TOPOGRAPHIC CONDITIONS FOR SPATIAL DISTRIBUTION OF DOLINES IN VALJEVO–MIONICA KARST, WESTERN SERBIA TOPOGRAFSKE RAZMERE ZA PROSTORSKO RAZPOREDITEV KRAŠKIH VRTAČ V MESTIH VALJEVO IN MIONICA, ZAHODNA SRBIJA Marko V. MILOŠEVIĆ1*, Jelena ĆALIĆ1 & Milovan MILIVOJEVIĆ1 Abstract UDC 52-323.7:551.435.82(497.11) Marko V. Milošević, Jelena Ćalić & Milovan Milivojević: Topographic conditions for spatial distribution of dolines in Valjevo–Mionica karst, western Serbia Valjevo–Mionica karst is a limestone area within the eastern- most flanks of the Internal Dinarides in western Serbia. In the spatial extent of 380 km2, it hosts typical karst landforms, pri- marily dolines, blind valleys, dry valleys and caves. Dolines are present on 75% of the total area, and the exact number of them within the area outline is 5319. The aim of the study is to de- termine the guidance factors for the spatial distribution of do- lines, primarily morphological, while lithological, tectonic and climatic factors are presented at the basic level. Morphologi- cal factors in this study are analysed through morphometrical characteristics and calculations, which include the elevation, the mean topographical slope and the landform classification based on geomorphons. Digital elevation models with resolu- tions 90 m and 30 m are used. Data sources for doline positions were the topographical maps of 1:25,000 scale. Spatial distribution of dolines in the study area is rather un- even. Three zones (clusters) of higher concentration may be distinguished, where 34% of the total study area hosts 72% of dolines. These three zones are the karsts of the villages Lelić, Bačevci and Robaje, divided by deep canyon valleys. Maximum density of dolines, judging by the Kernel density method, is 33 dolines per km2 in the zone of the Stapar village, at the north- western outskirt of the study area. The main factors influencing the spatial distribution of dolines are the topographical slope and the phases of morphological/hydrographical evolution of the area. Keywords: karst doline, Point Pattern Analysis, doline density, geomorphons, western Serbia. Izvleček UDK 52-323.7:551.435.82(497.11) Marko V. Milošević, Jelena Ćalić & Milovan Milivojević: Topografske razmere za prostorsko razporeditev kraških vrtač v mestih Valjevo in Mionica, zahodna Srbija Kras v mestih Valjevo in Mionica je apnenčasto območje na skrajnem vzhodnem pobočju Notranjih Dinaridov v zahodni Srbiji. Na površini 380 km2 so značilne kraške oblike, predvsem vrtače, slepe doline, suhe doline in jame. Vrtače se pojavljajo na 75 % celotnega območja, na tem območju jih je natančno 5.319. Cilj študije je določiti usmerjevalne dejavnike za prostorsko razporeditev vrtač, predvsem morfološko, na os- novni ravni pa so predstavljeni litološki, tektonski in podnebni dejavniki. Morfološki dejavniki so v tej študiji analizirani z morfometričnimi značilnostmi in izračuni, ki vključujejo nad- morsko višino, povprečje topografskega naklona in razvrstitev reliefnih oblik na podlagi geomorfološke dejavnosti. Upora- bljeni so digitalni modeli višin z ločljivostjo 90  m in 30  m. Vir podatkov za položaj vrtač so bili topografski zemljevidi v merilu 1 : 25.000. Prostorska razporeditev vrtač na proučevanem območju je precej neenakomerna. Razlikujemo lahko tri območja (gro- zde) z večjo koncentracijo vrtač, kjer je na 34  % celotnega proučevanega območja 72  % vrtač. Ta tri območja so kraška območja vasi Lelić, Bačevci in Robaje, ločujejo pa jih globoke kanjonske doline. Največja gostota vrtač po metodi Kernel Density Estimator je 33 vrtač na km2 na območju vasi Stapar na severozahodnem obrobju proučevanega območja. Glavni dejavniki, ki vplivajo na prostorsko razporeditev vrtač, so topo- grafski naklon in faze morfološkega/hidrografskega razvoja območja. Ključne besede: kraška vrtača, analiza točkovnih vzorcev, gos- tota vrtač, geomorfološke dejavnosti, zahodna Srbija. ACTA CARSOLOGICA 53/2-3, 187-201, POSTOJNA 2024 1 Serbian Academy of Sciences and Arts, Geographical Institute Jovan Cvijić, Đure Jakšića 9/3, Belgrade, Serbia, email: m.milosevic@gi.sanu.ac.rs * Corresponding author Prejeto/Received: 16. 7. 