedwith soil in 0.05m increments with a 1.10 g cm−3 soil bulk density(Fig. 2b). A highly permeable cloth was used to separate the sand andsoil layers. Each packed soil layer was lightly raked before placing thenext layer for homogeneity. The amount of soil in each layer was keptas constant as possible to maintain a constant soil bulk density and auniform spatial distribution. The transition section between the inlettank and the rill channel was formed and stabilized with cement(Fig. 2b). A 20-mmh−1 pre-rain was applied with the same procedureas the headcut advance test.
2.1.3.3. Sidewall expansion tests. The soil bed was firstly modified byremoving the inserted steel plates in the bed incision test, and then,bottom 10 cm of the soil bed was filled with sand to allow free drainageof excess water. A highly permeable cloth was used to separate the sandand soil layers. Soil was packed above the permeable cloth in 0.05mincrements at a 1.30 g cm−3 soil bulk density and a total depth of25 cm. A 0.01m non-erodible layer with a 1.30 g cm−3 soil bulkdensity, whose permeability was enough for water infiltration andstrength was large enough to resist detachment by the concentratedflow, was placed above the 25-cm soil layer. This layer consisted of a 5
Table 2Average rill widths under different experimental treatments.
Bedslope (°)
Designedinflow rate(L min−1)
Rill width (cm)
Headcut advance(include scour holeformation)a
Bed incisionb Sidewallexpansionc
15 1 4.7 ± 0.1 8 5.1 ± 0.12 4.9 ± 0.6 8 6.0 ± 0.33 6.3 ± 0.3 8 7.2 ± 0.44 7.5 ± 0.3 8 8.1 ± 0.3
20 1 4.2 ± 0.7 8 5.4 ± 0.72 5.1 ± 0.1 8 6.2 ± 0.13 7.0 ± 0.4 8 7.7 ± 0.44 8.2 ± 0.2 8 8.7 ± 0.1
20 1 8.9 ± 0.12 9.7 ± 0.33 10.8 ± 0.14 11.9 ± 0.4
a Average rill widths along hillslopes after headcut advance tests.b Fixed rill width of bed incision tests.c Average rill widths along hillslopes after sidewall expansion tests. Initial rill
widths were 4 and 8 cm for the former two and the third group of tests, re-spectively.
Table 3Average rill depths under different experimental treatments.
Bedslope (°)
Designedinflow rate(Lmin−1)
Rill depth (cm)
Headcut advance(include scour holeformation)a
Bed incisionb Sidewallexpansionc
15 1 3.9 ± 0.2 6.8 ± 0.1 42 7.5 ± 0.4 8.2 ± 0.5 43 9.9 ± 0.1 10.8 ± 0.1 44 11.5 ± 0.1 12.6 ± 0.4 4
20 1 6.4 ± 0.6 7.8 ± 0.2 42 9.2 ± 0.2 10.5 ± 0.6 43 11.3 ± 0.4 12.1 ± 0.6 44 11.7 ± 0.3 13.2 ± 0.4 4
20 1 42 43 44 4
a Average rill depths along hillslopes after headcut advance tests.b Average rill depths along hillslopes after bed incision tests.c Fixed rill depth of sidewall expansion tests.
Table 4Rill lengths under different experimental treatments.
Bedslope(°)
Designedinflow rate(Lmin−1)
Rill length (cm)
Headcut advance(include scour holeformation)a
Bed incisionb Sidewallexpansionc
15 1 29.7 ± 0.8 200 144.1 ± 1.02 76.2 ± 3.9 200 144.2 ± 0.13 85.9 ± 2.3 200 140.7 ± 1.34 97.5 ± 2.9 200 138.9 ± 1.1
20 1 44.9 ± 0.6 200 144.7 ± 4.22 83.9 ± 2.2 200 145.2 ± 0.43 104.0 ± 4.7 200 143.8 ± 0.64 121.1 ± 1.6 200 144.3 ± 1.5
20 1 140.5 ± 1.32 144.5 ± 3.43 144.9 ± 1.54 145.1 ± 0.1
a Rill lengths of 15-min experimental duration of headcut advance tests.b Fixed rill length of bed incision tests.c Fixed rill length with small variation (due to lengths of the transition sec-
tion showed small differences of< 5%) of sidewall expansion tests.
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to 3 mixture of soil to cement (Wells et al., 2013). The non-erodiblelayer was then sprayed with water until surface ponding occurred(Wells et al., 2013). To cure the non-erodible layer, a fan was used toblow air over the surface for 24 h. A 4-cm erodible layer with a1.10 g cm−3 soil bulk density was packed above the non-erodible layer.Then, either a 4 or 8 cm width, orthogonal aluminum channel mold wasused to make a pre-formed initial rill along the soil bed (1.2-m long,0.04 or 0.08-m wide, 0.04-m deep, Qin et al., 2018b). The transitionsection between the inlet tank and the pre-made rill channel wasformed and stabilized with cement (Fig. 2c). A 20-mmh−1 pre-rain wasapplied with the same procedure as the headcut advance test.
2.2. Erosion process monitoring
1) After the preparation of each soil bed, at the slope lengths of 70 and120 cm, two cameras (EOS 5D Mark II, Canon, Japan) were mounted1.5 m above the soil bed (Fig. 1). Then, appropriate adjustmentsincluding shooting type, scene mode, aperture, ISO, shutter speed,focus mode and focal length were made to both cameras (Qin et al.,2018a).
2) Targets parallel to the soil surface were setup at the boundary of thesoil bed (Fig. 2). A Total Station Laser Scanner (Nova MS50, LeicaGeosystem, Switzerland) was used to measure the exact relativecoordinates of each target.
