{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:58:38Z","timestamp":1760241518797,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,4,11]],"date-time":"2018-04-11T00:00:00Z","timestamp":1523404800000},"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>Bi-directional reflection distribution function (BRDF) defines anisotropy of the surface reflection. It is required to specify the boundary condition for radiative transfer (RT) modeling used in aerosol retrievals, cloud retrievals, atmospheric modeling, and other applications. Ground based measurements of reflected radiance draw increasing attention as a source of information about anisotropy of surface reflection. Derivation of BRDF from surface radiance requires atmospheric correction. This study develops a new method of retrieving BRDF on its whole domain, making it immediately suitable for further atmospheric RT modeling applications. The method is based on the integral equation relating surface-reflected radiance, BRDF, and solutions of two auxiliary atmosphere-only RT problems. The method requires kernel-based BRDF. The weights of the kernels are obtained with a quickly converging iterative procedure. RT modeling has to be done only one time before the start of iterative process.<\/jats:p>","DOI":"10.3390\/rs10040591","type":"journal-article","created":{"date-parts":[[2018,4,11]],"date-time":"2018-04-11T12:16:50Z","timestamp":1523449010000},"page":"591","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Method of Retrieving BRDF from Surface-Reflected Radiance Using Decoupling of Atmospheric Radiative Transfer and Surface Reflection"],"prefix":"10.3390","volume":"10","author":[{"given":"Alexander","family":"Radkevich","sequence":"first","affiliation":[{"name":"Science Systems and Applications, Inc., Hampton, VA 23666, USA"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,11]]},"reference":[{"key":"ref_1","first-page":"493","article-title":"In Situ BRDF Measurements of Selected Surface Materials to Improve Analysis of Remotely Sensed Multispectral Imagery","volume":"31","author":"Meister","year":"1996","journal-title":"ISPRS Arch."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1109\/36.134083","article-title":"Shinnery Oak Bidirectional Reflectance Properties and Canopy Model Inversion","volume":"30","author":"Deering","year":"1992","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"19721","DOI":"10.1029\/98JD01146","article-title":"Ground measurements of the polarized bidirectional reflectance of snow in the near-infrared spectral domain: Comparison with model results","volume":"103","author":"Leroux","year":"1998","journal-title":"J. Geophys. Res."},{"key":"ref_4","first-page":"D18106","article-title":"Spectral bidirectional reflectance of Antarctic snow: Measurements and parameterization","volume":"111","author":"Hudson","year":"2006","journal-title":"J. Geophys. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1109\/JSTARS.2012.2208264","article-title":"Analysis of BRDF and Albedo Retrieved by Kernel-Driven Models Using Field Measurements","volume":"6","author":"Huang","year":"2013","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/S0034-4257(00)00122-X","article-title":"Testing a LiSK BRDF Model with in Situ Bidirectional Reflectance Factor Measurements over Semiarid Grasslands","volume":"74","author":"Chopping","year":"2000","journal-title":"Remote Sens. Environ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1080\/02757250009532399","article-title":"Field and landscape BRDF optical wavelength measurements: Experience, techniques and the future","volume":"18","author":"Walthall","year":"2000","journal-title":"Remote Sens. Rev."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1080\/02757250009532411","article-title":"PARABOLA III\u2014A sphere-scanning radiometer for field determination of surface anisotropic reflectance functions","volume":"19","author":"Bruegge","year":"2000","journal-title":"Remote Sens. Rev."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/0034-4257(94)90080-9","article-title":"Retrieval of surface directional reflectance properties using ground level multiangle measurements","volume":"50","author":"Martonchik","year":"1994","journal-title":"Remote Sens. Environ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"6257","DOI":"10.1029\/1998JD200123","article-title":"A new method of retrieving surface bidirectional reflectance from ground measurements: Atmospheric sensitivity study","volume":"104","author":"Lyapustin","year":"1999","journal-title":"J. Geophys Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3495","DOI":"10.1364\/AO.40.003495","article-title":"Green\u2019s function method for the radiative transfer problem. I. Homogeneous non-Lambertian surface","volume":"40","author":"Lyapustin","year":"2001","journal-title":"Appl. Opt."},{"key":"ref_12","first-page":"D03210","article-title":"Multi-Angle Implementation of Atmospheric Correction (MAIAC): Part 1. Radiative Transfer Basis and Look-Up Tables","volume":"116","author":"Lyapustin","year":"2011","journal-title":"J. Geophys. Res."