An Analysis of the Earth’s Energy Budget

Stephen Paul Rathbone Wilde; Philip Mulholland

doi:doi:10.11648/j.ijaos.20200402.12

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An Analysis of the Earth’s Energy Budget

Stephen Paul Rathbone Wilde, Philip Mulholland

Published in International Journal of Atmospheric and Oceanic Sciences (Volume 4, Issue 2)

Received: 13 September 2020 Accepted: 27 September 2020 Published: 7 October 2020

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Abstract

In this paper we quantify and attribute by inspection the constituent elements of the power intensity radiant flux transmission for the atmosphere of the Earth, as recorded in the following two published sources; Oklahoma Climatological Survey and Kiehl and Trenberth. The purpose of our analysis is to establish the common elements of the approach used in the formulation of these works, and to conduct an assessment of the two approaches by establishing a common format for their comparison. By applying the standard analysis of a geometric infinite series feed-back loop to an equipartition (half up and half down) diabatic distribution used for the atmospheric radiant flux to all elements of the climate model; our analysis establishes the relative roles of radiant and mass-motion carried energy fluxes that are implicitly used by the authors in their respective analyses. Having established the key controls on energy flux within each model, we then conduct for the canonical model a series of “what-if” scenarios to establish the limits of temperature rise that can be achieved for specific variations in the controls used to calculate the global average temperature. Our analysis establishes that, for the current insolation and Bond albedo, the maximum temperature that can be achieved for a thermally radiant opaque atmosphere is a rise to 29°C. This global average temperature is achieved by a total blocking of the surface-to-space atmospheric window. In order to raise the global average atmospheric temperature to the expected value of 36°C for a putative Cretaceous hothouse world, it is therefore necessary to reduce the planetary Bond albedo. The lack of continental icecaps, and the presence of flooded continental shelves with epeiric seas in a global eustatic high stand sea level, is invoked as an explanation to support the modelling concept of a reduced global Bond albedo during the Cretaceous period. The geological evidence for this supposition is mentioned with reference to published sources.

Published in	International Journal of Atmospheric and Oceanic Sciences (Volume 4, Issue 2)
DOI	10.11648/j.ijaos.20200402.12
Page(s)	54-64
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

Radiation Budget, Climate Model, Atmospheric Window, Bond Albedo, Cretaceous Hothouse World

References

[1]	OK-FIRST Project Earth’s Energy Budget, 1997, Oklahoma Climatological Survey, 100 East Boyd Street, Suite 1210, Norman, OK 73019. Copyright © 1996-2005 Oklahoma Climatological Survey. All Rights Reserved.
[2]	Kiehl, J. T and Trenberth, K. E., 1997. Earth’s Annual Global Mean Energy Budget. Bulletin of the American Meteorological Society, Vol. 78 (2). pp. 197-208.
[3]	Wilde, S. P. R. and Mulholland, P. 2020. Return to Earth: A New Mathematical Model of the Earth’s Climate, International Journal of Atmospheric and Oceanic Sciences. Vol. 4, No. 2, 2020, pp. 36-53. doi: 10.11648/j.ijaos.20200402.11
[4]	Williams, D. R., 2019. Earth Fact Sheet. NASA NSSDCA, Mail Code 690.1, NASA Goddard Space Flight Center, Greenbelt, MD 20771.
[5]	Sagan, C. and Chyba, C., 1997. The Early Faint Sun Paradox: Organic Shielding of Ultraviolet-Labile Greenhouse Gases. Science, 276 (5316), pp. 1217–1221.
[6]	Jacob, D. J. 1999. Introduction to Atmospheric Chemistry. Princeton University Press.
[7]	Mann, M. 2020 One-Layer Energy Balance Model – Meteo 469 From Meteorology to Mitigation: Understanding Global Warming, Department of Meteorology and Atmospheric Science, Penn State College of Earth and Mineral Sciences.
[8]	Gale, A. S., 2000. The Cretaceous world. Biotic response to global change: the last 145 Million Years, pp. 4-19.
[9]	Golovneva, L. B., 2000. The Maastrichtian (Late Cretaceous) climate in the northern hemisphere. Geological Society, London, Special Publications, 181 (1), pp. 43-54.
[10]	Scotese, C. R., 2001. Atlas of Earth History, Volume 1, Paleogeography, PALEOMAP Project, Arlington, Texas, 52 pp.
[11]	Miskolczi, F. M., 2010. The stable stationary value of the earth's global average atmospheric Planck-weighted greenhouse-gas optical thickness. Energy & Environment, 21 (4), pp. 243-262.
[12]	Walliser, E. O. and Schöne, B. R., 2020. Paleoceanography of the Late Cretaceous northwestern Tethys Ocean: Seasonal upwelling or steady thermocline?. PLoS One, 15 (8), p. e0238040.
[13]	Leconte, J., Forget, F., Charnay, B., Wordsworth, R. and Pottier, A., 2013. Increased insolation threshold for runaway greenhouse processes on Earth-like planets. Nature, 504 (7479), pp. 268-271.
[14]	Simpson, G. C., 1928. Some Studies in Terrestrial Radiation. Royal Meteorological Society (London) Memoir, Vol II. No. 16, pp. 69-95.
[15]	Williams, D. R., 2018. Venus Fact Sheet. NASA NSSDCA, Mail Code 690.1, NASA Goddard Space Flight Center, Greenbelt, MD 20771.
[16]	Browning, G. L., 2020. The Unique, Well Posed Reduced System for Atmospheric Flows: Robustness In The Presence Of Small Scale Surface Irregularities. Dynamics of Atmospheres and Oceans, p. 101143.
[17]	Mulholland, P. and Wilde, S. P. R., 2020. An Inverse Climate Modelling Study of the Planet Venus. International Journal of Atmospheric and Oceanic Sciences. Vol. 4, No. 1, 2020, pp. 20-35. doi: 10.11648/j.ijaos.20200401.13.
[18]	Mulholland, P. and Wilde, S. P. R., 2020. An Iterative Mathematical Climate Model of the Atmosphere of Titan, Journal of Water Resources and Ocean Science. Vol. 9, No. 1, 2020, pp. 15-28. doi: 10.11648/j.wros.20200901.13.

