Effective surveyed area and its role in statistical landslide susceptibility assessments

Na . Haza ds Ea h Sys . Sci., 18, 2455–2469, 2018 h ps://doi.o g/10.5194/nhess-18-2455-2018 © Au ho (s) 2018. This wo k is dis ibu ed unde he C ea i e Commons A ibu ion 4.0 License. E ec i e su eyed a ea and i s ole in s a is ical landslide suscep ibili y assessmen s Txomin Bo nae xea1, Mau o Rossi2, I an Ma chesini2, and Massimiliano Al ioli2 1Depa men o Geog aphy, P ehis o y and A chaeology, Facul y o A s o he Uni e si y o he Basque Coun y UPV/EHU, c/ Tomás y Valien e, s/n, 01006, Vi o ia-Gas eiz, Spain 2Consiglio Nazionale delle Rice che, Is i u o di Rice ca pe la P o ezione Id ogeologica, ia Madonna Al a 126, 06128 Pe ugia, I aly Co espondence: Txomin Bo nae xea ( xomin.bo nae x[email p o ec ed]) Recei ed: 28 Ma ch 2018 – Discussion s a ed: 9 Ap il 2018 Re ised: 13 July 2018 – Accep ed: 21 Augus 2018 – Published: 14 Sep embe 2018 Abs ac . Geomo phological ield mapping is a con en ional me hod used o p epa e landslide in en o ies. The app oach is ypically hampe ed by he accessibili y and isibili y, du - ing ield campaigns o landslide mapping, o he di e en po ions o he s udy a ea. S a is ical signi icance o land- slide suscep ibili y maps can be signi ican ly educed i he classi ica ion algo i hm is ained in unsu eyed egions o he s udy a ea, o which landslide absence is ypically as- sumed, while igno ance abou landslide p esence should ac- ually be acknowledged. We compa e di e en landslide sus- cep ibili y zona ions ob ained by aining he classi ica ion model ei he in he en i e s udy a ea o in he only po ion o he a ea ha was ac ually su eyed, which we name e ec i e su eyed a ea. The la e was delinea ed by an au oma ic p o- cedu e speci ically de ised o he pu pose, which uses in o - ma ion ga he ed du ing su eys, along wi h landslide loca- ions. The me hod was es ed in Gipuzkoa P o ince (Basque Coun y), no h o he Ibe ian Peninsula, whe e digi al he- ma ic maps we e a ailable and a landslide su ey was pe - o med. We p epa ed he landslide suscep ibili y maps and he associa ed unce ain y wi hin a logis ic eg ession model, using bo h slope uni s and egula g id cells as he e e ence mapping uni . Resul s indica e ha he use o e ec i e su - eyed a ea o landslide suscep ibili y zona ion is a alid ap- p oach ha minimises he limi a ions s emming om unsu - eyed egions a landslide mapping ime. Use o slope uni s as mapping uni s, ins ead o g id cells, mi iga es he unce - ain ies in oduced by aining he au oma ic classi ie wi hin he en i e s udy a ea. Ou me hod pe ains o da a p epa a ion and, as such, he ele ance o ou conclusions is no limi ed o he logis ic eg ession bu a e alid o i ually all he ex- is ing mul i a ia e landslide suscep ibili y models. 1 In oduc ion Landslide suscep ibili y is de ined as he likelihood o a landslide occu ing in an a ea on he basis o he local e - ain and en i onmen al condi ions (B abb, 1984; Guzze i e al., 2005). Landslide suscep ibili y zona ion (LSZ) is im- po an o landslide mi iga ion plans, since i supplies plan- ne s and decision make s wi h essen ial in o ma ion (Van Den Eeckhau e al., 2012). A la ge numbe o LSZ s udies based on s a is ical me hodologies (Reichenbach e al., 2018) and compa a i e s udies (Cascini, 2008; Das e al., 2010; Schicke , 2010; Amo im, 2012; Blais-S e ens e al., 2012; T igila e al., 2015; Wang e al., 2015) we e published in he las decades. Many s a is ical me hods, aimed a es ima ing he p opensi y o a e i o y o expe ience slope ailu es, ely on landslide in en o y maps and spa ial hema ic laye s as p edisposing ac o s (E mini e al., 2005; Van Den Eeckhau e al., 2006; Camilo e al., 2017). In s a is ical landslide suscep ibili y models, such as he logis ic eg ession (LR) model adop ed in his wo k, he p epa a ion o he aining da a se is a undamen al and c i - ical s ep. Commonly, his equi es he selec ion o a sample o s able (wi hou landslides) and uns able (wi h landslides) mapping uni s. While ensu ing he p esence o a landslide is s aigh o wa d and can be suppo ed by he geomo pho- logical signa u es on he slope o by di ec obse a ion o Published by Cope nicus Publica ions on behal o he Eu opean Geosciences Union. 2456 T. Bo nae xea e al.: E ec i e su eyed a ea and i s ole in s a is ical landslide suscep ibili y assessmen s he e en s, he selec ion o landslide- ee a eas is mo e c i i- cal. Assuming as landslide- ee he loca ions o a s udy a ea whe e no landslides we e epo ed in a ield su ey is co ec only in he unlikely ci cums ance ha he landslide in en o y has been p epa ed by su eying e e y single si e o he s udy a ea and ollowing homogeneous c i e ia. In o he wo ds, any landslide- ee loca ion in an in en o y map should ha e been explici ly checked o be ee om landslides. Nowadays, he e a e me hods based on he isual in e p e- a ion o ae ial pho og aphs o digi al p ocessing o emo ely acqui ed op ical and ada image y (Ca ani e al., 2005; He - e a e al., 2009; Fio ucci e al., 2011, 2018; Casagli e al., 2017; Mondini, 2017; Al ioli e al., 2018b), which