{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T01:37:13Z","timestamp":1773365833603,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,4,6]],"date-time":"2021-04-06T00:00:00Z","timestamp":1617667200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41701383"],"award-info":[{"award-number":["41701383"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41801234"],"award-info":[{"award-number":["41801234"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003995","name":"Natural Science Foundation of Anhui Province","doi-asserted-by":"publisher","award":["1808085QD105"],"award-info":[{"award-number":["1808085QD105"]}],"id":[{"id":"10.13039\/501100003995","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shandong Provincial Key Laboratory of Water and Soil Conservation and Environmental Protection","award":["STKF201908"],"award-info":[{"award-number":["STKF201908"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>As a widely used ground-based optical instrument, the LAI-2000 or LAI-2200 plant canopy analyzer (PCA) (Li-Cor, Inc., Lincoln, NE) is designed to measure the plant effective leaf area index (Le) by measuring the canopy gap fraction at several limited or discrete view zenith angles (VZAs) (usually five VZAs: 7, 23, 38, 53, and 68\u00b0) based on Miller\u2019s equation. Miller\u2019s equation requires the probability of radiative transmission through the canopy to be measured over the hemisphere, i.e., VZAs in the range from 0 to 90\u00b0. However, the PCA view angle ranges are confined to several limited ranges or discrete sectors. The magnitude of the error produced by the discretization of VZAs in the leaf area index measurements remains difficult to determine. In this study, a theoretical deduction was first presented to definitely prove why the limited or discrete VZAs or ranges can affect the Le measured with the PCA, and the specific error caused by the limited or discrete VZAs was described quantitatively. The results show that: (1) the weight coefficient of the last PCA ring is the main cause of the error; (2) the error is closely related to the leaf inclination angles (IAs)\u2014the Le measured with the PCA can be significantly overestimated for canopies with planophile IAs, whereas it can be underestimated for erectophile IAs; and (3) the error can be enhanced with the increment of the discrete degree of PCA rings or VZAs, such as using four or three PCA rings. Two corrections for the error are presented and validated in three crop canopies. Interestingly, although the leaf IA type cannot influence the Le calculated by Miller\u2019s equation in the hemispheric space, it affects the Le measured with the PCA using the discrete form of Miller\u2019s equation for several discrete VZAs.<\/jats:p>","DOI":"10.3390\/rs13071405","type":"journal-article","created":{"date-parts":[[2021,4,6]],"date-time":"2021-04-06T21:44:47Z","timestamp":1617745487000},"page":"1405","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Error Analysis of LAI Measurements with LAI-2000 Due to Discrete View Angular Range Angles for Continuous Canopies"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1348-2355","authenticated-orcid":false,"given":"Jun","family":"Geng","sequence":"first","affiliation":[{"name":"School of Civil Engineering, Hefei University of Technology, Hefei 230009, China"},{"name":"Intelligent Interconnected Systems Laboratory of Anhui Province, Hefei University of Technology, Hefei 230009, China"}]},{"given":"Gang","family":"Yuan","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Hefei University of Technology, Hefei 230009, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8682-1293","authenticated-orcid":false,"given":"J. M.","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Geography and Program in Planning, University of Toronto, 100 St. George Street, Room 5047, Toronto, ON M5S 3G3, Canada"},{"name":"School of Geographical Science, Fujian Normal University, Fuzhou, Fujian 350007, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0245-9179","authenticated-orcid":false,"given":"Chunguang","family":"Lyu","sequence":"additional","affiliation":[{"name":"Shandong Provincial Key Laboratory of Water and Soil Conservation and Environmental Protection, College of Resources and Environment, Linyi University, Linyi 276000, China"}]},{"given":"Lili","family":"Tu","sequence":"additional","affiliation":[{"name":"School of Resources and Environment, Anhui Agricultural University, Hefei 230036, China"}]},{"given":"Weiliang","family":"Fan","sequence":"additional","affiliation":[{"name":"Department of Geography and Program in Planning, University of Toronto, 100 St. George Street, Room 5047, Toronto, ON M5S 3G3, Canada"},{"name":"Zhejiang A &amp; F University, Linan 311331, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0986-6479","authenticated-orcid":false,"given":"Qingjiu","family":"Tian","sequence":"additional","affiliation":[{"name":"Jiangsu Provincial Key Laboratory of Geographic Information Science and Technology, International Institute for Earth System Science, Nanjing University, Nanjing 210046, China"}]},{"given":"Zhaofu","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Hefei University of Technology, Hefei 230009, China"}]},{"given":"Tingye","family":"Tao","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Hefei University of Technology, Hefei 230009, China"}]},{"given":"Min","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Hefei University of Technology, Hefei 230009, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7176-218X","authenticated-orcid":false,"given":"Yongchao","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Hefei University of Technology, Hefei 230009, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0207-8800","authenticated-orcid":false,"given":"Jianwei","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Hefei University of