A Comparison of Urban Growth Probability Maps using Frequency Ratio and Logistic Regression Methods

†

: This work was researched by the supporting project to educate GIS experts.

Corresponding author: Chul-Uong Choi, Dept. of Geoinformatic Engineering, Pukyung National University, Busan 608-737, Korea, Tel.: +82-51-629-6655, E-mail: [email protected]

A Comparison of Urban Growth Probability Maps using Frequency Ratio and Logistic Regression Methods ^†

Park, So-Young* ․ Jin, Cheung-Kil* ․ Kim, Shin-Yup** ․ Jo, Gyung-Cheol** ․ Choi, Chul-Uong*

* De pt .ofGe oi nf or mat i cEngi ne e r i ng,PukyungNat i onalUni ve r s i t y

* * Envi r onme nt alDat aandI nf or mat i onOf f i c e ,Mi ni s t r yofEnvi r onme ntRe publ i cofKor e a

ABSTRACT

Top r e d i c tu r b a ng r o wt ha c c o r d i n gt oc h a n g e si nl a n dc o v e r ,p r o b a b i l i t yf a c t o r swe r ec a l c u l a t e da n dma p p e d .To p o g r a p h i c , g e o g r a p h i ca n ds o c i a la n dp o l i t i c a lf a c t o r swe r eu s e da sp r e d i c t i o nv a r i a b l e sf o rc o n s t r u c t i n gp r o b a b i l i t yma p so fu r b a n g r o wt h .Ur b a ng r o wt h - r e l a t e df a c t o r si n c l u d e de l e v a t i o n ,s l o p e ,a s p e c t ,d i s t a n c ef r o m r o a d ,r o a dr a t i o ,d i s t a n c ef r o m t h e ma i nc i t y ,l a n dc o v e r ,e n v i r o n me n t a lr a t i n ga n dl e g i s l a t i v er a t i n g .Ac c o u n t i n gf o rt h e s ef a c t o r s ,p r o b a b i l i t yma p so fu r b a n g r o wt hwe r ec o n s t r u c t e du s i n gf r e q u e n c yr a t i o( FR)a n dl o g i s t i cr e g r e s s i o n( LR)me t h o d sa n dt h ee f f e c t i v e n e s so ft h er e s u l t s wa sv e r i f i e db yt h er e l a t i v eo p e r a t i n gc h a r a c t e r i s t i c( ROC) .ROCv a l u e so ft h eu r b a ng r o wt hp r o b a b i l i t yi n d e x( UGPI )ma p s b yt h eFRa n dLRmo d e l swe r e0 . 9 3 7a n d0 . 9 4 0 ,r e s p e c t i v e l y .Th eLRma ph a das l i g h t l yh i g h e rROCv a l u et h a nt h e FRma p ,b u tt h en u me r i c a ld i f f e r e n c ewa ss l i g h t ,wi t hb o t hmo d e l ss h o wi n gs i mi l a rr e s u l t s .

Th eFRmo d e li st h es i mp l e s tt o o lf o rp r o b a b i l i t ya n a l y s i so fu r b a ng r o wt h ,p r o v i d i n gaf a s t e ra n de a s i e rc a l c u l a t i o n p r o c e s st h a no t h e ra v a i l a b l et o o l s .Ad d i t i o n a l l y ,t h er e s u l t sc a nb ee a s i l yi n t e r p r e t e d .I nc o n t r a s t ,f o rt h eLRmo d e l ,o n l y al i mi t e da mo u n to fi n p u td a t ac a nb ep r o c e s s e db yt h es t a t i s t i c a lp r o g r a m a n das e p a r a t ec o n v e r s i o np r o c e s sf o ri n p u t a n do u t p u td a t ai sn e c e s s a r y .I nc o n c l u s i o n ,a l t h o u g ht h eFRmo d e li st h es i mp l e s twa yt oa n a l y z et h ep r o b a b i l i t yo fu r b a n g r o wt h ,t h eLRmo d e li smo r ea p p r o p r i a t eb e c a u s ei ta l l o wsf o rq u a n t i t a t i v ea n a l y s i s .

Ke yWo r d s :Fr e q u e n c yRa t i o ,Lo g i s t i cRe g r e s s i o n ,Re l a t i v eOp e r a t i n gCh a r a c t e r i s t i c ,Ur b a nGr o wt h ,Ur b a nGr o wt h Pr o b a b i l i t yI n d e xMa p

Ⅰ.I nt r oduc t i on

A c i t yi sapl ac eo fpo l i t i c al ,e c o no mi cands o c i alac t i vi t i e s . Gl o bal l y,ur bani z at i o nhasi nc r e as e ddr as t i c al l yo ve rt hepas t c e nt ur y.Ur bani z at i o ni nf l ue nc e spo pul at i o ns i z eandde ns i t y, haswi de -r angi ngs o c i alande c o no mi ci mpl i c at i o nsanddr i ve s c hange si nl andus e(J e o nge tal . ,2 002).Sc ho l ar sge ne r al l y c l as s i f yur bangr o wt hi nt hr e eways :s pi l l o ve re xpa ns i o n,l e a p- f r o ggi nge xpa ns i o n,o rr a di a le xpa ns i o n( Ca dwa l l a de r ,1 9 8 5 ) .Spi l - l o ve re xpans i o no c c ur swhe nt heur bani z e dar e anat ur al l ye x- pandsi nt os ur r o undi ngar e ast oac c o mmo dat et hef unc t i o ns

andac t i vi t i e so ft hec e nt r alc i t y.Spi l l o ve re xpans i o nc r e at e s

c o mpl i c at e di s s ue s ,s uc hast r af f i cc o nge s t i o n,e nvi r o nme nt al

po l l ut i o n,r e duc t i o no fo pe ns pac eando bs o l e t e ne s so fado wn-

t o wnc o r e ,aswe l lhass o c i ali mpl i c at i o nsi fde ve l o pme nti s

di s o r de r e d(Le e ,2008) .Le apf r o ggi nge xpans i o no c c ur swhe n

t hef unc t i o nsandac t i vi t i e so ft hec e nt r alc i t ye xpandi nt o

ur bani z e dpat c he sbe yo ndt hec e nt r alr e gi o nbe c aus eo fde ve l -

o pme ntr e s t r i c t i o nsandnat ur albo undar i e so ft heur bani z e d

ar e a.Fi nal l y,r adi ale xpans i o nt ake spl ac ewhe nur bani z at i o n

s pr e adsal o ngan e xi s t i ngpr i nc i pl er o ads ys t e m.Suc h e x-

pans i o nf o r msas t ar -s hape dpat t e r nwi t ht hear mso fur bani -

z at i o npr o t r udi ngf r o m ac e nt r alc o r e .The s et hr e eme c hani s ms o f t e nc o mbi net oe xpandac i t y’ st e r r i t o r y(J e o ng,2001) .

Ur bani z at i o nhaspo t e nt i all ar ge - s c al ei mpac t sandunde r - s t andi ngho w ac i t yhasgr o wni si mpo r t antf o rur banman- age r sai mi ngf o rs us t ai nabl ec i t ye xpans i o n,f o r e c as t i ngur ban gr o wt ha nds e e ki ngvi abl eal t e r nat i ve s(Ka nga ndPa r k,20 00 ).

De ve l o pe dc o unt r i e ss uc hast heU. S.havewo r ke dt ode ve l o p pr e di c t i o nmo de l so fur bangr o wt hf o rt hes c i e nt i f i cmanage- me nto fur ban ar e asand have be ne f i t e d f r o m s t at e - o f - t he -ar tt e c hno l o gy s uc h asr e mo t es e ns i ngdat aandge o- gr aphi ci nf o r mat i o ns ys t e ms(GI S)( Ki m e tal . ,20 07).Rul e - bas e ds i mul at i o nmo de l sande mpi r i c ale s t i mat i o nmo de l sar e po pul arme t ho dsf o rpr e di c t i ngur bane xpans i o n.Rul e -bas e d s i mul at i o nmo de l sar emo s t l ybas e do nt hec e l l ul araut o mat a (CA)mo de l ,whi c hi sus e di nvar i o usUr banGr o wt hMo de l s (UGMs )andt heSl o pe ,Landus e ,Exc l us i o n,Ur bane xt e nt , Tr ans po r t at i o nandHi l l s hade(SLEUTH)mo de lde ve l o pe dby Pr o f .Ke i t hC.Cl ar ke(Bat t ye tal . ,198 9;Bat t yandXi e , 1994 ;Bat t yandXi e ,1997;Cl ar ke e tal . ,1997;Whi t e e tal . , 1997 ;Si l vaandCl ar ke ,2002).Rul e -bas e ds i mul at i o nmo de l s ar ebe s ts ui t e df o ri nc o r po r at i ngs pat i ali nt e r ac t i o ne f f e c t sand handl i ngt e mpo r aldynami c s .Ho we ve r ,CA mo de l sf o c uso n t hes i mul at i o no fs pat i alpat t e r nsr at he rt hano ni nt e r pr e t at i o n o runde r s t andi ng o ft hes pat i o t e mpo r alpr o c e s s e so fur ban gr o wt h.Empi r i c ale s t i mat i o nmo de l sus es t at i s t i c alt e c hni que s t omo de lt her e l at i o ns hi psbe t we e nl andus ec hange sandt he i r dr i ve r sbas e do nhi s t o r i c aldat a(HuandLo ,2 007).Huand Lo( 2007),Che ungandMas s e r(2003)andAl l e nandLu (200 3)appl i e dl o gi s t i cr e gr e s s i o n(LR)asane mpi r i c ale s t i - mat i o nme t ho dt omo de lur bangr o wt hi naGI Se nvi r o nme nt andt odi s c o ve rt her e l at i o ns hi pbe t we e nur bangr o wt hand t hedr i vi ngf o r c e s .Vo l dkampandFr e s c o(1996 )andVe r bug e tal .(200 2)us e dLR t oc al c ul at et hepr o babi l i t yo fi nput val ue sf o rt heCo nve r s i o no fLandUs ea ndi t sEf f e c t s(CLUE) mo de l .I nt hatmo de l ,l and-us epr o babi l i t yc anc hangedur i ng as i mul at i o nbyf e e dbac kme c hani s mso fl and-us epr ac t i c e s andpr o babi l i t ye f f e c t s .