allow his- o ical and e en landslide in en o ies o be p epa ed. How- e e , he adop ion o such me hods can be hampe ed by he lack o image y o image in e p e a ion expe ise, low pe o - mance o au oma ic classi ica ion and o he ac o s. Al e na- i ely, bibliog aphic sou ces like newspape s and news eeds, adminis a i e epo s o scien i ic li e a u e can be used o ob aining landslide in o ma ion. Ne e heless, he downside o hese ype o da a is ha hey a e a ely as accu a e as equi ed by LSZ s udies. As a consequence, some imes he bes op ion o ob aining a eliable landslide in en o y is a s aigh o wa d geomo phological ield mapping. A de ailed discussion abou he cha ac e is ics, ad an ages and limi a- ions o di e en app oaches o landslide mapping can be ound in Guzze i e al. (2012) San angelo e al. (2015) and Fio ucci e al. (2018). An ope a ional disad an age o ield-based landslide map- ping is he di icul y in su eying he whole a ea whe e he LSZ mus be ca ied ou , since some places can be inacces- sible o no isible om he accessible places. Di icul ies in su eying he landscape a ec he comple eness and he spa ial ep esen a i eness o he landslide in en o y and, as a esul , inclusion o non- isible a eas wi hin a landslide in- en o y in oduces a bias, since he p esence o absence o landslides canno be asce ained in po ions o he landscape. This unce ain y has ha dly been conside ed in exis ing s ud- ies ha use ield-based landslide in en o ies (Yesilnaca and Topal, 2005; Mu illo-Ga cía e al., 2015; Wang e al., 2017). On he o he hand, selec ion o an app op ia e e ain sub- di ision is also a c i ical s ep in LSZ analysis. The land su ace can be di ided in o po ions ollowing geomo pho- logic ea u es using e ain uni s, opog aphic uni s, geo- hyd ological uni s o slope uni s bu also conside ing he- ma ic laye s esul ing in unique condi ion uni s o admin- is a i e uni s, as well as egula g id cells pa i ions (Van Den Eeckhau e al., 2006; Reichenbach e al., 2018). Se- lec ion o di e en mapping uni s can esul in conside - able di e ences in he suscep ibili y assessmen (Ca a a e al., 2008). In his wo k, we conside ed g id cells and slope uni s (Ca a a e al., 1991, 1995; Guzze i e al., 2006; Al ioli e al., 2016; Zêze e e al., 2017; Rosi e al., 2018; Ba e al., 2018) and in es iga ed he e ec o he di e en ways o aining LSZ models wi hin bo h ypes o mapping uni s. We p opose an au oma ic and ep oducible p ocedu e o delinea e he ac ual a ea which was explici ly su eyed in p epa ing a landslide in en o y by geomo phological ield mapping, i.e. he e ec i e su eyed a ea (ESA), and o use such ele an in o ma ion in s a is ical analyses. The p o- cedu e allows us o ca y ou he calib a ion o a s a is ical model wi hin he ESA and hen o apply he esul ing sus- cep ibili y model o he whole a ea (WA) unde in es iga- ion. Mo eo e , we implemen ed an au oma ic app oach o he delinea ion o he ESA in a newly de eloped GRASS GIS module named .su ey.py. The so wa e delinea es he he- o e ical isible a eas om he poin s o iew eco ded du - ing a ield campaign by he GPS acks. Mos impo an ly, he ESA delinea ed by .su ey.py is an objec i e and ep o- ducible po ion o he s udy a ea di ec ly obse ed by he ge- omo phologis s, hus allowing us o a oid a bi a y assump- ions abou which si es we e ac ually su eyed and which ones we e no . This wo k aims a demons a ing ha he calib a ion o a landslide suscep ibili y model wi hin he ESA, ins ead o he WA ( he whole s udy a ea, encompassing he ESA), enhances he pe o mance o model i sel . In a es s udy a ea, we cali- b a ed he mul i a ia e logis ic eg ession model o landslide suscep ibili y in ou di e en ways, combining wo di e en calib a ion a eas (ESA and WA) wi h wo di e en mapping uni ypes: (i) a egula g id cell pa i ion wi h a g ound eso- lu ion o 5 m ×5 m and (ii) a slope uni (SU) pa i ion (con- sis ing o i egula e ain subdi isions bounded by d ainage and di ided lines). The pape is o ganised as ollows. Sec ion 2 p o ides an o e iew o he s udy a ea. Sec ion 3 shows he de ails abou da a acquisi ion, in pa icula he .su ey is desc ibed in Sec . 3.3 and SU delinea ion in Sec . 3.4. Sec ion 4 con ains a gene al desc ip ion abou he mul i a ia e me hod applied o model landslide suscep ibili y and he app oach ollowed o alida e model esul s, as well as a de ailed desc ip ion abou he se -up o he di e en model assessmen s. Resul s a e desc ibed in Sec . 5 and a e u he discussed in Sec . 6. E en ually, ou conclusions a e d awn in Sec . 7. 