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We produced the first daily gridded meteorological dataset at a 1-km spatial resolution across Serbia for 2000–2019, named MeteoSerbia1km. The dataset consists of five daily variables: maximum, minimum and mean temperature, mean sea-level pressure, and total precipitation. In addition to daily summaries, we produced monthly and annual summaries, and daily, monthly, and annual long-term means. Daily gridded data were interpolated using the Random Forest Spatial Interpolation methodology, based on using the nearest observations and distances to them as spatial covariates, together with environmental covariates to make a random forest model. The accuracy of the MeteoSerbia1km daily dataset was assessed using nested 5-fold leave-location-out cross-validation. All temperature variables and sea-level pressure showed high accuracy, although accuracy was lower for total precipitation, due to the discontinuity in its spatial distribution. MeteoSerbia1km was also compared with the E-OBS dataset with a coarser resolution: both datasets showed similar coarse-scale patterns for all daily meteorological variables, except for total precipitation. As a result of its high resolution, MeteoSerbia1km is suitable for further environmental analyses., Measurement(s) temperature of air • pressure • volume of hydrological precipitation Technology Type(s) weather station Factor Type(s) digital elevation model (DEM) • topographic wetness index (TWI) • Tropical Rainfall Measuring Mission/Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (TRMM/IMERG) Sample Characteristic - Environment climate Sample Characteristic - Location Serbia Machine-accessible metadata file describing the reported data: 10.6084/m9.figshare.14102393

Sediment transport time series have shown a severe change in the suspended sediment load transported by the Velika Morava River (Republic of Serbia) during the last few decades. The research objectives of this study were to determine the suspended sediment trends, and to assess the impact of variations in precipitation and human activities on the suspended sediment load. The causes and timing of this severe decrease were analyzed, and the results show that there has been a signifcant sudden shift downwards for the suspended sediment load (p

The assessment of the potential use of renewable energy resources requires reliable and precise data inputs for sustainable energy planning on a regional, national and local scale. In this study, we examine high spatial resolution grids of potential insolation and solar duration in order to determine the location of potential solar power plants in Montenegro. Grids with a 25-m spatial resolution of potential solar radiation and duration were produced based on observational records and publicly available high-resolution digital elevation model provided by the European Environment Agency. These results could be further used for the estimation and selection of a specific location for solar panels. With an average annual potential insolation of 1800 kWh/m² and solar duration of over 2000 h per year for most of its territory, Montenegro is one of the European countries with the highest potential for the development, production, and consumption of solar energy.

High resolution gridded mean daily temperature datasets are valuable for research and applications in agronomy, meteorology, hydrology, ecology, and many other disciplines depending on weather or climate. The gridded datasets and the models used for their estimation are being constantly improved as there is always a need for more accurate datasets as well as for datasets with a higher spatial and temporal resolution. We developed a spatio-temporal regression kriging model for Croatia at 1 km spatial resolution by adapting the spatio-temporal regression kriging model developed for global land areas. A geometrical temperature trend, digital elevation model, and topographic wetness index were used as covariates together with measurements from the Croatian national meteorological network for the year 2008. This model performed better than the global model and previously developed models for Croatia, based on MODIS land surface temperature images. The R2 was 97.8% and RMSE was 1.2 °C for leave-one-out and 5-fold cross-validation. The proposed national model still has a high level of uncertainty at higher altitudes leaving it suitable for agricultural areas that are dominant in lower and medium altitudes. The authors would like to thank to the National Oceanic and Atmospheric Administration (NOAA) for providing GSOD data and Croatian Meteorological and Hydrological Service (http://meteo.hr) for CMDT dataset. We would also like to thank Hengl et al. (2012) for reproducible research paper published in Theoretical and Applied Climatology Journal and the R-sig-geo community for developing free and open tools for space-time modeling.