Technology, Hefei 230009, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4825-3942","authenticated-orcid":false,"given":"Kaijian","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Hefei University of Technology, Hefei 230009, China"}]},{"given":"Jinchao","family":"Li","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Hefei University of Technology, Hefei 230009, China"}]},{"given":"Shaoteng","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Hefei University of Technology, Hefei 230009, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1111\/j.1365-3040.1992.tb00992.x","article-title":"Defining leaf area index for non-flat leaves","volume":"15","author":"Chen","year":"1992","journal-title":"Plant Cell Environ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/S0034-4257(02)00074-3","article-title":"Global products of vegetation leaf area and fraction absorbed PAR from year one of MODIS data","volume":"83","author":"Myneni","year":"2002","journal-title":"Remote Sens. Environ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4573","DOI":"10.1109\/TGRS.2019.2963366","article-title":"Path Length Correction for Improving Leaf Area Index Measurements Over Sloping Terrains: A Deep Analysis Through Computer Simulation","volume":"58","author":"Yin","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2","DOI":"10.2480\/agrmet.D-14-00023","article-title":"Estimation of rice yield by SIMRIW-RS, a model that integrates remote sensing data into a crop growth model","volume":"73","author":"Maki","year":"2017","journal-title":"J. Agric. Meteorol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2403","DOI":"10.1093\/jxb\/erg263","article-title":"Ground-based measurements of leaf area index: A review of methods, instruments and current controversies","volume":"54","author":"Breda","year":"2003","journal-title":"J. Exp. Bot."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2719","DOI":"10.3390\/s90402719","article-title":"Retrieving Leaf Area Index (LAI) Using Remote Sensing: Theories, Methods and Sensors","volume":"9","author":"Zheng","year":"2009","journal-title":"Sensors"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"29429","DOI":"10.1029\/97JD01107","article-title":"Leaf area index of boreal forests: Theory, techniques, and measurements","volume":"102","author":"Chen","year":"1997","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1016\/j.agrformet.2018.11.033","article-title":"Review of indirect optical measurements of leaf area index: Recent advances, challenges, and perspectives","volume":"265","author":"Yan","year":"2019","journal-title":"Agric. For. Meteorol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/j.rse.2014.08.032","article-title":"Indirect measurement of leaf area index on the basis of path length distribution","volume":"155","author":"Hu","year":"2014","journal-title":"Remote Sens. Environ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.agrformet.2003.08.001","article-title":"Review of methods for in situ leaf area index (LAI) determination Part II. Estimation of LAI, errors and sampling","volume":"121","author":"Weiss","year":"2004","journal-title":"Agric. For. Meteorol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.agrformet.2003.08.027","article-title":"Review of methods for in situ leaf area index determination\u2014Part I. Theories, sensors and hemispherical photography","volume":"121","author":"Jonckheere","year":"2004","journal-title":"Agric. For. Meteorol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1193","DOI":"10.1016\/j.agrformet.2008.02.014","article-title":"Intercomparison and sensitivity analysis of Leaf Area Index retrievals from LAI-2000, AccuPAR, and digital hemispherical photography over croplands","volume":"148","author":"Garrigues","year":"2008","journal-title":"Agric. For. Meteorol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/j.agrformet.2016.02.015","article-title":"Specular reflection in the signal of LAI-2000 plant canopy analyzer","volume":"221","author":"Kuusk","year":"2016","journal-title":"Agric. For. Meteorol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1007\/s00468-014-1115-x","article-title":"Estimation of foliage clumping from the LAI-2000 Plant Canopy Analyzer: Effect of view caps","volume":"29","author":"Chianucci","year":"2015","journal-title":"Trees"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.agrformet.2011.10.002","article-title":"Optimizing the sampling scheme for LAI-2000 measurements in a boreal forest","volume":"154\u2013155","author":"Majasalmi","year":"2012","journal-title":"Agric. For. Meteorol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.foreco.2007.04.039","article-title":"Calibration of LAI-2000 to estimate leaf area index (LAI) and assessment of its relationship with stand productivity in six native and introduced tree species in Costa Rica","volume":"247","author":"Arias","year":"2007","journal-title":"For. Ecol. Manag."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/s00468-005-0038-y","article-title":"Calibration of LAI-2000 canopy analyser with leaf area index in a young eucalypt stand","volume":"20","author":"Dovey","year":"2006","journal-title":"Trees"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0168-1923(95)02274-0","article-title":"Correcting LAI-2000 estimates for the clumping of needles in shoots of conifers","volume":"79","author":"Stenberg","year":"1996","journal-title":"Agric. For. Meteorol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1940","DOI":"10.1139\/x93-244","article-title":"Effects of clumping on estimates of stand leaf area index using the LI-COR LAI-2000","volume":"23","author":"Smith","year":"1993","journal-title":"Can. J. Forest Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1109\/TGRS.2016.2611651","article-title":"Retrieving Directional Gap Fraction, Extinction Coefficient, and Effective Leaf Area Index by Incorporating Scan Angle Information From Discrete Aerial Lidar Data","volume":"55","author":"Zheng","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Kuusk, A., Pisek, J., Lang, M., and M\u00e4rdla, S. (2018). Estimation of Gap Fraction and Foliage Clumping in Forest Canopies. Remote Sens. Basel., 10.","DOI":"10.3390\/rs10071153"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/0168-1923(86)90033-X","article-title":"Estimation of leaf area index from transmission of direct sunlight in discontinuous canopies","volume":"37","author":"Lang","year":"1986","journal-title":"Agric. For. Meteorol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1071\/BT9860349","article-title":"Leaf-area and average leaf angle from transmission of direct sunlight","volume":"34","author":"Lang","year":"1986","journal-title":"Aust. J. Bot."