{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T01:01:11Z","timestamp":1768352471585,"version":"3.49.0"},"reference-count":20,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,5,19]],"date-time":"2021-05-19T00:00:00Z","timestamp":1621382400000},"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-hemispherical reflectance (BHR), in the land surface research community also known as \u201cwhite-sky albedo\u201d, is independent of the directions of incidence and viewing. For vegetation canopies, it is also nearly independent of the leaf angle distribution, and therefore it can be considered an optical quantity that is only dependent on material properties. For the combination leaf canopy and soil background, the most influential material properties are the canopy LAI (leaf area index), optical properties of the leaves, and soil brightness. When the leaf and soil optical properties are known or assumed, one may estimate the canopy LAI from its white-sky spectral albedo. This is also because a simple two-stream radiative transfer (RT) model is available for the BHR of the leaf canopy and soil combination. In this contribution, crown clumping and lateral linear mixing effects are incorporated in this model. A new procedure to estimate soil brightness is introduced here, even under a moderate layer of green vegetation. The procedure uses the red and NIR spectral bands. A MODIS white-sky albedo product at a spatial resolution of 0.05\u00b0 is used as a sample input to derive global maps of LAI, soil brightness, and fAPAR at the local moments of minimum and maximum NDVI over a 20-year period. These maps show a high degree of spatial coherence and demonstrate the possible utility of products that can be generated with little effort by using a direct LUT technique.<\/jats:p>","DOI":"10.3390\/rs13101976","type":"journal-article","created":{"date-parts":[[2021,5,19]],"date-time":"2021-05-19T21:49:21Z","timestamp":1621460961000},"page":"1976","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Bi-hemispherical Canopy Reflectance Model with Surface Heterogeneity Effects for the Estimation of LAI and fAPAR from MODIS White-Sky Spectral Albedo Data"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4696-2144","authenticated-orcid":false,"given":"Wouter","family":"Verhoef","sequence":"first","affiliation":[{"name":"Water Resources Department, Faculty ITC, University of Twente, Hengelosestraat 99, 7514 AE Enschede, The Netherlands"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,19]]},"reference":[{"key":"ref_1","unstructured":"Schaaf, C., and Wang, Z. (2020, March 01). MCD43C3 MODIS\/Terra+Aqua BRDF\/Albedo Albedo Daily L3 Global 0.05Deg CMG V006 [Data Set]. NASA EOSDIS Land Processes DAAC. Available online: https:\/\/doi.org\/10.5067\/MODIS\/MCD43C3.006."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1474","DOI":"10.1364\/AO.9.001474","article-title":"Reflectance Nomenclature and Directional Reflectance and Emissivity","volume":"9","author":"Nicodemus","year":"1970","journal-title":"Appl. Opt."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/0034-4257(84)90057-9","article-title":"Light scattering by leaf layers with application to canopy reflectance modeling: The SAIL model","volume":"16","author":"Verhoef","year":"1984","journal-title":"Remote Sens. Environ."},{"key":"ref_4","unstructured":"Van de Hulst, H.C. (1980). Multiple Light Scattering, Academic Press."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/0034-4257(85)90072-0","article-title":"Earth observation modeling based on layer scattering matrices","volume":"17","author":"Verhoef","year":"1985","journal-title":"Remote Sens. Environ."},{"key":"ref_6","unstructured":"Knyazikhin, Y., Glassy, J., Privette, J.L., Tian, Y., Lotsch, A., Zhang, Y., Wang, Y., Morisette, J.T., Votava, P., and Myneni, R.B. (2021, February 28). MODIS Leaf Area Index (LAI) and Fraction of Photosynthetically Active Radiation Absorbed by Vegetation (FPAR) Product (MOD15) Algorithm Theoretical Basis Document, Available online: http:\/\/eospso.gsfc.nasa.gov\/atbd\/modistables.html."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"D02116","DOI":"10.1029\/2005JD005952","article-title":"Simplifying the interaction of land surfaces with radiation for relating remote sensing products to climate models","volume":"111","author":"Pinty","year":"2006","journal-title":"J. Geophys. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1335","DOI":"10.1080\/01431168508948283","article-title":"Canopy reflectance, photosynthesis and transpiration","volume":"6","author":"Sellers","year":"1985","journal-title":"Int. J. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1016\/j.rse.2016.09.017","article-title":"Fluspect-B: A model for fluorescence, reflectance and transmittance spectra","volume":"186","author":"Vilfan","year":"2016","journal-title":"Remote Sens. Environ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/j.rse.2017.03.004","article-title":"PROSPECT-D: Towards modeling leaf optical properties through a complete lifecycle","volume":"193","author":"Gitelson","year":"2017","journal-title":"Remote Sens. Environ."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/0034-4257(90)90100-Z","article-title":"PROSPECT: A model of leaf optical properties spectra","volume":"34","author":"Jacquemoud","year":"1990","journal-title":"Remote Sens. Environ."},{"key":"ref_12","unstructured":"Kauth, R.J., and Thomas, G.S. (July, January 29). The Tasseled Cap\u2014A Graphic Description of the Spectral-Temporal Development of Agricultural Crops as Seen by LANDSAT. Proceedings of the Symposium on Machine Processing of Remotely Sensed Data, LARS Symposia, West Lafayette, IN, USA."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/0034-4257(94)90134-1","article-title":"A Modified Soil Adjusted Vegetation Index","volume":"48","author":"Qi","year":"1994","journal-title":"Remote Sens. Environ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/0034-4257(88)90106-X","article-title":"A soil-adjusted vegetation index (SAVI)","volume":"25","author":"Huete","year":"1988","journal-title":"Remote Sens. Environ."},{"key":"ref_15","unstructured":"Baret, F., Guyot, G., and Major, D. (1989, January 10\u201314). TSAVI: A vegetation index which minimizes soil brightness effects on LAI or APAR estimation. Proceedings of the 12th Canadian Symposium on Remote Sensing Geoscience and Remote Sensing Symposium, Vancouver, BC, Canada."},{"key":"ref_16","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_17","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0034-4257(88)90041-7","article-title":"The derivation of a simplified reflectance model for the estimation of leaf area index","volume":"25","author":"Clevers","year":"1988","journal-title":"Remote Sens. Environ."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/0034-4257(89)90076-X","article-title":"The Application of a Weighted Infrared-Red Vegetation Index for Estimating Leaf Area Index by Correcting for Soil Moisture","volume":"29","author":"Clevers","year":"1989","journal-title":"Remote Sens. Environ."},{"key":"ref_19","first-page":"D09105","article-title":"Exploiting the MODIS albedos with the Two-stream Inversion Package (JRC-TIP): 1. Effective leaf area index, vegetation, and soil properties","volume":"116","author":"Pinty","year":"2011","journal-title":"J. Geophys. Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/0034-4257(94)90016-7","article-title":"On the Relationships between FAPAR and NDVI","volume":"49","author":"Myneni","year":"1994","journal-title":"Remote Sens. Environ."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/10\/1976\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:03:57Z","timestamp":1760162637000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/10\/1976"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,19]]},"references-count":20,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2021,5]]}},"alternative-id":["rs13101976"],"URL":"https:\/\/doi.org\/10.3390\/rs13101976","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5,19]]}}}