...by a small sample we may judge the whole piece... Miguel de Cervantes, 1605, inDon Quixote de la Mancha, Pt. I, Ch. 4
Abstract
The thermal-infrared (longwave) emission from a vegetated terrain is generally anisotropic, i.e., the emission temperature varies with the view direction. If a directional measurement of temperature is considered to be equal to the effective temperature of the hemispheric emission, then the estimate of the latter can be significantly in error. The view-direction (zenith angleθ eq ) at which the emission equivalence does hold is determined in our modeling study. In a two-temperature field-of-view (soil and plants),θ eq falls in a narrow range depending on plant density and canopy architecture.θ eq does not depend on soil and (uniform) plant temperatures nor on their ratio, even though the pattern of emission vs. the view direction depends crucially on this ratio. For a sparse canopy represented as thin, vertical cylindrical stalks (or vertical blades uniformly distributed in azimuth) with horizontal facets,θ eq ranges from 48 to 53° depending on the optical density of the vertical elements alone. When plant elements are modeled as small spheres,θ eq lies between 53 to 57° (for the same values of the canopy optical density). Only for horizontal leaves (a truly planophile canopy) is the temperature measured from any direction equal to the temperature of the hemispheric emission. When the emission temperature changes with optical depth within the canopy at a specified rate,θ eq depends to some extent on that rate. For practically any sparsely vegetated surface, a directional measurement at the zenith angle of 50° offers an appropriate evaluation of the hemispheric emission, since the error in the estimate will, at most, only slightly exceed 1% (around 4 W m−2). Estimates of the hemispheric emission through a nadir measurement, on the other hand, can be in error in some cases by about 10%, i.e., on the order of 40 W m−2.
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Otterman, J., Susskind, J., Brakke, T. et al. Inferring the thermal-infrared hemispheric emission from a sparsely-vegetated surface by directional measurements. Boundary-Layer Meteorol 74, 163–180 (1995). https://doi.org/10.1007/BF00715715
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DOI: https://doi.org/10.1007/BF00715715