Gaps in comprehension of demographic change in the region of ex-Yugoslavia after 1990, caused by a lack of reliable data series, frequent change of borders, and distinctive historical and cultural tradition in comparison to other post-communist societies, motivated us to contribute to the understanding of the spatial diffusion of recent profound fertility changes in South-Eastern Europe. We analysed changes in the spatial pattern and distribution of typical fertility indicators of the second demographic transition at the sub-national level in Serbia in order to find out whether these demographic shifts could be interpreted to be similar to those in Central and Eastern Europe. We found that differences in economic, historical, and cultural development between sub-regions of the country strongly affect spatial patterns of fertility change. Also, this paper suggests that the sub- regions forerunners of the first demographic transition could be considered as the cores of diffusion for the second demographic transition.

Regression kriging is one of the most popular spatial interpolation techniques. Its main strength is that it exploits both spatial autocorrelation as well as information contained in environmental covariates. While regression kriging is still dominant, in the past few years machine learning, especially random forest, is increasingly being used for mapping. Machine learning is more flexible than multiple linear regression and can thus make better use of environmental covariates. But machine learning typically ignores spatial autocorrelation. Several attempts have been made to include spatial autocorrelation in random forest, by adding distances to observation locations and other geometries to the set of covariates. But none of these studies have tried the obvious solution to include the nearest observations themselves and the distances to the nearest observations as covariates. In this study we tried this solution by introducing and testing Random Forest for Spatial Interpolation (RFSI). RFSI trains a random forest model on environmental covariates as well as nearest observations and their distances from the prediction point. We applied and evaluated RFSI for mapping daily precipitation in Catalonia for the 2016-2018 period. We trained four models (random forests, RFsp, pooled regression kriging and RFSI) using 63,927 daily precipitation observations from 87 GHCN-stations located in Catalonia. Maximum and minimum daily temperatures and IMERG precipitation estimates (derived from the GPM mission) were used as environmental covariates for all four models. Results based on 5-fold cross validation showed that RFSI (R-square 69.4%, RMSE 3.8 mm) significantly outperformed all random forest (R-square 50.6%, RMSE 3.8 mm), RFsp (R-square 55.5%, RMSE 4.6 mm) and pooled regression kriging (R-square 65.3%, RMSE 4.0 mm). Finetuning RFSI could potentially improve prediction accuracy even more. In addition to improved prediction accuracy, RFSI has the advantage that it uses much fewer spatial covariates than RFsp.

An approach for using lasso (Least Absolute Shrinkage and Selection Operator) regression in creating sparse 3D models of soil properties for spatial prediction at multiple depths is presented. Modeling soil properties in 3D benefits from interactions of spatial predictors with soil depth and its polynomial expansion, which yields a large number of model variables (and corresponding model parameters). Lasso is able to perform variable selection, hence reducing the number of model parameters and making the model more easily interpretable. This also prevents overfitting, which makes the model more accurate. The presented approach was tested using four variable selection approaches – none, stepwise, lasso and hierarchical lasso, on four kinds of models – standard linear model, linear model with polynomial expansion of depth, linear model with interactions of covariates with depth and linear model with interactions of covariates with depth and its polynomial expansion. This framework was used to predict Soil Organic Carbon (SOC) in three contrasting study areas: Bor (Serbia), Edgeroi (Australia) and the Netherlands. Results show that lasso yields substantial improvements in accuracy over standard and stepwise regression — up to 50 % of total variance. It yields models which contain up to five times less nonzero parameters than the full models and that are usually more sparse than models obtained by stepwise regression, up to three times. Extension of the standard linear model by including interactions typically improves the accuracy of models produced by lasso, but is detrimental to standard and stepwise regression. Regarding computation time, it was demonstrated that lasso is several orders of magnitude more efficient than stepwise regression for models with tens or hundreds of variables (including interactions). Proper model evaluation is emphasized. Considering the fact that lasso requires meta-parameter tuning, standard cross-validation does not suffice for adequate model evaluation, hence a nested cross-validation was employed. The presented approach is implemented as publicly available sparsereg3D R package.

