{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T03:33:35Z","timestamp":1775792015891,"version":"3.50.1"},"reference-count":129,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,2,27]],"date-time":"2018-02-27T00:00:00Z","timestamp":1519689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Chinese Natural Science Foundation Project","award":["41671363"],"award-info":[{"award-number":["41671363"]}]},{"name":"Chinese Natural Science Foundation Project","award":["41331171"],"award-info":[{"award-number":["41331171"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Rugged terrain, including mountains, hills, and some high lands are typical land surfaces around the world. As a physical parameter for characterizing the anisotropic reflectance of the land surface, the importance of the bidirectional reflectance distribution function (BRDF) has been gradually recognized in the remote sensing community, and great efforts have been dedicated to build BRDF models over various terrain types. However, on rugged terrain, the topography intensely affects the shape and magnitude of the BRDF and creates challenges in modeling the BRDF. In this paper, after a brief introduction of the theoretical background of the BRDF over rugged terrain, the status of estimating land surface BRDF properties over rugged terrain is comprehensively reviewed from a historical perspective and summarized in two categories: BRDFs describing solo slopes and those describing composite slopes. The discussion focuses on land surface reflectance retrieval over mountainous areas, the difference in solo slope and composite slope BRDF models, and suggested future research to improve the accuracy of BRDFs derived with remote sensing satellites.<\/jats:p>","DOI":"10.3390\/rs10030370","type":"journal-article","created":{"date-parts":[[2018,2,27]],"date-time":"2018-02-27T14:18:08Z","timestamp":1519741088000},"page":"370","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":133,"title":["Characterizing Land Surface Anisotropic Reflectance over Rugged Terrain: A Review of Concepts and Recent Developments"],"prefix":"10.3390","volume":"10","author":[{"given":"Jianguang","family":"Wen","sequence":"first","affiliation":[{"name":"State Key Laboratory of Remote Sensing Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing 100101, China"},{"name":"Joint Center for Global Change Studies (JCGCS), Beijing 100875, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5302-9849","authenticated-orcid":false,"given":"Qiang","family":"Liu","sequence":"additional","affiliation":[{"name":"Joint Center for Global Change Studies (JCGCS), Beijing 100875, China"},{"name":"College of Global Change and Earth System Science, Beijing Normal University, Beijing 100875, China"}]},{"given":"Qing","family":"Xiao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Remote Sensing Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing 100101, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3713-9511","authenticated-orcid":false,"given":"Qinhuo","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Remote Sensing Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing 100101, China"},{"name":"Joint Center for Global Change Studies (JCGCS), Beijing 100875, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Dongqin","family":"You","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Remote Sensing Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing 100101, China"},{"name":"Joint Center for Global Change Studies (JCGCS), Beijing 100875, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7154-6332","authenticated-orcid":false,"given":"Dalei","family":"Hao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Remote Sensing Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing 100101, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4569-6366","authenticated-orcid":false,"given":"Shengbiao","family":"Wu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Remote Sensing Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing 100101, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3770-6894","authenticated-orcid":false,"given":"Xingwen","family":"Lin","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Remote Sensing Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing 100101, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,2,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.isprsjprs.2011.10.008","article-title":"Combining the matter element model with the associated function of probability transformation for multi-source remote sensing data classification in mountainous regions","volume":"67","author":"Li","year":"2012","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_2","first-page":"9","article-title":"The effect of atmospheric and topographic correction methods on land cover classification accuracy","volume":"24","author":"Vanonckelen","year":"2013","journal-title":"Int. J. Appl. Earth Obs. Geoinf."