{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T11:13:46Z","timestamp":1774350826814,"version":"3.50.1"},"reference-count":56,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,10,20]],"date-time":"2018-10-20T00:00:00Z","timestamp":1539993600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["14-14-00956"],"award-info":[{"award-number":["14-14-00956"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The paper introduces a three-dimensional model to derive the spatial patterns of photosynthetically active radiation (PAR) reflected and absorbed by a non-uniform forest canopy with a multi-species structure, as well as a model algorithm application to retrieve forest canopy composition from reflected PAR measured along some trajectory above the forest stand. This radiative transfer model is based on steady-state transport equations, initially suggested by Ross, and considers the radiative transfer as a function of the structure of individual trees and forest canopy, optical properties of photosynthesizing and non-photosynthesizing parts of the different tree species, soil reflection, and the ratio of incoming direct and diffuse solar radiation. Numerical experiments showed that reflected solar radiation of a typical mixed forest stand consisting of coniferous and deciduous tree species was strongly governed by canopy structure, soil properties and sun elevation. The suggested algorithm based on the developed model allows for retrieving the proportion of different tree species in a mixed forest stand from measured canopy reflection coefficients. The method accuracy strictly depends on the number of points for canopy reflection measurements.<\/jats:p>","DOI":"10.3390\/rs10101661","type":"journal-article","created":{"date-parts":[[2018,10,23]],"date-time":"2018-10-23T08:43:36Z","timestamp":1540284216000},"page":"1661","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Application of a Three-Dimensional Radiative Transfer Model to Retrieve the Species Composition of a Mixed Forest Stand from Canopy Reflected Radiation"],"prefix":"10.3390","volume":"10","author":[{"given":"Natalia","family":"Levashova","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5140-3617","authenticated-orcid":false,"given":"Dmitry","family":"Lukyanenko","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1968-5404","authenticated-orcid":false,"given":"Yulia","family":"Mukhartova","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia"}]},{"given":"Alexander","family":"Olchev","sequence":"additional","affiliation":[{"name":"Department of Meteorology and Climatology, Faculty of Geography, Lomonosov Moscow State University, Moscow 119991, Russia"},{"name":"Laboratory of Biogeocenology, A.N.Severtsov Institute of Ecology and Evolution, Russian Academy of Science, Moscow 119071, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,20]]},"reference":[{"key":"ref_1","unstructured":"Ross, J. (1981). The Radiation Regime and Architecture of Plant Stands, Dr. W. Junk Publishers. ISBN-13 978-94-009-8649-7."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0065-2504(08)60063-X","article-title":"CO2 fluxes over plant canopies and solar radiation: A review","volume":"26","author":"Ruimy","year":"1995","journal-title":"Adv. Ecol. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1146\/annurev-earth-060614-105156","article-title":"Inference of climate sensitivity from analysis of earth\u2019s energy budget","volume":"44","author":"Forster","year":"2016","journal-title":"Annu. Rev. Earth Planet. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1038\/nclimate3278","article-title":"Energy budget constraints on climate sensitivity in light of inconstant climate feedbacks","volume":"7","author":"Armour","year":"2017","journal-title":"Nat. Clim. Chang."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Myneni, R., and Ross, J. (1991). Approximate analytical methods for calculating the reflection functions of leaf canopies in remote sensing applications. Photon Vegetation Interactions. Applications in Optical Remote Sensing and Plant Ecology, Springer. ISBN-13 978-3-642-75391-6.","DOI":"10.1007\/978-3-642-75389-3"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"10985","DOI":"10.1029\/JD092iD09p10985","article-title":"Radiation transfer in plant canopies: Transmission of direct solar radiation and the role of leaf orientation","volume":"92","author":"Verstraete","year":"1987","journal-title":"J. Geophys. Rev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0168-1923(89)90002-6","article-title":"A review on the theory of photon transport in leaf canopies","volume":"45","author":"Myneni","year":"1989","journal-title":"Agric. For. Meteorol."