HYDROLOGICAL PROCESSESHydrol. Process. (2010)Published online in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/hyp.7931

MHYDAS-Erosion: a distributed single-storm water erosionmodel for agricultural catchments

Silvio Jose Gumiere,1,2* Damien Raclot,3 Bruno Cheviron,2 Gregory Davy,3 Xavier Louchart,2

Jean-Christophe Fabre,2 Roger Moussa2 and Yves Le Bissonnais2

1 Institut national de la recherche scientifique (INRS), Centre—Eau Terre Environnement, 490 de la Couronne, Quebec, Qc, G1K 9A9, Canada2 INRA—UMR LISAH-Laboratoire d’etude des Interactions Sol—Agrosysteme—Hydrosysteme, 2 place Viala, Montpellier, 34060, France3 IRD—UMR LISAH-Laboratoire d’etude des Interactions Sol—Agrosysteme—Hydrosysteme, 2 place Viala, Montpellier, 34060, France

Abstract:

In this paper, we present MHYDAS-Erosion, a dynamic and distributed single-storm water erosion model developed as amodule of the existing hydrological MHYDAS model. As with many catchment erosion models, MHYDAS-Erosion is ableto simulate sediment transport, erosion and deposition by rill and interrill processes. Its originality stems from its capacityto integrate the impact of land management practices (LMP) as key elements controlling the sedimentological connectivityin agricultural catchments. To this end, the water-sediment pathways are first determined by a specific process-orientedprocedure defined and controlled by the user, which makes the integration of LMP easier. The LMP dynamic behavioursare then integrated into the model as a time-dependent function of hydrological variables and LMP characteristics. The firstversion of the model was implemented for vegetative filters and tested using water and sediment discharge measurementsat three nested scales of a densely instrumented catchment (Roujan, OMERE Observatory, southern France). The results ofdischarge and soil loss for simulated rainfall events have been found to acceptably compare with available data. The averageR2 values for water and sediment discharge are 0Ð82 and 0Ð83, respectively. The sensitivity of the model to changes in theproportion of LMP was assessed for a single rain event by considering three scenarios of the Roujan catchment managementwith vegetative filters: 0% (Scenario 1), 18% (Scenario 2, real case) and 100% (Scenario 3). Compared to Scenario 2 (realcase), soil losses decreased for Scenario 3 by 65% on the agricultural plot scale, 62% on the sub-catchment scale and 45% atthe outlet of the catchment and increased for Scenario 1 by 0% on the plot scale, 26% on the sub-catchment scale and 18%at the outlet of the catchment. Copyright 2010 John Wiley & Sons, Ltd.

KEY WORDS erosion modelling; sedimentological connectivity modelling; land management practice

Received 20 May 2010; Accepted 12 October 2010

INTRODUCTION

The distributed erosion models are intended to provideimportant information about the effects of soil loss andsediment exportation or redistribution for agricultural andwater quality concerns. Indications about the spatial pat-terns of sediment sources and sinks are useful to man-agers, planners and policy-makers for soil conservationissues. Aiming to develop such predictive skills, sev-eral process-oriented and physically based erosion modelshave been created. The European Soil Erosion Model(EUROSEM) (Morgan et al., 1998), the Kinematic Ero-sion Simulation Model (KINEROS) (Woolhiser et al.,1990), the Chemical Runoff and Erosion from Agricul-tural Management Systems (CREAMS) (Knisel, 1980),the Water Erosion Prediction Project (WEPP) (Ascoughet al., 1997), the Limburg Soil Erosion Model (LISEM)(De Roo et al., 1996) and the Soil and Water Assess-ment Tool (SWAT) (Arnold and Williams, 1995) esti-mate sediment concentrations in flow and soil loss over

* Correspondence to: Silvio Jose Gumiere, Institut national de larecherche scientifique (INRS), Centre—Eau Terre Environnement, 490de la Couronne, Quebec (Qc), Quebec, G1K 9A9, Canada.E-mail: silvio.gumiere@gmail.com

several scales in the catchment. However, these present-day erosion models do not give completely satisfyingresults about soil losses or predictions of sediment con-centration.

Jetten et al. (1999, 2003) identified many causes ofthese performance limitations. One of the limitationsappears because the parameters are held constant whiledescribing dynamic phenomena, which typically dependon rainfall intensity and duration. For example, the coher-ence of soil structure is affected by rainfall and results incrusting that changes the surface roughness and topsoilinfiltrability during a rainfall event. A further explana-tion cited by Jetten et al. (2003) is that the hydrologicalbehaviour of a catchment may be different for medium-and large-scale rain events; the interconnections betweenobjects may depend on time-dependent variables suchas rain and runoff intensity (Harvey, 2001; Fryirs et al.,2007). For example, some barriers constitute interfacesbetween landscape components that are normally notcrossed by runoff but may be overflown during large rainevents. As the connectivity is often complex in agricul-tural catchments because of anthropogenic management,it is fundamental to propose a model that takes into

Copyright 2010 John Wiley & Sons, Ltd.

S. J. GUMIERE ET AL.

account the dynamic hydrological-related behaviour ofthe land management practices (LMP).

Unfortunately, as argued by Gumiere et al. (2010),a major limitation of present-day water erosion modelsfor agricultural catchments is their inability to explic-itly describe the impacts of LMP on sedimentologicalconnectivity. Indeed, sedimentological connectivity hasbeen integrated into several models as an implicit param-eter by introducing the sediment delivery ratio (SDR)concept (e.g. AGricultural Non-Point Source PollutionModel (AGNPS) Young et al. (1989)), a ‘black box’method (Bracken and Croke, 2007) that does not aimfor a real understanding of the spatial and temporal pat-terns of sediment sources and sinks in the catchment.In LISEM (De Roo et al., 1996), the sedimentologi-cal connectivity has been treated by integrating LMPsin a spatially distributed manner. The model changesthe physical parameters to represent the existence ofLMPs in order to take their dynamic behaviour intoaccount. However, as argued by Gumiere et al. (2010),modifying physical parameters to reflect the existenceof LMPs may lead to the application of equations outof their domain of validity. The models that representa distributed LMP with a dynamic hydrological-relatedbehaviour (e.g. Vegetative Filter Strip Modeling System(VSFMOD) Munoz-Carpena et al. (1999)) are very com-plex and are not adapted to the catchment scale. Gumiereet al. (2010) therefore pointed out the need for a descrip-tion of intermediate complexity between the very detaileddescriptions of spatially isolated objects and the black boxdescriptions, which ignore processes governing sedimentfiltration.

