ACTAGEOGRAPHICA GEOGRAFSKI ZBORNIK SLOVENICA 2019 59 1 ACTA GEOGRAPHICA SLOVENICA GEOGRAFSKI ZBORNIK 59-1 • 2019 Contents Maja KOCJANČIČ, Tomislav POPIT, Timotej VERBOVŠEK Gravitational sliding of the carbonate megablocks in the Vipava Valley, SW Slovenia 7 Małgorzata KIJOWSKA-STRUGAŁA, Anna BUCAŁA-HRABIA Flood types in a mountain catchment: the Ochotnica River, Poland 23 Irena MOCANU, Bianca MITRICĂ, Mihaela PERSU Socio-economicimpactofphotovoltaicpark:TheGiurgiucountyruralarea,Romania 37 Andrej GOSAR The size of the area affected by earthquake induced rockfalls: Comparison of the1998 Krn Mountains (NW Slovenia) earthquake (Mw 5.6) with worldwide data 51 Matej GABROVEC, Peter KUMER Land-use changes in Slovenia from the Franciscean Cadaster until today 63 Mojca FOŠKI Using the parcel shape index to determine arable land division types 83 Mateja FERK, Matej LIPAR, Andrej ŠMUC, Russell N. DRySDALE, Jian ZHAO Chronology of heterogeneous deposits in the side entrance of Postojna Cave, Slovenia 103 Special issue – Green creative environments Jani KOZINA, Saša POLJAK ISTENIČ, Blaž KOMAC Green creative environments: Contribution to sustainable urban and regional development 119 Saša POLJAK ISTENIČ Participatory urbanism: creative interventions for sustainable development 127 Jani KOZINA, Nick CLIFTON City-region or urban-rural framework: what matters more in understandingthe residential location of the creative class? 141 Matjaž URŠIČ, Kazushi TAMANO The importance of green amenities for small creative actors in Tokyo: Comparing natural and sociocultural spatial attraction characteristics 159 ISSN 1581-6613 9 771581 661010 ACTA GEOGRAPHICA SLOVENICA 2019 ISSN: 1581-6613 COBISS: 124775936 UDC/UDK: 91© 2019, ZRC SAZU, Geografski inštitut Antona Melika Internationaleditorialboard/mednarodniuredniškiodbor: DavidBole(Slovenia),MichaelBründl(Switzerland),RokCiglič(Slovenia), Matej Gabrovec (Slovenia), Matjaž Geršič (Slovenia), Peter Jordan (Austria), Drago Kladnik (Slovenia), BlažKomac (Slovenia), Andrej Kranjc (Slovenia), Dénes Lóczy (Hungary), Simon McCharty (United Kingdom), SlobodanMarković (Serbia), Janez Nared (Slovenia), Drago Perko (Slovenia), Marjan Ravbar (Slovenia), Nika Razpotnik Visković(Slovenia), Aleš Smrekar (Slovenia), Annett Steinführer (Germany), Mimi Urbanc (Slovenia), Matija Zorn (Slovenia) Editor-in-Chief/glavni urednik: Blaž Komac; blaz@zrc-sazu.si Executive editor/odgovorni urednik: Drago Perko; drago@zrc-sazu.si Chief editor for physical geography/glavni urednik za fizično geografijo: Matija Zorn; matija.zorn@zrc-sazu.siChief editor for human geography/glavna urednica za humano geografijo: Mimi Urbanc; mimi@zrc-sazu.si Chief editor for regional geography/glavni urednik za regionalno geografijo: Drago Kladnik; drago.kladnik@zrc-sazu.si Chief editor for spatial planning/glavni urednik za regionalno planiranje: Janez Nared; janez.nared@zrc-sazu.si Chiefeditorforruralgeography/glavnaurednicazageografijopodeželja:NikaRazpotnikVisković;nika.razpotnik@zrc-sazu.si Chief editor for urban geography/glavni urednik za urbano geografijo: David Bole; david.bole@zrc-sazu.si Chief editor for geographic information systems/glavni urednik za geografske informacijske sisteme: Rok Ciglič; rok.ciglic@zrc-sazu.siChief editor for environmental protection/glavni urednik za varstvo okolja: Aleš Smrekar; ales.smrekar@zrc-sazu.si Editorial assistant/uredniški pomočnik: Matjaž Geršič; matjaz.gersic@zrc-sazu.si Issued by/izdajatelj: Geografski inštitut Antona Melika ZRC SAZUPublished by/založnik: Založba ZRC Co-published by/sozaložnik: Slovenska akademija znanosti in umetnosti Address/Naslov: Geografski inštitut Antona Melika ZRC SAZU, Gosposka ulica 13, SI – 1000 Ljubljana, Slovenija The papers are available on-line/prispevki so dostopni na medmrežju: http://ags.zrc-sazu.si (ISSN: 1581–8314) Ordering/naročanje: Založba ZRC, Novi trg 2, p. p. 306, SI – 1001 Ljubljana, Slovenija; zalozba@zrc-sazu.si Annual subscription/letna naročnina: 20 € for individuals/za posameznike, 28 € for institutions/za ustanove. Single issue/cena posamezne številke: 12,50 € for individuals/za posameznike, 16 € for institutions/za ustanove. Cartography/kartografija: Geografski inštitut Antona Melika ZRC SAZU Translations/prevodi: DEKS, d. o. o. DTP/prelom: SYNCOMP, d. o. o. Printed by/tiskarna: Tiskarna Present, d. o. o. Print run/naklada: 350 copies/izvodov The journal is subsidized by the Slovenian Research Agency and is issued in the framework of the Geography of Slovenia coreresearchprogramme(P6-0101)/revijaizhajaspodporoJavneagencijezaraziskovalnodejavnostRepublikeSlovenijein nastajav okviru raziskovalnega programa Geografija Slovenije (P6-0101). The journal is indexed also in/revija je vključena tudi v: SCIE – Science Citation Index Expanded, Scopus, JCR – Journal Citation Report/Science Edition, ERIH PLUS, GEOBASE Journals, Current geographical publications, EBSCOhost,Geoscience e-Journals, Georef, FRANCIS, SJR (SCImago Journal & Country Rank), OCLC WorldCat, Google scholar,and CrossRef. Oblikovanje/Design by: Matjaž Vipotnik. Front cover photography: Stone bridge over the Rak River on the outskirts of the Rakov Škocjan polje, which is otherwiseknown for its beautiful natural bridges (photograph: Matej Lipar).Fotografija na naslovnici: Kamniti most čez reko Rak na obrobju kraškega polja Rakov Škocjan, ki je sicer bolj znano počudovitih naravnih mostovih (fotografija: Matej Lipar). USINGTHEPARCELSHAPEINDEX TODETERMINEARABLELAND DIVISIONTYPES Mojca Foški The shapes or individual