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"812","DOI":"10.1029\/2011JD016465","article-title":"Shortwave radiation parameterization scheme for subgrid topography","volume":"117","author":"Helbig","year":"2012","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_4","first-page":"883","article-title":"An improved land-surface albedo algorithm with DEM in rugged terrain","volume":"11","author":"Wen","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.rse.2015.10.026","article-title":"Topographic radiation modeling and spatial scaling of clear-sky land surface longwave radiation over rugged terrain","volume":"172","author":"Yan","year":"2016","journal-title":"Remote Sens. Environ."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/j.rse.2015.04.027","article-title":"Retrieval of leaf area index in mountain grasslands in the alps from MODIS satellite imagery","volume":"165","author":"Pasolli","year":"2015","journal-title":"Remote Sens. Environ."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Zhao, P., Fan, W., Liu, Y., Mu, X., Xu, X., and Peng, J. (2016). Study of the remote sensing model of FAPAR over rugged terrains. Remote Sens., 8.","DOI":"10.3390\/rs8040309"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.rse.2006.03.002","article-title":"Reflectance quantities in optical remote sensing\u2014Definitions and case studies","volume":"103","author":"Schaepman","year":"2006","journal-title":"Remote Sens. Environ."},{"key":"ref_9","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_10","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/S0034-4257(02)00091-3","article-title":"First operational BRDF, albedo nadir reflectance products from MODIS","volume":"83","author":"Schaaf","year":"2002","journal-title":"Remote Sens. Environ."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.rse.2010.08.009","article-title":"Real-time retrieval of leaf area index from MODIS time series data","volume":"115","author":"Xiao","year":"2011","journal-title":"Remote Sens. Environ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2674","DOI":"10.1016\/j.rse.2011.06.001","article-title":"Algorithm for retrieval of the effective snow grain size and pollution amount from satellite measurements","volume":"115","author":"Zege","year":"2011","journal-title":"Remote Sens. Environ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.rse.2017.06.019","article-title":"Examination of Sentinel-2a multi-spectral instrument (MSI) reflectance anisotropy and the suitability of a general method to normalize MSI reflectance to nadir BRDFadjusted reflectance","volume":"199","author":"Roy","year":"2017","journal-title":"Remote Sens. Environ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.rse.2016.01.023","article-title":"A general method to normalize Landsat reflectance data to nadir BRDF adjusted reflectance","volume":"176","author":"Roy","year":"2016","journal-title":"Remote Sens. Environ."},{"key":"ref_15","first-page":"1855","article-title":"Operational BRDF effects correction for wide-field-of-view optical scanners (BREFCOR)","volume":"53","author":"Richter","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1016\/j.rse.2006.03.006","article-title":"Normalization of the directional effects in NOAA\u2013AVHRR reflectance measurements for an improved monitoring of vegetation cycles","volume":"102","author":"Bacour","year":"2006","journal-title":"Remote Sens. Environ."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"5469","DOI":"10.1109\/TGRS.2013.2289852","article-title":"GOST: A geometric-optical model for sloping terrains","volume":"52","author":"Fan","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"756","DOI":"10.1016\/j.rse.2012.06.018","article-title":"A physics-based atmospheric and BRDF correction for Landsat data over mountainous terrain","volume":"124","author":"Li","year":"2012","journal-title":"Remote Sens. Environ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1506","DOI":"10.1109\/JSTARS.2015.2416254","article-title":"Modeling land surface reflectance coupled BRDF for HJ-1\/CCD data of rugged terrain in Heihe river basin, China","volume":"8","author":"Wen","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4597","DOI":"10.1109\/TGRS.2017.2694483","article-title":"Modeling canopy reflectance over sloping terrain based on path length correction","volume":"55","author":"Yin","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1186","DOI":"10.1109\/36.338367","article-title":"Topographic effects on bidirectional and hemispherical reflectances calculated with a geometric-optical canopy model","volume":"32","author":"Schaaf","year":"1994","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.catena.2012.01.007","article-title":"Reflectance anisotropy for measuring soil surface roughness of multiple soil types","volume":"93","author":"Croft","year":"2012","journal-title":"Catena"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"6894","DOI":"10.1080\/01431161.2014.960616","article-title":"Effect of surface roughness, wavelength, illumination, and viewing zenith angles on soil surface BRDF using an imaging BRDF approach","volume":"35","author":"Wang","year":"2014","journal-title":"Int. J. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"5579","DOI":"10.1109\/TGRS.2013.2290590","article-title":"Hybrid geometric optical\u2013radiative transfer model suitable for forests on slopes","volume":"52","author":"Fan","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/0034-4257(89)90044-8","article-title":"Evaluation of topographic effects in remotely sensed data","volume":"30","author":"Proy","year":"1989","journal-title":"Remote Sens. Environ."