{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T09:38:47Z","timestamp":1762508327069,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2020,11,28]],"date-time":"2020-11-28T00:00:00Z","timestamp":1606521600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003246","name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","award":["ALWGO.2017.018"],"award-info":[{"award-number":["ALWGO.2017.018"]}],"id":[{"id":"10.13039\/501100003246","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Vegetation radiative transfer models (RTMs) are important tools to understand biosphere-atmosphere interactions. The four-stream theory has been successfully applied to solve the radiative transfer problems in homogeneous canopies for both incident solar radiation, thermal and fluorescence emission since 1984. In this note, we describe the development of a unified radiative transfer theory for optical scattering, thermal and fluorescence emission in multi-layer vegetation canopy, and provide a detailed mathematical derivation for the fluxes inside and leaving the canopy. This theory can be used to develop vegetation models for remote sensing applications and plant physiological processes, such as photosynthesis and transpiration. It can also be used to solve the radiative transfer problems in soil-water, soil-water-atmosphere, or soil-vegetation-atmosphere ensembles, besides the soil-vegetation system presented in the note.<\/jats:p>","DOI":"10.3390\/rs12233914","type":"journal-article","created":{"date-parts":[[2020,11,29]],"date-time":"2020-11-29T21:00:57Z","timestamp":1606683657000},"page":"3914","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Unified Four-Stream Radiative Transfer Theory in the Optical-Thermal Domain with Consideration of Fluorescence for Multi-Layer Vegetation Canopies"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4377-8560","authenticated-orcid":false,"given":"Peiqi","family":"Yang","sequence":"first","affiliation":[{"name":"Faculty of Geo-Information Science and Earth Observation (ITC), University of Twente, 7514AE Enschede, The Netherlands"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4696-2144","authenticated-orcid":false,"given":"Wout","family":"Verhoef","sequence":"additional","affiliation":[{"name":"Faculty of Geo-Information Science and Earth Observation (ITC), University of Twente, 7514AE Enschede, The Netherlands"}]},{"given":"Christiaan","family":"van der Tol","sequence":"additional","affiliation":[{"name":"Faculty of Geo-Information Science and Earth Observation (ITC), University of Twente, 7514AE Enschede, The Netherlands"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/0034-4257(90)90100-Z","article-title":"PROSPECT: A model of leaf optical properties spectra","volume":"34","author":"Jacquemoud","year":"1990","journal-title":"Remote Sens. Environ."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Li, X., and Strahler, A.H. (1986). Geometric-optical bidirectional reflectance modeling of a conifer forest canopy. IEEE Trans. Geosci. Remote Sens., 906\u2013919.","DOI":"10.1109\/TGRS.1986.289706"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1109\/36.752217","article-title":"An analytical hybrid GORT model for bidirectional reflectance over discontinuous plant canopies","volume":"37","author":"Ni","year":"1999","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1364\/JOSA.60.000372","article-title":"Plant-canopy irradiance specified by the Duntley equations","volume":"60","author":"Allen","year":"1970","journal-title":"JOSA"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/0034-4257(71)90085-X","article-title":"The calculation of the directional reflectance of a vegetative canopy","volume":"2","author":"Suits","year":"1971","journal-title":"Remote Sens. Environ."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/0034-4257(84)90057-9","article-title":"Light scattering by leaf layers with application to canopy reflectance modeling: The SAIL model","volume":"16","author":"Verhoef","year":"1984","journal-title":"Remote Sens. Environ."},{"key":"ref_7","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. Transf."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.agrformet.2012.10.004","article-title":"Canopy vertical heterogeneity plays a critical role in reflectance simulation","volume":"169","author":"Wang","year":"2013","journal-title":"Agric. For. Meteorol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.rse.2017.08.029","article-title":"The mSCOPE model: A simple adaptation to the SCOPE model to describe reflectance, fluorescence and photosynthesis of vertically heterogeneous canopies","volume":"201","author":"Yang","year":"2017","journal-title":"Remote Sens. Environ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/0034-4257(95)00253-7","article-title":"Modeling radiative transfer in heterogeneous 3-D vegetation canopies","volume":"58","author":"Demarez","year":"1996","journal-title":"Remote Sens. Environ."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"946","DOI":"10.1109\/36.508411","article-title":"Three-dimensional forest light interaction model using a Monte Carlo method","volume":"34","author":"North","year":"1996","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"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":"61","DOI":"10.1016\/0034-4257(92)90140-F","article-title":"Interaction of photons in a canopy of finite-dimensional leaves","volume":"39","author":"Knyazikhin","year":"1992","journal-title":"Remote Sens. Environ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1667","DOI":"10.3390\/rs70201667","article-title":"Discrete anisotropic radiative transfer (DART 5) for modeling airborne and satellite spectroradiometer and LIDAR acquisitions of natural and urban landscapes","volume":"7","author":"Yin","year":"2015","journal-title":"Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/0034-4257(85)90072-0","article-title":"Earth observation modeling based on layer scattering matrices","volume":"17","author":"Verhoef","year":"1985","journal-title":"Remote Sens. Environ."},{"key":"ref_16","unstructured":"Verhoef, W. (1998). Theory of Radiative Transfer Models Applied in Optical Remote Sensing of Vegetation Canopies, Wageningen University."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1808","DOI":"10.1109\/TGRS.2007.895844","article-title":"Unified optical-thermal four-stream radiative transfer theory for homogeneous vegetation canopies","volume":"45","author":"Verhoef","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1016\/j.cageo.2005.08.010","article-title":"FluorMODgui V3. 0: A graphic user interface for the spectral simulation of leaf and canopy chlorophyll fluorescence","volume":"32","author":"Miller","year":"2006","journal-title":"Comput. Geosci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3109","DOI":"10.5194\/bg-6-3109-2009","article-title":"An integrated model of soil-canopy spectral radiances, photosynthesis, fluorescence, temperature and energy balance","volume":"6","author":"Verhoef","year":"2009","journal-title":"BIogeosciences"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"111292","DOI":"10.1016\/j.rse.2019.111292","article-title":"The scattering and re-absorption of red and near-infrared chlorophyll fluorescence in the models Fluspect and SCOPE","volume":"232","author":"Vilfan","year":"2019","journal-title":"Remote Sens. Environ."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1007\/BF00386231","article-title":"A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species","volume":"149","author":"Farquhar","year":"1980","journal-title":"Planta"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/j.rse.2006.12.013","article-title":"Coupled soil\u2013leaf-canopy and atmosphere radiative transfer modeling to simulate hyperspectral multi-angular surface reflectance and TOA radiance data","volume":"109","author":"Verhoef","year":"2007","journal-title":"Remote Sens. Environ."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Kuusk, A. (1991). The hot spot effect in plant canopy reflectance. Photon-Vegetation Interactions, Springer.","DOI":"10.1007\/978-3-642-75389-3_5"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.rse.2014.07.022","article-title":"Two-stream remote sensing model for water quality mapping: 2SeaColor","volume":"157","author":"Salama","year":"2015","journal-title":"Remote Sens. Environ."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"111870","DOI":"10.1016\/j.rse.2020.111870","article-title":"The SPART model: A soil-plant-atmosphere radiative transfer model for satellite measurements in the solar spectrum","volume":"247","author":"Yang","year":"2020","journal-title":"Remote Sens. Environ."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/23\/3914\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:38:59Z","timestamp":1760179139000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/23\/3914"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,28]]},"references-count":25,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["rs12233914"],"URL":"https:\/\/doi.org\/10.3390\/rs12233914","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2020,11,28]]}}}