An Iterative Mathematical Climate Model of the Atmosphere of Titan

Philip Mulholland; Stephen Paul Rathbone Wilde

doi:doi:10.11648/j.wros.20200901.13

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An Iterative Mathematical Climate Model of the Atmosphere of Titan

Philip Mulholland, Stephen Paul Rathbone Wilde

Published in Journal of Water Resources and Ocean Science (Volume 9, Issue 1)

Received: 26 October 2019 Accepted: 4 January 2020 Published: 31 January 2020

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Abstract

Titan, the giant moon of the planet Saturn, is recognized to have meteorological processes involving liquid methane that are analogous to the water generated atmospheric dynamics of planet Earth. We propose here that the climatic features of Titan by contrast are more akin to those of the planet Venus, and that this structural similarity is a direct result of the slow daily rotation rate of these two terrestrial bodies. We present here a simple mathematical climate model based on meteorological principles, and intended to be a replacement for the standard radiation balance equation used in current studies of planetary climate. The Dynamic-Atmosphere Energy-Transport climate model (DAET) is designed to be applied to terrestrial bodies that have sufficient mass and surface gravity to be able to retain a dense atmosphere under a given solar radiation loading. All solar orbiting bodies have both an illuminated hemisphere of net energy collection and a dark hemisphere of net energy loss. The DAET model acknowledges the existence of these dual day and nighttime radiation environments and uses a fully transparent non-condensing atmosphere as the primary mechanism of energy storage and transport in a metrological process that links the two hemispheres. The DAET model has the following distinct advantages as a founding model of climate: It can be applied to all terrestrial planets, including those that are tidally locked. It is an atmospheric mass motion and energy circulation process, and so is fully representative of a Hadley cell; the observed fundamental meteorological process of a terrestrial planet’s climate. The diabatic form of the DAET model fully replicates the traditional vacuum planet equation, and as it applies to a totally transparent atmosphere it therefore demonstrates that thermal radiant opacity, due to the presence of polyatomic molecular gases, is not a fundamental requirement for atmospheric energy retention. For the adiabatic form of the DAET model, where the turbulent asymmetric daytime process of forced radiant convection applies, the intercepted solar energy is preferentially retained by the ascending air. The adiabatic DAET climate model shows that the atmospheric greenhouse effect of surface thermal enhancement is a mass motion process, and that it is completely independent of an atmosphere’s thermal radiant opacity.

Published in	Journal of Water Resources and Ocean Science (Volume 9, Issue 1)
DOI	10.11648/j.wros.20200901.13
Page(s)	15-28
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Climate Model, Titan Atmosphere, Atmospheric Dynamics, Terrestrial Planets

References

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[2]	Courtin, R. and Kim, S. J., 2002. Mapping of Titan's tropopause and surface temperatures from Voyager IRIS spectra. Planetary and Space Science, 50 (3), pp. 309-321.
[3]	Schaller, E. L., Brown, M. E., Roe, H. G. and Bouchez, A. H., 2006. A large cloud outburst at Titan's south pole. Icarus, 182 (1), pp. 224-229.
[4]	Del Genio, A. D. and Suozzo, R. J., 1987. A Comparative Study of Rapidly and Slowly Rotating Dynamical Regimes in a Terrestrial General Circulation Model. Journal of the Atmospheric Sciences, Vol. 44 (6), pp. 973-984.
[5]	European Space Agency. 2004. Titan’s True Colors. https://web.archive.org/web/20190803132846/https://www.astrobio.net/titan/titans-true-colors/.
[6]	Waite, J. H., Young, D. T., Cravens, T. E., Coates, A. J., Crary, F. J., Magee, B. and Westlake, J., 2007. The process of tholin formation in Titan's upper atmosphere. Science, 316 (5826), pp. 870-875.
[7]	Porco, C. C., Baker, E., Barbara, J., Beurle, K., Brahic, A., Burns, J. A., Charnoz, S., Cooper, N., Dawson, D. D., Del Genio, A. D. and Denk, T., 2005. Imaging of Titan from the Cassini spacecraft. Nature, 434 (7030), p. 159.
[8]	Sagan, C. and Chyba, C., 1997. The early faint sun paradox: Organic shielding of ultraviolet-labile greenhouse gases. Science, 276 (5316), pp. 1217-1221.
[9]	Persson, A. O., 2005. The Coriolis Effect: Four centuries of conflict between common sense and mathematics, Part I: A history to 1885. International Commission on the History of Meteorology 2, 24pp.
[10]	Williams, D. R., 2016. Solar System Small Worlds Fact Sheet NASA NSSDCA, Mail Code 690.1, NASA Goddard Space Flight Center, Greenbelt, MD 20771. https://nssdc.gsfc.nasa.gov/planetary/factsheet/galileanfact_table.html.
[11]	Limited Science, 2018. Possibility of life on Titan (Largest Planet of Saturn) Methane Sea of Titan https://limitedscience.com/possibility-of-life-on-titan/.
[12]	Knopf, W. 2019. NASA JPL WebGeocalc Titan Occultations https://wgc.jpl.nasa.gov:8443/webgeocalc/#OccultationFinder.
[13]	Williams, D. R., 2018. Saturn Fact Sheet NASA NSSDCA, Mail Code 690.1, NASA Goddard Space Flight Center, Greenbelt, MD 20771. https://nssdc.gsfc.nasa.gov/planetary/factsheet/saturnfact.html.
[14]	Li, L., Nixon, C. A., Achterberg, R. K., Smith, M. A., Gorius, N. J., Jiang, X., Conrath, B. J., Gierasch, P. J., Simon‐Miller, A. A., Flasar, F. M. and Baines, K. H., 2011. The global energy balance of Titan. NASA Reports Archive. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110023012.pdf.
[15]	Robinson, T. D. and Catling, D. C., 2014. Common 0.1 bar tropopause in thick atmospheres set by pressure-dependent infrared transparency. Nature Geoscience, 7 (1), pp. 12-15.
[16]	Connolly, R. and Connolly, M. 2019. Balloons in the Air: Understanding Weather and Climate. Center for Environmental Research and Earth Science. https://blog.friendsofscience.org/wp-content/uploads/2019/08/July-18-2019-Tucson-DDP-Connolly-Connolly-16x9-format.pdf.