The objective of this paper is to present a dynamic anddistributed single-storm water erosion model that is ableto take into account the effects of LMP on sedimentologi-cal connectivity in a dynamic way. The model is intendedfor application on agricultural headwater catchments cov-ering a few km2. On the basis of the knowledge of processrepresentation from present-day erosion modelling, ourmodel’s originality relies on its capacity to integrate thedynamic effects of LMPs. It may therefore be used toimprove the spatial and temporal modelling of within-catchment runoff and erosion or to plan and optimize theLMP set-up at the catchment scale. We present hereinan example of the model’s application at the Roujancatchment (southern France), which is equipped with anetwork of automatic sediment samplers at nested scales.The first part of this paper describes the model’s concepts,equations, input parameters and evaluation criteria as wellas the model’s limitations. We then present an applicationto the Roujan catchment and illustrate the sensitivity ofthe model to large variations in LMP implementations.

MODEL DESCRIPTION

Erosion module summary

The MHYDAS-Erosion has been developed under theOpenFLUID software development environment (Fabre

and Louchart, 2008; OpenFLUID, 2009) as a moduleof the hydrological MHYDAS model (Moussa et al.,2002). The catchment is subdivided into homogeneoushydrological units labelled ‘SUs’ for ‘surface units’and ‘RSs’ for ‘reach segments’. These two constitutiveelements were found to be necessary to take into accountthe variability and discontinuities of the agriculturalcatchments in a procedure extensively described byMoussa et al. (2002). SUs are polygons that representareas of SUs (e.g. agricultural plots), whereas RSs arelines that represent concentrated flow (e.g. drainagechannels and rivers). Where information is available,RSs may be determined by field observation and aerialphotography. Otherwise, RSs will be determined usingthe classic flow accumulation procedures included in theGeoMHYDAS software (Lagacherie et al., 2010) or othergeographical information system (GIS) tools.

At the SU, rain is partitioned between infiltration andrunoff according to the method of Morel-Seytoux (1978).Available runoff is thus derived from rain characteristics,saturated vertical hydraulic conductivity and initial watercontent. The one-dimensional Saint Venant equations arethen solved through a specific analytic method (Moussaand Bocquillon, 1996) for runoff transfer. Flow depthand velocity for concentrated flows in linear reach ele-ments are then obtained from the discharge partition withthe Manning formula by assuming the slope, shape andwidth of each reach segment is known. As in WEPP(Laflen et al., 1997), the erosion module enables a finerdecomposition of SUs into sub-elements of adaptablesizes representing rill and interrill areas associated withspecific phenomenologies. To ensure the stability of themodel according to the Courant–Friedrichs–Lewy (CFL)condition (Courant et al., 1928), we use a time stepfine enough to correctly track the highest possible flowvelocities. The parameterization and use of MHYDAS-Erosion are guided by the available GIS vector-basedenvironment. To be able to integrate the spatial and tem-poral impact of LMPs on water-sediment pathways andtransport, a specific connectivity module has been devel-oped in MHYDAS-Erosion. This module, described next,differentiates MHYDAS-Erosion from other catchment-scale water erosion models.

Spatial segmentation and representationof sedimentological connectivity

Unlike most catchment-scale water erosion models,MHYDAS-Erosion does not directly derive the water-sediment pathways from topography [Digital ElevationModel (DEM)], but they are instead determined by aprocess-oriented procedure defined and controlled by theuser. This procedure, developed by Lagacherie et al.(2010), consists of overlaying geographical informationlayers such as the location of the ditches, fields and sub-catchments limits, soil maps, land use, LMP localizationand DEM. The choice of which geographical inputs touse for segmentation is constrained by the objectives ofthe study. Figure 1 shows an example of a segmentationprocedure used in MHYDAS-Erosion. As a result, a

Copyright 2010 John Wiley & Sons, Ltd. Hydrol. Process. (2010)

DISTRIBUTED SINGLE-STORM WATER EROSION MODEL FOR CATCHMENTS

80

85

90

100

115

120

125

120

115

Catchment contourVine in rowsVineYoung vine plantingsRemoved vinesLucerneUncultivated (garrigues)Fallow landMarket gardeningOrchardWater basin

Catchment contourDrainage network

Catchment contourParcels

Catchment contour

Altitude (m)80-8586-9596-105106-115116-125

Plateau - Luvisols

Terrace - Regosols

Glacis - Cambisols

Lower parts - Cambisols

Catchment contour

Drainage networkLand registerTopography

Soil map Land use map

Combinespatial data

SU map RS map

Land management practicesParcels

Land management practices

Figure 1. Segmentation processes of MHYDAS

user-controlled spatial discretization of the catchmentin hydrological units (SU and RS) is derived, whichis associated with identification of the water-sedimentpathways and the location of the LMP. Depending on hisor her objectives, the user may ignore some informationlayers, lump some others or even merge limits or contoursthat define areas that are too small in an effort to onlyconsider elements over certain thresholds in length, widthor area. In this first version of MHYDAS-Erosion, thegoverning hydrological conditions affect the behaviourof the LMP while the topology is fixed: water-sedimentpathways stay unaffected during rain events.