For many decades, kriging and deterministic interpolation techniques, such as inverse distance weighting and nearest neighbour interpolation, have been the most popular spatial interpolation techniques. Kriging with external drift and regression kriging have become basic techniques that benefit both from spatial autocorrelation and covariate information. More recently, machine learning techniques, such as random forest and gradient boosting, have become increasingly popular and are now often used for spatial interpolation. Some attempts have been made to explicitly take the spatial component into account in machine learning, but so far, none of these approaches have taken the natural route of incorporating the nearest observations and their distances to the prediction location as covariates. In this research, we explored the value of including observations at the nearest locations and their distances from the prediction location by introducing Random Forest Spatial Interpolation (RFSI). We compared RFSI with deterministic interpolation methods, ordinary kriging, regression kriging, Random Forest and Random Forest for spatial prediction (RFsp) in three case studies. The first case study made use of synthetic data, i.e., simulations from normally distributed stationary random fields with a known semivariogram, for which ordinary kriging is known to be optimal. The second and third case studies evaluated the performance of the various interpolation methods using daily precipitation data for the 2016–2018 period in Catalonia, Spain, and mean daily temperature for the year 2008 in Croatia. Results of the synthetic case study showed that RFSI outperformed most simple deterministic interpolation techniques and had similar performance as inverse distance weighting and RFsp. As expected, kriging was the most accurate technique in the synthetic case study. In the precipitation and temperature case studies, RFSI mostly outperformed regression kriging, inverse distance weighting, random forest, and RFsp. Moreover, RFSI was substantially faster than RFsp, particularly when the training dataset was large and high-resolution prediction maps were made.

3D cadastral systems are more complex than traditional cadastral systems and they require more complex technical solutions and innovative use of developing technologies. Regarding data integrity and data consistency, 3D cadastral data should be maintained by a Database Management System (DBMS). Furthermore, there are still challenges regarding visualization of 3D cadastral data. A prototype of the 3D cadastral system based on a NoSQL database and a JavaScript application for 3D visualization is designed and tested in order to investigate the possibilities of using new technical solutions. It is assumed that this approach, with further development, could be a good basis for the development of a modern 3D cadastral system. MongoDB database is used for storing data and Cesium JavaScript library is used for 3D visualization. The system uses an LADM (Land Administration Domain Model) based data model. Additionally, script languages, libraries, application programming interfaces (APIs), software and data formats are used for the system development. The case study is based on the real cadastral data. The underground object and building units located below and above the ground level are used to test the proposed data model and the system&rsquo, s functionality. The proposed system needs further development in order to provide full support to a modern 3D cadastral system. However, it allows maintenance of 3D cadastral data and basic 3D visualization with the interactive approach.

This study considers the spatial and temporal dimensions of demographic trends in Serbia between 1961 and 2010. Using appropriate spatial autocorrelation statistics, spatial patterns of common demographic indicators including changes in population size, the rate of natural increase and infant mortality rate are investigated across municipalities of Serbia. Also, the impact of differential demographic rates according to ethnic origin on forming spatial clusters is implicitly considered. Different stages of demographic transition across municipalities at the start of the analyzed period determined the spatial pattern of clustered subregions; ethnic origin appeared to be a strong factor of differentiation regarding population dynamics. The two opposed areas regarding the transition of rates of natural increase and infant mortality were clustered; the southern included Kosovo and the least developed subregions of Central Serbia. The City of Belgrade and Kosovo have been the two hubs of population growth in Serbia over the past 50 years, while the strongest depopulation refers to the north and east border regions.

Support Vector Machines (SVM) is a machine learning (ML) algorithm commonly applied to the classification of remotely sensing data and more recently for modeling land use changes. However, in most geospatial applications the current literature does not elaborate on specifications of the SVM method with respect to data sampling, attribute selection and optimal parameters choices. Therefore the main objective of this study is to present and investigate the SVM technique for modeling urban land use change. The SVM model building procedure is presented together with the detailed evaluation of the output results with respect to the choice of datasets, attributes and the change of SVM parameters. Geospatial datasets containing nine land use classes and spatial attributes for the Municipality of Zemun, Republic of Serbia were used for years 2001, 2003, 2007 and 2011. The Correlation-based Feature Subset method, kappa coefficient, Area Under Receiver Operating Characteristic Curve (AUC) and kappa simulation were used to perform the model evaluation and compare the model outputs with the real land use datasets. The obtained results indicate that the SVM-based models perform better when implementing balanced data sampling, reduced data sets to informative subsets of attributes and properly identify the optimal learning parameters.