Wes e l e c t e d avar i e t y o ff ac t o r st hatc an af f e c tur ban gr o wt hwi t ht heai m o fe s t abl i s hi ngamo de lf o rur bangr o wt h i nKo r e abas e dt her e l at i o ns hi pbe t we e nt he s ef ac t o r sandur - bangr o wt h,aswe l last hepr o babi l i t yo fur bangr o wt h.Fac- t o r sr e l at e dt our bangr o wt hc anbet o po gr aphi c al ,ge o gr a- phi c al ,e nvi r o nme nt alands o c i ali nnat ur e .Toc al c ul at et he pr o babi l i t y o fur ban gr o wt h,LR and t hef r e que nc y r at i o

(FR)we r eus e d.TheFRi so f t e nappl i e dt ol ands l i der e s e ar - c h.Fo re xampl e ,Le ea ndSamba t h( 2 0 0 6 )a ndLe e e tal .( 200 0) c o ns t r uc t e d a l ands l i des ui t abi l i t y map us i ng t heFR and de mo ns t r at e dt hes ui t abi l i t yo ft heFRasapr e di c t o ro fl and- s l i depr o babi l i t y.Us i ngLRandFRme t ho ds ,wede ve l o pe dan ur bangr o wt hpr o babi l i t yi nde x(UGPI )mapsaf t e rc al c ul at - i ngt hepr o babi l i t yo fur bangr o wt h.Weal s oc al c ul at e dt he r e l at i veo pe r at i ngc har ac t e r i s t i c(ROC)t oe xami net hee f f e c- t i ve ne s so ft hemo de l sf o rur bangr o wt h-r e l at e df i e l ds .

Ⅱ.Mat e r i al sandMe t hods

1 .St udyAr ea

Thi sr e s e ar c hf o c us e do nt heRe publ i co fKo r e a( he r e af t e r Ko r e a),l o c at e do nt heKo r e anPe ni ns ul aatt hee as t e r nmo s t e ndo ft heAs i anc o nt i ne nt .Wee xami ne dt hee nt i r el andar e a o fKo r e a,i nc l udi ngJ e j udo ,wi t ht hee xc e pt i o no fs o mes mal l i s l andso nt hee as tandwe s tc o as t s ,i nc l udi ngUl l e ungI s l and andDokdo.Thes t udyar eal i esbet weent hel at i t udes34°

18′42 ″ a nd3 7 ° 2 2′4 3″ a ndt hel o ngi t ude s12 4 ° 1 9′3 0″ a nd 1 3 0 °5 2 ′3 1 ″ a ndc o ve r sa na r e ao f1 0 0 , 5 6 0 . 8 7km

( Re f e rt oFi - gur e1 ) .Te mpo r al l y,wef o c us e do nt hemi d-1 980 sandt he mi d-20 00s .

Wi t hi nKo r e a,c i t i e st hatado pt e de xpans i o n- o r i e nt e dand t o p-do wn de ve l o pme nts t ar t i ng i n t he 1960 shavegr o wn dr ama t i c al l y(J e o ng,200 1).Dur i ngt hee a r l y19 60s ,c i t i e st hat be c amehubso fi ndus t r i al i z at i o ns ho we dr api de xpans i o nand dur i ngt hel at e1960 s ,hi ghe c o no mi cgr o wt hf ue l e dur bani z a- t i o ne ve nmo r e .Thet r e ndo fur bani z at i o nc o nt i nue di nt ot he 1970 s ~19 80s ,r e s ul t i ngi nme ga-c i t i e ss uc hasSe o ul ,Bus an, Dae gu,I nc he o n,Gwangj u and Dae j e o n,aswe l las t he i r s at e l l i t ec i t i e sandi ndus t r i alc i t i e ss uc hasGumi ,Changwo n, Po hang,Ul s an,Ye o s uandGwangyang.Theur bani z at i o nr at e was o nl y appr o xi mat e l y 50% i n 1 970,buti tdr as t i c al l y i nc r e as e dt o99% by200 0.

Ame t r o po l i sa c c o mpani e dbyr api dur ba ngr o wt ho f t e nf a c e s

c o mpl i c at e dpr o bl e mss uc hast r af f i cc o nge s t i o n,po l l ut i o n,l o s s

o fo pe ns pac e ,ur bande c l i ne ,t hehaphaz ar de xpans i o n(Le e

andShi m,200 6).I nKo r e a,t hec o nc e nt r at i o no fpo pul at i o ni n

me t r o po l i t anar e ashasl e dt oi nc r e as e dl andpr i c e s ,ho us i ng

s ho r t age sandt r af f i cc o nge s t i o n,whi c hhavef ur t he rs pur r e d

s ubur bane xpans i o n( SaGo ngandKi m,2004) .Fur t he r mo r e ,

l ar ge -s c al er e s i de nt i alde ve l o pme nt si nme t r o po l i t anar e asand

Fi gu r e1 .St udyar ea

Le ge nd: J e j u Gwangj u Bus an J e o l l ana m-do Ul s a n Gye o ngs a ngna m-do Dae gu J e o l l abuk- do Dae j e o n Chungc he o ngna m-do Gye o ngs a ngbuk-do Chungc he o ngbuk- do Se o ul I nc he o n

Gye o nggi -do Ga ngwo n- do

t hei nt r o duc t i o n o fapar t me ntho us i ng i n quas i -agr i c ul t ur al z o ne shaveno tbe e nhar mo ni o uswi t hs ur r o undi ngl ands c ape s . Aso f t e nt hec as ewi t hi mpr o pe rur bande ve l o pme nt ,s o c i al pr o bl e mshavear i s e ni nt he s ear e as( Le e ,20 08).

Dat aname Dat at ype Sc al e Spat i alr e s o l ut i o n Da t e Dat as o ur c e To po gr aphi c al

f ac t o r

El e vat i o n Gr i d 25 , 0 00 3 0

2 00 0 KNGI I

Sl o pe Gr i d 25 , 0 00 3 0

As pe c t Gr i d 25 , 0 00 3 0

Ge o gr aphi c a l f ac t o r

Landc o ve r 1 98 0s I mage 25 , 0 00 3 0 19 85 ~1 98 8 KMOE

2 00 0s I mage 25 , 0 00 10→ 30 20 05 ~2 00 6 KMOE Di s t anc ef r o m r o ad Li ne→ gr i d 5 , 0 00 10→ 30 2 00 7 KMLTM

Ro adr at i o Li ne→ gr i d 5 , 0 00 10→ 30 2 00 7 Aut ho r s Di s t anc eo fur bana r e a Gr i d 25 , 0 00 10→ 30 2 00 7 Aut ho r s Envi r o nme nt als o c i a l

f ac t o r

Gr adeo fe nvi r o nme nt alva l ue Gr i d 25 , 0 00 10→ 30 2 00 5 KMOE Gr a deo fl e ga lr e s t r i c t i o n Gr i d 25 , 0 00 10→ 30 2 00 5 KMOE

a

:Ko r e aNat i o nalGe o gr aphi cI nf o r mat i o nI ns t i t ut e

b

:Ko r e aMi ni s t r yo fEnvi r o nme nt

c

:Ko r e aMi ni s t e ro fLand,Tr ans po r tandMa r i t i meAf f a i r s Tabl e1 .I nputdat a

2 .Spat i alDat abaseConst r uc t i onus i ngGI S

Di ve r s emat e r i al shavebe enus edt os t udyur bangr o wt h.

Al l e nandLu(2003)de f i ne df i vec at e go r i e sf o rr e s e ar c ho n ur bangr o wt h,i nc l udi ngnat ur e /e nvi r o nme nt alas pe c t s ,l and us e ,po pul at i o n/ho us i ng,i nf r as t r uc t ur e / f ac i l i t i e sandpo l i c i e s / s o c i alf ac t o r s .Addi t i o nal l y,KangandPar k(200 0)e xami ne d t o po gr aphi c ,ge o gr aphi c ,phys i c alands o c i alandpo l i t i c alf ac- t o r s .Fo l l o wi ngt he s es t udi e s ,wei nc o r po r at e dt o po gr a phi cf a c- t o r so fe l e vat i o nands l o pe ,aswe l lasge o gr aphi cf ac t o r so f l andc o ve r ,di s t anc ef r o m r o ad,r o adr at i oanddi s t anc ef r o m ur banar e aandf i nal l y,e nvi r o nme nt alands o c i alf ac t o r so f gr ade so fe nvi r o nme nt alval ueandl e galr e s t r i c t i o n(Re f o rt o Tabl e1).