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Myneni, R., and Ross, J. (1991). Fundamental equations of radiative transfer in leaf canopies, and iterative methods of their solution. Photon Vegetation Interactions. Applications in Optical Remote Sensing and Plant Ecology, Springer. ISBN-13 978-3-642-75391-6.","DOI":"10.1007\/978-3-642-75389-3"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/0168-1923(91)90069-3","article-title":"Modelling radiative transfer and photosynthesis in three dimensional vegetation canopies","volume":"55","author":"Myneni","year":"1991","journal-title":"Agric. For. Meteorol."},{"key":"ref_10","first-page":"9","article-title":"Canopy radiative transfer modeling","volume":"Volume 3","author":"Liang","year":"2018","journal-title":"Comprehensive Remote Sensing"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1016\/S0034-4257(99)00111-X","article-title":"A directional multispectral forest reflectance model","volume":"72","author":"Kuusk","year":"2000","journal-title":"Remote Sens. Environ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1080\/02757250009532389","article-title":"Monte Carlo ray tracing in optical canopy reflectance modelling","volume":"18","author":"Disney","year":"2000","journal-title":"Remote Sens. Rev."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0022-4073(01)00007-3","article-title":"A two-layer canopy reflectance model","volume":"71","author":"Kuusk","year":"2001","journal-title":"J. Quant. Spectrosc. Radiat. Transfer"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/S0034-4257(03)00143-3","article-title":"Simulation of hyperspectral and directional radiance images using coupled biophysical and atmospheric radiative transfer models","volume":"87","author":"Verhoef","year":"2003","journal-title":"Remote Sens. Environ."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"D02116","DOI":"10.1029\/2005JD005952","article-title":"Simplifying the interaction of land surfaces with radiation for relating remote sensing products to climate models","volume":"111","author":"Pinty","year":"2006","journal-title":"Atmospheres"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"D09111","DOI":"10.1029\/2006JD007821","article-title":"Third radiation transfer model intercomparison (RAMI) exercise: Documenting progress in canopy reflectance models","volume":"112","author":"Widlowski","year":"2007","journal-title":"Atmospheres"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"G02019","DOI":"10.1029\/2010JG001511","article-title":"RAMI4PILPS. An Intercomparison of Formulations for the Partitioning of Solar Radiation in Land Surface Models","volume":"116","author":"Widlowski","year":"2011","journal-title":"Geophys. Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"630","DOI":"10.1175\/1520-0469(1980)037<0630:TSATRT>2.0.CO;2","article-title":"Two-stream approximations to radiative transfer in planetary atmospheres: A unified description of existing methods and a new improvement","volume":"37","author":"Meador","year":"1980","journal-title":"J. Atmos. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/S0065-2687(08)60176-4","article-title":"Land surface processes and climate-surface albedos and energy balance","volume":"25","author":"Dickinson","year":"1983","journal-title":"Adv. Geophys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/02757258809532105","article-title":"Models of vegetation canopy reflectance and their use in estimation of biophysical parameters from reflectance data","volume":"4","author":"Goel","year":"1988","journal-title":"Remote Sens. Rev."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/0961-9534(96)00010-4","article-title":"Modelling three-dimensional distribution of photosynthetically active radiation in sloping coniferous stands","volume":"11","author":"Knyazikhin","year":"1996","journal-title":"Biomass Bioenergy"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/S0168-1923(97)00036-1","article-title":"Small-scale study of three-dimensional distribution of photosynthetically active radiation in a forest","volume":"88","author":"Knyazikhin","year":"1997","journal-title":"Agric. For. Meteorol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1127\/metz\/8\/1999\/107","article-title":"Is forest albedo measured correctly?","volume":"8","author":"Gravenhorst","year":"1999","journal-title":"Meteorol. Z."