3) Inflow rates were calibrated to the target flow rates (i.e. 1, 2, 3,4 Lmin−1) with a relative error smaller than 5% (Table 1). Afterfeeding the concentrated inflow, the runoff and sediment from thetests were captured in 5 L plastic buckets at 10–30 s intervals.Images were captured by two cameras at the same intervals(10–30 s) as manual sampling.
4) After each run, runoff samples were left over night to settle so thatthe excess water could be decanted. The samples were then dried in
an oven at 105 °C for 24 h and weighed to calculate runoff and soilloss.
2.3. Data analysis
Post analysis of the images data included: 1) paired image proces-sing in Agisoft Photoscan Professional 1.2.4 (Agisoft LLC, St.Petersburg, Russia) to create *.txt point clouds exporting; 2) construc-tion of high-precision DEMs (2mm×2mm resolution) using ArcGIS10.4 (ESRI Inc., Redlands, CA, USA) (Qin et al., 2018b, 2018c); and 3)rill morphology (length, width, depth) analysis based on the con-structed DEMs (Wells et al., 2016).
Due to various rill widths of different tests, instead of total sedimentyields, unit-rill width sediment deliveries of headcut advance, bed in-cision and sidewall expansion were calculated to analyze the con-tributions of individual processes to total rill erosion.
To ensure the independence of the data used to fit and validate theequation, 3/4 of the data (12 runs for headcut advance and bed incisiontests, and 18 runs for sidewall expansion tests) were randomly selectedto establish the equations, and the remaining 1/4 of the data were usedto validate the equations. The Nash-Sutcliffe simulation efficiency (ENS)and the determination coefficient (R2) were used for equations valida-tion (Nash and Sutcliffe, 1970). When ENS > 0.5 and R2 > 0.6, theprediction of the fitted equation could be regarded as acceptable(Santhi et al., 2001).
3. Results
3.1. Stages of rill erosion
Rill erosion processes change with time such that rill erosion can bedissected into stages (Figs. 3 and 4). Rill erosion is a comprehensive 3Dprocess that includes the scour hole formation stage, followed by theheadcut advance stage (integrated headcut advance, bed incision andsidewall expansion), and as the rill matures erosion is dominated by bedincision and further sidewall expansions stages. The headcut advance,bed incision and sidewall expansion processes interact with each otherand exhibit both independent and dependent features across spatial andtemporal scales during the whole process of rill evolution.
According to the experimental design of individual rill erosionprocesses, three key rill erosion points T1 (rill heads start moving up-stream), T2 (rill heads arrive at critical slope length) and T3 (rill bedsincise to plow pan) were assumed (Fig. 3). To fit the equations of rilllength, width and depth change with time of individual process, one-to-one correspondence time and sediment delivery data presented inprevious studies (Qin et al., 2018a; Qin et al., 2018b; Qin et al., 2018c)were used to analyze time-series of rill length, depth and width for twoslope gradients (15° and 20°), four inflow rates (1, 2, 3, 4 Lmin−1) andtwo initial rill widths (4 and 8 cm, only applied for sidewall expansiontest).
Fig. 3. A schematic diagram of individual rill erosion processes at different rillerosion stages (T1: rill heads start moving upstream; T2: rill heads arrive atcritical slope length, T3: rill beds incise to plow pan).
Fig. 4. Time series of rill length, width and depth (selected example from the treatment of 1 Lmin−1 inflow rate, 20° bed slope and 4 cm initial rill width).
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Based on the individual rill erosion process at different rill erosionstages shown in Fig. 3, empirical equations of rill length, width anddepth under simulated upslope inflow experiments on loessial hillslopeswere fitted. Three quarters of the data were used to fit the equationsand another quarter was used for equations verification.
3.1.1. Scour hole formation stageBefore headcuts advancing upstream, scour holes form under the
condition that boundary shear stress exceeds the critical shear stress forthe soil (Foster et al., 1977). A relatively small length of the rill channelis incised until the upslope inflow energy consumes to a degree thatcannot keep vertical incision or reaches a plow pan or a soil layer thathas relatively low erodibility (Gordon et al., 2007a). The small length ofa rill contributes only a small portion to the total rill length, andtherefore, it was negligible in the former research (Gordon et al.,2007b). Initial rill widths and depths were determined and would keepstable during the following headcut advance process (Fig. 4).
3.1.2. Headcut advance stageRill headcut advance stage integrated the processes of headcut ad-
vance, bed incision and sidewall expansion. Rill lengths increased withtime while rill widths and depths were constants equal to the initialheadcut widths and depths from T1 to T2 (Fig. 4). The reason of rillwidths and depths kept unchanged might be attributed to headcut ad-vance attains a steady state during which headcut geometry, migrationrate, and sediment yield remain constant (Bennett et al., 2000). Beforeheadcut advanced to critical slope lengths, e.g. 15min experimentalduration, rill length increased with the increases of inflow rate andslope gradient (Table 4). Therefore, rill widths and depths were in-dependent of time while only depended on bed slope and upslope in-flow rate. Both rill widths and depths increased with the increase of bedslope and inflow rates while rill depths tended to be similar when theinflow rate was 4 Lmin−1 under 15° and 20° slope gradient (Tables 2and 3). After scour hole formation, rill depths before T2 and rill widthsbefore T3 could be predicted by:
= =D q s R T T1.2987( ) ( 0.613, )2 0.3075 22 (1)
= =W q s R T T1.6502( ) ( 0.775, )2 0.1692 23 (2)
where D (cm) is average rill depths in different time series, W (cm) isaverage rill widths in different time series, q (Lmin−1m−1) is unit-rillwidth upslope inflow rate, s (mm−1) is slope gradient.
