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The Earth's radiative cooling is a key driver of climate. Determining how it is affected by greenhouse gas concentration is a core question in climate-change sciences. Due to the complexity of radiative transfer processes, current practices to estimate this cooling require the development and use of a suite of radiative transfer models whose accuracy diminishes as we move from local, instantaneous estimates to global estimates over the whole globe and over long periods of time (decades). Here, we show that recent advances in nonlinear Monte Carlo methods allow a paradigm shift: a completely unbiased estimate of the Earth's infrared cooling to space can be produced using a single model, integrating the most refined spectroscopic models of molecular gas energy transitions over a global scale and over years, all at a very low computational cost (a few seconds)., Competing Interests: Competing interests statement:The authors declare no competing interest.