Desertification Susceptibility Mapping Using Logistic Regression Analysis in the Djelfa Area, Algeria

26 Pages·2017·5.03 MB·English

remote sensing
Article
Desertification Susceptibility Mapping Using Logistic
Regression Analysis in the Djelfa Area, Algeria
FaridDjeddaoui1,2,*,MohammedChadli1andRichardGloaguen2
1 FacultyofEarthScience,GeographyandLandPlanning,UniversityofSciencesandTechnologyHouari
Boumediene(USTHB),BP32El-AliaBabEzzouar,Algiers16111,Algeria;[email protected]
2 Helmholtz-ZentrumDresden-Rossendorf,HelmholtzInstituteFreibergforResourceTechnologies,Division
“ExplorationTechnology”,Chemnitzerstrasse40,09599Freiberg,Germany;[email protected]
* Correspondence:[email protected]@gmail.com;Tel.:[phone]
Received:5July2017;Accepted:4October2017;Published:9October2017
Abstract: The main goal of this work was to identify the areas that are most susceptible to
desertification in a part of the Algerian steppe, and to quantitatively assess the key factors that
contributetothisdesertification. Intotal,139desertifiedzonesweremappedusingfieldsurveys
andphoto-interpretation. Weselected16spectralandgeomorphicpredictivefactors,whichapriori
play a significant role in desertification. They were mainly derived from Landsat 8 imagery and
Shuttle Radar Topographic Mission digital elevation model (SRTM DEM). Some factors, such as
the topographic position index (TPI) and curvature, were used for the first time in this kind of
study. Forthispurpose,weadaptedthelogisticregressionalgorithmfordesertificationsusceptibility
mapping, which has been widely used for landslide susceptibility mapping. The logistic model
wasevaluatedusingtheareaunderthereceiveroperatingcharacteristic(ROC)curve. Themodel
accuracywas87.8%. Weestimatedthemodeluncertaintiesusingabootstrapmethod. Ouranalysis
suggeststhatthepredictivemodelisrobustandstable. Ourresultsindicatethatlandcoverfactors,
includingnormalizeddifferencevegetationindex(NDVI)andrangelandclasses,playamajorrole
indeterminingdesertificationoccurrence,whilegeomorphologicalfactorshavealimitedimpact.
Thepredictivemapshowsthat44.57%oftheareaisclassifiedashighlytoveryhighlysusceptibleto
desertification. Thedevelopedapproachcanbeusedtoassessdesertificationinareaswithsimilar
characteristicsandtoguidepossibleactionstocombatdesertification.
Keywords: desertification;logisticregression;steppe;Djelfa
1. Introduction
Desertificationisaseriousworldwideenvironmentalproblem,withconsequenceswithrespectto
landcapacityandbiologicalproductivity[1]. Itcontinuestobeamajorenvironmentalissueinthe21st
century[2]. TheConventiontoCombatDesertificationdefineddesertificationas“landdegradationin
arid,semiarid,anddrysub-humidareasresultingfromclimaticvariationsandhumanactivities”[1,3,4].
Inthiscontext,thedesertificationphenomenonwasconsideredbytakingintoaccountthedegreeof
vulnerabilityortheresponseoftheecosystem[5].
InAlgeria,desertificationmainlyaffectsthearidsteppeareas,whichcoveratotalareaof20million
hectares. Theseareasaresubjecttodroughtsandanthropogenicpressurerelatedtoovergrazingand
improperlanduseforagriculture. Inrecentdecades,thewidespreaddegradationofvegetationcover
hasbeendeterminedasoneofthemainfactorscausingdesertification[6–10]. Today,theseareasarein
acriticalsituation. Studiesshowthatabouthalfoftheserangelandsaredesertifiedoronthethreshold
ofdesertification[11–15]. Thishasledtoseriousconsequenceswithrespecttoboththeeconomicand
socialaspectsofdevelopment,becausetheserangelandsareusedforextensivesheepfarmingand
playafundamentalroleintheagriculturaleconomyofthecountry[10].
RemoteSens.2017,9,1031;doi:10.3390/rs9101031 www.mdpi.com/journal/remotesensing
RemoteSens.2017,9,1031 2of26
Variedandmultipleactionshavebeentakentotackledesertification. Tobeeffective,theseactions
mustfocusontheidentificationofareasthatarevulnerabletodesertification,theareawhereitinitiated,
anditsdiffusion. Overthelastdecades,manydifferentmappingtechniqueshavebeenusedforthe
assessmentofdesertification,andalargenumberofstudieshaveevaluatedthephenomenon. These
studiesweremainlybasedonremotesensingapproachessuchaschangedetectionusingspectral
mixtureanalysis[16,17],multi-criteriaevaluation[18],bi-temporalchangedetectionmethods[19],
asupervisedclassificationapproach[20–22],long-termstudyusingNDVI,time-trends[23],image
differentiation [24], and image rationing [25]. However, change detection techniques face many
problems,themostimportantofwhichisthatobservedsignificantchangesmayberelatedtoother
factorsandnottothesubjectunderstudy[26].
