Modelling interrill erosion in small cultivated catchments

HYDROLOGICAL PROCESSESHydrol. Process. 16, 3215–3226 (2002)Published online 25 September 2002 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/hyp.1098

Modelling interrill erosion in small cultivated catchments

O. Cerdan,* Y. Le Bissonnais, A. Couturier and N. SabyInstitut National de la Recherche Agronomique, Unite de Science du Sol, Centre de Recherche d’Orleans, BP 20619, 45166 Cedex, France

Abstract:

On the cultivated plateau of the loess belt area, the redistribution of precipitation is controlled by topography, culturaltechniques and sealing processes. Recent multi-scale studies carried out in northern France have provided quantitativereferences of interrill erosion rates. These experimental references have highlighted significant differences and evolutiontrends of mean sediment concentration in interrill flow between different defined categories of soil surface conditions,vegetation and rainfall characteristics. Thus, a classification of sediment concentration in interrill flow has beenelaborated (Cerdan O, et al. 2002. Earth Surface Processes and Landforms 27(2): 193–205). The objective of thispaper is to incorporate these results in the elaboration of the interrill erosion module of the STREAM model. Atthe field scale, this classification is used to assign a potential sediment concentration value to each agricultural field.For situations where there is no, or insufficient, experimental references, the classification is completed using a fuzzylogic approach. At the catchment scale, sediment is transported in proportion of the runoff volumes computed withthe STREAM runoff module, and is deposited as a function of topography (vertical curvature, slope gradient), orvegetation cover. Sediment concentration thresholds were defined after field experiments; these thresholds define thelimits above which sediment mass is deposited. The erosion component of the model has been tested with a data setfrom a small (ca 90 ha) intensively cultivated catchment. The quality of prediction given by the root-mean-squareerror (RMSE) is ca 8 t of precision on sediment delivery at the catchment outlet for observed sediment delivery thatgoes from 0Ð075 to 21 t (with an RMSE of ca 0Ð9 t for observed sediment delivery below 1 t and of ca 10Ð6 t forobserved sediment delivery between 1 and ca. 21 t). The evaluation also showed that the results at the outlet of thecatchment are more sensitive to the concentration thresholds of the deposition rules than to the potential sedimentconcentration values assigned to each field. Copyright 2002 John Wiley & Sons, Ltd.

KEY WORDS interrill erosion; catchment; modelling; deposition

INTRODUCTION

In the north-western Paris Basin, and in many cultivated areas of the loessian belt in northern Europe, localauthorities and inhabitants have to face chronic damage induced by water erosion (Auzet et al., 1990; Papyand Douyer, 1991; Boardman et al., 1994). In the Haute-Normandie region (France), besides the flooding ofurban areas, the main costs are attributable to the pollution of drinking water sources both by sediments andagricultural chemicals. Erosion prediction models are necessary for the implementation of effective and adaptedsoil conservation measures. For a decade or so, much effort has been invested in the development of physicallybased models that reflect current advancement in the comprehension of erosion processes. The advantage ofthese types of model is in their potential to describe the dynamics of the erosive response. Consequently,the main difficulties are to account for the spatial and temporal variations of soil properties, which canoccur over short distances according to the active processes on the hillslopes, and to reflect the complexinteractions among the controlling factors. Therefore, it is clear that a major limitation is the availability ofthe necessary abundant input data (Bryan, 2000). Recent publications on the evaluation of models in terms ofeffective prediction are not encouraging (Favis-Mortlock, 1998; Nearing and Nicks, 1998; Folly et al., 1999;

* Correspondence to: Dr O. Cerdan, Institut National de la Recherche Agronomique, Unite de Science du Sol, Centre de Recherche d’Orleans,BP 20619, 45166 Cedex, France. E-mail: [email protected]

Received 8 June 2001Copyright 2002 John Wiley & Sons, Ltd. Accepted 18 February 2002

3216 O. CERDAN ET AL.

Jetten et al., 1999; Takken et al., 1999). These attempts of model ‘blind evaluation’ lead one to considerthe eventuality of accurate erosion prediction on real landscape with ‘some degree of humility’ (Boardman,1998: 18). The preoccupation with development of physically based models has been important in generatingresearch, but as stated by Bryan (2000: 408), ‘it is yet not clear that all the processes and interactions involvedin soil erodibility can be physically modelled’. Accordingly, Parsons et al. (1997) concluded that process-based modelling may be useful for identification of our present poor understanding of erosion processes, butit may not be a realistic tool for predicting soil erosion. De Roo (1998), after having tested the coupling ofa process-based model with a geographical information system (GIS), reached the conclusion that there is aneed for much simpler coupled GIS erosion models simulating only the dominant processes operating in thecatchment.