Each SU can be divided into ‘interrill’ and ‘rill’ areasassociated with specific processes (Figure 2). Rainfallenergy is the driving variable in interrill areas. Using theconceptualization made by Kinnell (2005), two processesare represented: raindrop detachment with transport byraindrop splash (RD-ST) and raindrop detachment withtransport by raindrop-induced flow transport (RD-RIFT).Processes accounted for in rill areas include raindropdetachment with transport by flow (RD-FT), flow detach-ment with transport by flow (FD-FT) and sedimentation.Separate phenomenologies are described in rill and inter-rill areas based on experimental observations but also in

an effort to respect the domain of validity of the mathe-matical formulations at our disposal in the context of thisstudy. Interrill areas often do not have sufficient waterheights for conventional flow equations to apply, whereasrill areas meet the validity criteria more frequently.

The connectivity module in MHYDAS-Erosion enablesthe user to integrate specific connectivity effects (those ofLMP, for example) between each pair of catchment com-ponents (SU-SU, SU-RS and RS-RS). It is inspired by thetypology developed by Harvey (2001), which lists thethree types of connections between catchment objects as(i) coupled, (ii) not coupled and (iii) dis-coupled. Regard-ing the connectivity behaviour between pairs of catch-ment components, we have added to the typology a fourthstate of connection: (iv) re-coupled. The connections aredefined as follows:

(i) Coupled, when landscape units have free transmis-sion of matter and energy (sediment and water)between two catchment components (e.g. hillslope-channel or channel-channel)

(ii) Not coupled, when landscape units show no linkagesbetween catchment components (bench terraces, bar-riers or vegetation)

Copyright 2010 John Wiley & Sons, Ltd. Hydrol. Process. (2010)

S. J. GUMIERE ET AL.

Figure 2. Specific segmentation of MHYDAS-Erosion: example of a sub-catchment of Roujan; x D homogeneous slope elements and L is thelength of a surface unit

(iii) Dis-coupled, when landscape units were previouslycoupled but for some reason became disconnected,which is often as a result of sedimentation processes

(iv) Re-coupled, when landscape units were previouslydisconnected but for some reason they became con-nected, which is often as the result of over-bankbarriers.

According to Harvey (2001) and Fryirs et al. (2007),time-variable connectivity is influenced by rain andrunoff intensity, initial moisture conditions, vegetationtype and location. In this first version of MHYDAS-Erosion, only vegetated filters have been included inaddition to the fixed coupled or non-coupled connectiv-ity behaviours. The behaviour of vegetated filters wasderived from flume experiments by Deletic (2001) andDeletic and Fletcher (2006). In these experiments, realgrass was used to filter water mixed with natural sedi-ment particles of d50 D 50 µm diameter. Deletic (2001)used slopes of 2 and 7% for three different grass den-sities, which is defined as the cross-section of flownot blocked by the grass blades and was fixed at 0Ð6,0Ð67 and 0Ð75 (�). A sediment trapping efficiency (Tr)

could be derived as a function of the runoff conditionand the vegetative filter characteristics. Deletic (2001)have defined the dimensionless particle fall number (Nf)(Figure 3).

Figure 3. Sediment trapping efficiency as a function of the adimensionalparticle fall number Nf for four sediment size fractions, from Deletic

(2005)

Copyright 2010 John Wiley & Sons, Ltd. Hydrol. Process. (2010)

DISTRIBUTED SINGLE-STORM WATER EROSION MODEL FOR CATCHMENTS

The sediment trapping efficiency Tr is calculated withthe equation proposed by Deletic (2005):

Tr D N0Ð69f

N0Ð69f C 4Ð95

�1�

whereNf D l Ð Vs

h Ð V�2�

Where l is the grass strip length (m), Vs is the Stokesvelocity for settling of the sediment particles (m s�1) andV is the mean flow velocity between grass blades (m s�1).The mean flow and settling velocities in the model arecalculated as follows:

V D q

B0 Ð h�3�

andVs D g

18 µ��s � ��d2

s �4�

where B0 is the grass density, � is the dynamic viscosityof water (kgs�1 m�1), � is the water density (kg m�3),�s is the sediment particle density (kg m�3) and ds is theparticle diameter (m). The cross-correlation coefficientbetween measured and calculated trapping efficienciesreached R2 D 0Ð85 (Deletic, 2005). Observing Figure 3,there is a high scattering of measured data around thecalculated line for the smallest sediment size fractions.According to Deletic (2005), the high dispersion is dueto measurement errors because ‘the concentration ofparticles below 5Ð8 µm was very small and thereforedifficult to measure accurately’. In MHYDAS-Erosion,Tr is calculated for each time step; thus, the sedimenttrapping efficiency is time-dependent. The parametersB0 and l are estimated from field observations for eachvegetative filter. As argued by Deletic (2001, 2005), theapproach based on the particle fall number is only validfor low sediment concentrations that do not influencesediment deposition.

MHYDAS-Erosion has been developed to be able toaccept every connectivity type as described by Harvey(2001): coupled, not coupled, dis-coupled and re-coupled.We have implemented a specific connectivity module totake into account topology changes during the simulation.However, only vegetative filters have been implementedin this first version of MHYDAS-Erosion, so only veg-etated filter connectivities change dynamically with therunoff amount.

Erosion processes represented in MHYDAS-Erosion

MHYDAS-Erosion is based on the mass conservationprinciple applied to sediment load proposed by Bennett(1974):

∂�Hc�

∂tC ∂�UHc�

∂xD Di C Dr � Dd �5�

where c(kg m�3) is the sediment concentration, t (s) istime, Di (kg m�2 s�1) is the sediment inflow rate due tointerrill erosion, Dr (kg m�2 s�1) is the sediment inflow

rate due to rill erosion and Dd (kg m�2 s�1) is the sedi-ment deposition rate, which eventually coexists with Dr.The implicit validity conditions (and hypotheses made)are that all particles travel at the same velocity, whichis the mean water velocity U. We consider only sus-pended load sediment transport and ignore bedload trans-port and particle dispersion. We assume that sedimentinflow concentration does not influence the hydrodynamicflow properties.

