{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T20:40:22Z","timestamp":1771274422703,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2015,2,9]],"date-time":"2015-02-09T00:00:00Z","timestamp":1423440000000},"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>Forest canopy leaf area index (LAI) is a critical variable for the modeling of climates and ecosystems over both regional and global scales. This paper proposes a physically based method to retrieve LAI and foliage area volume density (FAVD) profile directly from full-waveform Light Detection And Ranging (LiDAR) data using a radiative transfer (RT) model. First, a physical interaction model between LiDAR and a forest scene was built on the basis of radiative transfer theories. Next, FAVD profile of each laser shot of full-waveform LiDAR was inverted using the physical model. In addition, the missing LiDAR data, caused by high-density forest and LiDAR system limitations, were filled in based on the inverted FAVD and the ancillary CHM data. Finally, LAI of the study area was retrieved from the inverted FAVD at a 10-m resolution. CHM derived LAI based on the Beer-Lambert law was compared with the LAI derived from full-waveform data. Also, we compared the results with the field measured LAI. The values of correlation coefficient r and RMSE of the estimated LAI were 0.73 and 0.67, respectively. The results indicate that full-waveform LiDAR data is a reliable data source and represent a useful tool for retrieving forest LAI.     <\/jats:p>","DOI":"10.3390\/rs70201897","type":"journal-article","created":{"date-parts":[[2015,2,9]],"date-time":"2015-02-09T10:17:04Z","timestamp":1423477024000},"page":"1897-1914","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Forest Canopy LAI and Vertical FAVD Profile Inversion from Airborne Full-Waveform LiDAR Data Based on a Radiative Transfer Model"],"prefix":"10.3390","volume":"7","author":[{"given":"Han","family":"Ma","sequence":"first","affiliation":[{"name":"State Key Laboratory of Remote Sensing Science, Beijing Normal University, Beijing 100875, China"},{"name":"School of Geography, Beijing Normal University, Beijing 100875, China"},{"name":"College of Global Change and Earth System Science, Beijing Normal University,  Beijing 100875, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinling","family":"Song","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Remote Sensing Science, Beijing Normal University, Beijing 100875, China"},{"name":"School of Geography, Beijing Normal University, Beijing 100875, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4962-4888","authenticated-orcid":false,"given":"Jindi","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Remote Sensing Science, Beijing Normal University, Beijing 100875, China"},{"name":"School of Geography, Beijing Normal University, Beijing 100875, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,2,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1046\/j.1365-2486.1998.t01-1-00202.x","article-title":"Potentially complex biosphere responses to transient global warming","volume":"4","author":"Neilson","year":"1998","journal-title":"Global Change Biol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1093\/treephys\/22.15-16.1065","article-title":"How the environment, canopy structure and canopy physiological functioning influence carbon, water and energy fluxes of a temperate broad-leaved deciduous forest\u2014An assessment with the biophysical model canoak","volume":"22","author":"Baldocchi","year":"2002","journal-title":"Tree Physiol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1126\/science.275.5299.502","article-title":"Modeling the exchanges of energy, water, and carbon between continents and the atmosphere","volume":"275","author":"Sellers","year":"1997","journal-title":"Science"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1641\/0006-3568(2002)052[0019:LRSFES]2.0.CO;2","article-title":"LIDAR remote sensing for ecosystem studies","volume":"52","author":"Lefsky","year":"2002","journal-title":"Biosci."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Liang, S. (2004). Quantitative remote sensing of land surfaces, John Wiley & Sons.","DOI":"10.1002\/047172372X"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.rse.2013.02.018","article-title":"Investigating assumptions of crown archetypes for modelling LiDAR returns","volume":"134","author":"Calders","year":"2013","journal-title":"Remote Sens. Environ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"G00E09","DOI":"10.1029\/2009JG000933","article-title":"Estimation of tropical forest height and biomass dynamics using LIDAR remote sensing at la Selva, Costa Rica","volume":"115","author":"Dubayah","year":"2010","journal-title":"J. Geophys. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"L22S02","DOI":"10.1029\/2005GL023971","article-title":"Estimates of forest canopy height and aboveground biomass using icesat","volume":"32","author":"Lefsky","year":"2005","journal-title":"Geophys. Res. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"013537","DOI":"10.1117\/1.2795724","article-title":"Revised method for forest canopy height estimation from geoscience laser altimeter system waveforms","volume":"1","author":"Lefsky","year":"2007","journal-title":"J. Appl. