{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T19:08:37Z","timestamp":1782932917130,"version":"3.54.5"},"reference-count":46,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,2,11]],"date-time":"2018-02-11T00:00:00Z","timestamp":1518307200000},"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"]}]},{"DOI":"10.13039\/501100012166","name":"National Basic Research Program of China","doi-asserted-by":"publisher","award":["2013CB733401"],"award-info":[{"award-number":["2013CB733401"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Topography complicates the modeling and retrieval of land surface albedo due to shadow effects and the redistribution of incident radiation. Neglecting topographic effects may lead to a significant bias when estimating land surface albedo over a single slope. However, for rugged terrain, a comprehensive and systematic investigation of topographic effects on land surface albedo is currently ongoing. Accurately estimating topographic effects on land surface albedo over a rugged terrain presents a challenge in remote sensing modeling and applications. In this paper, we focused on the development of a simplified estimation method for snow-free albedo over a rugged terrain at a 1-km scale based on a 30-m fine-scale digital elevation model (DEM). The proposed method was compared with the radiosity approach based on simulated and real DEMs. The results of the comparison showed that the proposed method provided adequate computational efficiency and satisfactory accuracy simultaneously. Then, the topographic effects on snow-free albedo were quantitatively investigated and interpreted by considering the mean slope, subpixel aspect distribution, solar zenith angle, and solar azimuth angle. The results showed that the more rugged the terrain and the larger the solar illumination angle, the more intense the topographic effects were on black-sky albedo (BSA). The maximum absolute deviation (MAD) and the maximum relative deviation (MRD) of the BSA over a rugged terrain reached 0.28 and 85%, respectively, when the SZA was 60\u00b0 for different terrains. Topographic effects varied with the mean slope, subpixel aspect distribution, SZA and SAA, which should not be neglected when modeling albedo.<\/jats:p>","DOI":"10.3390\/rs10020278","type":"journal-article","created":{"date-parts":[[2018,2,12]],"date-time":"2018-02-12T10:50:38Z","timestamp":1518432638000},"page":"278","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["Simulation and Analysis of the Topographic Effects on Snow-Free Albedo over Rugged Terrain"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7154-6332","authenticated-orcid":false,"given":"Dalei","family":"Hao","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":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianguang","family":"Wen","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"},{"name":"Joint Center for Global Change Studies (JCGCS), Beijing 100875, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Baocheng","family":"Dou","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"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yong","family":"Tang","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"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,2,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Liang, S. (2003). Quantitative Remote Sensing of Land Surfaces, Wiley-Interscience.","DOI":"10.1002\/047172372X"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"990","DOI":"10.3390\/rs70100990","article-title":"Mapping surface broadband albedo from satellite observations: A review of literatures on algorithms and products","volume":"7","author":"Qu","year":"2015","journal-title":"Remote Sens."},{"key":"ref_3","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_4","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_5","doi-asserted-by":"crossref","unstructured":"Schaepman-Strub, G., Schaepman, M.E., Martonchik, J.V., Painter, T.H., and Dangel, S. (2009). Radiometry and reflectance: From terminology concepts to measured quantities. The SAGE Handbook of Remote Sensing, Sage Publications.","DOI":"10.4135\/9780857021052.n15"},{"key":"ref_6","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":"2002","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_7","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_8","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_9","unstructured":"Strahler, A.H., Muller, J., Lucht, W., Schaaf, C., Tsang, T., Gao, F., Li, X., Lewis, P., and Barnsley, M.J. (2017, October 01). MODIS BRDF\/Albedo Product: Algorithm Theoretical Basis Document. Version 5.0., Available online: https:\/\/modis.gsfc.nasa.gov\/data\/atbd\/atbd_mod09.pdf."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1109\/TGRS.2002.807751","article-title":"A direct algorithm for estimating land surface broadband albedos from MODIS imagery","volume":"41","author":"Liang","year":"2003","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1061\/(ASCE)1084-0699(2008)13:2(51)","article-title":"At-surface reflectance and albedo from satellite for operational calculation of land surface energy balance","volume":"13","author":"Tasumi","year":"2008","journal-title":"J. Hydrol. Eng."},{"key":"ref_12","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_13","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1109\/36.297978","article-title":"The polder mission: Instrument characteristics and scientific objectives","volume":"32","author":"Deschamps","year":"1994","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1072","DOI":"10.1109\/36.700992","article-title":"Multi-angle imaging spectroradiometer (MISR) instrument description and experiment overview","volume":"36","author":"Diner","year":"2005","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","unstructured":"Rutan, D., Charlock, T.P., Rose, F., Kato, S., Zentz, S., and Coleman, L. (2006). Global Surface Albedo from Ceres\/Terra Surface and Atmospheric Radiation Budget (SARB) Data Product, ACM."