{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T11:06:10Z","timestamp":1779793570178,"version":"3.53.1"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T00:00:00Z","timestamp":1776124800000},"content-version":"vor","delay-in-days":13,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100005911","name":"Najran University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100005911","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. King Saud Univ. \u2013 Eng. Sci."],"published-print":{"date-parts":[[2026,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Digital Elevation Models (DEMs) are fundamental to engineering projects, influencing the accuracy of hydrologic modeling, earthwork calculations, and infrastructure design. The resolution and quality of a DEM are primarily determined by the density of survey points and the interpolation algorithm used. This study presents a comparative evaluation of four common interpolation techniques\u2014Natural Neighbor (NN), Kriging, Inverse Distance Weighting (IDW), and Spline\u2014to generate a high-accuracy local DEM for a bare land area, typical of civil engineering project sites, on the Najran University campus, Saudi Arabia. A total of 7,026 high-precision GPS points were collected and divided into training (80%) and validation (20%) datasets. The vertical accuracy was assessed using Root Mean Square Error (RMSE) and the coefficient of determination (R\n                    <jats:sup>2<\/jats:sup>\n                    ). The results demonstrated that the Natural Neighbor interpolation method achieved superior performance with the lowest RMSE of 0.124\u00a0m and the highest R\n                    <jats:sup>2<\/jats:sup>\n                    of 0.969. Critically, the study evaluated the impact of data density by thinning the training dataset by 0% to 75%. It was found that a 75% reduction in data points\u2014which equates to a significant saving in surveying time and cost\u2014increased the RMSE by only\u2009~\u20092\u00a0cm when using the NN algorithm. This finding indicates that the Natural Neighbor method is not only the most accurate but also the most robust and cost-effective solution for generating reliable DEMs. The outcomes of this research provide a practical framework for engineers to optimize surveying efforts and produce high-fidelity terrain models essential for precise earthwork volume calculation, drainage design, and flood risk assessment in local-scale projects.\n                  <\/jats:p>","DOI":"10.1007\/s44444-026-00104-3","type":"journal-article","created":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T13:01:10Z","timestamp":1776171670000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Empirical optimization of DEM interpolation: a comparative study of four algorithms for minimum vertical error in topographic modeling"],"prefix":"10.1007","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9766-779X","authenticated-orcid":false,"given":"Ismail","family":"Elkhrachy","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,4,14]]},"reference":[{"key":"104_CR1","doi-asserted-by":"publisher","first-page":"43","DOI":"10.3846\/gac.2019.7921","volume":"45","author":"B Ajvazi","year":"2019","unstructured":"Ajvazi B, Czimber K (2019) A comparative analysis of different DEM interpolation methods in GIS case study of Rahovec, Kosovo. Geod Cartogr 45:43\u201348. https:\/\/doi.org\/10.3846\/gac.2019.7921","journal-title":"Geod Cartogr"},{"key":"104_CR2","doi-asserted-by":"publisher","first-page":"382","DOI":"10.1016\/j.measurement.2018.12.101","volume":"136","author":"E Akturk","year":"2019","unstructured":"Akturk E, Altunel AO (2019) Accuracy assessment of a low-cost UAV derived digital elevation model (DEM) in a highly broken and vegetated terrain. Measurement 136:382\u2013386","journal-title":"Measurement"},{"key":"104_CR3","unstructured":"A. S. of C. E. (ASCE) (1983) Map uses, scales and