2 S udy a ea The Gipuzkoa P o ince was selec ed as es s udy a ea. I is loca ed in he no h o he Ibe ian Peninsula along he wes - e n end o he Py enees and co e s an a ea o 1980 km2, wi h al i ude anging om he sea le el o 1528ma.s.l. Six wa- e sheds o di e en size d ain he s udy a ea and each he Can ab ian Sea (Fig. 1). The p o ince is cha ac e ised by a s eep mo phology wi h 55% o i s su ace ha ing a slope la ge han 15◦. The in es iga ed a ea is li hologically he e ogeneous (Fig. 1), wi h ma e ials anging om Paleozoic ocks o Qua- Na . Haza ds Ea h Sys . Sci., 18, 2455–2469, 2018 www.na -haza ds-ea h-sys -sci.ne /18/2455/2018/ T. Bo nae xea e al.: E ec i e su eyed a ea and i s ole in s a is ical landslide suscep ibili y assessmen s 2457 Figu e 1. Loca ion o he Gipuzkoa P o ince s udy a ea and simpli ied li hological map de eloped acco ding o he o iginal map o he spa ial da a se ice o he Basque Coun y. Coo dina es in deg ees, Uni e sal T ans e sal Me ca o (UTM) Zone 30N, Eu opean Da um ETRS 1989. e na y deposi s (EVE, 2010), and i co esponds o a hilly and moun ainous A lan ic landscape (Müche e al., 2010). The a e age annual p ecipi a ion is 1597mm (González- Hidalgo e al., 2011) wi h wo maximum pe iods: 34% in No embe –Janua y and 10% in Ap il. E en hough ain all is he p ima y igge ing ac o o shallow landslides (Pe - ley e al., 2005; Al ioli e al., 2018a), an h opogenic slope modi ica ions such as slope clea ings and o es ex ac ion ac i i ies also s ongly a ec landslide occu ence (Co omi- nas e al., 2017) in he a ea. 3 Da a p epa a ion 3.1 Landslide in en o y We p epa ed a landslide in en o y by a di ec geomo pholog- ical ield su ey, du ing he pe iod om June o Augus 2016. We collec ed in o ma ion abou he loca ion o each obse ed landslide, ou GPS poin s (c own, oe and wo lanks), pho- og aphs, ea u es o he su ounding a ea and in o ma ion abou he landslide ype, acco ding o he C uden and Va nes (1960) classi ica ion. Each documen ed landslide was d awn and digi ised using i s ou eco ded GPS waypoin s and pho og aphs as a e e ence. The QGIS so wa e and Google Ea h sa elli e image y we e used o he pu pose. Mo eo e , and mos impo an ly o de ine he ESA, we digi ised he ou e ollowed du ing he ield su ey. This in o ma ion was hen elabo a ed using a GRASS GIS module de eloped o he pu pose and included in his wo k as he Supplemen . As a esul o se e al ield ips, 793 indi idual land- slides we e collec ed; 746 o hem we e classi ied as shal- low mo emen s (Fig. 2a). Ou obse a ions oge he wi h he exis ing li e a u e (INGEMISA, 1995; IDE de Euskadi, 2014; Gipuzkoako Fo u Aldundia, unpublished da a) con- i med ha shallow slides a e he mos equen ype o land- slide in he s udy a ea. Consequen ly, in o de o conside only landslides igge ed by he same mechanisms, only shal- low mo emen s we e used o de e mine landslide p esence when de ining he dependen a iable in he suscep ibili y as- sessmen . Figu e 2b and c show he dis ibu ion o landslide sizes, highligh ing ha a di e ence o 5 o de s o magni ude exis s be ween he smalles and he la ges in en o ied shal- low slide. 3.2 Explana o y a iables The selec ion o he app op ia e explana o y a iables o build a landslide suscep ibili y model is an impo an s ep (Ayalew and Yamagishi, 2005; Schlögel e al., 2018), and no uni e sal c i e ia no guidelines exis o he pu pose. We ob ained ele an en i onmen al digi al laye s om he Spa ial Da a Se ice o he Basque Coun y1and c e- a ed 13 maps desc ibing he di e en explana o y a iables (see Table 2). To p oduce de i ed mo phome ic con inuous a iables, such as slope, sinusoidal slope, su ace a ea a- io (SAR), e ain we ness index (TWI), cu a u e, plan cu - a u e and p o ile cu a u e, we used a DEM as e laye wi h 5 m ×5 m spa ial esolu ion. sinusoidal slope is a de- i ed mo phome ic a iable p oposed by San acana Quin- as (2001) and Amo im (2012) o emphasise he ac ha shallow slides ypically occu in medium slope a eas, while hey seldom occu on slopes s eepe han 45◦. Fo ca ego ical a iables, such as li hology, pe meabili y, egoli h hickness, 1h p://www.geo.euskadi.eus (las access: 23 Janua y 2017) www.na -haza ds-ea h-sys -sci.ne /18/2455/2018/ Na . Haza ds Ea h Sys . Sci., 18, 2455–2469, 2018 2458 T. Bo nae xea e al.: E ec i e su eyed a ea and i s ole in s a is ical landslide suscep ibili y assessmen s Figu e 2. (a) Dis ibu ion o he shallow slides in en o y along he s udy a ea and ex ension o he e ec i e su eyed a ea (ESA). (b) P ob- abili y densi y plo o he shallow landslide size (a ea in m2) dis ibu ion. (c) Box plo o he same dis ibu ion. land use, ege a ion and aspec , we compu ed equency a io (FR) alues o each class and used hem as ela i e alues o hei ans o ma ion in o con inuous a iables (Lee and Min, 2001; Yilmaz, 2009; T igila e al., 2015). We acknowl- edge ha he FR alues can a y depending on he po ion o he e i o y conside ed o be he o al a ea (ESA o WA). In o de o pe o m a di ec compa ison, we decided o main- ain he same FR alues (calcula ed conside ing he WA) in all egula g id-cell-based suscep ibili y analyses. In his wo k, we i s adop ed g id cells as mapping uni s, and we applied a simpli ied and s a is ically o ien ed wo k- low ha ensu ed ha only signi ican a iables we e aken in o accoun as well as he non- edundancy o he con- ibu ed in o ma ion by each co a ia e (Ayalew and Yamag- ishi, 2005). To do his, he whole se o 13 a iables was con- side ed wi hin he LR analysis, and co ela ion coe icien s we e compu ed. We conside ed wo a iables o be collinea when hei co ela ion coe icien is g ea e han 0.5 wi h a signi icance le el o 0.01. In such a case, as an objec i e c i- e ion o a iable selec ion, he a iable wi h he highes p alue be ween he wo (see Sec . 