More intense rainfall may cause a range of negative impacts upon society and the environment. In this study we analysed trends in extreme ETCCDI (Expert Team on Climate Change Detection and Indices) rainfall indices in Montenegro for the period between 1951 and 2010. Montenegro has been poorly studied in terms of rainfall extremes, yet it contains the wettest Mediterranean region known as Krivošije. Several indices of precipitation extremes were assessed including the number of dry days and rainfall totals in order to identify trends and possible changes. A spatial pattern relationship between extreme rainfall indices and the North Atlantic Oscillation has also been examined. The results generally suggest that the number of days with precipitation decreased while rainfall intensity increased, particularly in south-western parts of the country. A slight tendency towards intense rainfall events is suggested. The examined rainfall indices and North Atlantic Oscillation over Montenegro seemed to be directly linked to changes in one of the major large-scale circulation modes such as the NAO pattern that is particularly evident during the winter season.

The latest applications of hedonic dwelling price models have included recent advances in spatial analysis that control for spatial dependence and heterogeneity. The study of spatial aspects of hedonic modelling pertains to spatial econometrics, which is relevant to this study because it clearly accounts for the influence and peculiarities related by space in real estate price modeling analysis.

The goal of this study is to analyse the predictive performance of the random forest machine learning technique in comparison to commonly used hedonic models based on multiple regression for the prediction of apartment prices. A data set that includes 7407 records of apartment transactions referring to real estate sales from 2008–2013 in the city of Ljubljana, the capital of Slovenia, was used in order to test and compare the predictive performances of both models. Apparent challenges faced during modelling included (1) the non-linear nature of the prediction assignment task; (2) input data being based on transactions occurring over a period of great price changes in Ljubljana whereby a 28% decline was noted in six consecutive testing years; and (3) the complex urban form of the case study area. Available explanatory variables, organised as a Geographic Information Systems (GIS) ready dataset, including the structural and age characteristics of the apartments as well as environmental and neighbourhood information were considered in the modelling procedure. All performance measures (R2 values, sales ratios, mean average percentage error (MAPE), coefficient of dispersion (COD)) revealed significantly better results for predictions obtained by the random forest method, which confirms the prospective of this machine learning technique on apartment price prediction.

Solar radiation is a key driving force for many natural processes. At the Earth’s surface solar radiation is the result of complex interactions between the atmosphere and Earth’s surface. Our study highlights the development and evaluation of a data base of potential solar radiation that is based on a digital elevation model (DEM) with a resolution of 90 m over Serbia. The main aim of this paper is to map solar radiation in Serbia using DEM. This is so far the finest resolution being applied and presented using DEM. The final results of the potential direct, diffuse and total solar radiation as well as duration of insolation databases of Serbia are portrayed as thematic maps that can be communicated and shared easily through the cartographic web map-based service. [Projekat Ministarstva nauke Republike Srbije, br. III 43007, III 47014, i TR 36035]

This document reports on the development of the first set of APOLLO training material within the context of the Task 6.2 Pilot training and execution. The current set of training material reflects the functionalities of APOLLO platform beta version and supports execution of beta phase of the pilots.

The representation of land use change (LUC) is often achieved by using data-driven methods that include machine learning (ML) techniques. The main objectives of this research study are to implement three ML techniques, Decision Trees (DT), Neural Networks (NN), and Support Vector Machines (SVM) for LUC modeling, in order to compare these three ML techniques and to find the appropriate data representation. The ML techniques are applied on the case study of LUC in three municipalities of the City of Belgrade, the Republic of Serbia, using historical geospatial data sets and considering nine land use classes. The ML models were built and assessed using two different time intervals. The information gain ranking technique and the recursive attribute elimination procedure were implemented to find the most informative attributes that were related to LUC in the study area. The results indicate that all three ML techniques can be used effectively for short-term forecasting of LUC, but the SVM achieved the highest agreement of predicted changes.