Otherapproacheshaveevaluateddesertificationusingkeyindicatorsatvariousgeographical
scales.TheMediterraneanDesertificationandLandUsemodel(MEDALUS),proposedforthefirsttime
in1999byKosmasetal.[27],showsclearadvantagesincomparisonwithothersimilarapproaches[3–5].
The effectiveness of this approach enabled its large-scale use in several Mediterranean countries,
including Italy, Algeria, Spain, Portugal, and Egypt. The model identifies areas sensitive to
desertificationduetoacombinationofvariousweightedparameters(i.e.,compositeindices)suchas
landcover,geology,soil,climate,andmanagementactions.However,theMEDALUSapproachfocuses
mainlyonthephysicallossofsoilbywatererosioninEuropeanMediterraneanenvironments[27],
whilethephenomenonofdesertificationinsemi-aridareasresultsfromboththenaturalenvironment
andsocio-economicconditions[28].
Inthiscontext, welookedformethodsthatdonotrequireadeterminednumberofvariables
and provide more freedom to introduce new variables, in particular socio-economic factors.
Additionally, it is more important to assess desertification and identify responsible factors than
toonlyevaluatesensitivity.
Wethusappliedlogisticregression,amultivariatestatisticalmethodwhichhasbeenwidelyused
to predict a categorical outcome, using many causality predictors [29]. Being simple to use, ithas
becomeawidelyacceptedmethodforabroadrangeofscientificdisciplines. Logisticregressionhas
beenappliedinthefieldofremotesensingforchangedetectioninlandcover[30]andforinsecttree
defoliationmapping[31].Logisticregressiontechniqueshavealsobeenusedinecology,particularlyfor
conservationplanningandwildlifemanagement[32,33]. Inearthsciences,logisticregressionanalysis
hasbeenimplementedwithdifferentgoals,forexampleinsoil-landscapemodelling[34]andprediction
ofpost-firesoilerosion[35],andithasbeenextensivelyusedforlandslidesusceptibilitymappingwith
varioustechniques[36–40]. Ourchoicewasbasedonthefactthatbothdesertificationandlandslides
arenaturalhazardscontrolledbynumerousvariablesandarecharacterizedbynon-linearity.
Theaimsofthisstudyweretoapplythelogisticmodeltoidentifythemostsusceptibleareasto
desertificationinacentralpartoftheAlgeriansteppe,andtoevaluateandprovideanexplanatory
modelofkeyfactorsassociatedwithdesertification. Toachievetheseobjectives,weusedthreemain
steps. The first step involved the identification and extraction of the predictive factors related to
desertification based on the characteristics of desertified areas. The second step was to determine
the best predictive model. The third step was to evaluate the contribution of each factor to the
phenomenonanddeterminethemostinfluentialfactors. Finally, thequalityofpredictionandthe
stability of the model were evaluated using two validation methods: the area under the receiver
operatingcharacteristic(ROC)curveandtheuncertaintymeasure.
Thisworkstressesthatanaccuratedesertificationsusceptibilitymap,associatedtoanexplanatory
modelofkeyfactors,providesareliabletoolfordesertificationriskmitigation.Suchtoolsarehelpfulin
theplanningphaseofdevelopmentalactivitiesandtotakeappropriatepreventivemeasures. Thiscan
alsobeextendedtoguidepossibleactionstocombatdesertificationinsimilarareas.
Remote Sens. 2017, 9, 1031 3 of 26
2. Study Area
The study area lies between latitudes 6°29′ and 5°36′N, and longitudes 35°15′ and 34°41′E,
covering an area of about 4097 km2 in the central part of Algeria, in a transition area between the
Hautes Plaines region and Saharan Atlas Mountain (Figure 1).
The climate is semi-arid and is strongly marked by a continental influence, with cold, wet
winters and hot, dry summers. Rainfall is scarce and irregular, with an average annual rainfall that
ranges between 200 and 400 mm. Precipitation usually occurs in the form of thunderstorms and
torrential rain, sometimes mixed with hail. The number of rainy days varies between 37 and 80 per
year. The average evaporation exceeds 2450 mm/year. The average annual temperature is generally
greater than 20 °C. The minimum temperature in the coldest month is 1.9 °C, while the maximum
temperature in the warmest months can exceed 37 °C [41,42]. The number of days of frost can reach
40 per year. The prevailing winds are mainly from the west and northwest in winter and the
southwest in summer. The mean wind speed is 2.7 m/s [43]; winds are sometimes violent due to the
amount of open space without any physical obstacles.