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3503","DOI":"10.1080\/01431160210154029","article-title":"Correcting satellite imagery for the variance of reflectance and illumination with topography","volume":"24","author":"Shepherd","year":"2003","journal-title":"Int. J. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"798","DOI":"10.1109\/36.842009","article-title":"Extending a turbid medium BRDF model to allow sloping terrain with a vertical plant stand","volume":"38","author":"Combal","year":"2000","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1080\/01431160410001735111","article-title":"Estimating surface solar radiation over complex terrain using moderate-resolution satellite sensor data","volume":"26","author":"Wang","year":"2005","journal-title":"Int. J. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"5397","DOI":"10.1080\/01431160903130903","article-title":"Scale effect and scale correction of land-surface albedo in rugged terrain","volume":"30","author":"Wen","year":"2009","journal-title":"Int. J. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/0019-1035(84)90054-X","article-title":"Bidirectional reflectance spectroscopy: 3. Correction for macroscopic roughness","volume":"59","author":"Hapke","year":"1984","journal-title":"Icarus"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"10356","DOI":"10.3390\/rs61110356","article-title":"Improved surface reflectance from remote sensing data with sub-pixel topographic information","volume":"6","author":"Roupioz","year":"2014","journal-title":"Remote Sens."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"NicoDEMus, F.E., Richmond, J.C., Hsia, J.J., Ginsberg, I.W., and Limperis, T. (1977). Geometrical Considerations and Nomenclature for Reflectance, Jones and Bartlett Publishers, Inc.. Radiometry.","DOI":"10.6028\/NBS.MONO.160"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1016\/j.rse.2003.07.004","article-title":"Generalizing the definition of the bi-directional reflectance distribution function","volume":"88","author":"Girolamo","year":"2003","journal-title":"Remote Sens. Environ."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1032","DOI":"10.1109\/TGRS.2002.1010890","article-title":"Definition and invariance properties of structured surface BRDF","volume":"40","author":"Snyder","year":"2002","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1016\/j.jqsrt.2007.01.025","article-title":"Rough-surface shadowing of self-affine random rough surfaces","volume":"106","author":"Parviainen","year":"2007","journal-title":"J. Quant. Spectrosc. Radiat. Transf."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1109\/TGRS.2002.1000325","article-title":"The effect of small topographic variations on reflectance","volume":"40","author":"Combal","year":"2002","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1080\/02757250009532407","article-title":"A review of reflectance nomenclature used in remote sensing","volume":"19","author":"Martonchik","year":"2000","journal-title":"Remote Sens. Rev."},{"key":"ref_38","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_39","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_40","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1109\/36.581987","article-title":"Second simulation of the satellite signal in the solar spectrum, 6S: An overview","volume":"35","author":"Vermote","year":"1997","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Berk, A., Conforti, P., Kennett, R., Perkins, T., Hawes, F., and Van Den Bosch, J. (2014). MODTRAN6: A major upgrade of the MODTRANradiative transfer code. Proc. SPIE.","DOI":"10.1117\/12.2050433"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1387","DOI":"10.1016\/j.rse.2011.01.019","article-title":"C-correction of optical satellite data over alpine vegetation areas: A comparison of sampling strategies for determining the empirical c-parameter","volume":"115","author":"Reese","year":"2011","journal-title":"Remote Sens. Environ."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2148","DOI":"10.1109\/TGRS.2005.852480","article-title":"SCS + C: A modified sun-canopy-sensor topographic correction in forested terrain","volume":"43","author":"Soenen","year":"2005","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.isprsjprs.2014.07.005","article-title":"A sun\u2013crown\u2013sensor model and adapted c-correction logic for topographic correction of high resolution forest imagery","volume":"96","author":"Fan","year":"2014","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1047","DOI":"10.5194\/hess-8-1047-2004","article-title":"Statistical representation of mountain shading","volume":"8","author":"Essery","year":"2004","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"5143","DOI":"10.1029\/2006JD007163","article-title":"Application of three-dimensional solar radiative transfer to mountains","volume":"111","author":"Chen","year":"2006","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"2631","DOI":"10.1080\/01431160110115834","article-title":"Geo-atmospheric processing of airborne imaging spectrometry data. Part 2: Atmospheric\/topographic correction","volume":"23","author":"Richter","year":"2002","journal-title":"Int. J. Remote Sens."