parcels are often well distinguished in the landscape. DOI: https://doi.org/10.3986/AGS.4574 UDC: 528.44(497.4Gorenje pri Divači) COBISS: 1.01 Using the parcel shape index to determine arable land division types ABSTRACT:Thispaperpresentsanewindexfordeterminingtheshapeoflandparcels.Parcelshapesare usuallyrepresenteddescriptively(i.e.ribbon-shaped,rectangular,irregularlyshaped),whichisuselessfor automateddistinguishingbetweenparcelshapesorfordetermininganddistinguishingbetweenthepatterns formed by parcels. Thus, wedeveloped aParcelShape Index(IOP)to describe parcel shape characteristics, andthentesteditinthetestareaofGorenjepriDivačitoanalyseselectedfields–asirregularblocks,enclo-sures,continuousstrips,andfurlongs. WefoundthatIOPallowsforadifferentiationofparcelsaccording to their shape as well as parcel patterns formed due to the individual types of dividing arable land. KEYWORDS:agriculturalland,parcels,ParcelShapeIndex,parcelshape,descriptivestatistics,hierarchical clustering, Slovenia Uporaba indeksa oblike parcel (IOP) za določanje tipa poljske razdelitve POVZETEK:Vprispevkupredstavljamonovindekszadoločanjeoblikeparcel.Oblikoparcelnajpogosteje podajamo opisno (trakasta, pravokotna, nepravilnih oblik), kar je neuporabno za avtomatizirano razlo-čevanje parcel po obliki in ugotavljanje ali razločevanje vzorcev, ki jih tvorijo parcele. Za opis oblikovnih značilnosti parcel smo izdelali indeks oblike parcele (IOP), ga preverili na testnem območju Gorenja pri Divači terz njim analizirali izbrana poljavgrudah,celkih,sklenjenihprogahindelcih. Ugotovili smo,da IOPomogočarazlikovanjeparcelpoobliki,kakortudirazlikovanjeparcelnihvzorcev,kijihtvorijoparcele v posameznem tipu poljske razdelitve. KLJUČNE BESEDE: kmetijska zemljišča, parcele, indeks oblike parcel, oblika parcel, opisna statistika, hierarhična analiza, Slovenija Mojca Foški University of Ljubljana, Faculty of Civil and Geodetic Engineering mfoski@fgg.uni-lj.si The paper was submitted for publication on March 15th, 2016. Uredništvo je prejelo prispevek 15. marca 2016. 1 Introduction Theshapedescribesthegeometricformoftwo-orthree-dimensionalspatialobjects(MacEachren1985), while according to The Standard Slovene Dictionary (Slovar slovenskega knjižnega jezika 2000) it is the appearance of a phenomenon in space. The shape is one of the most important characteristics of a spa-tialelementandisusuallyrepresenteddescriptively,i.e.thelakeiselongated,theparcelisrectangular,the cityisirregularlyshaped.Peopleperceivestandardshapes(round,rectangular,triangular)similarly;how­ever, it is difficult to represent irregular shapes in such a way that people perceive them similarly, i.e. in aunifiedmanner.Itisevenmoredifficulttocompareirregularly-shapedspatialphenomenawitheachother and observe their changing over time. Theprocessofdefiningshapewasparticularlyofrelevancetogeographicalstudyinthe1960s(Boyce and Clark 1964). Already in 1822, Ritter compared the area of a geographical phenomenon to that of the smallestcircumscribingcircle(Frolov1975).Theusefulnessofknowinganddeterminingshapesingeog­raphy was described in detail by Wentz (2000); for economic geography purposes Simons (1974) determined the shape of cities. In ecology (Eason 1992; Gutzwiller and Anderson 1992; Comber, Birnie and Hodgson 2003) topics such as the impact of territory shape in habitats on the distribution of plant and animal species are addressed; in landscape planning the impact of the shape of landscape structures on landscape appearance (hereinafter: landscape) is investigated (Krummel et al. 1987; Milne 1991; Rutledge 2003; McGarigal and Marks 1995; McGarigal 2013, 2015). The distinguishing between various shapes of spatial phenomena is relevant in remote sensing (Zhang et al. 2006). The shape of a phenome­non is significant in computer sciences (Sagiv, Reps and Wilhelm 2003) both in terms of visualisation or interpretation,i.e.computergeometry.Thedetectionanddistinguishingbetweenshapesattractedtheinter­est of psychology (Landau, Smith and Jones 1988). Land parcels are an important spatial phenomenon. They reflect the diversity of natural conditions andhumanadaptationtothelandscape(Kladnik1999). Inagricultural,forest,andbuilt-upareas,parcels aredistinguishedbyshape.Basedontheparcelshapeandtheparcelpatternwecandrawconclusionsabout naturalgeographicfeaturesofspace,suchasreliefshapes,gradient,andaltitude(FialkowskiandBitner2008). Accordingly,Ilešič(1950)consideredparcelshapetobethekeyfactorforfieldpatternclassification.Afield is a continuous area of arable land in a settlement (Slovar slovenskega knjižnega jezika 2000). Theshapeoffieldparcelsistheconsequenceofsettlement,landcultivationmethods(plough,ploughshare), andtheagriculturalregime(Ilešič1950;Blaznik1970).Thechangingofparcelshapesatthecontactofagri­culturalandbuilt-upspacespointstothepressuresofurbangrowth(IrwinandBockstael2004).Theshape ofparcelsisimportantforagricultureasitinfluencestheeconomicviabilityofmachiningoperations(Coelho, Pinto and Silva 2001; Tourino et al. 2003; Gonzalez, Alvarez and Crecente 2004; Gonzales, Marey and Alvarez2007;Aslan,GundogduandArici2007;Amiama,BuenoandAlvarez2008;LibecapandLueck2009; Zondonadi et al. 2013). Bielecka and Gasiorowski (2014) drew conclusions about land fragmentation in relationtoparcelshapes. Oksanen(2013)studiedlandparcelshapesinFinlandinrelationtotheautoma­tionofagriculturalprocesses,andDemetriou,StellwellandSee(2012),Demetriou,SeeandStellwell(2013), andDemetriou(2013,2014)studiedparcelshapeswhendevelopinganapplicationforlandconsolidation