N. Tunalıoğlu Test kvalitete metoda interpolacije na strmim predjelima za uporabu u modeliranju površine Tehnički vjesnik 19, 3(2012), 501-507 501 ISSN 1330-3651 UDC/UDK 528.42.02:519.652 QUALITY TEST OF INTERPOLATION METHODS ON STEEPNESS REGIONS FOR THE USE IN SURFACE MODELLING Nursu Tunalıoğlu Original scientific paper Surface modelling has been a widely used methodology for interdisciplinary facilities in all kinds of earth-related studies. There are many interpolation methods applied for model generation using the measured points, samples, on the ground. The quality of the outcomes of an interpolation method is highly related to the accuracy, quantity, and distribution of the selected samples reflecting the topography within the study area. This study aims to examine the quality of four interpolation methods, namely the methods Kriging, Modified Shepard’s, Inverse distance weighting, and Radial Basis Function, considering height differences between the neighbour stations. To check the quality of height components within the study area derived applying different interpolation models, four artificial surfaces with sudden height changes were created. The standard deviations used for comparison of the quality of interpolation models were determined using differences between the height values of control points. These values were set as true and interpolated values for the same points. Keywords: digital elevation model, earth topography, high resolution observed data, interpolation methods, surface modelling Test kvalitete metoda interpolacije na strmim predjelima za uporabu u modeliranju površine Izvorni znanstveni članak Modeliranje površine je široko korištena metodologija u svim vrstama istraživanja vezanih za tlo. Postoje mnoge metode interpolacije koje se koriste za razvijanje modela uporabom mjernih točaka, uzoraka, na tlu. Dobivena kvaliteta određene metode interpolacije uvelike ovisi o točnosti, količini i raspodjeli izabranih uzoraka koji odražavaju topografiju proučavanog područja. Cilj je ovoga rada ispitati kvalitetu četiriju metoda interpolacije, odnosno metoda Kriging, Modified Shepard’s, inverzno ponderiranje udaljenosti i Radial Basis Function, uzimajući u obzir visinske razlike između susjednih mjesta. Za provjeru kvalitete visinskih komponenti u okviru proučavanog područja, dobivenih primjenom različitih modela interpolacije, kreirane su četiri umjetne površine naglih promjena visine. Odstupanja od standarda korištena za usporedbu kvalitete modela interpolacije određena su primjenom razlika između vrijednosti visina na kontrolnim točkama. Te su vrijednosti uzete kao prave i interpolirane vrijednosti za iste točke. Ključne riječi: digitalni model elevacije, metode interpolacije, modeliranje površine, promatrani podaci visoke rezolucije, topografija tla 1 Introduction The physical surface (topography) of the solid earth including the oceanic and continental lithospheres is a body of 3D nature. In most studies related to the description of topography of the solid earth in a curvilinear or Cartesian coordinate system a height value is assigned to each pair of horizontal coordinates of a Riemannian 2D space [1]. Therefore, Digital Elevation Models (DEMs) are a crucial instrument for modelling the topography, as part or whole, of the earth’s surface. The outcomes of modelling should enable a variety of applications in earth and environmental sciences like Geographic Information System (GIS), infrastructure design, and engineering works including modelling of hydrology, water flow, and ground deformation [2 ÷ 7]. A digital elevation model defines the surface mathematically, usually determined for points of a regular area wide grid, applying a specific interpolation method to a set of selected uniform or non-uniform samples available within the study area [7]. The reached accuracy of a digital elevation model mainly depends on the quality, density, and distribution of the selected samples within the study area as well as on the mathematical model applied for interpolation of samples. The criteria for choice of the grid and mesh spanning are another important factor, which influences the accuracy of a DEM solution. The boundary of grid spanning must be in accordance with the samples available, in order to avoid any extrapolation [3, 7 ÷ 11]. Accordingly, surface modelling studies have become significant issue for planning earth related facilities as well as being a helpful tool to prepare future network plans over them. Surface modelling process requires a wide criteria combination including adequate distribution of the selecting sample points, number and settlement of the control points, grid intervals and interpolation method [12, 13]. In order to generate surface as closely as the real object properties, mathematical functions should be used to represent the features to obtain required surface quality based on these criteria. With the most widely used name, it is called as interpolation method and this method is involved in several stages of modelling procedure. Interpolation methods can be categorized according to different criteria and they can be used for different purposes [7]. As stated in Gong et al. [3], in the previous researches, numerous investigations have been conducted both for theoretical analysis and experimental testing [14] to assess the quality of DEMs. In this experimental study, to have a better understanding of digital elevation model generation on steepness regions, interpolation methods used for terrain modelling have been investigated through the created artificial areas, where the sudden height differences were observed. Four artificial surfaces have been created by means of deterministic surface function configurations and regions of interest have been bound by differential heights. Each sub region was investigated by four different interpolation methods, namely Kriging, Modified Shepard’s, Inverse Distance Weighting (IDW) and Radial Basis Function methods. The quality of the generated surface models was studied using the method of cross validation and the reference point settlement was produced by Jack-Knife method [15, 16, 17]. The reached