2024 DOI: https://doi.org/10.3986/ac.v53i2-3.13850 MARKO V. MILOŠEVIĆ, JELENA ĆALIĆ & MILOVAN MILIVOJEVIĆ 1. INTRODUCTION Throughout the history of karstology as a scientific dis- cipline, the most studied karst surface landforms have been the dolines. Their first thorough overview and classification was given by Jovan Cvijić (1893) in his thesis „Das Karstphänomen“ (Ford, 2007). Although his classification is morphographical in the introductory part, the subsequent pages provide the explanation of the solution process within the dolines, as well as their types: (1) „normal“ dolines (presently used equivalent term is „solution dolines“); (2) abysses (steep-sided dolines that continue downwards into caves); and (3) alluvial dolines. The term abyss is not present in con- temporary classifications, but it is worth mentioning in the context of the early awareness of the role of vertical shafts in connecting the surface and underground karst. The shortfall of Cvijić’s classification was the exclusion of the collapse as a doline morphogenetic process. A significant upgrade of systematical overviews of dolines was given by Cramer (1941), who reviewed virtually all available references of the time, including the terminology of karst surface forms in a number of native languages on three continents. His typology consists of five types of dolines: collapse, solution, suf- fosion, alluvial and „schwund“ dolines (a sub-type of suffosion dolines). During the upcoming decades, in the second half of the 20th century, the doline studies have been up- grading both in the approach and the methodology of research. The number of classifications was increasing. Jennings (1985) kept three Cramer’s types (collapse, so- lution and alluvial), but included subsidence and sub- jacent dolines. Ford and Williams (1989, 2007) offered four types in 1989 book (solution, collapse, subsidence, suffosion), but increased the number of doline types in 2007 edition to six, adding dropout, buried and cap- rock dolines, excluding the term subsidence dolines. Solution dolines genesis was diversified to two types of initiation, introducing the point recharge dolines and drawdown dolines (Ford & Williams, 2007). Systematic overview of doline morphogenetic processes was given by Gams (2000), while certain aspects of evolution and classifications were additionally elaborated by Sauro (2003). Engineering classification, rather similar to the aforementioned ones, was published by Waltham and Fookes (2005). The most recent state-of-the-art general review of karst dolines is given by De Waele and Gutier- rez (2022). Precise field measurements with mathemati- cal and statistical processing of small dolines morpholo- gy was carried out by Šušteršič (2006), comparing them approximately with a “paraboloid that hardly differs from a cone”. Pardo‐igúzquiza et al. (2016) studied the population of 3100 dolines of Sierra Gorda karst massif in southern Spain, highlighting the main areas of doline density, and determining that the doline size follows a fractal law. LiDAR-based studies of dolines have been presented by Telbisz et al. (2016, 2021, 2024) The first analyses of spatial distribution of karst depressions were given by Williams (1972) for New Guinea, and espe- cially by Kemmerly (1982), in his study of karst surface in south-eastern USA. Apart from depression density (no./km2), doline swallet order, and interdoline spacing, the author presented a multigenerational diffusion and competition process model, showing subpopulations, clustered sets containing second-order swallet dolines revealing geomorphic competition for catchment area, as well as a positive correlation between interdoline rim spacings of the small swallet order and the sum of their respective major axial lengths. Verbovšek and Ga- bor (2019) presented excellent morphometric analysis of spatial distribution of dolines, as well as delineation principles, pitting index, depth, circularity index, vol- ume, area, and orientation. Regarding the study area of Valjevo karst in west- ern Serbia, the first historical description of dolines was given by Pavlović (1889) who spotted them in the southeastern foothill of Vlašić Mt. In the subsequent pa- per on this matter (Pavlović, 1907), pedological and hy- drographical characteristics of dolines were described. Cvijić (1912) noted that the dolines are the most nu- merous landforms in the area of the Lelić village, pres- ently known in literature by the name Lelić karst. The author noted the linear distribution of dolines within the dry valleys, explaining it as a consequence of low- ering the groundwater level. Petrović (1951) observed the morphological differences among the dolines in the neighbouring karst area of Bačevci village (Bačevci karst) and the dependence of their distribution on par- ticular host landforms. Similar views on the dolines in the area were given