Method development to extract spatial association structure from soil polygon maps 65Sisák, I. et al. Hungarian Geographical Bulletin 64 (2015) (1) 65–78. Method development to extract spatial association structure from soil polygon maps István SISÁK1, Mihály KOCSIS1, András BENŐ1 and Gábor VÁRSZEGI2 DOI: 10.15201/hungeobull.64.1.6 Hungarian Geographical Bulletin 64 2015 (1) 65–78. 1 Department of Plant Production and Soil Science, Georgikon Faculty, University of Pannonia, H-8360 Keszthely, Deák F. u. 16. E-mails: talajtan@georgikon.hu, kocsis.mihaly@2010.georgikon.hu, beno.andras@gmail.com 2 Department of Agro-environment Coordination, Directorate of Plant and Soil Protection and Agro- environmental issues, National Food Chain Safety Offi ce H-1024 Budapest, Keleti K. u. 24. E-mail: varszegig@nebih.gov.hu Abstract Existing soil information systems contain mainly qualitative data on soilscapes, however, quantitative data would be necessary to more eff ectively guide digital soil mapping eff orts. Detailed analysis of small scale over- view maps off ers the most appropriate way to delineate soilscapes where they are available. In our study, the genetic soil map of Hungary have been used which displays the most complete representation of the Hungarian Soil Classifi cation System. Our goal was to analyse spatial association structure based on the boundary seg- ments between soil polygons. We transformed the polygons into lines. The features of each line segment were the names (or codes) of the soil polygons on both sides. Aft er omission soils with low representation (less than three polygons) and boundaries beside state border, forests and cities, 69 soil units were retained. We calculated a similarity matrix among soil types based on logarithm of ratios between existing segment lengths and theoretical segment lengths. The theoretical lengths were calculated with a Chi-squared calculation by using sums of lengths in rows and columns in the 69 × 69 matrix. The similarity matrix was converted into dis- similarity matrix to distinguish between complete dissimilarity (missing values) and complete similarity (main diagonal). Dissimilarity matrix was clustered and represented in a form of dendrogram both in original form and aft er dimension reduction with multidimensional scaling method. Our method has resulted a promising approach for delineating soilscapes in presence of overview soil maps. The study resulted fuzzy soilscapes with broad transition zones. The method could be refi ned by using variable sized moving window method and by combining boundary data with terrain, geology etc. Keywords soilscape quantifi cation, genetic soil map of Hungary, boundary segment based Chi-squared calculation, hierarchical clustering, multidimensional scaling Introduction Since the work of Dokuchaev, the axiom of the soil science is that soil forming factors (climate, geology, hydrology, biota, elevation, time and humans) and their specifi c interaction deter- mine soil formation and soil properties. Jenny, H. (1941) suggested that these complex rela- tionships should be described with mathemat- ical formulas thus, qualitative and quantitative Sisák, I. et al. Hungarian Geographical Bulletin 64 (2015) (1) 65–78.66 soilscapes or soil series in relation tables. This description is strictly qualitative (Finke, P. et al. 2001). Eff orts have been made to bett er defi ne the objects resulting from these group- ings (Hewitt, A.E. 1993) and to defi ne the criteria used in their construction (Hudson, B.D. 1990). Recent fi ndings provide more and more quantitative results on how soil bodies are associated (Behrens, T. et al. 2009; Hewitt, A.E. et al. 2010; Schmidt, K. et al. 2010). The latest nationwide digital soil map- ping projects in New Zealand (Hewitt, A.E. et al. 2010) or Ireland (Creamer, R. et al. 2014) adapt strong soilscape-based approach. In spite of the recent trend (Scull, P. et al. 2005) that predictive soil models shift from research to operational phase, Grinand, C. et al. (2008) observed that soil class prediction accuracy can only be approximated correctly if test samples are collected at a certain dis- tance from the training samples when pre- dicting unvisited areas. However, digital soil mapping approach- es which utilize soil information from ex- isting (usually small or medium scale) soil maps and fi eld observations perform much bett er than pure theoretical constructions (Mendonça-Santos, M.D.L. et al. 2008). Soil maps are physical representations of the