Modification of the RUSLE slope length and steepness factor (LS-factor) based on rainfall experiments at steep alpine grasslands

Method

Article

Modi

fication

of

the

RUSLE

slope

length

and

steepness

factor

(LS-factor)

based

on

rainfall

experiments

at

steep

alpine

grasslands

Simon

Schmidt

a,

*

,

Simon

Tresch

b,c,d

,

Katrin

Meusburger

e

a

EnvironmentalGeosciences,UniversityofBasel,Bernoullistrasse30,CH-4056Basel,Switzerland b

DepartmentofSoilSciences,ResearchInstituteofOrganicAgriculture(FiBL),Ackerstrasse113,CH-5070 Frick,Switzerland

c

FunctionalEcologyLaboratory,InstituteofBiology,UniversityofNeuchâtel,RueEmile-Argand11,CH-2000 Neuchâtel,Switzerland

d_{BiodiversityandConservationBiology,SwissFederalInstituteforForest,SnowandLandscapeResearch} (WSL),Zürcherstrasse111,CH-8903Birmensdorf,Switzerland

e

ForestSoilsandBiogeochemistry,SwissFederalInstituteforForest,SnowandLandscapeResearch(WSL), Zürcherstrasse111,CH-8903Birmensdorf,Switzerland

ABSTRACT

Theslopelengthandslopesteepnessfactor(LS-factor)isoneoffivefactorsoftheUniversalSoilLossEquation(USLE)

anditsrevisedversion(RUSLE)describingtheinfluenceoftopographyonsoilerosionrisk.TheLS-factorwas

originallydevelopedforslopeslessthan50%inclinationandhasnotbeentestedforsteeperslopes.Toovercomethis

limitation,weadaptedbothfactorsslopelengthLandslopesteepnessSforconditionsexperimentallyobservedat

Swissalpinegrasslands.ForthenewL-factor(Lalpine),amaximalflowpaththreshold,correspondingto100m,was

implementedtotakeintoaccountshortrunoffflowpathsandrapidinfiltrationthathasbeenobservedinour

experiments.FortheS-factor,afittedquadraticpolynomialfunction(Salpine)hasbeenestablished,compilingthe

mostextensiveempiricalstudies.Asamodelevaluation,uncertaintyintervalsarepresentedforthismodified

S-factor.Weobservedthatuncertaintyincreaseswithslopegradient.Insummary,theproposedmodificationofthe

LS-factortoalpineenvironmentsenablesanimprovedpredictionofsoilerosionriskincludingsteepslopes.

Empirical experiments (rainfall simulation, sediment measurements) were conducted on Swiss alpine

grasslandstoassessthemaximalflowlengthandslopesteepnessfactor(S-factor).

Flowaccumulationislimitedtoamaximalflowthreshold(100m)atwhichoverlandrunoffisrealisticinalpine

grassland.

SlopesteepnessfactorismodifiedbyafittedS-factorequationfromexistingempiricalS-factorfunctions.

©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://

creativecommons.org/licenses/by/4.0/).

*Correspondingauthor.

E-mailaddresses:[email protected],[email protected],[email protected](S.Schmidt),

simon.tresch@fibl.org(S.Tresch),[email protected](K.Meusburger).

https://doi.org/10.1016/j.mex.2019.01.004

2215-0161/©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http:// creativecommons.org/licenses/by/4.0/).

ContentslistsavailableatScienceDirect

MethodsX

ARTICLE INFO

Methodname:Lalpine,Salpine,LSalpine

Keywords:RevisedUniversalSoilLossEquation,Erosionmodeling,Switzerland,Terrainfeatures,Maximal,Flowlength

Articlehistory:Received13November2018;Accepted19January2019;Availableonline26January2019

Speci_ficationsTable

Subjectarea EnvironmentalScience

Morespecificsubjectarea Soilerosionmodeling

Methodname -Lalpine

-Salpine -LSalpine Nameandreferenceof

originalmethod

USLELS-factor:Wischmeier,W.H.,&Smith,D.D.(1978).Predictingrainfallerosionlosses. Washington.