4.1) was no aken in o con- side a ion in he inal un o he suscep ibili y LR model. Ad- di ionally, a iables wi h a p alue highe han he h eshold o 0.05 we e ejec ed. Then, conside ing he a iables ac ually used o he ap- plica ion o he s a is ical models wi h g id cells, we ha e u he es ic ed he se o a iables o be used wi h slope uni s (see Sec . 5.2). 3.3 De ini ion o he e ec i e su eyed a ea In his wo k we sugges he concep o ESA and aining o s a is ical models he ein, as an app oach o be used o ain a landslide suscep ibili y model, a oiding assump ions abou he p esence o absence o landslides in a eas no explici ly obse ed. We delinea ed he ESA by means o he newly de- eloped GRASS GIS py hon module .su ey.py (see Sup- plemen ). Inpu da a ha de ine he isible a ea (i.e. ESA in ou case) a e (i) a sample o poin s o be conside ed he poin s o iew, (ii) a DEM o he a ea and (iii) he maximum isible dis ance. The sample o poin s o iew, in ou case, was de ined esampling a gi en numbe o poin s along he eco ded pa h du ing he ield campaigns. This numbe o poin s depends on he maximum dis ance se be ween hem, and oge he wi h he selec ed DEM esolu ion he esul s can be di ec ly a ec ed. In a 10km2subse o he s udy a ea, we es ed he so wa e ou pu using (i) he maximum dis ance be ween sampled poin s o 50, 100, 200 and 500 m; (ii) he o iginal DEM a 5m esolu ion and esampled e sions o he DEM a 20, 50 and 100 m esolu ion; and (iii) maxi- mum isible dis ance o 500 m ( he la e was dic a ed by he la ges dis ance be ween he digi ised ield pa h and he a - hes landslide pixel in he subse o he s udy a ea). Resul s o he es a e summa ised in Table 1. We conside ed ha he bes se ing was he one which al- lows he o ali y o he landslides o be co e ed using he smalles numbe o poin s (la ge Dmax alue) and he lowe DEM esolu ion in o de o op imise he calcula ion ime. In ou case, conside ing he whole s udy a ea, he maximum isible dis ance was se o 1100m, in iew ha he la ges dis ance be ween he digi ised ield pa h and he a hes landslide pixel was 1092m. Then, and acco ding o he e- sul s o Table 1, we se he maximum sampling dis ance o 200 m and adop ed a DEM esolu ion o 100m. We can make sense o he nume ical alues o he pa ame- e s used in he .su ey.py module conside ing ha he min- imum size Ao an objec isible om a dis ance 1is gi en Na . Haza ds Ea h Sys . Sci., 18, 2455–2469, 2018 www.na -haza ds-ea h-sys -sci.ne /18/2455/2018/ T. Bo nae xea e al.: E ec i e su eyed a ea and i s ole in s a is ical landslide suscep ibili y assessmen s 2459 Table 1. Resul s o he se ing es o .su ey in a 10km2subse o he s udy a ea. The bes combina ion o se ings is highligh ed in bold. Name Resolu ion Dmax Pe cen age o (m) landslides wi hin (%) Su ey 5 5 50 35 Su ey 6 20 50 70 Su ey 7 50 50 95 Su ey 8 100 50 100 Su ey 9 5 100 30 Su ey 10 20 100 60 Su ey 11 50 100 95 Su ey 12 100 100 100 Su ey 13 5 200 30 Su ey 14 20 200 55 Su ey 15 50 200 85 Su ey 16 100 200 100 Su ey 17 5 500 0 Su ey 18 20 500 35 Su ey 19 50 500 60 Su ey 20 100 500 95 by Rod igues e al. (2010) and Minelli e al. (2014): A=2512 c,(1) whe e cis a s e adian o squa e minu es con e sion ac o , c≃1.18 ×107. Using 1=1100 m in Eq. (1), we ge A= 2.6 m2, meaning ha he smalles landslide in ou in en o y, wi h size 7.3 m2, would ac ually be iden i iable om a leas one poin along he ou e i he landslide si s wi hin he ESA. The esul ing ESA co e s 44.24 % o he en i e s udy a ea and i is shown in Fig. 2a. 3.4 Slope uni delinea ion Fo SU delinea ion we ha e adop ed he .slopeuni s so wa e desc ibed in Al ioli e al. (2016). The so wa e is a GRASS GIS module, as is he .su ey.py code p esen ed in his wo k, and i was designed o he au oma ic and adap i e delin- ea ion o SUs gi en a DEM and a se o use -de ined inpu pa ame e s. The code can be used o p oduce se e al SU pa - i ions, using di e en combina ions o he inpu pa ame e s, which can hus be uned acco ding o use -de ined c i e ia. We pa ially ollowed Al ioli e al. (2016), in ha we se- lec ed he bes SU pa i ion conside ing he quali y o e ain aspec segmen a ion. In addi ion, we pe o med p elimina y es s using he LR suscep ibili y model, showing ha he use o e y small SUs p o ides un ealis ic esul s, which can be unde s ood conside ing he limi ed a iabili y o a iables wi hin such small SU polygons. We concluded ha , in he case o he Gipuzkoa P o ince he mos sui able SU pa i ion o landslide suscep ibili y zona ion should be ob ained wi h he ollowing .slopeuni s inpu pa ame e s: low accumula- ion a ea h eshold =1 km2, minimum SU planime ic a ea a=0.15 km2, minimum ci cula a iance o e ain aspec wi hin each SU c=0.2, educ ion ac o =5 and h eshold alue o he cleaning p ocedu e cleansize=0.025 km2. As a esul , we ob ained a se o SUs which ange in size om 0.026 o 3.6 km2wi h an a e age o 0.28km2. A discussion o SU delinea ion and op imisa ion o inpu pa ame e s can be ound in Al ioli e al. (2016) and Schlögel e al. (2018), and i is beyond he scope o his wo k. 4 Modelling amewo k We p epa ed ou landslide suscep ibili y maps (LS maps), by means o a mul i a ia e LR model. Classi ica ion pe o - mances we e measu ed by means o a se o alida ion es s explained in he ollowing sec ions. We p epa ed he i s wo maps using 5 m ×5 m egula g id cells as mapping uni s. The wo maps di e because in one case he LR model was calib a ed wi hin he WA, and in he o he case wi hin he ESA (desc ibed in Sec . 