Soil detachment and transport by rainfall. The sedi-ment inflow rate due to interrill erosion is the conse-quence of a multi-stage process described by Kinnell(2005) in which soil aggregates are broken by rainfalland are eventually put into suspension before being trans-ported by splash and/or overland flows. The sedimentinflow rate due to interrill erosion is evaluated using inter-rill erodibility, which is expressed by aggregate stabil-ity measurements (Le Bissonnais, 1996; Gumiere et al.,2009). This choice was argued in Gumiere et al., 2009.The interrill detachment equation retained was developedempirically by Yan et al. (2008) initially for the ultisoilstype in China:

di D 0Ð23 Ð As Ð I2 Ð Sfactor �6�

where As is the index of stability calculated frommean weight diameter (MWD) measurements (Yan et al.,2008), I is the rainfall intensity (mm h�1) and Sfactor isthe slope factor calculated by (1Ð05–0Ð85 Ð e�4 sin �) where� is the slope angle (�). This empirical equation wastested by Zhi-Hua et al. (2010), and the results from thistest have shown a good relationship (R2 D 0Ð89) betweenmeasured and simulated values of interrill erosion for fivesoil types with different organic matter content.

The index of stability As in Equation (6) is based onthe work of Zhang and Horn (2001).

As D MWDSW � MWDFW

MWDSWð MWDSW � MWDWS

MWDSW�7�

where MWDSW (m) is the mean weight diameter obtainedby the slow-wetting treatment, MWDFW (m) is the meanweight diameter obtained by the fast-wetting treatmentand MWDWS (m) is the mean weight diameter obtainedby the stirring treatment.

The sediment inflow rate into rill due to interrillerosion is then calculated by multiplying the interrilldetachment (Equation (6)) by a coefficient that describesthe efficiency of transport on interrills (CETI ):

Di D di Ð CETI D 0Ð23 Ð As Ð I2 Ð Sfactor Ð CETI �8�

CETI is calculated from local runoff as

CETI D CETImax Ð �1 � e˛ÐR� �9�

where CETImax (�) is the maximum allowed value ofCETI, ˛ (�) is an empirical exponent depending onroughness and R (mm h�1) is the runoff amount.

Copyright 2010 John Wiley & Sons, Ltd. Hydrol. Process. (2010)

S. J. GUMIERE ET AL.

In the MHYDAS-Erosion, we consider that the waterheight on interrill areas is too shallow to apply thetransport equations used in conventional hydraulics. Theconcept of CETI was introduced to describe the effect ofthe perpendicular roughness on the interrill-to-rill erosioncontribution. CETImax values may vary in theory between0 and 1, but experiments conducted by Leguedois et al.(2005) and Nord (2006) gave values between 0Ð1 and 0Ð5.

Soil detachment and transport by runoff. The sedimentinflow rates due to rill erosion integrate two aspects intoa single equation. When the transport capacity of theflow exceeds sediment load, both particle detachment dueto excess shear stress exerted by the flow and sedimenttransportation appear in the equation proposed by Fosteret al. (1995) and further tested by Nord (2006):

Dr D Kr�� � �c�(

1 � qs

TC

)�10�

where Kr (s m�1) is rill erodibility, � (Pa) is the shearstress exerted on the bed by the flow, �c (Pa) is thecritical shear stress over which detachment is initiated, qs

(kg m�1 s�1) is the unit solid discharge by a 1 m widthof the flow calculated as qs D q Ð c and TC (kg m�1 s�1)is transport capacity, which measures the ability of theflow to carry a sediment load.

TC has been empirically related to values of � and �c

by Foster (1982):

TC D �� � �c�k �11�

where (m1/2 s2 kg�1/2) gives the efficiency of thetransport with recommended values of D 0Ð04 andk D 1Ð5 according to the work of Finkner et al. (1989).This formulation was chosen because TC is expressed asa function of the critical shear stress, which is a widelyused parameter (Knapen et al., 2007).

As the critical shear stress is highly related to soilcohesion COH (Pa), it is possible to approximate �c

by COH in the downstream direction (Nord, 2006). Thehydrodynamic shear stress exerted on the bed is � D �gHS, where � (kg m�3) is the density of water andg (m s�2) is gravitational acceleration. This expressionrigorously holds under the assumptions of a uniform flowover a small slope approximated by its sine or tangentwhen friction exerted by the bed on a given volume offluid equals the streamwise component of the weight ofthe fluid.

When qs > TC, deposition occurs (Foster et al., 1995):

Dd D vs

qÐ �qs � TC� �12�

where vs (m s�1) is the settling velocity defined bySoulsby (1997).

Settling velocity is said to apply over a wide range ofconcentrations up to c D 100 g l�1 and under which vs

was empirically defined as

vs D

ds

Ð[√

10Ð362C1Ð049Ð�1�cvol�4Ð7 Ðd3sŁ�10Ð36] �13�

where (m2 s�1) is the kinematic viscosity of water,ds (m) is the diameter of the particles, cvol (�) is theirvolumetric concentration in the flow and dsŁ (�) is theiradimensional sedimentological diameter.

The adimensional sedimentological diameter is takenfrom Julien (1998):

dsŁ D ds Ð[

��s/� � 1� Рg

2

]�14�

where �s(kg m�3) is the density of the particles.

Numerical methods and hydrology-erosion coupling

The hydrological and erosion equations are solvedindependently but successively within the same time stepof a priori fixed duration unless the CFL condition isbroken and the time grid needs to be refined. Sedimentconcentration is not supposed to affect the water flowbehaviour (Bennett, 1974). At a given time step, thehydrological variables qt

i, vti and ht

i (unit flow discharge,flow velocity and water height, respectively) are firstcalculated. The analytical solutions of the infiltrationand excess infiltration equations proposed by Morel-Seytoux (1984) and the analytical solution of the diffusiveflow equation proposed by Hayami (1951) are found.As debated by Moussa (1996), analytical solutions arepreferred to numerical schemes to preserve the stabilityand convergence of the results.

