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Journal of Hydrology

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Research papers

A three-process-based distributed soil erosion model at catchment scale onthe Loess Plateau of China

Jingya Caia, Zuhao Zhoua,⁎, Jiajia Liua, Hao Wanga, Yangwen Jiaa, Chong-Yu Xub

a State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, ChinabDepartment of Geosciences Hydrology, University of Oslo, Norway

A R T I C L E I N F O

This manuscript was handled by Huaming Guo,Editor-in-Chief with the assistance of DingbaoWang, Associate Editor

Keywords:Gullied rolling loess regionPhysically-basedSlope-gully-riverGully erosionGravitational erosion

A B S T R A C T

The Loess Plateau of China suffers from severe soil erosion. In the gullied rolling loess region, approximately halfof the sediment derives from gully areas, which are the most prominent topographical features of this region. Noexisting soil erosion models are appropriate in accuracy or applicability for the Loess Plateau because existingmodels only consider slope and river erosion processes at the catchment scale. The absence of the gully erosionprocess in these models significantly limits their application to the Loess Plateau. Taking this issue into account,a three-process-based distributed soil erosion model, denoted by WEP-SED, is proposed to investigate soil ero-sion in this region based on the Water and Energy transfer Processes in Large river basins (WEP-L) model. InWEP-SED, a sequential “slope-gully-river” structure is built for the physically-based simulation of soil erosionand sediment yield. In this structure, soil erosion is integrated from six parts with successive transport re-lationships. The proposed model is applied to the upstream region of the Wenjiachuan hydrological station in theKuye River basin. The simulated monthly average sediment transport rates from 1956 to 2010 at theWenjiachuan hydrological station agree well with the observations, with a correlation coefficient of 0.76, an NSEof 0.58, and a relative error of −5.60%. Furthermore, the simulated average annual amount of gully erosionreaches 60.30% of the total soil erosion, reflecting the fact that the gully erosion is a serious problem anddemonstrating that gully erosion must be considered separately in this area.

1. Introduction

Soil erosion is a geomorphic process in which soil particles, rockfragments, soil aggregates, and organic matter are detached from theirprimary location and are transported to another (Poesen, 2018). TheLoess Plateau in China suffers from severe soil erosion (Xu, 1999; Zhangand Liu, 2005). The large crisscrossed and permanent gullies that fill inthis region are unique features of the Loess Plateau, contributing sig-nificantly to the severe erosion (Tang and Chen, 1997; Xu et al., 2009).Erosion processes in a catchment that occur over slopes, gullies, andrivers are complicated. Previous studies have applied numerous soilerosion models to simulate soil erosion and sediment yield at thecatchment scale on the Loess Plateau, such as the Watershed ErosionPrediction Project (WEPP) (Zhang et al., 2005; Li et al., 2011), Soil andWater Assessment Tool (SWAT) (Zuo et al., 2016), Morgan-Morgan-Finney model (MMF) (Li et al., 2010), and Digital Yellow River Model(DYRIM) (Wang et al., 2007). However, no model has stood out interms of accuracy or applicability (Li et al., 2017).

The commonly used soil erosion models can be categorized into

three groups: empirical, conceptual, and physically-based(Hajigholizadeh et al., 2018). Empirical models employ statisticaltechniques to reveal the relationships between the factors and compo-nents using regressions (Wainwright and Mulligan, 2002). These em-pirical models, such as the Universal Soil Loss Equation (USLE) andRevised USLE (RUSLE), have simple computational processes and lowdata requirements (Wischmeier and Smith, 1978; Renard et al., 1997).These models may possibly perform well in one region but yield aninsufficient performance in other regions because they are limited tocertain conditions (Aksoy and Kavvas, 2005; Sadeghi et al., 2014).Conceptual models generally describe soil erosion and sediment trans-port processes without specific details (Hajigholizadeh et al., 2018;Merritt et al., 2003; Sorooshian, 1991). Conceptual models, therefore,can indicate the effects of land-use changes without requiring largeamounts of spatially and temporally distributed input data. Conceptualmodels suffer from problems associated with the identifiability of theirparameter values, which are obtained via calibration against observeddata, such as flow discharge and sediment transport rates (Jakeman andHornberger, 1993). The Erosion Productivity Index Calculator (original

https://doi.org/10.1016/j.jhydrol.2019.124005Received 30 May 2019; Received in revised form 10 July 2019; Accepted 29 July 2019

⁎ Corresponding author.E-mail address: zuhao_zhou@sina.com (Z. Zhou).

Journal of Hydrology 577 (2019) 124005

Available online 01 August 20190022-1694/ © 2019 Published by Elsevier B.V.

T

name) or Environmental Policy Integrated Climate (current name)(EPIC) (Williams et al., 1983) and Soil and Water Assessment Tool(SWAT) (Beven, 1989) are both typical conceptual erosion models.Physically-based models simulate the dynamic behavior of the con-cerned components in each soil erosion process, generally based on thetheoretical principles of kinematic wave procedures for routing sedi-ment (Morgan and Quinton, 2001). The conservation equations of mass,momentum, and energy are fundamental for simulating soil detach-ment, sediment deposition, and sediment transport (Kandel et al.,2004). Recently, physically-based models including the WatershedErosion Prediction Project (WEPP) (Laflen et al., 1991; NSERL, 1995),the Limburg Soil Erosion Model (LISEM) (De Roo et al., 1996), and theEUROpean Soil Erosion Model (EUROSEM) (Morgan et al., 1998) havebeen developed. These models are at the forefront of soil erosion re-search with several advantages, such as the incorporation of the un-derlying mechanisms of soil erosion and sediment transport (Pandeyet al., 2016). There is, however, still a significant problem where mostphysically-based models are not sufficiently applicable to the LoessPlateau because these models ignore the effects of gully erosion. Thesemodels usually only simulate two erosion processes, i.e., slope and rivererosion, which do not conform to the fact that gully erosion has a sig-nificant contribution on the Loess Plateau. Because of the steep andunstable slopes with loose soil material in gully areas, the erosionmechanisms at these sites are different from river erosion (Hessel andVan Asch, 2003). The structure of these two-process models do notcompetently reflect and elucidate distinct topographical features withhighly developed and heavily eroded gullies. Although gully erosionhas been considered in XIN-MIX-SED (Si et al., 2017) and DYRIM(Wang et al., 2007), the conceptual assumptions in XIN-MIX-SED,which is a lumped model, and the absence of scouring or depositionsimulation in gullies in DYRIM both leave room for improving gullyerosion simulations.