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"724","DOI":"10.1109\/36.752189","article-title":"The interrelationship of atmospheric correction of reflectances and surface BRDF retrieval: A sensitivity study","volume":"37","author":"Hu","year":"1999","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"17131","DOI":"10.1029\/97JD00201","article-title":"Atmospheric correction of visible to middle-infrared EOS-MODIS data over land surfaces: Background, operational algorithm and validation","volume":"102","author":"Vermote","year":"1997","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1109\/JSTARS.2010.2042281","article-title":"An evaluation of the use of atmospheric and BRDF correction to standardize Landsat data","volume":"3","author":"Li","year":"2010","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1080\/2150704X.2013.798709","article-title":"Testing the local applicability of MODIS BRDF parameters for correcting Landsat TM imagery","volume":"4","author":"Flood","year":"2013","journal-title":"Remote Sens. Lett."},{"key":"ref_52","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_53","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1109\/TGRS.1995.8746028","article-title":"A hybrid geometric optical radiative transfer approach for modeling albedo and directional reflectance of discontinuous canopies","volume":"33","author":"Li","year":"1995","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_54","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_55","doi-asserted-by":"crossref","first-page":"5421","DOI":"10.1080\/01431160903130911","article-title":"A realistic structure model for large-scale surface leaving radiance simulation of forest canopy and accuracy assessment","volume":"30","author":"Huang","year":"2009","journal-title":"Int. J. Remote Sens."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1016\/j.rse.2015.08.016","article-title":"The fourth phase of the radiative transfer model intercomparison (RAMI) exercise: Actual canopy scenarios and conformity testing","volume":"169","author":"Widlowski","year":"2015","journal-title":"Remote Sens. Environ."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/S0034-4257(98)00022-4","article-title":"An investigation of terrain effects on the inversion of a forest reflectance model","volume":"65","author":"Gemmell","year":"1998","journal-title":"Remote Sens. Environ."},{"key":"ref_58","first-page":"1183","article-title":"The Lambertian assumption and Landsat data","volume":"46","author":"Smith","year":"1980","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/S0034-4257(97)00177-6","article-title":"Topographic normalization of Landsat TM images of forest based on subpixel sun\u2013canopy\u2013sensor geometry","volume":"64","author":"Gu","year":"1998","journal-title":"Remote Sens. Environ."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1109\/36.581991","article-title":"A physically-based model to correct atmospheric and illumination effects in optical satellite data of rugged terrain","volume":"35","author":"Sandmeier","year":"1997","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"2875","DOI":"10.1080\/01431160802558618","article-title":"Parametrized BRDF for atmospheric and topographic correction and albedo estimation in Jiangxi rugged terrain, China","volume":"30","author":"Wen","year":"2009","journal-title":"Int. J. Remote Sens."},{"key":"ref_62","first-page":"94","article-title":"Parameterization of solar fluxes over mountain surfaces for application to climate models","volume":"116","author":"Lee","year":"2011","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"2403","DOI":"10.5194\/amt-6-2403-2013","article-title":"Mcclear: A new model estimating downwelling solar radiation at ground level in clear-sky conditions","volume":"6","author":"Oumbe","year":"2013","journal-title":"Atmos. Meas. Tech."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"8019","DOI":"10.3390\/rs70608019","article-title":"Modeling top of atmosphere radiance over heterogeneous non-Lambertian rugged terrain","volume":"7","author":"Mousivand","year":"2015","journal-title":"Remote Sens."},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Wu, S., Wen, J., Tang, Y., and Zhao, J. (2017, January 23\u201328). Modeling anisotropic bidirectional reflectance of sloping forest. Proceedings of the 2017 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Fort Worth, TX, USA.","DOI":"10.1109\/IGARSS.2017.8127848"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1080\/02757259709532337","article-title":"Vegetation canopy reflectance modeling\u2014Recent developments and remote sensing perspectives","volume":"15","author":"Strahler","year":"1997","journal-title":"Remote Sens. Rev."},{"key":"ref_67","first-page":"13","article-title":"Radiative transfer in plant communities","volume":"1","author":"Ross","year":"1975","journal-title":"Veg. Atmos."