The application of the principles of invariance to the radiative transfer equation in plant canopies

Barry D Ganapol, R. B. Myneni

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Solutions of the radiative transfer equation describing photon interactions with vegetation canopies are important in remote sensing since they provide the canopy reflectance distribution required in the interpretation of satellite acquired information. The general one-dimensional two-angle transport problem for a finite copy of arbitrary leaf angle distribution is considered. Analytical solutions are obtained in terms of generalized Chandrasekhar's X- and Y-functions by invoking the principles of invariance. A critical step in the formulation involves the decomposition of the integral of the scattering phase function into a product of known functions of the incident and scattered photon directions. Several simplified cases previously considered in the literature are derived from the generalized solution. Various symmetries obeyed by the scattering operator and reciprocity relations are formally proved.

Original languageEnglish (US)
Pages (from-to)321-339
Number of pages19
JournalJournal of Quantitative Spectroscopy and Radiative Transfer
Volume48
Issue number3
DOIs
StatePublished - 1992
Externally publishedYes

Fingerprint

canopies
Radiative transfer
Invariance
radiative transfer
invariance
Photons
canopies (vegetation)
Scattering
photons
scattering
leaves
remote sensing
Remote sensing
Satellites
Decomposition
reflectance
decomposition
formulations
operators
symmetry

ASJC Scopus subject areas

  • Spectroscopy
  • Atomic and Molecular Physics, and Optics

Cite this

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AB - Solutions of the radiative transfer equation describing photon interactions with vegetation canopies are important in remote sensing since they provide the canopy reflectance distribution required in the interpretation of satellite acquired information. The general one-dimensional two-angle transport problem for a finite copy of arbitrary leaf angle distribution is considered. Analytical solutions are obtained in terms of generalized Chandrasekhar's X- and Y-functions by invoking the principles of invariance. A critical step in the formulation involves the decomposition of the integral of the scattering phase function into a product of known functions of the incident and scattered photon directions. Several simplified cases previously considered in the literature are derived from the generalized solution. Various symmetries obeyed by the scattering operator and reciprocity relations are formally proved.

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