3.3). The hi d and ou h LS maps, ins ead, we e p epa ed wi h di e en mapping uni s, namely wi h SUs (desc ibed in Sec . 3.4) ins ead o g id cells, whe e calib a ion da a we e also changed conside ing da a wi hin WA in one case and wi hin ESA in he o he . We end up wi h ou maps, which we name as ollows: WA-PM (whole-a ea pixel map), ESA-PM (e ec i e su eyed a ea pixel map), WA-SUM (whole a ea o he slope uni s map) and ESA- SUM (e ec i e su eyed a ea o slope uni s map). 4.1 Logis ic eg ession We used logis ic eg ession (Hosme J . e al., 2013), one o he mul i a ia e s a is ical app oaches a ailable in he LAND-SE so wa e (Rossi and Reichenbach, 2016), o build he landslide suscep ibili y model in he es s udy a ea. The me hod is he mos used in he scien i ic li e a u e (Reichen- bach e al., 2018) and p o ed o be use ul and eliable in se e al s udies (Ne eslioglu e al., 2008; Van Den Eeckhau e al., 2012; T igila e al., 2015). The LR model wo ks wi h ei he con inuous o ca ego ical independen a iables, o a combina ion o he wo ypes, ega dless o whe he hey a e no mally dis ibu ed o no (Cos anzo e al., 2014). The ma hema ical ela ionship be ween he dependen di- cho omous a iable (p esence o absence o a landslide in he mapping uni ; Yin he ollowing) and he nindependen a iables (e.g. slope, li hology; X1,...,Xn), wi hin he LR model, eads as ollows: Y=β0+β1X1+... +βnXn,(2) whe e β0is he in e cep o he model and β1,...,βn he linea eg ession es ima e coe icien s. The independen (ex- plana o y) a iables, X1,...,Xn, included in ou case bo h con inuous and ca ego ical laye s ( he la e we e p e i- ously ans o med in o con inuous a iables, as desc ibed in www.na -haza ds-ea h-sys -sci.ne /18/2455/2018/ Na . Haza ds Ea h Sys . Sci., 18, 2455–2469, 2018 2460 T. Bo nae xea e al.: E ec i e su eyed a ea and i s ole in s a is ical landslide suscep ibili y assessmen s Table 2. Se o en i onmen al a iables in oduced o he whole-a ea pixel-based (WA-PM) and e ec i e su eyed-a ea pixel-based (ESA- PM) model calcula ion, oge he wi h he signi ican p- alue es ima e co esponding o each explana o y a iable (c . Sec . 4.1). The bes p edic o s we e labelled wi h an as e isk. Name Desc ip ion Signi ican p alue Con inuous WA-PM ESA-PM Slope The slope g adien in deg ees. 1.17 ×10−189 1.06 ×10−111 Sinusoidal slope The sinusoidal ma hema ical ans o ma ion applied o he slope a iable (Amo im, 2012) 1.00 ×10−155 7.57 ×10−134* Su ace a ea a io The ela ion be ween he heo e ical olume and he su ace o each pixel. 3.743 ×10−203* 1.89 ×10−99 Te ain we ness index The spa ial dis ibu ion o soil mois u e o sa u a ion (Yilmaz, 2009) 9.864 ×10−10* 0.126807342 Cu a u e The spa ial a ia ion o he slope g adien . 0.909592654 0.525989188 Plan cu a u e The cu a u e o he su ace pe pendicula o he di ec ion o he maximum slope. 0.9094261 0.525836679 P o ile cu a u e The cu a u e o he su ace in he di ec ion o he maximum slope. 0.909605174 0.526032985 Ca ego ical Li hology The o iginal ca ego ies ha e been eclassi ied by expe c i e ia (Geoeuskadi). 0* 0* Pe meabili y The o iginal ca ego ies ha e been eclassi ied by expe c i e ia (Geoeuskadi). 1.496 ×10−33* 7.632 ×10−72* Regoli h hickness The laye o he s udy a ea has been ob ained om he li ho- logical map (Geoeuskadi). 0* 0* Land use The o iginal ca ego ies ha e been eclassi ied by expe c i e ia (Geoeuskadi). 5.14 ×10−291 1.42 ×10−87 Vege a ion The o iginal ca ego ies ha e been eclassi ied by expe c i e ia (Geoeuskadi). 0* 1.596 ×10−173* Aspec I ep esen s he downslope di ec ion measu ed in deg ees clas- si ied in nine classes. 0* 0* Sec . 3.2); see Table 2 o he ull lis o a iables used in his wo k. Calib a ing an LR model amoun s o selec ing nume ical alues o he {βi}i=n i=1coe icien s in Eq. (2) ha maximise he ag eemen be ween model ou pu , i.e. landslide p obabili y: P=1 1+e−Y,(3) and empi ical landslide da a, in a aining a ea. The same al- ues o he coe icien s can hen be used o alida e he model p edic ion skills in a di e en a ea, whe e landslide condi- ions a e unknown o he model bu he same explana o y a iables laye s exis . In addi ion o he βcoe icien s, he LR me hod o e s a signi ican p alue o each explana o y a iable. The imple- men a ion o he glm unc ion o he R p og amming lan- guage lib a y2, used in he LAND-SE so wa e, is such ha i is possible o in es iga e he es ima ed s anda d e o o a s a is ic o he null hypo hesis o each o he coe icien s o he linea model. The p alue ep esen s he p obabili y o 2h ps://www. -p ojec .o g/ (las access: 6 Ma ch 2017) he pa ame e o be ze o: o p alues smalle han 0.05 he null hypo hesis ( anishing coe icien ) is ejec ed; hus he associa ed a iable is signi ican o he inal esul . So, he p alue can be conside ed an objec i e indica o o he selec- ion o he mos ele an a iables o be used in he s a is ical model (Schlögel e al., 2018). 