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On the Cooling-to-Space Approximation

Author(s): Jeevanjee, Nadir; Fueglistaler, Stephan

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Abstract: The cooling-to-space (CTS) approximation says that the radiative cooling of an atmospheric layer is dominated by that layer’s emission to space, while radiative exchange with layers above and below largely cancel. Though the CTS approximation has been demonstrated empirically and is thus fairly well accepted, a theoretical justification is lacking. Furthermore, the intuition behind the CTS approximation cannot be universally valid, as the CTS approximation fails in the case of pure radiative equilibrium. Motivated by this, we investigate the CTS approximation in detail. We frame the CTS approximation in terms of a novel decomposition of radiative flux divergence, which better captures the cancellation of exchange terms. We also derive validity criteria for the CTS approximation, using simple analytical theory. We apply these criteria in the context of both gray gas pure radiative equilibrium (PRE) and radiative–convective equilibrium (RCE) to understand how the CTS approximation arises and why it fails in PRE. When applied to realistic gases in RCE, these criteria predict that the CTS approximation should hold well for H2O but less so for CO2, a conclusion we verify with line-by-line radiative transfer calculations. Along the way we also discuss the well-known “τ = 1 law,” and its dependence on the choice of vertical coordinate.
Publication Date: Feb-2020
Electronic Publication Date: 22-Jan-2020
Citation: Jeevanjee, Nadir, and Stephan Fueglistaler. "On the cooling-to-space approximation." Journal of the Atmospheric Sciences 77, no. 2 (2020): 465-478. doi: 10.1175/JAS-D-18-0352.1
DOI: doi:10.1175/JAS-D-18-0352.1
ISSN: 0022-4928
EISSN: 1520-0469
Pages: 465-478
Type of Material: Journal Article
Journal/Proceeding Title: Journal of the Atmospheric Sciences
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.
Notes: Corrigendum included, published 10 April 2020, pages 1509-1510.

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