To simulate severe gully erosion, models must account for anotherissue, i.e., gravitational erosion, a critical factor that induces and con-tributes significantly to gully erosion on the Loess Plateau (Wang et al.,2007). The strong cohesion within dry loess gives gully banks extremelysteep or even vertical slopes. When the moisture of loess increases(usually due to rainfall), cohesion will rapidly decrease as a powerfunction of the moisture, leading to unstable banks and the easy col-lapse of large volumes of loess. Therefore, gravitational erosion ispredominant in gully areas with sidewall gradients of more than 25°and deeply cut gullies (Fu and Gulinck, 1994). There have been someachievements in research on the mechanism of gravitational erosion ingully areas (Wang et al., 2005), but these studies have infrequentlyimplemented the gravitational erosion model at the catchment scale. Inmost previous soil erosion models, gravitational erosion is either ig-nored or estimated with an experimental formula (Cai et al., 1996).

Considering these issues, this paper proposes a physically-baseddistributed and three-process soil erosion model, denoted by WEP-SED,to investigate soil erosion in gullied rolling loess regions of the LoessPlateau, based on the existing Water and Energy transfer Processes inLarge river basins (WEP-L) hydrological model. A three-level sequential“slope-gully-river” structure is built in WEP-SED to create a detailedsimulation of soil erosion and sediment transport. The proposed modelis applied to simulate soil erosion in the upstream region of theWenjiachuan hydrological station in the Kuye River basin.

The rest of the paper is organized as follows. The soil erosion model,WEP-SED, is first introduced in Section 2. Then, the study area andmodel database are described in Section 3. The simulation results areanalyzed in Section 4. Discussion follows in Section 5. Finally, severalconclusions are given in Section 6.

2. WEP-SED model

2.1. Hydrological cycle simulation

The soil erosion model is based on hydrological process and, in thisstudy, we use the WEP-L model for river basins (Jia et al., 2006) tosimulate the hydrological cycle. Previous studies have widely appliedthis model in different watersheds with various climate and geographicconditions (Jia et al., 2006; Zhou et al., 2018; Li et al., 2019).

Fig. 1(a) shows the vertical structure of the WEP-L within a contourband while Fig. 1(b) shows the horizontal structure of the WEP-L withina watershed. In this model, land use is divided into five groups within acontour band, i.e., Soil-Vegetation (SV), Non-irrigated Farmland (NF),Irrigated Farmland (IF), Water Body (WB), and Impervious Area (IA)groups. We simulate the horizontal processes in Fig. 1(b) for watertransport using the hydrodynamic model with the following expres-sions:

∂∂

+ ∂∂

=At

Qx

qL (1)

=S Sf 0 (2)

=Q An

R Sf2/3 1/2

(3)

where t is simulation time (s), A is the water area perpendicular to theflow direction (m2), x is the position along the flow direction (m), Q isdischarge (m3 s−1), qL is the lateral inflow along a gully or river per unitlength (m3 s−1 m−1), Sf is the friction slope, S0 is the river bed slope, n isthe Manning coefficient mainly depending on the river bed’s surfaceroughness, and R is the hydraulic radius determined by the cross-sec-tional wetted area and perimeter (m).

More details on WEP-L can be found in Jia et al. (2006). In this

Soil-Vegetation

RechargeUnconfined Aquifer

Aquitard

Confined Aquifer

Flow in

Flow out

Flow out

Flow in

Evaporation Heat Fluxes

Surface Runoff

Interflow

Interception Layer

SuctionDiffusion

Infiltration

Precipitation ShortwaveRadiation

LongwaveRadiation

AnthropogenicEnergy

Percolation

3rd Soil Layer

2nd Soil Layer Water Use Leakage

Exchange

Non-irrigatedFarmland

IrrigatedFarmland

DepressionLayer

Water Body ImperviousArea

"Mosaic Approach for Grouping Land Uses"

Transition Layer

GroundwaterLift

DiversionTranspiration

Root Layer

Top Soil Layer

River Flow

Overland Flow

Contour Band

Q1

Q2

Q3

Q4Q5

Q6Q7Q8

Q9

Sub-watershed

(a) (b)Fig. 1. A schematic illustration of the WEP-L model structure: (a) the vertical structure within a contour band and (b) the horizontal structure within a watershed.

J. Cai, et al. Journal of Hydrology 577 (2019) 124005

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study, we separately take into account the gully process to reflect severegully erosion on the Loess Plateau (Fig. 2) and propose a horizontalstructure for the three-process water transport, i.e., the “slope-gully-river” (Fig. 3). It is an improved version of WEP-L, a two-process watertransport mechanism including overland and river flow.

1: Slope-gully indicates gullies down-slope, such as rill and ephemeralgullies.

2: Gully indicates the gully at bottom of the slope, which is perpen-dicular to slope direction.