4.2 E alua ion o model pe o mance The pe o mance o s a is ical suscep ibili y models, i.e. o mul i a ia e bina y classi ie s, can be e alua ed by compa - ing hei p edic ions wi h he landslide da a used in he model calib a ion/ aining s ep (i.e. model i ing pe o mance) o wi h independen landslide da a (i.e. model p edic ion pe o - mance). The de ini ion o aining and alida ion inpu sam- ples is c ucial o de ec how well each model i s inpu da a bu also how good he model is a p edic ing new da a. The s a is ical me ics commonly used in he li e a u e (Co ominas and Ma ouli, 2011; Van Den Eeckhau e al., 2006; Lomba do e al., 2015; Reichenbach e al., 2018) o ha pu pose a e (i) con usion ma ices (con ingency ables) and hei g aphical ep esen a ion ( ou - old o con ingency Na . Haza ds Ea h Sys . Sci., 18, 2455–2469, 2018 www.na -haza ds-ea h-sys -sci.ne /18/2455/2018/ T. Bo nae xea e al.: E ec i e su eyed a ea and i s ole in s a is ical landslide suscep ibili y assessmen s 2461 plo s), (ii) ecei e ope a ing cha ac e is ic (ROC) cu es and hei associa ed a ea unde cu e (AUC) alue, (iii) classi i- ca ion e o plo s and (i ) Cohen’s kappa index. Fou - old (o con ingency) plo s a e isual ep esen a ions o he con usion ma ices epo ing he pe cen ages o he ue posi i es (TP), ue nega i es (TN), alse posi i es (FP) and alse nega i es (FN). ROC cu es a e a mo e complex ep esen a ion o he classi ica ion pe o mance based on di - e en p obabilis ic h eshold alues. The a ea unde he ROC cu e (AUC) is an indica o o he model pe o mance in p e- dic ing landslide suscep ibili y. AUC alues a y be ween 0 and 1, wi h highe alues indica ing be e p edic ion skills (Fawce , 2006). To es ima e he unce ain y associa ed wi h he landslide suscep ibili y alue assigned o each mapping uni , i is pos- sible o un mul iple ins ances o he LR model a ying, andomly, he inpu da a. In each un, he inpu is p epa ed by sampling he o iginal aining da a se wi h a boo s ap echnique, consis ing o a andom sampling wi h eplace- men (E on, 1992; Da ison and Hinkley, 1997; Rossi e al., 2010; Rossi and Reichenbach, 2016). Classi ica ion e o plo s summa ise he dis ibu ion o mul iple esul s and show he mean p obabili y es ima e o landslide spa ial occu ence o each mapping uni (xaxis), anked om low (le ) o high ( igh ) alues, ela ed o he a ia ion o he model es i- ma e (yaxis), measu ed by 2 s anda d de ia ions (2σ) o he p obabili y es ima es ob ained by he di e en model uns (Guzze i e al., 2006). The pa abolic model i ing equa ion esul ing om he poin cloud (i.e. using a non-linea leas squa e me hod), analy ically desc ibes he o e all model p e- dic ion pe o mance a iabili y. Cohen’s kappa index (κ) is an addi ional measu e o he eliabili y o a classi ica ion model (Cohen, 1960; Rossi e al., 2010), wi h highe alues ha also indica e a mo e accu a e p edic ion skill. In his s udy he p obabili y o landslide occu ence esul - ing om each model es ima e ( ained ei he wi hin he ESA o wi hin he WA) and o each conside ed mapping uni (ei- he g id cells o slope uni s) was eclassi ied in i e land- slide suscep ibili y classes, which we e labelled as e y low ( o suscep ibili y alues in he ange 0–0.2), low (0.2–0.45), medium (0.45–0.55), high (0.55–0.8) and e y high (0.8–1). Mo eo e , in o de o spa ially iden i y he pai wise ma ching deg ee be ween di e en model es ima es, we ad- di ionally adop ed a simpli ied classi ica ion o he landslide suscep ibili y. Each mapping uni was eclassi ied as s able o uns able conside ing a h eshold alue o 0.5. The di e - en maps, all o which we e p epa ed wi h he same mapping uni pa i ion, we e o e lapped. Then, he misma ch deg ee be ween g id cell and SU suscep ibili y maps was quan i ied in e ms o numbe o misma ched mapping uni s and o e all misma ched a ea. 4.3 Da a selec ion o landslide suscep ibili y The DEM a ailable o he s udy a ea consis s o 7.91 ×107 cells wi h 5m esolu ion. Fo landslide suscep ibili y assess- men , bo h using g id cells (i.e. pixels) and SUs, we p e- pa ed as e laye s co esponding o each a ailable explana- o y a iable, aligned o he DEM g id cells. We de ised a igo ous sampling p ocedu e o minimise possible s a is ical biases du ing aining/ alida ion pa i ion. The p ocedu e is sligh ly di e en o he g id cell and SU mapping uni s. In he i s case, a g id cell is conside ed uns able i i is loca ed wi hin any landslide polygon and s able i i is ou - side he landslide bounda ies. In he second case, an SU was conside ed uns able depending on he pe cen age o landslide a ea p esen wi hin i . In any case, he 75% o he uns able mapping uni s oge he wi h a simila numbe o s able map- ping uni s we e used o ain he LR model, and he emaining 25 %, also oge he wi h a simila numbe o s able mapping uni s o alida ion. The choice o an equal numbe o s a- ble and uns able mapping uni s was done on pu pose, and i is he s anda d p ocedu e equi ed by he