Abstract
The interactions between radiation and matter are essential for understanding the physical foundations of remote sensing. This chapter is devoted to a brief review of the statistical mechanical principles underlying the radiative processes. The interactions of thermal radiation with media, the Planck function for a notable example, are understood in terms of statistical mechanics. Another crucial theoretical element behind satellite remote sensing is the radiative transfer equation, which describes the propagation of photon energy over a distance by a simple transport equation known as the radiative transfer equation. In this chapter, the radiative transfer equation is derived in light of the Boltzmann equation of photons.
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Notes
- 1.
It would be more appropriate, for notational consistency with other multidimensional displacement elements such as \(\mathrm{{d}}^3\mathbf {x}\), to express a displacement of solid angle as \(\mathrm{{d}}^2\boldsymbol{\varOmega }\) rather than \(\mathrm{{d}}\varOmega \). In this book, however, the latter is adopted in accordance with convention in the literature.
- 2.
When the mass is smaller than the critical mass, the white dwarf would expand until the relativistic limit gives way to the non-relativistic regime where the equilibrium solution is dynamically stable.
- 3.
Wind is always subsonic in the troposphere, so that \(|\mathbf {U}| \gg |\mathbf {v}|\).
Reference
Rybicki GB, Lightman AP (1985) Radiative processes in astrophysics. Wiley, New York, NY. https://doi.org/10.1002/9783527618170
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Masunaga, H. (2022). Principles of Statistical Mechanics. In: Satellite Measurements of Clouds and Precipitation. Springer Remote Sensing/Photogrammetry. Springer, Singapore. https://doi.org/10.1007/978-981-19-2243-5_4
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DOI: https://doi.org/10.1007/978-981-19-2243-5_4
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