mental models of the mappers on how soil forming factors interact (Bui, E. 2004). They provide us a path through the almost infi - nite number of theoretically possible com- binations to the most probable outcome. In countries where small or medium scale soil maps exist their statistical analysis may help to defi ne homogenous soil regions or soils- capes and representative areas for detailed soil surveys (Behrens, T. et al. 2009; Schmidt, K. et al. 2010). The aim of our study was to evaluate an existing nationwide soil map of Hungary and to defi ne soil association rules which then can be used to delineate soil regions or soilscapes. We evaluated boundary line segments of neighbouring polygons and we were using Chi-squared method, hierarchical classifi cation and multidimensional scaling in the analysis. soil properties will be predictable. McBratney, A.B. et al. (2003) gave an overview on digital soil mapping (DSM) which is Jenny’s idea put into practice with help of GIS soft ware and geostatistical analysis. There is a tremendous complexity of soil associations in some landscapes and this requires segmentation of landscapes into soilscapes as a basis for digital soil mapping (McBratney, A.B. et al. 1991; Lagarcherie, P. et al. 2001; Schmidt, K. et al. 2010). Soilscape is a term introduced by Buol, S.W. et al. (1973) and conceptually extended by Hole, F.D. (1978) in the context of pedology. According to Lagarcherie, P. et al. (2001) soilscape is a landscape unit including a limited number of soil classes that are geographically dis- tributed according to an identifi able patt ern. Very often, mapping soilscapes from soil forming factor maps is more realistic than mapping soil classes. The primary task in mapping larger areas should be to account for these spatial soil-association patt erns as a basis to segment landscapes (Schmidt, K. et al. 2010). McSweeny, K. et al. (1994) proposed to set up a hierarchical multistage strategy to explain the variability of soils and soil properties in space. The second stage of the proposed method was a geomorphometric characterization of the landscape from dig- ital terrain models, which provides (i) a land surface representation to which other data are referenced and (ii) a division of the land surface into areas that correspond with soil patt erns. The recently adapted hierarchical approach to defi ne soilscapes follows the World Soils and Terrain Digital Database (SOTER) methodology (ISRIC, 1993). SOTER has become widely evaluated in European and broader context (Dobos, E. et al. 2001, 2005, 2010). However, these terrain-based approaches are more appropriate for fi ner scales as they mainly focus on deriving ter- rain facets instead of deriving larger homo- geneous geomorphological or pedological regions (Schmidt, K. et al. 2010). Existing soil information systems store data on association of soil bodies within 67Sisák, I. et al. Hungarian Geographical Bulletin 64 (2015) (1) 65–78. Despite limitations, approximate conver- sion is possible (Michéli, E. et al. 2006; Krasilnikov, P. et al. 2009). We applied the following procedure: 1. We considered the basic concepts of the Reference Soil Groups (RSGs) and their qualifi ers and specifi ers and we used them to express similar concepts in the HSCS with- out strict investigations of the detailed defi ni- tions and limits. 2. Whenever the HSCS expressed properties which were not part of the specifi er set of the given RSG, we used similar specifi ers from other RSGs but we added them in italics. 3. If the Hungarian concept was not includ- ed in the WRB concepts, we added a short explanation in italics. Codes are also an easy way to identify soil units in the fi gures and tables. We decided to provide approximate categories of an earlier version of the WRB (IUSS Working Group WRB, 2007) because this has been well known in the soil science community. Newly introduced changes (IUSS Working Group WRB, 2014) may not be well established be- yond experts in soil classifi cation. The HSCS contains 99 individual units ei- ther as soil types (e.g. 10 Lithic Leptosol) or sub-types (e.g. 31 Haplic Regosol, Calcaric). The code of the soil types can be divided by ten without remainder (see Table 1). The codes of the sub-types contain numbers in the place of the last digit other than zero. The MÉM- NAK (1983) soil map displays 81 diff erent soil units. However, some of them are represented only by three or less polygons and those were excluded from our analysis. On this way, 69 soil