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Reply to Comment byDesmet and GoversHELENA MITASOVA , JAROSLAV HOFIERKA ,MARIAN ZLOCHA & LOUIS IVERSONPublished online: 06 Aug 2010.

To cite this article: HELENA MITASOVA , JAROSLAV HOFIERKA , MARIANZLOCHA & LOUIS IVERSON (1997) Reply to Comment by Desmet and Govers,International Journal of Geographical Information Science, 11:6, 611-618, DOI:10.1080/136588197242220

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int. j. geographical information science, 1997, vol. 11, no. 6, 611 ± 618

Reply

Reply to Comment by Desmet and Govers

HELENA MITAÂ SÏ OVAÂGeographic Modeling Systems Laboratory, Department of Geography,220 Davenport Hall, University of Illinois at Urbana-Champaign, Urbana,IL 61801, USA.

JAROSLAV HOFIERKAMestsky u rad, Department of City Information System, RadnicÏ ne Na m. 16,085 01 Bardejov, Slovak Republic

MARIA N ZLOCHAFaculty of Natural Sciences, Comenius University, Mlynska Dolina,84215 Bratislava, Slovak Republic

and LOUIS IVERSONUSDA Forest Service, 359 Main Road, Delaware, OH 43015, USA.

1. Introduction

Our paper `Modelling the topographic potential for erosion and deposition usingGIS’ addressed the issues of computation of topographic parameters for modellingerosion and deposition in complex terrain. We focused on adequate terrain representa-tion and analysis using high accuracy interpolation techniques and unit streampower (USP) theory for estimation of spatial distribution of both erosion anddeposition. Besides the USP based model we have included also the Universal SoilLoss Equation (USLE) in its standard 1D formulation with the goal to illustratethe limitations of this still commonly used approach. The Comment by Desmet andGovers focuses in particular on the USLE and suggests its modi® cation which,according to the authors, is an appropriate generalization for its use in complexterrain.

In the following paragraphs we analyse the proposed formulation by Desmetand Govers and point out its severe limitations when applying it to complextopographic conditions.

2. USLE and erosion modelling in complex terrain

2.1. Exclusion of depositiona l areasThe USLE represents a detachment-limited case of erosion on mostly uniform

hillslopes and it is not applicabl e to areas experiencing net deposition (Foster andWischmeier 1974, Gri� n et al. 1988, Foster 1990 ). The Comment does not considerthis important fact, and the proposed USLE modi® cation predicts high erosion inlocations where typically deposition is observed ( ® gure 1). In the application pre-sented by the Comment, a signi® cant portion of the study area was masked outusing a soil map, however, the necessity to identify and eliminate the depositional

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Figure 1. Modi® ed USLE LS factor suggested by Desmet and Govers for the entire areaused in the Comment, computed for grid points and visualized in GRASS GIS. Dashedline indicates the masked out area. The problematic issues are (a) high erosion predictedin areas of deposition, (b) areas with high topographic potential for erosion eliminatedas depositional areas, (c) cut-o� erosion at its highest rates in areas of concentrated ¯ ow.

areas when using the proposed USLE modi® cation has not been explained by theComment. Moreover, masking out the depositional areas, instead of performing atransport capacity analysis as suggested by Foster and Wischmeier (1974), leads toa result with numerous problems which we describe in more detail in § 3.1.

The inability to predict deposition was cited in our paper (Mitasova et al. 1996,pp. 630, 631, 635) as the main factor limiting the application of the USLE in GIS.The USLE modi® cation presented by Desmet and Govers does not address thisproblem at all.

2.2. Soil loss as a detachment rate at a segment and at a pointDesmet and Govers argue, that to apply the USLE for a complex 1D hillslope

it is necessary to use the equation (12) presented in the Comment. However, thisequation is just a ® nite di� erence approximation of mean erosion rate for a homogen-eous hillslope segment derived by Foster and Wischmeier (1974) from a more generalequation representing erosion rate at a point , upon which our use of the USLE wasbased. The equivalence of these two equations can be demonstrated by computingthe topographic factor (L S )i at a point i with the slope length l i and the size of thehillslope segment D approaching zero, leading to:

(LS )i= limD � 0 C (l i+D )t+1 Õ l

t+1i

D D S

22 13t= (t+1) (li/22 13)tS (1 )

which is the equation (1) used in our paper (apart from a constant (t+1) which doesnot in¯ uence the spatial distribution), and where S is the slope factor. Computation

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Reply 613

of erosion rate at a point is consistent with our concept of spatial modelling basedon continuous multi-variate ® elds which allows us to use powerful and e� cientalgorithms (often more accurate than the ® nite di� erence approximations) for compu-tation of topographic parameters and for landscape process simulations (Mitasovaand Ho® erka 1993, Mitas et al. 1996).