accuracies for engineering and associated purposes. Committee on Cartographic Surveying,\u201d Surveying and Mapping Division ASCE New York, USA"},{"key":"104_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jher.2021.10.002","volume":"40","author":"M Avand","year":"2022","unstructured":"Avand M, Kuriqi A, Khazaei M, Ghorbanzadeh O (2022) DEM resolution effects on machine learning performance for flood probability mapping. J Hydro-Environ Res 40:1\u201316","journal-title":"J Hydro-Environ Res"},{"key":"104_CR5","unstructured":"Bobach TA (2009) Natural neighbor interpolation-critical assessment and new contributions. Technische Universit\u00e4t Kaiserslautern"},{"key":"104_CR6","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1061\/JSUEAX.0000538","volume":"106","author":"RL Brown","year":"1980","unstructured":"Brown RL (1980) Proposed manual on selection of map uses, scales, and accuracies for engineering and associated purposes map availability\u2014chapter VI. J Survey Mapping Division 106:149\u2013177","journal-title":"J Survey Mapping Division"},{"key":"104_CR7","unstructured":"Burrough PA, McDonnell RA, Lloyd CD (2015) Principles of geographical information systems. Oxford university press"},{"key":"104_CR8","doi-asserted-by":"publisher","first-page":"7082","DOI":"10.3390\/su17157082","volume":"17","author":"H Chen","year":"2025","unstructured":"Chen H, Seydehmet J, Li X (2025) Upscaling soil salinization in Keriya Oasis using Bayesian belief networks. Sustainability 17:7082. https:\/\/doi.org\/10.3390\/su17157082","journal-title":"Sustainability"},{"issue":"8\u201310","key":"104_CR9","doi-asserted-by":"publisher","first-page":"3159","DOI":"10.1080\/01431161.2017.1292074","volume":"38","author":"S Coveney","year":"2017","unstructured":"Coveney S, Roberts K (2017) Lightweight UAV digital elevation models and orthoimagery for environmental applications: data accuracy evaluation and potential for river flood risk modelling. Int J Remote Sens 38(8\u201310):3159\u20133180","journal-title":"Int J Remote Sens"},{"key":"104_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-77974-2","volume-title":"Computational geometry algorithms and applications","author":"M De Berg","year":"2008","unstructured":"De Berg M, Cheong O, Van Kreveld M, Overmars M (2008) Computational geometry algorithms and applications. Springer"},{"key":"104_CR11","doi-asserted-by":"crossref","unstructured":"Erdogan K (2013) Spline interpolation techniques. J Tech Sci Technol 47\u201352","DOI":"10.31578\/jtst.v2i1.56"},{"issue":"4","key":"104_CR12","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1191\/0309133306pp492ra","volume":"30","author":"PF Fisher","year":"2006","unstructured":"Fisher PF, Tate NJ (2006) Causes and consequences of error in digital elevation models. Prog Phys Geogr 30(4):467\u2013489","journal-title":"Prog Phys Geogr"},{"issue":"4","key":"104_CR13","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1002\/num.1690030408","volume":"3","author":"W Freeden","year":"1987","unstructured":"Freeden W (1987) A spline interpolation method for solving boundary value problems of potential theory from discretely given data. Numer Methods Partial Differ Equ 3(4):375\u2013398","journal-title":"Numer Methods Partial Differ Equ"},{"issue":"18","key":"104_CR14","doi-asserted-by":"publisher","DOI":"10.3390\/rs13183581","volume":"13","author":"PL Guth","year":"2021","unstructured":"Guth PL et al (2021) Digital elevation models: terminology and definitions. Remote Sens (Basel) 13(18):3581","journal-title":"Remote Sens (Basel)"},{"key":"104_CR15","doi-asserted-by":"publisher","first-page":"4870","DOI":"10.1002\/hyp.10965","volume":"30","author":"N Habtezion","year":"2016","unstructured":"Habtezion N, Tahmasebi Nasab M, Chu X (2016) How does DEM resolution affect microtopographic characteristics, hydrologic connectivity, and modelling of hydrologic processes. Hydrol Process 30:4870\u20134892. https:\/\/doi.org\/10.1002\/hyp.10965","journal-title":"Hydrol Process"},{"key":"104_CR16","unstructured":"Hofmann-Wellenhof B, Lichtenegger H, Collins J (2012) Global positioning system: theory and practice. Springer Science & Business Media"},{"key":"104_CR17","unstructured":"H\u00f6hle J, Potuckova M (2011) Assessment of the quality of digital terrain models."