Da t ao nt hea bo vef ac t o r swe r ec o l l e c t e df r o m r e l at e do r gani - z at i o nsandc o nve r t e di nt oas pac edat abas eus i ngAr c GI S9. 3 ( ESRI ,2 0 08 )andERDAS9 . 2( Le i c aGe o s ys t e msGe o s pat i al I magi ng,20 08 ).Dat aba s e swe r ec o nve r t e di nt o30 m ×30 mgr i d s i z eAr c I nf oGRI Df i l e s ,wi t h11 , 22 7ho r i z o nt a lgr i dpo i nt sand 19, 789ve r t i c algr i dpo i nt s ,f o rat o t alo f222, 171, 10 3po i nt s .

I naddi t i o n,49, 859po l ygo nswe r ee xt r ac t e df r o m ur banand bui l t -upar e asus i ngl andc o ve rmapsf r o m 1980sand20 00s madebyt heMi ni s t r yo fEnvi r o nme nt .Ur banandbui l t -up ar e asi nc l ude dr e s i de nt i al ,i ndus t r i alandc o mme r c i alz o ne s ,as we l lasr e c r e at i o nalf ac i l i t i e s ,t r ans po r t at i o nar e as ,publ i cf a- c i l i t i e sanddr ya r e as( i . e . ,ur banar e aso rar e aswi t hc o mpl e t e d de ve l o pme nt ).Smal l -s c al ede ve l o pme nta r e as( l e s st han1ha) we r eno ti nc l ude d.Tabl e1pr o vi de sde t ai l so nt hedat ac o m- pi l e di nt hedat abas e .

To po gr aphi cdat awe r eo bt ai nedf r o m adi gi t ale l evat i on

a :El e va t i o n b:Sl o pe c :As pe c t

d:19 80 sl a ndc o ve rmap e :Di s t a nc ef r o m r o ad f :Ro adr at i o Fi gur e2 .Par amet ermapsoft hes t u dyar ea

Le ge nd:a: 0～2 00 20 0～4 00 40 0～6 00 60 0～8 00 80 0 ～1, 0 00 1, 00 0 ～1, 2 00 1, 20 0 ～1, 4 00 1, 40 0 ～1, 6 00 1, 60 0 ～

b: 0～1 0 10 ～20 20 ～30 30 ～40 40 ～50 50 ～

c : No r t h Ea s t So ut h We s t Fl a t

d: Ur ban Fa r l and Fo r e s t Gr a s s l and We t l a nd Bar el a nd Wat e r s

e : Hi gh:4 , 7 75 9 Lo w:0

f : Hi gh:9 0. 6 Lo w:0

mo de l(DEM)c r e at e df r o m 1: 25, 000-s c al et o po gr aphi cmaps o ft heKNGI Iande l e vat i o n,gr adi e ntandas pe c twe r eanal y- z e d.Thegr adi e nti ndi c at e st hes l o pe ,whi l et heas pe c ti n- di c at e st hedi r e c t i o no fge o gr aphi ci nc l i ne .

Ont hebas i so fge o gr aphi cf ac t o r s ,1:2 5, 000-s c al el andc o v- e rmapswe r ede ve l o pe dbyt heKMOE.Thec o nve r s i o nc o de s andde f i ni t i o nso fl andc o ve ro nt hemapswe r easf o l l o w:1.

Wat e r ,2.Ur ban,3.Bar el and,4.We t l and,5.Gr as s l and,6.

Fo r e s tand7.Far ml and.I naddi t i o n,us i ng1:5 , 0 00-s c al er o ad

mapspr o duc e dbyt heKMLTM,t hedi s t anc e sf r o m r o ads

andt her o adr at i o swe r eanal yz e d.Di s t anc ef r o m r o adi n-

di c at e st hedi s t anc ef r o m t hepr i nc i pl er o ads ys t e m t ot he

c e nt e ro ft hede ve l o pme ntar e aandwasus e df o rt hedi s t anc e

f unc t i o ni nAr c Vi e w GI S3. 3t opr o duc eandanal yz et her o ad

g:Di s t a nc eo fur ba nar e a h:Gr adeo fe nvi r o nme nt a lval ue i :Gr adeo fl e galr e s t r i c t i o n

j :19 80 sur banar e a k:20 00 sur banar e a Fi gur e2 .Cont i nued

Le ge nd:g: Hi gh:9 0, 00 4. 5 Lo w :0 . 0

h: Fi r s t -c l as s Se c o nd- c l a s s Thi r d-c l as s Fo r t h- c l a s s Fi f t h-c l as s

i : Fi r s t -c l as s Se c o nd- c l a s s Thi r d-c l as s Fo r t h- c l a s s Fi f t h-c l as s

j : Ur ban No n-ur ban

j : Ur ba n No n- ur ba n

ne t wo r kbuf f e r .He r e ,t hepr i nc i pl er o ads ys t e m wasde f i ne d ast her o adst hatc o nne c t e di mpo r t antr e gi o ns ,i nc l udi ngal l nat i o nalhi ghways ,l o c alhi ghways ,nat i o nale xpr e s swaysand o t he rmaj o rt hr o ughwayso fme t r o po l i t anc i t i e sasde f i ne dby l o c algo ve r nme nt sunde rt heRo adAc t .Wedi dno ti nc l ude s mal lr o adss uc hasal l e yso f5m o rl e s sandagr i c ul t ur eand f i s hi ngvi l l ager o ads .Ther o adr at i oadde dval uet ot hegr i d- bas eac c o r di ngt ot henumbe ro fve hi c l el ane so ft her o ad ne t wo r kandt heac c umul at e dval uef o rz o nals t at i c swasc al - c ul at e df o rt her at i oo ft hee nt i r ear e af o re ac hde ve l o pme nt

ar e a.The r e f o r e ,t heac t ualr o adr at i odi s pl ayst her e l at i ver o ad o c c upa nc yr at i o ,no tt heo c c upanc yr at i o .Ur ba nar e aswe r e c o ns i de r e d t o c o ve r at l e as t 100 ha ac c o r di ng t o t he 1:25 , 0 00-s c al el andc o ve rmapso ft heKMOE andt hedi s - t anc ef unc t i o no fAr c GI S9. 3wasus e dt oge ne r at et hedo wn- t o wnbuf f e rf o rt heanal ys i s .

Forenvi r onment al /s o ci alf ac t or s ,weac qui r e ddat af r o m

t he1:2 5, 000-s c al eEnvi r o nme nt alCo ns e r vat i o nVal ueAs s e s s -

me ntMap(ECVAM)o ft heKMOE.TheECVAM i sat o po-

gr aphi cmapwi t hcol orcat egor i ess howi ngnat i onall and

c l as s i f i e di nt of i vegr ade s ,wi t hc l as s1r e pr e s e nt i ngt hemo s t envi r onment al l yval uabl el and.Themapwaspr oduce dby c o mpr e he ns i vee val uat i o no fvar i o usas pe c t so fe nvi r o nme nt al val ue ,wi t ht heai m o ff ur t he r i ngc o ns e r vat i o nandenvi r o n- me nt al l yf r i e ndl yl and-us epl anni ngandde ve l o pme nt .

Ⅲ.Re s ul t s

1 .Fr equenc yRat i oModel

I nge ne r al ,t opr e di c tur bani z at i o n,i ti sne c e s s ar yt oas s ume t hatur bangr o wt hi sde t e r mi ne dbyc e r t ai nur bangr o wt h- r e l at e df ac t o r sandt hatf ut ur eur bangr o wt hwi l lo c c urunde r t hes amec o ndi t i o nsaspas tur bangr o wt h.Us i nguni var i ant pr o babi l i t yanal ys e sandt heFRme t ho d,t hes pat i alr e l at i o n- s hi pbe t we e nt her e gi o nso fur bangr o wt hande ac hur ban gr o wt h-r e l at e d f ac t o rwasanal yz e d.Thi sr e l at i o ns hi p was us e dt ode t e r mi neho w e ac hf ac t o rwasr at e di nt heo ve r l ay anal ys i s(Le eandTal i b,2 005);i . e . ,t hec o r r e l at i o nanal ys i s wasdi vi de di nt ot her at i of o rt heur bani z at i o nar e abe t we e n t hes c o peo fe ac hf ac t o randt ypebyt her at i of o re ac hgr ade o ff ac t o ri nt hee nt i r ear e a(Le e e tal . ,2000).I nt hec as eo f ur bangr o wt h,i fwes e tt heur bangr o wt ho c c ur r e nc ee ve ntt o ber e pr e s e nt e d by af ac t o r ,‘ B’ ,andt heat t r i but e so ft he f ac t o rwe r ede no t e d by ‘ D’ ,t he n t heFR o f‘ D’wast he c o ndi t i o nalpr o babi l i t yr at i o(Le eandSamba t h,2 00 6) .Val ue s o f1we r ec o ns i de r e dave r age ,whe r e asval ue sgr e at e rt han1 i ndi c at e dahi ghe rc o r r e l at i o nwi t hur bangr o wt handval ue s l e s st han1s ho we dl o we rc o r r e l at i o ns .TheUGPIus e dt he f o l l o wi ng f o r mul a (1) t o de t e r mi negr adeval ue so fe ac h f ac t o r ,s t ar t i ngwi t haf ac t o rval ueo f1andt he ns ummi ng t het o t alval ue(Le e e tal . ,20 00).