Rill lengths showed linear relationship with time in the former re-search (Robinson and Hanson, 1994). Therefore, from T1 to T2, rilllength in this study could be expressed by a linear equation:
= =L qs T R T T T(2.685ln( ) 1.184) ( 0.959, )21 2 (3)
where L (cm) is rill lengths in different time series, T (s) is time, q and sare the same as those in Eqs. (1) and (2).
3.1.3. Bed incision stageAs soon as rill heads advance to a critical slope length, headcuts stop
moving upslope (Figs. 3 and 4). Rill length kept stable as was the sameas the length of T2 due to the headcuts had arrived at a critical slopelength (Fig. 4). Shapes of initial rill channel formed. Overland flowconcentrates in the headcut-made rill channel and facilitates flow shearstress further incising into rill bed. Rill depths continue increasing withtime before non-erodible layer exposed to concentered flow (Figs. 3 and4). Rill flow shear stress erosion (soil particles slowly and homo-geneously entrained by rill flow) and secondary headcut/knickpointerosion occur simultaneously (Qin et al., 2018a). Average rill depthsincreased with the increase of inflow rate and bed slope (Table 3).Therefore, rill lengths from T2 to the end and rill depths from T2 to T3
could be predicted by:
= >L qs T T T(2.685ln( ) 1.184) ( )2 2 (4)
= + = <D q s q s T R T T T1.2987( ) 0.0034( ) ( 0.944, )2 0.3075 2 0.7872 22 3 (5)
3.1.4. Sidewall expansion stageOnce concentrated flow incises into a certain depth where 1) the
sidewall height reaches critical bank height that critical stress requiredfor tension cracking is satisfied (Stefanovic and Bryan, 2007) or 2) plowpan or non-erodible soil layer is exposed to rill flow that may contributeto the energy of the flowing water shifts from a vertical force to ahorizontal force (Wells et al., 2013), bed incision halted. Rill flow startsundercutting bank toe and rill erosion steps into the final stage (Figs. 3and 4). Sidewall expansion dominates the following process. Averagerill widths increment along hillslope increased with the increase ofinflow rate and bed slope while with the decrease of initial rill width(Table 2). Rill lengths and depths kept stable. Rill depths and widthsfrom T3 to the end could be predicted with:
= + >D q s q s T T T1.2169( ) 0.0034( ) ( )2 0.3208 2 0.78723 3 (6)
= + = >W q s W e R T T1.6502( ) ( 0.944, 3)qs2 0.1692i
0.4164( ) 2T1.861(7)
where Wi (cm) is initial rill width determined by initial headcut whichcould be represented by Eq. (2).
The verification indicates that both the determination coefficient(R2) and the Nash-Sutcliffe simulation efficiency (ENS) of the aboveequations are> 0.6, which attains a satisfactory level of accuracy giventhe complexity of the processes tested. Eqs. (1) to (7) focuses on the rilllength, width and depth of simplified individual rill erosion processes.Within the context of overland flow in the absence of rainfall, theseequations have merit as a means to predict rill length, width and depthevolution on steep loessial hillslopes.
3.2. Contribution of individual rill erosion processes to total rill erosion rate
To compare the contribution of individual rill erosion processes tototal rill erosion, sediment delivery per unit rill width was calculatedbased on sediment discharge of headcut advance, bed incision andsidewall expansion due to varied rill widths under different treatments(Table 5). Unit-rill width sediment delivery of total rill erosion variedbetween 58 and 887 and 84–920 kg h−1m−1 under the slope gradientsof 15° and 20°, respectively (Table 5). The unit-rill width sedimentdeliveries of headcut advance, bed incision and sidewall expansionincreased with the increases of inflow rate and slope gradient.
Headcut advance occupied the largest portion of rill erosion(44.0%–68.4%), followed by bed incision (27.1%–44.1%) and sidewallexpansion (3.8%–11.9%). The overall percentage of headcut advancedecreased while bed incision and sidewall expansion increased with theincrease of inflow rate under both gentle and steep slope gradients(Table 5). The percentage of headcut advance to rill erosion in thisstudy corroborated researches by Han et al. (2002) and Jia et al. (2005).Those authors found that headcut advance, as a highly turbulent andthree-dimensional erosional system, accounts for roughly 60% of rillerosion before headcut advance to a critical slope length on hillslopes.However, sidewall expansion contribution to rill erosion in this studywas far less than the former studies (Blong et al., 1982; Simon et al.,2000; Larionov et al., 2008). Their viewpoints were that sidewallfailure, which provides the main sediment source during the final stageof channel development, contributes as much as 80% of the total erodedsediment from small-scale rills to incised gullies and streams in loessareas of the United States and more than half of the channel volume inNew South Wales, Australia. Govers' (1987) study showed that mass
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movement contributed 37% of the total sediment yield in a large rill ona Belgian silt loam. The big difference between our research and theformer results might be attributed to the ignorance of interactions ofchannel headcut advance and bank failure at the beginning of thechannel evolution process.
3.3. Apportioning the contributions of rill widths and depths
Rill widths was firstly determined at the scour hole formation stage,and then, kept constant at the headcut advance and bed incision stages.Rill widths increased at the sidewall expansion stage (Figs. 3 and 4).Both headcut advance and sidewall expansion processes contributed torill width increment. Headcut advance process contributed 63%–83%to the whole rill width increment. The contribution percentage de-creased with the increase of bed slope and inflow rate (Fig. 5). Sidewallexpansion process contributed 17%–37% to the whole rill width in-crement. The contribution percentage increased with the increased bedslope and inflow rate.