LAND-SE so - wa e o landslide suscep ibili y assessmen , because he LR model equi es a balanced da a se , in which he numbe o s able and uns able cases a e simila (Felicísimo e al., 2013; Cos anzo e al., 2014). Fo egula g id-cell-based models, we selec ed a andom 558 landslides (75%) o model aining and con e ed hem in o as e laye s (84623 uns able pixels). The emaining 188 landslides (25 %) used o alida ion we e also as e ised (29 247 uns able pixels). This is a a iance wi h he usual andom selec ion o uns able pixels, in which a gi en pe - cen age o g id cells a e sampled wi hin landslide polygons. He e we selec whole landslides and conside all he pixels encompassed by he landslide bodies as aining/ alida ion samples. We an he expe imen wi h h ee di e en ain- ing/ alida ion andom se s, con aining he abo e pe cen - ages. This exe cise allowed us o con i m ha he andom selec ion o he landslide in en o y does no a ec he model esul s in a ele an way, because in all he cases he model classi ica ion pe o mances we e e y simila . In o de o choose one single da a se o u he compa a i e analyses, he da a se wi h he bes classi ica ion esul was selec ed. Then, aining se s we e selec ed as ollows: 84623 uns able pixels and an equal numbe o s able pixels we e selec ed as aining se s. Two di e en se s we e selec ed a andom, i s wi hin WA and hen wi hin ESA. We made su e ha uns able pixels we e exac ly he same in he wo cases, because we wan ed he only di e ence o be ha he s able pixels we e sampled wi hin he WA in he i s case and wi hin he ESA in he second case. Finally, in o de o gua an ee he compa a- bili y o he p edic ion pe o mances, one unique alida ion sample was c ea ed as ollows: he emaining 29 247 uns able pixels oge he wi h an equal numbe o s able pixels selec ed a andom wi hin he emaining s able pixels wi hin he ESA. www.na -haza ds-ea h-sys -sci.ne /18/2455/2018/ Na . Haza ds Ea h Sys . Sci., 18, 2455–2469, 2018 2462 T. Bo nae xea e al.: E ec i e su eyed a ea and i s ole in s a is ical landslide suscep ibili y assessmen s Conce ning he SU-based models, we i s pa i ioned he s udy a ea in o 6907 SUs wi h he echnique ou lined in Sec . 3.4. SU bounda ies do no ma ch hose o he depen- den o explana o y a iables laye s, allowing he p esence o di e en classes o alues inside each SU. Mo eo e , he p esence o one single landslide pixel wi hin a slope uni was no conside ed enough o label his SU as uns able. The e- o e, ins ead o a bi a ily de ining a gi en h eshold alue in o de o conside an SU as uns able, we decided o use he o e all landslide densi y in he WA. Fo his eason, we con- side ed o be uns able hose SUs con aining 0.15 % o mo e uns able pixels and s able o he wise. We used as explana o y a iables he mean and he s anda d de ia ion o he mo pho- me ic a iables o each SU and he pe cen age o he a ea co e ed by each class o he ca ego ical laye s. In 304 cases he SU con ained 0.15 % o mo e uns able pixels, so we se- lec ed a andom 228 o hem (75%) o aining, and he emaining 76 (25%) we e used o alida ion. Like in g id cell app oaches, we c ea ed wo di e en aining samples whe e uns able SUs we e exac ly he same, and only he s a- ble SUs a y in each case. The i s aining sample includes 228 s able SUs selec ed a andom along he WA. The sec- ond aining sample includes an equal numbe o s able SU uni s selec ed a andom among hose ha a leas pa ially o e lap he ESA. Addi ionally, 76 SUs labelled as uns able we e selec ed om he whole se o alida ion. The alida- ion sample was comple ed by adding a andom selec ion o he same numbe o SUs labelled as s able and which a leas pa ially o e lap he ESA. Thus, he alida ion sample con- ained 152 SUs (76 uns able and 76 s able). E en ually, since he ESA is an app oxima ion o he eal su eyed a ea, we s ess ha we always selec ed s able map- ping uni s o alida ion only i hey a e ully o pa ially wi hin he ESA, because no e idence exis s ha a mapping uni alling en i ely ou side he ESA is ac ually ee om landslides. Mo eo e , i a po ion o an SU alls wi hin he ESA, i implies ha a leas one pa o he SU was obse ed. The e o e, using his app oach, we can emo e a leas hose SUs ha we e no su eyed a all. 5 Resul s 5.1 Suscep ibili y maps using g id cells We an he LR model using he pixel-based da a se s wice: once using he en i e aining pixel sample and once using he e ec i e aining pixel sample as dependen a iables. We de ined he ob ained esul s as whole-a ea pixel map (WA- PM) and e ec i e su eyed-a ea pixel map (ESA-PM). In bo h WA-PM and ESA-PM, we i s used he same 13 explana o y a iables lis ed in Table 2, and hen we se- lec ed o each model assessmen he mos ele an explana- o y a iables conside ing he collinea i y be ween each pai o a iables and he signi icance (p alue) o he eg ession es ima es (see Sec . 