   ^{  (Fo r mul a 1)}

Whe r e , FR=Rat i ngo fe ac hf ac t o rt ypeo rr ange

Tabl e2s ho wst her e l at i o ns hi pbe t we e nt heo c c ur r e nc eo f ur bangr o wt hande ac hf ac t o r .Ase l e vat i o ni nc r e as e d,t he f r e que nc yo fur bangr o wt hge ne r al l yde c r e as e d.I npar t i c ul ar , e l e vat i o nsr angi ngf r o m 0~100m s ho we dahi ghpr o babi l i t y o fur bangr o wt h.Ther e l at i o ns hi pbe t we e ns l o peandur ban gr o wt hs ho we dt hatur bangr o wt hge ne r al l yo c c ur r e dwhe n s l o pe sr ange df r o m 1 ~12 ° .Sl o pe sl e s st han1 2°s ho we dr at i o s

>1,whi c h i ndi c at e sa hi gh pr o babi l i t y o fur ban gr o wt h o c c ur r e nc e .Fo rs l o pe ss t e e pe rt han12° ,t her at i owas<1,i n- di c at i ngal o w pr o babi l i t yo fur bangr o wt h.Thes l o peanal y- s e ss ho we dt hatur bangr o wt hwasmo s te xt e ns i veandmo s t c o mmo no ne as t -f ac i ngands o ut h-f ac i ngs l o pe s .

Weal s oas s e s s e dt hei nf l ue nc eo fr o ads ,aswe l lase xi s t i ng ur banandbui l t -upar e aso nt heo c c ur r e nc eo fur bangr o wt h.

Fo rt hi spur po s e ,t hedi s t anc e st or o adsaswe l lasur banand bui l t - upa r e aswe r ei de nt i f i e dbybuf f e r i ng;di s t anc e s<5 , 00 0m s ho we d r at i o s>1,i ndi c at i ng a hi gh pr o babi l i t y o fur ban gr o wt h,whe r e asdi s t anc e s>5, 00 0m s ho we dr at i o s<1 ,i ndi c a- t i ng a l o w pr o babi l i t y o fur ban gr o wt h.I n addi t i o n,t he pr o babi l i t yo fur bande ve l o pme nti nc r e as e dc l o s e rt opr i nc i pl e r o ad s ys t e ms .Fur t he r mo r e ,asr o ad de ns i t y i nc r e as e d,t he ur bangr o wt h f r e que nc yge ne r al l yi nc r e as e d.Spe c i f i c al l y,a r o adr at i oi nt her angeo f40~70% i ndi c at e dahi ghpr o ba- bi l i t yo fur bangr o wt h.Mo r e o ve r ,di s t anc e s<10, 000m f r o m e xi s t i ngur banc e nt e r ss ho we dr at i o s>1,i ndi c at i ngahi gh pr o babi l i t yo fur bangr o wt h,whe r e ast her at i owas<1at di s t anc e s>1 0, 000m,i ndi c at i ngal o w pr o babi l i t yo fur ban gr o wt h.Thi sr e s ul ts ugge s t e dt hat ,i nge ne r al ,c i t i e se xpande d f r o m e xi s t i ngdo wnt o wnar e as .

Whe nt her e l at i o ns hi pbe t we e nur bangr o wt ho c c ur r e nc e and l and c o ve rwas e xami ne d,t he pr o babi l i t y o fur ban gr o wt hwashi ghe s ti ne xi s t i ngur banar e as ,f o l l o we dbybar e l ands ,we t l ands ,gr as s l andsandf ar ml andsandwasl o we s ti n wat e rand f o r e s tar e as .I n Ko r e a,mo unt ai no usar e asar e pr o t e c t e dandur bani z at i o nmo s t l yo c c ur svi at hede ve l o pme nt o ff ar mi ngandgr as s l andar e as .

Whe nur bangr o wt hwase val uat edagai ns tt hegr adeof e nvi r o nme nt alval ue ,gr o wt hwasgr e at e ri nar e asas s i gne da gr adeo f5.Thi sme anst hatde ve l o pme ntmo s to f t e no c c ur s i nr e gi o nswhe r et hec o ns e r vat i o nval uei sr e l at i ve l yl o w and i sl e s sl i ke l yi nar e aso fhi ghe re nvi r o nme nt alval uewhi c har e gener al l ywel lpr ot ect ed.Ther el at i ons hi pbet weenur ban gr o wt ho c c ur r e nc eandt hegr adeo fl e galr e s t r i c t i o nz o ne s s ho we dhi ghe rur bangr o wt ho c c ur r e nc eval ue si nr e gi o nsas - s i gne dgr ade so f3and5.Thi ss ugge s t st hatl ar ge -s c al ede- ve l o pme nti st aki ngpl ac ei nl e galr e s t r i c t i o nz o ne s ,gi ve nt hat t her at i owas>1i nar e asas s i gne dagr adeo f3 ,whi c hi n- di c at e sahi ghl e gi s l at i vec o ns e r vat i o nval ue .The s er e s ul t sar e c o nt r a r yt ot ho s eo ft hee nvi r o nme nt a lgr ade( Re f r et oTa bl e2 ) .

TheUGPImap,s ho wni nFi gur e3,i nc l ude sf i vec at e go r i e s

o fc l as s i f i c at i o ns .

Cl a s s e s Do mai n( %) (A)

Ur bangr o wt h (%)( B)

Rat i o (A/ B)

El e va t i o n

0 ~2 5 3 1. 80 12 . 0 7 2. 63 2 5~5 0 2 2. 92 8 . 0 9 2. 83 51 ~1 00 2 3. 17 13 . 6 4 1. 70 10 0~2 00 1 3. 95 19 . 6 3 0. 71 20 0~3 00 4. 59 14 . 2 0 0. 32 30 0~4 00 1. 73 9 . 8 8 0. 18 40 0~5 00 0. 84 6 . 9 0 0. 12 50 0~6 00 0. 44 4 . 8 8 0. 09 60 0~7 00 0. 30 3 . 5 7 0. 08 70 0~8 00 0. 16 2 . 6 9 0. 06 80 0~9 00 0. 04 1 . 9 0 0. 02 9 00 ~1 00 0 0. 03 1 . 2 1 0. 02 1 00 0~1 10 0 0. 01 0 . 7 0 0. 02 1 10 0~1 20 0 0. 00 0 . 3 7 0. 01 1 20 0~1 30 0 0. 00 0 . 1 8 0. 02 1 30 0~1 40 0 0. 01 0 . 0 8 0. 14

Sl o pe

0~3 5 0. 56 24 . 7 4 2. 04 3~6 2 3. 09 9 . 8 8 2. 34 6 ~1 2 1 9. 06 18 . 3 4 1. 04 1 2~1 8 5. 43 18 . 3 3 0. 30 1 8~2 4 1. 47 15 . 4 3 0. 10 2 4~3 0 0. 31 9 . 3 2 0. 03 3 0~3 6 0. 09 3 . 4 2 0. 03 3 6~4 2 0. 00 0 . 5 4 0. 01

As pe c t

N 1 8. 56 23 . 0 3 0. 81 E 2 6. 86 25 . 2 9 1. 06 S 2 6. 39 23 . 3 4 1. 13 W 2 2. 58 25 . 5 5 0. 88

Di s t anc e f r o m r o a d

1 ~2, 50 0 8 8. 46 97 . 4 1 1. 10 2, 50 0~5 , 0 00 8. 45 1 . 2 1 0. 14 5 , 0 00 ~1 0, 00 0 0. 65 1 . 6 5 0. 39 1 0, 00 0~2 0, 00 0 0. 52 1 . 0 7 0. 49 2 0, 00 0~3 0, 00 0 0. 16 0 . 2 7 0. 57 3 0, 00 0~4 0, 00 0 0. 05 0 . 0 7 0. 72 4 0, 00 0~5 0, 00 0 0. 01 0 . 0 2 0. 24

Ro ad r at i o

0 ~1 0 7 0. 18 95 . 6 0 0. 73 1 0~2 0 1 2. 29 2 . 7 4 4. 49 2 0~3 0 6. 56 0 . 7 3 9. 01 3 0~4 0 5. 44 0 . 5 0 1 0. 79 4 0~5 0 3. 42 0 . 2 6 1 2. 96 5 0~6 0 1. 48 0 . 1 1 1 3. 00 6 0~7 0 0. 54 0 . 0 4 1 3. 59

Ur ban di s t anc e

0 ~5, 00 0 2 9. 81 10 . 9 1 2. 73 5 , 0 00 ~1 0, 00 0 2 1. 68 15 . 4 5 1. 40 1 0, 00 0~1 5, 00 0 1 5. 30 16 . 3 6 0. 94 1 5, 00 0~2 0, 00 0 1 0. 72 14 . 6 2 0. 73 2 0, 00 0~2 5, 00 0 8. 39 13 . 4 8 0. 62 2 5, 00 0~3 0, 00 0 4. 78 9 . 0 2 0. 53 3 0, 00 0~4 0, 00 0 4. 79 10 . 4 0 0. 46 4 0, 00 0~5 0, 00 0 2. 54 6 . 2 1 0. 41 5 0, 00 0~6 0, 00 0 1. 21 2 . 0 4 0. 59 6 0, 00 0~7 0, 00 0 0. 49 0 . 9 9 0. 50 7 0, 00 0~8 0, 00 0 0. 20 0 . 3 9 0. 51 8 0, 00 0~9 0, 00 0 0. 08 0 . 1 4 0. 55 Tabl e2 .FRFac t oro nur bangr owt h