Rill depths was firstly determined at the scour hole formation stage,and then, kept constant at the headcut advance and sidewall expansionstages. Rill depths showed significant increase at the bed incision stage(Figs. 3 and 4). Both headcut advance and bed incision processes con-tributed to rill depth increment. Contribution of headcut advance pro-cess to rill depth increment (35%–49%) was smaller than the con-tribution of bed incision process to rill depth increment (51%–65%)(Fig. 5). Contribution percentage of bed incision process decreased withthe increased upslope inflow rate. In addition, contribution of headcutadvance to rill width was larger than that to rill depth, which showed a
comprehensive effect of soil critical shear stress, vertical and horizontalshear stress of concentrated flow.
3.4. Empirical equations of rill erosion at different individual erosionprocesses
Based on the contribution of individual rill erosion processes (Fig. 3)and data in Table 5, regression analysis quantified the sediment dis-charge for individual rill erosion processes. These results indicated that:1) rill erosion based on headcut advance was the dominate process atthe initial stage of rill development (T1≤ T≤ T2); 2) rill erosion basedon bed incision was the dominating process at the middle stage of rilldevelopment (T2< T≤ T3); 3) rill erosion based on sidewall expansionwas the dominate process at the final stage of rill development (T> T3).Three quarters of the data were used to fit the equations while anotherone quarter were used for verification. Equations of sediment dischargeof a single rill channel are:
= = < =SL q s R P n T T T160.94 ln ( )–670.5 ( 0.923, 0.005, 12, )2 21 2
(8)
= = < = <SL q s R P n T T T0.3752 –2.5505 ( 0.983, 0.005, 12, )2 22 3 (9)
= = < = >SL q s R P n T T0.0077 ( ) ( 0.964, 0.005, 12, )2 1.3909 23 (10)
where SL (kg h−1m−1) is unit-rill width sediment discharge of a singlerill channel, q and s are the same as those in Eqs. (1) and (2).
Verifications of the above three equations indicated that the averagerelative error (RE) of Eqs. (8), (9) and (10) were −3.9%, −9.9%,−8.1%, the determination coefficients (R2) were 0.923, 0.983, 0.964
Table 5Unit-rill width sediment deliveries of individual rill erosions processes and their contributions to total unit-rill width sediment delivery.
Bed slope (°) Designed inflow rate (Lmin−1) Unit-rill width sediment delivery (kg h−1m−1) Contribution of individual process on rill erosion (%)
Totala Headcut advance Bed incision Sidewall collapse Headcut advance Bed incision Sidewall collapse
15 1 58.8 36.8 18.3 3.7 62.6 31.0 6.41 60.3 39.0 17.3 4.0 64.7 28.7 6.62 330.8 201.9 113.5 15.3 61.0 34.3 4.62 355.3 232.4 106.7 16.2 65.4 30.0 4.63 603.2 386.3 163.2 53.7 64.0 27.1 8.93 600.4 381.0 170.0 49.4 63.5 28.3 8.24 877.3 468.1 310.7 98.5 53.4 35.4 11.24 886.9 465.1 318.8 102.9 52.4 35.9 11.6
20 1 84.0 55.7 24.0 4.3 66.3 28.6 5.11 95.0 64.9 26.4 3.6 68.4 27.8 3.82 429.9 247.2 152.0 30.7 57.5 35.4 7.12 398.7 240.7 129.3 28.6 60.4 32.4 7.23 667.3 347.4 261.1 58.8 52.1 39.1 8.83 706.1 377.7 266.6 61.8 53.5 37.8 8.74 908.3 414.0 386.4 107.9 45.6 42.5 11.94 919.5 404.2 405.8 109.6 44.0 44.1 11.9
a Total unit-rill width sediment delivery equals to the sum of unit-rill width sediment delivery of headcut advance, bed incision and sidewall expansion tests.
Fig. 5. Contributions of rill widths and depths under different experimental treatments.
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and the Nash-Sutcliffe simulation efficiencies (ENS) were 0.822, 0.937,0.845, respectively. This validation result shows that Eqs. (8), (9) and(10) fitted in this study attains a satisfactory level of accuracy and itsprediction results are acceptable (Santhi et al., 2001).
4. Discussion
Headcut advance, bed incision and sidewall expansion interact witheach other in both temporal and spatial scales and show both depen-dent and independent features (Fig. 3). For the whole rill erosion pro-cess, the above three processes either occurred simultaneously or con-secutively. One process may lay an underlying surface for another two(e.g. forming of channel through the headcut advance process is aprerequisite for bed incision and sidewall expansion). Following arediscussions of pairwise interactions among the above three individualprocesses.
4.1. Interactions of headcut advance and bed incision
Bed incision and headcut advance are two complementary pro-cesses. Initiation of headcut advance coincides with the initiation of bedincision to form a rill headcut. From T1 to T2, rill length increased withtime while rill depth kept constant as it was determined in the scourhole formation stage (Fig. 4). The depth of the headcut at the scour holestage is influenced by: 1) tillage depth which depends on farmingequipment; 2) soil erodibility between adjacent soil layers, e.g. parentmaterial horizon, organic horizon and plow pan; and 3) upslope con-centrated flow energy (Bennett et al., 2000; Gordon et al., 2007b; Wellset al., 2013; Shen et al., 2015; He et al., 2017). The most active phase ofrill erosion occurs during the headcut advance stage. Once secondaryheadcuts form, there is a balance between upstream sediment deliveryand available transporting power of the concentrated flow (Simon andRinaldi, 2006). As a result, the dominate process can alternate amongbed incision, headcut advance, widening, and deposition. During thebed incision process, the increase in rill depth is largely determined bysecondary headcut incision process (Zhu et al., 1995; Qin et al., 2018a).
4.2. Interactions of headcut advance and sidewall expansion
Interactions of headcut advance and sidewall expansion are re-flected in the following measure: initial rill width was determinedduring the scour hole formation stage while kept constant duringheadcut advance stage (from T1 to T2) (Fig. 4). Initial rill width waslargely depended upon the upslope concentrated flow characteristics(flow width and velocity). When analyzing rill width increment, at-tention should be paid to the width increases caused by initial headcutadvance and sidewall expansion after headcut advance to a criticalslope length.