by Jovanović (1956), Lazarević (1996) and Dragićević (2007). The aims of this study are: (a) to define the out- lines of Valjevo–Mionica karst; (b) to test multiple ter- rain analysis methodological procedures in function of dolines study, (c) to determine the total number, mor- phological patterns and density of dolines, (d) to deter- mine the dependence between the spatial distribution of dolines and the morphometric and morphological characteristics of the area, and (e) to test the depen- dence of doline distribution on morphostructural pat- tern. 188 ACTA CARSOLOGICA 53/2-3 – 2024 TOPOGRAPHIC CONDITIONS FOR SPATIAL DISTRIBUTION OF DOLINES IN VALJEVO–MIONICA KARST, WESTERN SERBIA 2. STUDY AREA 2.1. OUTLINE OF THE VALJEVO–MIONICA KARST Valjevo–Mionica Karst is a karstic terrain in western Serbia, at the eastermost outskirts of the Internal Dina- rides. The spatial extent, as well as the name of the area, has varied during the exploration history. In the works of Cvijić (1912), Petrović (1951) and Dinić (1959) the karstic area is considerably smaller, consisting of two components – Bačevci karst and Lelić karst. Jovanović (1956) offered extremely large extension of the karst area, which includes the mountains Medvednik, Jablan- ik, Povlen, Maljen, as well as Vlašić (NW of Valjevo, not visible on Figure 1 below), naming it Valjevo Karst. This name and the detailed outline of the area has been used by Lazarević (1996) as well, encompassing karst in the watersheds of Jablanica, Gradac and Ribnica rivers, but excluding Vlašić Mt. In order to perform GIS analyses of any studied area, a precisely determined outline is needed, based on a set of relevant criteria. In this case, the selected data includ- ed lithological, morphological and hydrographical char- acteristics, as well as the administrative territorial units. Limestone terrains with pronounced karstic landscapes are present in northwestern, western, central, southern and eastern parts of the Valjevo municipality, extend- ing further to the east to the western and central parts of Mionica municipality (Figure 1). Apart from the main karst area (A), which includes about 93% of the territo- ry, there are additional five karst fragments („exclaves“) (Table 1). The largest part of the Valjevo–Mionica karst lies within the Kolubara River watershed (including the rivers Obnica, Jablanica, Gradac, Lepenica and Ribnica), while the peripheral units in the western part belong to the watersheds of the Jadar River and the Trešnjica River. Table 1: Spatial units, percentages of karst, and the respective num- ber of dolines. Unit km2 Karst areas (%) number of dolines Share in total area % A 352,73 92,75 5218 98,00 B 1,07 0,30 29 0,50 C 1,73 0,45 9 0,2 D 15,38 4,05 63 1,3 E 3,56 0,93 0 0 F 5,80 1,52 0 0 Σ 380,27 100 5319 100 Figure 1: Position and outline of the Valjevo–Mionica karst (profiles refer to Figure 13). ACTA CARSOLOGICA 53/2-3 – 2024 189 2.2. PHYSICAL-GEOGRAPHICAL CONDITIONS As a north-easternmost part of the Dinaric orogen, the present Valjevo-Mionica area dates back to the late Mesozoic and early Cenozoic, the time of the closure of a part of the Neotethys called the Vardar Ocean (Cvetković et al., 2019). During the Mesozoic, the ocean hosted the deposition of the Triassic, Jurassic and Cre- taceous limestones which afterwards gradually uplifted to the present positions. Compression of carbonates has been caused by the collision of the African and Euro- pean plates (Stampfli & Borel, 2002). Within the karst area, pure Triassic limestones are present on 55% of the territory, while the remaining part is composed of Jurassic and Cretaceous limestones with marls, shales, sandstones and dolomites. About 4.5% of the area is built of non-carbonate rocks enclaves consisting of al- luvial sediments, porphyry and pyroclastics (Mojsilović et al., 1975). MARKO V. MILOŠEVIĆ, JELENA ĆALIĆ & MILOVAN MILIVOJEVIĆ Figure 2: A – Solution doline in Bačevac; B – Lined-up dolines in a blind valley in Dračić; C – Solution doline in Lelić; D – Lined-up dolines in a blind valley in Lelić; E – Collapse doline in Osečenica; F – Cultivated doline in Robaje, (inset sketches in A, C, E redrawn after Waltham and Fookes, 2005). 