The behavior of reinforced concrete under long-term loading is an important topic when designing concrete structures. Creep and shrinkage of concrete and long-term deflections of concrete structures, mainly reinforced concrete beams, have been studied for many decades but because of the long-term nature of these tests, existing experiments are relatively scarce. More importantly, there are significant challenges when carrying out these tests. These include achieving optimal beam design to ensure a realistic stress distribution with a developed cracked state, measuring deflections from self-weight, adequately measuring elastic deflections and strains, and instantaneously applying the imposed load. The problem is exacerbated with the advent of sustainable structural concretes containing recycled and waste materials-green concretes; they possess specific properties and experimental results for these concretes are even scarcer. In this paper, an experimental setup, designed to test the structural behavior of reinforced concrete beams in a four-point bending test under long-term loading, is described. Six full-scale beams were produced from natural aggregate concrete, recycled aggregate concrete and high-volume fly ash concrete-two beams from each concrete type, one loaded after 7 and the other after 28 days. The load consisted of beam self-weight and imposed permanent load. The beam design procedure is explained, which enabled an adequate stress distribution and crack formation with a minimum imposed load. A method was developed to use geodetic equipment and measurements to determine the deflection from self-weight and a special support and loading structure were designed to enable instant imposed load application and the measurement of elastic deflections and strains. The complete test setup, equipment and procedure are explained and the advantages and deficiencies of this approach are discussed.

The content of trace elements (As, Cd, Co, Cr, Cu, Hg, Mn, Ni, Pb and Zn) in surface soils in the area surrounding the largest coal-fired power plant in Serbia was determined to assess the contribution of emissions to pollution. Analysis of mutual associations between the trace elements and their correlation with soil particle size fractions indicated anthropogenic origin at most sampling sites. Enrichment factor analysis confirmed these findings. Common patterns in trace element concentrations of the analysed soils were identified by hierarchical cluster analysis. Explanatory spatial analysis, used for characterization and mapping of spatial variability patterns, revealed the highest concentrations of trace elements in areas in predominant wind directions. (C) 2012 Elsevier B.V. All rights reserved.

Prevailing climatic conditions and local topography can be classified as the most influential environmental factors that affect the spatial dispersion of pollutants emanating from industrial sources. In this study, the combined effects of these factors were considered with respect to terrain exposure in order to explain the complex spatial trend of Arsenic (As) concentration that was atmospherically-deposited from one of the largest Copper Mining and Smelting Complexes in Europe, Bor in Serbia. Several exposure parameters were created and employed as spatial covariates within the so-called “Spline-Then-Krige” approach for producing maps of As concentration at three standard soil depth layers (0–5 cm, 5–15 cm and 15–30 cm). The exposure parameters were created to quantify two different aspects of terrain exposure: Geometrical (Proximity) and Topographical exposure. Regression analysis confirmed the presence of a significant statistical association between the As data and all exposure parameters. The trend model showed good overall accuracy explaining 52% of the variance in As data for the surface soil layer, 49% for the middle layer and 35% for the deepest layer. Relative importance analysis revealed the importance of considering a more general model that includes interactions between exposure parameters. The kriging interpolation improved, to some extent, the regression accuracy for all three layers with R2 values ranging from 55% for the surface layer to the 36% for the deepest soil layer. The prediction maps show that As contamination levels are well above allowable Serbian agricultural concentration limits (As < 25 mg/kg) for approximately 78% of the mapping area, thereby indicating that long term smelting activity leaves significant consequences on soil even on deeper unexposed layers. Journal of Geochemical Exploration (2017), 179: 25-35