Soils are characterized by the presence of limestone accumulation and low organic matter
RcoemnotteenSte ns[.1200]1. 7,T9h,1e0s3e1 soils are generally shallow, however some soils located in depressions3 oafr2e6
relatively deep and rich.
The vegetation consists mainly of patches of grasses that do not fully cover the ground, such as
2. StudyArea
Alfa (Stipa tenacissima), and white Wormwood (Artemisia herba alba) [41]. These perennial grasses
occupTyh ea slaturgdey paarreta olfi ethseb teetrwrietoerny,l aetsiptuedcieasll6y◦ i2n9 (cid:48)thaen Sdo5u◦t3h6. (cid:48)TNh,ea fnodreslotsn wgihtuicdhe soc3c5u◦p1y5 (cid:48)thane dm3o4u◦n4t1a(cid:48)iEn,
rcaonvgeerisn agrea nbraigrehat aonfda baoiruyt. 4T0h9e7 mkamin2 tirneeth sepececinetsr aalrep tahret oAfleAplpgoer Piain,ein, Haotlrman osiatkio, nanadre taheb ePthwoeeennictiahne
JHuanuipteesr.P Rlaainngeeslraengdio anlsaon cdovSaerhsa arann imAtploasrtManotu pnatrati nof( Fthige uarreea1 )o.f study [44].

FFiigguurree 11.. SSiimmpplliififieeddm maappo foNf NorothrthA lAgelgriearisah oshwoinwginthg ethstee pspteepzpoen ezoenxea mexinaemdininedth iins stthuids ys.tTuhdey.b lTahcke
brelactcakn rgelcetainndgilcea itnedsitchaetesst uthdeie sdtuadreieadw airtehaa whiitlhl sah hadilel smhaadpe. map.
3. Methodology
Theclimateissemi-aridandisstronglymarkedbyacontinentalinfluence,withcold,wetwinters
andhot,drysummers. Rainfallisscarceandirregular,withanaverageannualrainfallthatranges
3.1. Methods
between200and400mm. Precipitationusuallyoccursintheformofthunderstormsandtorrential
rain,Tshoem esteilmecetsiomn ixoef dawn itahphparoilp.riTahtee nmuomdbele riso fsruabinjeyctd atoy stvhaer inesatbuertew oeef nth3e7 adnedpe8n0dpenert yaenadr.
Tinhdeeapveenrdaegnete vvaaprioarbalteiso.n Inex ace leidnsea2r4 5r0egmremss/iyoena rm. Todheela, vtherea gdeepanenndueanltt evmapriearbalteu rmeuissgt ebnee rcaolnlytignrueoautesr.
than20◦C.Theminimumtemperatureinthecoldestmonthis1.9◦C,whilethemaximumtemperature

inthewarmestmonthscanexceed37◦C[41,42]. Thenumberofdaysoffrostcanreach40peryear.
Theprevailingwindsaremainlyfromthewestandnorthwestinwinterandthesouthwestinsummer.
Themeanwindspeedis2.7m/s[43];windsaresometimesviolentduetotheamountofopenspace
withoutanyphysicalobstacles.
Soils are characterized by the presence of limestone accumulation and low organic matter
content[10]. Thesesoilsaregenerallyshallow,howeversomesoilslocatedindepressionsarerelatively
deepandrich.
Thevegetationconsistsmainlyofpatchesofgrassesthatdonotfullycovertheground, such
asAlfa(Stipatenacissima),andwhiteWormwood(Artemisiaherbaalba)[41]. Theseperennialgrasses
occupyalargepartoftheterritory,especiallyintheSouth. Theforestswhichoccupythemountain
rangesarebrightandairy. ThemaintreespeciesaretheAleppoPine,Holmoak,andthePhoenician
Juniper. Rangelandalsocoversanimportantpartoftheareaofstudy[44].
RemoteSens.2017,9,1031 4of26
3. Methodology
3.1. Methods
Theselectionofanappropriatemodelissubjecttothenatureofthedependentandindependent
variables. In a linear regression model, the dependent variable must be continuous. However,
thephenomenonofdesertificationisdichotomousandisbestdescribedbymultivariatestatistical
models, suchaslogisticregressionordiscriminantanalysis[45]. Inthisstudy, weappliedlogistic
regression,whichdescribestherelationshipbetweenadependentvariable(theresponsefactor)thatis
usuallytheoccurrenceornotofanevent,andseveralindependentvariables(thepredictivefactors)
thatinfluencetheoccurrenceofthisevent[46]. Logisticregressionhasbeenfrequentlyusedinmany
fieldssuchassocial,health,andearthsciencesaswellasecology.
