{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T23:38:34Z","timestamp":1776469114254,"version":"3.51.2"},"reference-count":55,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2017,12,2]],"date-time":"2017-12-02T00:00:00Z","timestamp":1512172800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Examining climate-related satellite data that strongly relate to seasonal phenomena requires appropriate methods for detecting the seasonality to accommodate different temporal resolutions, high signal variability and consecutive missing values in the data series. Detection of satellite-based Land Surface Temperature (LST) seasonality is essential and challenging due to missing data and noise in time series data, particularly in tropical regions with heavy cloud cover and rainy seasons. We used a semi-parametric approach, involving the cubic spline function with the annual periodic boundary condition and weighted least square (WLS) regression, to extract annual LST seasonal pattern without attempting to estimate the missing values. The time series from daytime Aqua eight-day MODIS LST located on Phuket Island, southern Thailand, was selected for seasonal extraction modelling across three different land cover types. The spline-based technique with appropriate number and placement of knots produces an acceptable seasonal pattern of surface temperature time series that reflects the actual local season and weather. Finally, the approach was applied to the morning and afternoon MODIS LST datasets (MOD11A2 and MYD11A2) to demonstrate its application on seasonally-adjusted long-term LST time series. The surface temperature trend in both space and time was examined to reveal the overall 10-year period trend of LST in the study area. The result of decadal trend analysis shows that various Land Use and Land Cover (LULC) types have increasing, but variable surface temperature trends.<\/jats:p>","DOI":"10.3390\/rs9121254","type":"journal-article","created":{"date-parts":[[2017,12,4]],"date-time":"2017-12-04T11:16:38Z","timestamp":1512386198000},"page":"1254","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":46,"title":["Annual Seasonality Extraction Using the Cubic Spline Function and Decadal Trend in Temporal Daytime MODIS LST Data"],"prefix":"10.3390","volume":"9","author":[{"given":"Noppachai","family":"Wongsai","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani Campus, Chang Wat Pattani 94000, Thailand"}]},{"given":"Sangdao","family":"Wongsai","sequence":"additional","affiliation":[{"name":"Faculty of Technology and Environment, Prince of Songkla University, Phuket Campus, Chang Wat Phuket 83120, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2809-2376","authenticated-orcid":false,"given":"Alfredo","family":"Huete","sequence":"additional","affiliation":[{"name":"Climate Change Cluster, University of Technology Sydney, City Campus, Ultimo, NSW 2007, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2017,12,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.rse.2012.12.008","article-title":"Satellite-derived land surface temperature: Current status and perspectives","volume":"131","author":"Li","year":"2013","journal-title":"Remote Sens. Environ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"342","DOI":"10.3390\/rs5010342","article-title":"Retrieving clear-sky surface skin temperature for numerical weather prediction application from geostationary satellite data","volume":"5","author":"Scarino","year":"2013","journal-title":"Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3951","DOI":"10.3390\/rs5083951","article-title":"Evaluation of land surface temperature operationally retrieved from Korean geostationary satellite (COMS) data","volume":"5","author":"Cho","year":"2013","journal-title":"Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3084","DOI":"10.1080\/01431161.2012.716540","article-title":"Land surface emissivity retrieval from satellite data","volume":"34","author":"Li","year":"2013","journal-title":"Int. J. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"133","DOI":"10.5721\/EuJRS20144709","article-title":"Seasonality of MODIS LST over Southern Italy and correlation with land cover, topography and solar radiation","volume":"47","author":"Stroppiana","year":"2014","journal-title":"Eur. J. Remote Sens."},{"key":"ref_6","unstructured":"Wan, Z. (2017, September 01). Collection-6 MODIS Land Surface Temperature Products Users\u2019 Guide. Available online: https:\/\/icess.eri.ucsb.edu\/modis\/LstUsrGuide\/usrguide.html."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2780","DOI":"10.1080\/01431161.2014.890304","article-title":"Land-surface temperature dynamics in the Upper Mekong Basin derived from MODIS time series","volume":"35","author":"Frey","year":"2014","journal-title":"Int. J. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/978-3-319-15967-6_6","article-title":"Analysing a 13 Years MODIS Land Surface Temperature Time Series in the Mekong Basin","volume":"Volume 22","author":"Kuenzer","year":"2015","journal-title":"Remote Sensing Time Series"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Zhao, G., Dong, J., Liu, J., Zhai, J., Cui, Y., He, T., and Xiao, X. (2017). Different patterns in daytime and nighttime thermal effects of urbanization in Beijing-Tianjin-Hebei urban agglomeration. Remote Sens., 9.","DOI":"10.3390\/rs9020121"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"83","DOI":"10.3390\/rs3010083","article-title":"Satellite-observed urbanization characters in Shanghai, China: Aerosols, urban heat island effect, and land\u2013atmosphere interactions","volume":"3","author":"Jin","year":"2011","journal-title":"Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"742","DOI":"10.1016\/j.scitotenv.2017.07.217","article-title":"Temporal