Land c o ve r

Wat e r 1 . 4 7 1 . 9 4 0. 76 Ur ban 24 . 0 4 2 . 1 1 1 1. 41 Bar el and 5 . 4 8 1 . 2 8 4. 28 We t l and 0 . 8 8 0 . 7 6 1. 16 Gr as s l and 6 . 1 8 3 . 7 4 1. 65 Fo r e s t 17 . 5 4 66 . 4 2 0. 26 Far ml a nd 44 . 4 0 23 . 7 5 1. 87

Gr adeo f e nvi r o n- me nt al va l ue

0 2 . 2 5 6 . 1 2 0. 37 1 6 . 1 7 36 . 1 6 0. 17 2 7 . 1 7 21 . 8 9 0. 33 3 0 . 7 4 6 . 6 5 0. 11 4 6 . 7 2 14 . 4 8 0. 46 5 76 . 9 4 14 . 7 0 5. 23

Gr adeo f l e gal r e s t r i c t i o n

z o ne s

1 11 . 2 9 21 . 2 6 0. 53 2 7 . 8 7 38 . 2 7 0. 21 3 33 . 8 8 21 . 5 2 1. 57 4 5 . 2 4 8 . 3 6 0. 63 5 41 . 7 1 10 . 5 9 3. 94 ( Tabl e2 .Cont i nued)

Fi gu r e3 .Ur bangr o wt hpr obabi l i t yi ndexmappr o du c edf r o m t he f r equ enc yr at i omodel

Le ge nd: Ve r yhi gh, Hi gh

Mi ddl e , Lo w

Ve r yl o w

2 .Logi st i cRegr ess i onModel

LR,at ypeo fmul t i var i at eanal ys i s ,i sus e f ulf o rpr e di c t i ng t hepr e s e nc eo rabs e nc eo fac har ac t e r i s t i co ro ut c o mebas e d o nval ue so fas e to fpr e di c t o rvar i abl e s(Le eandSambat h, 2006 ).TheLR mo de lwasde ve l o pe dbyMc Fadde n(1 973) andLandi sandZhang(1 997)ando t he r shaveappl i e di tf o r mo de l i ng ur ban gr o wt h.The LR mo de li sbas e d o n t he r ando m ut i l i t yt he o r yandt hedi s c r e t ec ho i c et he o r yi nur ban e c o no mi c ss t udy.Spe c i f i c al l y,t hee f f i c ac y o fc e r t ai n l and me as ur abl e st obe ne f i tc o ns ume r s ,i nc l udi ngbi d-r e ntandl and pr i c e ,ar ee val uat e dby ade ve l o pe rbas e do n f unc t i o nso f at t r i but e ss uc hast hec har ac t e r i s t i c so fl andc o ve r(Ki m e t al . ,2007) .Theke yt oLR i st hatt hede pe nde ntvar i abl ei s di c ho t o mo us .Thei nde pe nde ntvar i abl e si n t hi smo de lar e pr e di c t o r so ft hede pe nde ntvar i abl eandc anbeme as ur e do n ano mi nal ,o r di nal ,i nt e r val ,o rr at i os c al e .Ther e l at i o ns hi p be t we e nt hede pe nde ntvar i abl eandi nde pe nde ntvar i abl e si s no nl i ne ar(Ye s i l nac arand To pal ,2 005 ).Qua nt i t at i ve l y,t he r e l at i o ns hi pbe t we e nt heo c c ur r e nc eandi t sde pe nde nc yo n s e ve r alvar i abl e sc anbee xpr e s s e das

  

  

  

(Fo r mul a2) whe r e pi st hepr o babi l i t yo fane ve nto c c ur r i ng.I nt hi sc as e , t heval ueo f pi st hee s t i mat e dpr o babi l i t yo fur bangr o wt h o c c ur r e nc e .Thepr o babi l i t yvar i e sf r o m 0t o1o nanS-s hape d c ur ve .I no t he rwo r ds ,ast heval ueo ft hei nde pe nde ntvar i a- bl ewi t ht hes t at i cr e l at i o ns hi pwi t h pge t shi ghe r ,t hepr o ba- bi l i t yt ogr o w i nt oac i t ybe c o me sl ar ge r ,whe r e asast heval - ueo ft hei nde pe nde ntvar i abl ede c r e as e s ,s odo e st hepr o ba- bi l i t y o fur ban gr o wt h.Addi t i o nal l y, zi st hel i ne arc o m- bi nat i o n.I tf o l l o wst hatLRi nvo l ve sf i t t i ngane quat i o no ft he f o l l o wi ngf o r m t ot hedat a:

  





 



⋯ 



(Fo r mul a3) whe r e , 

i st hei nt e r c e pto ft hemo de l , 

  ⋯

ar et hec o e f f i c i e nt so ft heLRmo de land 

  ⋯

ar et hei nde pe nde ntvar i abl e s .Us i ng LR e quat i o n,al o gi t f unc t i o nc anbee xpr e s s e das( Le eandSambat h,20 06):

ln 

  

  

 

  







(Fo r mul a4)

Name l y,t hel e f tc o o r di nat eo ft heLRmo de li se xpr e s s e di n t henat ur ali nde xval ueo ft heval uedi vi de dbyt hepr o ba-

bi l i t yo fc o nve r s i o nt our banus e( 

)t ot hepr o babi l i t yo fr e- mani ngast heno n- ur banus e   

 .Thec o nve r s i o n o f pr o babi l i t yi nt ol o gi ti sno n-l i ne arandt hust her e l at i o ns hi p be t we e nt hel o gi tandi nde pe nde ntvar i abl ei ss ho wnasal i n- e armo de l .Us i ngt hi spr o c e s s ,t hec o e f f i c i e ntwase s t i mat e d byt hemaxi mum l i ke l i ho o dme t ho d( Ki m e tal . ,2007) .

Asaf i r s ts t e pi nt heanal ys i s ,amaps howi ngt hear e a af f ect e dbyur banandbui l t -upar easandt hef ac t ormaps (el e vat i on,s l o pe,di s t anc ef r om r o ad,r oaddens i t y,di s t anc e f r o m ur banar e a,l andc o ve r ,e nvi r o nme nt alc o ns e r vat i o nva- l ue )i nr as t e rf o r matwe r ec o nve r t e di nt oASCI If o r mat .The s t at i s t i c a lpac kageSPSSVe r .1 8. 0(SPSSI nc ,20 09)wast he n us e dt oe s t i mat et hec o r r e l at i o nbe t we e nur bangr o wt hand f ac t o r saf f e c t i ngur bangr o wt h.I nt hi spr o c e s s ,ac o e f f i c i e nt wasas s ume d us i ng t hemaxi mum l i ke l i ho o d me t ho d.The e s t i mat e dr e s ul t sar es ho wni nTabl e3andt he p-val uewas 0. 05o rl e s sf o ral lvar i abl e se xc e ptASP,LU( 5 )( gr a s s l a nd) a ndLU( 6 )( f o r e s t ) ;t he s eva r i a bl e swe r es ho wnt obeme a- ni ngf ulatas i gni f i c anc el e ve lo f5%.I no t he rwo r ds ,wi t ht he e xc e pt i o no ft het hr e eabo vevar i abl e s ,t hi smo de li ndi c at e da s t at i s t i c al l y s i gni f i c antpr o babi l i t y o fc i t y e xpans i o n.Wi t h r e s pe c tt ot hec o ns e c ut i vevar i abl e s ,t hel o gi s t i cc o e f f i c i e nt so f ASP(as pe c t ),RDD(r o adr at i o )andENV( gr a deo fe nvi r o n- me nt alval ue )we r es t at i s t i c al l ys i gni f i c ants uc ht hat ,ast he i r val ue si nc r e as e d,t he r ewasahi ghe rpr o babi l i t yo fur bande- ve l o pme nt .Co nve r s e l y,f o rt hel o gi s t i cc o e f f i c i e nt so fHEI (e l e vat i o n),SLO (s l o pe ) ,RD( di s t a nc ef r o m r o a d) ,UD( di s - t a nc ef r o m ur ba na r e a )andLAW ( gr a deo fl e ga lva l ue ) ,a st he va l uede c r e a s e d,t hepr o babi l i t yo fur bande ve l o pme nti nc r e a- s e d.Fo rt heno n-c o ns e c ut i vevar i abl e s ,t hel o gi s t i c sc o e f f i - c i e nt sf o rt hel andc o ve rc at e go r i e so fLU (1)(wat e r s ),LU (3)( bar el and) ,LU (4)(we t l and)andLU (6)(f o r e s t )i n- di c at e d a hi ghe rpo s s i bi l i t y o fde ve l o pme ntt han f o rt he gr as s l andandf ar ml andl andc o ve rc at e go r i e s .