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Philip Mulholland, Stephen Paul Rathbone Wilde. (2020). An Iterative Mathematical Climate Model of the Atmosphere of Titan. Journal of Water Resources and Ocean Science, 9(1), 15-28. https://doi.org/10.11648/j.wros.20200901.13

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ACS Style

Philip Mulholland; Stephen Paul Rathbone Wilde. An Iterative Mathematical Climate Model of the Atmosphere of Titan. J. Water Resour. Ocean Sci. 2020, 9(1), 15-28. doi: 10.11648/j.wros.20200901.13

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AMA Style

Philip Mulholland, Stephen Paul Rathbone Wilde. An Iterative Mathematical Climate Model of the Atmosphere of Titan. J Water Resour Ocean Sci. 2020;9(1):15-28. doi: 10.11648/j.wros.20200901.13

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@article{10.11648/j.wros.20200901.13,
  author = {Philip Mulholland and Stephen Paul Rathbone Wilde},
  title = {An Iterative Mathematical Climate Model of the Atmosphere of Titan},
  journal = {Journal of Water Resources and Ocean Science},
  volume = {9},
  number = {1},
  pages = {15-28},
  doi = {10.11648/j.wros.20200901.13},
  url = {https://doi.org/10.11648/j.wros.20200901.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.wros.20200901.13},
  abstract = {Titan, the giant moon of the planet Saturn, is recognized to have meteorological processes involving liquid methane that are analogous to the water generated atmospheric dynamics of planet Earth. We propose here that the climatic features of Titan by contrast are more akin to those of the planet Venus, and that this structural similarity is a direct result of the slow daily rotation rate of these two terrestrial bodies. We present here a simple mathematical climate model based on meteorological principles, and intended to be a replacement for the standard radiation balance equation used in current studies of planetary climate. The Dynamic-Atmosphere Energy-Transport climate model (DAET) is designed to be applied to terrestrial bodies that have sufficient mass and surface gravity to be able to retain a dense atmosphere under a given solar radiation loading. All solar orbiting bodies have both an illuminated hemisphere of net energy collection and a dark hemisphere of net energy loss. The DAET model acknowledges the existence of these dual day and nighttime radiation environments and uses a fully transparent non-condensing atmosphere as the primary mechanism of energy storage and transport in a metrological process that links the two hemispheres. The DAET model has the following distinct advantages as a founding model of climate: It can be applied to all terrestrial planets, including those that are tidally locked. It is an atmospheric mass motion and energy circulation process, and so is fully representative of a Hadley cell; the observed fundamental meteorological process of a terrestrial planet’s climate. The diabatic form of the DAET model fully replicates the traditional vacuum planet equation, and as it applies to a totally transparent atmosphere it therefore demonstrates that thermal radiant opacity, due to the presence of polyatomic molecular gases, is not a fundamental requirement for atmospheric energy retention. For the adiabatic form of the DAET model, where the turbulent asymmetric daytime process of forced radiant convection applies, the intercepted solar energy is preferentially retained by the ascending air. The adiabatic DAET climate model shows that the atmospheric greenhouse effect of surface thermal enhancement is a mass motion process, and that it is completely independent of an atmosphere’s thermal radiant opacity.},
 year = {2020}
}

