Abstract
A Fast and Accurate Numerical Method for Radiative Transfer in the Atmosphere
Highlights
Photons travel from the Sun to the Earth and participate to its thermal balance
To simulate sufficiently many photons numerically to reach a numerical equilibrium is currently very difficult [3]; one must recourse to continuum mechanics and write energy conservations, the equations of radiative transfer (see [1, 4, 11] and (1),(2) below)
The spectrum of sunlight received is given by the Planck function with the Sun temperature while the Earth emits infrared light according to the Planck function with the Earth temperature
Summary
Photons travel from the Sun to the Earth and participate to its thermal balance. The photons may interact with the atoms in the Earth atmosphere before reaching the ground. The spectrum of sunlight received is given by the Planck function with the Sun temperature while the Earth emits infrared light according to the Planck function with the Earth temperature. These provides boundary conditions to the radiative transfer partial differential equations. The problem is difficult because the solution has numerical singularities (see [9] for a review of the numerical methods) The side effect of this proof is an existence result for the radiative transfer equations with frequency dependent absorption and scattering coefficients. Numerical tests conclude this study with some comments on the effect of greenhouse gases on the temperature in the atmosphere
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