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"1958","DOI":"10.1109\/LGRS.2015.2440438","article-title":"Comparison of five slope correction methods for leaf area index estimation from hemispherical photography","volume":"12","author":"Cao","year":"2015","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_69","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_70","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1109\/36.134078","article-title":"Geometric-optical bidirectional reflectance modeling of the discrete crown vegetation canopy: Effect of crown shape and mutual shadowing","volume":"30","author":"Li","year":"1992","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_71","first-page":"987","article-title":"An analytical hybrid GORT model for bidirectional reflectance over discontinuous plant canopies","volume":"37","author":"Ni","year":"2002","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"964","DOI":"10.1109\/LGRS.2017.2690988","article-title":"A 3-D topographic-relief-correlated Monte Carlo radiative transfer simulator for forest bidirectional reflectance estimation","volume":"14","author":"Jin","year":"2017","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/j.rse.2013.01.013","article-title":"RAPID: A radiosity applicable to porous individual objects for directional reflectance over complex vegetated scenes","volume":"132","author":"Huang","year":"2013","journal-title":"Remote Sens. Environ."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1109\/LGRS.2013.2275072","article-title":"An improved method for retrieving land surface albedo over rugged terrain","volume":"11","author":"Gao","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_75","unstructured":"Ashdown, I. (1994). Radiosity: A Programmer\u2019s Perspective, John Wiley & Sons, Inc."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"1418","DOI":"10.1016\/j.jqsrt.2009.02.030","article-title":"Bidirectional reflectance of rough particulate media: Ray-tracing solution","volume":"110","author":"Parviainen","year":"2009","journal-title":"J. Quant. Spectrosc. Radiat. Transf."},{"key":"ref_77","first-page":"873","article-title":"Bidirectional reflectance of Gaussian random surfaces and its scaling properties","volume":"30","author":"Despan","year":"1998","journal-title":"Math. Geosci."},{"key":"ref_78","doi-asserted-by":"crossref","unstructured":"Barsky, S., and Petrou, M. (2005). The Shadow Function for Rough Surfaces, Kluwer AcaDEMic Publishers.","DOI":"10.1007\/s10851-005-0484-6"},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.1364\/JOSA.57.001105","article-title":"Theory for off-specular reflection from roughened surfaces","volume":"57","author":"Torrance","year":"1967","journal-title":"J. Opt. Soc. Am."},{"key":"ref_80","doi-asserted-by":"crossref","unstructured":"Hapke, B. (1993). Theory of Reflectance and Emittance Spectroscopy: Photometric Effects of Large-Scale Roughness, Cambridge University Press.","DOI":"10.1017\/CBO9780511524998"},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"22788","DOI":"10.1364\/OE.23.022788","article-title":"Modified polarized geometrical attenuation model for bidirectional reflection distribution function based on random surface microfacet theory","volume":"23","author":"Liu","year":"2015","journal-title":"Opt. Express"},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1145\/965141.563893","article-title":"Models of light reflection for computer synthesized pictures","volume":"11","author":"Blinn","year":"1977","journal-title":"ACM SIGGRAPH Comput. Graph."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"5281","DOI":"10.1029\/JB073i016p05281","article-title":"Reradiation and thermal emission from illuminated craters on the lunar surface","volume":"73","author":"Buhl","year":"1968","journal-title":"J. Geophys. Res."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1145\/97880.97909","article-title":"A model for anisotropic reflection","volume":"24","author":"Poulin","year":"1990","journal-title":"ACM SIGGRAPH Comput. Graph."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1023\/A:1008061730969","article-title":"Bidirectional reflection distribution function of thoroughly pitted surfaces","volume":"31","author":"Koenderink","year":"1999","journal-title":"Int. J. Comput. Vis."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1109\/TAP.1966.1138758","article-title":"Note on the effect of shadowing on the backscattering of waves from a random rough surface","volume":"14","author":"Brockelman","year":"1966","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"668","DOI":"10.1109\/TAP.1967.1138991","article-title":"Geometrical shadowing of a random rough surface","volume":"15","author":"Smith","year":"1967","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1006\/icar.1999.6141","article-title":"Radar scattering from a self-affine fractal surface: Near-nadir regime","volume":"141","author":"Shepard","year":"1999","journal-title":"Icarus"},{"key":"ref_89","unstructured":"Kelemen, C., and Szirmay-Kalos, L. (2001, January 3\u20137). A microfacet based coupled specular-matte BRDF model with importance sampling. Proceedings of the Eurographics 2011, Manchester, UK."