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/j.agrformet.2004.02.005","article-title":"Estimation of leaf area index and covered ground from airborne laser scanner (LiDAR) in two contrasting forests","volume":"124","author":"Valladares","year":"2004","journal-title":"Agr. Forest Meteorol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1007\/s10342-010-0381-4","article-title":"Retrieval of forest structural parameters using LiDAR remote sensing","volume":"129","author":"Nieuwenhuis","year":"2010","journal-title":"Eur. J. Forest Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1016\/S0264-3707(02)00046-7","article-title":"Validation of vegetation canopy LiDAR sub-canopy topography measurements for a dense tropical forest","volume":"34","author":"Hofton","year":"2002","journal-title":"J. Geodyn."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1016\/j.rse.2010.10.003","article-title":"Extracting LiDAR indices to characterise multilayered forest structure using mixture distribution functions","volume":"115","author":"Jaskierniak","year":"2011","journal-title":"Remote Sens. Environ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1989","DOI":"10.1109\/36.851780","article-title":"Decomposition of laser altimeter waveforms","volume":"38","author":"Hofton","year":"2000","journal-title":"Geosci. Remote Sens., IEEE Transactions on"},{"key":"ref_15","unstructured":"Persson, \u00c5., S\u00f6derman, U., T\u00f6pel, J., and Ahlberg, S. (2005, January 12\u201314). Visualization and analysis of full-waveform airborne laser scanner data. Proceedings of ISPRS WG III\/3, III\/4, V\/3 Workshop \u201cLaser Scanning 2005\u201d, Enschede, the Netherlands."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.isprsjprs.2005.12.001","article-title":"Gaussian decomposition and calibration of a novel small-footprint full-waveform digitising airborne laser scanner","volume":"60","author":"Wagner","year":"2006","journal-title":"Int. J. Photogramm. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.rse.2011.11.015","article-title":"Estimation of 3D vegetation structure from waveform and discrete return airborne laser scanning data","volume":"118","author":"Lindberg","year":"2012","journal-title":"Remote Sens. Environ."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.rse.2006.09.036","article-title":"Forest vertical structure from glas: An evaluation using lvis and srtm data","volume":"112","author":"Sun","year":"2008","journal-title":"Remote Sens. Environ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jaridenv.2007.04.010","article-title":"Using airborne LiDAR to predict leaf area index in cottonwood trees and refine riparian water-use estimates","volume":"72","author":"Farid","year":"2008","journal-title":"J. Arid Environ."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1628","DOI":"10.1016\/j.rse.2009.03.006","article-title":"LiDAR-based mapping of leaf area index and its use for validating globcarbon satellite lai product in a temperate forest of the southern USA","volume":"113","author":"Zhao","year":"2009","journal-title":"Remote Sens. Environ."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"682","DOI":"10.3390\/rs4030682","article-title":"Extracting more data from LiDAR in forested areas by analyzing waveform shape","volume":"4","author":"Adams","year":"2012","journal-title":"Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.isprsjprs.2008.09.007","article-title":"Full-waveform topographic LiDAR: State-of-the-art","volume":"64","author":"Mallet","year":"2009","journal-title":"Int. J. Photogramm. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2509","DOI":"10.1029\/1999GL010484","article-title":"Modeling laser altimeter return waveforms over complex vegetation using high-resolution elevation data","volume":"26","author":"Blair","year":"1999","journal-title":"Geophys. Res. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2617","DOI":"10.1109\/36.885208","article-title":"Modeling LiDAR returns from forest canopies","volume":"38","author":"Sun","year":"2000","journal-title":"Geosci. Remote Sens., IEEE Trans."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1109\/LGRS.2005.856706","article-title":"Inversion of a LiDAR waveform model for forest biophysical parameter estimation","volume":"3","author":"Koetz","year":"2006","journal-title":"Geosci. Remote Sens. Lett., IEEE"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1943","DOI":"10.1109\/36.951085","article-title":"Modeling LiDAR waveforms in heterogeneous and discrete canopies","volume":"39","author":"Jupp","year":"2001","journal-title":"Geosci. Remote Sens, IEEE Trans."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/j.rse.2012.05.005","article-title":"Retrieval of vertical LAI profiles over tropical rain forests using waveform LIDAR at la Selva, Costa Rica","volume":"124","author":"Tang","year":"2012","journal-title":"Remote Sens. Environ."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.rse.2013.02.021","article-title":"Direct retrieval of canopy gap probability using airborne waveform LiDAR","volume":"134","author":"Armston","year":"2013","journal-title":"Remote Sens. Environ."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.rse.2013.12.010","article-title":"Sensitivity of direct canopy gap fraction retrieval from airborne waveform LiDAR to topography and survey characteristics","volume":"143","author":"Chen","year":"2014","journal-title":"Remote Sens. Environ."