Download Radiation in the Atmosphere: A Course in Theoretical by Wilford Zdunkowski PDF

By Wilford Zdunkowski

Concept and functions of radiative move for graduate scholars and researchers in meteorology and comparable sciences.

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The photon budget equation finally results in the so-called radiative transfer equation (RTE) which is a linear integro-differential equation for the radiance Iν (r, Ω, t). Let us consider a six-dimensional (6-D) volume element in (x, y, z, ϑ, ϕ, ν)-space with side lengths ( x, y, z, ϑ, ϕ, ν). This volume element is assumed to be fixed in time t. 1) where V = x y z is the ordinary volume element in space. In order to simplify the notation, the dependence of different variables on (r, Ω, t) will henceforth be omitted except where confusion is likely to occur.

For ease of notation the subscript ν will henceforth be omitted from all radiative quantities. 48) where B(s) = B(T (s)) is the Planck function which depends on frequency and local temperature. 48) will be motivated in the Appendix to this chapter. In a plane–parallel medium the only spatial variable is the altitude z. The direction of the radiation is defined by the angle ϑ with respect to the z-axis and by the azimuth angle ϕ counted from an arbitrary origin. 4 The RTE for a horizontally homogeneous atmosphere 39 From the figure it is also seen that for upward directed radiance µ > 0 while for downward directed radiance µ < 0.

1 Mass flux entering the left face and leaving the right face of a cube with volume d x d y dz. ∂ Nν ∂t insc ∂ Nν ∂t em : Scattering of photons with frequency ν and arbitrary direction Ω into the desired direction Ω (inscattering). : Emission of photons with frequency ν in direction Ω. The individual contributions of these processes to the photon budget equation will now be discussed in detail. 1 The exchange of photons The exchange of photons can be treated in analogy to the continuity equation for the mass in fluid mechanics.

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