units were retained and converted into approximate WRB units (Table 1). Data analysis In the fi rst step we determined the length of each line segment between the soil cat- egory polygons (soil types or sub-types). The boundary lines at the state border or in the neighbourhood of forests, lakes or towns were not considered since only one of the Materials and methods The genetic soil map of Hungary and the conversion of its categories into WRB categories There was a nationwide campaign in Hun- gary in the 1970’s and 1980’s to renew the old land evaluation system based on de- tailed new soil maps. The genetic soil map (MÉM-NAK, 1983) was released as a part of the preparation phase for the fi ne-scale soil mapping. The purpose of the 1:200,000 scale map was to gather all the available informa- tion and to give orientation for the fi eld work before the detailed soil surveys. The latest fi eld guide for soil mapping and an offi cial version of the Hungarian Soil Classifi cation System (HSCS) was published (Horváth, B. et al. 1987) as part of the project and it served as a compulsory tool for fi eld surveyors. Soil classifi cation system did not change much between 1983 (release of the genetic map) and 1989 (release of the fi eld guide). Slight changes were introduced but basic concepts and categories stayed intact. The genetic soil map is the most complete display of the HSCS and also contains data on parent mate- rial, texture and chemical reaction but does not show soil data for the area of forests and larger towns. We completed and improved the digital version (AIR, 2013) of the genet- ic soil map of Hungary. We used only soil classes of HSCS (soil types, sub-types) in our analysis and did not use other data. In Table 1 we provide an approximate con- version between HSCS soil units of the ge- netic soil map (MÉM-NAK, 1983) based on the work of Horváth, B. et al. (1989) and the IUSS Working Group WRB (2007). We should state that clear one-to-one conversion is not possible at all because of the diff erent soil in- vestigation methods, diff erent limit values of the individual properties and partly because of the diff erent concepts. We still decided to use this conversion since one of the declared primary objectives of the WRB is to serve as “common language” between national soil classifi cation systems. Sisák, I. et al. Hungarian Geographical Bulletin 64 (2015) (1) 65–78.68 Ta bl e 1. A pp ro xi m at e co nv er si on o f t he u ni ts in th e H un ga ri an S oi l C la ss ifi ca ti on S ys te m in to W R B c at eg or ie s So il un it co d es 1 So il un it n am es in th e H un ga ri an S oi l C la ss ifi ca ti on S ys te m 1 (i n H un ga ri an in th e br ac ke ts ) A pp ro xi m at e eq ui va le nt in th e W R B cl as si fi ca ti on 2 10 St on y, r oc ky s ke le ta l s oi l ( K öv es s zi kl ás v áz ta la j) (N ud i- )L it hi c L ep to so l 20 G ra ve lly s ke le ta l s oi l ( K av ic so s vá zt al aj ) H yp er sk el et ic L ep to so l 31 C al ca re ou s ea rt hy b ar re n (K ar bo ná to s fö ld es k op ár ) H ap lic R eg os ol , C al ca ri c 41 C al ca re ou s bl ow n sa nd (K ar bo ná to s fu tó ho m ok ) P ro ti c A re no so l, A ri d ic , C al ca ri c 42 N on -c al ca re ou s bl ow n sa nd (N em k ar bo ná to s fu tó ho m ok ) P ro ti c A re no so l, no t c al ca re ou s 45 „K ov ár vá ny ” bl ow n sa nd (K ov ár vá ny os fu tó ho m ok ) L am el li c A re no so l 51 C al ca re ou s hu m ic s an d (K ar bo ná to s hu m us zo s ho m ok ) H ap lic A re no so l, C al ca ri c 52 N on -c al ca re ou s hu m ic s an d (N em k ar bo ná to s hu m us zo s ho m ok ) H ap lic A re no so l, no t c al ca re ou s 53 C al ca re ou s m ul ti la ye re d h um ic s an d (K ar bo ná to s tö bb r ét eg ű hu m us zo s ho m ok ) H ap lic A re no so l, C al ca ri c w it h bu ri ed A ho ri zo n( s) 54 N on -c al ca re ou s m ul ti la ye re d h um ic s an d (N em k ar bo ná to s tö bb r ét eg ű hu m us zo s ho m ok ) H ap lic A re no so l n ot c al ca re ou s w it h bu ri ed A h or iz on (s ) 60 H um us -c ar bo na t e s oi l ( H um us zk ar bo ná t t al aj ) H ap lic R eg os ol , H um ic , C al ca ri c 71 B la ck r en d zi na (F ek et e re nd zi na ) R en d zi c L ep to so l b la ck u su al ly o n lim e- st on e 72 B ro w n re nd zi na (B ar na r en d zi na ) R en d zi c L ep to so l b ro w n us ua lly o n do lo m it e 11 2 N on po d zo lic b ro w n fo re st s oi l w it h cl ay il lu vi at io n (N em p od zo lo s ag ya g- be m os ód ás os b ar na er d őt al aj – B E T ) H ap