In complex system modelling it is necessary to determine ‘basic physical principles’. The hydrologicregimes are driven by dominant processes, or a combination of dominant processes, that are dependent uponthe environment (Falkenmark and Chapman, 1989) and, for a given catchment, upon the period—in relation torainfall regimes, moisture condition variations (Ambroise, 1999) and cultural operations. With these dominantprocesses can be associated integrative parameters. On the cultivated plateau of the loess belt area, theredistribution of rainfall is controlled by the topography, cultural techniques (which lead to complete changein surface cover and soil surface properties), and by sealing processes. In order to characterize the dominantsurface processes leading to overland flow, several research efforts have been carried out in northern France(Boiffin et al., 1988; Papy and Boiffin, 1988, 1989; Auzet et al., 1990). Experiments have been implementedboth in the laboratory and in the field, at various scales ranging from small plots (Fox and Le Bissonnais, 1998;Martin, 1999; Chaplot and Le Bissonnais, 2000) up to catchments (Le Bissonnais et al., 1998). Thereby a setof reference runoff and erosion data was collected under a variety of different situations in terms of weatherconditions, surface state, land use and agricultural practices. On the basis of these reference data, a simpleevent-based runoff model (STREAM) able to simulate the effect of conservation measures in small cultivatedcatchments was elaborated (Souchere et al., 1998; Cerdan et al., 2001). To avoid overparameterization andthe associated uncertainties, the STREAM runoff model focuses on the more integrating parameters combinedin an expert-based approach by developing decision rules in the form of matching tables. To allow detailedspatial description of the catchment and better visualization of the output, the model is integrated in a GIS.

Recent multi-scale studies have provided quantitative references of interrill erosion (Benkhadra, 1997;Lecomte, 1999; Martin, 1999). These experimental references have highlighted significant differences andevolution trends of mean sediment concentration in interrill flow between different defined categories of soilsurface conditions, vegetation and rainfall characteristics. Thus a classification of sediment concentration ininterrill flow that accounts for parameter interactions has been elaborated (Cerdan et al., 2002a). The objectiveof this paper is to incorporate these results in the elaboration of the interrill erosion module of the STREAMmodel. The development of the interrill module follows two main steps: (i) at the field scale, the classificationof sediment concentration is used to quantify the sensitivity of the agricultural fields to interrill erosion; (ii) atthe catchment scale, the results of the STREAM runoff module are used to route the sediment. Finally, a firstevaluation of the model is carried out using catchment data.

CALCULATION OF POTENTIAL SEDIMENT CONCENTRATION AT THE FIELD SCALE

The calculation of potential sediment concentration at the field scale is based on the classification establishedby Cerdan et al. (2002a) presented in Table I. It has been elaborated after the analysis of a database composedof 673 natural rainfall events with sediment concentration measurements at the field or plot scale collectedunder a variety of different situations in terms of weather conditions, soil surface properties, vegetationcover and agricultural practices. The selected parameters are orientated roughness in four classes (0–1 cm;1–5 cm; 5–10 cm; >10 cm), vegetation cover in two classes (0–20%; 21–100%), surface sealing in fourclasses ((i) non-sealed: initial fragmentary structure with all fragments clearly distinguishable; (ii) structural

Copyright 2002 John Wiley & Sons, Ltd. Hydrol. Process. 16, 3215–3226 (2002)

MODELLING INTERRILL EROSION 3217

Table I. Potential sediment concentration range (g l�1) in the flow. Values in bold correspond to combination based on fieldexperiment references (Cerdan et al., 2002a), the others are evaluated with a fuzzy logic-based method

Roughness (cm) Vegetationcover (%)

Max 6 minintensity (mm h�1)