planning in Cyprus. In studying the parcel shape it is essential that the shape is changed into a numerical value – index of shape(Wentz 2000). Thisway wecancompareand observethe changingofparcel shapesand parcelpat- terns formed by the parcels. Shape indices fall into two classes: indices with one variable (single-parameter indices), which give avalueforonlyoneproperty,andindiceswithseveralvariables(multipleparameterindices),whichdescribe the characteristics of a shape with the use of more complex mathematical functions. Shape is usually too complextobedescribedusingasingleparameter(Ehler,CowenandMackey1996;Wentz2000),orrather several independent single-parameter indices are needed to describe a complex shape (Oksanen 2013; Demetriou2014),andtheseindicesshouldmeetcertaincriteria(LeeandSallee1970;Wentz1997;Wentz2000; Demetriou, See and Stillwell 2013): • different numerical values must be ascribed to different shapes, • similar shapes must have similar values, • indices must be useful both with concave and convex phenomena, • indices must identify holes in polygons, • indices must be independent of the size of phenomena, • indices must be independent of movements, rotations, and scale, • the input data must be prepared simply, • indices must be easy to understand and the results easy to interpret, • indices must have a value range (as a rule, the value increases from 0 to 1) and it must be determined which shape has the value of 1, and • the values obtained must reflect human perception of a spatial phenomenon. In terms of the shape feature that we want to describe, we distinguish between indices describing the perimeter, plane characteristics, and geometry (Zhang and Lu 2004; Chaudhuri 2013). Thebasichypothesisisthatusinganumericalvalue–theshapeindex–wedescribetheshapeofaspa­tialphenomenon,suchasaparcel. Accordingly, wedevelopedaParcel ShapeIndex(IOP). The studywas narrowed down to those parcels that are in fields. Ilešič (1950) proposed a system of dividing arable land based,infact,onparcelshape;hedividedSlovenianfieldsintobasictypes(irregularblocks,furlongs,con­tinuous strips, and enclosures) and transitional types (transitional shapes between irregular blocks and furlongs,divisionintoirregularorblockfurlongs,combinationofcontinuousstripsandregularfurlongs). Accordingly, parcels in areas with blocks and enclosures have distinctly irregular shapes, while parcels in areaswithfurlongsaregenerallyrectangular,withasideratioupto1:10,whilecontinuousstripsaredis­tinctlybelt-likeorrectangularwithasideratioevenupto1:100.Theindex’sadequacywascheckedagainst the basic arable land types, while their applicability was checked in the classification of various types of arable and division. 2 Methods The method consists of four steps: • IOP determination, • testing of IOP on a sample case of the field at Gorenje pri Divači (hereinafter: Gorenje), • determination of IOP for parcels of basic types of arable land division and statistical processing of IOP values, and • hierarchical clustering of fields. IOPdeterminationwasbasedontheliteratureandcharacteristicsofarablelandparcelshapesinSlovenia, usingseveralsingle-parameterindices:indicesforperimeter,plane,andparcelgeometrydescription.The indiceswerestandardisedusingavaluefunction(Beinat1997;Malczewski1999,2011;Sharifi,Herwijnen andToorn2004).Arectangularparcelwitha1:2sideratiowasselectedasthereferenceparcelshape.This side ratio is the first whole side ratio value that distinguishes a rectangle from a square. Weselected22testfieldsamongfieldsasirregularblocks,furlongs,continuousstrips,andenclosures (Table2).TheareasofthesefieldsweredeterminedusingIlešič’soriginalclassification(1950)(e.g.Arjavas,Predoslje,Kokra,BitnjeandŽabnica,Zatolmin)and/orthedatafromtheFranciscanCadastre(Internet1), digital orthophotos, and land cadastre data acquired through the Surveying and Mapping Authority of the Republic of Slovenia in 2015, whereby various landscape types were considered (Perko, Hrvatin and Ciglič 2015; Figure 1). The field divisions were based on geographical dividing lines (to the stream, road, forest, and village) or the cadastral municipality boundary. The fields were named after the closest settlement (e.g. Arja vas) or a geographical area (e.g. Trška gora). Thedatafromthelandcadastredepiction,basedonwhichtheIOPwascalculated,wereorganisedby excluding all parcels designated as built-up or related land or body of water according to the Register of Existing Agricultural and Forest Land Use (Internet 2). In cases of agricultural buildings (e.g. a granary ora hayrack) with landunderthebuilding(parcel),thislandwasaggregatedwiththeneighbouringparcel. IOP was calculated for 13,725 land parcels in all test fields. Indicators of descriptive statistics were calculated forall test fields(Table2): number ofparcelsinafield (N), minimumvalue(MIN),maximum value (MAX), average value (AVG), median (Me), mode (Mo), standard deviation (.), asymmetry coef-ficient(y1),andcoefficientofkurtosis(y2).TheobtainedIOPvalueswereshownonhistograms(10classes, class width 0.1). Statistical values were demonstrated using a box-and-whiskers plot (Figure 8). Figure 1: Distribution of test fields by various landscape types of Slovenia. p Inthelaststep,weclassifiedthefieldsintogroupsusingWard’shierarchicalclusteringmethod(Breskvar ŽaucerandKošmelj2006;Bastič2006;Figure9).Indicatorsofdescriptivestatisticswereusedfortheclus­ ter analysis, and Euclidian distance was used as cluster criterion. Statistical data processing and depiction using histograms and box-and-whiskers plots demonstrated whetherIOPreflectedtheparcelshapesconcernedandwhethertheparcelshapewas,infact,characteristic for the various types of arable land division according to Ilešič. The analysis was based on the data from the land cadastre depiction by the Surveying and Mapping AuthorityoftheRepublicinSlovenia,acquiredin2015,inArcGis10.3;MicrosoftExcel2010andIBMSPSS23 software were used for calculations and statistical processing. 