Sediment mass balance equations (Equation (5)) aresolved at each time step using a backward explicit finitedifference scheme. The volumetric concentration of thesuspended sediment in the flow ci at t C t is calculatedusing values of qt

i, vti, ht

i and cti.

Model input parameters

As MHYDAS takes into account many spatially dis-tributed hydrological and erosion processes, each inputparameter may also be spatially distributed among homo-geneous SUs. Values of the Manning’s roughness coef-ficient, soil cohesion, soil aggregate stability, interrillerodibility and rill erodibility may be developed fromland use and soil maps. The model requires an initial soilmoisture content (�i) as an initial condition. MHYDAS-Erosion needs the spatial distribution of parameters onhydrological units and reaches. Table I shows the inputparameters required to run MHYDAS-Erosion. Theyhave specific values for each hydrological object (SU orRS).

To run successfully, MHYDAS-Erosion also needsgeometrical indications pertaining to each SU or RSsuch as its area, mean slope and distance to the nextstreamwise unit. These values may be calculated usingthe DEM if available, or they can be informed by fieldobservations. Sensitivity analyses performed by Chevironet al. (2010) identified the most sensitive parameters forMHYDAS-Erosion: ks, Nrill, Kr and As.

Copyright 2010 John Wiley & Sons, Ltd. Hydrol. Process. (2010)

DISTRIBUTED SINGLE-STORM WATER EROSION MODEL FOR CATCHMENTS

Table I. Input parameters necessary to run MHYDAS-Erosion

Parameter Description Unit

SUks Saturated hydraulic

conductivitym s�1

hc Air entry potential m�r Soil residual moisture m3 m�3

�s Soil saturation moisture m3 m�3

nSU Manning’s roughness coef. s m�1/3

As Aggregate stability index —Nrill Number of rills —W Rill width md50sed Median sediment diameter m�c Critical soil shear stress PaTransfcode Interface type indicator —Kr Rill erodibility s m�1

Cetimax Max transport coef frominterrill erosion

—

Strip.width Vegetated filter width mStrip.density Density of vegetation on the

filter—

RSks Saturated hydraulic

conductivitym s�1

nRS Manning’s roughness coef. s m�1/3

Kr Rill erodibility s m�1

�c Critical soil shear stress Pa

MODEL APPLICATION AT THE ROUJANCATCHMENT

We acknowledge that a validation of this model is beyondthe scope of an introductory paper, and this sectionis rather intended to demonstrate briefly some of thecapabilities of MHYDAS-Erosion and dynamic erosionmodels in general. More extensive field applications areintended for subsequent publications.

The Roujan catchment

The MHYDAS-Erosion was applied on a small agri-cultural catchment called the Roujan catchment (43Ð300N, 3Ð190 E, area D 0Ð91 km2), which is a densely instru-mented catchment included in the experimental researchobservatory named OMERE (Mediterranean Observa-tory of Rural Environmental and Water http://www.umr-lisah.fr/omere). It is located in southern France, 60 kmwest of Montpellier and has a Mediterranean climate. Thecatchment has been equipped with hydro-meteorologicalmeasurement devices since 1992 (meteorological station,rain gauges, stream flow recorders, automatic sedimentsamplers and Venturi flumes). Since 2005, the catchmenthas had seven points of automatic sediment concentrationsampling, which are dispatched as shown in Figure 4.The localization of LMPs as well as their characteris-tics was measured in situ. Field observations conductedduring summer 2009 showed that only 22% of the agri-cultural plots bear a land management practice.

Annual rainfall varies between 500 and 1400 mm ina bimodal temporal distribution with two major rainyperiods: one in spring and the other in autumn. Rainfall

Figure 4. Meteorological, hydrological and sedimentological equipmentof the Roujan agricultural catchment

Table II. Main rainfall characteristics for calibration and valida-tion events; Imean is the mean rainfall intensity recorded with a5-min time step, Imax is the 5-min maximum intensity and IPA5

is an index of antecedent rainfall events

Event 1 Event 2 Event 3

Season Spring Autumn AutumnDuration (min) 170 1810 955Total rainfall (mm) 33 92 85Ð5Imean (mm h�1) 11Ð65 3Ð05 64Imax (mm h�1) 48Ð96 37Ð44 74IPA5 19Ð88 2Ð96 94Erosion point 1 (ton/ha) 1Ð03 1Ð01 2Ð33Erosion point 2 (ton/ha) 2Ð02 1Ð15 3Ð19Erosion point 3 (ton/ha) 0Ð06 0Ð03 0Ð03Runoff point 1 (mm) 13Ð08 41Ð37 44Ð91Runoff point 2 (mm) 23Ð97 82Ð53 77Ð29Runoff point 3 (mm) 0Ð84 3Ð32 2Ð83

is usually of high intensity and short duration. The meanannual temperature is about 14 °C, and the mean annualPenman evapotranspiration is 1090 mm. Soils of thecatchment have developed from marine, lacustrine orfluvial sediments (Moussa et al., 2002). The catchmentis mainly covered by vineyards and is divided into 237agricultural plots. Agricultural plot areas vary between320 and 22 427 m2. A survey (Lennartz et al., 1997)identified two main treatments against weeding. In thefirst one, herbicides are applied over the whole fieldwithout any tillage. In the second one, soil is tilledwith a rotovator between vine rows at least once duringthe growing period between March and October. Thedrainage network is formed by man-made ditches andgenerally follows the limits of agricultural plots. The totallength of the ditch network is 11 069 m.

Copyright 2010 John Wiley & Sons, Ltd. Hydrol. Process. (2010)

S. J. GUMIERE ET AL.

Rainfall event characteristics and observation values

Three contrasting rainfall events were chosen to repre-sent a large variety of rainfall events: a short event withmedian rainfall intensity (event 1), a long event with rel-atively low rainfall intensity (event 2) and a short eventwith high rainfall intensity (event 3). The main charac-teristics of the three rainfall events are shown in Table II.

