{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T03:33:31Z","timestamp":1775792011183,"version":"3.50.1"},"reference-count":51,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2015,6,18]],"date-time":"2015-06-18T00:00:00Z","timestamp":1434585600000},"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>Topography affects the fraction of direct and diffuse radiation received on a pixel and changes the sun\u2013target\u2013sensor geometry, resulting in variations in the observed radiance. Retrieval of surface\u2013atmosphere properties from top of atmosphere radiance may need to account for topographic effects. This study investigates how such effects can be taken into account for top of atmosphere radiance modeling. In this paper, a system for top of atmosphere radiance modeling over heterogeneous non-Lambertian rugged terrain through radiative transfer modeling is presented. The paper proposes an extension of \u201cthe four-stream radiative transfer theory\u201d (Verhoef and Bach 2003, 2007 and 2012) mainly aimed at representing topography-induced contributions to the top of atmosphere radiance modeling. A detailed account for BRDF effects, adjacency effects and topography effects on the radiance modeling is given, in which sky-view factor and non-Lambertian reflected radiance from adjacent slopes are modeled precisely. The paper also provides a new formulation to derive the atmospheric coefficients from MODTRAN with only two model runs, to make it more computationally efficient and also avoiding the use of zero surface albedo as used in the four-stream radiative transfer theory. The modeling begins with four surface reflectance factors calculated by the Soil\u2013Leaf\u2013Canopy radiative transfer model SLC at the top of canopy and propagates them through the effects of the atmosphere, which is explained by six atmospheric coefficients, derived from MODTRAN radiative transfer code. The top of the atmosphere radiance is then convolved with the sensor characteristics to generate sensor-like radiance. Using a composite dataset, it has been shown that neglecting sky view factor and\/or terrain reflected radiance can cause uncertainty in the forward TOA radiance modeling up to 5 (mW\/m2\u00b7sr\u00b7nm). It has also been shown that this level of uncertainty can be translated into an over\/underestimation of more than 0.5 in LAI  (or 0.07 in fCover) in variable retrieval.<\/jats:p>","DOI":"10.3390\/rs70608019","type":"journal-article","created":{"date-parts":[[2015,6,18]],"date-time":"2015-06-18T10:08:36Z","timestamp":1434622116000},"page":"8019-8044","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":80,"title":["Modeling Top of Atmosphere Radiance over Heterogeneous Non-Lambertian Rugged Terrain"],"prefix":"10.3390","volume":"7","author":[{"given":"Alijafar","family":"Mousivand","sequence":"first","affiliation":[{"name":"Department Geoscience and Remote Sensing (GRS), Delft University of Technology, Stevinweg 1, 2628 CN Delft, 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 & Earth Observation (ITC), University of Twente,  P.O. Box 217, 7500 AE Enschede, The Netherlands"}]},{"given":"Massimo","family":"Menenti","sequence":"additional","affiliation":[{"name":"Department Geoscience and Remote Sensing (GRS), Delft University of Technology, Stevinweg 1, 2628 CN Delft, The Netherlands"}]},{"given":"Ben","family":"Gorte","sequence":"additional","affiliation":[{"name":"Department Geoscience and Remote Sensing (GRS), Delft University of Technology, Stevinweg 1, 2628 CN Delft, The Netherlands"}]}],"member":"1968","published-online":{"date-parts":[[2015,6,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1016\/j.rse.2010.12.009","article-title":"Estimating forest variables from top-of-atmosphere radiance satellite measurements using coupled radiative transfer models","volume":"115","author":"Laurent","year":"2011","journal-title":"Remote Sens. Environ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/j.rse.2006.07.014","article-title":"Neural network estimation of LAI, fAPAR, fCover and LAI\u00d7Cab, from top of canopy MERIS reflectance data: Principles and validation","volume":"105","author":"Bacour","year":"2006","journal-title":"Remote Sens. Environ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/j.rse.2007.02.018","article-title":"LAI, fAPAR and fCover CYCLOPES global products derived from VEGETATION Part 1: Principles of the algorithm","volume":"110","author":"Baret","year":"2007","journal-title":"Remote Sens. Environ."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0034-4257(02)00035-4","article-title":"Retrieval of canopy biophysical variables from bidirectional reflectance: Using prior information to solve the ill-posed inverse problem","volume":"84","author":"Combal","year":"2002","journal-title":"Remote Sens. Environ."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/978-0-387-75181-8_15","article-title":"Estimation of land surface parameters through modeling inversion of earth observation optical data","volume":"Volume 25","author":"Gomez","year":"2009","journal-title":"Advances in Modeling Agricultural Systems"},{"key":"ref_6","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_7","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1080\/014311697219286","article-title":"Multi-Sensor analysis of NDVI, surface temperature and biophysical variables at a mixed grassland site","volume":"18","author":"Goetz","year":"1997","journal-title":"Int. J. Remote Sens."