Inourcase,logisticregressionwassimplertousecomparedtodiscriminantanalysisbecauseof
themixtureofnumericalandcategoricalvariables. Thelogisticregressionmodelcanautomatically
generatenecessarydummyvariables[37]. Also,discriminantanalysisrequiresanormaldistribution
ofindependentvariables,whichisnotalwaysavailablefornaturaldataoriginatingfrom,forexample,
landuseandlandcover[45].
Additionally,manyresearchershavepreferredtouselogisticregressionduetoitssimilarityto
linearregressionasitreliesonsimpletests[37,45], whileaddingafunctionthatallowsprediction
of the probability of the event and describes complex nonlinear relations that often characterise
naturalphenomena. Logisticregressionalsoallowsforestimationoftheoddsratio,whichprovides
informationonthestrengthanddirectionoftheassociationbetweenthedependentvariableandthe
independentvariables[47].
Inoursituation,theindependentbinaryvariablewasusedtopresentthepresenceortheabsence
ofdesertification. Thelogisticmodelcanbeexpressedinitssimplestformwiththefollowingequation:
1
p = (1)
1+e−z
where pistheprobabilityofdesertificationoccurrencethatvariesfrom0to1onans-shapedcurve,
andzisthelinearlogisticmodel,whichvariesfrom−∞to+∞,andcanbedefinedas:
∑
z = α+ β X (2)
i i
whereαistheinterceptofthemodel,β (i=1,2,3,... ,n)aretheestimatedslopecoefficientsofthe
i
logisticmultiplesregressionmodel,andX (i=1,2,3,... ,n)representstheindependentvariable.
i
Thelogisticmodelfordesertificationcanberepresentedas:
1
p = (3)
1+e−α+∑βiXi
Logisticregressionlooksforthe“bestfit”equationasinlinearregression,butwithadifferent
method. Instead of using the least-square method for best fit, it uses the maximum likelihood
method[37].Theunknownvaluesofαandβareestimatedusingthedataoftheindependentvariables.
Theobserveddataineachpixeleitherhaveavalueof0,meaningtheabsenceofdesertification,or1,
meaningthepresenceofdesertification. Withtheseestimates,wecalculatedtheprobabilityofthe
desertificationfortheremainingpixels,usingtheobservedvaluesoftheindependentvariables[45].
3.2. CausalFactorsandDesertification
Predictivefactorsusedtoassessdesertificationmayvaryfromoneregiontoanother. Forthis
reason,wetestedasetofkeyfactorsthatprovideinformationaboutdesertificationcommonlyusedin
theliterature[3,5,27,28]andwethenselectedthosethatseemedtobemostadequateforourstudy
area. Wealsofacedconstraintsrelatedtothelackofdataincountriessubjecttodesertification[48],
RemoteSens.2017,9,1031 5of26
andattemptingtocompensateforthisdeficitbyusingremotesensingdataisausefultoolformapping
manyfactors.
Sixteenpredictivefactorswereselectedaspotentialdeterminantsofdesertificationandprepared
asthematiclayers. Thesefactorsbelongtooneofthefollowingfourcategories: soil,geomorphological,
environmental,andsocioeconomicfactors.
All maps of the factors were converted to the same pixel size equalling 30 m, similar to the
resolutionofmapsderivedfromLandsat8imageryandSRTMDEM.
The logistic model used in this study can process continuous or categorical data, or both.
The categorical form factors include land cover, slope aspect, and lithology. The others factors,
suchasslopeandelevation,haveacontinuousform.
Categoricalvariablesshouldbeencodedinordertocreateanewsetofdummybinaryvariables
foreachclassofthecategoricalvariable[37,38,49]. Avalueof1isassignedtothetargetclass,andthe
value0isassignedtotheotherclasses. Eachcategoricalfactorgeneratesanumberofbinarymaps
equaltothenumberofclassescontainedinthisfactor. Forexample,15binarymapswereproduced
forthelandcovermap,whichcontains15classes.
3.2.1. SoilFactors
Soilisanimportantfactorinsemi-aridzones. Desertificationwillproceedwhenthesoildepth
isnotcapableofsustainingacertainminimumofvegetationcover[27]. Duetotheabsenceofdata
regardingsoilcharacteristics,suchastexture,soildepth,andorganicmatter,weusedalithologicalmap
toobtainpropertiesoftherocksandtheirsusceptibilitytodesertification. Thelithologicalmapstudy
involvedeightlithologicalunitsprovidedbytheNationalAgencyforRegionalPlanning—Algeria[50].