lic L uv is ol 12 1 Po d zo lic p se ud og le y br ow n fo re st s oi l ( Po d zo lo s ps ze ud og le je s B E T ) A lb ic S ta gn ic L uv is ol , M an ga ni fe rr ic 12 2 P se ud og le y br ow n fo re st s oi l w it h c l ay il lu vi at io n (A gy ag be m os ód ás os p sz eu d o- gl ej es B E T ) St ag ni c L uv is ol 13 1 Ty pi ca l R am an n’ s br ow n fo re st s oi l ( T íp us os R am an n- fé le B E T ) H ap lic C am bi so l, E ut ri c, S ilt ic 13 2 R us t b ro w n R am an n’ s br ow n fo re st s oi l ( R oz sd ab ar na e rd őt al aj ) B ru ni c A re no so l, E ut ri c, C hr om ic 14 1 Ty pi ca l b ro w n fo re st s oi l w it h al te rn at in g th in la ye rs o f c la y su bs ta nc e („ ko vá rv án y” ) ( T íp us os ko vá rv án yo s B E T ) B ru ni c L am el lic A re no so l 14 3 „K ov ár vá ny ” br ow n fo re st s oi l w it h cl ay il lu vi at io n (A gy ag be m os ód ás os k ov ár vá ny os B E T ) L am el lic L uv is ol 16 1 C al ca re ou s ch er no ze m b ro w n fo re st s oi l ( K ar bo ná to s cs er no zj om B E T ) H ap lic C am bi so l, H um ic , C al ca ri c 16 2 N on -c al ca re ou s ch er no ze m b ro w n fo re st s oi l ( N em k ar bo ná to s cs er no zj om B E T ) H ap lic C am bi so l, H um ic 17 1 C al ca r e ou s ch er no ze m s oi ls w it h fo re st r es id ue s (K ar bo ná to s er d őm ar ad vá ny os c se rn oz jo m ) L uv ic P ha eo ze m , C al ca ri c 17 2 N on -c al ca re ou s ch er no ze m s oi ls w it h fo re st r es id ue s (N em k ar bo ná to s er d őm ar ad vá ny os c se r- no zj om ) L uv ic P ha eo ze m , n ot c al ca re ou s 69Sisák, I. et al. Hungarian Geographical Bulletin 64 (2015) (1) 65–78. Ta bl e 1. C on ti nu ed So il un it co d es 1 So il un it n am es in th e H un ga ri an S oi l C la ss ifi ca ti on S ys te m 1 (i n H un ga ri an in th e br ac ke ts ) A pp ro xi m at e eq ui va le nt in th e W R B cl as si fi ca ti on 2 18 0 L ea ch ed c he rn oz em s oi l ( K ilú gz ott c se rn oz jo m ) H ap lic C he rn oz em , P ac hi c 19 1 Ty pi ca l c al ca re ou s ch er no ze m s oi l ( T íp us os m es ze s va gy m és zl ep ed ék es c se rn oz jo m ) C al ci c C he rn oz em , P ac hi c, S ilt ic 19 2 L ow la nd c al ca re ou s ch er no ze m s oi ls (A lf öl d i m es ze s va gy m és zl ep ed ék es c se rn oz jo m ) (E nd os al ic ) C al ci c C he rn oz em , P ac hi c 20 1 C al ca re ou s m ea d ow c he rn oz em s oi ls (K ar bo ná to s ré ti c se rn oz jo m ) B at hy gl ey ic C al ci c C he rn oz em , P ac hi c 20 2 N on -c al ca re ou s m ea d ow c he rn oz em s oi l ( N em k ar bo ná to s ré ti c se rn oz jo m ) B at hy gl ey ic C he rn oz em , P ac hi c, n ot ca lc ar eo us 20 3 M ea d ow c he rn oz em s oi l, sa lt y in d ee pe r ho ri zo ns (M él yb en s ós r ét i c se rn oz jo m ) E nd os al ic B at hy gl ey ic C he rn oz em , P ac hi c 20 4 M ea d ow c he rn oz em s oi ls , s ol on et z- li k e in d ee pe r ho ri zo ns (M él yb en s zo lo ny ec es r ét i c se rn oz jo m ) B at hy gl ey ic C he rn oz em , P ac hi c w it h so di c- it y in th e pa re nt m at er ia l 20 5 So lo ne tz -l ik e m ea d ow c he rn oz em s oi l ( Sz ol on ye ce s ré ti c se rn oz jo m ) B at hy gl ey ic C he rn oz em , P ac hi c w it h so di c- it y in th e su bs ur fa ce s oi l h or iz on 21 1 C al ca re ou s te rr ac e ch er no ze m s oi l ( K ar bo ná to s te ra sz c se rn oz jo m ) C al ci c E nd ofl u vi c C he rn oz em 22 1 C al ca re ou s so lo nc ha k so il (K ar bo ná to s sz ol on cs ák ) C al ci c So lo nc ha k, C ar bo na ti c 23 1 C al ca re ou s so lo nc ha k- so lo ne tz s oi l ( K ar bo ná to s sz ol on cs ák -s zo lo ny ec ) C al ci c Sa lic S ol on et z (C ar bo na ti c) 23 2 C al ca re ou s an d s ul ph at e- co nt ai ni ng s ol on ch ak -s ol on et z so il (K ar bo ná ts zu lf át os s zo lo nc sá k- sz ol o- ny ec ) C al ci c Sa lic S ol on et z (C ar bo na ti c Su lp ha ti c) 24 1 Sh al lo w m ea d ow s ol on et z so il (K ér ge s ré ti s zo lo ny ec ) C al ci c So lo ne tz w it h an A h or iz on s ha llo w er th an 7 c m 24 2 M ed iu m m ea d ow s ol on et z so il (K öz ep es en m él y ré ti s zo lo ny ec ) C al ci c So lo ne tz w it h an A h or iz on b et w ee n 7 an d 20 c m 24 3 D ee p m ea d ow s ol on et z so il (M él y ré ti s zo lo ny ec ) C al ci c So lo ne tz w it h an A h or iz on d ee pe r th an 2 0 cm 25 1 M ed iu m m ea d ow s ol on et z tu rn in g in to s te pp e fo rm at io n (K öz ep es en m él y sz ty ep es ed ő ré ti sz ol on ye c) M ol lic C al ci c So lo ne tz 28 1 Su lp ha te - o r ch lo ri d