Theo bt ai ne de quat i o nf o rpr e di c t i ngur bangr o wt hwasas f o l l o ws :

               

                 

              

              

(Fo r mul a5)

Cl a s s De gr e eo f f r e e do m

Be t a c o e f f i c i e nt

St anda r d

e r r o r Wal d

As ympt o t i c s i gni f i c a nc e pr o babi l i t y

Exp(B)

As ympt o t i c95 % c o nf i de nc ei nt e r va l Lo we rbo und Uppe rbo und HEI 1 -0 . 0 01 0. 00 0 67 . 3 67 0 . 0 00 0 . 9 99 0 . 9 98 0. 99 9 SLO 1 -0 . 0 61 0. 00 4 2 07 . 5 60 0 . 0 00 0 . 9 40 0 . 9 33 0. 94 8 ASP 1 0 . 0 06 0. 01 7 0 . 1 21 0 . 7 28 1 . 0 06 0 . 9 73 1. 04 0 RD 1 0 . 0 00 0. 00 0 42 . 0 61 0 . 0 00 1 . 0 00 1 . 0 00 1. 00 0 RDD 1 0 . 1 29 0. 00 7 3 86 . 6 64 0 . 0 00 1 . 1 37 1 . 1 23 1. 15 2 UD 1 0 . 0 00 0. 00 0 14 . 5 26 0 . 0 00 1 . 0 00 1 . 0 00 1. 00 0 LAW 1 -0 . 4 89 0. 01 6 9 34 . 6 19 0 . 0 00 0 . 6 13 0 . 5 94 0. 63 3 ENV 7 0 . 6 21 0. 01 4 1 , 9 72 . 3 11 0 . 0 00 1 . 8 61 1 . 8 11 1. 91 3

LU 1 - - 8 96 . 7 85 0 . 0 00 - - -

LU(1 ) 1 2 . 7 90 0. 21 2 1 73 . 7 82 0 . 0 00 16 . 2 80 10 . 7 53 2 4. 65 0 LU(2 ) 1 -1 . 2 74 0. 13 0 96 . 7 89 0 . 0 00 0 . 2 80 0 . 2 17 0. 36 0 LU(3 ) 1 5 . 8 60 0. 71 5 67 . 1 99 0 . 0 00 3 50 . 6 50 86 . 3 80 1, 42 3. 42 6 LU(4 ) 1 1 . 4 66 0. 18 6 62 . 0 53 0 . 0 00 4 . 3 30 3 . 0 07 6. 23 5 LU(5 ) 1 -0 . 3 00 0. 21 9 1 . 8 82 0 . 1 70 0 . 7 41 0 . 4 83 1. 13 7 LU(6 ) 1 0 . 2 71 0. 13 1 4 . 3 07 0 . 0 38 1 . 3 11 1 . 0 15 1. 69 4 LU(7 ) 1 -1 . 0 07 0. 05 1 3 97 . 7 10 0 . 0 00 0 . 3 65 0 . 3 31 0. 40 3 Co ns t a nt 1 -0 . 5 34 0. 09 9 28 . 8 75 0 . 0 00 0 . 5 86 - - Tabl e3 .Logi s t i cr egr e s s i onanal y s i sr es u l t s

Topr e di c tt hepo s s i bi l i t yo fur bangr o wt ho c c ur r e nc ei n e ac hgr i d,pr o babi l i t ywasc al c ul at e df r o m ( Yi l maz ,2009 )

   

( Fo r mul a6)

Fi nal l y,t heUGPImapwaso bt ai ne dbyc o nve r t i ngt hef i l e i nt or as t e rf o r mat(Re f e rt oFi gur e4).

3 .Val i dat i onoft heModel sUs ed

Weus e dFRandLRmo de l st oe s t i mat et hepr o babi l i t yo f ur bangr o wt hwhi l ee xami ni ngt hes t r e ngt hsandwe akne s s e s o fe ac ho ft hemo de l s .TheFRi st hes i mpl e s tme t ho d.The c al c ul at i o npr o c e s si se as i l yunde r s t o o d,asar et hei nputand r e s ul t sval ue sf o rde t e r mi ni ngf ac t o r sr e l at e dt our bangr o wt h.

I naddi t i o n,FR mo de l i ngc anbec o nduc t i ngwi t ho uthavi ng t oc o nve r tt hedat a,me ani ngt hati tc anbec o nve ni e nt l yand qui ckl yus edf ort echni calappl i cat i ons .Fur t her mor e,al l c al c ul at i o nsc anbemadedi r e c t l ywi t hi nt heGI Spr o gr am and t he r e f or e ,avas tamo untofdat acanbee as i l yandqui c kl y pr o c e s s e d.Co nve r s e l y,LRhast headvant ageo fal l o wi ngf o r quant i t at i veanal ys i so ft her e l at i o ns hi pbe t we e nur bani z at i o n andf ac t o r sofoc cur r e nc e.Howe ve r ,t hes t at i s t i c alpr ogr am t e nde dt of ai lwhe nl ar geamo unt so fdat awe r ee nt e r e d.I n

Fi gur e4 .Ur bangr o wt hpr o babi l i t yi ndexmappr oduc edf r o m t he l o gi s t i cr egr es s i onmo del

Le ge nd: Ve r yhi gh, Hi gh

Mi ddl e , Lo w

Ve r yl o w

addi t i o n,i twasne c e s s ar yt oc o nve r tt hedat as t r uc t ur e di n t heGI Si nt oaf o r m r e adabl ebyt hes t at i s t i c alpr o gr am and e ac hc o e f f i c i e nto ft hec l as s i f i c at i o ndat af o rc al c ul at i ngt he ur bani z at i o npr o babi l i t yf o r mul ahadt ober e -e nt e r e di nt ot he dat abas e(Le e e tal . ,2000).

St at i s t i calmet hodsar eneededt oval i dat es uchmodel s be c aus ei ti se s s e nt i alt okno w amo de l ' spr e di c t i o nac c ur ac y.

Re c e nt l y,t heROCme t ho dwasi nt r o duc e dt ot hef i e l do fl and us e/coverchangemodel i ngt omeas ur et her el at i ons hi p be t we e ns i mul at e dc hangeandr e alc hange(Po nt i nus ,200 0;

Schnei derandPont i nus ,2001).Ac co r di ngt oSc hne i de rand Pont i nus(2001),t oas s es st hequal i t yofamodel ,i ti s advant ageous(1)t ous eani ndi cat orot hert hanper cent s ucces s ,(2)t omeas ur ei t sper f or manceoveravar i et yof s cenar i osofquant i t yofchangeand(3)t oi l l us t r at et he val i dat i o nwi t haf i gur e .TheROCs at i s f i e sal lo ft he s ego al s .

UGPIval ue so fal lc e l l si nt hes t udyar e awe r edi vi de di nt o 100c l as s e s ,wi t hac c umul at e d1% i nt e r val s .Toc o mpar et he r e s ul t squant i t at i ve l y,t he ROC val ue swe r e r e -c al c ul at e d, wi t ht het o t alar e agi ve naval ueo f1andr e pr e s e nt i ngpe r - f e c tpr e di c t i o n.Thus ,t heROCc anbeus e dt oas s e s st hepr e- di c t i o nac c ur ac yqual i t at i ve l y(Le eandSambat h,20 06).The ROCi ss ho wni nFi gur e5.

Fi gur e5pl o t st her at eo ft r uepo s i t i ve so nt heve r t i c alaxi s ver s ust her at eoff al s epos i t i ve sont hehor i z ont alaxi sf or

Fi gu r e5 .Ar eau nde rt heROC c ur v e ,r epr es e nt i ngt hequal i t yof t hemodel s

Le ge nd: FRROC, LRROC

e ac ho ft hemo de l s .A ROCval ueo f1i ndi c at e st hatt he r ei s ape r f e c ts pat i alagr e e me ntbe t we e nt heac t ualgr o wt hmap andt hepr e di c t e dpr o babi l i t ymap.A ROCval ueo f0. 5i st he agr e e me ntt hatwo ul dbee xpe c t e dduet oc hanc e ,i . e . ,t hec e l l val ue so nt hepr e di c t e dpr o babi l i t yi magewe r eas s i gne dt o r ando m l o c at i o ns(Po nt i nusandSc hne i de r ,2001;HuandLo , 2007 ).

TheROCval ue so ft heFRandLRwe r e0. 937and0. 940, r e s pe c t i ve l y;t hus ,t he i rr e s pe c t i vepr e di c t i o nac c ur ac i e swe r e 93. 7% and94 . 0 %.Bo t hmo de l ss ho we ds i mi l arac c ur ac y,al - t ho ught heLRmapappe ar e dt obes l i ght l ymo r eac c ur at e .