190 ACTA CARSOLOGICA 53/2-3 – 2024 Valjevo-Mionica karst lies in the elevation belt from 160 m to 1301 m. Morphogenetic types of land- forms include fluvial, karst and mass movement forms. Fluvial landforms are river valleys, river terraces and alluvial plains, while the gorges of the Sušica, Gradac and Ribnica rivers are fluviokarstic forms. Karstic land- forms are dolines, dry valleys, blind valleys and caves (Petnička, Degurićka, Šalitrena, Ribnička, Lenčina, Dragov Ponor, etc). According to the Köppen climate classification, the studied area belongs to the Cfb type – warm and humid, with warm summers (Milovanović et al., 2017). The mean annual air temperature is 9°С to 11°С, while the average yearly precipitation is 800-1000 mm, depend- ing on the elevation (Milovanović et al., 2018). The plu- viometric regime is of continental type – the maximum precipitation occurs in late spring and early summer (May, June), while the minimum is during the winter (February). All permanent rivers flowing through the Valjevo-Mionica karst are of allogenic character (Ob- nica, Jablanica, Gradac, Lepenica and Ribnica). Among the sinking rivers, the longest are Jazina (6.2 km), Plandište (5.3 km), Bukovik (2.8 km) and Osečenički Potok (2.7 km). Forests cover 52% of the Valjevo-Mion- ica karst, mostly deciduous (96.5%) and, in small per- centage, coniferous forests (3,5%) 3. DATA SOURCES AND METHODS The primary data sources for doline locations have been the 1:25,000 scale topographical maps, published by the Military-Geographical Institute from Belgrade. Using this scale, all technically “visible” dolines deeper than 2.5 m were mapped, meaning that there was no generaliza- tion of the doline number, as it is the case with the scales 1:50,000 and 1:100,000 (Borisov, 2014). This implies that the spatial relations of doline distribution on 1:25,000 scale topographical maps are credible, regardless of the fact that they do not show the dolines of less than 2.5 m depth. During the process of digitizing, the dolines are defined as points positioned exactly on the graphi- cal mark for the bottom of the doline (Pahernik, 2012). More precisely, this is the (-) (minus sign) below the low- est closed contour. In cases when the dolines are marked without the contours, but only with a topographical sym- bol, the lowest point is considered to be positioned in the very center of the symbol. Data source on the topographical characteristics of the terrain (slope and elevation of the areas with dolines) was the Digital Elevation Model (DEM) of 90 m resolution (SRTM). Morphological analyses of landforms were car- ried out using the 30 m resolution DEM (SRTM). Lithological composition data have been obtained in the process of digitizing and vectorization of the Basic geological map 1:100.000 (sheets Valjevo, Gornji Mila- novac and Vladimirci) and subsequent classification to three groups: (1) pure limestones (Triassic and Creta- ceous limestones; Triassic schisty limestones; Triassic limestone breccias), (2) limestones combined with other lithologies (Permian limestones with shales; Cretaceous marls, sandstones and limestones), and (3) non-carbon- ate rocks (alluvial sediments, porphyry and pyroclastic rocks). Within the process of determining the spatial distri- bution of dolines, the Point Pattern Analysis (PPA) was used (Yuan et al., 2020). The main characteristics of dis- tribution were determined using the descriptive statistics (Gong, 2002; O'Sullivan & Unwin, 2010). The dolines in the area of Valjevo-Mionica karst were subject to the analyses of the central tendency and dispersion (deter- mining the standard deviation and standard deviational ellipse). Variations in the doline density were analysed using the Global and Local density. The global density is a relation between the total number of the dolines within a studied territory and its total area (homogenous den- sity). On the other hand, in order to determine the het- erogeneous density, the methods for local density were applied. In this context, the analysis of square (quadrat) density at the level of 1 km2 was used, as well as the Ker- nel density in the search radius of 568 m. Geomorphons are a new method of digital repre- sentation and analysis of landforms which does not rely on differential geometry (Stepinski & Jasiewicz, 2011). They are the basic microstructures of landscapes, con- sidered to be simultaneously relief attributes and relief types (Jasiewicz & Stepinski, 2013). This method of auto- classification is based on the concept of a local ternary pattern, the values of which may be 0, +1, or -1. The value is defined in relation to the central (focal) cell. The neigh- boring cell will have the value of “+1” if its value is larger than the value of the central cell. If the values are equal, it will have the value “0”, while for