S-factor:McCool,D.K.,Brown,L.C.,Foster,G.R.,Mutchler,C.K.,&Meyer,L.D.(1987).Revised SlopeSteepnessFactorfortheUniversalSoilLossEquation.TransactionsoftheASAE,30, 1387–1396.https://doi.org/doi:10.13031/2013.30576.

S-factor:Smith,D.D.,&Whitt,D.(1948).Estimatingsoillossesfromfieldareas.Agricultural Engineering,29,394–396.

Resourceavailability -SAGAGIS(http://www.saga-gis.org;[31])

-RSAGA(https://cran.r-project.org/web/packages/RSAGA/index.html;[30])

Methoddetails

ExistingapproachesforS-andL-factorparametrization

TheLS-factorisaproductoftheslopelength(L-)andtheslopesteepness(S-factor).Themost widelyusedslopelengthfactorrepresentstheratioofobservedsoillossrelatedtothesoillossofa standardizedplot(22.13m).OriginallyWischmeierandSmith[1]definedtheL-factorasEq.(1):

L¼ ₂₂

l

_:13
m

ð1Þ where

l

representsthelengthoftheslopeinmetersandmthedifferentslopesteepness.Later,Eq.(2)

wasadaptedfortheRUSLE-approachtobetterdescribesoillosswithincreasingslope steepness. Desmetand Govers [2] transformed theoriginal L-factor(Eq. (1))into a GIS-approach(Eq. (2)) consideringtheflowaccumulationandaddingaratioofrilltointerrillerosion(Eq.(3)):

Li;j¼

Ai;jin þD2

 mþ1

Ami;jinþ1

Dmþ2Xm_i;j22:13m ð2Þ

whereAi,j-inistheflowaccumulationinm2attheinletofagridcell(i,j).Disthegridcellsizeinmand

Xi;jequalstosinai;jþcosai;jwhereai,jistheaspectofthegridcell(i,j).Thecoefficientm(Eq.(3))

representstheratioofrillandinterrillerosionandiscalculatedbytheβ-value(Eq.(4)):

witharangebetween0(ratioofrilltointerrillerosioncloseto0)and1.

b

¼ 0:0896sinu

0:56þ3ðsin

u

Þ0:8

h i ð4Þ

where

u

istheslopeangleindegrees.

FortheS-factor,mostoftentheempiricfunctionproposedbyMcCooletal.[3]isusedtodetermine theslope steepnessfactorin theRevisedUniversalSoil LossEquation (RUSLE).McCoolet al.[3] differentiatetherelationbetweensoillossandslopesteepnessinradians(s)withtwofunctions.One forslopeswithaninclinationlessthan9%andtheothergreaterorequal9%.Thefunctionsareas follows:

S¼10:8sþ0:03 for slope steepness in percent<9% ð5Þ S¼16:8s0:50 for slope steepness in percent9% ð6Þ TheS-factorafterMcCooletal.[3]isparticularrecommendedforareaswithlowsummerrainfall amounts[4].ManyotherempiricalS-factorsweredevelopedsincethe1940s(Table1)butallS-factors haveincommonthatempiricalevidenceandthusvalidityislimitedtoslopegradientslessthan50%. ProposedadaptionoftheL-factor

Often,GISmodeledpotentialflowpathlengthonslopes,expressedasflowaccumulationina GIS-environment,isdrivenbygravityandtheoreticallyunlimited[13].Inparticularcases,thesepotential flowpathlengthscanreachmanykilometersandenormousrunoffvolumes.Theflowaccumulation canbeconstrainedbystreetsorhousesasendingpointsofthepotentialflowpathsasdiscussedby Winchelletal.[14].