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Stephen Paul Rathbone Wilde, Philip Mulholland. (2020). An Analysis of the Earth’s Energy Budget. International Journal of Atmospheric and Oceanic Sciences, 4(2), 54-64. https://doi.org/10.11648/j.ijaos.20200402.12

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ACS Style

Stephen Paul Rathbone Wilde; Philip Mulholland. An Analysis of the Earth’s Energy Budget. Int. J. Atmos. Oceanic Sci. 2020, 4(2), 54-64. doi: 10.11648/j.ijaos.20200402.12

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Stephen Paul Rathbone Wilde, Philip Mulholland. An Analysis of the Earth’s Energy Budget. Int J Atmos Oceanic Sci. 2020;4(2):54-64. doi: 10.11648/j.ijaos.20200402.12

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@article{10.11648/j.ijaos.20200402.12,
  author = {Stephen Paul Rathbone Wilde and Philip Mulholland},
  title = {An Analysis of the Earth’s Energy Budget},
  journal = {International Journal of Atmospheric and Oceanic Sciences},
  volume = {4},
  number = {2},
  pages = {54-64},
  doi = {10.11648/j.ijaos.20200402.12},
  url = {https://doi.org/10.11648/j.ijaos.20200402.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijaos.20200402.12},
  abstract = {In this paper we quantify and attribute by inspection the constituent elements of the power intensity radiant flux transmission for the atmosphere of the Earth, as recorded in the following two published sources; Oklahoma Climatological Survey and Kiehl and Trenberth. The purpose of our analysis is to establish the common elements of the approach used in the formulation of these works, and to conduct an assessment of the two approaches by establishing a common format for their comparison. By applying the standard analysis of a geometric infinite series feed-back loop to an equipartition (half up and half down) diabatic distribution used for the atmospheric radiant flux to all elements of the climate model; our analysis establishes the relative roles of radiant and mass-motion carried energy fluxes that are implicitly used by the authors in their respective analyses. Having established the key controls on energy flux within each model, we then conduct for the canonical model a series of “what-if” scenarios to establish the limits of temperature rise that can be achieved for specific variations in the controls used to calculate the global average temperature. Our analysis establishes that, for the current insolation and Bond albedo, the maximum temperature that can be achieved for a thermally radiant opaque atmosphere is a rise to 29°C. This global average temperature is achieved by a total blocking of the surface-to-space atmospheric window. In order to raise the global average atmospheric temperature to the expected value of 36°C for a putative Cretaceous hothouse world, it is therefore necessary to reduce the planetary Bond albedo. The lack of continental icecaps, and the presence of flooded continental shelves with epeiric seas in a global eustatic high stand sea level, is invoked as an explanation to support the modelling concept of a reduced global Bond albedo during the Cretaceous period. The geological evidence for this supposition is mentioned with reference to published sources.},
 year = {2020}
}

