Abstract
We present a radiative transfer model for Earth-Like-Planets (ELP). The model allows the assessment of the effect of a change in the concentration of an atmospheric component, especially a greenhouse gas (GHG), on the surface temperature of a planet. The model is based on the separation between the contribution of the short wavelength molecular absorption and the long wavelength one. A unique feature of the model is the condition of energy conservation at every point in the atmosphere. The radiative transfer equation is solved in the two stream approximation without assuming the existence of an LTE in any wavelength range. The model allows us to solve the Simpson paradox, whereby the greenhouse effect (GHE) has no temperature limit. On the contrary, we show that the temperature saturates, and its value depends primarily on the distance of the planet from the central star. We also show how the relative humidity affects the surface temperature of a planet and explain why the effect is smaller than the one derived when the above assumptions are neglected.
Highlights
The influence of concentration changes of atmospheric gases on the surface temperature of planetary atmospheres is a leading thread in current planetary research [7]
Due to the importance of the problem, it is desirable to have a model which can predict correctly the greenhouse effect and its dependence on various changes, while at the same time being sufficiently simple to provide a tool to understand the details of the radiative transfer physical processes affecting this problem
The model consists of two parts – radiative transfer and the molecular absorption dependent optical depth
Summary
The influence of concentration changes of atmospheric gases on the surface temperature of planetary atmospheres is a leading thread in current planetary research [7]. Due to the importance of the problem, it is desirable to have a model which can predict correctly the greenhouse effect and its dependence on various changes, while at the same time being sufficiently simple to provide a tool to understand the details of the radiative transfer physical processes affecting this problem. The molecular absorption, with its large variation in wavelength, and the total optical depth of planetary atmospheres, are such that the atmosphere contains spectral windows through which the planetary radiation can leak to space almost freely. Our treatment differs in several points: We impose the energy conservation at each layer, we redefine the absorption coefficients, we apply the radiative transfer and not the diffusion approximation, and we find the temperature feedback directly from the radiative equation and not from the diffusion approximation for the far infrared part of the spectrum
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