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TY  - JOUR
T1  - An Iterative Mathematical Climate Model of the Atmosphere of Titan
AU  - Philip Mulholland
AU  - Stephen Paul Rathbone Wilde
Y1  - 2020/01/31
PY  - 2020
N1  - https://doi.org/10.11648/j.wros.20200901.13
DO  - 10.11648/j.wros.20200901.13
T2  - Journal of Water Resources and Ocean Science
JF  - Journal of Water Resources and Ocean Science
JO  - Journal of Water Resources and Ocean Science
SP  - 15
EP  - 28
PB  - Science Publishing Group
SN  - 2328-7993
UR  - https://doi.org/10.11648/j.wros.20200901.13
AB  - Titan, the giant moon of the planet Saturn, is recognized to have meteorological processes involving liquid methane that are analogous to the water generated atmospheric dynamics of planet Earth. We propose here that the climatic features of Titan by contrast are more akin to those of the planet Venus, and that this structural similarity is a direct result of the slow daily rotation rate of these two terrestrial bodies. We present here a simple mathematical climate model based on meteorological principles, and intended to be a replacement for the standard radiation balance equation used in current studies of planetary climate. The Dynamic-Atmosphere Energy-Transport climate model (DAET) is designed to be applied to terrestrial bodies that have sufficient mass and surface gravity to be able to retain a dense atmosphere under a given solar radiation loading. All solar orbiting bodies have both an illuminated hemisphere of net energy collection and a dark hemisphere of net energy loss. The DAET model acknowledges the existence of these dual day and nighttime radiation environments and uses a fully transparent non-condensing atmosphere as the primary mechanism of energy storage and transport in a metrological process that links the two hemispheres. The DAET model has the following distinct advantages as a founding model of climate: It can be applied to all terrestrial planets, including those that are tidally locked. It is an atmospheric mass motion and energy circulation process, and so is fully representative of a Hadley cell; the observed fundamental meteorological process of a terrestrial planet’s climate. The diabatic form of the DAET model fully replicates the traditional vacuum planet equation, and as it applies to a totally transparent atmosphere it therefore demonstrates that thermal radiant opacity, due to the presence of polyatomic molecular gases, is not a fundamental requirement for atmospheric energy retention. For the adiabatic form of the DAET model, where the turbulent asymmetric daytime process of forced radiant convection applies, the intercepted solar energy is preferentially retained by the ascending air. The adiabatic DAET climate model shows that the atmospheric greenhouse effect of surface thermal enhancement is a mass motion process, and that it is completely independent of an atmosphere’s thermal radiant opacity.
VL  - 9
IS  - 1
ER  -

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Author Information

Philip Mulholland

Mulholland Geoscience, Weybridge, Surrey, UK
Stephen Paul Rathbone Wilde

Mulholland Geoscience, Weybridge, Surrey, UK

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Philip Mulholland, Stephen Paul Rathbone Wilde. (2020). An Iterative Mathematical Climate Model of the Atmosphere of Titan. Journal of Water Resources and Ocean Science, 9(1), 15-28. https://doi.org/10.11648/j.wros.20200901.13

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ACS Style

Philip Mulholland; Stephen Paul Rathbone Wilde. An Iterative Mathematical Climate Model of the Atmosphere of Titan. J. Water Resour. Ocean Sci. 2020, 9(1), 15-28. doi: 10.11648/j.wros.20200901.13

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AMA Style

Philip Mulholland, Stephen Paul Rathbone Wilde. An Iterative Mathematical Climate Model of the Atmosphere of Titan. J Water Resour Ocean Sci. 2020;9(1):15-28. doi: 10.11648/j.wros.20200901.13