2.2. Soil erosion simulation

This study builds a three-process soil erosion model, i.e., the WEP-SED, to improve the WEP-L model by adding a new soil erosion andsediment transport module to it, enabling it to simulate soil and water

loss on the Loess Plateau. Following the general physical process of soilerosion and sediment transport sequence in Fig. 3, Fig. 4 shows aflowchart of the WEP-SED with all components included in this newmodel.

2.2.1. Slope soil erosion

(1) Raindrop splash erosion

Hydraulic soil erosion generally begins with raindrop splashes.These can destroy soil texture and weaken the cohesive force of theinner soil, which detaches the original soil away from its source viaoverland flow. Splash erosion mainly occurs on bare land and is si-mulated based on the experimental results reported by Wu and Zhou(1991):

=E a E I α·( · ) ·rain rainb c

1 1 01 1 (4)

where E1 is the splash erosion intensity (kg m−2 s−1), Erain is the unitrainfall kinetic energy (J m−2 mim−1), which was estimated fromrainfall intensity, Irain is the rainfall intensity (mm min−1), α0 is theslope angle (°), and a1, b1, and c1 are experimental coefficients. a1, b1,and c1 are 1.675·10−5, 0.544 and 0.471, respectively, according toWu and Zhou (1991).

(2) Overland flow erosion

Flow detaching effects on slope soil induce overland flow erosion.The detached soil can be estimated based on the flow discharge andslope gradient (He et al., 2003) with the following equation:

= + + +E a q b q tanα c tanα d· · · ·2 2 2 0 2 0 2 (5)

where E2 is the soil detachment rate (kgm−2 s−1), qis the flow dis-charge per unit width converted from discharge in He et al. (2003)(m2 s−1), anda2, b2, c2, and d2 are experimental coefficients. a2, b2, c2,and d2 are 1.26, 102, 0.04, and 0.0005, respectively, according to Heet al. (2003).

The total soil loss on bare land, i.e., E3, is constrained by the sedi-ment transport capacity of overland flow defined in Eq. (6) (Prosser andRustomji, 2000). The portion of soil that exceeds the sediment transportcapacity is deposited.

= +E a q tanα L E Emin( · ·( ) · , )b cSlo3 3 0 1 23 3 (6)

where E3 is the total soil loss intensity on bare land between slope-

Fig. 2. Crisscrossed gullies on the Loess Plateau of China (Photoed by ZuhaoZhou).

Sub-watershed

Contour band

Rainfall

Conflux & Sediment transportGravity erosion

Conflux & Sediment transportin River:

Runoff & Overland flow erosionSplash erosion

on Slope:

in Gully2:

Conflux & Erosion in slope-gully1

Fig. 3. A schematic illustration of the three-process hydrological and soil erosion simulation in the WEP-SED model.

J. Cai, et al. Journal of Hydrology 577 (2019) 124005

3

gullies (kg m−2 s−1), LSlo is the length of the contour band (m), and a3,b3, and c3 are experimental coefficients. a3 will be obtained by cali-bration. b3 and c3 are two topographically influenced parameters withthe recommended values of 1.4 and 1.4, respectively, as Prosser andRustomji (2000).

Overland flow erosion mainly occurs on underlying surfaces, in-cluding forests, grasslands, bare, and slope croplands. Of these types ofunderlying surfaces, the erosion intensity and sediment transport onforests, grasslands, bare, and slope croplands can be determined with anadjustment coefficient in the following equation:

= + + +E E C F C F C F F·( · · · )F F G G S S B4 3 (7)

where E4 is the comprehensive intensity of soil loss on bare land (kgm−2 s−1), CF, CG, and CS are the adjustment coefficients for soil lossintensity in forests, grasslands, and sloped croplands, respectively, andFF, FG, FS, and FB are the area proportions of forests, grasslands, slopedcroplands, and bare lands, respectively, in the current contour band.

(3) Soil erosion in a slope-gully

The newly eroded sediment in slope-gully is determined by sub-tracting the inflow sediment from the sediment transport capacity offlow in slope-gully with an erosion coefficient. Then the sedimenttransport rate in slope-gully can be derived as follows:

= − +Qs K T Q Qs Qs·( · )SG SG SG SG SG2 1 1 (8)

= ⎧⎨⎩

=+ − >−

QsE Ac jE Ac Qs R j

· & 1[ · ·(1 )] 1SG j

j j

j j SG j T1,

4,

4, 2, 1 (9)

where QsSG2, QsSG1 are the outflow and inflow sediment transport rateof slope-gully in the current contour band, respectively (kg s−1), KSG isthe soil erosion coefficient in slope-gully determined by calibration, T isthe sediment transport capacity of flow (kg m−3), QSG is the flow dis-charge of slope-gully in the current contour band (m3 s−1), subscript j isthe serial number of contour band, Ac is the contour band area (m2),and RT is the sediment reduction efficiency of terrace, which is taken asthe ratio of the controlled area by terraces and the total catchment areaabove terraces (Liu, 2016).

The sediment transport capacity of flow T is determined with the

equation derived by Zhang (1992) as follows:

=+

−TC γ v

κ g R ωln h

d2.5·[

(0.0022 / )·· · · ·

· (6·

)]sγ γ

γ

w3

50

0.62s m

m (10)

= − −κ κ C γ C γ·[1 4.2· / ·(0.365 / )]s s0 (11)

= ⎛

⎝⎜ − ⎞

⎠⎟ −ω ω

C γ

dC γ· 1

/

2.25··(1 1.25· / )s

s050

3.5

(12)

where κ and κ0 are the Karman constants of muddy and clear water,respectively, and κ0 is 0.4, γs and γm are the unit weights of dry soil andmuddy flow, respectively (Nm−3), g is the gravitational acceleration(N kg−1), ω and ω0 are the settling velocities of a sediment particle inthe muddy and clear water, respectively (m s−1), C is the sedimentconcentration (kg m−3), v is the flow velocity (m s−1), d50 is the mediansoil particle diameter (m), i.e., the ratio of soil particles smaller than aspecific diameter of 50%, and is obtained from the Yellow River SedimentBulletin by Yellow River Conservancy Commission, Ministry of WaterResources of China. And hw is the flow depth (m).

