Assessing spatial interpolation based on sampling size and point geometry in elevation mapping applications

Keywords: Spatial Interpolation, Kriging, Inverse Distance Weighting, Accuracy Assessment, Elevation Map


In order to produce a correct elevation map, it is necessary to use not only the accurate technology for data acquisition, but also to utilize an appropriate method of interpolation, which will reflect the topographic features in a reliable manner. The first key element in elevation map production is the proper geometrical distribution of measurement points. The second key component is the density of measurement points, which indicates the distance between pairs in the dataset. In this study, two different types of sampling design were taken into account, random and systematic sampling, to create the elevation map. In random sampling, 33 points were used with the distance in the range of 15–30 km. In systematic sampling, a total of 100 points were utilized located at the distance of 5 km apart. Then, two distinct methods of interpolation were applied to produce a map: deterministic (Inverse Distance Weighting) and geostatistical (Ordinary Kriging with application of the Gaussian, Exponential, and Spherical fitting separately). These methods were compared using a statistical approach to validate the predictive abilities of the chosen interpolation methods. As the results showed, the geostatistical method, namely, Ordinary Kriging with Exponential fitting, revealed better performance compared to the deterministic. It was seen that the overall performance of the interpolated map varies with the number of points in the dataset and strongly relates to the sampling design. In the case of systematic sampling, the accuracy of the map was found to be much better compared to the results of random sampling. It was also proposed to use the error maps in order to identify areas with the maximum residuals. It became apparent that in the case of random sampling, the greatest errors were mostly concentrated in the areas where distances between the measured points were fairly large. By contrast, in the case of systematic sampling, the largest residuals were found in areas with complex topological patterns, especially in the regions with a steep slope gradient. Choosing the appropriate method of interpolation with the minimum error is of great importance in geostatistical operations and topographic engineering. Thus, the current manuscript may serve as a guideline in making the right decision concerning the interpolation method in elevation mapping applications of 1:2000000–1:1000000 scales.

Author Biography

Maryna O. Batur
Graduate School, Geomatics Engineering Department, Istanbul Technical University, Istanbul, Turkey


1. Ahmad, A., 2011. Digital mapping using low altitude UAV. Pertanika Journal of Science and Technology, 19(S), 51-58.
2. Alexandrov, A., T. Hristova, K. Ivanova, M. Koeva, T. Madzharova & V. Petrova, 2004. Application of QuickBird satellite imagery for updating cadastral information. In XX Congress of ISPRS, Istanbul, 386- 391.
3. Altić, M., 2019. Military Cartography of WWII: The British Geographical Section of the General Staff and the US Army Map Service and their Production of the Topographic Map Series of the Balkans (1939–1945). The Cartographic Journal, 56(4), 295-320.
4. Azpurua, M. A., & Dos Ramos, K., 2010. A comparison of spatial interpolation methods for estimation of average electromagnetic field magnitude. Progress in Electromagnetics Research M, 14, 135-145.
5. Chatterjee, S., & Hadi, A. S., 2015. Regression analysis by example. John Wiley & Sons.
6. de Berg, M., O. Cheong, M. van Kreveld & M. Overmars, 2008. Delaunay triangulations: height interpolation. Computational Geometry: Algorithms and Applications, 191-218.
7. Ferreira, I. O., D. D. Rodrigues, G. R. D. Santos & L. M. F. Rosa, 2017. In bathymetric surfaces: IDW or Kriging? Boletim de Ciências Geodésicas, 23, 493-508.
8. Harman, B. I., H. Koseoglu & C. O. Yigit, 2016. Performance evaluation of IDW, Kriging and multiquadric interpolation methods in producing noise mapping: A case study at the city of Isparta, Turkey. Applied Acoustics, 112, 147-157.
9. Huang, Z., H. Wang & R. Zhang, 2012. An improved kriging interpolation technique based on SVM and its recovery experiment in oceanic missing data. American Journal of Computational Mathematics, Vol.2 No.1(2012), Article ID:17976, 5 pages.
10. Luh, L. C., H. Setan, Z. Majid, A. K. Chong & Z. Tan, 2014. High resolution survey for topographic surveying. In IOP Conference Series: Earth and Environmental Science (Vol. 18, No. 1, p. 012067). IOP Publishing.
11. McRoberts, R. E., E. O. Tomppo & R. L. Czaplewski, 2015. Sampling designs for national forest assessments. Knowledge Reference for National Forest Assessments; FAO: Rome, Italy, 23-40.
12. Poklad G. G. and Gridnev S. T., 2013. Geodeziya: Uchebnoye posobiye dlya vuzov. [Geodesy: Textbook for Universities]. Akademicheskiy Proyekt. (In Russian).
13. Shi, Y., L. Li & L. Zhang, 2007. Application and comparing of IDW and Kriging interpolation in spatial rainfall information. In Geoinformatics 2007: Geospatial Information Science (Vol. 6753, p. 67531I). International Society for Optics and Photonics.
14. Tusat, E., 2018. A comparison of the accuracy of VRS and static GPS measurement results for production of topographic map and spatial data: a case study on CORS-TR. Tehnički vjesnik, 25(1), 158-163.
15. Williamson, I., & Enemark, S. 1996. Understanding cadastral maps. Australian surveyor, 41(1), 38-52.
16. Zůvala, R., E. Fišerová & L. Marek, 2016. Mathematical aspects of the kriging applied on landslide in Halenkovice (Czech Republic). Open Geosciences, 8(1), 275-288.
How to Cite
Batur, M. (2022). Assessing spatial interpolation based on sampling size and point geometry in elevation mapping applications. Journal of Geology, Geography and Geoecology, 31(1), 3-9.