Abstract
Distributions of temperature and longwave radiation are predicted from a state of maximum entropy production (MaxEP) due to meridional heat flux in the atmospheres of the Earth, Mars, Titan and Venus, and the predicted distributions are compared with observational results. In the predictions, we use a multi-box energy balance model that takes into account the effects of obliquity and latitudinal variation of albedo on shortwave absorption. It is found that the predicted distributions are generally in agreement with observations of the Earth, Titan and Venus, suggesting the validity of the MaxEP state for these planets. In the case of Mars, the predicted distributions do not agree well with the observations when compared with those predicted from a state of no meridional heat flux. A simple analysis on advective heat flux using a two-box model shows that the Martian atmosphere is so scant that it cannot carry the heat energy that is necessary for the MaxEP state by advection. These results suggest that the validity of the MaxEP state for a planetary atmosphere is limited when the total amount of atmosphere is not enough to sustain the advective heat flux that is necessary for the MaxEP state.
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Notes
- 1.
We have assumed that the declination δ is constant with respect to daily change of h.
- 2.
A cyclic orbit is assumed in this study. For a more general case with eccentricity see, e.g., [17].
- 3.
In this sense, there do not seem to be multiple maxima for this simple model system with a fixed albedo distribution (cf. [16]).
- 4.
The difference can been seen in the numerical factor in each formulation: 2 in Eq. (11.21) whereas 2(3γ)1/2 ≈ 1.62 in their formulation, with γ = 31/2/π − 1/3 [15]. Their analysis also includes the planetary rotation rate, which turns out to be not important for slowly rotating planets where Eq. (11.18) is approximately valid.
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Acknowledgments
The authors wish to express their cordial thanks to the organizers of the MaxEP Workshop, Canberra, Sept. 2011, where the motivation for this work has been stimulated. Acknowledgment is also given to Dr. Ralph D. Lorenz for valuable comments on Titan’s atmosphere, to Dr. Robert K. Niven for stimulating our interest in thermodynamics of planetary atmospheres, and to Dr. Ehouarn Millour for sending us the original Mars Climate Database. Valuable comments from two anonymous reviewers are also gratefully acknowledged.
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Fukumura, Y., Ozawa, H. (2014). Entropy Production in Planetary Atmospheres and Its Applications. In: Dewar, R., Lineweaver, C., Niven, R., Regenauer-Lieb, K. (eds) Beyond the Second Law. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40154-1_11
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