2.2.2. Gravitational erosionAmong various types of gravitational erosion, collapses, and land-

slides are the most dominant on the Loess Plateau (Cai et al., 1996). Inthis study, gravitational erosion mainly considers collapses simulatedbased on the mechanical equilibrium principle. The collapsed soil blockcan be generalized as a quadrangular prism unit, which has a trape-zoidal transect (i.e., the profile of a collapsed soil block perpendicularto the direction of flow, similar to the bold polygon in Fig. 5).

The mass of the collapsed soil block in Fig. 5 can be estimated viageometrical analysis with the following equation:

= +m ρ L d h d tanθ· ·( · 1/2· · )m s2 (13)

where m is the mass of the collapsed soil block per unit length of gullyper day (kg m−1 day−1), ρm is the soil density (including the watercontained in the soil) (kg m−3), L is the average length of the collapsedsoil block (along the flow direction) per meter of gully length per day(m m−1 day−1), d is the thickness of the collapsed soil block (i.e., theheight of the trapezoidal transect) (m), θ is the inclined angle between

Fig. 4. A flowchart of the WEP-SED model.

J. Cai, et al. Journal of Hydrology 577 (2019) 124005

4

the scouring surface plane and horizontal plane (°), and hs is thethickness of the outer edge of the collapsed soil block (i.e., the upperwidth of the trapezoidal transect) (m). The geometric parameters L, d,and θ are roughly estimated as 0.004mm−1 day−1, 0.1 m, and 20°,respectively, according to the information provide by local folks. For acollapsed soil block, we can use the torque equilibrium equation tocalculate hs (Wang et al., 2007).

The sidewall of the gully is usually stable because both gravity andcohesion affect the soil simultaneously. However, the cohesion innerthe loess is sensitive to moisture and decreases rapidly as moisture in-creases, usually caused by rainfall. At the same time, cracks appear inthe soil that fills with rainfall and concurrently increase the waterpressure on its soil block, resulting in the collapse of the sidewall. Atthis moment, there is a balance in the torque on the soil block, as shownin Eq. (14), with which hs can be calculated. Once the flow depth, hw, ina gully reaches the soil block, the soil block is assumed to collapse aspredicted in the torque-balanced situation (Eq. (21)):

+ − =P L L G L c L L L· · · · ·2 · 0T G C C (14)

=P γ h12

· · 2(15)

= + −L h d tanθ h· /2T s (16)

=G m g· (17)

= ++

L d h d tanθh d tanθ

·(3· · )3·(2· · )G

s

s (18)

= + −c w12000 462.27· 2.5283 (19)

= + −L h d tanθ h( · )/2C s (20)

> − +h H h d tanθ( · )w s (21)

where P is the water pressure of the collapsed soil block per unit length(Nm−1), LP is the force arm corresponding to P (m), G is the gravity ofthe collapsed soil block per unit length of gully per day (Nm−1 day−1),LG is the force arm corresponding to soil gravity (m), c is the cohesionforced on the soil block per unit area (Nm−2), LC is the force arm thatcorresponds to c (m), w is the soil water content (%), h is the soil crackdepth (m), and H is the gully depth (m).

2.2.3. Sediment transport in gullies and riversSediment transport processes in both gullies and rivers are simu-

lated based on the theory of non-equilibrium sediment transport.Considering sediment derived laterally from slopes along a channel(gully or river), we can improve the non-equilibrium sediment transportequation as follows:

= − − +d Q Cdx

α B ω C T Qs( · ) · · ·( )xx x l (22)

where Cx is the sediment concentration at position× (kg m−3), Tx isthe sediment transport capacity at position× (kg m−3), α is the sa-turation recovery coefficient, which generally varies between 0.02 and1.78 with a mean value of 0.50, B is the channel width (m), and Qsl isthe lateral sediment transport rate within a unit length of channel (kgs−1 m−1).

Furthermore, we integrate Eq. (22) over the channel length to cal-culate the sediment concentration at the gully and river estuary:

⎜ ⎟= + − + ⎛⎝

− + ⎞⎠

−− −( )C T C T e T T QsQ

lq

α ω le( )· · ·

· ·1

α ω lq l α ω l

q2 2 1 1· ·

1 2· ·

(23)

where C2 and C1 are the sediment concentration at the channel estuaryand entrance, respectively (kg m−3) (C1 is 0 for the gully and riverwhere there are no upper sub-watersheds; otherwise, sediment from allupper sub-watersheds should be added), and T2 and T1 are the sedimenttransport capacity at the channel estuary and entrance, respectively (kgm−3). These variables are calculated with Eq. (10) using the corre-sponding C2 and C1. The iterative method is necessary to calculate C2

because the value of T2 is related to C2. And l is the channel length (m).The lateral sediment sources, Qsl, are different for a gully and for a

river. In a gully, lateral sediment sources include portions of sedimentfrom the slope-gully in the lowest contour band and portions fromgravitational erosion. In a river, gully sediment is also a source of lat-eral sediment except for the portions of sediment from the slope-gully.Therefore, we calculate lateral sediment for the gully, Qsl,G, and river,Qsl,R, with the following different equations:

= +Qs p Qs l m· / /86400l G SG n G, 2, (24)

= − + −Qs p Qs R C Q l[(1 )· (1 )· · ]/l R SG n CK G G R, 2, (25)

where p is the proportion of slope sediment that enters the gully, QsSG2,nis the slope-gully transport rate in the lowest contour band (kg s−1), lGis the gully length (m), CG is the sediment concentration in the gully ofthe currently simulated sub-basin (kg m−3), QG is the gully discharge ofthe currently simulated sub-basin (m3 s−1), lR is the river length (m),and RCK is the sediment reduction efficiency of check dam. A re-presentative value of 0.7 is suggested for RCK (Xu et al., 2004).