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.agrformet.2016.05.009","article-title":"Quantifying the impact of woody material on leaf area index estimation from hemispherical photography using 3D canopy simulations","volume":"226\u2013227","author":"Woodgate","year":"2016","journal-title":"Agric. For. Meteorol."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Zou, J., Zhuang, Y., Chianucci, F., Mai, C., Lin, W., Leng, P., Luo, S., and Yan, B. (2018). Comparison of Seven Inversion Models for Estimating Plant and Woody Area Indices of Leaf-on and Leaf-off Forest Canopy Using Explicit 3D Forest Scenes. Remote Sens. Basel, 10.","DOI":"10.3390\/rs10081297"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zou, J., Leng, P., Hou, W., Zhong, P., Chen, L., Mai, C., Qian, Y., and Zuo, Y. (2018). Evaluating Two Optical Methods of Woody-to-Total Area Ratio with Destructive Measurements at Five Larix gmelinii Rupr. Forest Plots in China. Forests, 9.","DOI":"10.3390\/f9120746"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/S0168-1923(00)00090-3","article-title":"Sampling methodology for LAI measurements with LAI-2000 in small forest stands","volume":"101","author":"Nackaerts","year":"2000","journal-title":"Agric. For. Meteorol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/0168-1923(94)02175-J","article-title":"Non-destructive measurement of leaf area in olive (Olea europaea L.) trees using a gap inversion method","volume":"73","author":"Villalobos","year":"1995","journal-title":"Agric. For. Meteorol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/S0168-1923(01)00284-2","article-title":"A practical scheme for correcting multiple scattering effects on optical LAI measurements","volume":"110","author":"Leblanc","year":"2001","journal-title":"Agric. For. Meteorol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.agrformet.2016.02.001","article-title":"Comparison of optical LAI measurements under diffuse and clear skies after correcting for scattered radiation","volume":"221","author":"Pearse","year":"2016","journal-title":"Agric. For. Meteorol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"981","DOI":"10.1093\/treephys\/14.7-8-9.981","article-title":"Performance of the LAI-2000 plant canopy analyzer in estimating leaf area index of some Scots pine stands","volume":"14","author":"Stenberg","year":"1994","journal-title":"Tree Physiol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1071\/BT9670141","article-title":"A formula for average foliage density","volume":"15","author":"Miller","year":"1967","journal-title":"Aust. J. Bot."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.jhydrol.2013.02.032","article-title":"Estimation of watershed-level distributed forest structure metrics relevant to hydrologic modeling using LiDAR and Landsat","volume":"487","author":"Varhola","year":"2013","journal-title":"J. Hydrol."},{"key":"ref_34","first-page":"53","article-title":"Application of 3D triangulations of airborne laser scanning data to estimate boreal forest leaf area index","volume":"59","author":"Majasalmi","year":"2017","journal-title":"Int. J. Appl. Earth Obs."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Eckrich, C.A., Flaherty, E.A., and Ben-David, M. (2013). Estimating Leaf Area Index in Southeast Alaska: A Comparison of Two Techniques. PLoS ONE, 8.","DOI":"10.1371\/journal.pone.0077642"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1683","DOI":"10.1007\/s00468-016-1400-y","article-title":"Influence of the exclusion distance among trees on gap fraction and foliage clumping index of forest plantations","volume":"30","author":"Geng","year":"2016","journal-title":"Trees"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1781","DOI":"10.1016\/j.agrformet.2009.06.001","article-title":"The computation of foliage clumping index using hemispherical photography","volume":"149","author":"Gonsamo","year":"2009","journal-title":"Agric. For. Meteorol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.agrformet.2004.09.006","article-title":"Methodology comparison for canopy structure parameters extraction from digital hemispherical photography in boreal forests","volume":"129","author":"Leblanc","year":"2005","journal-title":"Agric. For. Meteorol."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/j.agrformet.2010.11.009","article-title":"Comparison of methods for measuring gap size distribution and canopy nonrandomness at J\u00e4rvselja RAMI (RAdiation transfer Model Intercomparison) test sites","volume":"151","author":"Pisek","year":"2011","journal-title":"Agric. For. Meteorol."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/7\/1405\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T14:11:27Z","timestamp":1760364687000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/7\/1405"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,6]]},"references-count":39,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2021,4]]}},"alternative-id":["rs13071405"],"URL":"https:\/\/doi.org\/10.3390\/rs13071405","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4,6]]}}}