This paper presents the application of indicator kriging as a geostatistical method for the purpose of creating maps of precipitation occurrence probabilities on the territory of the Republic of Serbia for distinctive months during 2009. The difference between this approach to mapping and standard isohyetal maps, which describe precipitation intensity, lies in the fact that this approach points to the potential of the occurrence of a certain amount of precipitation at a specific location for a given time period. U radu je dat prikaz primene geostatističke metode indikatorskog kriginga za potrebe izrade karata verovatnoća pojave kišnih padavina na teritoriji Republike Srbije za karakteristične mesece u toku 2009. godine. Razlika između ovakvog pristupa kartiranju i standardnih izohijetnih karata koje opisuju intenzitet padavina je u tome što ovaj pristup ukazuje na potencijal pojave određene količine padavina na nekoj lokaciji za dati vremenski interval.

Very often, outputs provided by GIS functions and analysis are assumed as exact results. However, they are influenced by certain uncertainty which may affect the decisions based on those results. It is very complex and almost impossible to calculate that uncertainty using classical mathematical models because of very complex algorithms that are used in GIS analyses. In this paper we discuss an alternative method, i.e. the use of stochastic Monte Carlo simulations to estimate the uncertainty of flow accumulation. The case study area included the broader area of the Municipality of Cacak, where Monte Carlo stochastic simulations were applied in order to create one hundred possible outputs of flow accumulation. A statistical analysis was performed on the basis of these versions, and the "most likely" version of flow accumulation in association with its confidence bounds (standard deviation) was created. Further, this paper describes the most important phases in the process of estimating uncertainty, such as variogram modelling and chooses the right number of simulations. Finally, it makes suggestions on how to effectively use and discuss the results and their practical significance.

More widely used geostatistical methods for modeling distributed phenomena requires the evaluation of the quality of the product (maps) obtained by their application. The method of evaluation of uncertainty i.e. quality of the map was described on the example of a map of mean annual air temperature in Serbia for the period from the years 1991 to 2009 that was obtained from a relatively small number of samples for the whole country area (110 meteorological stations). The uncertainty of the map, obtained by kriging interpolation was evaluated by applying a Monte Carlo simulation modeling method. [Projekat Ministarstva nauke Republike Srbije, br. III47014, br. III43007 i br. TR 36009]

Cartographic presentation of heterogeneity/homogeneity in the spatial distribution of population is still a major problem in modern geography, and other geo-sciences as well. The traditional method of thematic or choropleth mapping rarely gives satisfactory results. This paper analyzes the applicability of dasymetric mapping method for the modelling of spatial distribution of population. Although it is a relatively old method, it becomes widely used following the development of computer technology, GIS and satellite imagery, and its applicability is increasing in social, economic and other sciences and disciplines. After showing the basis and development of dasymetric mapping, the authors present possible application of this method in the population distribution modelling of Vojvodina.

This paper presents possibilities of applying the geographically weighted regression method in mapping population change index. During the last decade, this contemporary spatial modeling method has been increasingly used in geographical analyses. On the example of the researched region of Timocka Krajina (defined for the needs of elaborating the Regional Spatial Plan), the possibilities for applying this method in disaggregation of traditional models of population density, which are created using the choropleth maps at the level of statistical spatial units, are shown. The applied method is based on the use of ancillary spatial predictors which are in correlation with a targeted variable, the population change index. For this purpose, spatial databases have been used such as digital terrain model, distances from the network of I and II category state roads, as well as soil sealing databases. Spatial model has been developed in the GIS software environment using commercial GIS applications, as well as open source GIS software. Population change indexes for the period 1961-2002 have been mapped based on population census data, while the data on planned population forecast have been used for the period 2002-2027.