e- co nt ai ni ng s ol on ch ak -l ik e m ea d ow s oi ls (S zu lf át os v ag y kl or id os s zo lo nc - sá ko s ré ti ta la j) M ol lic G le ys ol w it h sa lt a cc um ul at io n in th e su rf ac e ho ri zo n (S ul ph at ic o r C hl or id ic ) 28 2 C al ca re ou s so lo nc ha k- lik e m ea d ow s oi ls (K ar bo ná to s sz ol on cs ák os r ét i t al aj ) M ol lic G le ys ol , C al ca ri c w it h sa lt a cc um u- la ti on in th e su rf ac e ho ri zo n (C ar bo na ti c) 29 1 So lo ne tz -l ik e m ea d ow s oi ls (S zo lo ny ec es r ét i t al aj ) M ol lic G le ys ol , ( H yp o- )s od ic 29 2 St ro ng ly s ol on et zi ze d s ol on et z- lik e m ea d ow s oi ls (E rő se n sz ol on ye ce s ré ti ta la j) M ol lic G le ys ol , S od ic 30 1 C al ca re ou s m ea d ow s oi ls (K ar bo ná to s ré ti ta la j) C al ci c M ol lic G le ys ol 30 2 N on -c al ca re ou s m ea d ow s oi ls (N em k ar bo ná to s ré ti ta la j) M ol lic G le ys ol , n ot c al ca re ou s Sisák, I. et al. Hungarian Geographical Bulletin 64 (2015) (1) 65–78.70 Ta bl e 1. C on ti nu ed So il un it co d es 1 So il un it n am es in th e H un ga ri an S oi l C la ss ifi ca ti on S ys te m 1 (i n H un ga ri an in th e br ac ke ts ) A pp ro xi m at e eq ui va le nt in th e W R B cl as si fi ca ti on 2 30 3 M ea d ow s oi ls , s al ty in d ee pe r ho ri zo ns (M él yb en s ós r ét i t al aj ) E nd os al ic M ol lic G le ys ol 31 1 C al ca re ou s al lu vi al m ea d ow s oi ls (K ar bo ná to s ön té s ré ti ta la j) Fl uv ic M ol lic G le ys ol , C al ca ri c 31 2 N on -c al ca re ou s al lu vi a l m ea d ow s oi ls (N em k ar bo ná to s ön té s ré ti ta la j) Fl uv ic M ol lic G le ys ol , n ot c al ca re ou s 32 1 Ty pi ca l m ar sh y m ea d ow s oi ls (T íp us os lá po s ré ti ta la j) H is ti c G le ys ol 33 1 C al ca re ou s ch er no ze m m ea d ow s oi ls (K ar bo ná to s cs er no zj om r ét i t al aj ) C al ci c G le yi c C he rn oz em , ( Pa c h ic ) 33 2 N on -c al ca re ou s ch er no ze m m ea d ow s oi ls (T íp us os c se rn oz jo m r ét i t al aj ) G le yi c C he rn oz em , ( Pa ch ic ) 33 3 C he rn oz em m ea d ow s oi ls ,s al ty -l ik e in d ee p- er la ye rs (M él yb en s ós c se rn oz jo m r ét i t al aj ) E nd os al ic G le yi c C h e rn oz em 33 4 C he rn oz em m ea d ow s oi ls , s ol on et z- lik e in d ee pe r la ye rs (M él yb en s zo lo ny ec es c se rn oz jo m r ét i ta la j) G le yi c C he rn oz em w it h so di ci ty in th e su bs ur fa ce s oi l h or iz on 33 5 So lo ne tz -l ik e ch er no ze m m ea d ow s oi ls (S zo lo ny ec es c se rn oz jo m r ét i t al aj ) G le yi c C h e rn oz em w it h so di ci ty in th e pa re nt m at er ia l 35 0 Pe at -b og s oi ls (R ét lá p ta la j) Fi br ic H is to so l 36 0 D ra in ed a nd c ul ti va te d lo w m oo r fe n so ils (L ec sa po lt é s te lk es ít ett r ét lá p ta la j) H is to so l, D ra in ic in g en er al 36 1 D ra in ed p ea t- bo g so il (L ec sa po lt tő ze gl áp ) H em ic H is to so l D r a in ic 36 2 D ra in ed p ea ty fe n so il (L ec sa po lt tő ze ge s lá p) H em ic H is to so l, D ra in ic w it h le ss th an 5 0 cm d ee p H is ti c ho ri zo n 36 3 D ra in ed fe n so il w it h hi gh ly d ec om po se d p ea ty s ub st an ce ‘k ot u’ (L ec sa po lt k ot us lá p) Sa pr ic H is to so l, D ra in ic 36 4 C ul ti va te d lo w m oo r fe n so il (T el ke sí te tt r ét lá p) H em ic H is to so l, D ra in ic w it h re gu la te d w at er le ve l 37 0 So ils o f m ar sh a nd a llu vi al fo re st s (M oc sá ri e rd őt al aj ) H ap lic G le ys ol , D ys tr ic (a lt er na ti ve : A cr ic G le ys ol ) 38 1 C al ca re ou s re ce nt a llu vi al s oi ls (K ar bo ná to s ny er s ön té s ta la j) H ap lic F lu vi so l, C al ca ri c 39 1 C al ca re ou s hu m ic a llu vi al s oi ls (K ar bo ná to s hu m us zo s ön té s ta la j) H ap lic F lu vi so l, H um ic , C al ca ri c 39 2 N on -c al ca re ou s hu m ic a llu vi al s oi ls (N em k ar bo ná to s hu m us zo s ön té s ta la j) H ap lic F lu vi so l, H um ic , n ot c al ca re ou s 39 3 C al ca re ou s m ul ti la ye re d h um ic a llu vi al s oi ls (K ar bo ná to s, tö bb r ét eg ű hu m us zo s ön té s ta la j) H ap lic F lu vi so l, H um ic , C al ca ri c w it h bu ri ed A h or iz on in th e up pe r 15 0 cm 39 4 N on -c al ca re ou s m ul ti la ye re d h um ic a llu vi al s oi ls (N em k ar bo ná to s tö bb r ét eg ű hu m us zo s ön té s ta la j) H ap lic F lu vi so l, H um ic w it h bu ri ed A h or i- zo n in th e up pe r 15 0 cm , n ot c al ca re ou s 39 5 M ea d ow -l ik e hu m ic a llu vi al s oi ls (R ét i ö nt és ta la j) M ol lic G le yi c Fl uv is ol 40 2 Sl op e d ep os it s of fo re st s oi ls (E rd őt al aj e re d e t ű le jtő ho rd al ék ta la jo k) C ol lu vi c R eg os ol d er iv ed m ai nl y fr om Lu vi so ls a nd C am bi so ls 1 A cc or d in g to H or vá th , B . e t a l. 19 89 , 2 A cc or d in g to IU SS W or ki ng G ro up W R B 2 00 7. 