In2016,weconducted19differentrainfallsimulationexperimentsonsouthfacingslopesinanalpine environment(ValPiora,Switzerland)withdifferentconditionsregardingsoilmoisture(dry,moist), steepness(36–82_{),and vegetation(low,medium,fullvegetationcover)to observetheflowpath}

lengths.Therainfallsimulationswererealizedwith anEijkelkampmini rainfall simulator (type M1.09.06. E,Eijkelkamp,NL;Fig.1)forerosiontestswitha rainfallintensityof640mm/handanenergyof 4Jmm1m2.ThisrainfallenergyiscomparablewiththeaveragerainfallenergyofValPiora(station Piotta;5.6Jmm1m2;[15]).Regardlessoftheconditions,ourobservationsrevealedshortsurfaceflow pathlengthsatthescaleofmeterswitharapidinfiltrationintoshallowalpinesoils(seeAppendixA.

Table1

ReviewofselectedS-factors(S).

Source function Description

Zingg[5] _S¼ s

9

1:4 s=slopesteepnessinpercent

Musgrave[6] _S¼ s

9

1:35 s=slopesteepnessinpercent

SmithandWhitt[7] _{S¼0:025þ0:052s}4

3 s=slopesteepnessinpercent

Smith[8] S¼0:00650s2_{þ0:0453sþ0:065 s=slopesteepnessinpercent}

Smith[8] S¼0:044þ0:10s0:00073s2 _{s=slopesteepnessinpercent}

WischmeierandSmith[1] _S¼65:4sinu2_{þ4:56sinuþ0:0654} u_{=slopesteepnessinradians}

McCooletal.[9] _S¼ sinu

0:00896

 0:6 u=slopesteepnessinradians

Foster[10] _S¼3ðsinuÞ0:8_{þ0:56 u}=slopesteepnessinradians

McCooletal.[3] S¼16:8sinu0:5 u=slopesteepnessinradians

McCooletal.[3] S¼10:8sinuþ0:03 u=slopesteepnessinradians

Nearing[11] S¼ 1:5þ 17

1þe2:36:1sinu u=slopesteepnessinradians

Liuetal.[12] S¼21:91sinu0:96 u=slopesteepnessinradians

supplementarymaterial).Ourmeasurementsandobservationsshow,thatpotentialflowpathswithout consideringinfiltrationisnotrealisticforalpineenvironmentsandthus,requestingamaximalflow thresholdfortheestimationoftheslopelengthfactorL.McCooletal.[16]andWinchelletal.[14]limited theslope lengthto a maximalthresholdof 333m(1000feet)aslonger slopelength appearonly occasionally.AccordingtoMcCooletal.[16],theusualthresholdinmanycasesis121m(400feet).Asa compromiseoftheir suggestionandourobserved shortflowpathlengthsintheSwissAlps,wedecidedto limitthemaximalflowlengthto100m.

ThethresholdisimplementedasaconditioneitherdirectlyinSAGAGISorinRSAGAaftercreating theflowaccumulationgrid:

Aalpinei;jin ¼ifelseAi;jin >thresh;thresh;Ai;jin ð7Þ

whereAalpinei,j-inistheconstraintflowaccumulationinm2attheinletofagridcell(i,j)consideringa

thresholdvaluethresh.ThatconstraintflowaccumulationvalueisinsertedintotheL-factorequation forthealpineenvironment(Eq.(8)):

Lalpinei;j¼

Aalpinei;jinþD2

 mþ1

Amalpineþ1 i;jin

Dmþ2Xm_i;j22:13m ð8Þ

LikewisetoEq.(2),DisthegridcellsizeinmandXi;jequalstosinai;jþcosai;jwhereai,jistheaspectof

thegridcell(i,j).Thecoefficientmistheratioofrill(β-value)tointerrillerosionaccordingtotheabove mentionedEqs.(3)and(4).

ForourcalculationofL-factorusinga2mresolutionDigitalElevationModel,themaximalflow lengthof100m,correspondstoathresholdof50cellsmultipliedbythecellsizeof2m(Fig.2).

Additionally, maximalflowpathlengthwasconstrainedbyafieldblockcadaster.Thecadaster defineshydrologicalunitsofcontinuousagriculturalland,thatareseparatedbylandscapeelements actingasflowboundaries(e.g.,forests,streets,urbanareas,waterbodies,orditches)followingthe approachofWinchelletal.[14].

