{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T04:56:56Z","timestamp":1780462616440,"version":"3.54.1"},"reference-count":39,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2016,2,6]],"date-time":"2016-02-06T00:00:00Z","timestamp":1454716800000},"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>Space-time interpolation is widely used to estimate missing or unobserved values in a dataset integrating both spatial and temporal records. Although space-time interpolation plays a key role in space-time modeling, existing methods were mainly developed for space-time processes that exhibit stationarity in space and time. It is still challenging to model heterogeneity of space-time data in the interpolation model. To overcome this limitation, in this study, a novel space-time interpolation method considering both spatial and temporal heterogeneity is developed for estimating missing data in space-time datasets. The interpolation operation is first implemented in spatial and temporal dimensions. Heterogeneous covariance functions are constructed to obtain the best linear unbiased estimates in spatial and temporal dimensions. Spatial and temporal correlations are then considered to combine the interpolation results in spatial and temporal dimensions to estimate the missing data. The proposed method is tested on annual average temperature and precipitation data in China (1984\u20132009). Experimental results show that, for these datasets,  the proposed method outperforms three state-of-the-art methods\u2014e.g., spatio-temporal kriging, spatio-temporal inverse distance weighting, and point estimation model of biased hospitals-based area disease estimation methods.<\/jats:p>","DOI":"10.3390\/ijgi5020013","type":"journal-article","created":{"date-parts":[[2016,2,9]],"date-time":"2016-02-09T13:45:23Z","timestamp":1455025523000},"page":"13","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["A Hybrid Method for Interpolating Missing Data in Heterogeneous Spatio-Temporal Datasets"],"prefix":"10.3390","volume":"5","author":[{"given":"Min","family":"Deng","sequence":"first","affiliation":[{"name":"Department of Geo-Informatics, Central South University, Changsha 410083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2696-8234","authenticated-orcid":false,"given":"Zide","family":"Fan","sequence":"additional","affiliation":[{"name":"Department of Geo-Informatics, Central South University, Changsha 410083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiliang","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Geo-Informatics, Central South University, Changsha 410083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianya","family":"Gong","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing,  Wuhan University, Wuhan 430079, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2016,2,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1317","DOI":"10.3390\/ijgi3041317","article-title":"Accuracy and effort of interpolation and sampling: Can GIS help lower field costs?","volume":"3","author":"Simpson","year":"2014","journal-title":"ISPRS Int. J. Geo-Inf."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1564","DOI":"10.1002\/joc.1992","article-title":"Improving estimation of missing values in daily precipitation series by a probability density function-preserving approach","volume":"30","author":"Simolo","year":"2010","journal-title":"Int. J. Climatol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"220","DOI":"10.3390\/ijgi4010220","article-title":"Assessment of spatial interpolation methods to map the bathymetry of an Amazonian hydroelectric reservoir to aid in decision making for water management","volume":"4","author":"Curtarelli","year":"2015","journal-title":"ISPRS Int. J. Geo-Inf."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/0169-8095(95)00067-4","article-title":"Comparative studies of various missing data treatment methods\u2014Malaysian experience","volume":"42","author":"Tang","year":"1996","journal-title":"Atmos. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"7452","DOI":"10.1175\/JCLI-D-12-00633.1","article-title":"Interpolation of missing temperature data at meteorological stations using P-BSHADE","volume":"26","author":"Xu","year":"2013","journal-title":"J. Clim."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/S0167-7152(00)00131-0","article-title":"Estimating and modeling space-time correlation structures","volume":"51","author":"Myers","year":"2001","journal-title":"Stat. Probab. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1023\/A:1007528426688","article-title":"Geostatistical space-time models: A review","volume":"31","author":"Kyriakidis","year":"1999","journal-title":"Math. Geol."},{"key":"ref_8","unstructured":"Kilibarda, M., Tadic, M.P., Hengl, T., Lukovic, J., and Bajat, B. Publicly Available Global Meteorological Data Sets: Sources, Representation, and Usability for Spatio-temporal Analysis. Available online: http:\/\/dailymeteo.org\/content\/publicly-available-global-meteorological-data-sets-sources-representation-and-usability."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/2013JD020542","article-title":"A new estimate of the China temperature anomaly series and uncertainty assessment in 1900\u20132006","volume":"119","author":"Wang","year":"2014","journal-title":"J. Geophys. Res.: Atmos."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/S0167-9473(02)00081-6","article-title":"Space-time variograms and a functional form for total air pollution measurements","volume":"41","author":"Myers","year":"2002","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/S0198-9715(03)00018-8","article-title":"Interpolation methods for spatio-temporal geographic data","volume":"28","author":"Li","year":"2004","journal-title":"Comput. Environ. Urban Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1080\/13658810802672469","article-title":"Geographically and temporally weighted regression for modeling space-time variation in house prices","volume":"24","author":"Huang","year":"2010","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Cressie, N.A.C. (1993). Statistics for Spatial Data, Wiley.","DOI":"10.1002\/9781119115151"},{"key":"ref_14","unstructured":"Dutilleul, P.R.L. (2011). Spatio-Temporal Heterogeneity: Concepts and Analyses, Cambridge University Press."