Non-sealed Structuralseal

Transitionalseal

Sedimentaryseal

0–1 0–20 0–10 0–1 1–5 0–1 1–510–40 0–1 5–10 1–5 5–10

>40 1–5 10–15 5–10 10–1521–100 0–10 0–1 0–1 0–1 0–1

10–40 0–1 1–5 0–1 1–5>40 1–5 5–10 1–5 5–10

2–5 0–20 0–10 0–1 0–1 0–1 0–110–40 1–5 10–15 5–10 10–15

>40 5–10 15–25 10–15 15–2521–100 0–10 0–1 1–5 0–1 1–5

10–40 0–1 5–10 1–5 5–10>40 1–5 10–15 5–10 10–15

5–10 0–20 0–10 1–5 5–10 5–10 10–1510–40 5–10 10–15 10–15 15–25

>40 10–15 25–35 15–25 25–3521–100 0–10 0–1 5–10 1–5 5–10

10–40 1–5 10–15 5–10 10–15>40 5–10 15–25 10–15 15–25

>10 0–20 0–10 1–5 10–15 5–10 10–1510–40 5–10 15–25 10–15 15–25

>40 10–15 25–35 25–35 25–3521–100 0–10 1–5 5–10 5–10 10–15

10–40 5–10 10–15 10–15 15–25>40 10–15 25–35 15–25 25–35

seal: altered fragmentary state with local structural seal; (iii) transitional seal: generalized structural seal withlocal appearance of depositional seal; (iv) sedimentary seal: continuous state with depositional seal), andrainfall event maximum 6 min intensity in three classes (0–10 mm h�1; 10–40 mm h�1; >40 mm h�1).More detailed descriptions of roughness and surface seal characterization can be found in Bresson and Boiffin(1990) and in Ludwig et al. (1995). Nearing and co-workers (Nearing et al., 1999; Nearing, 2000), on thebasis of numerous data from replicated plot pairs, showed that data from soil erosion plots contain a greatamount of unexplained variability. Cerdan et al. (2002a) also found that some variability still remains in thesediment concentration even with many replicates for the same parameter combinations. Therefore, instead ofa single value, a range of sediment concentration incorporating variation observed in the fields was assignedto each situation (Table I).

In this study, the experimental references cover most of the situations present in Table I that are likelyto generate runoff and erosion. The combinations of parameter classes that are not represented are eithersituations that have a low probability of occurrence (e.g. a sedimentary seal developed on a roughnessexceeding 10 cm and with a crop cover of 100%), or situations that are not very sensitive to runoff anderosion (Cerdan et al., 2002a). In such a context were expertise is available, it is relatively straightforward tofill in the missing values. However, for conditions where experimental references would be less accessible,the evaluation of ‘unknown situations’ can be enhanced with the use of multiple criteria analysis methods,and particularly the complete aggregation one (Pereira and Duckstein, 1993). It consists in ranking eachclass cj of the factors F present in Table I by giving them a mark between zero and one. For any cj,the notation �F�cj� represents the degree of contribution of the class cj of the factor F to ‘erosion’.�F�cj� D 0 indicates that cj of F does not contribute to ‘erosion’ and �F�cj� D 1 means that cj of



F is the most erosive class. Furthermore, �F�c1� > �F�c2� implies that class 1 is more erosive thanclass 2. In this framework, �F can be viewed as a membership function of a fuzzy set (Zimmermann,1985).

The next step is to aggregate the membership function of the fuzzy sets (i.e. the ranking of the classesof all the factors) in order to obtain a global evaluation of all the situations (i.e. of all the combinationsof the different classes). Dubois and Prade (1987) have assessed different fuzzy set aggregation operators.The parameterized and weighted mean has held our attention because it can account for interaction processesbetween the different factors. If �(situation) is the global evaluation, the parameterized and weighted meancan be expressed as:

��situation� D[∑

i

�pi�Fi�cj�˛

]1/˛

with∑

i

pi D 1 �1�

where pi is the weight associated with the factor i, �Fi�cj� is the membership function of the class j of the

factor i, and ˛ is a parameter to be defined during the system optimization.To solve Equation (1), the parameters pi, �Fi

�cj� and ˛ are optimized by maximizing the coefficient ofcorrelation between the available experimental data and the evaluated data. For the optimization, as suggestedby Yager (1993), the system is initiated by introducing human expertise. A value is pre-allocated by the expertto the different classes according to their degree of influence (e.g. for the vegetation cover factor, the classVc1 (0–20%) is allocated 0Ð8 and the class Vc2 (21–60%) is 0Ð2, Vc2 being evaluated as less contributingto ‘erosion’ than Vc1). Once the system is optimized, the estimated parameter values are used to calculateall the situations present in Table I.

SEDIMENT DELIVERY AT THE CATCHMENT SCALE

Table I describes potential sediment concentration ranges in the flow for various land uses and soil surfaceconditions on plots from 10 to 500 m2 and an average slope gradient of ca 3Ð1. If we plot the sedimentconcentration versus runoff volume for the same events that compose the database, it shows a decrease insediment concentration with an increase in runoff volume (Figure 1). At the plot scale, and in the range ofour experimental conditions, the sediment load is therefore not transport limited but is detachment limited.At that scale no deposition has been observed.

However, at the catchment scale, deposition processes have to be taken into account. Deposition occurswhen sediment load in the flow exceeds its transport capacity. In the STREAM model, decrease intransport capacity has been taken into account according to change in topography (vertical curvature,slope gradient), or reduction of the flow rate either by increase in infiltration rate or by increase invegetation cover. Deposition also occurs along the flow pathway in runoff tailing, which is not readilytaken into account in the model. Figure 2 displays a general flow diagram of the STREAM interrill erosionmodel.

Sediments are routed with the flow. Two different cases are considered, whether the simulated pixelcorresponds to: I, an area that has the potential to infiltrate a part or the totality of the upslope runon;or II, an area producing runoff.