2.3. Assessment methods

To assess the agreement between the model simulations and ob-servations, and to calibrate the model, we used three indicators: thecorrelation coefficient (R), the Nash–Sutcliffe Efficiency (NSE), and theRelative Error (RE) to statistically analyze the model results.

R is used to assess the agreement between the observed and calcu-lated monthly average discharge and sediment transport rate using thefollowing equation:

=∑ − −

∑ − ∑ −

=

− −

=

−

=

−

O O M M

O O M MR

( )( )

( ) ( )

iI

i i

iI

i iI

i

1

12

12

(26)

where Oi is the field observation,−

O is the average of Oi, Mi is the si-mulation, i is the time serial number, and I is the total number of ob-servations. R ranges from 0 to 1 and values closer to 1 represent im-proved simulation results.

The NSE is also used to assess the agreement between the observedand calculated monthly average discharge and sediment transport rate.It uses the following equation (Nash and Sutcliffe, 1970):

= −∑ −

∑ −=

=

−O M

O ONSE 1

( )

( )iI

i i

iI

i

12

12 (27)

where NSE ranges from −∞ to 1. Values of NSE > 0.50 indicate anacceptable level of performance for streamflow and sediment transportsimulation (Moriasi et al., 2007).

θ

h

H

d

hs

hw

Crack water pressure

Gravity

Cohesion

Pivot point

LC

LG

LP

Fig. 5. A schematic of gravitational erosion.

J. Cai, et al. Journal of Hydrology 577 (2019) 124005

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RE is used in water and sediment balance analysis to assess overallmodel performance for the runoff volume and sediment yield. The RE iscalculated with the following equation:

=∑ − ∑

∑∙= =

=

O t M t

O tRE

Â·Δ Â·Δ

·Δ100%i

Ii i i

Ii i

iI

i i

1 1

1 (28)

where tΔ iis the time interval between observations (s), RE rangesfrom -∞ to +∞ and values closer to 0 represent improved simulationresults.

3. Study area and database

3.1. Kuye river basin

The proposed model is applied to simulate soil erosion in the regionupstream of the Wenjiachuan hydrological station in the Kuye Riverbasin (Fig. 6), which has an area of 8515 km2. The basin is located inthe eastern section of the transition zone between the Loess Plateau andthe Mu Us Desert. There are occurrences of sparse vegetation, loose soil,broken terrain, and dense gullies in this area, with an average annualprecipitation of 415mm. The interannual variability in precipitation is

high, with a maximum of 696mm in 1964 and a minimum of 129mmin 1965, i.e., only 20% of the maximum value. The seasonal pre-cipitation distribution is also unevenly distributed, July and Auguststorms accounting for 52% of the annual rainfall. Furthermore, a singlestorm may account for 10% of the annual rainfall (Hessel and Van Asch,2003).

These geomorphological and climatic features render the study areaone of the main sources of sediment in the Yellow River basin. Theaverage annual runoff measured at the Wenjiachuan hydrological sta-tion from 1953 to 2000 was 612 million m3. The runoff in July andAugust accounted for 45% of the annual runoff, with uneven distribu-tion throughout a year. The measured average annual sediment load is100 million tons, which is more uneven than that of the runoff. Thesediment load in July and August accounted for 90% of the annualtotal. The maximum historical sediment concentration at theWenjiachuan hydrological station is 1700 kgm−3, which is the max-imum sediment concentration recorded for rivers globally. Therefore,this region has attracted significant attention for various hydrologicalstudies.

Fig. 6. The study area: (a) Location, (b) DEM, and (c) contour band division results.

J. Cai, et al. Journal of Hydrology 577 (2019) 124005

6

3.2. Inputs and standard database

3.2.1. Model input dataModel input data mainly include hydro-meteorological data, un-

derlying surface data (such as land use and soil and water conserva-tion), topographic soil data (such as DEMs and soil types), and gully andriver data (such as water system structures).

Hydro-meteorological data include daily rainfall, average tempera-ture, sunshine, relative humidity, and wind speed at the main meteor-ological stations (there are 6 stations in the study area) from 1956 to2010 provided by the China Meteorological Administration. For theunderlying surface data, land use data were derived from Landsat TMdata (1:1,000,000) for years 1980, 1985, and 1995 obtained from theInstitute of Geographic Sciences and Natural Resources Research,Chinese Academy of Sciences. Land use before 1980 is assumed to beidentical to that of 1980. The linear interpolation method was used tocalculate land use for other years. Soil and water conservation measuresmainly include artificial forests, artificial grasslands, terraces, andcheck dams, obtained from China Water Statistical Yearbooks.

We used ASTER GDEM data (http://www.gscloud.cn/) with a spa-tial resolution of 30m. Hydro-geological parameters, such as the hy-draulic conductivity and specific yield, were provided by the YellowRiver Conservancy Commission of the Ministry of Water Resources.