Landsurfacetemperature(LST)isalsoanimportantparameterinthephysicsofEarthsurface
processes[51],andcanbeusedtoexplainthedynamicofdesertification[52,53]. LSTisestimatedusing
thermalbands10and11oftheLandsat-8ThermalInfraredSensor(TIRS).Weappliedamethodwidely
usedtocalculatetheLST[54],basedontheestimationoflandsurfaceemissivityextractedusingthe
NDVI.WeusedanimageacquiredinMay2015,thesameimagethatwasusedfortheextractionof
theNDVI.
ThefollowingequationwasusedtocalculatetheLST:
T
LST = B (4)
1+(λ×T /ρ)ln(ε)
B
whereT istheat-satellitebrightnesstemperature,calculatedfromtheradiancewhichwasderived
B
fromthedigitalnumberaccordingtoUnitedStatesGeologicalSurveyUSGSmethodology[55]. λis
thewavelengthoftheemittedradiance(11.5um). Forρ=h×c/σ(1.438×10−2mK),histhePlanck
constant(h=6.6261×10−34Js),σistheBoltzmannconstant(σ=1.3806×10−23J/K),cisthespeed
of light (c = 2.9979 × 108 m/s), and (ε) is the land surface emissivity, calculated using the NDVI
image[56,57].
3.2.2. GeomorphologicalFactors
Inordertoassessdesertification,previousstudieshaveidentifiedawiderangeoffactorsrelatedto
landformcharacteristics[3,4,58–62]. Amongthose,geomorphologicalcharacteristicsplayanimportant
roleindesertificationprocesses[63,64]andidentifyingdesertificationthroughwindandwatererosion
in dry areas is relatively easy [63,65]. In this category, six predictive factors which describe the
morphologyofthelandscapewereused.
Elevationisaninfluentialfactorintheerosionofthelandscape[27]. Inthisstudy,elevationwas
derivedfromthenewdigitalelevationmodelfromtheShuttleRadarTopographyMission,knownas
“SRTMPlusV3”,witharesolutionof1arc-second(~30m)[66]. Elevationwasusedtocreatetheother
geomorphologicalfactors.
RemoteSens.2017,9,1031 6of26
TheTPIcomparestheelevationofeachpixeltotheaverageelevationofthesurroundingpixels[67].
ApositiveTPIvaluemeansthattheareaislocatedhigherthanitsaveragesurroundings,aswithridges
forexample. However,negativevaluesmeanthattheareaislowerthantheaverage,forexamplein
thecaseofavalleyfloor[68]. TheTPIiscalculatedwiththefollowingequation[68,69]:
TPI= E −E (5)
C A
withE beingtheelevationofthecentralpixel,andE theaverageelevationaroundit. Weexecuted
C A
analgorithmintheQGISprocessingtoolboxinordertocomputetheTPIforthestudyarea,andwe
usedamovingwindowof10pixels.
The hypsometric integral (HI) helps to estimate the erosional status of a watershed [70,71],
and is inversely correlated with the amount of material removed by erosion [72]. The lowest
values of HI (HI < 0.35) are commonly found in long-lived landforms, where the average
topography is low and a few relict highs, such as inselbergs or mesas, are preserved. In contrast,
the highest HI values (HI > 0.6) are found in young or rejuvenated landscapes, where the
average topography is high and incised by an entrenched drainage system. Average HI values
(0.35<HI<0.6)arefoundinmaturelandformsassociatedtoasetofconcaveorV-shapedvalleys[73].
Thehypsometricintegraliscalculatedusingthefollowingequation[74]:
h −h
HI= mean min (6)
h −h
max min
with h , h , and h being the mean, minimum, and maximum elevations of the analysed
mean min max
area,respectively.
Slopegradientandslopeaspectarekeyfactorsthatcontrolsoilerosion[75]aswellasthetypes
of cultivation, and determine the grazing areas [76]. The slope aspect notably influences the local
environment[77]andisconsideredanimportantfactorforlanddegradationprocesses,whichaffect
severalelementssuchastemperature,evaporation,andvegetation[78].
Curvature illustrates a line formed by the intersection of a plane with the land surface [79].
Itsimportanceliesinthefactthatthesusceptibilityoftheterraintoerosionvariesdependingonthe
curvature[80]. Anegativevaluemeansthatthesurfaceislocallyconvex,apositivevaluemeansthe
surfaceislocallyconcave,andavalueof0meansthatthesurfaceisflat[39,68].
3.2.3. EnvironmentalFactors
Environmental factors play an important role in the desertification process [64]. Past studies
showedthatlandcover,drainage,andclimaticconditionsareindicatorsthatallowthecharacterization
ofsoilconditionsduringerosionandprocessesassociatedtodesertification[28,59,81].
Sixparameterswereusedasenvironmentalpredictivefactorsofdesertification: precipitation,
NDVI,landcover,drainagedensity,distancetodrainage,andevapotranspiration.
