{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T18:37:44Z","timestamp":1761676664771,"version":"build-2065373602"},"reference-count":54,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,10,1]],"date-time":"2018-10-01T00:00:00Z","timestamp":1538352000000},"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":["41230747, 41271346, 41571329, 91425301, 41501359, 41271354"],"award-info":[{"award-number":["41230747, 41271346, 41571329, 91425301, 41501359, 41271354"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The Clumping Index (\u03a9) was introduced to quantify the spatial distribution pattern of vegetation elements. It is crucial to improve the estimation accuracy of vital vegetation parameters, such as Leaf Area Index (LAI) and Gross Primary Production (GPP). Meanwhile, the parameterization of \u03a9 is challenging partly due to the varying observations of canopy gaps from different view angles. Many previous studies have shown the increase of \u03a9 with view zenith angle through samples of gap size distribution from in situ measurements. In contrast, remote sensing retrieval algorithms only assign a constant value for each biome type to roughly correct the clumping effect as a compromise between the accuracy and efficiency. In this paper, analytical models are proposed that estimate the directional clumping index (\u03a9(\u03b8)) of crop and forest at canopy level. The angular variation trend and magnitude of crop \u03a9(\u03b8) was analyzed within row structure where vegetation elements are randomly spaced along rows. The forest model predicts \u03a9(\u03b8) with tree density, distribution pattern, crown shape, trunk size, and leaf area and angle distribution function. The models take into account the main directional characteristics of clumping index using easy-to-measure parameters. Test cases showed that \u03a9(\u03b8) magnitude variation for black spruce forest was 102.3% of the hemispherical average clumping index (    \u03a9 \u02dc    ), whereas the Larch forest had 48.7% variation, and row crop variation reached 32.4%. This study provided tools to assess \u03a9(\u03b8) of discontinuous canopies.<\/jats:p>","DOI":"10.3390\/rs10101576","type":"journal-article","created":{"date-parts":[[2018,10,2]],"date-time":"2018-10-02T08:23:50Z","timestamp":1538468630000},"page":"1576","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Modeling the Directional Clumping Index of Crop and Forest"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6512-2066","authenticated-orcid":false,"given":"Jingjing","family":"Peng","sequence":"first","affiliation":[{"name":"Earth System Science Interdisciplinary Center\/Cooperative Institute for Climate and Satellites-Maryland, University of Maryland, College Park, MD 20742, USA"}]},{"given":"Wenjie","family":"Fan","sequence":"additional","affiliation":[{"name":"Institute of RS and GIS, Peking University, Beijing 100871, China"},{"name":"Beijing Key Laboratory of Spatial Information Integration &amp; Its Applications, Beijing 100871, China"}]},{"given":"Lizhao","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Civil and Environmental Engineering, University of Maryland, College Park, MD 20742, USA"}]},{"given":"Xiru","family":"Xu","sequence":"additional","affiliation":[{"name":"Institute of RS and GIS, Peking University, Beijing 100871, China"},{"name":"Beijing Key Laboratory of Spatial Information Integration &amp; Its Applications, Beijing 100871, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1413-9199","authenticated-orcid":false,"given":"Jvcai","family":"Li","sequence":"additional","affiliation":[{"name":"Institute of RS and GIS, Peking University, Beijing 100871, China"},{"name":"Beijing Key Laboratory of Spatial Information Integration &amp; Its Applications, Beijing 100871, China"}]},{"given":"Beitong","family":"Zhang","sequence":"additional","affiliation":[{"name":"Institute of RS and GIS, Peking University, Beijing 100871, China"}]},{"given":"Dingfang","family":"Tian","sequence":"additional","affiliation":[{"name":"Institute of RS and GIS, Peking University, Beijing 100871, China"},{"name":"Beijing Key Laboratory of Spatial Information Integration &amp; Its Applications, Beijing 100871, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1016\/S0034-4257(02)00150-5","article-title":"Multi-angular optical remote sensing for assessing vegetation structure and carbon absorption","volume":"84","author":"Chen","year":"2003","journal-title":"Remote Sens. Environ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1341","DOI":"10.1016\/j.agrformet.2008.03.011","article-title":"Assessing the effects of the clumping phenomenon on BRDF of a maize crop based on 3D numerical scenes using DART model","volume":"148","author":"Duthoit","year":"2008","journal-title":"Agric. For. Meteorol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.landurbplan.2014.04.006","article-title":"Influence of canopy structural characteristics on cooling and humidifying effects of Populus tomentosa community on calm sunny summer days","volume":"127","author":"Qin","year":"2014","journal-title":"Landsc. Urban Plan."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1016\/j.rse.2005.05.003","article-title":"Global mapping of foliage clumping index using multi-angular satellite data","volume":"97","author":"Chen","year":"2005","journal-title":"Remote Sens. Environ."