trends of surface urban heat islands and associated determinants in major Chinese cities","volume":"609","author":"Yao","year":"2017","journal-title":"Sci. Total Environ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"333","DOI":"10.3390\/rs1020333","article-title":"Estimating daily land surface temperatures in mountainous environments by reconstructed MODIS LST data","volume":"2","author":"Neteler","year":"2010","journal-title":"Remote Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/j.rse.2011.12.019","article-title":"A daily merged MODIS Aqua\u2013Terra land surface temperature data set for the conterminous United States","volume":"119","author":"Crosson","year":"2012","journal-title":"Remote Sens. Environ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.rse.2012.04.024","article-title":"Estimating air surface temperature in Portugal using MODIS LST data","volume":"124","author":"Benali","year":"2012","journal-title":"Remote Sens. Environ."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3822","DOI":"10.3390\/rs6053822","article-title":"Surface temperatures at the continental scale: Tracking changes with remote sensing at unprecedented detail","volume":"6","author":"Metz","year":"2014","journal-title":"Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4539","DOI":"10.1109\/JSTARS.2015.2464094","article-title":"An effective interpolation method for MODIS land surface temperature on the Qinghai\u2013Tibet plateau","volume":"8","author":"Yu","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.rse.2017.04.008","article-title":"A framework for the retrieval of all-weather land surface temperature at a high spatial resolution from polar-orbiting thermal infrared and passive microwave data","volume":"195","author":"Duan","year":"2017","journal-title":"Remote Sens. Environ."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.rse.2013.08.027","article-title":"New refinements and validation of the collection-6 MODIS land-surface temperature\/emissivity product","volume":"140","author":"Wan","year":"2014","journal-title":"Remote Sens. Environ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1633","DOI":"10.5194\/hess-11-1633-2007","article-title":"Updated world map of the K\u00f6ppen\u2013Geiger climate classification","volume":"11","author":"Peel","year":"2007","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_20","unstructured":"(2017, July 15). Global Subsets Tool: MODIS Collection 6 Land Products, Available online: https:\/\/modis.ornl.gov\/cgi-bin\/MODIS\/global\/subset.pl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.isprsjprs.2017.02.003","article-title":"Cross-satellite comparison of operational land surface temperature products derived from MODIS and ASTER data over bare soil surfaces","volume":"126","author":"Duan","year":"2017","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Wahba, G. (1990). Spline Models for Observational Data, Society for Industrial and Applied Mathematics (SIAM).","DOI":"10.1137\/1.9781611970128"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/00401706.1974.10489142","article-title":"Spline function in data analysis","volume":"16","author":"Wold","year":"1974","journal-title":"Technometrics"},{"key":"ref_24","unstructured":"Smith, R.E., Price, J.M., and Howser, L.M. (1974). A Smoothing Algorithm Using Cubic Spline Functions."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1002\/j.1538-7305.1983.tb04381.x","article-title":"Smoothing with periodic cubic splines","volume":"62","author":"Graham","year":"1983","journal-title":"Bell Syst. Tech. J."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2790","DOI":"10.1109\/78.720380","article-title":"Data smoothing by cubic spline filters","volume":"46","author":"Feng","year":"1998","journal-title":"IEEE T. Signal Proces."},{"key":"ref_27","first-page":"98","article-title":"Efficient cubic spline interpolation implemented with FIR filters","volume":"5","author":"Manjabacas","year":"2013","journal-title":"Int. J. Comput. Inf. Syst. Ind. Manag. Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1109\/TASSP.1978.1163154","article-title":"Cubic splines for image interpolation and digital filtering","volume":"26","author":"Hou","year":"1978","journal-title":"IEEE T. Acoust. Speech."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3453","DOI":"10.5194\/amt-10-3453-2017","article-title":"Smoothing data series by means of cubic splines: Quality of approximation and introduction of a repeating spline approach","volume":"10","author":"Wendt","year":"2017","journal-title":"Atmos. Meas. Tech."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zhang, H., Pu, R., and Liu, X. (2016). A New Image Processing Procedure Integrating PCI-RPC and ArcGIS-Spline Tools to Improve the Orthorectification Accuracy of High-Resolution Satellite Imagery. Remote Sens., 8.","DOI":"10.3390\/rs8100827"},{"key":"ref_31","first-page":"54","article-title":"Denoising of hyperspectral imagery by cubic smoothing spline in the wavelet domain","volume":"20","author":"Chen","year":"2014","journal-title":"High Technol. Lett."},{"key":"ref_32","unstructured":"Yu, G., Di, L., Yang, Z., Chen, Z., and Zhang, B. (2012, January 2\u20134). Crop condition assessment using high temporal resolution satellite images. Proceedings of the 2012 First International Conference on Agro-Geoinformatics, Shanghai, China."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/s00271-011-0287-z","article-title":"Estimating seasonal evapotranspiration from temporal satellite images","volume":"30","author":"Singh","year":"2012","journal-title":"Irrig. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Mao, F., Li, X., Du, H., Zhou, G., Han, N., Xu, X., Liu, Y., Chen, L., and Cui, L. (2017). Comparison of two data assimilation methods for improving MODIS LAI time series for bamboo forests. Remote Sens., 9.","DOI":"10.3390\/rs9050401"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"126","DOI":"10.2134\/agronj1976.00021962006800010033x","article-title":"Smoothing Data with Cubic Splines","volume":"68","author":"Kimball","year":"1976","journal-title":"Agron. J."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1111\/j.1439-0388.2009.00829.x","article-title":"Selection of locations of knots for linear splines in random regression test-day models","volume":"127","author":"Jamrozik","year":"2010","journal-title":"J. Anim. Breed. Genet."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1080\/0143116031000116417","article-title":"Quality assessment and validation of the MODIS global land surface temperature","volume":"25","author":"Wan","year":"2004","journal-title":"Int. J. Remote Sens."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/S0167-9473(02)00343-2","article-title":"Bounded optimal knots for regression splines","volume":"45","author":"Molinari","year":"2004","journal-title":"Comput. Stat. Data Anal."},{"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 Intelligence (IJCAI), Montreal, QC, Canada."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/j.cam.2010.05.016","article-title":"Efficient algorithms for robust generalized cross-validation spline smoothing","volume":"235","author":"Lukas","year":"2010","journal-title":"J. Comput. Appl. Math."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"044004","DOI":"10.1088\/1748-9326\/5\/4\/044004","article-title":"Land surface skin temperature climatology: Benefitting from the strengths of satellite observations","volume":"5","author":"Jin","year":"2010","journal-title":"Environ. Res. Lett."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"8728","DOI":"10.3390\/rs70708728","article-title":"Mapping of daily mean air temperature in agricultural regions using daytime and nighttime land surface temperatures derived from TERRA and AQUA MODIS data","volume":"7","author":"Huang","year":"2015","journal-title":"Remote Sens."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Noi, P.T., Kappas, M., and Degener, J. (2016). Estimating daily maximum and minimum land air surface temperature using MODIS land surface temperature data and ground truth data in northern Vietnam. Remote Sens., 8.","DOI":"10.3390\/rs8121002"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"951","DOI":"10.3390\/rs70100951","article-title":"Estimation of daily air temperature based on MODIS land surface temperature products over the Corn Belt in the US","volume":"7","author":"Zeng","year":"2015","journal-title":"Remote Sens."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/j.rse.2009.10.002","article-title":"Evaluation of MODIS land surface temperature data to estimate air temperature in different ecosystems over Africa","volume":"114","author":"Vancutsem","year":"2010","journal-title":"Remote Sens. Environ."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/0167-9473(93)90217-H","article-title":"Fitting additive models to regression data","volume":"15","author":"Breiman","year":"1993","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_47","unstructured":"Gunnip, J. (2006). Analyzing Aggregated AR(1) Processes. [Master\u2019s Thesis, University of Utah]."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Brockwell, P.J., and Davis, R.A. (2002). Introduction to Time Series and Forecasting, Springer. [2nd ed.].","DOI":"10.1007\/b97391"},{"key":"ref_49","first-page":"1241","article-title":"Implement of filter to remove the autocorrelation\u2019s influence on the Mann-Kendall test: A case in hydrological series","volume":"8","author":"Miao","year":"2010","journal-title":"J. Food Agric. Environ."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1177\/1094428104263672","article-title":"Using generalized estimating equations for longitudinal data Analysis","volume":"7","author":"Ballinger","year":"2004","journal-title":"Organ. Res. Methods"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Wang, M. (2014). Generalized Estimating Equations in Longitudinal Data Analysis: A Review and Recent Developments. Adv. Statist., 2014.","DOI":"10.1155\/2014\/303728"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1093\/biomet\/73.1.13","article-title":"Longitudinal data analysis using generalized linear models","volume":"73","author":"Liang","year":"1986","journal-title":"Biometrika"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"32141","DOI":"10.1029\/1998JD200032","article-title":"Discriminating clear sky from clouds with MODIS","volume":"103","author":"Ackerman","year":"1998","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_54","unstructured":"Swets, D.L., Reed, B.C., Rowland, J.D., and Marko, S.E. (1999, January 17\u201321). A weighted least-squares approach to temporal NDVI smoothing. Proceedings of the 1999 ASPRS Annual Conference: From Image to Information, Portland, OR, USA."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1016\/j.rse.2004.03.014","article-title":"A simple method for reconstructing a highquality NDVI time-series data set based on the Savitzky\u2013Golay filter","volume":"91","author":"Chen","year":"2004","journal-title":"Remote Sens. Environ."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/9\/12\/1254\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:52:24Z","timestamp":1760208744000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/9\/12\/1254"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,2]]},"references-count":55,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2017,12]]}},"alternative-id":["rs9121254"],"URL":"https:\/\/doi.org\/10.3390\/rs9121254","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,12,2]]}}}