},{"issue":"4","key":"104_CR18","doi-asserted-by":"publisher","first-page":"398","DOI":"10.1016\/j.isprsjprs.2009.02.003","volume":"64","author":"J H\u00f6hle","year":"2009","unstructured":"H\u00f6hle J, H\u00f6hle M (2009) Accuracy assessment of digital elevation models by means of robust statistical methods. ISPRS J Photogramm Remote Sens 64(4):398\u2013406. https:\/\/doi.org\/10.1016\/j.isprsjprs.2009.02.003","journal-title":"ISPRS J Photogramm Remote Sens"},{"issue":"1","key":"104_CR19","doi-asserted-by":"publisher","first-page":"49","DOI":"10.14358\/PERS.75.1.49","volume":"75","author":"P Hu","year":"2009","unstructured":"Hu P, Liu X, Hu H (2009) Accuracy assessment of digital elevation models based on approximation theory. Photogramm Eng Remote Sensing 75(1):49\u201356","journal-title":"Photogramm Eng Remote Sensing"},{"key":"104_CR20","doi-asserted-by":"publisher","first-page":"433","DOI":"10.4430\/bgo00477","volume":"64","author":"M Iurcev","year":"2023","unstructured":"Iurcev M, Pettenati F (2023) Exploring error estimation methods for natural neighbour interpolation preliminary research and analysis. Bull Geophys Oceanogr 64:433\u2013448. https:\/\/doi.org\/10.4430\/bgo00477","journal-title":"Bull Geophys Oceanogr"},{"key":"104_CR21","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejrh.2022.101122","volume":"42","author":"W Jiang","year":"2022","unstructured":"Jiang W, Yu J, Wang Q, Yue Q (2022) Understanding the effects of digital elevation model resolution and building treatment for urban flood modelling. J Hydrol Reg Stud 42:101122","journal-title":"J Hydrol Reg Stud"},{"issue":"14","key":"104_CR22","doi-asserted-by":"publisher","first-page":"2981","DOI":"10.1080\/0143116031000086835","volume":"24","author":"DB Kidner","year":"2003","unstructured":"Kidner DB (2003) Higher-order interpolation of regular grid digital elevation models. Int J Remote Sens 24(14):2981\u20132987","journal-title":"Int J Remote Sens"},{"issue":"6","key":"104_CR23","first-page":"119","volume":"52","author":"DG Krige","year":"1951","unstructured":"Krige DG (1951) A statistical approach to some basic mine valuation problems on the Witwatersrand. J Southern African Institute Min Metall 52(6):119\u2013139","journal-title":"J Southern African Institute Min Metall"},{"issue":"10","key":"104_CR24","doi-asserted-by":"publisher","DOI":"10.3390\/aerospace9100606","volume":"9","author":"K Lee","year":"2022","unstructured":"Lee K, Lee WH (2022) Earthwork volume calculation, 3D model generation, and comparative evaluation using vertical and high-oblique images acquired by unmanned aerial vehicles. Aerosp 9(10):606","journal-title":"Aerosp"},{"key":"104_CR25","unstructured":"Li L, Heap AD (2008) A review of spatial interpolation methods for environmental scientists."},{"key":"104_CR26","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1016\/j.envsoft.2013.12.008","volume":"53","author":"J Li","year":"2014","unstructured":"Li J, Heap AD (2014) Spatial interpolation methods applied in the environmental sciences: a review. Environ Model Softw 53:173\u2013189","journal-title":"Environ Model Softw"},{"key":"104_CR27","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1016\/j.compenvurbsys.2009.11.002","volume":"34","author":"J Li","year":"2010","unstructured":"Li J, Wong DW (2010) Effects of DEM sources on hydrologic applications. Comput Environ Urban Syst 34:251\u2013261. https:\/\/doi.org\/10.1016\/j.compenvurbsys.2009.11.002","journal-title":"Comput Environ Urban Syst"},{"issue":"3","key":"104_CR28","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1111\/j.1467-9671.2012.01343.x","volume":"16","author":"X