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1538","DOI":"10.1016\/j.agrformet.2008.05.008","article-title":"Evaluation of land surface radiation balance derived from moderate resolution imaging spectroradiometer (MODIS) over complex terrain and heterogeneous landscape on clear sky days","volume":"148","author":"Ryu","year":"2008","journal-title":"Agric. For. Meteorol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1109\/LGRS.2013.2280696","article-title":"An improved land-surface albedo algorithm with DEM in rugged terrain","volume":"11","author":"Wen","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_18","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_19","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_20","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_21","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_22","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_23","unstructured":"Manninen, T., Andersson, K., and Riihel\u00e4, A. (2011, January 5\u20139). Topography Correction of the CM-SAF Surface Albedo Product SAL. Proceedings of the EUMETSAT Meteorological Satellite Conference, Oslo, Norway."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1080\/01431168808954889","article-title":"Radiometric correction for atmospheric and topographic effects on landsat mss images","volume":"9","author":"Kawata","year":"1988","journal-title":"Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s12665-015-4656-4","article-title":"Calculation of albedo on complex terrain using MODIS data: A case study in Taihang mountain of China","volume":"74","author":"Li","year":"2015","journal-title":"Environ. Earth Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"4565","DOI":"10.1080\/01431161.2017.1320442","article-title":"Spatial, seasonal, and topographical patterns of surface albedo in Norwegian forests and cropland","volume":"38","author":"Cherubini","year":"2017","journal-title":"Int. J. Remote Sens."},{"key":"ref_27","unstructured":"Ashdown, I. (1994). Radiosity: A Programmer\u2019s Perspective, John Wiley & Sons, Inc."},{"key":"ref_28","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_29","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_30","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_31","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_32","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_33","doi-asserted-by":"crossref","first-page":"398","DOI":"10.3390\/rs3020398","article-title":"Sky-view factor as a relief visualization technique","volume":"3","author":"Zaksek","year":"2011","journal-title":"Remote Sens."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Hapke, B. (2012). Theory of Reflectance and Emittance Spectroscopy: Second Edition, Cambridge University Press.","DOI":"10.1017\/CBO9781139025683"},{"key":"ref_35","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_36","doi-asserted-by":"crossref","first-page":"S56","DOI":"10.1016\/j.rse.2008.01.026","article-title":"Prospect+sail models: A review of use for vegetation characterization","volume":"113","author":"Jacquemoud","year":"2009","journal-title":"Remote Sens. Environ."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.ecolmodel.2005.10.045","article-title":"The role of sensitivity analysis in ecological modelling","volume":"203","author":"Cariboni","year":"2007","journal-title":"Ecol. Model."},{"key":"ref_38","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_39","first-page":"82","article-title":"Topographic effects on surface bidirectional reflectance scaling","volume":"1","author":"Liang","year":"1997","journal-title":"J. Remote Sens."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/0034-4257(91)90028-5","article-title":"The radiosity method in optical remote sensing of structured 3-d surfaces","volume":"36","author":"Borel","year":"1991","journal-title":"Remote Sens. Environ."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/0034-4257(91)90032-2","article-title":"A computer graphics-based model for scattering from objects of arbitrary shapes in the optical region","volume":"36","author":"Goel","year":"1991","journal-title":"Remote Sens. Environ."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/s10546-004-7403-z","article-title":"Variation of surface albedo and soil thermal parameters with soil moisture content at a semi-desert site on the western Tibetan plateau","volume":"116","author":"Wang","year":"2005","journal-title":"Bound. Layer Meteorol."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.still.2004.12.009","article-title":"Tillage and surface moisture effects on bare-soil albedo of a tropical loamy sand","volume":"85","author":"Oguntunde","year":"2006","journal-title":"Soil Tillage Res."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/0034-4257(89)90088-6","article-title":"A physical model for predicting bidirectional reflectances over bare soil","volume":"27","author":"Pinty","year":"1989","journal-title":"Remote Sens. Environ."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1175\/1520-0450(1992)031<0194:MSSIFS>2.0.CO;2","article-title":"Modeling surface solar irradiance for satellite applications on a global scale","volume":"31","author":"Pinker","year":"1992","journal-title":"J. Appl. Meteorol."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1075","DOI":"10.1080\/01431160802348101","article-title":"Simple correction of multiple reflection effects in rugged terrain","volume":"30","author":"Sirguey","year":"2009","journal-title":"Int. J. Remote Sens."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/2\/278\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:54:38Z","timestamp":1760194478000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/2\/278"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,11]]},"references-count":46,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,2]]}},"alternative-id":["rs10020278"],"URL":"https:\/\/doi.org\/10.3390\/rs10020278","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,2,11]]}}}