Sidewall expansion may decrease the convergent flow depth andvelocity and cause irregularities along the sidewalls. Surface flow pathconvergence can result in tributaries developing on the outer bank ofrills due to bed scour. Then, new headcut may develop and advanceupstream (Stefanovic and Bryan, 2007). Comprehensive influence ofheadcut advance and sidewall expansion, which involve interactionsbetween bed erosion by surface shear forces and toe erosion of side-walls by fluvial action, deserves to be further studied.
4.3. Interactions of bed incision and sidewall expansion
Though there was no direct interaction between bed incision andsidewall expansion (no overlapped processes during the final two stagesof rill erosion, Fig. 3), bed incision lays a foundation for the sidewallexpansion. Bed incision can be considered a quintessential feature of anon-equilibrium fluvial system. Sidewall expansion reflects the inter-action between hydraulic forces at the bed, bank toe and gravitationalforces in the bank (Simon et al., 2000; Stefanovic and Bryan, 2007).
Before rill depth reaching the plow pan, soil particles along the rillbed are readily entrained by rill flows due to excess shear stress and aresubsequently transported along the rill. The effectiveness of the shearforces shifts from vertical (incision) to horizontal (widening) once therill bed reaches a less-erodible layer. The erodibility and critical shearof rill sidewall and rill bed are the determining factors of the transitionfrom bed incision to sidewall expansion. Field observations showed thatparticle size distribution of sidewalls represents the cohesive strength todetachment which determines the bank erosion rates (Simon andRinaldi, 2006). Bed incision results in higher and often steeper side-walls that can lead to failure. Bank collapse typically occurs whenchannel incision increases the effective bank height and angle to thepoint at which gravitational forces exceed soil shear strength(Stefanovic and Bryan, 2007). Simon and Rinaldi (2006) indicated thatbed incision decreased with increased resistance of channel bed anddecreased resistance of channel sidewall. Widening will be the dom-inate process if bed clay content increases and if banks are composed ofsignificantly weaker materials, such as increases in sand content.Therefore, not only the bed material influences bed incision but also thesidewall (bank) material may impact widening.
After headcut advance past a critical slope length, secondaryheadcuts increase the effective bank height (Stefanovic and Bryan,2007). In response, sidewalls can become susceptible to mass failureresulting in channel widening (Simon and Rinaldi, 2006). Our studyassumes that sidewall expansion is accelerated when rill bed incisioncontacts a less-erodible layer or plow pan which facilitates widening. Inthe future, both the bed incision process with and without non-erodiblelayer and the subsequent sidewall expansion process should be em-phasized and incorporated into predictive models for hillslope soil lossand rill network development (Stefanovic and Bryan, 2007; Wells et al.,2013).
5. Conclusions
Simulated upslope inflow experiments focusing on headcut advance,bed incision, sidewall expansion and their interactions under a set ofslope gradients, inflow rates and initial widths were conducted toquantify contributions of individual rill erosion processes to rill devel-opment. Findings concluded that: 1) Headcut advance, bed incision andsidewall expansion dominate different rill erosion stages and interactwith each other through dependent and independent features acrossspatial and temporal scales; 2) Before headcuts advanced to a criticallength, headcut advance interacts with bed incision and sidewall ex-pansion to determine the initial rill depth and width. Bed incision wasthe dominate process before rill bed reached a non-erodible layer, andsidewall expansion was the dominate process after the non-erodiblelayer was exposed to concentrated flow; 3) Headcut advance con-tributed the largest amount of rill erosion (44%–68%), followed by bedincision (27%–44%) and sidewall expansion (3.8%–12%). Headcutadvance and bed incision contributed 63%–83% and 51%–65% to totalrill width and depth increment, respectively; 4) Prediction equations forlength, width and depth of a single rill and empirical equations of rillerosion among three key erosion points (T1: rill heads start movingupstream, T2: rill heads arrive at critical slope length, T3: rill beds inciseto plow pan) were fitted and validated.
Rill erosion is a comprehensive combination of individual processesthat influence, stimulate and restrict with each other. Results of thecontributions of individual rill erosion processes can provide the sci-entific basis for the development of process-based rill erosion modelsand the protection of valuable soil resources from degradation process.
Acknowledgements
This study was supported by the National Natural ScienceFoundation of China (Grant No.41571263), National Key R&D Programof China (Grand NO. 2016YFE0202900), the National Natural Science
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Foundation of China (Grant NO. 51639005), the External CooperationProgram of Chinese Academy of Sciences (Grant NO.161461KYSB20170013) and the Postdoctoral Innovation TalentsSupport Program of China (Grand NO. BX20190177) fund.
References
Allen, P.M., Arnold, J.G., Auguste, L., White, J., Dunbar, J., 2018. Application of a simpleheadcut advance model for gullies. Earth Surf. Process. Landf. 43 (1), 202–217.https://doi.org/10.1002/esp.4233.
Alonso, C.V., Bennett, S.J., 2002. Predicting head cut erosion and migration in con-centrated flows typical of upland areas. Water Resour. Res. 38 (12), 31−39. https://doi.org/10.1029/2001WR001173.
Babazadeh, H., Ashourian, M., Shafai-Bajestan, M., 2017. Experimental study of headcuterosion in cohesive soils under different consolidation types and hydraulic para-meters. Environ. Earth Sci. 76, 438. https://doi.org/10.1007/s12665-017-6776-5.
Bennett, S.J., 1999. Effect of slope on the growth and migration of headcuts in rills.Geomorphology 30 (3), 273−290. https://doi.org/10.1016/S0169-555X(99)00035-5.