ProposedadaptionoftheS-factor

In2014,weconductedatotalof16rainfallsimulationsonalpineslopestoassessthesoillossrates relatedtodifferentslopeinclinations(Table2;[17]).Theexperimentswereconductedatanorthand southfacingslopebothwithgrasslandcoverinthemountainsoftheUrserenValley,Switzerland.At eachslopetwotransectswereselectedwithslopegradientrangingfrom20to90%.Weuseda_field hybridrainfallsimulatormodifiedafterSchindlerWildhaberetal.[18]withanintensityof60mmh1, whichiscomparabletoahighrainfalleventinthisarea.

Theexperimentalsitesshowedsmallvariationinvegetationcover,soilerodibility,andslopelength (duetotheeffectofslopeangle),thereforeallexperimentalplotswerenormalizedtoaveragevaluesof

therespectivefactors.S-factorswerefittedtoobservedsoillossversussineoftheslopeangleusingan exponential,power,andpolynomialequationtotheoriginaldatasetwithallobservationandadataset excludingoneoutlier(N 13),andthreeoutliers(N 12,13,16).ThenineregressionlinesyieldR2

estimatesbetween0.18and0.70,butdifferlargelywithincreasingslopesteepness.Thisrangeof S-factorswithincreasingsteepnessiscomparabletopreviousdevelopedempiricalS-factorequations (Table1,Fig.1).Therefore,wedecidedthatafittedfunction(SalpineinTable1,Fig.3)complyingthe

mostimportantS-factorsfromtheliteraturewouldbemostsuitabletodescribethesoillossbehavior

Fig.2.Constraintflowaccumulationgridwithamaximalflowpathlengthof100m.

Table2

RainfallsimulationmeasurementsatthetwostudysitesonsteepalpineslopesinSwitzerlandunderconsiderationofdifferent inclinationsandvegetationcover.

No _inclination (₎ vegetation cover(%) measuredsediment rate(tha1yr1) normalizeda_sediment rate(tha1yr1)

normalizeda_{sedimentratewithout} outliers(tha1yr1) 1 17 23 13.8 8.5 8.5 2 22 33 0.6 0.7 0.7 3 11 27 0.0 0.0 0.0 4 27 41 1.2 1.6 1.6 5 31 35 0.2 0.2 0.2 6 35 34 6.8 5.6 5.6 7 42 53 9.4 19.0 19.0 8 39 26 31.0 17.4 17.4 9 11 33 0.6 0.7 0.7 10 17 36 1.4 1.8 1.8 11 22 47 1.3 2.0 2.0 12 27 33 34.3 40.6 13 31 63 26.1 111.3 14 35 38 11.1 13.1 13.1 15 39 34 40.2 26.0 26.0 16 42 40 75.4 69.8 a

atsteepslopes.TheaggregatedSfunctionandisaquadraticpolynomicfunctionwithprogressive growth(Eq.(9)):

Salpine¼0:0005s2þ0:7956s0:4418 ð9Þ

wheresistheslopesteepnessinpercent.

SalpineisveryclosetotheempiricalnormalizedfunctionproposedbyMusgrave[6]foraslope

steepnessof9%.

TheSwissLS-factormapincludingtheAlps

TheresultingmodeledmeanLSalpine-factorofSwitzerlandis14.8.TheLS-factorincreaseswith

elevationgradientfromameanof7.0inthezone<1500ma.s.l.to30.4inthezone>1500ma.s.l.A clusterofhighestmeanLS-factorscanbefoundacrosstheAlps(Fig.4).ThelowestmeanLS-factorsare

Fig.3.ReviewandbehaviorofdifferentempiricalS-factorfunctionsandthefittedfunctionforsteepalpineenvironments (Salpine).

intheSwisslowlands.South-westernfacingslopeshavehigherLS-factors(17.6)comparedtoplain surfaces(0.04)andnorthfacingslopes(12.5).

