Reflectance quantities in optical remote sensing—definitions and case studies

The remote sensing community puts major efforts into calibration and validation of sensors, measurements, and derived products to quantify and reduce uncertainties. Given recent advances in instrument design, radiometric calibration, atmospheric correction, algorithm development, product development, validation, and delivery, the lack of standardization of reflectance terminology and products becomes a considerable source of error. This article provides full access to the basic concept and definitions of reflectance quantities, as given by Nicodemus et al. [Nicodemus, F.E., Richmond, J.C., Hsia, J.J., Ginsberg, I.W., and Limperis, T. (1977). Geometrical Considerations and Nomenclature for Reflectance. In: National Bureau of Standards, US Department of Commerce, Washington, D.C. URL: http://physics.nist.gov/Divisions/Div844/facilities/specphoto/pdf/geoConsid.pdf.] and Martonchik et al. [Martonchik, J.V., Bruegge, C.J., and Strahler, A. (2000). A review of reflectance nomenclature used in remote sensing. Remote Sensing Reviews, 19, 9–20.]. Reflectance terms such as BRDF, HDRF, BRF, BHR, DHR, black-sky albedo, white-sky albedo, and blue-sky albedo are defined, explained, and exemplified, while separating conceptual from measurable quantities. We use selected examples from the peer-reviewed literature to demonstrate that very often the current use of reflectance terminology does not fulfill physical standards and can lead to systematic errors. Secondly, the paper highlights the importance of a proper usage of definitions through quantitative comparison of different reflectance products with special emphasis on wavelength dependent effects. Reflectance quantities acquired under hemispherical illumination conditions (i.e., all outdoor measurements) depend not only on the scattering properties of the observed surface, but as well on atmospheric conditions, the object's surroundings, and the topography, with distinct expression of these effects in different wavelengths. We exemplify differences between the hemispherical and directional illumination quantities, based on observations (i.e., MISR), and on reflectance simulations of natural surfaces (i.e., vegetation canopy and snow cover). In order to improve the current situation of frequent ambiguous usage of reflectance terms and quantities, we suggest standardizing the terminology in reflectance product descriptions and that the community carefully utilizes the proposed reflectance terminology in scientific publications.