Model parameterization and calibrationfor the application at Roujan

Almost all input parameters were obtained from fieldobservations. As MHYDAS takes into account many spa-tially distributed hydrological and erosion processes, thevalues of each input parameter may also be spatiallydistributed among homogeneous SUs. The model param-eterization was constrained by land-use data availability:values of the Manning’s roughness coefficient, the soilcohesion, the soil aggregate stability, the aggregate stabil-ity index and the rill erodibility were developed from landuse and soil maps. The initial soil moisture in the surfacelayers (�i) was deduced from analyses of the antecedentrainfall events.

The parameters measured or observed in the field weregeometrical characteristics of the ditch network such asreach depth, reach width and the Manning’s roughnesstogether with soil water properties and aquifer geom-etry (Lagacherie et al., 2010). Soil properties such asthe residual water content and the water content at nat-ural saturation were obtained from soil maps, and thevalues of �r and �s for each soil texture were basedon the USDA values. One parameter to be calculatedfrom hydrological data analysis at the field scale is thehydraulic conductivity at natural saturation Ks, becauseKs essentially depends on tillage practices. The hydro-logical units were grouped into three classes of hydraulicconductivity corresponding to the three major land useson the Roujan catchment: class 1 D non-tilled vineyards,class 2 D tilled vineyards and class 3 D other land uses,which are mainly fallow land and scrubland. Chahinian(2004) and Chahinian et al. (2006b) had shown on non-tilled fields that Ks D 5 mm h�1, which is quite similarto the infiltrability values measured on the same fieldat a 1 m2 scale by Leonard and Andrieux (1998). Asimilar approach was also applied by Chahinian et al.(2006a) on a tilled experimental field (3200 m2) in theRoujan catchment. Results showed that the values of Ks

decrease from 30 mm h�1 just after tillage in the springto 5 to 10 mm h�1 at the end of summer, and they areconsistent with the infiltrability values measured by rain-fall simulations. For the other land use types, the valueof the hydraulic conductivity Ks was taken to be equalto 30 mm h�1, which is an average of the values ofinfiltrability (25 to 35 mm h�1) measured by rainfall sim-ulations on fallow and scrubland, as no observed runoffdata at the field scale were available. Note that the infil-trability of fallow and scrubland is high all year roundbecause of permanent vegetation with dense root sys-tems, which creates large macroporosity in the surfacelayers. In the same way, values of the aggregate stabil-ity index were derived from tillage practices: non-tilledvineyards were attributed a value of As D 0Ð15, tilledvineyards were attributed a value of As D 0Ð30 and otherland uses were attributed a value of As D 0Ð70. Eventhough non-tilled vineyards exhibit very few aggregateson the soil surface, aggregate stability gives informationabout the size and cohesion of soil fragments resultingfrom breakdown by water and the susceptibility to crustformation. In fact, Le Bissonnais et al. (2007) and Blavetet al. (2009) have shown that the aggregate stability ofnon-tilled (chemically weeded) vineyards was lower thantilled vineyards and was much lower than vegetated sur-faces.

The model was calibrated using data from the plotscale (non-tilled vineyards Le Bissonnais et al. (2007))for each rainfall event, which defined a data set of param-eters for land use class 1. Using the Nash–Sutcliffeefficiency and R2 as evaluation criteria, a trial-and-error calibration procedure was made. The thresholdvalues for Nash–Sutcliffe efficiency and R2 were 0Ð50and 0Ð60, respectively. Above these values, simula-tions were considered acceptable. The values of Ks

and As were used as calibration parameters. Aftercalibration, the values of Ks and As for land useclass 2 and class 3 were calculated using the sameproportionality found in the experiments for Ks andAs.

Table III shows the calibrated parameters after the cali-bration procedure. The values of Ks and As are physicallypossible and are on the same order of magnitude as thosemeasured in the laboratory or field experiments.

To evaluate the influence of LMPs on model responses,we performed two virtual tests with 0 and 100% of

Table III. Calibrated parameters for each rainfall event and each land use class

Non-tilled vineyards Tilled vineyards Scrublands and others

Ks (mm h�1) As Ks (mm h�1) As Ks (mm h�1) As

Event 1 4Ð57 0Ð65 7Ð71 0Ð83 24Ð9 0Ð15Event 2 4Ð61 0Ð75 7Ð78 0Ð79 25Ð1 0Ð17Event 3 7Ð85 0Ð39 13Ð24 0Ð24 42Ð7 0Ð096

Average 5Ð68 0Ð60 9Ð58 0Ð62 30Ð90 0Ð14SDT 1Ð88 0Ð19 3Ð17 0Ð33 10Ð22 0Ð04CV 0Ð33 0Ð31 0Ð33 0Ð53 0Ð33 0Ð28

Copyright 2010 John Wiley & Sons, Ltd. Hydrol. Process. (2010)

DISTRIBUTED SINGLE-STORM WATER EROSION MODEL FOR CATCHMENTS

Table IV. Evaluation criteria and their respective ranges; Yi isthe observed value, OYi is the simulated value, n is the sample

size and Y is the mean of the observed values

Criteria Equation Range

ENS ENS D

n∑iD1

�Yi � OYi�2

n∑iD1

�Yi � Y�2

[�1, 1]

RMSE RMSE D√

1n

∑niD1�Yi � OYi�2 [0, C1]

R2 R2 D

n∑iD1

�Yi � Y�� OYi � QYi�

√√√√ n∑iD1

�Yi � Y�2

n∑iD1

� OYi � QYi�2

2

[0, 1]

RVE RVE D

n∑iD1

�Yi � OYi�

n∑iD1

Yi

[�1, C1]

PEP PEP D max�Yi� � max� OYi�max�Yi�

ð 100 [�1, C1]

the agricultural plots bearing vegetated filters, whichwe compared to the real situation (22% of agricul-tural plots bearing vegetated filters). The grass stripcharacteristics were similar to grass density with 3-m-wide strip widths, and the slopes were obtained fromfield observations for the real case. For our sensitiv-ity tests, we maintained the same distribution of eachcharacteristic, used the same calibrated parameters asin reality and considered a class 1 event to be aver-age.