},{"key":"ref_5","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: Part I. Theories, sensors and hemispherical photography","volume":"121","author":"Jonckheere","year":"2004","journal-title":"Agric. For. Meteorol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/0168-1923(94)90107-4","article-title":"A comparison of optical and direct methods for estimating foliage surface area index in forests","volume":"71","author":"Fassnacht","year":"1994","journal-title":"Agric. For. Meteorol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/S0168-1923(99)00114-8","article-title":"Inversion of gap frequency data in forest stands","volume":"98\u201399","author":"Nilson","year":"1999","journal-title":"Agric. For. Meteorol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1316","DOI":"10.1109\/36.628798","article-title":"A four-scale bidirectional reflectance model based on canopy architecture","volume":"35","author":"Chen","year":"1997","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/j.isprsjprs.2010.03.002","article-title":"Expanding global mapping of the foliage clumping index with multi-angular POLDER three measurements: Evaluation and topographic compensation","volume":"65","author":"Pisek","year":"2010","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_10","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_11","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1093\/oxfordjournals.aob.a083148","article-title":"Comparative physiological studies on the growth of field crops: I. Variation in net assimilation rate and leaf area between species and varieties, and within and between years","volume":"11","author":"Watson","year":"1947","journal-title":"Ann. Bot."},{"key":"ref_12","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_13","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_14","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_15","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","year":"2003","journal-title":"J. Exp. Bot."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"29455","DOI":"10.1029\/97JD01175","article-title":"Characterizing canopy nonrandomness with a multiband vegetation imager (MVI)","volume":"102","author":"Kucharik","year":"1997","journal-title":"J. Geophys. Res. Atmos. (1984\u20132012)"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"375","DOI":"10.2307\/2402028","article-title":"Photosynthesis in Sitka spruce (Picea sitchensis (Bong.) Carr.). III. Measurements of canopy structure and interception of radiation","volume":"11","author":"Norman","year":"1974","journal-title":"J. Appl. Ecol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/0168-1923(95)02291-0","article-title":"Optically-based methods for measuring seasonal variation of leaf area index in boreal conifer stands","volume":"80","author":"Chen","year":"1996","journal-title":"Agric. For. Meteorol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1016\/j.agrformet.2010.01.009","article-title":"On the correct estimation of effective leaf area index: Does it reveal information on clumping effects?","volume":"150","author":"Ryu","year":"2010","journal-title":"Agric. For. Meteorol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1158","DOI":"10.1111\/j.1365-3040.2005.01353.x","article-title":"Foliage randomness and light interception in 3-D digitized trees: An analysis from multiscale discretization of the canopy","volume":"28","author":"Sinoquet","year":"2005","journal-title":"Plant Cell Environ."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1093\/treephys\/19.11.695","article-title":"Characterization of radiation regimes in nonrandom forest canopies: Theory, measurements, and a simplified modeling approach","volume":"19","author":"Kucharik","year":"1999","journal-title":"Tree Physiol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1016\/0034-4257(94)00059-V","article-title":"A fast, invertible canopy reflectance model","volume":"51","author":"Kuusk","year":"1995","journal-title":"Remote Sens. Environ."},{"key":"ref_23","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_24","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_25","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.rse.2004.02.007","article-title":"Evaluation of the MODIS LAI algorithm at a coniferous forest site in Finland","volume":"91","author":"Wang","year":"2004","journal-title":"Remote Sens. Environ."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.rse.2011.12.008","article-title":"Global clumping index map derived from the MODIS BRDF product","volume":"119","author":"He","year":"2012","journal-title":"Remote Sens. Environ."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.rse.2013.07.014","article-title":"Retrieving vegetation clumping index from Multi-angle Imaging SpectroRadiometer (MISR) data at 275m resolution","volume":"138","author":"Pisek","year":"2013","journal-title":"Remote Sens. Environ."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.agrformet.2014.10.011","article-title":"Shortwave radiation transfer through a plant canopy covered by single and double layers of plastic","volume":"201","author":"Graefe","year":"2015","journal-title":"Agric. For. Meteorol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.agrformet.2015.02.018","article-title":"On the angular dependency of canopy gap fractions in pine, spruce and birch stands","volume":"206","author":"Rautiainen","year":"2015","journal-title":"Agric. For. Meteorol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"5178","DOI":"10.1080\/01431161.2015.1049383","article-title":"The effect of clumping on canopy scattering and its directional properties: A model simulation using spectral invariants","volume":"36","author":"Stenberg","year":"2015","journal-title":"Int. J. Remote Sens."},{"key":"ref_31","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_32","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.foreco.2014.12.026","article-title":"Influence of woody tissue and leaf clumping on vertically resolved leaf area index and angular gap probability estimates","volume":"340","author":"Piayda","year":"2015","journal-title":"For. Ecol. Manag."