},{"key":"ref_90","unstructured":"Shirley, P., Smits, B., Hu, H., and Lafortune, E. (1997, January 13\u201316). A practitioners\u2019 assessment of light reflection models. Proceedings of the 1997 IEEE the Fifth Pacific Conference on Computer Graphics and Applications, Seoul, Korea."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1175\/JHM487.1","article-title":"Fractal distribution of snow depth from LIDAR data","volume":"7","author":"Deems","year":"2006","journal-title":"J. Hydrometeorol."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1002\/(SICI)1096-9837(199908)24:9<763::AID-ESP9>3.0.CO;2-J","article-title":"Comparison of slope estimates from low resolution DEMs: Scaling issues and a fractal method for their solution","volume":"24","author":"Zhang","year":"2015","journal-title":"Earth Surf. Processes Landf."},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1023\/A:1019211120818","article-title":"Spatial statistics of wind flow and blowing-snow fluxes over complex topography","volume":"100","author":"Essery","year":"2001","journal-title":"Bound.-Layer Meteorol."},{"key":"ref_94","first-page":"10122","article-title":"Scaling and parametrization of clear-sky solar radiation over complex topography","volume":"112","author":"Essery","year":"2007","journal-title":"J. Geophys. Res."},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1029\/2008JF001038","article-title":"Probabilistic description of topographic slope and aspect","volume":"114","author":"Vico","year":"2009","journal-title":"J. Geophys. Res. Earth Surf."},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"724","DOI":"10.1364\/JOSAA.24.000724","article-title":"Statistical ray method for deriving reflection models of rough surfaces","volume":"24","author":"Sun","year":"2007","journal-title":"J. Opt. Soc. Am. Opt. Image Sci. Vis."},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1109\/TAP.1965.1138443","article-title":"Shadowing of random rough surfaces","volume":"13","author":"Beckmann","year":"1965","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1109\/TAP.1966.1138636","article-title":"Comments on \u201cshadowing of random surfaces\u201d","volume":"14","author":"Shaw","year":"1966","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1121\/1.1910308","article-title":"Shadowing of randomly rough surfaces","volume":"41","author":"Wagner","year":"1967","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1145\/2897824.2925943","article-title":"Multiple-scattering microfacet BSDFs with the Smith model","volume":"35","author":"Heitz","year":"2016","journal-title":"ACM Trans. Graph."},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1109\/8.841905","article-title":"Effect of correlation between shadowing and shadowed points on the Wagner and Smith monostatic one-dimensional shadowing functions","volume":"48","author":"Bourlier","year":"2000","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1109\/8.999622","article-title":"One- and two-dimensional shadowing functions for any height and slope stationary uncorrelated surface in the monostatic and bistatic configurations","volume":"50","author":"Bourlier","year":"2002","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1080\/08120099.2014.884983","article-title":"Comparison of free high resolution digital elevation data sets (ASTERGDEM2, SRTM v2.1\/v4.1) and validation against accurate heights from the Australian national gravity database","volume":"61","author":"Rexer","year":"2014","journal-title":"Aust. J. Earth Sci."},{"key":"ref_104","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1109\/36.58986","article-title":"Rapid calculation of terrain parameters for radiation modeling from digital elevation data","volume":"28","author":"Dozier","year":"1990","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_105","first-page":"48","article-title":"Understanding the masking-shadowing function in microfacet-based BRDFs","volume":"3","author":"Heitz","year":"2014","journal-title":"J. Comput. Graph. Tech."},{"key":"ref_106","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1080\/17538947.2013.866701","article-title":"Issues in the application of digital surface model data to correct the terrain illumination effects in Landsat images","volume":"8","author":"Li","year":"2015","journal-title":"Int. J. Digit. Earth"},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/S0022-1694(98)00189-9","article-title":"A comparison of drainage networks derived from digital elevation models at two scales","volume":"210","author":"Wang","year":"1998","journal-title":"J. Hydrol."},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1002\/(SICI)1099-1085(20000430)14:6<987::AID-HYP980>3.0.CO;2-A","article-title":"Differences in topographic characteristics computed from 100- and 1000-m resolution digital elevation model data","volume":"14","author":"Wolock","year":"2015","journal-title":"Hydrol. Processes"},{"key":"ref_109","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1002\/(SICI)1096-9837(199906)24:6<557::AID-ESP6>3.0.CO;2-Y","article-title":"A cross-scale comparison of drainage basin characteristics derived from digital elevation models","volume":"24","author":"Yin","year":"2015","journal-title":"Earth Surf. Processes Landf."