Intheabsenceofreliableandaccurateprecipitationdatafromclimatologicalstations,wechose
toworkontwotypesofdata. ThefirstisthedecadalrainfallisohyetsmapprovidedbytheNational
Agency of Water Resources—Algeria, published in 2002 [82]. The second precipitation data was
derivedfromtheTropicalRainfallMeasuringMission(TRMM).Thesedatahavebeenwidelyused
withgoodperformance[83,84]. Weusedanaveragemonthlypixel-basedprecipitationratewitha
spatialresolutionof0.25degrees(3B43v7)whichspansaperiodof17years(1998–2014).
TheNDVIhasbeenwidelyusedasanindicatortoassessandmonitorlandcoverchangeand
desertification[23,60,85]. NDVIwasobtainedfromthereflectance(ρ)oftheLandsat8imageacquired
inMay2015(level1A)whichwascompletedafteratmosphericcorrectionusingtheFastLine-of-Sight
AtmosphericAnalysisofSpectralHypercubes(FLAASH)model.
Land cover information was extracted with 15 classes from the map produced by the High
Commissariat for Steppe Development [86]. Drainage conditions were largely used as influential
RemoteSens.2017,9,1031 7of26
parameterstoevaluatedesertification[28,60].Thedrainagedensitywascalculatedfromthedrainage
networkwitha100-pixelradiuscircle,usinga30-mresolutionSRTMDEM[68]. Bufferzonesaround
thedrainagenetworkwereusedtoderivethedistancetodrainage. Theextractionofthesedrainage
parameterswasperformedusingtheTecDEMtoolbox.
Theincreaseinevapotranspirationratesleadstoareductioninsoilmoisture,andaworsening
of the desertification process [87–89]. In this study, we used the evapotranspiration isohyets map
providedbytheNationalAgencyofWaterResources—Algeria[90].
3.2.4. SocioeconomicFactors
Desertification is associated with the natural environment as well as socio-economic
conditions[28]. Severalattemptshavebeenmadetointegratethesocio-economicaspecttoassess
desertification[91–94]. Accordingtoanewdesertificationparadigmwhichmusttakeintoaccountthe
socio-economicdimension[48],wetriedtoincludetwosocio-economicindicatorsthatarerelatedto
thephenomenonofdesertification.
Overgrazing is a clear cause of desertification [92] and is one of the factors responsible for
degradationinourstudyarea[7]duetotheimportanceandnumberoflivestock. Intheabsenceof
alivestockdistributionmap,wecalculatedthelivestockdensitybydividingthenumberoflivestock
by the surface of the rangeland for each municipality in the study area. We used the numbers of
livestockdeclaredbytheagriculturalservicesdirectorateoftheDjelfaprovincein2014.
Theincreaseinruralpopulationdensityalsoleadstolanddegradation[95],puttingmorepressure
onpastures,andcroplandexpansion. Intheabsenceofrecentstatisticsfortheruralpopulation,we
estimated numbers for 2015 with the geometric method [96], by using the growth rate observed
betweenthelasttwopopulationcensusesof1998and2008. Afterward,wecalculatedthedensityby
dividingtheruralpopulationnumberbytheareaofrangelandforeachmunicipalityinthestudyarea.
3.2.5. TheDesertificationInventoryResponseFactor
Thedependentvariableusedtoevaluatethelogisticmodelisthesusceptibilitytodesertification.
Wefocusedmainlyonareasthatarecharacterizedbyanadvanceddegradationofvegetalcoverbecause
itisthemostimportantaspectofdesertificationintheregion[6–10]. Intheabsenceofupdatedmaps
thatindicatethedistributionofdesertifiedareas,weexploitedthedetectionchangemapbetween1984
and2014producedbyDjeddaouietal.[97]asaguidetoselectinglargeareaswherechangeexisted.
Bothdesertifiedandnon-desertifiedzonesweremappedduringfieldworkcarriedoutbetweenApril
andMay2015. Thecriteriaadoptedinourstudytodiscriminatedesertifiedandnondesertifiedareas
wasthedegreeoflanddegradation. Thescaleextendsfromtheadvancedvegetalcoverdegradationto
theappearanceofsand. ThistaskwassupplementedbytheinterpretationofGoogleEarthimages.
Intotal,139desertifiedzonesweremappedinthestudyarea,withmeasurementsvaryingbetween
0.10and55.91hectares. Wefollowedanorth–southgradientinordertotakeintoaccountalltypesof
geomorphologicalsetsandclimatechange. Therasterdataofdesertifiedzonesconsistof8439pixels
measuring30minsize.
3.3. InputDatabaseforLogisticRegressionAnalysis
Toestimatethecoefficientsofthelogisticmodel,wecreateddatasetscontainingthevaluesofthe
independentvariablesandthestatusofthedependentvariableforthesamepixels.