2.1 IOP determination and its verification on the sample case of Gorenje 2.1.1 Indices for describing plane characteristics: compactness index /Ikom In this group we typically use indices describing the ratio between area (A) and perimeter (P) (Santiago andBribiesca2009;Li,GoodchildandChurch2013),whichareoften referredtoascompactnessindices. Besides the initially produced factor P/A proposed by Ritter (Frolov 1975) other indices are also used, e.g. indices of ratios 4A/P2 (Miller 1953), A/P2 (Gonzalez, Alvarez and Crecente 2004), P/2 A (Aslan, Gundogdu and Arici 2007) and A/0.282 P · (Chan and So 2006). The most frequently used compactnessindexwasdevelopedbyOsserman(1978)andisalsousedhere;itisdescribedbytheequation 4.A ’ I= kom P2 The equation’s advantage is that . shifts the value area of the initial indices in the range of 0 to 1. Thevalueof1describesthemostcompactphenomenon –thecircle.Wentz(2000)foundthatthisindex is not the most appropriate for very diversified phenomena, but it is insensitive to scale, displacement, and rotation variations, independent of the size of the phenomenon, and applicable to both raster and vector data (Sonka, Hlavac and Boyle 1993; Santiago and Bribiesca 2009; Oksanen 2013; Bielecka and Gasiorowski 2014). Indices from this group also have some shortcomings. In particular, they do not reflect the charac­teristics of a shape, but rather compactness according to a comparable geometric shape, i.e. a circle in ourcase(MacEachren1985;Angel,ParentandCivco2010).Theycannotbeusedtomeasurefeaturessuch asthepresenceof holes, expansion, or fragmentation. Parcel shapes should not be described using only these indices as they only take into account the area and perimeter characteristics (Demetriou, See and Stillwell 2013). wasstandardisedtodetermineparcelcompactness,becausetheparcelswere,ofcourse,notround. I’kom Indeterminingthevaluefunctionsixthdegree polynomial wasused(Demetriou2014),whilethe function wasdeterminedsothatfortheparcelswithasideratio(of1:2)whoseI’komequals0.70,thevalueIkom =0.99 wasassumed,whilefortheparcelswithI’kom lessthan0.33(sideratio1:8)thevalueofIkom =0wasassumed (Figures 2 and 3). Other values were determined using the value function (Figure 2): ’ ’6 ’5 ’)4 I = VI ) = - . (I) + .(I ) - . (I +1 ( 372 614 1319 19 1820 87 kom kom kom i kom i k om i ’3 ’2’ .(I ) - 414 436 . (I ) + 66 207 (I ) - 3. 122722 . 3908 kom i kom i kom i The value function is determined so that all parcels with a side ratio up to 1:4 get a higher compact­ness index, whichallows for differentiationfrom longer parcels(with side ratio over 1:8) (Figure 3). The compactnessindexwascalculatedforthetestcaseofGorenjeandgraphicallyshown(Figure5A)in10equal classes with a degree of 0.1. I'kom Figure 2: Value function for determining Ikom I' kom 1.0 0.8 0.6 0.4 0.2 0.0 0.93 0.99 0.88 0.79 0.70 0.59 0.60 0.50 0.44 0.38 0.32 0.34 0.31 0.28 0.26 0.12 0.02 0.00 0.00 0.00 1 : 1 1 : 2 1 : 3 1 : 4 1 : 5 1 : 6 1 : 7 1 : 8 1 : 9 1 : 10 Rectangular plotratio I'kom Ikom Figure3:RatiobetweenindexI’anditsstandardisedvalueI.Ihasthemaximumvalueforparcelswithasideratioof1:2;whileitequals0 kom komkom with parcels with a side ratio above 1:8. 2.1.2 Indices of the special characteristics of the geometry of the phenomenon: Perforation Index/Iluk Somecharacteristicsofphenomenacannotbedescribedusingthecompactnessindex,soweusedWentz’s perforationindex(2000),bysubtractingitfrom1: B I=1 - i luk A i whereBi isthetotalareaofallholesinobjectiandAiisthetotalareaofobjecti. Theparcelswithoutholeswereascribedthemaximumvalueof1,whilethevalueof0couldnotbe reached.IntheGorenjetestarea(Figure5B)weonlyshowedparcelswithanIluk otherthan1,anddue toreasonsofclaritytheparcelswiththeperforationindexof1werenotcoloured. 2.1.3 Indices for perimeter description Index of Edge Roughness/Inaz Theseindicesdescribetheroughnessoftheedgeofageographicalobject.Onthebasisoftheratiobetween anobjectanditscorrespondingconvexhull,theyaremostfrequentlyusedtodescribetheperimeterchar­acteristics.Theamplitudeindex((P–Pk)/P)considerstheratiobetweentheperimeterofanobject(P) andtheperimeteroftheconvexhull(Pk),whiletheconvexityindex((Ak–A)/Ak)considerstheratiobetween theareaofobjectAandtheareaoftheconvexhull(Ak)(Brinkhoffetal.1998).ChaninSo(2006)used thecomparablesurfacearearatio,Iivarinenetal.(1997),Angel,ParentandCivco(2010),andZondonali etal.