71Sisák, I. et al. Hungarian Geographical Bulletin 64 (2015) (1) 65–78. neighbouring polygons had soil data. Then we calculated the sum of lengths for each soil category combinations and thus, we got a square matrix with dimensions of 69 by 69. The values in the main diagonal were dis- missed (set to zero) since they represented the same category with slightly different properties (texture or pH). Then we calcu- lated the following theoretical length for each matrix element: Lij -est = ΣLi × ΣLj / Ltot, where Lij -est = the estimated length for an individ- ual category combination, Li = the total length of the i-th category in the rows of the matrix, Lj = the total length of the j-th category in the columns of the matrix, Ltot = the total length of all categories (grand total of the matrix). Then we have calculated the following P similarity (neighbourhood) matrix: Pij = log [ (Lij / Lij -est)) × 100 ], where Lij = the actual length for an individual category combination. This is the logarithm of the percent ratio between actual and theoreti- cal lengths. Zero values in the main diagonal and missing combinations have no logarithm thus, in this similarity matrix we cannot dis- tinguish between complete similarity (main diagonal) and complete dissimilarity (non-ex- istent combinations). To alleviate this problem, we converted the similarity matrix into P`ij dissimilarity (distance) matrix. All length ra- tios were less than 100,000 thus, we selected 5 (= log 100,000) as the maximum dissimilarity. We performed hierarchical cluster analysis with P`ij matrix and presented the results in form of a dendogram. The dimensionality of this matrix is 69 with regard to the soil cat- egories as variables. However, the dissimilar- ity matrix had several missing combinations and we assumed that the dimensionality can be signifi cantly reduced without much loss of information. We applied the multidimen- sional scaling procedure to fi nd a simpler and more general structure. Then we applied the hierarchical clustering to the new matrix again and represented the results with an- other dendogram. We used ArcGIS 10.0 for map data handling and interpretation and SPSS 13.0 for data analysis. Results and discussion The frequency distribution of the P`ij distance (dissimilarity) matrix has been shown in Figure 1 without the values of 5 and 0. The histogram was calculated from the full matrix which means that all values are in duplicate. The distribution is close to the normal. For the half matrix when each combination is consid- ered only once, there are 2,346 possible com- binations between 69 soil categories but only 779 of them (33.2%) really exist which means that soil categories can be neighbours of only a subset of other categories which is trivial. Chi-square statistics are often used for overlaid categorical maps in land use change studies (Pontius, Jr. R.G. 2002). However, the appropriateness of method drew also criti- cism because mapped area has no clear, sta- tistically independent “case” thus, its error model is fl awed (Chrisman, N.R. 1989) and the pixel size or the area of measurement unit will determine the “degree of freedom” P’ij = { 0 if Pij = 05 – Pij if Pij > 0 5 if Pij = missing Fig. 1. Data distribution in the dissimilarity matrix Sisák, I. et al. Hungarian Geographical Bulletin 64 (2015) (1) 65–78.72 in the test. Similar objections are true for Chi-squared statistics with line segments. However, we did not use the Chi-square cal- culation in our study to test any signifi cance; we just calculated the Pij matrix elements from segment lengths in a similar way as in Chi-square method without entering into the questioned test calculation. The resulting dendogram calculated from the fi rst, not simplifi ed distance matrix can be seen in Figure 2. Aft er reducing the dimen- sionality with the PROXSCALE procedure, we got 5 dimensions instead of the previous 69 whereby 7 percent of the information was lost as indicated by the stress-test of the proce- dure. The second hierarchical clustering with the reduced, fi ve-dimensional matrix has re- sulted the dendogram shown in Figure 3. There are numerous