Statistical evaluation criteria

The statistical evaluation criteria used in this workwere the Nash–Sutcliffe efficiency (ENS), the root meansquare error (RMSE), the coefficient of determination(R2), the relative volume error (RVE) and the per-cent error in the peak (PEP). These criteria were cho-sen because they reflect different evaluation proper-ties of the model (Dawson et al., 2007) calculatedas functions of time for each tested rainfall event.Table IV shows the evaluation criteria and their respec-tive ranges.

Results and discussion for the Roujan application

In this section, we discuss the results obtained by themodel in its application to the Roujan catchment. Thediscussion is illustrated with results obtained from threeMediterranean rainfall events: one in the spring and twoin the autumn.

Figure 5 shows the sedigraphs obtained at points thatare draining the sub-catchments on three nested scalesfor three rainfall events in the Roujan catchment andafter calibration. Judging visually from the curves, our

model has simulated fairly well the observed sedimentdischarge at all measurement points for the three rain-fall events. The most poorly simulated event was event2, which was characterized by a long rainfall dura-tion and low mean rainfall intensity. As proposed byNearing (2000), models that tend to better simulatehigh-intensity rainfall events may poorly simulate low-intensity ones. Our model tends to perform better at theglobal catchment scale than at the plot or sub-catchmentscales.

The values of the Nash–Sutcliffe efficiency ENS, theRMSE, the R2, the RVE and the PEP for the three rain-fall events at the three measurement points are givenin Table V. We have chosen these efficiency criteriabecause they provide information about the dynamicbehaviour of the model over time. Another reason tochoose these indicators is their adimensionality (exceptfor RMSE); this allows the comparison of informa-tion among different space scales (in this applica-tion, points 1, 2 and 3). It is important to remem-ber that the model is intended to simulate sedimentdischarge and hydrology at any part of the catch-ment.

From Table V, the Nash–Sutcliffe efficiency rangesfor water discharge from 0Ð34 to 0Ð73 with an averagevalue of 0Ð60 when including the three scales and thethree rainfall events. For erosion, the Nash–Sutcliffe effi-ciency ranges from 0Ð22 to 0Ð84 with an average valueof 0Ð58 when including the three scales and the threerainfall events. These values are close to the require-ments made by Nearing (2000) for calibrated erosionmodels (efficiency > 0Ð60) for the erosion at the scaleof the plot. Event 2 is poorly simulated compared tothe others, which may be explained by its low meanrainfall intensity (because MHYDAS-Erosion is better atsimulating stronger events) or by exfiltration phenomenathat are very likely to occur in the Roujan catchment inautumn. Even at such low intensities, the 30-h durationof event 2 gathers enough water to initiate exfiltration towhich our model is totally blind without further develop-ments.

From Table V, it is observed that the average RMSEfor water discharge and sediment discharge are about25 l s�1 and 0Ð09 kg s�1, respectively; both values arisefrom calculations on the three scales and three rainfallevents. The RMSE has the same units as the observedand simulated values. Generally, higher RMSE valuesindicate poor performance of the model. The average R2

for water discharge is 0Ð82, and it is 0Ð83 for sedimentdischarge. This parameter is interpreted to mean that themodel can explain well the water discharge and the sed-iment discharge at all three tested scales.

The RVE values for water and sediment discharge are0Ð08 and �0Ð01, respectively, which indicate a limitedoverestimation of the transferred water along with a slightunderestimation of the exported sediment mass. From anagricultural point of view, the RVE is the most repre-sentative performance model indicator because it givesthe total erosion and total runoff difference in a direct

Copyright 2010 John Wiley & Sons, Ltd. Hydrol. Process. (2010)

S. J. GUMIERE ET AL.

0.00

0.06

0.12

(a)

time (hh:mm)

Sed

imen

t Dis

char

ge (

kg/s

)

simulatedobserved

23:00 00:00 01:00

(d)

0.00

00.

010

time (hh:mm)

Sed

imen

t Dis

char

ge (

kg/s

)

simulatedobserved

05:00 15:00 01:00

(g)

0.00

0.10

0.20

time (hh:mm)

Sed

imen

t Dis

char

ge (

kg/s

)

simulatedobserved

09:00 10:00 11:00

0.0

0.4

0.8

(b)

time (hh:mm)

Sed

imen

t Dis

char

ge (

kg/s

)

simulatedobserved

23:00 00:00 01:00

(e)

0.00

0.10

0.20

time (hh:mm)

Sed

imen

t Dis

char

ge (

kg/s

)

simulatedobserved

05:00 15:00 01:00

(h)

0.0

0.4

0.8

time (hh:mm)

Sed

imen

t Dis

char

ge (

kg/s

)

simulatedobserved

09:00 10:00 11:00

0.0

0.5

1.0

1.5

2.0

(c)

time (hh:mm)

Sed

imen

t Dis

char

ge (

kg/s

)

simulatedobserved

23:00 00:00 01:00

(f)

0.00

0.10

0.20

0.30

time (hh:mm)

Sed

imen

t Dis

char

ge (

kg/s

)

simulatedobserved

05:00 15:00 01:00

(i)

0.0

0.5

1.0

1.5

2.0

time (hh:mm)

Sed

imen

t Dis

char

ge (

kg/s

)

simulatedobserved

09:00 10:00 11:00

Figure 5. Observed and simulated sediment discharges for the three rainfall events at the three measurement scales for the Roujan catchment: (a) point1, event 1; (b) point 2, event 1; (c) point 3, event 1; (d) point 1, event 2; (e) point 2, event 2; (f) point 3, event 2; (g) point 1, event 3; (h) point 2,

event 3 and (i) point 3, event 3

Figure 6. Scenarios for spatial distributions of LMPs

way. Previews of the total runoff and erosion volumesare very useful to decision-makers when planning soilconservation practices. The values of RVE obtained tendto indicate that MHYDAS-Erosion may be used for thesepurposes. The average error in the peak (PEP) was 12Ð5%for water discharge and 0Ð69% for sediment discharge,which also indicates good prediction of the peak values.