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"11937","DOI":"10.1029\/2000JD900493","article-title":"Radiation transfer model intercomparison (RAMI) exercise","volume":"106","author":"Pinty","year":"2001","journal-title":"Atmospheres"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Myneni, R.B., and Ross, J. (1991). and Myneni, R.B. Applications of Radiative Transfer Models for Remote Sensing of Vegetation Conditions and States. Photon-Vegetation Interactions: Applications in Optical Remote Sensing and Plant Physiology, Springer.","DOI":"10.1007\/978-3-642-75389-3"},{"key":"ref_26","unstructured":"Gholz, H., Nakane, K., and Shimoda, H. (1997). Modeling radiative transfer through forest canopies: Implications for canopy photosynthesis and remote sensing. The Use of Remote Sensing in the Modeling of Forest Productivity, Kluwer."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.jqsrt.2017.01.015","article-title":"The spectral invariant approximation within canopy radiative transfer to support the use of the EPIC\/DSCOVR oxygen B-band for monitoring vegetation","volume":"191","author":"Marshak","year":"2017","journal-title":"J. Quant. Spectrosc. Radiat. Trans."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.rse.2017.05.033","article-title":"Estimation of leaf area index and its sunlit portion from DSCOVR EPIC data: Theoretical basis","volume":"198","author":"Yang","year":"2017","journal-title":"Remote Sens. Environ."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1058","DOI":"10.1002\/2017GL076622","article-title":"Recent Changes in Global Photosynthesis and Terrestrial Ecosystem Respiration Constrained from Multiple Observations","volume":"45","author":"Li","year":"2018","journal-title":"Geophys. Res. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1080\/00411459008203890","article-title":"Radiative transfer in three dimensional leaf canopies","volume":"19","author":"Myneni","year":"1990","journal-title":"Transp. Theory Stat. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Marshak, A., and Davis, A.B. (2005). Three dimensional radiative transfer in vegetation canopies. Three Dimensional Radiative Transfer in the Cloudy Atmosphere, Springer.","DOI":"10.1007\/3-540-28519-9"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1080\/2150704X.2013.782112","article-title":"Optical properties of leaves and needles for boreal tree species in Europe","volume":"4","author":"Stenberg","year":"2013","journal-title":"Remote Sens. Lett."},{"key":"ref_33","unstructured":"Abakumova, M., Gorbarenko, E.V., Nezval, E.I., and Shilovzeva, O.A. (2012). Climatological Resources of Solar Energy in Moscow Region, Librocom. (In Russian)."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Myneni, R., and Ross, J. (1991). Discrete Ordinates Method for Photon Transport in Leaf Canopies. Photon Vegetation Interactions. Applications in Optical Remote Sensing and Plant Ecology, Springer. ISBN-13 978-3-642-75391-6.","DOI":"10.1007\/978-3-642-75389-3"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/0041-5553(75)90133-0","article-title":"Values of the nodes and weights of ninth to seventeenth order Gauss-Markov quadrature formulae invariant under the octahedron group with inversion","volume":"15","author":"Lebedev","year":"1975","journal-title":"USSR Comput. Math. Math. Phys."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Tikhonov, A.N., Goncharsky, A.V., Stepanov, V.V., and Yagola, A.G. (1995). Numerical Methods for the Solution of Ill-Posed Problems, Kluwer Academic Publishers.","DOI":"10.1007\/978-94-015-8480-7"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1029\/96GB00349","article-title":"TURC: A diagnostic model of continental gross primary productivity and net primary productivity","volume":"10","author":"Ruimy","year":"1996","journal-title":"Global Biogeochem. Cycles"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1641\/0006-3568(2004)054[0547:ACSMOG]2.0.CO;2","article-title":"A continuous satellite derived measure of global terrestrial primary production","volume":"54","author":"Running","year":"2004","journal-title":"BioScience"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1016\/j.rse.2003.11.008","article-title":"Satellite-based modeling of gross primary production in an evergreen needleleaf forest","volume":"89","author":"Xiao","year":"2004","journal-title":"Remote Sens. Environ."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1093\/treephys\/28.4.499","article-title":"Variation in photosynthetic light-use efficiency in a mountainous tropical rain forest in Indonesia","volume":"28","author":"Ibrom","year":"2008","journal-title":"Tree Physiol."