Bennett, S.J., Casalí, J., 2001. Effect of initial step height on headcut development inupland concentrated flows. Water Resour. Res. 37 (5), 1475−1484. https://doi.org/10.1029/2000WR900373.
Bennett, S.J., Alonso, C.V., Prasad, S.N., Römkens, M.J.M., 2000. Experiments on headcutgrowth and migration in concentrated flows typical of upland areas. Water Resour.Res. 36 (7), 1911−1922. https://doi.org/10.1029/2000WR900067.
Bingner, R.L., Wells, R.R., Momm, H.G., Rigby, J.R., Theurer, F.D., 2016. Ephemeral gullychannel width and erosion simulation technology. Nat. Hazards 80 (3), 1949−1966.https://doi.org/10.1007/s11069-015-2053-7.
Blong, R.J., Graham, O.P., Veness, J.A., 1982. The role of sidewall process in gully de-velopment; some N.S.W. example. Earth Surf. Process. Landf. 7, 381−385. https://doi.org/10.1002/esp.3290070409.
Bryan, R.B., Poesen, J., 1989. Laboratory experiments on the influence of slope length onrunoff, percolation and rill development. Earth Surf. Process. Landf. 14, 211−231.https://doi.org/10.1002/esp.3290140304.
Casalí, J., López, J.J., Giráldez, J.V., 2003. A process-based model for channel degrada-tion: application to ephemeral gully erosion. Catena 50 (2–4), 435−447. https://doi.org/10.1016/S0341-8162(02)00127-3.
Chaplot, V., Brown, J., Dlamini, P., Eustice, T., Janeau, J., Jewitt, G., Lorentz, S., Martin,L., Nontokozo-Mchunu, C., Oakes, E., Podwojewski, P., Revil, S., Rumpel, C., Zondi,N., 2011. Rainfall simulation to identify the storm-scale mechanisms of gully bankretreat. Agric. Water Manag. 98 (11), 1704−1710. https://doi.org/10.1016/j.agwat.2010.05.016.
Chen, A., Zhang, D., Peng, H., Fan, J., Xiong, D., Liu, G., 2013. Experimental study on thedevelopment of collapse of overhanging layers of gully in Yuanmou Valley, China.Catena 109, 177−185. https://doi.org/10.1016/j.catena.2013.04.002.
Dabney, S.M., Vieira, D.A.N., Yoder, D.C., Langendoen, E.J., Wells, R.R., Ursic, M.E.,2014. Spatially distributed sheet, rill and ephemeral gully erosion. J. Hydrol. Eng. 20(6), C4014001–C4014009. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001120.
Darby, S.E., Alabyan, A.M., Van de Wiel, M.J., 2002. Numerical simulation of bankerosion and channel migration in meandering rivers. Water Resour. Res. 38 (9), 1−2.https://doi.org/10.1029/2001WR000602.
El Kadi Abderrezzak, K., Die Moran, A., Mosselman, E., Bouchard, J., Habersack, H.,Aelbrecht, D., 2014. A physical, movable-bed model for non-uniform sedimenttransport, fluvial erosion and bank failure in rivers. J. Hydro Environ. Res. 8 (2),95−114. https://doi.org/10.1016/j.jher.2013.09.004.
Evans, R., Boardman, J., 2003. Curtailment of muddy floods in the Sompting catchment,South Downs, West Sussex, southern England. Soil Use Manag. 19, 223−231.https://doi.org/10.1079/SUM2003193.
Favis-Mortlock, D., 1998. A self-organizing dynamic systems approach to the simulationof rill initiation and development on hillslopes. Comput. Geosci. 24 (4), 353−372.https://doi.org/10.1016/S0098-3004(97)00116-7.
Foster, G.R., Meyer, L.D., Onstad, C.A., 1977. An erosion equation derived from basicerosion principles. Transactions of the ASAE 20 (4), 678−682. https://doi.org/10.13031/2013.35627.
Fox, G.A., Wilson, G.V., 2010. The role of subsurface flow in hillslope and streambankerosion: a review of status and research needs. Soil Sci. Soc. Am. J. 74 (3), 717−733.https://doi.org/10.2136/sssaj2009.0319.
Gordon, L.M., Bennett, S.J., Bingner, R.L., Theurer, F.D., Alonso, C.V., 2007a. Simulatingephemeral gully erosion in AnnAGNPS. Trans. ASABE 50 (3), 857−866. https://doi.org/10.13031/2013.23150.
Gordon, L.M., Bennett, S.J., Wells, R.R., Alonso, C.V., 2007b. Effect of soil stratificationon the development and migration of headcuts in upland concentrated flows. WaterResour. Res. 43 (W07412), 1−12. https://doi.org/10.1029/2006WR005659.
Gordon, L.M., Bennett, S.J., Wells, R.R., 2011. Evolution of rill networks on soil-mantledexperimental landscapes driven by rainfall and base level adjustments. LandformAnalysis 17, 57−63.
Govers, G., 1987. Spatial and temporal variability in rill development processes at theHuldenberg experimental site. Catena Suppl. 8, 17–34.
Govindaraju, R.S., Kavvas, M.L., 1992. Characterization of the rill geometry over straighthillslopes through spatial scales. J. Hydrol. 130, 339−365. https://doi.org/10.1016/0022-1694(94)90061-2.
Grigor'Ev, V.Y., 2007. Semi-empirical model of the rill erosion of soils. Eurasian SoilScience 40 (11), 1217−1226. https://doi.org/10.1134/S1064229307110105.
Han, P., Ni, J.R., Li, T.H., 2002. Headcut and bank landslip in rill evolution. Journal of
Basic Science and Engineering 10 (2), 115−125. (In Chinese). 10.16058/j.issn.1005-0930.2002.02.003.