I—if �R � It�a < 0, for a pixel ˛ with i upslope pixels then:

md˛ D∑

mui C�R � I˛t�a

∑mui∑

Vui

where md˛ is the mass of sediment leaving the pixel ˛, mui is the mass of sediment coming from upslopepixel i, Vui is the runon volume from upslope pixel i, R is the rainfall height, I˛ is the infiltration capacityof the pixel ˛, t is the rainfall duration, and a is the pixel area.



0

10

20

30

40

50

60

70

80

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00

Runoff volume (l)

Sed

imen

t con

cent

ratio

n (g

/l)

Figure 1. Sediment concentration in the flow versus runoff volume for 500 natural rainfall-runoff events at the plot scale. (Plot size rangingfrom 10 to 500 m2; the volumes have been normalized for an area of 20 m2�

II—if �R � It�a ½ 0, for a pixel ˛ with i upslope pixels:

md˛ D∑

mui C �R � I˛t�aSC˛

where SC˛ is the potential sediment concentration of pixel ˛.Sediments are deposited according to change in topography (vertical curvature, slope gradient), or change

in vegetation cover. Topographical thresholds have been defined after field observations made by Cerdan et al.(2002b). From a discriminant analysis carried out on deposit location, it appeared that pixels that containeddeposits in relation with topography had a slope intensity <2% and a vertical curvature < � 0Ð55. Belowthese thresholds a sediment mass that corresponds to a concentration in excess of 10 g l�1 is deposited.For the deposits induced by vegetation cover, a distinction has been made between permanent grasslandand agricultural fields with a high vegetation cover. Lecomte (1999) has studied the effect of a 6 m longvegetated filter strip, located downslope of a 60 m long plot, on runoff and interrill erosion. Results show thatvegetative filter strips had a strong effect on sediment transport with mean measured sediment concentrationat the outlet below 2 g l�1 (Figure 3). These concentrations correspond to those reported in the literature forsimilar experiments (e.g. Van Dijk et al., 1996). A threshold value of 5 g l�1 was determined above whichcorresponding exceeding sediment mass is deposited.

At the edge of well-developed crops deposits are also often observed (Takken et al., 1999; Beuselincket al., 2000; Cerdan et al., 2002b). On the basis of measurements made at the outlet of plots with vegetationcover exceeding 61 % (Table II), a threshold value of sediment concentration of 10 g l�1 was chosen.

Therefore, for each pixel ˛, ifmd˛

�R � I˛t�a C Vui> SCt

then md˛ D [�R � I˛t�a C Vui]SCt, With SCt the threshold value of sediment concentration above whichdeposition starts. Figures 4 and 5 display an example of a rainfall event simulated with the STREAM model.



Infiltration moduleRunoff volume/height

Potential sedimentconcentration in the flow

Runoff direction

Surface sealingRoughness

Vegetation cover

Rainfall duration and meanintensity

Slope aspect, tillage direction, roughnessWaterways (ditches, backfurrow)

Rainfall maximum 6-minintensity

EntrainmentDeposition

Vegetation coverSlope, Vertical curvature

Figure 2. Flow diagram of the STREAM interrill erosion model

EVALUATION OF THE MODEL

The evaluation of the model has been carried out with a data set from a small (ca 90 ha) intensively cultivatedcatchment where erosion is mainly reported as being of the form interrill. The exception is for the culturalseason 1999–2000, where two sets of extreme events have led to rill and ephemeral gully erosion (Cerdanet al., 2002b). The Blosseville catchment is located in the northwestern part of the Paris Basin (Pays deCaux). The area is covered by Luvisols, which are very sensitive to soil sealing because of low clay content(13 to 17%) and low organic matter content (1 to 2%). The soil characteristics show very little variabilitywithin the catchment. The topography is relatively smooth : areas with slope gradients greater than 5% accountfor less than 10% of the total catchment surface. The outlet of the catchment is equipped with a calibratedflume and an automatic water level gauge allowing continuous runoff output measurement. Rainfall eventsused for the evaluation are presented in Table III. Sediment delivery has been calculated from water-loadedsamples collected manually at the outlet of the catchment. Manual measurements have the advantage ofallowing flexible adaptation of sampling frequency to runoff rate variations. However, to obtain the wholesedigraph, this implies that one needs to be present on the monitored site for the duration of the rainfall event,which in our context, where rainfall duration can exceed 24 h, is not always possible. The STREAM runoffcalculation is not dynamic and works with rainfall inputs at the time step of the event, such as rainfall eventmean intensity. As a consequence, when sediment concentration measurements do not cover the entire rainfall



0.00

1.00

2.00

3.00

4.00

5.00

6.001 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Rainfall events number