(2013)usedtheratiobetweentheperimeterofobjectPanditsconvexpolygonPk,whichwasalso usedhere;theedgeroughnessindexwaswrittenas: P I= naz P k Theindexhasthevalueof1iftheparcelisconvex.Withthevaluenearing0,diameterroughnessincreas-es.Thevalueof1isascribedtoallconvexparcels,whilethevalueof0isunattainable.Thecalculationof InazinthetestfieldofGorenjeisshownintenequalclasseswitharateof0.1(Figure5C),redshadesindi­catingjagged-edgedparcels,whilethedarknessoftheblueindicatessmootheredges. Figure 4: Value function for standardising the number of vertices (Iogl). Figure 5: Compactness Index (A), Perforation Index (B), Index of Vertices (C), and Edge Roughness Index (D) for Gorenje. p AB CD Acta geographica Slovenica, 59-1, 2019 91 Legend 0.1 0 0.1 0.2 0.3 km0.0–0.1 0.2–0.3 0.4–0.5 0.6–0.7 0.8–0.9Map by: Mojca FoškiSource: GURS, 20150.1–0.2 0.9–1.0 © 2018, UL, FGG 0.3–0.4 0.5–0.6 0.7–0.8 Index of Vertices (Iogl) Indices of the number of perimeter vertices are frequently used to describe the characteristics of a parcel perimeter (Brinkhoff et al. 1998; Demetriou, Stellwell and See 2012). The reference parcel has four ver­tices;byincreasingthenumberofvertices,thedeviationfromarectangleincreases.Parcelswiththreevertices alsoconsiderablydeviatefromarectangle. Thestandardisationofthenumberofverticesinavaluerange from 0 to 1 was made using a value function after Demetriou (2014) (Figure 4), where xi is the number of vertices: 407.76 4280.97 20959.323 49141.25 45677.80 I=V(x )=14.45 - + - + - ogl i 23 45 xxx x x iii ii All parcels with more than 10 vertices were ascribed the value of 0. The index of vertices was calcu­lated for Gorenje. We showed the parcels with Iogl other than 0 (Figure 5 D). 2.2 Parcel Shape Index (IOP) The parcel shape index can be written using the equation: n Iw . jj j=1 IOP= n where Ij is one of the aforementioned indices and Wj is the index weight. If the indices are equally weighted (with a value of 1), then for each parcel i IOP is calculated as the arithmetic mean of four single-parameter indices: I +I +I +I kom naz luk ogl IOP= 4 The Pearson correlation coefficient between the indices of compactness, roughness, perforation, and verticesforthe722parcelsinGorenjeislow(Table1),indicatingtheindices’mutualindependence,which satisfies one of the basic criteria for combining single-parameter indices. Table 1: The Pearson correlation coefficient between the indices for Gorenje. Correlation coefficient Ikom I naz I ogl Iluk Ikom 0.24 –0.19 0.045 I naz –0.30 0.20 Iogl Iluk –0.25 IOP is in the range of 0 to 1. Given the value functions in the standardisation procedure, the value of 1isascribedtotheparcelswithasideratioof1:2,withoutholes,withfourvertices,andwithacompletely smooth edge. The depiction of IOP in the four value classes (Figure 6 below) shows that the parcels with distinctly irregular shapes (jaggedness, holes)are in the lowest class, while rectangular parcels with a low side ratio are in the highest class. The parcels within a class are visually similar (Figure 6); IOP is applic­ablebothinconvexandconcaveparcels,independentofparcelsize,insensitivetoscaleandrotationvariations, and easy to calculate, and thus meets all the criteria for determining indices. Figure 6: IOP in 10 classes with a rate of 0.1 (page 93) and in four classes with a rate of 0.25 (page 94) for Gorenje. p p. 93–94 Legend IOP 0.0–0.10.1–0.20.2–0.30.3–0.40.4–0.50.5–0.60.6–0.70.7–0.80.8–0.90.9–1.0 0.1 0 0.1 0.2 0.3 km Mapby:MojcaFoški Source:GURS,2015 ©2018,UL, FGG Legend 0.1 0 0.1 0.2 0.3 km 0.00–0.25 0.50–0.75Map by: Mojca FoškiSource: GURS, 20150.25–0.50 0.75–1.00 © 2018, UL, FGG 3 IOP results in the selected test cases IOPwascalculatedfor22selectedfields(Table2,Figure1)inirregularblocks,furlongs,continuousstrips, and enclosures. For each test field we calculated the indicators of descriptive statistics for IOP, while the distributionofIOPvalueswasshownonhistograms(Table2)andbox-and-whiskersplots(Figure7).The statistical values were compared and it was determined whether IOP reflected the actual characteristics ofaparcelshapeandiftheparcelshapewas,infact,characteristicforthevarioustypesofarablelanddivi­sion according to Ilešič. Using the hierarchical clustering method, the fields were clustered into groups, and the results were depicted using a dendrogram (Figure 8). Weuseddescriptivestatistics,histograms(Table2),acomparisonofbox-and-whiskersplots(Figure7), and depiction of hierarchicalclustering(Figure8) totrytoestablish similarities betweenparcelshapesand the patterns formed by the parcels. The IOP distribution in fields as furlongs and fields as irregular blocks isverysimilar(withtheexceptionsofVinjoleandTrškagora),wheretwomodesareobserved(0.35and0.75). Thiswasalsoconfirmedbytheclassificationintothesamegroupusingthehierarchicalclusteringmethod. The parcel shapes in areas of continuous strips also show great similarity. The mode class is 0.3-0.4 or 0.4-0.5. The narrowest is the second quartile (maximum densification of parcels), while the asymme­trycoefficient(y2)ispositiveinalltestfields(asymmetrytotheright).Thefieldsareclassifiedascontinuousstrips,exceptforKlečeandPodgora.ThefieldsofBujeandŽerovnicaalsobelongtothisgroup,eventhough Ilešičclassifiedthemasfurlongs(belt-likefurlongs),whiletheirparcelshapewasdistinctlybelt-like,which is characteristic for parcels in continuous strips. Theanalysedfieldsasfurlongscanbeclassifiedintotwogroups(Figure8).ThefirstgroupisArjavas, Predoslje,Kleče,andPodgora,andthesecondgroupisTrškagora,Stržišče,Sovjak,Sedlarjevo,andVinjole. Thegroupsarecombinedinthenextaggregation.IlešičclassifiedVinjoleandTrškagoraaswinegrowingblocks, whileintermsofparcelshape(rectangularwitha smallsideratio)thefieldsare comparabletofurlongs. Table 2: Descriptive statistics and IOP histograms for all fields considered. Mojca Foški, Using the parcel shape index to determine arable land division types Figure 7: Box-and-whiskers plots for IOPs for all selected test fields shown on the same graph for fields as irregular blocks, furlongs, continuous strips, and enclosures. Figure 8: Dendrogram of the hierarchical clustering of fields into groups using Ward’s method. 