TY - JOUR

T1 - On the cooling-to-space approximation

AU - Jeevanjee, Nadir

AU - Fueglistaler, Stephan

N1 - Funding Information:
Acknowledgments. This research was supported by NSF Grants AGS-1417659 and AGS-1660538, and NJ was supported by a Hess fellowship from the Princeton Department of Geosciences. NJ thanks Jacob Seeley and Robert Pincus for helpful feedback and encouragement, as well as Daniel Koll and two anonymous reviewers for very helpful reviews. RFM output and R scripts used in producing this manuscript are available at https://github.com/jeevanje/ 18cts.git.
Publisher Copyright:
© 2020 American Meteorological Society.

PY - 2020/2/1

Y1 - 2020/2/1

N2 - 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 ‘‘t 5 1 law,’’ and its dependence on the choice of vertical coordinate.

AB - 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 ‘‘t 5 1 law,’’ and its dependence on the choice of vertical coordinate.

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U2 - 10.1175/JAS-D-18-0352.1

DO - 10.1175/JAS-D-18-0352.1

M3 - Article

AN - SCOPUS:85082883555

VL - 77

SP - 465

EP - 478

JO - Journals of the Atmospheric Sciences

JF - Journals of the Atmospheric Sciences

SN - 0022-4928

IS - 2

ER -