Togeneratethedesertificationsusceptibilitymap,thelogisticregressionmodelneededpixelswith
orwithoutthepresenceofdesertification[49]. Severalmethodsofsamplingareusedforsusceptibility.
Manystudiesconfirmthatthebestsamplingmethodiswhentheratioofpixelswithdesertificationto
pixelswithoutdesertificationisequalto1[38,98,99]. Thus,weusedthesamenumberofsamplesfor
boththepresenceandabsenceofdesertification.
Pixelswithdesertificationwererandomlysubdividedintotwosets. Thetrainingdatasetfor
the regression analysis included 69.45% of the pixels (5861 pixels), and the validation data set for
RemoteSens.2017,9,1031 8of26
accuracyassessmentincludedtheremaining30.55%(2578pixels). Wethenselectedanumberofpixels
withoutdesertificationthatwasequaltothenumberofpixelswithdesertification,reachingatotal
of8439pixels. Thesepixelswerealsosubdividedintotrainingandvalidationdatasets(69.45%and
30.55%,respectively). Thus,thefinaldatabaseconsistedof16,878pixels.
Wepreparedatablecontaininganequalnumberofdesertifiedandnon-desertifiedpixels.Thefirst
columncontainedthestatusofthedependentvariabletodesertificationforthe11,722analysedpixels.
Avalueof1wasassignedifthepixelwasdesertifiedand0otherwise. Theothercolumns,oneper
independentvariable,containedthevaluesoftheindependentvariablesforthe11,722pixels.
ThelogisticregressionanalysiswasperformedusingtheRpackage“stats”[100]. Outputαandβ
valueswereusedtocalculatethelinearlogisticmodelz.
Finally,weintroducedtheinputfileforlogisticanalysisasadatatable,whichwasanalysedwith
Rsoftwaretoextractthevalueαandβofthemodel,andcouldthenbeusedtocalculatethevalueofz.
3.4. VariablesSelectionandModelDevelopment
Using statistical tests, we checked if the independent variables would affect the predictive
variableornot,sothatonlysignificantvariableswouldberetainedinthelogisticregressionanalysis.
We performed a bivariate analysis to verify the relationship between the dependent variable and
each independent variable; all non-significant associations with p > 0.05 were excluded from the
model. Thisanalysisallowedustoexcludevariablesthatpresentedasingularity,whichisatypeof
redundancythatappearsafterthecreationofthedummyvariables. WeusedPearson’schi-squared
(χ2)testtoevaluatetherelationforthequalitativevariables,andtheStudent’st-testforthequalitative
variables[101].
Priortoobtainingthefinalmodelwithsignificantvariables,buildinganumberofmodelswith
thelargestpossiblenumberofindependentvariablesispreferableinordertocheckwhichvariables
aresignificantinthemodelwiththepresenceofallothervariables[102].
Inthisstudy,backwardsselectionwasused. Theinputvariableswereperformedmanually,based
onintroducingthevariablesonebyone. Wedidnotusetheautomaticmethodbecauseitselectsthe
predictorsonlyonthebasisofstatisticalcriteria. Thistypeofselectionispreferablewhenthesearch
fieldislessexploredandtheknowledgeoftheeffectofeachindependentvariableislimited. Moreover,
itishighlysensitivetothemulticollinearity[102,103]. Afterenteringeachvariable,theWaldstatistics
werecomputedtocheckthecontributionofindividualpredictorsinthemodel. Wegenerallykeptall
variableswithap-value<0.05[38,40,47]. Inotherwords,weacceptedtheseindependentvariablesas
influentialpredictors.
Inordertoensurethatweconsideredtheleastnumberofallsignificantvariables,theresulting
modelwastestedagainbasedonthesignificanceofthelikelihoodratio. Duringthisstep,weentered
andremovedvariables. Aftereachentry,wecalculatedthelikelihoodratioforbothmodels. Ifthere
wasasignificantchangebetweenthetwolikelihoodratios,(wherethep-valuewaslessthan0.05),
thefirstmodelwaskeptwithoutchanges[40,104].
ThegoodnessoffitofthemodelwasalsoevaluatedusingCoxandSnell,andNagelkerkepseudo
R2 tests[105],whicharesimilartothecoefficientofdeterminationR2 inordinarylinearregression.
TheCoxandSnellpseudoR2 valuedidnotexceed1. Nagelkerke’spseudoR2 isabetterversionof
theCoxandSnellpseudoR2andisoftenpreferredbecauseitsvaluevariesbetween0and1[40,105].
UsuallyaR2valuehigherthan0.2indicatesarelativelygoodfit[106].