Ⅳ.Conc l us i ons

Gl o bal l y,ur bani z at i o nhasi nc r e as e ddr amat i c al l ys i nc et he 20t hc e nt ur y,c aus i nge nvi r o nme nt aldamage ,aswe l lass o c i al ande c o no mi ci s s ue s ,di s o r de r l yde ve l o pme ntando t he rpr o- bl e ms .Re s e ar c he r shaves o ughtwayst oanal yz eandf o r e c as t t hegr o wt hpat t e r no fc i t i e st opr o mo t ee nvi r o nme nt al l yf r i e nd- l yande f f i c i e ntnat i o nall andde ve l o pme nt .Re c e nt l y,r e mo t e s e ns i ngdat aandge o gr aphi ci nf o r mat i o ns ys t e mshavebe e n us e df o rt hi spur po s eandur bangr o wt hf o r e c as t i nghasbe e n c o nduc t e dus i ngt heCA appr o ac h.TheCA appr o ac h has be e nus e di nmanys t udi e ss i nc ei twasi nt r o duc e dbyCl ar ke e tal .(1 997).Us i ngo urur bangr o wt hpr e di c t i o nmo de l ,we i de nt i f i e dvar i abl e st hatwe r emo s tc l o s e l yc o nne c t e dt our ban gr o wt hf r o m pas tt opr e s e ntandus e dt he m asi nputdat af o r pr e di c t i ngur bangr o wt h(J ung,2002) .Manyr e s e ar c he r shave appl i e dLRi nur banmo de l i ngt heanal yt i c alhi e r ar c hypr o c e s s andar t i f i c i alne ur alne t wo r kappr o ac he shaveal s or e c e nt l y be e nus e di nur banr e s e ar c h.

I nt hi ss t udy,wec o mpar e dt womo de ls ys t e msf o rpr e di c t - i ngur bangr o wt hi nKo r e aandf o rc al c ul at i ngvar i abl e st hat de t e r mi neur bangr o wt h.Ur bangr o wt hvar i abl e sar et ypi c al l y c al c ul at e dus i ngavar i e t yo fme t ho ds ,whi c hdi f f e rde pe ndi ng o nt hemo de landi nputval ue s .I nt hi ss t udy,weappl i e dt he LRandFRme t ho ds .Ur bangr o wt hvar i abl e swe r ec al c ul at e d andt hef o r e c as t i ngac c ur ac i e so ft het wome t ho dswe r ec o m- par e dbas e do nt heROC.Wec o ns i de r e d‘ ur bangr o wt h’t obe al andc o ve rc hangef r o m no n-ur banus et our banus e .

Thei nputdat af o rur ban gr o wt hanal ys i si nc l ude de l e-

vat i o n,s l o pe ,as pe c t ,l andc o ve r ,di s t anc ef r o m r o ad,r o adr a-

t i o ,di s t anc ef r o m ur banar e a,gr adeo fe nvi r o nme nt alval ue

andgr adeo fl e galr e s t r i c t i o n.Theanal yz e ddat af o re ac hf ac-

t o rwe r ec o nve r t e di nt oGRI Df o r matandt heur bangr o wt h var i abl ewasc al c ul at e dbyt heFRandLRappr o ac he s .The n t hec o r r e l at i o nbe t we e ne ac hf ac t o randur bangr o wt hwas c al c ul at e d.

Fo rt heFRanal ys i s ,t o po gr aphi cf ac t o r ss ho wi ngaval ueo f 1o rmo r ei nc l ude dane l e vat i o no f50m o rl e s s ,agr adi e nto f 12°o rl e s sande as t e r no rs o ut he r nas pe c t .Ot he rge o gr aphi c f ac t o r ss ho wi nghi ghe rFRval ue si nc l ude dc l o s epr o xi mi t yt o r o ads ,ahi ghe rr o adr at eandc l o s e rpr o xi mi t yt oane xi s t i ng c i t y.Hi ghval ue swe r eal s os ho wnf o rur banl andc o ve rf o l - l o we dbybar el and,we t l and,gr as s l and,f ar ml andando t he r l andc o ve r s .Thee nvi r o nme nt alands o c i alf ac t o r ss ho wi ng hi ghur bani z at i o npr o babi l i t i e swe r el andswi t hagr ade5e n- vi r o nme nt alr at i ngandgr ade so f3o r5f o rl e galr e s t r i c t i o ns . Ther e s ul t so ft heLR anal ys i ss ho we ds t at i c al l ys i gni f i c ant l o gi s t i cc o e f f i c i e ntval ue sf o ras pe c t ,r o adr at i o ,gr adeo fe nvi - r o nme nt alval ueandl andc o ve rc at e go r i e so fwat e r ,bar el and, we t l andandf o r e s t .

TheFR mo de lus e dhe r ee nabl e dt hee as i e s tandf as t e s t c al c ul at i o nswi t he as i l yi nt e r pr e t e dr e s ul t s .Co nve r s e l y,f o rt he LR,o nl yal i mi t e dnumbe ro fdat ac o ul dbei nputt ot hes t at - i s t i c alpr o gr am andi nputando ut putdat ahadt obec o nve r t - t e d.TheROCanal ys i so ft heUGPImapspr e par e dus i ngt he t womo de l ss ho we d93. 7% ac c ur ac ybyt heFR and94. 0%

ac c ur ac ybyLR f o rpr e di c t i ngur bani z at i o n.Thus ,t het wo mo de l sgaver e l at i ve l y s i mi l arac c ur ac y,al t ho ugh t heLR mo de lwass l i ght l ymo r eac c ur at e .

I n Yi l maz ’ s( 2009)s t udy o fl ands l i de s ,ac c ur ac i e swe r e 82. 6% f o raFRmo de l ,84 . 2 % f o raLRmo de land85 . 2 % f o r anar t i f i c i alne ur alne t wo r k.Thus ,i nt he i rc as et o o ,LRwas mo r eac c ur at et han t heFR.Ho we ve r ,Le eand Sambat h (200 6)r e po r t e dt hatt heFRwas86. 97% ac c ur at e ,whi l eLR was8 6. 37% ac c ur at e .Le eandPr adhan( 2007)f o undt hat t heFRs ho we d93. 04 % ac c ur ac ywhi l eLRhadahi ghe rac- c ur ac yo f90. 34 %.Thus ,whi l epr e vi o uss t udi e shaves ho wn s o medi f f e r e nc e sbe t we e nFRandLRac c ur a c i e s ,i nmo s tc as - e st he s eme t ho dshavepr o duc e ds i mi l arr e s ul t s .

Af t e ranal yz i ngt heme r i t sanddi s advant age s ,aswe l las t heac c ur ac i e so fe ac hmo de l ,wec o nc l udet hate ve nt ho ugh t heFRc anbee as i l yappl i e d,LRi smo s tappr o pr i at ef o rur - bangr o wt hanal ys i sbe c aus ei tc anbeus e dt oe xami net he c o r r e l at i o n be t we e n e ac h f ac t o rand ur ban gr o wt h.UGPI mapsc o ns t r uc t e dus i ngLR andFR mo de l ss ho we dpo s s i bl e s pat i aldi s t r i but i o nso fur bani z at i o nac c o r di ngt ot heamo unt

o fur bangr o wt h.Ther e s ul t so ft hi ss t udyc anbeus e df o r pl anni ng ur ban de ve l o pme nt and l and us e manage me nt . Addi t i o nal l y,t hec al c ul at e dpr o babi l i t i e so fur bane xpans i o n c anbeus e dasi nputdat awhe nat t e mpt i ngt opr e di c tur ban gr o wt h.Themo r eac c ur at et hepr o babi l i t yval ue ,t hebe t t e ri t c anc o nt r i but et opr e di c t i ngac t ualur bangr o wt h.

Toi mpr o veac c ur ac yandr e l i abi l i t y,addi t i o nalf ac t o r si n- c l udi ngs o c i alande c o no mi cvar i abl e saswe l last heur ban gr o wt h-r e l at e df ac t o r sus e di nt hi spape rs ho ul dbeappl i e dt o r e al -wo r l d mo de l sand addi t i o nalr e s e ar c h s ho ul d bec o n- duc t e d.Addi t i o nal l y,t hi spape rde pe ndso nROC val ue st o ve r i f yt her e l i abi l i t yo ft hemo de l sho we ve r ,t heROCdo e sno t ac c o untf o rt hes pat i alar r ange me nto ft hemo de l ’ ss uc c e s s e s ande r r o r s .The r e f o r eROCana l ys i ss ho ul dbes uppl e me nt e dwi t h vi s ualc o mpar i s o nsandaddi t i o nalme as ur e so fas s o c i at i o nt hat ac c o untf o rs pat i alpat t e r nsus i ngpe r c e nt agec o r r e c t i o nso r anyc hi -s quar e -bas e ds t at i c ,ass ugge s t e dbyPo nt i nusand Sc hne r de r( 2 0 0 1 )( Co ns t a nz a ,1 9 8 9 ;Tur ne r e ta l . ,1 9 8 9 ) .La s t l y, mo r ei n- de pt hr e s e ar c ho nur bangr o wt hs ho ul dbec o nduc t e d us i ngur bangr o wt hmo de l s .

Ref er enc es

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2 .Ba t t y,M. ,P.Lo gl e yandS.Fo t he r i ngham( 1 9 8 9)Ur bangr o wt ha nd f o r m:Sc a l e ,f r a c t a lge o me t r ya nddi f f us i o n- l i mi t e da ggr e ga t i o n.Envi r o n- me ntandPl anni ngA:Pl anni nga ndDe s i gn21 :1 4 47 - 1 4 7 2.

3 .Ba t t y,M.a ndY.Xi e ( 1 9 94 )Fr o m c e l l st oc i t i e s .Envi r o nme ntand Pl a nni ngB:Pl a nni nga ndDe s i gn2 1 :S3 1- S48 .