2.3. Extension to two-dimensional topographyOur paper is in agreement with Desmet’s and Govers’ argument that the standard

USLE is not appropriate for two-dimensional applications, as we have explicitlystated on pp. 633 and 635, and shown by the ® gures 3 and 4 in our original paper(Mitasova et al. 1996).

To remedy this problem, Desmet and Govers replace the slope length by upslopearea, use the equation in its ® nite di� erence approximation and assume that thesechanges make the USLE applicable to complex terrain. However, with these modi-® cations the new equation does not represent the standard or, as the comment says,classical’ USLE, which is a one-dimensional model, and, in fact, several problematicissues arise:

(a) As opposed to process-based models, empirical equations are not readilyapplicable to conditions di� erent from those for which they were developed.Because the USLE factors were derived from data for uniform hillslopes,there is no guarantee that these factors are valid if slope length is replacedby upslope area. Foster (1990, p. 430) writes: A major limitation of the USLEis that it does not explicitly represent hydrologic and erosion processes. Forexample, if an adjustment is made in the USLE to account for an e� ect ofruno� , every US LE factor, except perhaps R, must be modi® ed.’

(b) Similarly as for the one-dimensional formulation, the modi® ed USLE isrestricted to detachment-limited erosion, for which the impact of slope changecan be neglected (Foster and Wischmeier 1974). While this case is commonfor uniform hillslopes, it is not generally applicable to complex topography(Gri� n et al. 1988, Foster 1990 ). Terrain shape, represented by both pro® leand tangential curvatures (Mitasova and Ho® erka 1993) causes an increaseor decrease in water ¯ ow velocity with consequent change in the ratio betweendetachment and transport capacities. This change results in increased erosionin convex areas with accelerated ¯ ow and net deposition in concave areas(Foster 1990, Mitas et al. 1996, Mitas and Mitasova, forthcoming). Thisimportant phenomenon is completely neglected in the proposed USLE modi-® cation, thus making it incapable to predict erosion and deposition patternscommonly observed in landscapes and reported in numerous studies (e.g.,Sutherland 1991, Busacca et al. 1993, Quine et al. 1994 ).

3. Examples of application

3.1. Example presented in the CommentTo support their arguments, Desmet and Govers present an example of the USLE

application to an area with complex terrain; however, they compare approacheswhich represent di� erent aspects of erosion processes, in particular:

(a) Standard USLE, which we have shown not to be applicable to complexterrain (Mitasova et al. 1996, pp. 630, 633, 635);

(b) Modi® cation of the USLE representing erosion rates for hillslope segments

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H. Mita sÏ ova et al.614

for the detachment capacity-limited case which is applicable only to areaswithout deposition;

(c) USP-based index, which, according to Moore and Burch (1986 a) is a measureof the sediment transport capacity of ¯ owing water at the point of interest inthe landscape’. This index assumes transport capacity-limited erosion whichis di� erent from the case modelled by the USLE, as explained e.g., by Foster(1990), (1994), Mitas and Mitasova (forthcoming). To obtain the erosionrates for this case, a directional derivative (Mitasova et al. 1996) or ® nitedi� erence (Moore and Burch 1986 b) of the USP index must be computed.

The correlation between the modi® ed USLE LS factor and the USP index, presentedby Desmet and Govers, just shows that for certain situations, the values of topo-graphic factors for detachment and transport capacity are correlated which is dueto both being functions of run-o� and slope angle. However, this does not prove orindicate, that the modi® ed USLE is suitable for complex terrain. As we have alreadymentioned, the result computed by the modi® ed equation for the LS factor illustratesseveral problems associated with their modi® cation and application of the USLE( ® gure 1):

(a) Prediction of high erosion in concave areas where deposition is typicallyobserved, with part of these areas later masked out;

(b) Inadequate procedure used for elimination of depositional areas, where themasked out areas include terrain with high topographic potential for erosion;

(c) Unrealistic transition between the erosional and depositional areas, especiallyin hollows with concentrated ¯ ow when, according to their prediction, theerosion abruptly disappears at its peak value.

Therefore, the theoretical and practical aspects of the presented example do notjustify the general applicability of the modi® ed USLE to complex terrain.

3.2. Comparison with ® eld observationsWe have applied the standard USLE, modi® ed USLE, and the USP based model

to an area at the Scheyern Experimental Farm in Germany (Auerswald et al. 1996).For comparison, we included also the results of a process-based erosion simulationby the SIMWE model which is described elsewhere (Mitas et al. 1996, 1997, Mitasand Mitasova, forthcoming). The results of these models are evaluated using the® eld observations representing depths of colluvial deposits and loss of radio tracerswhich is proportional to erosion rate.

