Unified optical-thermal four-stream radiative transfer theory for homogeneous vegetation canopies

W. Verhoef, Q. Xiao, L. Jia, Z. Su

Research output: Contribution to journalArticleAcademicpeer-review

228 Citations (Scopus)


Foliage and soil temperatures are key variables for assessing the exchanges of turbulent heat fluxes between vegetated land and the atmosphere. Using multiple-view-angle thermal-infrared (TIR) observations, the temperatures of soil and vegetation may be retrieved. However, particularly for sparsely vegetated areas, the soil and vegetation component temperatures in the sun and in the shade may be very different depending on the solar radiation, the physical properties of the surface, and the meteorological conditions. This may interfere with a correct retrieval of component temperatures, but it might also yield extra information related to canopy structure. Both are strong reasons to investigate this phenomenon in some more detail. To this end, the relationship between the TIR radiance directionality and the component temperatures has been analyzed. In this paper, we extend the four-stream radiative transfer (RT) formalism of the Scattering by Arbitrarily Inclined Leaves model family to the TIR domain. This new approach enables us to simulate the multiple scattering and emission inside a geometrically homogenous but thermodynamically heterogeneous canopy for optical as well as thermal radiation using the same modeling framework. In this way top-of-canopy thermal radiances observed under multiple viewing angles can be related to the temperatures of sunlit and shaded soil and sunlit and shaded leaves. In this paper, we describe the development of this unified optical-thermal RT theory and demonstrate its capabilities. A preliminary validation using an experimental data set collected in the Shunyi remote sensing field campaign in China is briefly addressed
Original languageEnglish
Pages (from-to)1808-1822
JournalIEEE Transactions on Geoscience and Remote Sensing
Issue number6
Publication statusPublished - 2007


  • gap probability model
  • bidirectional reflectance
  • nonisothermal surfaces
  • light-scattering
  • forest canopy
  • temperature
  • emissivity
  • radiance
  • soil


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