the smaller value than the central cell, the value will be “-1”. The neighbouring cells are not necessarily the ones in the direct contact with the central cell, but also those within the line-of- sight along 8 main directions. The values 0, +1, or -1 are defined by flatness threshold (t), which is the minimal TOPOGRAPHIC CONDITIONS FOR SPATIAL DISTRIBUTION OF DOLINES IN VALJEVO–MIONICA KARST, WESTERN SERBIA ACTA CARSOLOGICA 53/2-3 – 2024 191 value of the right triangle (line-of-sight angle, zenith or nadir) considered to be considerably different from the horizon (Stepinski & Jasiewicz, 2011). Theoretically, the ternary pattern may support 6561 possible variations, but they can be mainly depicted with 10 geomorphons: flat, peak, ridge, shoulder, spur, slope, pit, valley, footslope and hollow (Jasiewicz & Stepinski, 2013). Input data for geomorphons are of raster character (DEM), as well as scale parameters (Frankl et al. 2016). The 30 m DEM was used for the analysis (SRTM). Among the scale param- MARKO V. MILOŠEVIĆ, JELENA ĆALIĆ & MILOVAN MILIVOJEVIĆ 0 5 10 15 20 25 30 35 40 45 50 L 3 L 15 L 50 Figure 5: Distribution of geomor- phons in Valjevo-Mionica karst, for search radius values (L) 3, 15 and 50. Flat Ci Peak Ci Ridge Ci Shoulder Ci Spur Ci Slope Ci Hollow Ci Footslope Ci Valley Ci Depression Ci +1 0 -1 Ci - The Cell of interest Figure 3: Geomorphons for the most typical terrain forms (authors’ design). Figure 4: Geomorphons for different values of the search radius (L). 192 ACTA CARSOLOGICA 53/2-3 – 2024 TOPOGRAPHIC CONDITIONS FOR SPATIAL DISTRIBUTION OF DOLINES IN VALJEVO–MIONICA KARST, WESTERN SERBIA eters, the Outer Search Radius was used (distance in me- ters or cells from the main cell, L) and flatness threshold (t) (Atkinson et al., 2020). Aiming to optimize the size of the search radius, comparative analysis was carried out for L=3 (90), 15 (450), 50 (1500) (Figure 5), while the value 1 was used for the flatness threshold (t). Optimiza- tion of the Outer Search Radius was carried out in order to determine the first-order landforms within which the dolines are present as second-order landforms. 4. RESULTS Dolines are present on 75% of the Valjevo-Mionica karst area, where the total of 5319 positions was mapped. Fig- ure 6b shows the overview of their spatial distribution descriptive statistics. The central tendency point, with the coordinates X 7411258, Y 4897608 is situated in the Brangović village. The circle around the central tendency point has a radius which corresponds to the value of one standard deviation (standard distance). The circle en- compasses 65% of the mapped dolines, which implies their normal distribution within the Valjevo-Mionica karst. The main (longer) axis of the standard deviation ellipse, which follows the direction of largest dispersion of dolines, is oriented in NW-SE direction (288°–108°) (Figure 6b). The analysis of doline density in the studied area in- cluded three measure types. The first type, the global density (in our case, 14 dolines per km2), shows the ho- mogeneous distribution, regardless of the local differ- ences, thus giving a rather poor research potential. The second measure type is the quadrat (square) density for 1 km2 spatial units, which showed the largest values – as many as 81 dolines per 1 km2 in Robaje village (Figure 6). According to this measure, 79% of the territory has the doline density less than 30 dolines per km2, and only in 2% the density is larger than 50 dolines per km2. Apart from Robaje, large doline densities are present in the villages of Rajković, Osečenica, Brežđe, Stapar and Lelić. The problem with this measure is that it shows ho- mogenous distribution of dolines within a quadrat, not depicting the fine spatial differences. In order to show Figure 6: Quadrat (square) density of dolines in Valjevo-Mionica karst. ACTA CARSOLOGICA 53/2-3 – 2024 193 these differences, the third measure type is used – Kernel density. The maximum value in this type of density is 33 dolines per km2, registered in Robaje, Brežđe and Stapar. Generally, the densities are larger in the eastern part of the research area, in comparison with the western part. The largest areas are characterised with the doline den- sity of 2-5 dolines per km2 (28.6 %), followed by the areas with 5-10 dolines per km2 (26%), and finally 1 doline per km2 on 21.6% of the total area. The areas with very high doline density, 25-33 per km2 are the least represented, taking only 1% of the total area. These zones are spatially