He, J., Sun, L., Gong, H., Cai, Q., 2017. Laboratory studies on the influence of rainfallpattern on rill erosion and its runoff and sediment characteristics. Land Degrad. Dev.28 (5), 1615−1625. https://doi.org/10.1002/ldr.2691.
Hossain, M.B., Sakai, T., Hossain, M.Z., 2011. River embankment and bank failure: astudy on geotechnical characteristics and stability analysis. Am. J. Environ. Sci. 7 (2),102−107. https://doi.org/10.3844/ajessp.2011.102.107.
Istanbulluoglu, E., 2005. Implications of bank failures and fluvial erosion for gully de-velopment: field observations and modeling. J. Geophys. Res. 110, F1014. https://doi.org/10.1029/2004JF000145.
Jia, Y., Kitamura, T., Wang, S., 2005. Numerical simulation of head-cut with a two-layered bed. International Sediment Research 20 (3), 185−193.
Lal, R., 2002. Gully Erosion. Encyclopedia of Soil Science. Marcel Dekker, New York, pp.630–632.
Larionov, G.A., Gendugov, V.M., Dobrovol'Skaya, N.G., Kiryukhina, Z.P., Litvin, L.F.,2008. Mechanisms of lateral erosion in rills on slopes. Eurasian Soil Science 41 (3),294−301. https://doi.org/10.1134/S1064229308030071.
Lawler, D.M., Couperthwaite, J., Bull, L.J., Harris, N.M., 1997. Bank erosion events andprocesses in the upper Severn basin. Hydrology & Earth System Sciences 1 (3),523−534.
Liu, L., Liu, Q., An, J., Yu, J., 2015. Rill morphology and deposition characteristics on rowsideslopes under seepage conditions. Soil Use Manag. 31, 515−524. https://doi.org/10.1111/sum.12222.
Mancilla, G.A., Chen, S., McCool, D.K., 2005. Rill density prediction and flow velocitydistributions on agricultural areas in the Pacific Northwest. Soil Tillage Res. 84 (1),54−66. https://doi.org/10.1016/j.still.2004.10.002.
Martinez-Casasnovas, J.A., Ramos, M.C., Poesen, J., 2004. Assessment of sidewall erosionin large gullies using multi-temporal DEMs and logistic regression analysis.Geomorphology 58 (1–4), 305−321. https://doi.org/10.1016/j.geomorph.2003.08.005.
Masoodi, A., Noorzad, A., Majdzadeh Tabatabai, M.R., Samadi, A., 2018. Application ofshort-range photogrammetry for monitoring seepage erosion of riverbank by la-boratory experiments. J. Hydrol. 558, 380−391. https://doi.org/10.1016/j.jhydrol.2018.01.051.
Midgley, T.L., Fox, G.A., Wilson, G.V., Felice, R.C., Heeren, D.M., 2013. In situ pipe flowexperiments on contrasting streambank soils. Trans. ASABE 56 (2), 479−488.https://doi.org/10.13031/2013.42685.
Nash, J.E., Sutcliffe, J.V., 1970. River flow forecasting through conceptual models part I-adiscussion of principles. J. Hydrol. 10 (3), 282–290. https://doi.org/10.1016/0022-1694(70)90255-6.
Nearing, M.A., Lane, L.J., Alberts, E.E., Laflen, J.M., 1990. Prediction technology for soilerosion by water: status and research needs. Soil Science Society of American Journal54, 1702−1711. https://doi.org/10.2136/sssaj1990.03615995005400060033x.
Nichols, M.H., Nearing, M., Hernandez, M., Polyakov, V.O., 2016. Monitoring channelhead erosion processes in response to an artificially induced abrupt base level changeusing time-lapse photography. Geomorphology 265, 107–116. https://doi.org/10.1016/j.geomorph.2016.05.001.
Qin, C., Zheng, F., Zhang, J.X., Xu, X., Liu, G., 2018a. A simulation of rill bed incisionprocesses in upland concentrated flows. Catena 165, 310−319. https://doi.org/10.1016/j.catena.2018.02.013.
Qin, C., Zheng, F., Wells, R.R., Xu, X., Wang, B., Zhong, K., 2018b. A laboratory study ofchannel sidewall expansion in upland concentrated flows. Soil Tillage Res. 178,22−31. https://doi.org/10.1016/j.still.2017.12.008.
Qin, C., He, C., Zheng, F., Han, L., Zeng, C., 2018c. Quantitative research of rill headadvancing process on loessial hillslope. Transactions of the Chinese Society ofAgricultural Engineering 34 (6), 160−167. (In Chinese). 10.11975/j.issn.1002-6819.2018.06.020.
Qin, C., Wells, R.R., Momm, H.G., Xu, X., Wilson, G.V., Zheng, F., 2019. Photogrammetricanalysis tools for channel widening quantification under laboratory conditions. SoilTillage Res. 191, 306–316. https://doi.org/10.1016/j-still.2019.04.002.
Rinaldi, M., Darby, S.E., 2007. Modelling river-bank-erosion processes and mass failuremechanisms: progress towards fully coupled simulations[M]. In: Helmut Habersack,H.P., Massimo, R. (Eds.), Developments in Earth Surface Processes. Elsevier, pp.213−239.
Robinson, K.M., Hanson, G.J., 1994. Large-scale headcut erosion testing. Soil and WaterDivision of ASAE 38 (2), 429–434. https://doi.org/10.13031/2013.27849.
Römkens, M.J.M., Prasad, S.N., Whisler, F.D., 1990. Process studies in hillslope hydrology[M]. In: Anderson, M.G., Burt, T.P. (Eds.), Surface Sealing and Infiltration. JohnWiley, New York.