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1002\/qj.49710644911","article-title":"The albedo of a tropical evergreen forest","volume":"106","author":"Pinker","year":"1980","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1175\/1520-0442(1997)010<0919:OOAARB>2.0.CO;2","article-title":"Observations of albedo and radiation balance over postforest land surfaces in the eastern Amazon basin","volume":"10","author":"Giambelluca","year":"1997","journal-title":"J. Clim."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"959","DOI":"10.1175\/1520-0450(1987)026<0959:HRVOVC>2.0.CO;2","article-title":"Hemispherical reflectance variations of vegetation canopies and implications for global and regional energy budget studies","volume":"26","author":"Kimes","year":"1987","journal-title":"J. Clim. Appl. Meteorol."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1175\/1520-0450(2000)039<0231:TIOTDV>2.0.CO;2","article-title":"Diurnal Variation of Albedo on the Remote Sensing of the Daily Mean Albedo of Grassland","volume":"39","author":"Grant","year":"2000","journal-title":"J. Clim. Appl. Meteorol."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s13595-012-0246-8","article-title":"Asymmetric competition increases leaf inclination effect on light absorption in mixed canopies","volume":"70","author":"Simioni","year":"2013","journal-title":"Ann. For. Sci."},{"key":"ref_46","first-page":"193","article-title":"Ein Model f\u00fcr die Kronenraumstruktur und die r\u00e4umliche Verteilung der Nadeloberflache in einem Fichtenbestand","volume":"165","author":"Kranigk","year":"1994","journal-title":"Allg. For. Jagdztg."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"32257","DOI":"10.1029\/98JD02462","article-title":"Synergistic algorithm for estimating vegetation canopy leaf area index and fraction of absorbed photosynthetically active radiation from MODIS and MISR data","volume":"103","author":"Knyazikhin","year":"1998","journal-title":"J. Geophys. Res."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1080\/02757250009532396","article-title":"Inversion methods for physically-based models","volume":"18","author":"Kimes","year":"2000","journal-title":"Remote Sens. Rev."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"8436","DOI":"10.3390\/rs70708436","article-title":"Mapping Forest Canopy Height over Continental China Using Multi-Source Remote Sensing Data","volume":"7","author":"Ni","year":"2015","journal-title":"Remote Sens."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1441","DOI":"10.1038\/s41467-017-01530-3","article-title":"Mapping functional diversity from remotely sensed morphological and physiological forest traits","volume":"8","author":"Schneider","year":"2017","journal-title":"Nat. Commun."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Shen, X., and Cao, L. (2017). Tree-species classification in subtropical forests using airborne hyperspectral and LiDAR data. Remote Sens., 9.","DOI":"10.3390\/rs9111180"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/S0034-4257(98)00035-2","article-title":"Determining forest species composition using high spectral resolution remote sensing data","volume":"65","author":"Martin","year":"1998","journal-title":"Remote Sens. Environ."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"4515","DOI":"10.3390\/rs6054515","article-title":"Evaluating the potential of WorldView-2 data to classify tree species and different levels of ash mortality","volume":"6","author":"Waser","year":"2014","journal-title":"Remote Sens."},{"key":"ref_54","first-page":"468","article-title":"Using Lagrange principle for solving linear ill-posed problems with a priori information","volume":"14","author":"Zhang","year":"2013","journal-title":"Numer. Methods Program."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1080\/17415977.2012.700711","article-title":"Recovering aerosol particle size distribution function on the set of bounded piecewise-convex functions","volume":"21","author":"Wang","year":"2013","journal-title":"Inverse Probl. Sci. Eng."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1515\/jiip-2014-0047","article-title":"An optimal regularization method for convolution equations on the source wise represented set","volume":"23","author":"Zhang","year":"2015","journal-title":"J. Inverse Ill-Posed Probl."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/10\/1661\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:26:55Z","timestamp":1760196415000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/10\/1661"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,20]]},"references-count":56,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2018,10]]}},"alternative-id":["rs10101661"],"URL":"https:\/\/doi.org\/10.3390\/rs10101661","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,20]]}}}