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@article{10.11648/j.wros.20200901.13,
  author = {Philip Mulholland and Stephen Paul Rathbone Wilde},
  title = {An Iterative Mathematical Climate Model of the Atmosphere of Titan},
  journal = {Journal of Water Resources and Ocean Science},
  volume = {9},
  number = {1},
  pages = {15-28},
  doi = {10.11648/j.wros.20200901.13},
  url = {https://doi.org/10.11648/j.wros.20200901.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.wros.20200901.13},
  abstract = {Titan, the giant moon of the planet Saturn, is recognized to have meteorological processes involving liquid methane that are analogous to the water generated atmospheric dynamics of planet Earth. We propose here that the climatic features of Titan by contrast are more akin to those of the planet Venus, and that this structural similarity is a direct result of the slow daily rotation rate of these two terrestrial bodies. We present here a simple mathematical climate model based on meteorological principles, and intended to be a replacement for the standard radiation balance equation used in current studies of planetary climate. The Dynamic-Atmosphere Energy-Transport climate model (DAET) is designed to be applied to terrestrial bodies that have sufficient mass and surface gravity to be able to retain a dense atmosphere under a given solar radiation loading. All solar orbiting bodies have both an illuminated hemisphere of net energy collection and a dark hemisphere of net energy loss. The DAET model acknowledges the existence of these dual day and nighttime radiation environments and uses a fully transparent non-condensing atmosphere as the primary mechanism of energy storage and transport in a metrological process that links the two hemispheres. The DAET model has the following distinct advantages as a founding model of climate: It can be applied to all terrestrial planets, including those that are tidally locked. It is an atmospheric mass motion and energy circulation process, and so is fully representative of a Hadley cell; the observed fundamental meteorological process of a terrestrial planet’s climate. The diabatic form of the DAET model fully replicates the traditional vacuum planet equation, and as it applies to a totally transparent atmosphere it therefore demonstrates that thermal radiant opacity, due to the presence of polyatomic molecular gases, is not a fundamental requirement for atmospheric energy retention. For the adiabatic form of the DAET model, where the turbulent asymmetric daytime process of forced radiant convection applies, the intercepted solar energy is preferentially retained by the ascending air. The adiabatic DAET climate model shows that the atmospheric greenhouse effect of surface thermal enhancement is a mass motion process, and that it is completely independent of an atmosphere’s thermal radiant opacity.},
 year = {2020}
}

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TY  - JOUR
T1  - An Iterative Mathematical Climate Model of the Atmosphere of Titan
AU  - Philip Mulholland
AU  - Stephen Paul Rathbone Wilde
Y1  - 2020/01/31
PY  - 2020
N1  - https://doi.org/10.11648/j.wros.20200901.13
DO  - 10.11648/j.wros.20200901.13
T2  - Journal of Water Resources and Ocean Science
JF  - Journal of Water Resources and Ocean Science
JO  - Journal of Water Resources and Ocean Science
SP  - 15
EP  - 28
PB  - Science Publishing Group
SN  - 2328-7993
UR  - https://doi.org/10.11648/j.wros.20200901.13
AB  - Titan, the giant moon of the planet Saturn, is recognized to have meteorological processes involving liquid methane that are analogous to the water generated atmospheric dynamics of planet Earth. We propose here that the climatic features of Titan by contrast are more akin to those of the planet Venus, and that this structural similarity is a direct result of the slow daily rotation rate of these two terrestrial bodies. We present here a simple mathematical climate model based on meteorological principles, and intended to be a replacement for the standard radiation balance equation used in current studies of planetary climate. The Dynamic-Atmosphere Energy-Transport climate model (DAET) is designed to be applied to terrestrial bodies that have sufficient mass and surface gravity to be able to retain a dense atmosphere under a given solar radiation loading. All solar orbiting bodies have both an illuminated hemisphere of net energy collection and a dark hemisphere of net energy loss. The DAET model acknowledges the existence of these dual day and nighttime radiation environments and uses a fully transparent non-condensing atmosphere as the primary mechanism of energy storage and transport in a metrological process that links the two hemispheres. The DAET model has the following distinct advantages as a founding model of climate: It can be applied to all terrestrial planets, including those that are tidally locked. It is an atmospheric mass motion and energy circulation process, and so is fully representative of a Hadley cell; the observed fundamental meteorological process of a terrestrial planet’s climate. The diabatic form of the DAET model fully replicates the traditional vacuum planet equation, and as it applies to a totally transparent atmosphere it therefore demonstrates that thermal radiant opacity, due to the presence of polyatomic molecular gases, is not a fundamental requirement for atmospheric energy retention. For the adiabatic form of the DAET model, where the turbulent asymmetric daytime process of forced radiant convection applies, the intercepted solar energy is preferentially retained by the ascending air. The adiabatic DAET climate model shows that the atmospheric greenhouse effect of surface thermal enhancement is a mass motion process, and that it is completely independent of an atmosphere’s thermal radiant opacity.
VL  - 9
IS  - 1
ER  -

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