Niche analysis methods developed within the biogeography community are routinely used for species distribution modeling of wildlife and endangered species. So far, such techniques have not been used to explain distribution of people in an area, nor to assess spatio-temporal dynamics of human populations. In this paper, the MaxEnt approach to species distribution modeling and publicly available gridded predictors were used to analyze the population dynamics in Southern Serbia (South Pomoravlje Region) for the period 1961-2027. Population values from the census administrative units were first downscaled to 200 m grid using a detailed map of populated places and dasymetric interpolation. In the second step, a point pattern representing the whole population (468,500 inhabitants in 2002) was simulated using the R package spatstat. MaxEnt was then used to derive habitat suitability index (HSI) as a function of gridded predictors: distance to roads, elevation, slope, topographic wetness index, enhanced vegetation index and land cover classes. HSI and environmental predictors were further used to explain spatial patterns in the population change index (PCI) through regression modeling. The results show that inhabiting preference for year 1961 is mainly a function of topography (TWI, elevation). The HSI for year 2027 shows that large portions of remote areas are becoming less preferred for inhabiting. The results of cross-validation in MaxEnt show that distribution of population is distinctly controlled by environmental factors (AUC > 0.84). Population decrease is particularly significant in areas >25 km distant from the main road network. The results of regression analysis show that 40% of variability in the PCI values can be explained with these environmental maps, distance to roads and urban areas being the main drivers of migration process. This approach allows precise mapping of demographic patterns that otherwise would not be visible from the census data alone.

A period of fifty years has been reached since the introduction of the first applications based upon geographical information systems (GIS). GIS has not only influenced the development of methods, collection techniques, processing, manipulation and visualization of spatial data. It influenced also the expansion of scientific research in geosciences, as well as the technical disciplines that are engaged in spatial analysis. Nowadays, GIS is becoming the tool for verification and practical implementation of models and algorithms that have been developed within the frame of basic scientific disciplines. The meaning of the GIS acronym is becoming more and more related to term of Geographical or Geo Information Sciences. Scientific concepts that are increasingly applied in GIS are more emphasized in that way. GIS computational techniques, required also the development of geographical data models that should effectively support GIS operations. These models represent formal equivalents of conceptual models used by people in observing geographic phenomena. Spatial phenomena used to be mapped as clearly defined points with known coordinates, or as lines which connect the very same points, or as polygons with exactly defined borders. They were mapped previously in analog form and nowadays in digital format. This approach of perceiving a space, data analyses and visualization of spatial quires is limited on the application of basic rules of Boolean algebra and binary logic, with final results presented as classical thematic maps. The need for a mathematical model that would describe uncertainty of spatial data, resulted in the introduction of the theory of fuzzy sets in spatial analysis. Moreover, this model will provide a solution for visualization and grouping up of spatial phenomena in classes which do not have clearly defined borders.

During the last decade, the development of computational technique has influenced wider implementation of numerical methods in different software applications, which are oriented to processing, presentation, and analysis of spatial data. This is particularly the case for geostatistical methods, which were developed for analysis of the data, which include spatial components. Those methods provide analytical processing and description of spatial continuity, which is an important characteristic for numerous natural phenomena. Implementation of classical statistical methods does not allow the perception of spatial distribution of natural phenomena. The development GIS (Geographical Information Systems) applications, especially geostatistical modules, enabled a lot of users dealing with spatial modeling and analysis to apply them in their work.

Digital terrain models (DTMs) represent segments of spatial data bases related to presentation of terrain features and landforms. Square grid elevation models (DEMs) have emerged as the most widely used structure during the past decade because of their simplicity and simple computer implementation. They have become an important segment of Topographic Information Systems (TIS), storing natural and artificial landscape in forms of digital models. This kind of a data structure is especially suitable for morph metric terrain evaluation and analysis, which is very important in environmental and urban planning and Earth surface modeling applications. One of the most often used functionalities of Geographical information systems software packages is indivisibility or view shed analysis of terrain. Indivisibility determination from analog topographic maps may be very exhausting, because of the large number of profiles that have to be extracted and compared. Terrain representation in form of the DEMs databases facilitates this task. This paper describes simple algorithm for terrain view shed analysis by using DEMs database structures, taking into consideration the influence of uncertainties of such data to the results obtained thus far. The concept of probability maps is introduced as a mean for evaluation of results, and is presented as thematic display.