},{"key":"ref_8","unstructured":"Moreno, J.F., Menenti, M., Baret, F., Rast, M., Leroy, M., and Shaepman, M. (2003, January 21\u201325). Retrieval of vegetation properties from combined hyperspectral\/multiangular optical measurements: Results from the DAISEX campaigns. Proceedings of the IEEE International Geoscience and Remote Sensing Symposium, Toulouse, France."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/j.rse.2005.10.006","article-title":"Inversion of a forest reflectance model to estimate structural canopy variables from hyperspectral remote sensing data","volume":"100","author":"Schlerf","year":"2006","journal-title":"Remote Sens. Environ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"638","DOI":"10.1016\/j.jenvman.2006.08.018","article-title":"LAI inversion algorithm based on directional reflectance kernels","volume":"85","author":"Tang","year":"2007","journal-title":"J. Environ. Manag."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2603","DOI":"10.1016\/j.rse.2011.05.016","article-title":"Inversion of a coupled canopy\u2013atmosphere model using multi-angular top-of-atmosphere radiance data: A forest case study","volume":"115","author":"Laurent","year":"2011","journal-title":"Remote Sens. Environ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.rse.2014.01.023","article-title":"Global sensitivity analysis of the spectral radiance of a soil\u2013vegetation system","volume":"145","author":"Mousivand","year":"2014","journal-title":"Remote Sens. Environ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/j.rse.2006.12.013","article-title":"Coupled soil-leaf-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_14","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/j.rse.2014.10.030","article-title":"Multi-Temporal, multi-sensor retrieval of terrestrial vegetation properties from spectral\u2013directional radiometric data","volume":"158","author":"Mousivand","year":"2015","journal-title":"Remote Sens. Environ."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/S0034-4257(01)00240-1","article-title":"Design and analysis of numerical experiments to compare four canopy reflectance models","volume":"79","author":"Bacour","year":"2002","journal-title":"Remote Sens. Environ."},{"key":"ref_16","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_17","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S1474-7065(03)00003-2","article-title":"Remote sensing data assimilation using coupled radiative transfer models","volume":"28","author":"Verhoef","year":"2003","journal-title":"Phys. Chem. Earth"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/S0924-2716(01)00022-3","article-title":"SENSOR: A tool for the simulation of hyperspectral remote sensing systems","volume":"55","author":"Wiest","year":"2001","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/S0034-4257(96)00238-6","article-title":"Vegetation water and dry matter contents estimated from top-of-the-atmosphere reflectance data: A simulation study","volume":"61","author":"Fourty","year":"1997","journal-title":"Remote Sens. Environ."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2340","DOI":"10.1109\/TGRS.2008.2011616","article-title":"Simulation of optical remote-sensing scenes with application to the EnMAP hyperspectral mission","volume":"47","author":"Guanter","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/0034-4257(88)90120-4","article-title":"Multispectral sensor data simulation modeling based on the multiple scattering LOWTRAN code","volume":"26","author":"Isaacs","year":"1988","journal-title":"Remote Sens. Environ."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"762","DOI":"10.1109\/36.35965","article-title":"Simulation of optical remote sensing systems","volume":"27","author":"Kerekes","year":"1989","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","first-page":"3877","article-title":"End-to-end simulation and analytical model of remote-sensing systems: Application to CRISM","volume":"48","author":"Parente","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"20779","DOI":"10.1029\/93JD02071","article-title":"Coupled surface-atmosphere reflectance (CSAR) Model 1. Model description and inversion on synthetic data","volume":"98","author":"Rahman","year":"1993","journal-title":"J. Geophys. Res."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Schott, J.R., D. Brown, S., V. Raqueno, R., N. Gross, H., and Robinson, G. (1998, January 14). In advanced synthetic image generation models and their application to multi\/hyperspectral algorithm development. Proceedings of the 27th AIPR Workshop: Advances in Computer-Assisted Recognition, Washington, DC, USA.","DOI":"10.1117\/12.339823"},{"key":"ref_26","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_27","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.rse.2011.10.034","article-title":"Simulation of Sentinel-3 images by four-stream surface\u2013atmosphere radiative transfer modeling in the optical and thermal domains","volume":"120","author":"Verhoef","year":"2012","journal-title":"Remote Sens. Environ."