fragmented, stretched along the direction NW (Stapar) – SE (Robaje) (Figure 7). In Valjevo-Mionica karst, three spatial clusters with largest number of dolines may be differentiated. The clusters include 34% of the total territory, with 72% of the total number of dolines. These regions are divided by canyon valleys of the rivers Sušica/Jablanica, Gradac, Lepenica and Ribnica. Two of these regions have been previously named as Lelić and Bačevci karst. The third MARKO V. MILOŠEVIĆ, JELENA ĆALIĆ & MILOVAN MILIVOJEVIĆ Figure 7: Kernel density of dolines in Valjevo-Mionica karst. Figure 8: Distribution of dolines in Valjevo-Mionica karst by elevation and mean slope, presented as the heat map. 194 ACTA CARSOLOGICA 53/2-3 – 2024 karst region, with largest densities of dolines in all mea- sure types is the Robaja karst (Figure 9). As previously determined in many publications, the slope of the topographic surface plays a significant role in spatial distribution of dolines (Telbisz et al., 2007; Pa- hernik, 2012; Artugyan & Urdea, 2016; Lončar & Grcić, 2022; Mihevc & Mihevc, 2021). In Valjevo-Mionica karst, the dolines are situated in the slope interval from 0° to 22° (Figure 8). With the increase of the slope, the number of dolines decreases. Out of the total number of dolines, 96% are situated on the mildly inclined slopes, up to 12°. On the slopes exceeding 20° there are only 13 dolines (less than 1%). Judging by the Kernel density, the number of dolines TOPOGRAPHIC CONDITIONS FOR SPATIAL DISTRIBUTION OF DOLINES IN VALJEVO–MIONICA KARST, WESTERN SERBIA Figure 9: Elevation distribution of dolines in Valjevo-Mionica karst. 0 10 20 30 40 50 60 70 80 90 100 1-2 2-5 5-10 10-15 15-20 20-25 25-35 % Doline density 0-200 m 200-400 m 400-600 m 600-800 m 800-900 m > 900 m Figure 10. Distribution of doline densities in the elevation belts. ACTA CARSOLOGICA 53/2-3 – 2024 195 per km2 decreases with slope increase. The average slope of the topographic surface with 1 doline/ km2 is 10° (in the interval 6° to 19°). For the density of 6 dolines/km2, the average slope is 8° (interval 2° to 13°), while the aver- age slope for the densities exceeding 15 dolines/km2 is 5° (1° to 12° interval). There are seven elevation belts in the Valjevo-Mion- ica karst with the spans of 200 m and 100 m. The low- est point lies within the zone where the Lepenica River leaves the karst area (at 160 m a.s.l.), while the highest one is the top of the Povlen Mt at 1301 m (Figure 9). Dolines are concentrated in the elevation belt from 187 m and 988 m. Most of the dolines are situated between 200 m and 400 m a.s.l. (42%) and 400 m to 600 m (40%). There is only one doline below 200 m (in the Lepenica River valley), while 79 dolines are situated at the eleva- tions higher than 900 m (north-eastern slopes of Pov- len Mt. and Medvednik Mt). The areas with the highest Kernel densities (25-35 dolines per km2) are dominantly situated in the elevation span from 200 m to 400 m a.s.l. Other areas are present at the elevations 400 m to 600 m (9%) and 800 m to 900 m (1%). There are areas of 20-25 MARKO V. MILOŠEVIĆ, JELENA ĆALIĆ & MILOVAN MILIVOJEVIĆ 0 5 10 15 20 25 30 35 peak ridge spur slope hollow valley depression Terrain Doline Figure 12: Geomorphon structure of Valjevo-Mionica karst and the dolines on particular units. Figure 11: Geomorphons of Valjevo-Mionica karst (L=50). 196 ACTA CARSOLOGICA 53/2-3 – 2024 dolines per km2 in the elevation belt between 800 m and 900 m a.s.l. (Figure 10). Using the geomorphon method, relief of the Valjevo-Mionica karst was defined by the values of the Outer Search Radius values of 50 cells (L=50) and flat- ness threshold (t), value 1. Input data refer to the 30 m resolution DEM, meaning that the generated relief ele- ments have the length up to 1500 m. The structure of geomorphons does not show three elements: flat, shoul- der and footslope (Figure 11). Other elements are present with various percentages. The most dominant are slope (29%) and spur (23%). The least present elements (be- low 5%) are depression (3.5%) and peak (4.5%). Dolines are situated in geomorphons corresponding to valley (23%), slope (19.5%), spur (15.5%), hollow (15%), ridge (14.5%), depression (8.4%) and peak (3.5%). Structure of geomorphons within which the dolines are formed is not a consequence of the total geomorphon structure of the Valjevo-Mionica karst, because the correlation between the mentioned values is not significant (Figure 12). 