The actual water system, with a spatial resolution of 1:250,000provided by the National Geomatics Center of China, is used to modifythe DEMs to improve the accuracy of the simulated river network. Thegully and river cross-sections are generalized into an inverted isoscelestrapezoid. The upper bottom widths, lower bottom widths, and depthsof the sections are required for the model and obtained by averaging thefield measured values of several typical gullies and rivers.

3.2.2. Standard databaseThe available observational data for both monthly discharge and

sediment transport rate at the Wenjiachuan hydrological gauge stationcover 55 years, from 1956 to 2010, during which the observation seriesis completely continuous, as well as the model input database. Theseobservational data were obtained from the Annual HydrologicalReports of the People’s Republic of China.

4. Results

4.1. Model calibration and verification

4.1.1. Calibration resultsObservations at the Wenjiachuan hydrological gauge station from

1956 to 1984 are used to calibrate the WEP-SED. Using the assessmentmethods in Section 2.3, the parameters of hydrological cycle, in-dependent of the soil erosion simulation, are first calibrated via refer-ring to Jia et al. (2006). Then, the key soil erosion parameters are ca-librated, as shown in Table 1. And other soil erosion parameters not

listed in Table 1 are directly determined according to previous researchand field surveys without calibration.

Figs. 7 and 8 show the observed and simulated monthly dischargeand sediment transport rate from 1956 to 1984 after the calibration.

Figs. 7 and 8 show that the simulations are consistent with theobservations, especially for peak values. The NSE is larger than 0.50and the absolute relative error is smaller than 10% both for dischargeand sediment transport rate. All three statistical indicators showed inFigs. 7 and 8 demonstrate acceptable model performance. Further, theerror between the simulations and observations in Fig. 8 is similar tothe error in Fig. 7. It reflects that a large error between the simulatedand observed sediment transport rate corresponds to a large error in thedischarge simulation, which indicates that the soil erosion model issignificantly affected by the hydrological model.

4.1.2. Verification resultsAfter model parameter calibration, the observations from 1985 to

2010 are used for model verification. Figs. 9 and 10 show the observedand simulated monthly discharge and sediment transport rate duringthe verification period.

The calibrated WEP-SED performs well during the verificationperiod as the NSE is larger than 0.75 and relative error is smaller than5%. The three indicators are surprisingly better than those in the cali-bration period. The high R, NSE and low RE surely verify the modelperformance.

4.2. Gully erosion results

Gully erosion is an important and independent process of soil ero-sion on the Loess Plateau. Gully erosion occupies a large part of totalsoil erosion, larger than both slope and river erosion. To further in-vestigate the contribution of gully erosion, Fig. 11 shows annual gullyerosion and its contribution ratio to the total erosion from 1956 to2010.

The average contribution of gully erosion to the total erosion is60.30% from 1956 to 2010. This result is similar to the statisticsshowing that 60–70% of the sediment derives from gully erosion in thegullied rolling loess region (Fang et al., 1998).

Because heavy storm always occurs in several months from July toAugust, gully erosion appears to have significant variation throughout ayear, as shown in Figs. 12 and 13.

Both the amount and contribution of gully erosion vary from monthto month, and 84.86% of gully erosion occurs during July to August,conforming to the characteristic that sediment load in July and Augustaccounted for 90% of the annual total. The results of gully erosion from1956 to 2010 in Figs. 11–13 provide strong evidence that gully erosionmust be considered separately from river process to better simulate soilerosion in this area, especially for the rainy seasons.

4.3. Gravitational erosion analysis

As previously mentioned, gravitational erosion is an importantprocess during soil erosion, and improvements to simulate gravitationalerosion also contribute significantly to improve WEP-SED performancecompared with previous soil erosion models.

Fig. 14 shows that gravitational erosion contributes 8.07% of thetotal soil erosion. In particular, the contribution ratio of gravitationalerosion to total erosion is even larger than that of gully erosion inseveral years, indicating that sediment derived from gravitational ero-sion is not completely transported out but deposited in gullies. Con-sidering recorded gravitational erosion in the Liudaogou, Chabagou,and Wuding River basins near the Kuye River basin, this result, i.e., acontribution ratio of approximately 10% for the gravitational erosion atWenjiachuan is reliable (Guo, 2018). These results confirm that gullyerosion and gravitational erosion in gully areas should be consideredseparately.

Table 1Calibrated values of key soil erosion parameters in WEP-SED for Kuye Riverbasin.

Parameter Symbol Unit Value

Coefficient for sediment transport capacity of overlandflow

a3 – 1.0

Adjustment coefficients for soil loss intensity in forests CF – 0.1Adjustment coefficients for soil loss intensity in

grasslandsCG – 0.2

Adjustment coefficients for soil loss intensity in slopedcroplands

CS – 0.7

Soil erosion coefficient in slope-gully KSG – 1.0Saturation recovery coefficient in gully α – 0.50Saturation recovery coefficient in river 0.06Proportion of slope sediment entering the gully p – 0.6

J. Cai, et al. Journal of Hydrology 577 (2019) 124005

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0

100

200

300

400

5000

100

200

300

400

500

1956 1958 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984

Pre

cipi

tatio

n (m

m)

Mon

thly

dis

char

ge (m

3 /s)

Year

Precipitation Observed Simulated

R: 0.87 NSE: 0.72 RE: -5.42%

Fig. 7. The observed and simulated monthly discharge during the calibration period at the Wenjiachuan hydrological station.

0

100

200

300

400

5000

30

60

90

120

150

1956 1958 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984

Pre

cipi

tatio

n (m

m)

Mon

thly

tran

spor

t rat

e (t/

s)

Year

Precipitation Observed Simulated

R: 0.74 NSE: 0.54 RE: -8.10%

Fig. 8. The observed and simulated monthly sediment transport rate during the calibration period at the Wenjiachuan hydrological station.

