In climate change/global warming studies, the Stefan Boltzmann formula is often used to estimate the amount of radiant energy which escapes outward into outer space from earth. The formula is derived under the assumption that the relevant emissivity of the emitter is a constant for all wave lengths, and its temperature exponent is 4. However, the Earth’s greenhouse gases permit radiations to pass through the atmosphere freely only in some specific wave length windows. It is shown that the wave length dependence of emissivity can change the effective temperature exponent of the Stefan Boltzmann formula. (Source: Lam, H. S. (2007). On the Effective Stefan-Boltzmann Temperature Exponent of the Earth).

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