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2152","DOI":"10.1016\/j.rse.2009.05.019","article-title":"Assessing forest structural and physiological information content of multi-spectral LiDAR waveforms by radiative transfer modelling","volume":"113","author":"Morsdorf","year":"2009","journal-title":"Remote Sens. Environ."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1051\/agro:19990302","article-title":"Three-dimensional plant modelling for remote sensing simulation studies using the botanical plant modelling system","volume":"19","author":"Lewis","year":"1999","journal-title":"Agronomie"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1343","DOI":"10.1080\/01431160903380664","article-title":"A monte carlo radiative transfer model of satellite waveform LiDAR","volume":"31","author":"North","year":"2010","journal-title":"Int. J. Remote Sens."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.agrformet.2012.03.014","article-title":"Measuring forests with dual wavelength LiDAR: A simulation study over topography","volume":"161","author":"Hancock","year":"2012","journal-title":"Agr. Forest Meteorol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/S0034-4257(99)00056-5","article-title":"Direct and indirect estimation of leaf area index, fapar, and net primary production of terrestrial ecosystems","volume":"70","author":"Gower","year":"1999","journal-title":"Remote Sens. Environ."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"6211","DOI":"10.1364\/AO.34.006211","article-title":"Plant canopy gap-size analysis theory for improving optical measurements of leaf-area index","volume":"34","author":"Chen","year":"1995","journal-title":"Appl. Opt."},{"key":"ref_36","unstructured":"Zhuo, F., Jindi, W., Jinling, S., Hongmin, Z., Huaguo, H., and Baisong, C. (2009, January 12\u201317). Comparison of three indirect field measuring methods for forest canopy leaf area index estimation. Proceedings of Geoscience and Remote Sensing Symposium, 2009 IEEE International, IGARSS 2009."},{"key":"ref_37","unstructured":"Hug, C., Ullrich, A., and Grimm, A. (2004, January 3\u20136). Litemapper-5600-a waveform-digitizing LiDAR terrain and vegetation mapping system. Proceedings of International Archives of Photogrammetry, Remote Sensing and Spatial Information Science, Freiburg, Germany."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1152","DOI":"10.1016\/j.agrformet.2009.02.007","article-title":"Modeling approaches to estimate effective leaf area index from aerial discrete-return LiDAR","volume":"149","author":"Richardson","year":"2009","journal-title":"Agr. Forest Meteorol."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/0002-1571(71)90092-6","article-title":"A theoretical analysis of the frequency of gaps in plant stands","volume":"8","author":"Nilson","year":"1971","journal-title":"Agr. Meteorol."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0962492900002518","article-title":"Sequential quadratic programming","volume":"4","author":"Boggs","year":"1995","journal-title":"Acta Numerica"},{"key":"ref_41","first-page":"44","article-title":"LiDAR remote sensing for forestry","volume":"98","author":"Dubayah","year":"2000","journal-title":"J. For."},{"key":"ref_42","unstructured":"Jinling, S., Jindi, W., Zhuo, F., Bengyu, W., and Xin, A.T. (2008). Institute of Forest Resource Information Techniques, Chinese Academy of Forestry."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/2005GL024028","article-title":"Geoscience laser altimeter system (glas) on the icesat mission: On-orbit measurement performance","volume":"32","author":"Abshire","year":"2005","journal-title":"Geophys. Res. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/S0924-2716(99)00002-7","article-title":"The laser vegetation imaging sensor: A medium-altitude, digitisation-only, airborne laser altimeter for mapping vegetation and topography","volume":"54","author":"Blair","year":"1999","journal-title":"Int. J. Photogramm. Remote Sens."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1511","DOI":"10.1080\/01431160701736364","article-title":"Quantifying the influence of slope, aspect, crown shape and stem density on the estimation of tree height at plot level using LiDAR and insar data","volume":"29","author":"Breidenbach","year":"2008","journal-title":"Int. J. Remote Sens."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.agrformet.2014.01.009","article-title":"Improvement of spatially continuous forest LAI retrieval by integration of discrete airborne LiDAR and remote sensing multi-angle optical data","volume":"189\u2013190","author":"Ma","year":"2014","journal-title":"Agr. Forest Meteorol."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/7\/2\/1897\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:42:30Z","timestamp":1760215350000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/7\/2\/1897"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,9]]},"references-count":46,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2015,2]]}},"alternative-id":["rs70201897"],"URL":"https:\/\/doi.org\/10.3390\/rs70201897","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,9]]}}}