5. DISCUSSION Spatial variability of karst dolines is present in the area of Valjevo-Mionica karst. It may be caused by lithologi- cal composition, tectonic pattern, relief, climate, etc. (Öztürk et al., 2018). This paper primarily focuses on the impact of relief to the spatial distribution of dolines. The relevant elements are morphometry (surface slope) and elevation. Landform analysis is based on digital classifi- cation based on geomorphons. The input data for both mentioned geomorphological characteristics were digital elevation models with the resolutions of 90 m (for mor- phometry) and 30 m (for morphology). Regarding the slopes of the areas with dolines occur- rence, Valjevo-Mionica karst confirms that the number and density of dolines is inversely related with the in- crease of slopes, due to the relation between surface and underground runoff. In the study area, the slope interval of doline occurrence is between 0° and 22°. Several pub- lications report that the slopes of surfaces populated by dolines have a considerably larger span, from 0° to almost 32°-35°, such as in the Dinaric karst (Pahernik, 2000; Marković et al., 2016, Lončar & Grcić, 2022), Carphatian Mts karst (Artugyan & Urdea 2016), and Missouri, USA (Orndorff et al. 2000). The insight to the input data for these localities shows that DEMs of higher resolutions (30 m) were used. In the case of Valjevo-Mionica karst, after testing the options for 30 m DEM vs. 90 m DEM, we opted for a smaller resolution (DEM 90 m) for the purpose of general surface slope determination, because it turned out to be smoother, without the imprints of particular dolines to the slope of the overall area. Simi- lar choices and conclusions were applied by Telbisz et al. (2007) for the karst of Mt. Miroč (Serbia), Faivre and Pahernik (2007) for Brač Island (Croatia) and Mihevc & Mihevc (2021) in Slovenia. In Valjevo-Mionica karst, the significance of eleva- tion for the doline occurrence was not clearly detected. The largest number of dolines, as well as the largest den- sity (33 dolines per km2), was detected in the elevation belt 200-600 m a.s.l. Marković et al. (2016) pointed to the genetic significance of elevation for doline development (increased densities), in terms of microclimate condi- tions), while Milošević et al (2022) pointed to tension joints on top of anticline crests (comparable to Tîrlă and Vijulie, 2013). At the level of morphostructures, dolines are “sec- ondary” landforms, occurring on (or within) first-order landforms, such as mountain plateaus, levelled surfaces, large depressions (uvalas, poljes), etc. Hydrographical and morphometric characteristics of these landforms may stimulate or modify formation and development of dolines. This study uses geomorphons as the indica- tors for the analysis of morphological characteristics of the research area and particularly on the distribution and density of dolines. In order to get a better insight to the relation be- tween dolines and geomorphons, we introduced group- ing of elements following a runoff criterion – wheter the water converges towards a geomorphon or diverges from it. Using this criterion, it is possible to group three cat- egories: (1) concave (valley, depression, hollow), (2) con- vex (spur, ridge, peak) and (3) slopes. 47% of the research area belongs to the first category, 33.5% to the second and 19.5% to the third. Concave geomorphons correspond to pocket valleys (cf. Lipar & Ferk, 2015), blind valleys, dry valleys; convex geomorphons correspond to ridges/ divides, while slopes mostly refer to long valley sides. In case of Valjevo-Mionica karst, almost 50% of dolines are situated along concave geomorphons, mostly on bot- toms (thalwegs) of former fluvial valleys, as opposed to the cases typical for karst plateaus (Orndorff et al., 2000, Artugyan & Urdea, 2016). Smaller valleys transformed to dry valleys, blind valleys and hanging valleys, trans- forming the environment to typically karstic (Lazarević, 1988). Former thalwegs became the locations of lined- TOPOGRAPHIC CONDITIONS FOR SPATIAL DISTRIBUTION OF DOLINES IN VALJEVO–MIONICA KARST, WESTERN SERBIA ACTA CARSOLOGICA 53/2-3 – 2024 197 up dolines, phenomenon which was observed by Cvijić (1912) as well. The mentioned characteristics point to the advanced stage of karstification (Bočić et al., 2016; Petrović et al., 2016). As mentioned before, dolines of Valjevo-Mionica karst are mostly grouped to three spa- tial clusters – Lelić karst, Bačevci karst and Robaja karst, divided by canyons of allogenic rivers. The results of the study indicate that the karst area initially had a fluvial development phase. With the increase of the hydraulic gradient and drop of the groundwater levels, only allo- genic rivers managed to keep their activity, by the pro- cess of incision and formation of canyon valleys. Deep incision up to 270 m (at the location Manastirica/Ribnica and somewhat less elsewhere) resulted in intensification of the karst process. Doline density is in accordance with the interpreta- tion of geomorphons, especially within the depressions. Depression geomorphons indicate the places of dry val- leys confluences, adding also to the radial distribution of dolines apart from linear. 