Sed

imen

t con

cent

ratio

n (g

/l)

1 to 22: 20% of vegetation cover23 to 28: 40% of vegetation cover29 to 30: 60% of vegetation cover31 to 31: 80% of vegetation cover32 to 35: 100% of vegetation cover

Figure 3. Sediment concentration below a 6 m grass strip on 60 m long plots (after Lecomte (1999))

Table II. Sediment concentration (g l�1)at the outlet of plots (ranging from 20to 500 m2 in size) with vegetation cover

between 61 and 100%

Number of observations 167Mean 3Ð32Median 1Ð33Standard deviation 6Ð17

event, the effective duration of the event used for the simulation was calibrated so as to reproduce correctlythe measured runoff volume that corresponds to the sampled rainfall. Therefore, only the erosion componentof the model is tested in this evaluation.

For the evaluation of the model, two sets of simulations have been realized. One with the minimum valueof the potential sediment concentration range presented in Table I, and one with the maximum. The relativeerrors, as well as the other average index of goodness-of-fit, have been calculated on the average of the twosediment deliveries obtained with the maximum and minimum values of the potential sediment concentrationrange (Tables IV to VI).

The observed sediment delivery values at the catchment outlet vary over several orders of magnitude, from75 kg up to 21Ð3 t. It is therefore difficult to find an index of goodness-of-fit for a set of simulations ofdifferent events. Most of the index values for a series of simulations consist of an average of the differentindex values calculated for each simulation (Table V). Thus, the goodness-of-fit determined for a small erosiveevent is given as equal an importance as at calculated for a major erosive event. For example, the qualityof prediction given by the root-mean-square error (RMSE) is ca 8 t of precision on sediment delivery at thecatchment outlet for an observed sediment delivery that goes from 0Ð075 to 21 t. In fact, quality of predictionis a function of sediment yield importance, with an RMSE of ca 0Ð9 t for an observed sediment deliverybelow 1 t and of ca 10Ð6 t for an observed sediment delivery between 1 and ca 21 t (Table VI). RMSE is



Blosseville catchmentevent of the 26/10/1994

< 1

1−5

5−10

10−15

15−25

> 25

potential sedimentconcentration (g/l)

field boundaries

0 250 500 m

Scale

Figure 4. Map of potential sediment concentration for the simulated rainfall event

Blosseville catchmentevent of the 26/10/1994

FR

0−1

1 −5

5−40

40−350

350−3000

3000−25000

soil loss (kg)

deposits > 0.02 m3

catchment boundary

field boundaries

F flume

R raingauge

0 250 500 m

Scale

Figure 5. Map of the soil losses for the simulated rainfall event



Table III. Characteristics of the rainfall events used for the evaluation

Date Rainfallheight(mm)

48 hantecedent

rainfall

Max 6 minintensity

(mm h�1)

Meanintensity

(mm h�1)

Duration(h)

Runoffvolume (l)

Max Q(l s�1)

Sedimentdelivery (t)

13/10/93 37Ð6 40Ð9 19Ð2 2Ð3 7Ð03 6 218 003 409Ð84 21Ð3314/10/93 3Ð3 42Ð3 2Ð4 0Ð8 0Ð95 59 395 6Ð35 0Ð0715/10/93 10Ð9 41Ð3 22Ð8 4Ð4 1Ð75 1 593 681 271Ð64 5Ð1522/12/93 7Ð4 28Ð0 14Ð4 0Ð9 2Ð6 431 548 46Ð70 2Ð9524/05/94 17Ð5 7Ð3 6 1Ð3 3Ð38 1 396 520 97Ð04 0Ð9426/10/94 12Ð0 24Ð4 24 1Ð6 5Ð00 99 220 8Ð83 0Ð1826/10/94 28Ð3 32Ð8 27Ð6 2Ð4 9Ð60 2 434 736 221Ð84 13Ð3827/10/94 10Ð2 58Ð1 25Ð2 1Ð3 4Ð05 476 544 19Ð79 1Ð0026/01/95 8Ð0 33Ð3 6 2Ð5 1Ð6 1 244 075 60Ð38 5Ð8619/12/94 4Ð6 6Ð8 13Ð2 1Ð9 0Ð7 154 006 46Ð42 0Ð3216/02/95 12Ð2 2Ð9 20 1Ð4 3Ð0 2 542 440 564Ð67 14Ð31

Table IV. Observed and predicted sediment delivery. Simulated maximum and simulated minimum refer tothe simulated sediment delivery obtained with the maximum and minimum value of the potential sediment

concentration range

Date Observedsediment

delivery (t)

Simulatedmaximum (t)

Simulatedminimum (t)