},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/j.cageo.2003.07.005","article-title":"Analysis of errors of derived slope and aspect related to DEM data properties","volume":"30","author":"Zhou","year":"2004","journal-title":"Comput. Geosci."},{"key":"ref_111","unstructured":"Fleming, M.D., and Hoffer, R.M. (1979). Machine Processing of Landsat MSS Data and DMA Topographic Data for Forest Cover Type Mapping, Purdue University."},{"key":"ref_112","first-page":"1109","article-title":"Vector-based slope and aspect generation algorithm","volume":"53","author":"Ritter","year":"1987","journal-title":"Am. Soc. Photogramm. Remote Sens."},{"key":"ref_113","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1109\/PROC.1981.11918","article-title":"Hill shading and the reflectance map","volume":"69","author":"Horn","year":"1981","journal-title":"IEEE Proc."},{"key":"ref_114","first-page":"834","article-title":"The geomorphological characterisation of digital elevation models","volume":"13","author":"Wood","year":"1996","journal-title":"Diss. Theses-Gradworks"},{"key":"ref_115","unstructured":"Unwin, D.J., and Doomkamp, J.C. (2010, January 22\u201226). Introductory spatial analysis. Proceedings of the Parallel Problem Solving from Nature\u2014PPSN IV, Berlin, Germany."},{"key":"ref_116","unstructured":"Chu, T.H., and Tsai, T.H. (1995, January 21\u201324). Comparison of accuracy and algorithms of slope and aspect measures from DEM. Proceedings of the GIS AM\/FM ASIA\u201995, Bangkok, Thailand."},{"key":"ref_117","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/S0098-3004(98)00032-6","article-title":"A comparison of algorithms used to compute hill slope as a property of the DEM","volume":"24","author":"Jones","year":"1998","journal-title":"Comput. Geosci."},{"key":"ref_118","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.cageo.2004.09.018","article-title":"Solar radiation modelling","volume":"31","author":"Podobnikar","year":"2005","journal-title":"Comput. Geosci."},{"key":"ref_119","doi-asserted-by":"crossref","first-page":"4616","DOI":"10.1002\/2013JD020892","article-title":"Parameterization of the spatially averaged sky view factor in complex topography","volume":"119","author":"Helbig","year":"2014","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_120","doi-asserted-by":"crossref","first-page":"4004","DOI":"10.1364\/AO.37.004004","article-title":"Correction of satellite imagery over mountainous terrain","volume":"37","author":"Richter","year":"1998","journal-title":"Appl. Opt."},{"key":"ref_121","doi-asserted-by":"crossref","first-page":"31","DOI":"10.3189\/172756402781817635","article-title":"Retrieval of snow reflectance from Landsat data in rugged terrain","volume":"34","author":"Xin","year":"2002","journal-title":"Ann. Glaciol."},{"key":"ref_122","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. Atmos."},{"key":"ref_123","doi-asserted-by":"crossref","first-page":"21077","DOI":"10.1029\/95JD02371","article-title":"On the derivation of kernels for kernel-driven models of bidirectional reflectance","volume":"100","author":"Wanner","year":"1995","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_124","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1016\/S0034-4257(01)00214-0","article-title":"A spectralon BRF data base for MISR calibration applications","volume":"77","author":"Bruegge","year":"2001","journal-title":"Remote Sens. Environ."},{"key":"ref_125","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/S0034-4257(98)00120-5","article-title":"Modeling BRF and radiation regime of boreal and tropical forests: I. BRF","volume":"68","author":"Guillevic","year":"1999","journal-title":"Remote Sens. Environ."},{"key":"ref_126","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1109\/JSTARS.2010.2048745","article-title":"The angular & 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_127","doi-asserted-by":"crossref","first-page":"1331","DOI":"10.1109\/JSTARS.2013.2271502","article-title":"The angular and spectral kernel-driven model: Assessment and application","volume":"7","author":"You","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_128","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1109\/TGRS.2016.2613899","article-title":"Forward a small-timescale BRDF\/albedo by multisensor combined BRDF inversion model","volume":"55","author":"Wen","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_129","doi-asserted-by":"crossref","first-page":"916","DOI":"10.1109\/LGRS.2017.2687702","article-title":"Evaluation of atmospheric effects on land-surface directional reflectance with the coupled RAPID and VLIDORT models","volume":"14","author":"Huang","year":"2017","journal-title":"IEEE Geosci. Remote Sens. Lett."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/3\/370\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:56:46Z","timestamp":1760194606000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/3\/370"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,27]]},"references-count":129,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2018,3]]}},"alternative-id":["rs10030370"],"URL":"https:\/\/doi.org\/10.3390\/rs10030370","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,2,27]]}}}