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.jqsrt.2013.05.007","article-title":"A new look at decoupling of atmospheric radiative transfer and anisotropic surface reflection","volume":"127","author":"Radkevich","year":"2013","journal-title":"JQSRT"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.jqsrt.2017.07.022","article-title":"Iterative discrete ordinates solution of the equation for surface-reflected radiance","volume":"202","author":"Radkevich","year":"2017","journal-title":"JQSRT"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"20455","DOI":"10.1029\/92JD01411","article-title":"A bidirectional reflectance model of the Earth\u2019s surface for the correction of remote sensing data","volume":"97","author":"Roujean","year":"1992","journal-title":"J. Geophys. Res."},{"key":"ref_16","unstructured":"Lewis, P. (1995, January 10\u201314). The utility of kernel-driven BRDF models in global BRDF and albedo studies. Proceedings of the Geoscience and Remote Sensing Symposium, Firenze, Italy."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"977","DOI":"10.1109\/36.841980","article-title":"An algorithm for the retrieval of albedo from space using semiempirical BRDF models","volume":"38","author":"Lucht","year":"2000","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/S0034-4257(02)00100-1","article-title":"Land surface albedo retrieval via kernel-based BRDF modeling: I. Statistical inversion method and model comparison","volume":"84","author":"Pokrovsky","year":"2002","journal-title":"Remote Sens. Environ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1016\/S0034-4257(03)00100-7","article-title":"Detecting vegetation structure using a kernel-based BRDF model","volume":"86","author":"Gao","year":"2003","journal-title":"Remote Sens. Environ."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2184","DOI":"10.1016\/j.rse.2011.04.012","article-title":"Variability in surface BRDF at different spatial scales (30 m\u2013500 m) over a mixed agricultural landscape as retrieved from airborne and satellite spectral measurements","volume":"115","author":"Gatebe","year":"2011","journal-title":"Remote Sens. Environ."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1109\/JSTARS.2010.2048745","article-title":"The Angular and Spectral Kernel Model for BRDF and Albedo Retrieval","volume":"3","author":"Liu","year":"2010","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/B978-0-12-409548-9.10346-X","article-title":"Inversion of Lumped Parameters Using BRDF Kernels","volume":"3","author":"Roujean","year":"2018","journal-title":"Compre Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1072","DOI":"10.1175\/JAS3386.1","article-title":"Airborne Spectral Measurements of Ocean Directional Reflectance","volume":"62","author":"Gatebe","year":"2005","journal-title":"J. Atmos. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/j.rse.2012.09.002","article-title":"Multi-angle implementation of atmospheric correction for MODIS (MAIAC): 3. Atmospheric correction","volume":"127","author":"Lyapustin","year":"2012","journal-title":"Remote Sens. Environ."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1175\/1520-0477(1998)079<0831:OPOAAC>2.0.CO;2","article-title":"Optical Properties of Aerosols and Clouds: The Software Package OPAC","volume":"79","author":"Hess","year":"1998","journal-title":"BAMS"},{"key":"ref_26","unstructured":"Mishchenko, M.I., Travis, L.D., and Lacis, A.A. (2002). Scattering, Absorption, and Emission of Light by Small Particles, Cambridge University Press."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/0034-4257(89)90015-1","article-title":"A reflectance model for the homogeneous plant canopy and its inversion","volume":"27","author":"Nilson","year":"1989","journal-title":"Remote Sens. Environ."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/S0034-4257(02)00091-3","article-title":"First Operational BRDF, Albedo and Nadir Reflectance Products from MODIS","volume":"83","author":"Schaaf","year":"2002","journal-title":"Remote Sens. Environ."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/S0034-4257(02)00101-3","article-title":"Land surface albedo retrieval via kernel-based BRDF modeling: II. An optimal design scheme for the angular sampling","volume":"84","author":"Pokrovsky","year":"2002","journal-title":"Remote Sens. Environ."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0034-4257(98)00031-5","article-title":"AERONET\u2014A federated instrument network and data archive for aerosol characterization","volume":"66","author":"Holben","year":"1998","journal-title":"Remote Sens. Environ."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/4\/591\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:00:20Z","timestamp":1760194820000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/4\/591"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,11]]},"references-count":30,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,4]]}},"alternative-id":["rs10040591"],"URL":"https:\/\/doi.org\/10.3390\/rs10040591","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2018,4,11]]}}}