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Goovaerts, P. (1997). Geostatistics for Natural Resources Evaluation, Oxford University Press.","DOI":"10.1093\/oso\/9780195115383.001.0001"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/0166-0462(95)02111-6","article-title":"Simple diagnostic tests for spatial dependence","volume":"26","author":"Anselin","year":"1996","journal-title":"Reg. Sci. Urban Econ."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1905","DOI":"10.1068\/a301905","article-title":"Geographically weighted regression: A natural evolution of the expansion method for spatial data analysis","volume":"30","author":"Fotheringham","year":"1998","journal-title":"Environ. Plan. A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.cageo.2009.06.005","article-title":"Modelling the spatial distribution of DEM error with geographically weighted regression: An experimental study","volume":"36","year":"2010","journal-title":"Comput. Geosci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1080\/13658816.2013.865739","article-title":"Geographically weighted regression with a non-Euclidean distance metric: A case study using hedonic house price data","volume":"28","author":"Lu","year":"2014","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1175\/JTECH-1657.1","article-title":"Performance of quality assurance procedures for an applied climate information system","volume":"22","author":"Hubbard","year":"2005","journal-title":"J. Atmos. Ocean. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1520","DOI":"10.1175\/JTECH1790.1","article-title":"Sensitivity analysis of quality assurance using the spatial regression approach\u2014A case study of the maximum\/minimum air temperature","volume":"22","author":"Hubbard","year":"2005","journal-title":"J. Atmos. Ocean. Technol."},{"key":"ref_22","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_23","doi-asserted-by":"crossref","first-page":"1044","DOI":"10.1016\/j.cageo.2007.07.010","article-title":"An adaptive inverse-distance weighting spatial interpolation technique","volume":"34","author":"Lu","year":"2008","journal-title":"Comput. Geosci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1094\/Phyto-78-240","article-title":"Analysis of epidemics using spatio-temporal autocorrelation","volume":"78","author":"Reynolds","year":"1988","journal-title":"Phytopathology"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1198\/106186006X132178","article-title":"Covariance tapering for interpolation of large spatial datasets","volume":"15","author":"Furrer","year":"2006","journal-title":"J. Comput. Graph. Stat."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1073","DOI":"10.1016\/j.cageo.2007.09.020","article-title":"Geostatistics with the Matern semivariogram model: A library of computer programs for inference, Kriging and simulation","volume":"34","year":"2008","journal-title":"Comput. Geosci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"464","DOI":"10.1016\/j.cageo.2010.10.010","article-title":"Parallel ordinary Kriging interpolation incorporating automatic variogram fitting","volume":"37","author":"Pesquer","year":"2011","journal-title":"Comput. Geosci."},{"key":"ref_28","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 Trans. Geosci. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1023\/A:1021368723926","article-title":"Spatio-temporal covariance functions generated by mixtures","volume":"34","author":"Ma","year":"2002","journal-title":"Math. Geol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/s00477-007-0154-x","article-title":"Recent developments on the construction of spatio-temporal covariance models","volume":"22","author":"Ma","year":"2008","journal-title":"Stochast. Environ. Res. Risk Assess."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/S0167-7152(00)00200-5","article-title":"Space-time analysis using a general product-sum model","volume":"52","author":"Myers","year":"2001","journal-title":"Stat. Probab. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1023\/A:1019861427772","article-title":"Non-separable space-time covariance models: Some parametric families","volume":"34","author":"Myers","year":"2002","journal-title":"Math. Geol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1002\/1099-095X(200102)12:1<11::AID-ENV426>3.0.CO;2-P","article-title":"Product-sum covariance for space-time modeling: An environmental application","volume":"12","author":"Myers","year":"2001","journal-title":"Environmetrics"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.envsoft.2013.06.011","article-title":"A B-SHADE based best linear unbiased estimation tool for biased samples","volume":"48","author":"Hu","year":"2013","journal-title":"Environ. Model. Softw."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1080\/13658810802443457","article-title":"Geographical detectors-based health risk assessment and its application in the neural tube defects study of the Heshun region, China","volume":"24","author":"Wang","year":"2010","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1080\/13658810701674970","article-title":"Regionalization with dynamically constrained agglomerative clustering and partitioning (REDCAP)","volume":"22","author":"Guo","year":"2008","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.ecoinf.2012.02.001","article-title":"Regionalization of forest pattern metrics for the continental United States using contiguity constrained clustering and partitioning","volume":"9","author":"Kupfer","year":"2012","journal-title":"Ecol. Inf."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1007\/s10651-008-0090-z","article-title":"Coregionalization analysis with a drift for multi-scale assessment of spatial relationships between ecological variables 1. Estimation of drift and random components","volume":"16","author":"Pelletier","year":"2009","journal-title":"Environ. Ecol. Stat."},{"key":"ref_39","unstructured":"Kohavi, R. (1995, January 20\u201325). A study of cross-validation and bootstrap for accuracy estimation and model selection. Proceedings of the 14th International Joint Conference on Artificial, Montreal, QC, Canada."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/5\/2\/13\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:18:57Z","timestamp":1760210337000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/5\/2\/13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,6]]},"references-count":39,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,2]]}},"alternative-id":["ijgi5020013"],"URL":"https:\/\/doi.org\/10.3390\/ijgi5020013","relation":{},"ISSN":["2220-9964"],"issn-type":[{"value":"2220-9964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,2,6]]}}}