Liu","year":"2012","unstructured":"Liu X, Hu P, Hu H, Sherba J (2012) Approximation theory applied to DEM vertical accuracy assessment. Trans GIS 16(3):397\u2013410","journal-title":"Trans GIS"},{"key":"104_CR29","first-page":"1","volume":"61","author":"X Liu","year":"2023","unstructured":"Liu X et al (2023) Feature-fusion segmentation network for landslide detection using high-resolution remote sensing images and digital elevation model data. IEEE Trans Geosci Remote Sens 61:1\u201314","journal-title":"IEEE Trans Geosci Remote Sens"},{"issue":"9","key":"104_CR30","doi-asserted-by":"publisher","first-page":"1044","DOI":"10.1016\/j.cageo.2007.07.010","volume":"34","author":"GY Lu","year":"2008","unstructured":"Lu GY, Wong DW (2008) An adaptive inverse-distance weighting spatial interpolation technique. Comput Geosci 34(9):1044\u20131055","journal-title":"Comput Geosci"},{"issue":"4","key":"104_CR31","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1007\/s12518-020-00307-6","volume":"12","author":"W Maleika","year":"2020","unstructured":"Maleika W (2020) Inverse distance weighting method optimization in the process of digital terrain model creation based on data collected from a multibeam echosounder. Appl Geomat 12(4):397\u2013407","journal-title":"Appl Geomat"},{"key":"104_CR32","first-page":"3","volume":"1","author":"DM Mark","year":"2003","unstructured":"Mark DM (2003) Geographic information science: defining the field. Found Geogr Inform Sci 1:3\u201318","journal-title":"Found Geogr Inform Sci"},{"key":"104_CR33","unstructured":"Maune DF (2007) Digital elevation model technologies and applications: the DEM users manual. Asprs Publications"},{"issue":"1","key":"104_CR34","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1080\/15230406.2013.762138","volume":"40","author":"Q Meng","year":"2013","unstructured":"Meng Q, Liu Z, Borders BE (2013) Assessment of regression kriging for spatial interpolation\u2013comparisons of seven GIS interpolation methods. Cartogr Geogr Inf Sci 40(1):28\u201339","journal-title":"Cartogr Geogr Inf Sci"},{"key":"104_CR35","doi-asserted-by":"publisher","first-page":"2630","DOI":"10.3390\/rs12162630","volume":"12","author":"JL Mesa-Mingorance","year":"2020","unstructured":"Mesa-Mingorance JL, Ariza-L\u00f3pez FJ (2020) Accuracy assessment of digital elevation models (DEMs) a critical review of practices of the past three decades. Remote Sens 12:2630. https:\/\/doi.org\/10.3390\/rs12162630","journal-title":"Remote Sens"},{"issue":"1","key":"104_CR36","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1002\/hyp.3360050103","volume":"5","author":"ID Moore","year":"1991","unstructured":"Moore ID, Grayson RB, Ladson AR (1991) Digital terrain modelling: a review of hydrological, geomorphological, and biological applications. Hydrol Process 5(1):3\u201330. https:\/\/doi.org\/10.1002\/hyp.3360050103","journal-title":"Hydrol Process"},{"key":"104_CR37","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.isprsjprs.2022.03.016","volume":"188","author":"CJ Okolie","year":"2022","unstructured":"Okolie CJ, Smit JL (2022) A systematic review and meta-analysis of Digital elevation model (DEM) fusion pre-processing, methods and applications. ISPRS J Photogramm Remote Sens 188:1\u201329. https:\/\/doi.org\/10.1016\/j.isprsjprs.2022.03.016","journal-title":"ISPRS J Photogramm Remote Sens"},{"key":"104_CR38","unstructured":"Podobnikar T (2009) Methods for visual quality assessment of a digital terrain model. Sapiens 2(2)"},{"issue":"21","key":"104_CR39","doi-asserted-by":"publisher","first-page":"1","DOI":"10.3390\/rs12213522","volume":"12","author":"L Polidori","year":"2020","unstructured":"Polidori L, El Hage M (2020) Digital elevation model quality assessment methods: a critical review. Remote Sens Basel 12(21):1\u201336. https:\/\/doi.org\/10.3390\/rs12213522","journal-title":"Remote Sens