0

100

200

300

400

5000

50

100

150

200

250

300

1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009

Pre

cipi

tatio

n (m

m)

Mon

thly

dis

char

ge (m

3 /s)

Year

Precipitation Observed Simulated

R: 0.88 NSE: 0.78 RE: 4.76%

Fig. 9. The observed and simulated monthly discharge during the verification period at the Wenjiachuan hydrological station.

0

100

200

300

400

5000

15

30

45

60

75

1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009

Pre

cipi

tatio

n (m

m)

Mon

thly

tran

spor

t rat

e (t/

s)

Year

Precipitation Observed Simulated

R: 0.86 NSE: 0.75 RE: 1.80%

Fig. 10. The observed and simulated monthly sediment transport rate during the verification period at the Wenjiachuan hydrological station.

J. Cai, et al. Journal of Hydrology 577 (2019) 124005

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5. Discussion

5.1. Model performance assessment

A complete model assessment is then performed for the entireperiod covering the 55 years and the results are listed in Table 2 andshown in Fig. 15. Both simulated runoff and sediment yield are smallerthan observed, as the relative errors are negative. The linearly fittedrelationship between simulated and observed monthly discharge iscloser to the 1:1 line (exact fit) in Fig. 15(a). All three indicators for thesimulated discharge perform better than those of the simulated sedi-ment transport rate as expected. However, the three indicators for si-mulated sediment transport rate are higher than those of previous re-search results for the Loess Plateau, where NSE was less than 0.5 andthe relative error was larger than 20% (Li et al., 2017). The long si-mulation period and daily timescale further demonstrate the feasibilityand efficiency of WEP-SED to simulate soil erosion. The simulationresults of the WEP-SED model are reliable for further analyses related tosoil erosion on the Loess Plateau.

However, there are several differences between the simulations andobservations that cannot be ignored. In both Figs. 8 and 10, the largepeak value corresponds to a large error, which significantly contributesto a poor NSE value. Therefore, improvements in model accuracy for

0

50

100

150

2000

10000

20000

30000

40000

50000

Con

tribu

tion

ratio

to to

tal e

rosi

on(%

)

Gul

ly e

rosi

on (t

/km

2 )

Year

Gully erosion

Gully erosion ratio

60 percent line

Fig. 11. Annual gully erosion from 1956 to 2010 in the Kuye River basin upstream of the Wenjiachuan hydrological station.

0

50

100

150

200

250

3000

5000

10000

15000

20000

25000

30000

35000

40000

1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010

Rat

io (%

)

Mon

thly

gul

ly e

rosi

on (t

/km

2 )

Year

Monthly gully erosion

Monthly gully erosion ratio

60 percent line

Fig. 12. Monthly gully erosion from 1956 to 2010 in the Kuye River basin upstream of the Wenjiachuan hydrological station.

0

50

100

150

2000

500

1000

1500

2000

1 2 3 4 5 6 7 8 9 10 11 12

Rat

io (%

)

Ave

rage

moo

nthl

y gu

lly e

rosi

on (t

/km

2 )

Month

Erosion

Ratio

Fig. 13. Average monthly gully erosion from 1956 to 2010 in the Kuye Riverbasin upstream of the Wenjiachuan hydrological station.

J. Cai, et al. Journal of Hydrology 577 (2019) 124005

9

the peak value simulation of the sediment transport rate require moreresearch.

5.2. Effects from discharge simulation

The simulated average annual sediment yield is close to the ob-servations throughout the 55 years, only with a relative error of−5.60%. However, the simulation results are affected significantly bythe discharge. To further investigate the performance of WEP-SEDduring high- and low-flow years, we divided these years into two

groups, with the average annual discharges from 1956 to 2010, asshown in Figs. 16 and 17. The high-flow group consists of 22 yearsincluding 1958, 1959, 1961, 1962, 1964, 1966–1971, 1973,1976–1979, 1984, 1985, 1988, 1992, 1994, and 1996.

The model performs differently in the high- and low-flow cases. Itunderestimates the sediment yield during high-flow years but over-estimates that during low-flow years with relative errors of approx-imate −12% and 6%, respectively. However, the calibrated modelperforms worse during low-flow years, with only 0.53 and 0.19 for Rand NSE respectively in terms of sediment transport rate, than high-flow years. This is mainly a continuation of the large error in dischargesimulations during the low-flow years as listed in Table 3.

5.3. Model improvements in applicability

The uncertainty in the performance of the WEP-SED is the result ofmany factors. Several limitations in the model structure and input dataare the most relevant.

(i) The sediment transport process in a slope-gully is simplified, withsoil erosion estimated directly by transport capacity. In gulliedrolling loess regions, the loose soil particles on the slope and in theslope-gully can easily be carried away by runoff. Therefore, soilerosion is usually limited by sediment transport capacity, which is

0

50

100

150

200

250

3000

500

1000

1500

2000

2500

3000

Rat

io (%

)

Gra

vita

tiona

l ero

sion

(t/k

m2 )

Year

Gravitational erosion

Gravitational erosion ratio

Fig. 14. Average annual gravitational erosion from 1956 to 2010 in the Kuye River basin upstream of the Wenjiachuan hydrological station.

Table 2Monthly simulation results of discharge and sediment transport rate at theWenjiachuan hydrological station.