},{"key":"ref_28","first-page":"3889","article-title":"On hyperspectral image simulation of a complex woodland area","volume":"48","author":"Zhang","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_29","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":"J. Geophys. Res."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1016\/j.rse.2013.07.032","article-title":"A Bayesian object-based approach for estimating vegetation biophysical and biochemical variables from APEX at-sensor radiance data","volume":"139","author":"Laurent","year":"2013","journal-title":"Remote Sens. Environ."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/0034-4257(93)90073-7","article-title":"Using Landsat-5 thematic mapper and digital elevation data to determine the net radiation field of a Mountain Glacier","volume":"43","author":"Gratton","year":"1993","journal-title":"Remote Sens. Environ."},{"key":"ref_32","unstructured":"Sanpedro, M.d.C.G. (2008). Optical and Radar Remote Sensing Applied to Agricultural Areas in Europe. [Ph.D. Thesis, D\u00e9livr\u00e9 par l'Universit\u00e9 Toulouse III]."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1407","DOI":"10.1080\/01431160802438555","article-title":"On the application of the MODTRAN4 atmospheric radiative transfer code to optical remote sensing","volume":"30","author":"Guanter","year":"2009","journal-title":"Int. J. Remote Sens."},{"key":"ref_34","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_35","doi-asserted-by":"crossref","unstructured":"Schott, J.R. (2007). Remote Sensing: The Image Chain Approach, Oxford University Press.","DOI":"10.1093\/oso\/9780195178173.001.0001"},{"key":"ref_36","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_37","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/0098-3004(81)90026-1","article-title":"A faster solution to the horizon problem","volume":"7","author":"Dozier","year":"1981","journal-title":"Comput. Geosci."},{"key":"ref_38","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_39","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/0960-1481(93)90104-O","article-title":"Calculating solar radiation for inclined surfaces: Practical approaches","volume":"3","author":"Hay","year":"1993","journal-title":"Renew. Energy"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0038-092X(60)90062-1","article-title":"The interrelationship and characteristic distribution of direct, diffuse and total solar radiation","volume":"4","author":"Liu","year":"1960","journal-title":"Solar Energy"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1016\/j.renene.2011.06.042","article-title":"On the proper analytical expression for the sky-view factor and the diffuse irradiation of a slope for an isotropic sky","volume":"37","author":"Rakovec","year":"2012","journal-title":"Renew. Energy"},{"key":"ref_42","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_43","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_44","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_45","unstructured":"Berk, A., Anderson, G.P., Acharya, P.K., Hoke, M.L., Chetwynd, J.H., Bernstein, L.S., Shettle, E.P., Matthew, M.W., and Adler-Golden, S.M. (2003). MODTRAN4 Version 3 Revision 1 User\u2019s Manual, Air Force Research Laboratory. Technical Report."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/S0034-4257(98)00045-5","article-title":"MODTRAN cloud and multiple scattering upgrades with application to AVIRIS","volume":"65","author":"Berk","year":"1998","journal-title":"Remote Sens. Environ."},{"key":"ref_47","unstructured":"Schl\u00e4pfer, D., and Nieke, J. (2005, January 27\u201330). Operational simulation of at sensor radiance sensitivity using the MODO\/MODTRAN4 environment. Proceedings of the 4th EARSeL Workshop on Imaging Spectroscopy. New Quality in Environmental Studies, Warsaw, Poland."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1117\/12.366315","article-title":"Atmospheric correction for short-wave spectral imagery based on MODTRAN4","volume":"3753","author":"Adler","year":"1999","journal-title":"Proc. SPIE"},{"key":"ref_49","unstructured":"Brockmann, C., Kirches, G., Kirches, S., Gei\u00dfler, J., Kr\u00e4mer, U., Faber, E., Soria, G., Mattar, C., Jimenez, J.C., and Franch, B. (2011). Sentinel-3 Experimental Campaign (SEN3EXP) Final Report, ESA Publications Division. ESA Contract No. 22661\/09\/I-LG."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1080\/014311697218593","article-title":"Correction of atmospheric and topographic effects for high spatial resolution satellite imagery","volume":"18","author":"Richter","year":"1997","journal-title":"Int. J. Remote Sens."},{"key":"ref_51","first-page":"18","article-title":"Sentinel-2 \u2013 the optical high-resolution mission for GMES operational services","volume":"131","author":"Martimort","year":"2007","journal-title":"ESA Bull."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/7\/6\/8019\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:48:05Z","timestamp":1760215685000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/7\/6\/8019"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6,18]]},"references-count":51,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2015,6]]}},"alternative-id":["rs70608019"],"URL":"https:\/\/doi.org\/10.3390\/rs70608019","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,6,18]]}}}