LMP scenario test. The next step was to test themodel response to spatial organizations of LMPs, whichare essentially grass strips at the Roujan catchmentthat are placed between agricultural plots and drainagechannels or between agricultural plots. Three scenar-ios were tested. Scenario 1 simulates the case when0% of the agricultural plots bears a grass strip. Sce-nario 2 is the real percentage of grass strips in theRoujan catchment, which was obtained from field obser-vations. Scenario 3 simulates the case when 100% ofthe agricultural plots bears a 3-m-wide grass strip. InFigure 6, Scenario 3 shows soil loss decreases of 65%on the agricultural plot scale, 62% on the sub-catchmentscale and 45% at the outlet of the catchment whencompared to Scenario 1. Scenario 2 shows a reduc-tion of 26% at the sub-catchment scale and 18% atthe outlet of the catchment in comparison with Sce-nario 1. The objective here was to identify the sensitivitytrends of MHYDAS-Erosion when varying the spatialdistributions of LMP, which are reduced here to grassstrips.

The model’s ability to replicate spatial erosion andsediment patterns within the whole catchment remainsto be confirmed by comparing predictions for ero-sion feature distributions such as rill and gully densi-ties.

Copyright 2010 John Wiley & Sons, Ltd. Hydrol. Process. (2010)

DISTRIBUTED SINGLE-STORM WATER EROSION MODEL FOR CATCHMENTS

Tabl

eV

.Su

mm

ary

ofm

odel

effic

ienc

y

Eve

nt1

Eve

nt2

Eve

nt3

Sedi

men

tdi

scha

rge

Wat

erdi

scha

rge

Sedi

men

tdi

scha

rge

Wat

erdi

scha

rge

Sedi

men

tdi

scha

rge

Wat

erdi

scha

rge

Inde

xes

Poin

t1

Poin

t2

Poin

t3

Poin

t1

Poin

t2

Poin

t3

Poin

t1

Poin

t2

Poin

t3

Poin

t1

Poin

t2

Poin

t3

Poin

t1

Poin

t2

Poin

t3

Poin

t1

Poin

t2

Poin

t3

EN

S0Ð5

90Ð4

90Ð5

90Ð6

50Ð7

30Ð7

10Ð3

00Ð2

20Ð6

20Ð3

70Ð0

340Ð3

80Ð7

20Ð8

40Ð8

20Ð6

70Ð7

20Ð6

5R

MSE

0Ð02

0Ð11

0Ð32

1Ð94

5Ð91

44Ð44

0Ð00

0Ð03

0Ð07

1Ð67

8Ð34

49Ð53

0Ð02

0Ð09

0Ð19

3Ð84

10Ð27

105Ð5

0R

20Ð8

10Ð7

50Ð9

00Ð9

30Ð8

80Ð9

20Ð5

80Ð7

70Ð8

30Ð7

10Ð6

30Ð6

80Ð8

80Ð9

30Ð9

30Ð8

40Ð8

90Ð9

0R

VE

0Ð10

�0Ð16

�0Ð09

�0Ð11

0Ð19

0Ð11

0Ð16

0Ð30

0Ð07

�0Ð31

�0Ð20

0Ð41

�0Ð31

0Ð25

�0Ð42

0Ð04

0Ð14

0Ð48

PEP

8Ð60

�25Ð8

124

Ð35�1

9Ð03

�1Ð33

37Ð53

35Ð22

�49Ð5

020

Ð5416

Ð4435

Ð1945

Ð743Ð9

2�1

4Ð77

3Ð66

12Ð46

�58Ð8

044

Ð30 CONCLUSION

In this study, a small-scale, physically based, distributederosion model has been presented and found suitable tosimulate event-based runoff and erosion on agriculturalcatchments of limited extension. Test results have shownthat the model reproduces fairly well the temporal dynam-ics and spatial distributions of water and sediment dis-charge by identifying sediment sources and sinks withinthe catchment from calculations involving three nestedscales (agricultural plot, sub-catchment and catchment).

The model responded as expected and has a strongsensitivity to simulated variations in the proportion ofLMPs; it predicted decreasing soil losses when the per-centage of vegetated filters (grass strips) was increased.The sedimentological connectivity represented in themodel seems to provide better results related to total sed-iment outflow.

The model gives distributed information about erosionand sediment flow into the catchment. It can give infor-mation about the impact of LMPs on the sedimentologicalconnectivity. With this model, it is possible to test differ-ent spatial organizations of LMPs. Such a test can provideimportant information to planners and decision-makersabout agricultural catchment management.

Not all described problems related to water erosionmodelling were addressed during development of theMHYDAS-Erosion module. Some classical or specificlimitations remain: the number of rills on agriculturalplots is defined a priori as in the WEPP model; thedynamics of surface crusting during a rainfall eventis not described; and LMPs are supposed to modifysedimentological connectivity only and not to alter water-sediment pathways. More complex parameterizationswere possible but questionable as they are time-intensiveand increase the risk of equifinality. As voiced byBoardman (2006), ‘we should not be disappointed bymodelling performance (and limitations); models are stilldeveloping, and unsatisfactory results (and limitations)may indicate which aspects of models are most in needof further development’. The next steps of this work areto include the effects of LMPs on hydrological variablesand to quantify the sensibility of MHYDAS-Erosion tothe spatial distribution of LMPs.

ACKNOWLEDGEMENTS

We are grateful to the two anonymous reviewers forhelping and useful comments to improve the qualityof the manuscript. We also thank the ANR (NationalResearch Agency) for funding the project MESOEROS.The first author thanks the support of the NationalCounsel of Technological and Scientific Development(CNPQ-Brazil).

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