Mean (t) Relative error(%) on themean value

13/10/93 21Ð33 41Ð25 41Ð27 41Ð26 93Ð514/10/93 0Ð07 0Ð48 0Ð51 0Ð50 562Ð715/10/93 5Ð15 15Ð97 15Ð99 15Ð98 210Ð322/12/93 2Ð95 4Ð29 4Ð42 4Ð36 47Ð724/05/94 0Ð94 0Ð16 1Ð98 1Ð07 13Ð926/10/94 0Ð18 1Ð21 1Ð21 1Ð21 571Ð426/10/94 13Ð38 24Ð35 24Ð38 24Ð37 82Ð127/10/94 1Ð00 4Ð99 5 4Ð99 395Ð026/01/95 5Ð86 1Ð19 1Ð56 1Ð37 328Ð919/12/94 0Ð32 2Ð89 6Ð39 4Ð64 20Ð816/02/95 14Ð31 15Ð66 24Ð04 19Ð85 38Ð8

Table V. Average index of goodness-of-fit

Coefficient ofdetermination

R2

Mean errorME

RMSE AUE

n∑iD1

� OYi � Y�2

n∑iD1

�Yi � Y�2

1n

n∑iD1

[Yi � OYi]

√√√√ 1n

n∑iD1

[Yi � OYi]2 1

n

n∑iD1

100 ð∣∣∣∣∣Yi � OYi

Yi

∣∣∣∣∣

most influenced by the biggest erosive event; when this event is removed, it decreases from ca 8 t to 5Ð4 t(Table VI). Conversely, the average unsigned error (AUE) is ca 375 % for an observed sediment deliverybelow 1 t and of ca 82 % for an observed sediment delivery between 1 and ca 21 t (Table VI). The AUE ismost influenced by the smallest erosive event.



Table VI. Calculation of index of goodness-of-fit for different evaluation data sets

Index A: all events(n D 11)

B: sedimentdelivery

�1 t (n D 5)

C: sedimentdelivery

>1 t (n D 6)

Without thesmallest

event

Without thebiggestevent

A B A C

r 0Ð96 0Ð67 0Ð93 0Ð96 0Ð59 0Ð92 0Ð84R2 0Ð92 0Ð45 0Ð87 0Ð92 0Ð34 0Ð85 0Ð70ME (t) �4Ð92 �1Ð24 �7Ð92 �5Ð37 �1Ð55 �3Ð42 �5Ð51RMSE (t) 7Ð91 0Ð86 10Ð57 8Ð29 1Ð06 5Ð39 7Ð38AUE (%) 215Ð01 374Ð37 82Ð21 180Ð2 327Ð3 227Ð17 79Ð96

Another way to evaluate the model is to plot simulated versus observed sediment delivery and let thepotential user decide whether or not to reject the model, as a given error can be perfectly adequate for oneuser but totally unacceptable for another (Quinton, 1994). Figure 6 shows a plot of the average of the twosediment deliveries obtained with the maximum and minimum values of the potential sediment concentrationrange, with vertical bars showing the difference between the minimum and maximum. Although for someclasses the difference in sediment concentration between the two values can be important (5 to 10 g l�1), thesimulated maximum and minimum erosion deliveries at the outlet are very similar for most of the events.This effect is the result of the concentration threshold of the deposition rules, even though these thresholdsare determined on the basis of upper limits observed in field conditions.

At the catchment scale, deposition processes can have a more important effect on sediment delivery at theoutlet than the erodibility of the areas emitting sediment particles, even for an intensely cultivated catchmentwith very little grassland or forest.

CONCLUSION

An interrill erosion module of the STREAM model has been elaborated. The model is based on recent multi-scale studies, which have provided quantitative references of interrill erosion. The results of these experimental

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30

Measured erosion (T)

Sim

ulat

ed e

rosi

on (

T)

Figure 6. Simulated versus measured sediment delivery at the outlet of the Blosseville catchment for 11 rainfall events. Plotted are theaverage of the two sediment deliveries obtained with the maximum and minimum values of the potential sediment concentration range;

vertical bars show the difference between minimum and maximum



references have been incorporated in decision rules in the form of matching tables that incorporate thedominant parameters influences and interactions. At the field scale, a potential sediment concentration valueis determined as a function of vegetation cover, orientated roughness, surface sealing and the maximum 6 minintensity of the rainfall event. As shown in recent studies (e.g. Nearing et al., 1999; Cerdan et al., 2002a), datafrom soil erosion plots contain a great amount of unexplained variability; therefore, instead of a single value, arange of sediment concentration incorporating variation observed in the field was assigned to each situation. Atthe catchment scale, sediment is transported in proportion to the runoff volumes computed with the STREAMrunoff module and particles are deposited according to topography (vertical curvature, slope gradient), or tovegetation cover rates. Sediment concentration thresholds were defined after field experiments; these thresholdsdefine the limits above which sediment mass is deposited. For the deposits induced by vegetation cover, adistinction has been made between permanent grassland and agricultural fields with a high vegetation cover.