Basel"},{"key":"104_CR40","doi-asserted-by":"publisher","first-page":"27376","DOI":"10.48084\/etasr.9338","volume":"15","author":"K Qaraghuli","year":"2025","unstructured":"Qaraghuli K, Jasim BS, Murshed MF, Gaaz TS (2025) Comparison of IDW and spline interpolation for topographic accuracy assessment using geomatics approaches. Eng Technol Appl Sci Res 15:27376\u201327381. https:\/\/doi.org\/10.48084\/etasr.9338","journal-title":"Eng Technol Appl Sci Res"},{"issue":"3","key":"104_CR41","doi-asserted-by":"publisher","first-page":"236","DOI":"10.3390\/geomatics2030014","volume":"2","author":"D Rodriguez-Perez","year":"2022","unstructured":"Rodriguez-Perez D, Sanchez-Carnero N (2022) Multigrid\/multiresolution interpolation: reducing oversmoothing and other sampling effects. Geomatics 2(3):236\u2013253","journal-title":"Geomatics"},{"key":"104_CR42","unstructured":"Sibson R (1981) A brief description of natural neighbour interpolation. Interpreting multivariate data, 374"},{"key":"104_CR43","doi-asserted-by":"publisher","first-page":"98","DOI":"10.20884\/1.jidr.2025.21.2.47","volume":"21","author":"R Susatio","year":"2025","unstructured":"Susatio R, Riyanto IA, Wilopo W, Hendrayana H (2025) Comparative evaluation of Idw and spline interpolation methods for analyzing groundwater table depth and elevation. J Ilm Din Rekayasa 21:98\u2013106","journal-title":"J Ilm Din Rekayasa"},{"issue":"2","key":"104_CR44","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1080\/02723646.1981.10642213","volume":"2","author":"CJ Willmott","year":"1981","unstructured":"Willmott CJ (1981) On the validation of models. Phys Geogr 2(2):184\u2013194","journal-title":"Phys Geogr"},{"key":"104_CR45","unstructured":"Wilson JP, Gallant JC (2000) Terrain analysis: principles and applications. John Wiley & Sons"},{"key":"104_CR46","unstructured":"Wood J (1996) The geomorphological characterisation of digital elevation models,\u201d University of Leicester (United Kingdom)"},{"issue":"11","key":"104_CR47","doi-asserted-by":"publisher","first-page":"4243","DOI":"10.1007\/s11269-024-03862-4","volume":"38","author":"Z Zandsalimi","year":"2024","unstructured":"Zandsalimi Z, Feizabadi S, Yazdi J, Salehi Neyshabouri SAA (2024) Evaluating the impact of digital elevation models on urban flood modeling: A comprehensive analysis of flood inundation, hazard mapping, and damage estimation. Water Resour Manage 38(11):4243\u20134268","journal-title":"Water Resour Manage"},{"key":"104_CR48","doi-asserted-by":"publisher","first-page":"435","DOI":"10.3390\/ijgi7110435","volume":"7","author":"J Zhang","year":"2018","unstructured":"Zhang J, Xu W, Qin L, Tian Y (2018) Spatial distribution estimates of the urban population using DSM and DEM data in China. ISPRS Int J Geoinf 7:435. https:\/\/doi.org\/10.3390\/ijgi7110435","journal-title":"ISPRS Int J Geoinf"}],"container-title":["Journal of King Saud University \u2013 Engineering Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44444-026-00104-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s44444-026-00104-3","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44444-026-00104-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T10:51:29Z","timestamp":1779792689000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s44444-026-00104-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4]]},"references-count":48,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2026,4]]}},"alternative-id":["104"],"URL":"https:\/\/doi.org\/10.1007\/s44444-026-00104-3","relation":{},"ISSN":["1018-3639","2213-1558"],"issn-type":[{"value":"1018-3639","type":"print"},{"value":"2213-1558","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4]]},"assertion":[{"value":"18 November 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 February 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 April 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of interest"}}],"article-number":"32"}}