96 4 Discussion IOP is the arithmetic mean of four mutually independent single-parameter indices that also consider theholesinparcels,which wasnotfoundwithotherauthors(Tourinoet al. 2003;Aslan, Gundogduand Arici 2007; Amiama, Bueno and Alvarez 2008; Zondonadi et al. 2013; Demetriou 2014; Bielecka and Gasiorowski2014).InSlovenia,parcelswithholesaretheconsequenceofnaturalgeographicfeaturesand specifics of the Franciscan Cadastre, where for each type of land use a separate parcel was determined, even though neighbouring parcels belonged to the same proprietor (Ferlan 2005). In cases where a field wasinthemiddleofameadow oraatthebottomofasinkholethereareholesinparcelspreservedtothe presentday.InSlovenia,holesarepresentmostlyinirregularblocksandenclosures,andexceptionallyalso inareasofcontinuousstrips(Bitnje),sowefeelthatthisfeatureshouldbetakenintoaccountinIOP.Ahole in a parcel decreases IOP, while the proportion of parcels with lower IOP increases in the pattern, which is characteristic for irregular blocks and enclosures. Someauthorsdeterminedparcelshapeonlybyusingthecompactnessindex(BieleckaandGasiorowski 2014; Oksanen 2013; Zondonadi et al. 2013), which has several shortcomings (Demetriou, See, and Stillwell 2013). The values were standardised to a reference parcel shape only by Demetriou (2014). This standardisationtoareferenceparcelshapeisnecessary,eventhoughthedeterminationofareferencepar­cel varies depending on the study purpose. Using this standardisation we delineated the rectangles with a more favourable side ratio (up to 1:8) from distinctly elongated rectangles (belts). The IOP calculation for the Gorenje test area demonstrated (Figure 6) that parcels in the individual classes are visually similar. But then over a larger sample (all 22 fields, 13,725 parcels) it became evident that the IOP value for long and narrow parcels in the area of continuous strips was similar to the values ofirregularparcelsintheareasofirregularblocks,i.e.between0.30and0.45(Figure10).Futureworkshould includeanindextoimprovethedeterminationofthecharacteristicsofverylongandnarrowparcels(e.g.ratio between the shortest and the longest diagonal of a parcel). Despite this deficiency, the statistical data analysis of various types of arable land division (Figure 7) and hierarchical clustering (Figure 8) demonstrated that IOP allows for distinguishing between fields as continuous strips from other types of fields mostly because these two types of parcel shapes usually do notoccurtogether.InSlovenia,continuousstripsaremorefrequentinplains,inparticularinSorškopolje (Ilešič1950),andareareflectionofsystematicsettlement(Blaznik1970),whileirregularblocksarechar­acteristicofamorediverseterrainandareclassifiedastheoldesttypeofarablefielddivision(Blaznik1970). Figure 9: Sections from the land cadastre depiction (Geodetska uprava RS 2015; above) and sections from the Franciscan Cadastre (Arhiv RS; below) with cases of holes in irregular blocks (Zatolmin, A), continuous strips (Bitnje, B), and enclosures (Pernice, C). IOP=03. 5 IOP=037 . Figure10:ThecaseofsimilarIOPvaluesfortwoparcelsdifferent inshape. This arable land division analysis is mostly based on the study results by Ilešič from 1950. His study remains the only study for the area of the entire Slovenia and to date has not been systematically revised. ThisiswhytherearedeviationsbetweenIlešič’sdefinitionoftheindividualarablelandtypesandtheresults indicated by the IOP analysis in parcels from 2015. IOP allows for the classification of fields and even the exclusion and aggregation of fields that stand outaccordingtotheirparcelshapecharacteristics.ThefieldswithaproportionofIOPabove0.7(Vinjole, Sedlarjevo, Sovjak, Stržišče and Trška gora), which were classified either as irregular blocks or furlongs according to Ilešič, should be classified into a new group. We noticed deviations in the classification of fields based on parcel shapes with furlongs and contin­uousstrips.IlešičclassifiedthefieldsofKlečeandPodgoraascontinuousstrips,whileaccordingtoIOPthey wereclassifiedasfurlongsduetotheshorterstrips.BujeandŽerovnicawereclassifiedasfurlongsbecause of short strips. Basedonthestatisticaldifferencesbetweenfieldswecanidentifysomenewgroupsandproposeimprove­mentsuponIlešič’sfieldclassification.Thisisthecasewithwinegrowingareas,whichareeitherconsidered irregular blocks or furlongs. This way we confirmed the working hypothesis about the possibility of pro­ducing a numerical index for describing parcel shapes to be used to determine and classify fields. The use of the Parcel Shape Index has a wide ranging applicability. Parcel shape is important in agri­culture in termsof the rational useof individual parcels (Zondonadi et al. 2013), while in Slovenia parcel shapeshouldbeincludedinidentifyingprotectedfarmsteadsandusedintheanalysisofGERK(Graphical Unit of Agricultural Land) and RABA (Register of Existing Agricultural and Forest Land Use) data kept by the ministry responsible for agriculture. The parcel shape is, of course, not the only criterion for determining arable land division types, so it would be advisable to determine indices for other field characteristics, such as land distribution (Simmons1964;Januszewski1968;Igbozurike1974;Gosar1978;RazpotnikVisković2012)andlanduse diversity (McGarigal in Marks 1995; McGarigal 2013, 2015). 