Both the standard and modi® ed USLE predict high erosion rates in areas withthe thickest layers of deposits ( table 1, ® gures 2 (a),(b)) . The highest erosion rates fora pro® le (table 1) are predicted at the middle section of the hillslope, well below theconvex area, which experienced the highest loss of radio tracers as well as the lowestyields (table 1, ® gure 2 (a),(b)). The USP-based model (Mitasova et al. 1996) re¯ ects

Figure 2. Index representing topographic potential for erosion and deposition for (a) standardUSLE, (b) modi® ed USLE, (c) USP based model, (d ) SIMWE model; draped overterrain with cross section showing measured depth of colluvial deposits (dark blue,10 Ö exaggerated ). Points represent the locations where radio tracers and crop yielddata used in table 1 were measured. Figure was created using Nviz programme forGRASS GIS (Brown and Astley 1996).

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Table 1. Field observations and topographic erosion ( Õ ) and deposition (+ ) indexes for acomplex pro® le shown in ® gure 2. Crop yields and tracer losses are averages fromthree similar pro® les. The values are non-dimensional and relative because theyare combined with di� erent types of constants representing rainfall, cover and soilproperties to estimate actual erosion rates.

Site location Bottom Middle Upper Top

Yield [dt ha Õ 1] 51 41 38 55Tracer change [%/year] +12 Õ 3 Õ 5 Õ 2Deposits depth[cm] +35 +22 0 +16

USLE LS Õ 1 9 Õ 11 0 Õ 4 0 Õ 1 5Mod. USLE LS Õ 3 0 Õ 8 5 Õ 2 0 Õ 0 8USP er Õ /dep+ +1 7 +0 1 Õ 4 2 Õ 0 9

the distribution of erosion and deposition signi® cantly better, with the highest neterosion predicted on the upper, convex part of the hillslope and deposition in itsconcave part ( ® gure 2 (c)). The comparison with location of colluvial deposits andlinear erosion features (see Mitas et al. 1996) shows that the USP-based modelcorrectly predicts both the highest deposition as well as the highest erosion in thehollow, while both USLE models predict only erosion in this area ( ® gure 2 (a),(b)).The USP-based model prediction is also close to the result computed by the SIMWEmodel which is based on the solution of bivariate, continuity of mass equation( ® gure 2 (d ) , Mitas et al. 1996, 1997, Mitas and Mitasova, forthcoming).

Observations similar to those indicated by the ® eld data from the ScheyernExperimental Farm were reported in numerous other papers (e.g., Busacca et al.1993, Sutherland 1991) including a paper co-authored by Desmet and Govers (Quineet al. 1994, p. 80), where the authors observed `maximum 137Cs loss from the slopeconvexities and evidence of 137Cs gain in both the slope concavities and along themain thalweg.’ This comparison with ® eld data clearly demonstrates that neither theoriginal nor the modi® ed USLE are generally applicable to complex terrain becausethey are not capable of describing commonly observed erosion/deposition patternsin landscapes.

4. Conclusion

Although the USLE is a useful tool for estimation of soil loss from essentiallyuniform hillslopes, the presented theoretical arguments and practical examples dem-onstrate, that our statement (Mitasova et al. 1996, p. 631), that direct applicationof USLE to complex terrain within GIS is rather restricted’ was correct. The proposedUSLE modi® cation is of limited value for modelling of erosion in landscapes becauseit neglects important physical processes, especially deposition, and the results clearlycontradict experimental data.

Almost 30 years ago Meyer and Wischmeier (1969, p. 227) wrote about the USLEand similar empirical equations: Since the purpose of these past equations was toprovide a planning tool for conservation technicians, brevity and simplicity weremore essential than great detail. They were not designed to meet the present needfor a detailed mathematical model to simulate soil erosion as a dynamic process andto describe soil movement at all locations along slope at any time.’ The advances inGIS technology, fast personal computers, as well as the experimental work associated

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with the Water Erosion Prediction Project-WEPP (Flanagan and Nearing, 1995)have created conditions for practical implementation of new models (e.g., Fosteret al. 1995, Mitas et al. 1996, Mitas and Mitasova, forthcoming, Hong andMostaghimi 1995) addressing the need for the replacement of empirical equationsby distributed process based models as identi® ed and explained by Meyer andWischmeier (1969).

Acknowledgments

We would like to thank Lubos Mitas, from the National Center forSupercomputing Applications, Urbana, Illinois for his insightful discussions. We alsoexpress our gratitude to Karl Auerswald from the Technical University Muenchen,Germany, and to Steven Warren from the USA Construction Engineering ResearchLaboratory (USA CERL) for providing the experimental data used in this reply andfor valuable discussions and correspondence.

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