The adjustment of the logistic regression model is generally sensitive to collinearity between
independent variables [46]. Multicollinearity poses a problem because it increases the variance of
theregressionlogisticscoefficients. Thevarianceinflationfactor(VIF)isusuallyusedtocheckthe
multicollinearitydiagnosis. Inourstudy,wecalculatedtheVIFforeachvariable. Ifthevaluewas
greaterthan1.5,thevariablewasexcludedfromthemodel[38,107].
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3.5. ModelPredictionandUncertainties
Modelvalidationisakeystepandhelpstoevaluatethereliabilityofthemodelbeforeitcanbe
usedforpracticalapplications.
Inordertoassesstheaccuracyofthemodel,weusedaquantitativemeasurementmethod,called
theareaundertheROCcurve,onaseparatedesertificationvalidationsetinvolving30%ofthetotal
desertificationpixels. TheareaundertheROCcurveiscommonlyusedasametrictomeasurethe
goodnessofasusceptiblemodel[45,68,108,109]. Alargeareaunderthecurveindicatesgoodmodel
performance. The curve is a two-dimensional plot where the y-axis represents the probability of
acorrectlypredictedresponsetoaneventintermsofsensitivityortruepositiverate,andthex-axis
representstheprobabilityofanincorrectpredictedresponsetoanevent,intermsofspecificityorfalse
positiverate[40]. Ifalldesertifiedareasarecorrectlypredicted,theareaunderthecurvewillequal1,
butingeneralanareaunderthecurvegreaterthan0.5isacceptable[110–113].
Tofacilitatetheinterpretationoftheresultsforusersandtohelpthedecision-makertotakethe
appropriateactiontocombatdesertification,weclassifiedthedesertificationsusceptibilitymapbased
ontheliterature.Inpreviousstudies,thenumberofsusceptibilityclassesvariedcommonlyfromtwoto
five[68,107,114].Inordertoaligntheresultsofourstudywithotherpriorstudiesondesertification,the
probabilitymapwasdividedintofivesusceptibilityclasses: veryhigh,high,moderate,low,andsafe.
Inthisstudy,weusednaturalbreaksclassesbasedontheJenksoptimizationprocedure.Thisprocedure
determinesthebestarrangementofvaluesintoseveralclassesthatmaximizesbetween-classvariance
andminimizeswithin-classvariance[115,116].
Uncertainty is an important test that has been applied by different researchers to measure
the quality of susceptibility mapping [68,117,118]. First, we tested the sensitivity of the model to
the changes in the input training dataset using a bootstrapping technique. Fifty desertification
susceptibilitymapsweregeneratedusing50differenttrainingdatasetsthatwererandomlyselected,
involving70%ofthepixelswithdesertification. Foreachmap,wekeptthesamepredictivefactors
oftheresultingmodel. Then,wecalculatedtheareaundertheROCcurveforeachofthese50maps,
usingthevalidationdatasetsinvolving30%ofpixelswithdesertification. Thesensitivityofthemodel
wasrepresentedbyaboxplotdiagram,whichexpressesthevariationoftheareaundertheROCcurve.
Thesecondmeasureofuncertaintyincludedtheestimationofthemodel’serror. Forthispurpose,
werandomlyselected20,000pixels. Foreachmodel,weobtaineddescriptivestatistics,includingthe
meanandstandarddeviationfromthe50estimatedsusceptibilitymapsusingtheseselectedpixels.
Foreachmodel,wecalculatedthemeanandstandarddeviation. Theerrorplotsshowthemeanvalue
inthex-axisagainsttheirtwostandarddeviationsofsusceptibilityestimatesinthey-axis.[68,117,118].
4. Results
4.1. EvaluationofPredictiveFactors
Inordertoclarifythecharacteristicsofthedesertifiedareas,weevaluatedtherelationshipsbetweenthe
desertifiedarea,representedbythetrainingandvalidationdatasets,anddesertification-predictivefactors.
TheNDVIwasbetween−0.54and0.92intheareastudy. Desertifiedareashadvaluesbetween
0.08and0.29,andmorethan96%ofthedesertifiedareashadanNDVIvaluebelow0.22(Figure2B).
Thestudyareaincluded12typesofland-cover/use: agriculture,grazedcropland,sebkha,rangelands,
forest,afforestation,espartograss,dunes,uncultivatedareas,urbanareas,andcultivatedrangelands.
Over64%ofthedesertifiedareaswerefoundinrangelands,and20%ofdesertifiedareaswerefound
inagriculturalzones(Figure2E).
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Over43%ofthedesertifiedareaswerefoundinareaswithannualprecipitationbelow300mm,
andthatpercentagerosetomorethan98%forareaswithlessthan400mmofannualprecipitation
(Figure2A).Thestudyareacontainedeighttypesoflithostratigraphicunits: alluvium,conglomeratic