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Chen, J.M., Mo, G., Pisek, J., Liu, J., Deng, F., Ishizawa, M., and Chan, D. (2012). Effects of foliage clumping on the estimation of global terrestrial gross primary productivity. Glob. Biogeochem. Cycles, 26.","DOI":"10.1029\/2010GB003996"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Leblanc, S.G., Fernandes, R., and Chen, J.M. (2002, January 24\u201328). Recent advancements in optical field leaf area index, foliage heterogeneity, and foliage angular distribution measurements. Proceedings of the 2002 IEEE International Geoscience and Remote Sensing Symposium (IGARSS\u201902), Toronto, ON, Canada.","DOI":"10.4095\/219868"},{"key":"ref_35","first-page":"67","article-title":"Examination of the extinction coefficient in the Beer-Lambert law for an accurate estimation of the forest canopy leaf area index","volume":"8","author":"Saitoh","year":"2012","journal-title":"For. Sci. Technol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/0168-1923(93)90005-3","article-title":"Evaluation of structure description requirements for predicting gap fraction of vegetation canopies","volume":"65","author":"Andrieu","year":"1993","journal-title":"Agric. For. Meteorol."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1709","DOI":"10.1007\/s11430-010-4078-9","article-title":"Crop area and leaf area index simultaneous retrieval based on spatial scaling transformation","volume":"53","author":"Fan","year":"2010","journal-title":"Sci. China Earth Sci."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"15536","DOI":"10.3390\/rs71115536","article-title":"Estimating Crop Albedo in the Application of a Physical Model Based on the Law of Energy Conservation and Spectral Invariants","volume":"7","author":"Peng","year":"2015","journal-title":"Remote Sens."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"906","DOI":"10.1109\/TGRS.1986.289706","article-title":"Geometric-optical bidirectional reflectance modeling of a conifer forest canopy","volume":"6","author":"Li","year":"1986","journal-title":"IEEE Trans. Geosci. Remote"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1007\/s11430-016-5082-6","article-title":"A unified model of bidirectional reflectance distribution function for the vegetation canopy","volume":"60","author":"Xu","year":"2017","journal-title":"Sci. China Earth Sci."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"824","DOI":"10.1007\/s11430-012-4380-9","article-title":"A unified canopy bidirectional reflectance (BRDF) model for row ceops","volume":"55","author":"Yan","year":"2012","journal-title":"Sci. China Earth Sci."},{"key":"ref_42","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":"Agric. Meteorol."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/0034-4257(95)00195-6","article-title":"Retrieving leaf area index of boreal conifer forests using Landsat TM images","volume":"55","author":"Chen","year":"1996","journal-title":"Remote Sens. Environ."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1111\/jvs.12361","article-title":"Spatial distribution and association patterns in a tropical evergreen broad-leaved forest of north-central Vietnam","volume":"27","author":"Nguyen","year":"2015","journal-title":"J. Veg. Sci."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/0034-4257(91)90024-Z","article-title":"A forest canopy reflectance model and a test case","volume":"37","author":"Nilson","year":"1991","journal-title":"Remote Sens. Environ."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/BF00033451","article-title":"Spatial analysis of density dependent pattern in coniferous forest stands","volume":"64","author":"Franklin","year":"1985","journal-title":"Vegetatio"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1214\/aoms\/1177732245","article-title":"On a new class of \u201ccontagious\u201d distributions, applicable in entomology and bacteriology","volume":"10","author":"Neyman","year":"1939","journal-title":"Ann. Math. Stat."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Li, J., Fan, W., Liu, Y., Zhu, G., Peng, J., and Xu, X. (2016). Estimating Savanna Clumping Index Using Hemispherical Photographs Integrated with High Resolution Remote Sensing Images. Remote Sens., 9.","DOI":"10.3390\/rs9010052"},{"key":"ref_49","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_50","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/j.rse.2004.05.010","article-title":"Lidar remote sensing for modeling gross primary production of deciduous forests","volume":"92","author":"Kotchenova","year":"2004","journal-title":"Remote Sens. Environ."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Ross, J.K. (1981). The Radiation Regime and the Architecture of Plant Stands, Junk W. In Pubs.","DOI":"10.1007\/978-94-009-8647-3"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1016\/j.rse.2007.06.011","article-title":"A voxel-based lidar method for estimating crown base height for deciduous and pine trees","volume":"112","author":"Popescu","year":"2008","journal-title":"Remote Sens. Environ."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.foreco.2014.04.027","article-title":"Canopy space filling and tree crown morphology in mixed-species stands compared with monocultures","volume":"327","author":"Pretzsch","year":"2014","journal-title":"For. Ecol. Manag."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/0169-2046(88)90017-5","article-title":"Geometric solids for simulation of tree crowns","volume":"15","author":"McPherson","year":"1988","journal-title":"Landsc. Urban Plan."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/10\/1576\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:23:32Z","timestamp":1760196212000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/10\/1576"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,1]]},"references-count":54,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2018,10]]}},"alternative-id":["rs10101576"],"URL":"https:\/\/doi.org\/10.3390\/rs10101576","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2018,10,1]]}}}