Qualityassessmentandmethoduncertainties

TheoriginalLS-factorhasitsorigininempiricalfieldexperimentsandisdevelopedforamaximum slopesteepnessof50%. Validationofexistingequationsforslopesthataresteeper than50%isa challenge. However, while previous studies at inclinations _>25% with approximately 20 plot measurements([19],24plots;[20],19plots;[12],9plots;[21],22plots;[18],6plots)weresuccessful indelineatingandS-factorequation,inourcasethevariabilityofthedataimpededauniquesolution oftheS-factorequation.Toaccountforthishighvariabilityandstillexistinguncertainty,theway forwardistoincludethevariabilityintheLS-factorcalculation.

WeinvestigatedthedeviationinpercentageofourproposedSalpinetoaconservativefunctionanda

ratherprogressivefunction.Theconservativefunction(Scons)isbasedonthetranslatedandscaledsine

functionsofEqs.(5)and(6)byMcCooletal.[3]withaproportionalandslightlydigressivegrowth.The progressivefunction(Sprog)isaquadraticpolynomicfunctionaccordingtoSmithandWhitt[7]witha

progressivegrowth,butahighercoefficientthantheherepresentedfittedfunctionSalpine(Eq.(10))for

Salpine.

Sprog¼0:00650s2þ0:0453sþ0:065 ð10Þ

wheresistheslopesteepnessinpercent.

Lowuncertaintyhasadeviationcloseto0%.Higherpercentagesequalstoahigherdeviationof Scons/progtoSalpine.

Fig.5.DeviationinpercentageofSalpinetoSconsasanindicatorofqualityfortheproposedSalpine-factor.Salpineisalumped S-factorofatotalof12empiricS-factorequationsoftheliterature(Eq.(9)).Itcanbeseenasanapproximationtothehighslope gradientsinalpineenvironments.SconscomplieswiththeproposedS-factorofMcCooletal.[3](Eqs.(5)and(6)).Thedeviation ispresentedinpercentage.

ThedeviationofSalpinetoSconsshowshigherdeviationsinareaswithlessslopegradiants(partsof

Swissmidland)(Fig.5).ThesteepslopeareasintheAlpshavedeviationsof25%–50%.Bothfunctions, SalpineandSconspredictthesteepalpine environmentin acomparable way.Thedeviationof the

progressiveS-factor(Sprog)andSalpinedivergemuchmoreintheAlpswhereastheequationsare

ratherfittinginflatterregions(Fig.6).Asharpedgeoflowdivergencetohighdivergenceismarkedby thenorthernAlpinefoothillwithincreasingslopegradients.

Thisrelationshipof deviationandslope gradientisnot surprisingastheuncertaintyofmany equationsriseswithslopesteepness(cf.Fig.3).García-Ruizetal.[22]identifiedanincreasingtrendof uncertaintyfor624measurederosionratesandslopegradientsacrosstheworldforslopesteepness >11_.

TheLS-FactormapoftheSwissagriculturallanduseunitisvisuallycompatiblewiththe LS-factormapsof theEuropean Unionprovidedby Panagoset al.[23](Fig. 7).Incontrasttothe modeling of the total country area by Panagos et al. [23] we constrained the LS-factor to agriculturalsoilsincl.grasslandsusinga_fieldcadaster.Themaindifferencesarefoundonsteeper slopes>50%, whichhavebeenexcludedintheEuropeanapproach.Furthermore,theEuropean mapreliesontheconservativeEqs.(5)and(6)byMcCooletal.[3].Additionally,differentspatial resolutionsofDigital ElevationModels(2mversus25m) arein_fluencingtheslope andaspect mappingandthustheLS-factor[24–26].

