{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T11:39:00Z","timestamp":1767008340259,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2016,6,17]],"date-time":"2016-06-17T00:00:00Z","timestamp":1466121600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>In some digital Earth engineering applications, spatial interpolation algorithms are required to process and analyze large amounts of data. Due to its powerful computing capacity, heterogeneous computing has been used in many applications for data processing in various fields. In this study, we explore the design and implementation of a parallel universal kriging spatial interpolation algorithm using the OpenCL programming model on heterogeneous computing platforms for massive Geo-spatial data processing. This study focuses primarily on transforming the hotspots in serial algorithms, i.e., the universal kriging interpolation function, into the corresponding kernel function in OpenCL. We also employ parallelization and optimization techniques in our implementation to improve the code performance. Finally, based on the results of experiments performed on two different high performance heterogeneous platforms, i.e., an NVIDIA graphics processing unit system and an Intel Xeon Phi system (MIC), we show that the parallel universal kriging algorithm can achieve the highest speedup of up to 40\u00d7 with a single computing device and the highest speedup of up to 80\u00d7 with multiple devices.<\/jats:p>","DOI":"10.3390\/ijgi5060096","type":"journal-article","created":{"date-parts":[[2016,6,17]],"date-time":"2016-06-17T10:09:24Z","timestamp":1466158164000},"page":"96","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["OpenCL Implementation of a Parallel Universal Kriging Algorithm for Massive Spatial Data Interpolation on Heterogeneous Systems"],"prefix":"10.3390","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5051-3061","authenticated-orcid":false,"given":"Fang","family":"Huang","sequence":"first","affiliation":[{"name":"School of Resources &amp; Environment, University of Electronic Science and Technology of China, 2006 Xiyuan Avenue, West Hi-Tech Zone, Chengdu 611731, China"},{"name":"Institute of Remote Sensing Big Data, Big Data Research Center, University of Electronic Science and Technology of China, 2006 Xiyuan Road, West Hi-Tech Zone, Chengdu 611731, China"}]},{"given":"Shuanshuan","family":"Bu","sequence":"additional","affiliation":[{"name":"School of Resources &amp; Environment, University of Electronic Science and Technology of China, 2006 Xiyuan Avenue, West Hi-Tech Zone, Chengdu 611731, China"}]},{"given":"Jian","family":"Tao","sequence":"additional","affiliation":[{"name":"Center for Computation &amp; Technology, Louisiana State University, 2039 Digital Media Center, Baton Rouge, LA 70803, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8431-1441","authenticated-orcid":false,"given":"Xicheng","family":"Tan","sequence":"additional","affiliation":[{"name":"International School of Software, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}]}],"member":"1968","published-online":{"date-parts":[[2016,6,17]]},"reference":[{"key":"ref_1","unstructured":"Li, J. (2008). A Review of Spatial Interpolation Methods for Environmental Scientists, Geoscience Australia."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1007\/BF01033884","article-title":"Variogram models for regional ground water geochemical data","volume":"14","author":"Myers","year":"1982","journal-title":"Math. Geol."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Ozelkan, E., Chen, G., and Ustundag, B.B. (2016). Spatial estimation of wind speed: A new integrative model using inverse distance weighting and power law. Int J Digit Earth.","DOI":"10.1080\/17538947.2015.1127437"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4771","DOI":"10.1109\/TGRS.2013.2284489","article-title":"Spatial interpolation to predict missing attributes in GIS using semantic kriging","volume":"52","author":"Bhattacharjee","year":"2014","journal-title":"IEEE Ttrans. Geosci. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/0034-4257(94)90057-4","article-title":"Kriging in the shadows: Geostatistical interpolation for remote sensing","volume":"49","author":"Rossi","year":"1994","journal-title":"Remote Sens. Environ."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1080\/01431161.2011.584078","article-title":"Geostatistical interpolation of missing data and downscaling of spatial resolution for remotely sensed atmospheric methane column concentrations","volume":"33","author":"Zhang","year":"2012","journal-title":"Int. J. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/BF00898283","article-title":"An application of disjunctive kriging for earthquake ground motion estimation","volume":"18","author":"Carr","year":"1986","journal-title":"Math. Geol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1111\/rge.12018","article-title":"A comparative study for 3D surface modeling of coal deposit by spatial interpolation approaches","volume":"63","author":"Dag","year":"2013","journal-title":"Resour. Geol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3731","DOI":"10.1029\/2000WR900232","article-title":"Cost-effective long-term groundwater monitoring design using a genetic algorithm and global mass interpolation","volume":"36","author":"Reed","year":"2000","journal-title":"Water Resour Res. Water Resour. Res."},{"key":"ref_10","unstructured":"Cressie, N., and Kang, E.L. (2010). Proximal Soil Sensing, Springer."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1190\/1.1442852","article-title":"Automated interpolation of two-dimensional seismic grids into three-dimensional data volume","volume":"55","author":"Kao","year":"1990","journal-title":"Geophysics"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1080\/01490419.2014.902883","article-title":"Assessment of 3D Spatial interpolation methods for study of the marine pelagic environment","volume":"37","author":"Sahlin","year":"2014","journal-title":"Mar. Geodes."},{"key":"ref_13","unstructured":"Loubier, J.C. (2010). Spatial Interpolation for Climate Data, ISTE."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/s10661-006-8498-0","article-title":"The parameter optimization in the inverse distance method by genetic algorithm for estimating precipitation","volume":"117","author":"Chang","year":"2006","journal-title":"Environ. Monit. Assess."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/S1364-8152(01)00008-1","article-title":"Using spatial interpolation to construct a comprehensive archive of Australian climate data","volume":"16","author":"Jeffrey","year":"2001","journal-title":"Environ. Model. Softw."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1016\/j.cageo.2010.05.024","article-title":"Explorations of the implementation of a parallel IDW interpolation algorithm in a Linux cluster-based parallel GIS","volume":"37","author":"Huang","year":"2011","journal-title":"Comput. Geosci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1111\/j.1467-9868.2007.00633.x","article-title":"Fixed rank kriging for very large spatial data sets","volume":"70","author":"Cressie","year":"2008","journal-title":"J. R. Stati. Soc."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1007\/978-90-481-2322-3_32","article-title":"Parallel geostatistics for sparse and dense datasets","volume":"16","author":"Ingram","year":"2010","journal-title":"Quant. Geol. Geostat."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1080\/02693799508902032","article-title":"Massively parallel processing of spatial statistics","volume":"9","author":"Armstrong","year":"1995","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_20","unstructured":"Gajraj, A., Joubert, W., and Jones, J. A Parallel Implementation of Kriging with a Trend, Available online: http:\/\/www.osti.gov\/scitech\/servlets\/purl\/544698-DhOroO\/webviewable\/."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1297","DOI":"10.1016\/j.parco.2003.04.001","article-title":"Distributed frameworks and parallel algorithms for processing large-scale geographic data","volume":"29","author":"Hawick","year":"2003","journal-title":"Parall. Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1276","DOI":"10.1016\/j.cageo.2009.12.008","article-title":"Leveraging the power of multi-core platforms for large-scale geospatial data processing: Exemplified by generating DEM from massive LiDAR point clouds","volume":"36","author":"Guan","year":"2010","journal-title":"Comput. Geosci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1481","DOI":"10.1016\/j.parco.2003.04.003","article-title":"A quadtree approach to domain decomposition for spatial interpolation in Grid computing environments","volume":"29","author":"Wang","year":"2003","journal-title":"Parall. Comput."},{"key":"ref_24","unstructured":"Kerry, K.E., and Hawick, K.A. (1998). High-Performance Computing and Networking, Springer."},{"key":"ref_25","unstructured":"Pedelty, J.A., Morisette, J.T., Smith, J.A., Schnase, J.L., Crosier, C.S., and Stohlgren, T.J. High Performance Geostatistical Modeling of Biospheric Resources, Available online: https:\/\/esto.nasa.gov\/conferences\/estc2003\/papers\/A4P4(Schnase).pdf."},{"key":"ref_26","first-page":"1","article-title":"An overview of energy efficiency techniques in cluster computing systems","volume":"16","author":"Valentini","year":"2011","journal-title":"Cluster Comput."