5 Conclusions The paper shows that IOP values and statistical indicators vary among fields as irregular blocks, enclo­sures, continuous strips, and furlongs. Ilešič’s classification of fields in the selected test fields was mostly confirmed. Out of 22 fields 17 were classified in line with Ilešič’s system. But because Ilešič also included otherindicators in the determinationof arablelanddivisiontypes, such as land fragmentation,the num­berofindicesconsideredshouldbeincreased.UsingthehierarchicalclusteringmethodandbasedonIOP fieldscanbeclassifiedintoclasses,whichallowsforconfirmationandimprovementupontheexistingtyp­ification.Eventhoughitisverydifficulttodescribeallthevisualcharacteristicsofaspatialobjectusingshape indices(WilliamsandWentz2008),doingsononethelesslimitsanindividual’ssubjectivity.Furthermorethe transformationofashape’scharacteristicstonumericalvaluesallows foreasier processingandcomparison of data. IOP could help us to observe the changing of parcel shapes (e.g. in a field). This would be partic­ularlyapplicablewhereagriculturalandbuilt-uplandmeet,wherethetransformationoftheshapeofaparcel into (as a rule) a square indicates the purpose of transforming agricultural land into built-up land. 6 References Amiama,C.,Bueno,J.,Alvarez,C.J.2008:Influenceofthephysicalparametersoffieldsandthecropyield ontheeffectivefieldcapacityofaself-propelledforageharvester.BiosystemsEngineering100-2.DOI: https://doi.org/10.1016/j.biosystemseng.2008.03.004 Angel,S.,Parent,J.,Civco,D.L.2010:Tencompactnesspropertiesofcircles:measuringshapeingeography. CanadianGeographer-GeographeCanadien54-4.DOI:https://doi.org/10.1111/j.1541-0064.2009.00304.x Aslan,T.,Gundogdu,K.,Arici,I.2007:Somemetricindicesfortheassessmentoflandconsolidationprojects. Pakistan Journal of Biological Sciences 10-9. Bastič, M. 2006: Metode raziskovanja. Maribor. Beinat, E. 1997: Value functions for environmental management. Dordrecht. Bielecka, E., Gasiorowski, J. 2014: Land fragmentation analysis using morphometric parameters. The 9th International Conferenc Environmental Engineering. DOI: https://doi.org/10.3846/enviro.2014.205 Blaznik, P. 1970: Gospodarska in družbena zgodovina Slovencev. Poljska razdelitev. Ljubljana. Boyce, R., Clark, W. 1964: The concept of shape in geography. Geographical Review 54-4. Breskvar Žaucer L., Košmelj K. 2006: Metode za razvrščanje enot v skupine; osnove in primer. Acta agri­ culturae Slovenica 87-2. Brinkhoff,T.,Kriegel,H.P.,Schneider,R.,Braun,A.1998:Measuringthecomplexityofpolygonalobjects. Munich. Chan, A. H. S., So, D. K. T. 2006: Measurement and quantification of visual lobe shape characteristics. InternationalJournalofIndustrialErgonomics36-6.DOI:https://doi.org/10.1016/j.ergon.2005.10.005 Chaudhuri, D. 2013: Global contour and region based shape analysis and similarity measures. Defence Science Journal 63-1. DOI: https://doi.org/10.14429/dsj.63.3767 Coelho, C., Pinto, P. A., Silva, M. 2001: A systems approach for the estimation of the effects of land con-solidationprojects(LCPs):Amoduleanditsapplication.AgriculturalSystems68-3.DOI:https://doi.org/ 10.1016/S0308-521X(00)00061-5 Comber,A. J.,Birnie,R. V., Hodgson,M2003:A retrospectiveanalysisof land coverchange using polygon shape index. Global Ecology and Biogeography 12-3. Demetriou,D.2013:LACONISS:ALandConsolidationIntegratedSupportSystemforplanninganddecision making. Zfv-Journal of Geodesy, Geoinformation and Land Management 138-2. Demetriou,D.2014:Thedevelopmentofanintegratedplanninganddecisionsupportsystem(IPDSS)for land consolidation. London. DOI: https://doi.org/10.1007/978-3-319-02347-2. Demetriou, D., See, L., Stillwell, J. 2013: A parcel shape index for use in land consolidation planning. Transactions in GIS 17-6. DOI: https://doi.org/10.1111/j.1467-9671.2012.01371.x. Demetriou, D., Stillwell, J., See, L. 2012: Land consolidation in Cyprus: Why is an integrated planning and decision support system required? Land Use Policy 29-1. DOI: https://doi.org/10.1016/ j.landusepol.2011.05.012 Eason,P.1992:Optimizationofterritoryshapeinheterogeneoushabitats–afield-studyofthered-capped cardinal (Paroaria-Gularis). Journal of Animal Ecology 61-2. DOI: https://doi.org /10.2307/5332 Ehler, G. B., Cowen, D. J., Mackey, H. E. jr. 1996: Development of a shape fitting tool for site evaluation. 7th International symposium on spatial data handling. DOI: https://doi.org / 10.2307/490799 Ferlan, M. 2005: Geodetske evidence. Ljubljana. Fialkovski, M., Bitner, A. 2008: Universal rules for fragmentation of land by humans. Landscape Ecology 23-9. DOI: https://doi.org/10.1007/s10980-008-9268-x Frolov,Y.S.1975:Measuringshapeofgeographicalphenomen–historyofissues.SovietGeographyReview and Translation 16-10. Gonzalez, X. P.,Alvarez, C. J.,Crecente,R. 2004:Evaluationoflanddistributionswithjointregardtoplot size and shape. Agricultural Systems 82-1. DOI: https://doi.org/10.1016/j.agsy.2003.10.009 Gonzalez, X. P., Marey, M. F., Alvarez, C. J. 2007: Evaluation of productive rural land patterns with joint regardtothesize,shapeanddispersionofplots.AgriculturalSystems92-1-3.DOI:https://doi.org/10.1016/ j.agsy.2006.02.008 Gosar, L. 1978: Prispevek k preučevanju razdrobljenosti posesti. Geografski vestnik 50. Gutzwiller, K. J., Anderson, S. H. 1992: Interception of moving organisms:influences of patch shape, size and orientation on community structure. Landscape Ecology 6-4. DOI: https://doi.org/10.1007/ BF00129707 Igbozurike, M. U. 1974: Land tenure relations, social relations and the analysis of special discontinuity. Area 6-2. Iivarinen, J., Peura, M., Särelä, J., Visa, A. 1997: Comparison of combined shape descriptors for irregular objects.BritishMachineVisionConferenceEssex.Internet:http://www.bmva.org/bmvc/1997/papers/062/ bmvc97.htm (10.8.2015). Ilešič, S. 1950: Sistemi poljske razdelitve na Slovenskem. Ljubljana. Internet 1: http://arsq.gov.si (20.2.2015). Internet 