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Possible Bounds on the Earth's Surface Temperature: From the Perspective of a Conceptual Global-Mean Model

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  • 1 Lamont–Doherty Earth Observatory, Columbia University, Palisades, New York
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Abstract

A global-mean model is used here to elucidate possible bounds on the surface temperature of a simplified ocean–atmosphere system. Extending previous one-dimensional models, it has included as internal variables the low-level and high-level cloud covers and the turbulent wind at the surface. The main hypothesis for the model closure is that the conversion rate from the solar to the kinetic energy—or, equivalently, the rate of internal entropy production—is maximized, which has been applied with considerable success in past latitudinal models. From the model derivation, it is found that the surface temperature is narrowly bounded below by the onset of the greenhouse effect and above by the rapid increase of the saturation vapor pressure. Because both are largely intrinsic properties of water, the resulting surface temperature is mostly insensitive to detailed balances or changing external conditions. Even with a 50% change of the solar constant from its present-day value, the model temperature has varied by only about 10 K. The reason that the heat balances can be maintained is an internal adjustment of the low cloud cover, which offsets the solar effect. The model offers a plausible explanation of an equable climate in the geological past so long as there is a substantial ocean.

Corresponding author address: Hsien-Wang Ou, Lamont–Doherty Earth Observatory, Columbia University, Palisades, NY 10964. Email: dou@ldeo.columbia.edu

Abstract

A global-mean model is used here to elucidate possible bounds on the surface temperature of a simplified ocean–atmosphere system. Extending previous one-dimensional models, it has included as internal variables the low-level and high-level cloud covers and the turbulent wind at the surface. The main hypothesis for the model closure is that the conversion rate from the solar to the kinetic energy—or, equivalently, the rate of internal entropy production—is maximized, which has been applied with considerable success in past latitudinal models. From the model derivation, it is found that the surface temperature is narrowly bounded below by the onset of the greenhouse effect and above by the rapid increase of the saturation vapor pressure. Because both are largely intrinsic properties of water, the resulting surface temperature is mostly insensitive to detailed balances or changing external conditions. Even with a 50% change of the solar constant from its present-day value, the model temperature has varied by only about 10 K. The reason that the heat balances can be maintained is an internal adjustment of the low cloud cover, which offsets the solar effect. The model offers a plausible explanation of an equable climate in the geological past so long as there is a substantial ocean.

Corresponding author address: Hsien-Wang Ou, Lamont–Doherty Earth Observatory, Columbia University, Palisades, NY 10964. Email: dou@ldeo.columbia.edu

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