diff erences between the two dendograms but generally, the sec- ond one has a much more separated structure between the branches than the fi rst one. The following two soil types are loosely as- sociated with each other and they are rather separated from other categories in the fi rst dendogram (Figure 2): 202: Bathygleyic Chernozem, Pachic, not calcareous, 301: Calcic Mollic Gleysol. They lost their separation from other branches, but retained some degree of their association as members of the same group (cluster 3c in Figure 3) aft er dimensionality reduction, however, they were directly as- sociated with other soil categories: 202: Bathygleyic Chernozem, Pachic, not calcareous, 363: Sapric Histosol, Drainic, 364: Hemic Histosol, Drainic with regulated water level and 301: Calcic Mollic Gleysol, 172: Luvic Phaeozem, not calcareous. The dimensionality reduction may bring forward relationships which explain soil for- mation processes such as Stagnic Luvisol (112) became associated with Colluvic Regosol de- rived mainly from Luvisols and Cambisols (402) in cluster 5b (Figure 3) which association was not so close in the fi rst dendogram (Figure 2). There are very closely related soil catego- ries which, in theory, should express diff er- ent degree of groundwater infl uence coupled with strong organic matter accumulation such as Bathygleyic Chernozems (201–205) and Gleyic Chernozems (331–335) as seen in Figure 3 (clusters 1 and 2c). However, even the latest offi cial fi eld guide (Horváth, B. et al. 1989) does not provide enough support to tell them apart in the fi eld. Our analysis points out specifi c weaknesses in the HSCS which need more precise defi nitions as part of the necessary future development of the HSCS according to the diagnostic principles (Michéli, E. et al. 2006; Krasilnikov, P. et al. 2009). Figure 4 shows the map of soil clusters indicated in Figure 3. There is a clear regional distribution of clusters within the area of the country. The clusters marked with “A” are situated on the Great Plain (South-East part of Hungary) and to lesser extent on the Small Hungarian Plain (North-West part). Most of the clusters marked with “D” are situated on the hilly regions with some remarkable exceptions (D_3b and D_4b) which are associated with sandy regions and large rivers on the Great Hungarian Plain. The lead soil types within the clusters are provided in Table 2. At that, we followed the method of Schmidt, et al. (2010) instead of trying to characterize the complete soil associations. Further investigation of the association rules and their regional diff erenc- es can be the objective of future studies. The major soil type gives more than 2/3 of the area within the cluster in fi ve clusters, this ratio is between 1/3 and 2/3 in four clusters and it is below 1/3 in two clusters. The latt er two are on lowland where the genetic soil map shows larger pedodiversity. Close proximity in the dendogram may originate from strong association in one re- gion but in other region this relatedness does not exist sometimes simply because one of the soil categories is not present in the other re- gion. This observation is most striking for the cluster 5a (Mollic Gleysol, not calcareous and associated soils). Stagnic Luvisols are included in this cluster (code 121 and 122) and they are 73Sisák, I. et al. Hungarian Geographical Bulletin 64 (2015) (1) 65–78. Fig. 2. Dendogram derived by hierarchical clustering from the original dissimilarity matrix Sisák, I. et al. Hungarian Geographical Bulletin 64 (2015) (1) 65–78.74 Fig. 3. Dendogram derived by hierarchical clustering from the dissimilarity matrix aft er dimension reduction 75Sisák, I. et al. Hungarian Geographical Bulletin 64 (2015) (1) 65–78. common near the Western border of Hungary. The cluster presents itself in other parts of the country but Stagnic Luvisols do not. Soils in a landscape are associated spatially as well as taxonomically (Hole, F.D. 1978). However, spatially associated soils might not be associated taxonomically (Campbell, J.B. and Edmons, W.J. 1984). Thus, a spatial approach seems appropriate to derive soils- capes as a basis for subsequent digital soil- mapping purposes (Schmidt, K. et al. 2010). According to the summarizing works by McBratney, A.B. et al. (2003) and Scull, P. et al. (2003) tree-based methods are rapidly gain- ing popularity as means to develop predic- tion rules that can be rapidly and repeatedly Fig. 4. Map of the soil type clusters Table 2. Clusters in the dendogram