3.2). As a esul , o each case, only he a iables ma ked wi h an as e isk in Table 2 we e in oduced in he inal LR analysis. Using he alida ion pixel sample, we e alua ed he p e- dic ion skills o he pixel suscep ibili y maps. Inspec ion o he ou - old o con ingency plo s (Fig. 3a, d) e eals ha WA-PM co ec ly p edic ed he 63.58 % (TP+TN) o he ob- se ed uns able and s able mapping uni s, whe eas ESA-PM was capable o co ec ly p edic ing a highe numbe o map- ping uni s (65.45%). The ROC cu es (Fig. 3b, e) also indi- ca e be e p edic ion skills in ESA-PM (AUC=0.7) han in WA-PM (AUC =0.68) and he same happens o he Cohen’s kappa index (Fig. 3; k=0.309 e sus k=0.272). Mo eo e , he classi ica ion e o plo s (Fig. 3c, ) p o ide an es ima e o he e o associa ed wi h he p edic ed suscep ibili y al- ues, which do no exceed 0.1 s anda d de ia ions in any case, highligh ing he eliabili y o he esul s. And inally, he mu- ual misma ch map (Fig. 5e) shows ha 14.8% (co espond- ing o an ex ension o 293km2) o he mapping uni s lipped hei landslide suscep ibili y class in WA-PM and ESA-PM. 5.2 Suscep ibili y maps using slope uni s Due o he subdi ision o ca ego ical a iables in classes and o he use o mean and s anda d de ia ion o mo phome - ic a iables, he in oduc ion o he o iginal 13 explana o y a iables would esul in 56 new a iables in which many o hem (all hose classes belonging o he same ca ego i- cal a iable) would be highly co ela ed. Fo his eason, he a iable selec ion app oach used in he pixel-based case is no iable when wo king wi h SUs and a speci ic a iable selec ion app oach o SU models would equi e u he in- es iga ion. Thus, o his wo k, he mos app op ia e se o explana o y a iables, among hose conside ed o be he mos ele an in pixel-based model assessmen , was selec ed by expe c i e ia. Conside ing his se o a iables as a s a ing poin , we selec ed new se s o explana o y a iables o e al- ua e landslide suscep ibili y using SUs, i.e. o calcula e he whole-a ea slope uni map (WA-SUM) and he e ec i e a ea slope uni map (ESA-SUM). Taking in o accoun ha he au- oma ic p ocedu e o he SU de ini ion al eady included he low accumula ion calcula ion, used o TWI es ima ion, and he aspec componen , we ejec ed aspec and TWI o a oid spu ious co ela ions. We selec ed he ollowing se o a i- ables used o p oduce bo h pixel-based maps such as li hol- ogy, pe meabili y, egoli h hickness and ege a ion, and we added slope. The eason o choosing slope o e sinusoidal slope o SAR is due o he ac ha hese wo a e de i a i e a iables o he o me . Mo eo e , we conside slope mo e sui able ea u e o desc ibe he a e age mo phology wi hin SU han sinusoidal slope o SAR, so we decided o selec i in o de o simpli y ou in e p e a ion o he esul s. Using he alida ion SU sample, we assessed he p edic- ion skills o he SU maps. Fo he WA-SUM he 65.13% o he 152 alida ion mapping uni s we e co ec ly classi ied Na . Haza ds Ea h Sys . Sci., 18, 2455–2469, 2018 www.na -haza ds-ea h-sys -sci.ne /18/2455/2018/ T. Bo nae xea e al.: E ec i e su eyed a ea and i s ole in s a is ical landslide suscep ibili y assessmen s 2463 Figu e 3. Pixel-based LR models p edic ion pe o mance esul s: summa y ables o he Cohen’s kappa index, a ea unde he ROC cu e (AUC), o e all accu acy ((TP+TN)/(TP+TN+FP+FN)) and o e all e o a e ((FP+FN)/(TP+TN+FP+FN)). (a, d) Fou - old o con in- gency plo s; (b, e) ROC cu es; (c, ) classi ica ion e o plo s and he quad a ic eg ession i cu es ( ed line). (TP+TN) (Fig. 4a). The ROC cu e p o ides AUC =0.69, and he co esponding Cohen’s kappa is k=0.302 (Fig. 4b). Conce ning he classi ica ion e o plo (Fig. 4c), i can be obse ed ha in he SUs wi h high and low landslide sus- cep ibili y p obabili y (p obabili y >0.8 and <0.2) he 2σ alue s ays below 0.2, bu a iabili y in he es ima es be- comes la ge o in e media e suscep ibili ies. This e eals a conside able a ia ion in he s able/uns able classi ica ion o he e i o y, which implies low eliabili y, a leas o he in- e media e p obabili ies (Guzze i e al., 2006). Fo he ESA- SUM, 63.82 % o he 152 alida ion mapping uni s we e co ec ly classi ied (TP+TN) (Fig. 4d) wi h AUC =0.71, sligh ly la ge wi h espec o he o he SU model assessmen , whe eas he Cohen’s kappa index pe o med sligh ly wo se, being k=0.276 (Fig. 4). The classi ica ion e o plo shows a conside able a ia ion in in e media e p obabili ies (Fig. 4 ), while he unce ain y is lowe o high and low p obabili ies. Ne e heless, he quad a ic i cu es indica e a lowe o e all a iabili y o ESA-SUM han o WA-SUM. Visual inspec ion o he SU suscep ibili y maps (Fig. 5b, d) shows simila i ies be ween WA-SUM and ESA-SUM. The di e ence is g aphically p esen ed h ough he misma ch map (Fig. 5 ), whe e 12.6 % o he mapping uni s (co e- sponding o an ex ension o 247km2) change hei landslide suscep ibili y class, be ween WA-SUM and ESA-SUM. 6 Discussion The numbe o scien i ic publica ions ocusing on landslide suscep ibili y zona ion has no ably inc eased o e he las decades (Gu ié ez e al., 2010; Rossi and Reichenbach, 2016; Libe a oscioli e al., 2017; Valagussa e al., 2017; Zhou e al., 2018; Reichenbach e al., 2018) and, nowadays, he e is a huge a ie y o applica ions and compa isons which p o- ide an eno mous ange o app oaches wi h which o p epa e www.na -haza ds-ea h-sys -sci.ne /18/2455/2018/ Na . Haza ds Ea h Sys . Sci., 18, 2455–2469, 2018