{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T02:57:24Z","timestamp":1774321044695,"version":"3.50.1"},"reference-count":45,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2014,1,29]],"date-time":"2014-01-29T00:00:00Z","timestamp":1390953600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>An extended Fourier approach was presented to improve the retrieved leaf area index (LAIr) of herbaceous vegetation in a time series from an alpine wetland. The retrieval was performed from the Aqua MODIS 8-day composite surface reflectance product (MYD09Q1) from day of year (DOY) 97 to 297 using a look-up table (LUT) based inversion of a two-layer canopy reflectance model (ACRM). To reduce the uncertainty (the ACRM inversion is ill-posed), we used NDVI and NIR images to reduce the influence of the soil background and the priori information to constrain the range of sensitive ACRM parameters determined using the Sobol\u2019s method. Even so the uncertainty caused the LAIr versus time curve to oscillate. To further reduce the uncertainty, a Fourier model was fitted using the periodically LAIr results, obtaining LAIF. We note that the level of precision of the LAIF potentially may increase through removing singular points or decrease if the LAIr data were too noisy. To further improve the precision level of the LAIr, the Fourier model was extended by considering the LAIr uncertainty. The LAIr, the LAI simulated using the Fourier model, and the LAI simulated using the extended Fourier approach (LAIeF) were validated through comparisons with the field measured LAI. The R2 values were 0.68, 0.67 and 0.72, the residual sums of squares (RSS) were 3.47, 3.42 and 3.15, and the root-mean-square errors (RMSE) were 0.31, 0.30 and 0.29, respectively, on DOY 177 (early July 2011). In late August (DOY 233), the R2 values were 0.73, 0.77 and 0.79, the RSS values were 38.96, 29.25 and 27.48, and the RMSE values were 0.94, 0.81 and 0.78, respectively. The results demonstrate that the extended Fourier approach has the potential to increase the level of precision of estimates of the time varying LAI.<\/jats:p>","DOI":"10.3390\/rs6021171","type":"journal-article","created":{"date-parts":[[2014,1,29]],"date-time":"2014-01-29T11:16:56Z","timestamp":1390994216000},"page":"1171-1190","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["An Extended Fourier Approach to Improve the Retrieved Leaf Area Index (LAI) in a Time Series from an Alpine Wetland"],"prefix":"10.3390","volume":"6","author":[{"given":"Xingwen","family":"Quan","sequence":"first","affiliation":[{"name":"School of Resources and Environment, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Binbin","family":"He","sequence":"additional","affiliation":[{"name":"School of Resources and Environment, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Resources and Environment, University of Electronic Science and Technology of China, Chengdu 611731, China"},{"name":"Department of Geography, Planning and Environment, East Carolina University, Greenville,  NC 27858, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhi","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Resources and Environment, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xing","family":"Li","sequence":"additional","affiliation":[{"name":"School of Resources and Environment, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,1,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.rse.2006.07.016","article-title":"Combining vegetation index and model inversion methods for the extraction of key vegetation biophysical parameters using Terra and Aqua MODIS reflectance data","volume":"106","author":"Houborg","year":"2007","journal-title":"Remote Sens. 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