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The stochastic Beer-Lambert-Bouguer law for discontinuous vegetation canopies

Abstract : The 3D distribution of canopy foliage affects the radiation regime and retrievals of canopy biophysical parameters. The gap fraction is one primary indicator of a canopy structure. Historically the Beer-Lambert-Bouguer law and the linear mixture model have served as a basis for multiple technologies for retrievals of the gap (or vegetation) fraction and Leaf Area Index (LAI). The Beer-Lambert-Bouguer law is a form of the Radiative Transfer (RT) equation for homogeneous canopies, which was later adjusted for a correlation between fitoelements using concept of the clumping index. The Stochastic Radiative Transfer (SRT) approach has been developed specifically for heterogeneous canopies, however the approach lacks a proper model of the vegetation fraction. This study is focused on the implementation of the stochastic version of the Beer-Lambert-Bouguer law for heterogeneous canopies, featuring the following principles: 1) two mechanisms perform photon transport- transmission through the turbid medium of foliage crowns and direct streaming through canopy gaps, 2) the radiation field is influenced by a canopy structure (quantified by the statistical moments of a canopy structure) and a foliage density (quantified by the gap fraction as a function of LAI), 3) the notions of canopy transmittance and gap fraction are distinct. The derived stochastic Beer-Lambert-Bouguer law is consistent with the Geometrical Optical and Radiative Transfer (GORT) derivations. Analytical and numerical analysis of the stochastic Beer-Lambert-Bouguer law presented in this study provides the basis to reformulate widely used technologies for retrievals of the gap fraction and LAI from ground and satellite radiation measurements.
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Submitted on : Saturday, May 14, 2022 - 4:12:33 PM
Last modification on : Monday, July 4, 2022 - 9:44:47 AM

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N. Shabanov, J. -P. Gastellu-Etchegorry. The stochastic Beer-Lambert-Bouguer law for discontinuous vegetation canopies. Journal of Quantitative Spectroscopy and Radiative Transfer, 2018, 214, pp.18-32. ⟨10.1016/j.jqsrt.2018.04.021⟩. ⟨insu-03668274⟩

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