Items Indicator Calibrationperiod

Verificationperiod

Whole period

1956–1984 1985–2010 1956–2010

Discharge R 0.87 0.88 0.87NSE 0.72 0.78 0.75RE (%) −5.42 4.76 −2.24

Sedimenttransport rate

R 0.74 0.86 0.76NSE 0.54 0.75 0.58RE (%) −8.10 1.80 −5.60

0

50

100

150

200

250

300

0 100 200 300

Sim

ulat

ed(m

3 /s)

Observed (m3/s)

(a)

1:1 line

Linear fit

R: 0.87NSE: 0.75RE: -2.24%

0

25

50

75

100

125

0 25 50 75 100 125

Sim

ulat

ed(t/

s)

Observed (t/s)

(b)

1:1 line

Linear fit

R: 0.76NSE: 0.58RE: -5.60%

Fig. 15. Monthly discharge (a) and sediment transport rate (b) at the Wenjiachuan hydrological station from 1956 to 2010.

J. Cai, et al. Journal of Hydrology 577 (2019) 124005

10

mainly determined by hydrodynamic conditions (Gong et al.,2011). However, if this model is applied in regions out of the LoessPlateau, the sediment transport Eq. (22) should be investigated forslope-gully.

(ii) Although the results of the gravitational erosion in this study arereliable for the Loess Plateau, considering only collapses as grav-itational erosion may limit the applicability of the WEP-SED in thewatersheds where collapses do not dominate gravitational erosion.The gravitational erosion in the form of landslides can be simu-lated as Wang et al. (2007).

(iii) Human activities have a large influence on the runoff and soilerosion on the Loess Plateau. A significant reduction of both flowdischarge and sediment transport rate without a decrease in pre-cipitation can be found in Figs. 9 and 10. This is the effect of soiland water conservation measures. However, these measures, suchas terraces and check dams whose effects are quantified with asediment reduction efficiency, are difficult to simulate accuratelybecause of the lack of data. Multi-source data combined with re-mote sensing data will be helpful for the applicability of WEP-SED.

6. Conclusions

This study develops a three-process-based distributed soil erosionmodel based on the WEP-L. The newly developed soil erosion modelrefines traditional two-process models for the Loess Plateau in China,resulting in an innovative approach to separating gully erosion processfrom traditional river erosion process. The physically-based gully ero-sion process clearly explains the link between slope soil erosion andriver sediment transport. In particular, this research advances our un-derstanding of gravitational erosion based on mechanical equilibriumprinciple, which yields a more accurate and applicable model. We ap-plied the WEP-SED to analyze soil erosion in the Kuye River basin. Thesimulated monthly sediment transport rate from 1956 to 2010 at the

Wenjiachuan hydrological station is similar to observations with acorrelation coefficient of 0.76, an NSE of 0.58, and a relative error of−5.60%, which demonstrates the efficiency and accuracy of the WEP-SED. The calculated average annual amount of gully erosion is largerthan that of slope and river erosion, which reflects the facts that theformer is a serious problem in the gullied rolling loess regions of theLoess Plateau, and that the gully erosion process is essential to simu-lating soil erosion in this area. An analysis of the sediment transportrate influenced by the flow discharge indicates that the physical pro-cesses associated with runoff and soil erosion are tightly coupled witheach other.

This study is a preliminary attempt to perform physically-based si-mulations of soil erosion in the overall processes and this subject re-quires further research. Insufficient standard data, including observedgully and gravitational erosion, limit the applicability of the WEP-SED.Further improvements should concentrate on enhancing data qualityfor model implementation and testing, especially for the para-meterization. Moreover, both terraces and check dams are importantdue to their effects on sediment reduction in erosion. The effects of soiland water conservation, as well as spatial and temporal variation inunderlying surfaces, will be further investigated to improve the

0

100

200

300

400

5000

30

60

90

120

150

1958 1961 1964 1967 1969 1971 1976 1978 1984 1988 1994

Pre

cipi

tatio

n (m

m)

Mon

thly

tran

spor

t rat

e (t/

s)

Year

Precipitation Observed Simulated

R: 0.77 NSE: 0.59 RE: -12.16%

Fig. 16. The observed and simulated monthly sediment transport rate in the high-flow group at the Wenjiachuan hydrological station.

0

80

160

240

320

4000

16

32

48

64

80

1956 1960 1965 1974 1980 1982 1986 1989 1991 1995 1998 2000 2002 2004 2006 2008 2010

Pre

cipi

tatio

n (m

m)

Mon

thly

tran

spor

t rat

e (t/

s)

Year

Precipitation Observed Simulated

R: 0.53 NSE: 0.19 RE: 6.08%

Fig. 17. The observed and simulated monthly sediment transport rate in the low-flow group at the Wenjiachuan hydrological station.

Table 3Group simulation results of monthly discharge and sediment transport rate from1956 to 2010 at Wenjiachuan hydrological station.

Items Number ofyears

Discharge Sediment transport rate

R NSE RE (%) R NSE RE (%)

Whole period 55 0.87 0.75 −2.24 0.76 0.58 −5.60High-flow

group22 0.89 0.79 −6.35 0.77 0.59 −12.16

Low-flowgroup

33 0.68 0.32 −1.00 0.53 0.19 6.08

J. Cai, et al. Journal of Hydrology 577 (2019) 124005

11

mechanisms involved in the three-process-based soil erosion model onthe Loess Plateau.

Declaration of Competing Interest

The authors declare that they have no known competing financialinterests or personal relationships that could have appeared to influ-ence the work reported in this paper.

Acknowledgments

This work was supported by the National Key Research andDevelopment Program of China (2016YFC0402405), the NationalNatural Science Foundation of China (No. 51779270, 41601032), andthe Foundation of State Key Laboratory of Simulation and Regulation ofWater Cycle in River Basin (SKL2018TS04). The reviewers and editorsare acknowledged for their comments, which significantly improvedthe quality of the manuscript.

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