2: http://rkg.gov.si/ GERK (20.2.2015). Irwin, E. G., Bockstael, N. E. 2004: Land Use externalities, open space preservation, and urban sprawl. RegionalScienceandUrbanEconomics34-6.DOI:https://doi.org/10.1016/j.regsciurbeco.2004.03.002 Januszewski,J.1968:IndexofLandConsolidationasacriterionofthedegreeofconcentration.Geographica Polonica 14. Kladnik, D. 1999: Leksikon geografije podeželja. Ljubljana. Krummel, J. R, Gardner, R. H., Sugihara, G., O’Neill, R. V. O., Coleman, P. R. 1987: Landscape patterns in a disturbed environment. Oikos 48. Landau, B., Smith, L. B., Jones, S. S. 1988: The importance of shape in early lexical learning. Cognitive Development 3-3. DOI: https://doi.org/10.1016/0885-2014(88)90014-7 Lee, D., Sallee, T. 1970: A method of measuring shape. Geographical Review 60-4. Li,W.,Goodchild,M.F.,Church,R.2013:Anefficientmeasureofcompactnessfortwo-dimensionalshapes anditsapplicationinregionalizationproblems.InternationalJournalofGeographicalInformationScience 27-6. DOI: https://doi.org/10.1080/13658816.2012.752093 Libecap,G.,Lueck,D.2009:Thedemarcationoflandandtheroleofcoordinatinginstitutions.TheNational Bureau of Economic Research. Working Papers Series 14942. MacEachren,A.1985:Compactnessofgeographicshape:comparisonandevaluationofmeasures.Geografiska Annaler B, Human Geography 67-1. Malczewski, J. 1999: GIS and multi-criteria decision analysis. New York. Malczewski, J. 2011: Local weighted linear combination. Transactions in GIS 15-4. DOI: https://doi.org/ 10.1111/j.1467-9671.2011.01275.x McGarigal,K.2013:Landscapepatternmetrics.Encyclopediaofenvironmetrics.Chichester.DOI:https://doi.org/ 10.1016/0169-2046(91)90034-J McGarigal,K.2015:Fragstatshelp.UniversityofMassachusetts.Internethttp://www.umass.edu/landeco/ research/fragstats/documents/fragstats.help.4.2.pdf (10.9. 2015). McGarigal,K.,Marks,B.J.1995:Fragstats:Spatialpatternanalysisprogramforquantifyinglandscapestruc­ture. Washington. Miller, V. C. 1953: A quantitative geomorphic study of the drainage basin characteristics in the Clinch Mountainarea,VirginiaandTennessee.TechnicalReport3.ColumbiaUniversityDepartmentofGeology. New York. Milne, B. T. 1991:The utilityof fractal geometryinlandscapedesign. Landscapeand Urban Planning21, 1-2. DOI: https://doi.org/10.1016/0169-2046(91)90034-J Oksanen,T.2013:Shape-describingindicesforagriculturalfieldplotsandtheirrelationshiptooperational efficiency.ComputerandElectronicsinAgriculture98.DOI:https://doi.org/10.1016/j.compag.2013.08.014 Osserman, R. 1978. The isoperimetric inequality. Bulletin of the American Mathematical Society 84-6. Internet:http://www.ams.org/journals/bull/1978-84-06/S0002-9904-1978-14553-4/S0002-9904-1978­14553-4.pdf (10.5.2015). Perko,D.,Hrvatin,M.,Ciglič,R.2015:MetodologijanaravnepokrajinsketipizacijeSlovenije.Actageographica Slovenica 55-2. DOI: https://doi.org/10.3986/AGS.1938 RazpotnikVisković,N.2012:Vlogamešanihkmetijvgospodarski,okoljskiinprostorskipreobrazbiobmestij. Doktorska disertacija. Univerza v Ljubljani, Interdisciplinarni podiplomski študij prostorskega in urbanističnega planiranja. Ljubljana. Rutledge,D.2003:Landscapeindicesasmeasuresoftheeffectsoffragmentation:Canpatternreflectprocess? Wellington. Sagiv,M.,Reps,T.,Wilhelm,R. 2003:Parametricshapeanalysisvia3-valuedlogic. ACMTransactionson Programming Languages and Systems 24-3. DOI: https://doi.org/10.1145/514188.514190 Santiago, R. S., Bribiesca, E. 2009: State of the art of compactness and circularity measures. International Mathematical Forum 4-27. Sharifi,A.,Herwijnen,M.,Toorn,W.2004:Spatialdecisionsupportsystems.LectureNotes.ITC,International Institute for Geo-Information Science and Earth Observation. Enschede. Simmons, A. J. 1964: An Index of Farm Structure, with a Nottinghamshire example. Nottingham. Simons, P. L. 1974: Measuring shape distortions of retail market areas. Geographical Analysis 6-4. DOI: https://doi.org/10.1111/j.1538-4632.1974.tb00518.x Slovar slovenskega knjižnega jezika 2000: Internet: http://bos.zrc-sazu.si/sskj.html (15.11.2015). Sonka, M., Hlavac, V., Boyle, R., 1993: Image processing, analysis, and machine vision. Boston. DOI: https://doi.org/10.1007/978-1-4899-3216-7 Tourino,J.,Parapar,J.,Doallo,R.,Boullon,M.,Rivera,F.,Bruguera,J.,Gonzalez,X.Crecente,R.,Alvarez, C. 2003: A GIS-embedded system to support land consolidation plans in Galicia. International JournalofGeographicalInformationScience17-4.DOI:https://doi.org/10.1080/1365881031000072636 Wentz, E. 1997: Shape analysis in GIS. Internet: http://www.mapcontext.com/autocarto/proceedings/ auto-carto-13/pdf/shape-analysis-hi-gis.pdf (15.4.2015). Wentz,E.2000:Ashapedefinitionforgeographicapplicationsbasedonedge,elongation,andperforation. Geographical Analysis 32-2 DOI: https://doi.org/10.1111/j.1538-4632.2000.tb00419.x Williams,E.A.,Wentz,E.2008:Patternanalysisbasedontype,orientation,size,andshape. Geographical Analysis 40-2. DOI: https://doi.org/10.1111/j.1538-4632.2008.00715.x Zhang, D., Lu, G. 2004: Review of shape representation and description techniques. Pattern Recognition 37-1. DOI: https://doi.org/10.1016/j.patcog.2003.07.008 Zhang,S.Q.,Zhang,J.,Li,F.,Cropp,R.2006:Vectoranalysistheoryonlandscapepattern(vatlp).Ecological Modelling 193, 3-4. DOI: https://doi.org/10.1016/j.ecolmodel.2005.08.022 Zondonadi, R. S., Luck, J. D., Stombaugh, T. S., Shearer, S. A. 2013: Evaluating field shape descriptors for estimating off-target application area in agricultural fields. Computers and electronics in agriculture 96. DOI: https://doi.org/10.1016/j.compag.2013.05.011