6. CONCLUSIONS Following the aims of the study given in the introductory chapter, the conclusions are related to (a) proper nam- ing of the study area following the geographic naming conventions, (b) methodological issues, (c) numbers and spatial patterns of dolines, (d) terrain slope issues, and (e) morphostructures. • Naming of the study area followed the principles of the spatial extent of karstified limestones on one hand, MARKO V. MILOŠEVIĆ, JELENA ĆALIĆ & MILOVAN MILIVOJEVIĆ profile a-a’ profile c-c’ profile d-d’ 0 2 4 6 8 10 12 km m 400 300 0 2 4 6 8 10 km m 500 400 300 0 2 4 6 8 9 km R ov ni a cc um ul at io n G ra da c G ra da c m 700 600 500 400 profile b-b’ 0 2 4 6 8 km m 600 500 400 300 G ra da c M an as ti ri ca L ep en ic a R ib ni ca 20 0m 27 0m 23 0m1 15 m 18 0m 17 0m Ja bl an ic a 16 5m60 m 0,0 10,0 20,0 30,0 40,0 50,0 60,0 70,0 80,0 90,0 100,0 peak ridge spur slope hollow valley depression 1_2/km² 3_5/km² 6_10/km² 11_15/km² 16_20/km² 21_25/km² 26_35/km² Figure 13: Canyons of the rivers Jablanica, Gradac and Ribnica, which divide Lelić karst (а-а', b-b'), Bačevci karst (c-c') and Robaja karst (d-d'). Gray lines symbolize fractures and bedding (as artwork). Profiles are indicated on Figure 1. Figure 14: Doline density distribu- tion in particular types of geomor- phons. 198 ACTA CARSOLOGICA 53/2-3 – 2024 and the existence of the formal administrative units (municipalities of Valjevo and Mionica) on the other hand. Instead of the former naming of this karstic area as Valjevo karst, the appropriate naming is Valjevo– Mionica karst. The total area size is 380 km2. • The determined total number of dolines (5319) can- not be considered as absolutely exact, due to the tech- nical limitations of the main data source – the topo- graphical map 1:25.000 – in which the depressions of less than 2.5 m depth are not visible. However, the advantage of the maps in this scale is that the content is not generalised, meaning that their relative spatial relations are preserved. Consequently, the density of dolines, as well as their uneven distribution, may be considered correct and reliable. Higher resolution DEMs do not necessarily provide better detection of the number of dolines, but only the higher accuracy. For particularly high resolutions (1 m), the criteria for doline detection are difficult to determine (Mihevc & Mihevc, 2021; Utlu & Öztürk, 2023, Telbisz et al., 2024). • Detected dolines in Valjevo–Mionica karst are un- evenly distributed. The chosen indicator was Kernel density measure in the search radius of 568 m, show- ing 33 dolines/km2 in the Stapar village and 31 dolines/ km2 in the villages of Brežđe, Rajković and Robaje. The dolines are grouped in three clusters – Lelić, Bačevci and Robaje, where 34% of the total karst areas host as much as 72% of the total number of dolines. • Despite the lithological and climatic homogenity within Valjevo–Mionica karst, doline distribution is heterogenous. In many existing literature sources, this is explained as a tectonic control of dolines distribu- tion (Faivre 1992; Faivre & Reiffsteck, 1999, 2002; Faivre & Pahernik 2007; Öztürk et al., 2018 a,b). As opposed to that kind of interpretation, our study area reveals the significance of topographic slope and the degree of morphological and hydrographical evolu- tion of the surrounding river valleys. As for the topo- graphic surface slope, 96.5% dolines are situated on the surfaces up to 12°, maximally up to 22°. Morpho- logical evolution of the area is characterised by the intensive karstification, resulting from the fast inci- sion of allogenic rivers, thus inducing high hydraulic gradients within the karst aquifers. Geomorphological outcomes are visible as dry valleys, blind valleys and hanging valleys, while the previous thalwegs are dot- ted with lined-up dolines. 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