ItshouldbeconsideredthatthenumberofrainfallexperimentsfortheL-factor(n=19)andthe S-factor(S=16)isshortandlimitedonlytograsslandswhicharethepredominantlanduseatSwiss alpineslopes[27].Rainfallsimulationsinalpineenvironmentsaredifficulttoconductduetotheharsh terrainandclimateconditions.Often,thetemporalperiodformeasurementsislimitedbythelate meltoutofsnowcoverandtheshortvegetationperiod[28].TobettermodeltheS-factorforsteep

Fig.6. DeviationinpercentageofSalpinetoSprogasanindicatorofqualityfortheproposedSalpine-factor.Salpineisalumped S-factorofatotalof12empiricS-factorequationsoftheliterature(Eq.(9)).Itcanbeseenasanapproximationtothehighslope gradientsinalpineenvironments.SprogcomplieswiththeproposedS-factorofSmithandWhitt[7](Eq.(10)).Thedeviationis presentedinpercentage.

alpineslopesfurthermeasurements(e.g.,rainfallsimulationexperiments)areneededtoconstrain S-factorassessmentforsteepslopes.

Additionalinformation

Introduction

TheslopelengthfactorLandslopesteepnessfactorS,oftenlumpedtogetherasthetopographic factorLS.TheLS-factorisoneofthefactors(Rrainfallerosivity,Ccoverandmanagementfactor,Ksoil erodibility,Psupportpractices)oftheUniversalSoilLossEquation(USLE)anditsrevisedversion (RUSLE)[1,29].LSisafactorthatdescribestheinfluenceofthetopographytothesoilerosionriskby consideringthelengthofaslopeandtheinfluenceofsurfacerunoffwhichcanbeactiveonerodingsoil materialbeforeitin_filtratesorcontinuousasinter_flow.Furthermore,itincludesthesteepnessofa slopeasrunoffonsteeperslopeshasahighergravityandthereforeismorerelevantforerosion.

WiththeavailabilityofDigitalElevationModelsthecalculationofLS-factorsinGISenvironments wasmadepossibleevenforlarge-scaleerosionmodelingapproaches.Winchelletal.[14]revealeda reasonableagreementofGIS-basedLS-factorandfieldmeasuredLS-factorsoftheUSNaturalResource InventorydatabasefortheMississippiCatchment.

Originally,theLS-factorwasassessedona9%steepslopewithalengthof22.13m(72.6feet)[1]. Owingtoitsempiricalcharacter,LS-factorsareusuallylimitedtoamaximumslopeangleof50% (26.6)[3,12].AsSwitzerlandisacountrywithahighelevationgradientfrom192ma.s.l.to4633ma.s. l.(meanelevation1288ma.s.l.)andameanslopegradientofupto36%(20),anotnegligiblefraction ofslopes(4.7%)exceedsthelimitationof50%.Yet,nouniformequationtoassesstheLS-factorforsteep slopeslikeinthealpineenvironmentofSwitzerlandwaspresentedtothescientificcommunity.Onlya fewstudiesaredealingwithLS-factorsonsteepslopes(e.g.[12]).Forexample,slopes>50%were disregardedinthemostrecentEuropeanUnion_’sLS-factormapbyPanagosetal.[23].

Fig.7. LS-factorfortheSwissagriculturalarea(incl.Liechtenstein)embeddedintheEuropeanUnion’sLS-factormap(fortotal countryarea)byPanagosetal.[23].

Datastatement

RawdataweregeneratedatSwisstopoandprovidedonlyforscientificpurposes.Deriveddata supportingthefindingsofthisstudyareavailablefromthecorrespondingauthorSSonrequest. Acknowledgments

ThisworkwassupportedbytheSwissFederalOfficefortheEnvironment(FOEN)(grantnumbersN N222-0350andNP182-1535).TheauthorswouldliketothankChristineAlewellforthemethodological supportandPascalBircherfortheadviceindatahandlingwithSAGAGIS/RSAGAandtheupgradeofthe existingfieldblockcadasterofSwitzerland.OurthankgoestoM.Schulthess,C.Keller,N.Bongni,S. Rothenbühler,andA.Aeschbachforthesupportinthefieldandthefootage.TheauthorsthankSwisstopo formakingtheir dataavailableforthisresearch.Theauthorswouldliketothanktwoanonymousreferees fortheirvaluablecommentsandsuggestionstoimprovethequalityofthepaper.

AppendixA.Supplementarydata

Supplementarymaterialrelatedtothisarticlecanbefound,intheonlineversion,atdoi:https://doi. org/10.1016/j.mex.2019.01.004.

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