4 .Ba t t y,M.a ndY.Xi e ( 1 9 9 7)Po s s i bl eur ba na ut o ma t a .Envi r o nme nt andPl anni ngB:Pl anni nga ndDe s i gn24 :1 7 5- 1 9 2 .

5 .Ca dwa l l a de r ,M. ( 19 8 5 )Ana l ys i sUr ba nGe o gr a phy.Ne wJ e r s e y:Pr e n- t i c e - Hal lI nc .Engl e wo o dCl i f f s .

6 .Cl a r ke ,K.C. ,S.Ho ppe na ndL.Ga ydo s ( 1 9 97 )A s e l f - mo di f yi ngc e l - l ul ara ut o mat o nmo de lo fhi s t o r i c alur bani z at i o ni nt heSa nFr a nc i s c o Ba yAr e a .Envi r o nme nta ndpl a nni ngB :Pl a nni nga ndde s i gn24 : 24 7 - 2 6 1.

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8 .Hu,Z.a ndC.P.Lo ( 2 00 7 )Mo de l i ngur ba ngr o wt hi nAt l a nt aus i ng l o gi s t i cr e gr e s s i o n.Co mput e r s .Envi r o nme nta ndUr banSys t e ms31 : 66 7 - 6 8 8.

9 .J e o ng,J .J . ( 2 0 0 1)Ce l l ul araut o ma t amo de l i ngf o rt heana l ys i sa ndpr e- di c t i o no fur ba ngr o wt hi nSe o ulme t r o po l i t a na r e a .Ph.D.Di s s e r t a t i o n.

Uni ve r s i t yo fSe o ul .

1 0 .J e o ng,J .J . ,C.M.Le ea ndY.I . ( 2 0 02 )De ve l o pme nto fc e l l ul a ra u- t o ma t amo de lf o rt heur ba ngr o wt h.Ko r e aPl a nne r sAs s o c i at i o n3 7 : 2 7 - 4 3 .

1 1 .Ka ng,B.K. ,I .Kwe o na ndT.H.Ki m( 1 9 9 9)Anana l ys i sme t ho do l o-

gyo fs pa t i a ll o c a t i o na lc ha r a c t e randc ha ngeo fur ba nmi c r ol a ndus e

wi t hGI S& s t at i s t i c a la nal ys i s .TheJ o ur na lo fGI SAs s o c i a t i o no f

Ko r e a5 :2 7 - 4 1.

1 2 .Ka ng,Y.O.a ndS.H.Pa r k( 2 0 0 0 )A s t udyo nt heur ba ngr o wt h f o r e c a s t i ngf o rt heSe o ulme t r o po l i t a na r e a.TheKo r e anGe o gr a phi c a l So c i e t y3 5:6 2 1 -6 3 9 .

1 3 .Ki m,J .I . ,G.W.Hwang,C.H.Ye oa nd H.W.Chung( 2 0 0 7) Mo de l i ngf ut ur eur bangr o wt ha ndi t sa ppl i c a t i o n:Thei nt e r gr at e d a ppr o a c h.Ko r e aPl a nne r sAs s o c i a t i o n.4 2 :31 - 4 8 .

1 4 .La ndi s ,J .D.andM.Za ng(1 9 9 7 )Mo de l i ngLa ndUs eChange :The Ne xtGe ne r a t i o no ft heCa l i f o r ni aUr ba nFut ur e sMo de l .s ubmi t t e dt o t hel a ndus emo de l i ngwo r ks ho p,USGSEROSda t aCe nt e r ,J un5 - 6 , USA:Si o uxFal l s ,So ut hDa ko t a .

1 5 .Le e ,H.Y.andJ .H.Shi m( 2 0 06 )A me as ur e me nto ft hes pat i al s t r uc t ur alc ha ngebyt heur ba ngr o wt h:A c a s eo fYo ngi n- Si .J o ur na l o ft heKo r e a nUr banGe o gr a phi c alSo c i e t y9 :1 5 -2 9 .

1 6 .Le e ,H.Y. ( 2 0 0 8 )Ana na l ys i so nde ve l o pme ntc a pa c i t yo fa nur ba ni - z e da r e af o rur bangr o wt hma nage me nt .J o ur na lo ft heKo r e a nUr ban Ge o gr aphi c a lSo c i e t y1 1:1 - 1 8.

1 7 .Le e ,S.andB.Pr a dha n(2 0 0 7 )Lands l i deha z ar dma ppi nga tSe l a ngo r , Mal a ys i aus i ngf r e que nc yr a t i oa ndl o gi s t i cr e gr e s s i o nmo de l s .La nd- s l i de s4 :33 - 4 1 .

1 8 .Le e ,S.a ndJ .A.Ta l i b( 20 0 5 )Pr o babi l i s t i cl ands l i des us c e pt i bi l i t ya nd f ac t o re f f e c ta na l ys i s .Envi r o nme nt a lGe o l o gy47 :9 8 2- 9 9 0 . 1 9 .Le e ,S.a ndT.Sa mbat h( 2 0 0 6 )Lands l i des us c e pt i bi l i t yma ppi ngi n

t heDa mr e iRo me lar e a .Ca mbo di aus i ngf r e que nc yr a t i oa ndl o gi s t i c r e gr e s s i o nmo de l s .Envi r o nme nt a lGe o l o gy5 0 :8 4 7 - 85 5 .

2 0 .Le e ,S. ,Y.J .Ki m andJ .D.Mi n( 2 0 0 0 )De ve l o pme nto fs pat i all a nd- s l i dei nf o r ma t i o ns ys t e m anda ppl i c a t i o no fs pat i all a nds l i dei nf o r - ma t i o n.TheJ o ur nalo fGI SAs s o c i a t i o no fKo r e a8 :1 4 1 - 1 53 . 2 1 .Mc Fa dde n.D. ( 1 9 7 3 )Co ndi t i o na lLo gi tAna l ys i so fQua nt i t a t i veCho i c e

Be ha vi o r .i nP.Za r e mbka de ,Fr o nt i e r si nEc o no me t r i c s .Ne w Yo r k:

Ac a de mi cPr e s s .

2 2 .Po nt i nus ,J .R.G. ( 2 0 00 )Quant i f i c a t i o ne r r o rve r s usl o c a t i o ne r r o ri n c o mpa r i s o no fc a t e go r i c a lma ps .Pho t o gr amme t r i cEngi ne e r i ngand Re mo t eSe ns i ng66 ( 8 ) :1 0 1 1 - 10 1 6 .

2 3 .Po nt i nus ,R.G.a ndL.Sc hne i de r ( 2 00 1 )La nd-c o ve rc ha ngemo de l va l i da t i o nbyanROCme t ho df o rt heI ps wi c hwa t e r s he d,Mas s ac hu- s e t t s ,USA.Agr i c ul t ur e ,Ec o s ys t e msa ndEnvi r o nme nt8 5 :2 39 - 2 4 8 . 2 4 .SaGo ng,H.S.a ndT.J .Ki m( 20 0 4 )Anana l ys i so nf a c t o ro fme t r o- po l i t a n ur bani z at i o n i n c a pi t a lr e gi o n.Pl a nni ng and Po l i c y.2 78 : 9 8 - 1 0 8.

2 5 .Sc hne i de r ,L.andR.G.Po nt i nus ( 2 0 0 1 )Mo de l i ngl a ndus ec ha ngei n t heI ps wi c hwa t e r s he d,Mas s ac hus e t t s ,USA.Agr i c ul t ur e ,Ec o s ys - t e msa ndEnvi r o nme nt8 5 :8 3- 9 4 .

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2 7 .Tur ne r ,M.G. ,R.Co ns t a nz aandF.H.Skl ar (1 9 8 9 )Me t ho dst oe vau- a t et hepe r f o r ma nc eo fs pa t i a ls i mul a t i o nmo de l s .Ec o l o gi c a lMo de l - l i ng4 8 :1- 1 8 .

2 8 .Whi t e ,R. ,G.Enge l e nandI .Ul j e e(1 9 9 7 )Theus eo fc o ns t r ai ne dc e l - l ul araut o ma t af o rhi gh- r e s o l ut i o nmo de l l i ngo fur banl a ndus edy- na mi c s .Envi r o nme nta nd Pl anni ng B:Pl a nni ng a nd De s i gn 2 4 : 3 2 3 - 2 43 .

2 9 .Ye s i l nac ar ,E.a ndT.To pa l ( 2 00 5 )Lands l i des us c e pt i bi l i t ymappi ng:

ac o mpa r i s o no fl o gi s t i cr e gr e s s i o na ndne ur alne t wo r ksme t ho dsi na me di um s c a l es t udy.He nde kr e gi o nTur ke t .Engi ne e r i ngGe o l o gy7 9 : 2 5 1 - 2 66 .

3 0 .Yi l ma z ,I . ( 20 0 9 )La nds l i des us c e pt i bi l i t y ma ppi ngus i ngf r e que nc y r at i o .l o gi s t i cr e gr e s s i o n.a r t i f i c i a lne ur a lne t wo r ksa ndt he i rc o mpa r - i s o n:A c a s es t udyf r o m Katl ands l i de sTo kat - Tur ke y.Co mput e r s a ndGe o s c i e nc e s3 5 :1 1 2 5 - 11 3 8 .

Received : 8 March, 2010

Received in Revised : 30 April, 2010 (1st) 2 December, 2010 (2nd) Accepted : 8 December, 2010

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