The erosion component of the model has been tested with a data set from a small (ca 90 ha) intensivelycultivated catchment. The quality of prediction given by the RMSE is ca 8 t of precision on sediment deliveryat the catchment outlet for observed sediment delivery that goes from 0Ð075 to 21 t (with an RMSE ofca 0Ð9 t for observed sediment delivery below 1 t and of ca 10Ð6 t for observed sediment delivery between1 and ca 21 t). From the evaluation, it also appeared that the results at the outlet are more sensitive to theconcentration threshold of the deposition rules than to the potential sediment concentration values assigned toeach field. The use of sediment concentration thresholds allows one to modulate the transport capacity of theflow as a function of topographical factors and to account for flow resistance by vegetation when instantaneousvalues of runoff and sediment discharge are not available. However, the definition of the thresholds can beproblematic with regard to the nature of the available experimental references. Even with databases that covera wide range of situations, they do not explicitly include direct flow hydraulic property measurements, whichare difficult to obtain in natural conditions. Therefore, the thresholds have been determined on the basisof values above which deposition has always been observed. This ‘minimum assumption’ approach, whichcan be refined provided the necessary reference data become available, explains the general overestimationtrend of the model (Figure 6). The results of this study suggest that there is a need for a sediment transportformula that could satisfactorily be applied with non-instantaneous hydraulic data, and, in particular, one thatenables the simulation of the progressive decrease in sediment concentration when loaded water flows throughgrassland. The importance of deposition in interrill erosion processes also highlights the limits of approachesbased only on erodibility parameters, which may not be relevant when modelling erosion processes at thecatchment scale, even when sediment load is detachment limited.

ACKNOWLEDGEMENT

This work was funded by the EU-CEO Research Project FLOODGEN (ENV.4 CT96-0368), the PESERAproject (Pan European Soil Erosion Risk Assessment, QLK5-CT-1999-01323) and by the PNRH (RIDESproject).

REFERENCES

Ambroise B. 1999. La dynamique du cycle de l’eau dans un bassin versant. Processus, Facteurs, Modeles . H.G.A.: Bucharest; 200 pp.Auzet AV, Boiffin J, Papy F, Maucorp J, Ouvry JF. 1990. An approach to the assessment of erosion forms and erosion risk on agricultural

land in the northern Paris Basin, France. In Soil Erosion on Agricultural Land . Boardman J, Foster DL, Dearing JA (eds). Wiley:Chichester; 383–400.

Benkhadra H. 1997. Battance, ruissellement et erosion diffuse sur les sols limoneux cultives: determinisme et transfert d’echelle de la parcelleau petit bassin versant. Universite d’Orleans, Thesis 214 pp.

Beuselinck L, Steegen A, Govers G, Nachtergaele J, Takken I, Poesen J. 2000. Characteristics of sediment deposits formed by intenserainfall events in small catchments in the Belgian Loam Belt. Geomorphology 32: 69–82.

Boardman J. 1998. Modelling soil erosion in real landscapes: a Western European perspective. In Modelling Soil Erosion by Water .Boardman J, Favis-Mortlock D (eds). Springer-Verlag: Berlin, Heidelberg; 17–29.



Boardman J, Ligneau L, De Roo A, Vandaele K. 1994. Flooding of property by runoff from agricultural land in northwestern Europe.Geomorphology 10: 183–196.

Boiffin J, Papy F, Eimberck M. 1988. Influence des systemes de culture sur les risques d’erosion par ruissellement concentre. I—analysedes conditions de declenchement de l’erosion. Agronomie 8: 663–673.

Bresson LM, Boiffin J. 1990. Morphological characterisation of soil crust development stages on an experimental field. Geoderma 47:301–325.

Bryan RB. 2000. Soil erodibility and processes of water erosion on hillslope. Geomorphology 32: 385–415.Cerdan O, Souchere V, Lecomte V, Couturier A, Le Bissonnais Y. 2001. Incorporating soil surface crusting processes in an expert-based

runoff and erosion model STREAM (Sealing Transfer Runoff Erosion Agricultural Modification). Catena 46: 189–205.Cerdan O, Le Bissonnais Y, Souchere V, Martin P, Lecomte V. 2002a. Concentration of suspended particles in interrill flow. Earth Surface