and the major soil type in the cluster Cluster No. in Figure 3 Legend in Figure 4 Approximate WRB equivalent of the major soil type in the cluster and its code No. Area % within the cluster 1 A_1 205: Bathygleyic Chernozem, Pachic with sodicity in the subsur-face soil horizon 20.3 2a 2b 2c A_2a–A_2c 51: Haplic Arenosol, Calcaric 291: Mollic Gleysol, (Hypo-)sodic 201: Bathygleyic Calcic Chernozem, Pachic 45.3 68.7 72.1 3a 3b 3c D_3a–D_3c 162: Haplic Cambisol, Humic 141: Brunic Lamellic Arenosol 301: Calcic Mollic Gleysol 37.7 76.5 71.5 4a 4b D_4a–D_4b 132: Brunic Arenosol, Eutric, Chromic 131: Haplic Cambisol, Eutric, Siltic 55.3 25.5 5a 5b D_5a–D_5b 302: Mollic Gleysol, not calcareous 112: Haplic Luvisol 56.8 84.7 Sisák, I. et al. Hungarian Geographical Bulletin 64 (2015) (1) 65–78.76 evaluated. Because of the clear advantages, several authors applied tree-based methods for soil mapping problems (Hengl, T. et al. 2007; Grinand, C. et al. 2008; Cambule, A.H. et al. 2013; Sun, X.L. et al. 2011; Häring, T. et al. 2012; Pásztor, L. et al. 2013). Complex simi- larity (relatedness) or dissimilarity (distance) matrices and their analysis in tree form are routine procedures in several disciplines such as in psychology (Pecora, L.M. et al. 1995) genetics (Yu, J. et al. 2005) or in scientometrics (Boyack, K.W. et al. 2005). One of the early publications is on representing demographic data (Hartigan, J.A. 1967). However, there is no evidence in the scien- tifi c literature that boundary line segments between soil polygons would have ever been analyzed and spatial association rules would have been extracted as trees from legacy soil maps. Compared to other regionalization studies (Schmidt, K. et al. 2010; Lilburne, L.R. et al. 2012), we used only boundary segments and soil classes on both sides of the line in- stead of complex data sets on soil, terrain, ge- ology and other surface properties and ana- lyzed the whole data set instead of subsett ing by moving window method with rasterized data (Behrens, T. et al. 2009; Schmidt, K. et al. 2010). The consequence of our approach is that the region boundaries are rather fuzzy with large mosaicked transition zones around the more homogenous core zones (Figure 4). Variable sized moving window method (Behrens, T. et al. 2009; Schmidt, K. et al. 2010) combined with our boundary line approach may result more homogenous soilscapes. This combination of methods may alleviate the problem of Stagnic Luvisols mentioned above where existing associations in one re- gion were false in another region in spite of the presence of the same cluster simply be- cause one soil class was missing. Conclusions There are three nationwide legacy soil maps in Hungary. The fi rst one was published in 1953 at a scale of 1:200,000 (Mattyasovszky, J. et al. 1953), the second one (popularly called AGROTOPO) was published between 1983 and 1988 on 1:100,000 sheets (Várallyay, Gy. et al. 1979, 1980; MÉM 1983–1988) and the third one (genetic soil map) was compiled by the experts of the agricultural extension agency of the agricultural ministry in 1983 at scale of 1:200,000 (MÉM-NAK 1983). The genetic soil map provides the most complete display of the HSCS thus it is the most ap- propriate basis for soilscape analysis. Despite its relative completeness, it does not contain all the soil types and sub-types of the HSCS. Further digital soil mapping works are need- ed since spatial resolution of existing maps are insuffi cient to the requirements of the policy making (Pásztor, L. et al. 2013; Sisák, I. and Benő, A. 2012, 2014). In conclusion, our method has resulted a promising approach for delineating soils- capes in presence of overview soil maps. We used the method for whole area of Hungary but it has resulted fuzzy soilscapes with broad transition zones. The method could be refi ned by using variable-sized moving window method and by combining bound- ary data with terrain, geology etc. Acknowledgement: Present article was published in the frame of the project TÁMOP-4.2.2.A-11/1/KONV- 2012-0064. The project is realized with the support of the European Union, with the co-funding of the European Social Fund. The data analysis was sup- ported by the OTKA K101065 project 77Sisák, I. et al. Hungarian Geographical Bulletin 64 (2015) (1) 65–78. REFERENCES AIR 2013. Agrár-környezetgazdálkodási Indormációs rendszer (Information System for the Agri-envi- ronmental schemes). Nyilvános térképek (Open access maps). 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