Santhi, C., Arnold, J.G., Williams, J.R., Hauck, L.M., Dugas, W.A., 2001. Application of awatershed model to evaluate management effects on point and nonpoint sourcepollution. Transactions of the ASAE 44 (6), 1559−1570. https://doi.org/10.13031/2013.7041.
Shen, H., Zheng, F., Wen, L., Lu, J., Jiang, Y., 2015. An experimental study of rill erosionand morphology. Geomorphology 231, 193−201. https://doi.org/10.1016/j.geomorph.2014.11.029.
Simon, A., Rinaldi, M., 2006. Disturbance, stream incision, and channel evolution: theroles of excess transport capacity and boundary materials in controlling channel re-sponse. Geomorphology 79 (3–4), 361−383. https://doi.org/10.1016/j.geomorph.2006.06.037.
Simon, A., Curini, A., Darby, S.E., Langendoen, E.J., 2000. Bank and near-bank processesin an incised channel. Geomorphology 35, 193−217. https://doi.org/10.1016/S0169-555X(00)00036-2.
Slattery, M.C., Bryan, R.B., 1992. Hydraulic conditions for rill incision under simulatedrainfall: a laboratory experiment. Earth Surf. Process. Landf. 17, 127−146. https://
C. Qin, et al. Catena 181 (2019) 104099
10
doi.org/10.1002/esp.3290170203.Soil Science Society of America, 2008. Glossary of Soil Science Terms. Soil Science Society
of America Inc, Madison, WI.Stefanovic, J.R., Bryan, R.B., 2007. Experimental study of rill bank collapse. Earth Surf.
Process. Landf. 32 (2), 180−196. https://doi.org/10.1002/esp.1396.Thomas, J.T., Iverson, N.R., Burkart, M.R., 2009. Bank-collapse processes in a valley-
bottom gully, western Iowa. Earth Surf. Process. Landf. 34 (1), 109−122. https://doi.org/10.1002/esp.1699.
USDA NRCS, 1999. Soil Taxonomy: A Basic System of Soil Classification for Making andInterpreting Soil Surveys. [M]//Agricultural Handbook 436, 2nd edition. U.S.Government Printing Office, Washington DC.
Vandekerckhove, L., Poesen, J., Govers, G., 2003. Medium-term gully headcut retreatrates in Southeast Spain determined from aerial photographs and ground measure-ments. Catena 50 (2), 329−352. https://doi.org/10.1016/S0341-8162(02)00132-7.
Wang, Y., Kuang, S., Su, J., 2016. Critical caving erosion width for cantilever failures ofriver bank. International Journal of Sediment Research 31 (3), 220−225. https://doi.org/10.1016/j.ijsrc.2016.05.003i.
Wells, R.R., Alonso, C.V., Bennett, S.J., 2009. Morphodynamics of headcut developmentand soil erosion in upland concentrated flows. Soil Sci. Soc. Am. J. 73 (2), 521−530.https://doi.org/10.2136/sssaj2008.0007.
Wells, R.R., Bennett, S.J., Alonso, C.V., 2010. Modulation of headcut soil erosion in rillsdue to upstream sediment loads. Water Resour. Res. 46 (12), 1−16. https://doi.org/10.1029/2010WR009433.
Wells, R.R., Momm, H.G., Rigby, J.R., Bennett, S.J., Bingner, R.L., Dabney, S.M., 2013. Anempirical investigation of gully widening rates in upland concentrated flows. Catena
101, 114−121. https://doi.org/10.1016/j.catena.2012.10.004.Wells, R.R., Momm, H.G., Bennett, S.J., Gesch, K.R., Dabney, S.M., Cruse, R., Wilson,
G.V., 2016. A measurement method for rill and ephemeral gully erosion assessments.Soil Sci. Soc. Am. J. 80 (1), 203–214. https://doi.org/10.2136/sssaj2015.09.0320.
Wilcox, J., Benoit, T., Mink, L., 2001. Evaluation of Geomorphic Restoration TechniquesApplied to Fluvial Systems. Feather river coordinated resource management group,pp. 43–47 Section 4.
Wirtz, S., Seeger, K.M., Ries, J.B., 2012. Field experiments for understanding and quan-tification of rill erosion processes. Catena 91, 21−34. https://doi.org/10.1016/j.catena.2010.12.002.
Woodward, D.E., 1999. Method to predict cropland ephemeral gully erosion. Catena 37,393−399. https://doi.org/10.1016/S0341-8162(99)00028-4.
Zheng, F., 1989. Critical slope length and slope gradient for the occurrence of rill erosion.Soil and Water Conservation in China 8, 23–24 (in Chinese).
Zhou, P., Wang, Z., 1987. Soil erosion rainfall standard in the loess plateau. Bulletin ofSoil Water Conservation 7 (1), 38–44 (in Chinese).
Zhu, X.M., 1956. Soil erosion classification at the loessial region. Acta Pedol. Sin. 4 (2),99–116 (in Chinese).
Zhu, J.C., Gantzer, C.J., Peyton, R.L., Albberts, E.E., Anderson, S.H., 1995. Simulatedsmall-channel bed scour and head cut erosion rates compared. Soil Sci. Soc. Am. J.59, 211−218. https://doi.org/10.2136/sssaj1995.03615995005900010032x.
Zhu, Y.H., Visser, P.J., Vrijling, J.K., 2008. Soil headcut erosion: Process and mathema-tical modeling[M]. In: Kusuda, T., Yamanishi, H., Spearman, J., Gailani, J.Z. (Eds.),Sediment and Ecohydraulics: Intercoh 2005. Elsvier, Amsterdam, pp. 125−136.
C. Qin, et al. Catena 181 (2019) 104099
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