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Strzelczyk, J., Porzycka, S., and Lesniak, A. (2009, January 12\u201314). Analysis of ground deformations based on parallel geostatistical computations of PSInSAR data. Proceedings of the International Conference on Geoinformatics, Fairfax, VA, USA.","DOI":"10.1109\/GEOINFORMATICS.2009.5293261"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.cageo.2013.04.029","article-title":"Visualizing 3D\/4D environmental data using many-core graphics processing units (GPUs) and multi-core central processing units (CPUs)","volume":"59","author":"Li","year":"2013","journal-title":"Comput. Geosci."},{"key":"ref_29","first-page":"197","article-title":"Parallel processing of massive remote sensing images in a GPU architecture","volume":"33","author":"Liu","year":"2014","journal-title":"Comput. Inform."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2382","DOI":"10.1109\/TC.2014.2366754","article-title":"Ultra-scalable CPU-MIC acceleration of mesoscale atmospheric modeling on Tianhe-2","volume":"64","author":"Xue","year":"2015","journal-title":"IEEE Trans. Comput."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1417","DOI":"10.1109\/TITB.2010.2072963","article-title":"GPGPU-aided ensemble empirical-mode decomposition for EEG analysis during anesthesia","volume":"14","author":"Chen","year":"2010","journal-title":"IEEE Trans. Inf. Technol. Biomed."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.cageo.2012.11.013","article-title":"Accelerating universal Kriging interpolation algorithm using CUDA-enabled GPU","volume":"54","author":"Cheng","year":"2013","journal-title":"Comput. Geosci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1109\/MCSE.2012.23","article-title":"From GPGPU to Many-core: NVIDIA Fermi and Intel many integrated core architecture","volume":"14","author":"Heinecke","year":"2012","journal-title":"Comput. Sci. Eng."},{"key":"ref_34","first-page":"87","article-title":"Performance optimization methods for boosting MIC-based parallel computing","volume":"11","author":"Wang","year":"2013","journal-title":"J. Shenzhen Inst. Inf. Technol."},{"key":"ref_35","unstructured":"Gaster, B., Howes, L., Kaeli, D.R., Mistry, P., and Schaa, D. (2011). Heterogeneous Computing with OpenCL, Morgan Kaufmann."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1016\/0098-3004(96)00021-0","article-title":"Multivariate interpolation to incorporate thematic surface data using inverse distance weighting (IDW)","volume":"22","author":"Bartier","year":"1996","journal-title":"Comput. Geosci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1109\/MM.2008.31","article-title":"NVIDIA Tesla: A unified graphics and computing architecture","volume":"28","author":"Lindholm","year":"2008","journal-title":"IEEE Micro"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Duran, A., and Klemm, M. (2012, January 2\u20136). The Intel\u00ae many integrated core architecture. Proceedings of the 2012 International Conference on High Performance Computing and Simulation (HPCS), Madrid, Spain.","DOI":"10.1109\/HPCSim.2012.6266938"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1109\/MCSE.2010.69","article-title":"OpenCL: A parallel programming standard for heterogeneous computing systems","volume":"12","author":"Stone","year":"2010","journal-title":"Comput. Sci. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Chil\u00e8s, J.P., and Delfiner, P. (2012). Geostatistics: Modeling Spatial Uncertainty, John Wiley & Sons, Inc.","DOI":"10.1002\/9781118136188"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1023\/A:1007563809463","article-title":"Variogram model selection via nonparametric derivative estimation","volume":"32","author":"Gorsich","year":"2000","journal-title":"Math. Geol."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1080\/00031305.1992.10475879","article-title":"An introduction to kernel and nearest-neighbor nonparametric regression","volume":"46","author":"Altman","year":"1992","journal-title":"Am. Stat."},{"key":"ref_43","unstructured":"Kirk, D.B., and Hwu, W.M.W. (2012). Programming Massively Parallel Processors: A Hands-on Approach, Morgan Kaufmann."},{"key":"ref_44","unstructured":"Tsuchiyama, R., Nakamura, T., Lizuka, T., Asahara, A., Miki, S., and Tagawa, S. (2010). The OpenCL Programming Book, Fixstars Corporation."},{"key":"ref_45","first-page":"113","article-title":"Reevaluating Amdahl\u2019s law and Gustafson\u2019s law","volume":"160","author":"Shi","year":"2010","journal-title":"Microbiol. Read. Engl."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/5\/6\/96\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:25:36Z","timestamp":1760210736000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/5\/6\/96"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6,17]]},"references-count":45,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2016,6]]}},"alternative-id":["ijgi5060096"],"URL":"https:\/\/doi.org\/10.3390\/ijgi5060096","relation":{},"ISSN":["2220-9964"],"issn-type":[{"type":"electronic","value":"2220-9964"}],"subject":[],"published":{"date-parts":[[2016,6,17]]}}}