Processes and Landforms 27(2): 193–205.Cerdan O, Le Bissonnais Y, Couturier A, Bourennane H, Souchere V. 2002b. Rilling development on cultivated hillslopes during two

extreme events. Soil and Tillage Research submitted for publication.Chaplot V, Le Bissonnais Y. 2000. Field measurements of interrill erosion under different slopes and plot sizes. Earth Surface Processes

and Landforms 25: 145–153.De Roo APJ. 1998. Modelling runoff and sediment transport in catchments using GIS. Hydrological Processes 12: 905–922.Dubois D, Prade H. 1987. Theorie des Possibilites . Masson: Paris.Falkenmark M, Chapman T. 1989. Comparative Hydrology—an Ecological Approach to Land and Water Resources . UNESCO: Paris; 479 pp.Favis-Mortlock DT. 1998. Evaluation of field-scale erosion models on the UK South Downs. In Modelling Soil Erosion by Water . Boardman J,

Favis-Mortlock D (eds). Springer-Verlag: Berlin, Heidelberg; 43–53.Folly A, Quinton JN, Smith RE. 1999. Evaluation of the EUROSEM model using data from the Catsop watershed, the Netherlands. Catena

37: 507–519.Fox DM Le Bissonnais Y. 1998. A process-based analysis of the influence of aggregate stability on surface crusting, infiltration, and interrill

erosion. Soil Science Society of America Journal 62(3): 717–724.Jetten V, De Roo A, Favis-Mortlock D. 1999. Evaluation of field-scale and catchment-scale soil erosion models. Catena 37: 521–541.Le Bissonnais Y, Fox D, Bresson L-M. 1998. Incorporating crusting processes in erosion models. In Modelling Soil Erosion by Water .

Boardman J, Favis-Mortlock D (eds). Springer-Verlag: Berlin, Heidelberg; 237–246.Lecomte V. 1999. Transfert de produits phytosanitaires par le ruissellement et l’erosion de la parcelle au bassin versant: processus,

determinisme et modelisation spatiale. Thesis, ENGREF; 242 pp.Ludwig B, Boiffin J, Chadoeuf J, Auzet AV. 1995. Hydrological structure and erosion damage caused by concentrated flow in cultivated

catchments. Catena 25: 227–252.Martin P. 1999. Reducing flood risk from sediment-laden agricultural runoff using intercrop management techniques in northern France.

Soil and Tillage Research 52: 233–245.Nearing MA. 2000. Evaluating soil erosion models using measured plot data: accounting for variability in the data. Earth Surface Processes

and Landforms 25: 1035–1043.Nearing MA, Nicks AD. 1998. Evaluation of the Water Erosion Prediction Project (WEPP) model for hillslopes. In Modelling Soil Erosion

by Water . Boardman J, Favis-Mortlock D (eds). Springer-Verlag: Berlin, Heidelberg; 43–53.Nearing MA, Govers G, Norton LD. 1999. Variability in soil erosion data from replicated plots. Soil Science Society of America Journal

63(6): 1829–1835.Papy F, Boiffin J. 1988. Influence des systemes de culture sur les risques d’erosion par ruissellement concentre. II—evaluation des possibilites

de maıtrise du phenomene dans les exploitations agricoles. Agronomie 8(9): 745–756.Papy F, Boiffin J. 1989. The use of farming systems for the control of runoff and erosion. In Soil Erosion Protection Measures in Europe.

Schwertmann U, Rickson RJ, Auerswald K (eds). Catena Verlag: Cremlingen; 29–38.Papy F, Douyer C. 1991. Influence des etats de surface du territoire agricole sur le declenchement des innondations catastrophiques.

Agronomie 11(3): 201–215.Parsons AJ, Wainwright J, Abrahams AD, Simaton RJ. 1997. Distributed dynamic modelling of interrill overland flow. Hydrological

Processes 11: 1833–1859.Pereira JMC, Duckstein L. 1993. A multiple criteria decision-making approach to GIS-based land suitability evaluation. International Journal

of Geographical Information Systems 7(5): 407–424.Quinton JN. 1994. Validation of physically based erosion models, with particular reference to EUROSEM. In Conserving Soil Resources:

European Perspectives . Rickson RJ (ed.). CAB International: Wallingford, Oxfordshire; 300–313.Souchere V, King D, Daroussin J, Papy F, Capillon A. 1998. Effects of tillage on runoff direction: consequences on runoff contributing area

within agricultural catchments. Journal of Hydrology 206: 256–267.Takken I, Beuselinck L, Nuchtergaele J, Govers G, Poesen J, Degraer G. 1999. Spatial evaluation of a physically-based distributed erosion

model (LISEM). Catena 37: 431–447.Van Dijk PM, Kwaad FJPM, Klapwijk M. 1996. Retention of water and sediment by grass strips. Hydrological Processes 10(8): 1069–1080.Yager RR. 1993. Families of OWA operators. Fuzzy Sets and Systems 59: 125–148.Zimmermann HJ. 1985. Fuzzy Set Theory and its Application. Martinous Nijhoff: Boston, MA, USA.


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Modelling interrill erosion in small cultivated catchments