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TY  - JOUR
T1  - An Analysis of the Earth’s Energy Budget
AU  - Stephen Paul Rathbone Wilde
AU  - Philip Mulholland
Y1  - 2020/10/07
PY  - 2020
N1  - https://doi.org/10.11648/j.ijaos.20200402.12
DO  - 10.11648/j.ijaos.20200402.12
T2  - International Journal of Atmospheric and Oceanic Sciences
JF  - International Journal of Atmospheric and Oceanic Sciences
JO  - International Journal of Atmospheric and Oceanic Sciences
SP  - 54
EP  - 64
PB  - Science Publishing Group
SN  - 2640-1150
UR  - https://doi.org/10.11648/j.ijaos.20200402.12
AB  - In this paper we quantify and attribute by inspection the constituent elements of the power intensity radiant flux transmission for the atmosphere of the Earth, as recorded in the following two published sources; Oklahoma Climatological Survey and Kiehl and Trenberth. The purpose of our analysis is to establish the common elements of the approach used in the formulation of these works, and to conduct an assessment of the two approaches by establishing a common format for their comparison. By applying the standard analysis of a geometric infinite series feed-back loop to an equipartition (half up and half down) diabatic distribution used for the atmospheric radiant flux to all elements of the climate model; our analysis establishes the relative roles of radiant and mass-motion carried energy fluxes that are implicitly used by the authors in their respective analyses. Having established the key controls on energy flux within each model, we then conduct for the canonical model a series of “what-if” scenarios to establish the limits of temperature rise that can be achieved for specific variations in the controls used to calculate the global average temperature. Our analysis establishes that, for the current insolation and Bond albedo, the maximum temperature that can be achieved for a thermally radiant opaque atmosphere is a rise to 29°C. This global average temperature is achieved by a total blocking of the surface-to-space atmospheric window. In order to raise the global average atmospheric temperature to the expected value of 36°C for a putative Cretaceous hothouse world, it is therefore necessary to reduce the planetary Bond albedo. The lack of continental icecaps, and the presence of flooded continental shelves with epeiric seas in a global eustatic high stand sea level, is invoked as an explanation to support the modelling concept of a reduced global Bond albedo during the Cretaceous period. The geological evidence for this supposition is mentioned with reference to published sources.
VL  - 4
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ER  -

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Author Information

Stephen Paul Rathbone Wilde

Mulholland Geoscience, Weybridge, Surrey, UK
Philip Mulholland

Mulholland Geoscience, Weybridge, Surrey, UK

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Stephen Paul Rathbone Wilde, Philip Mulholland. (2020). An Analysis of the Earth’s Energy Budget. International Journal of Atmospheric and Oceanic Sciences, 4(2), 54-64. https://doi.org/10.11648/j.ijaos.20200402.12

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ACS Style

Stephen Paul Rathbone Wilde; Philip Mulholland. An Analysis of the Earth’s Energy Budget. Int. J. Atmos. Oceanic Sci. 2020, 4(2), 54-64. doi: 10.11648/j.ijaos.20200402.12

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AMA Style

Stephen Paul Rathbone Wilde, Philip Mulholland. An Analysis of the Earth’s Energy Budget. Int J Atmos Oceanic Sci. 2020;4(2):54-64. doi: 10.11648/j.ijaos.20200402.12

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@article{10.11648/j.ijaos.20200402.12,
  author = {Stephen Paul Rathbone Wilde and Philip Mulholland},
  title = {An Analysis of the Earth’s Energy Budget},
  journal = {International Journal of Atmospheric and Oceanic Sciences},
  volume = {4},
  number = {2},
  pages = {54-64},
  doi = {10.11648/j.ijaos.20200402.12},
  url = {https://doi.org/10.11648/j.ijaos.20200402.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijaos.20200402.12},
  abstract = {In this paper we quantify and attribute by inspection the constituent elements of the power intensity radiant flux transmission for the atmosphere of the Earth, as recorded in the following two published sources; Oklahoma Climatological Survey and Kiehl and Trenberth. The purpose of our analysis is to establish the common elements of the approach used in the formulation of these works, and to conduct an assessment of the two approaches by establishing a common format for their comparison. By applying the standard analysis of a geometric infinite series feed-back loop to an equipartition (half up and half down) diabatic distribution used for the atmospheric radiant flux to all elements of the climate model; our analysis establishes the relative roles of radiant and mass-motion carried energy fluxes that are implicitly used by the authors in their respective analyses. Having established the key controls on energy flux within each model, we then conduct for the canonical model a series of “what-if” scenarios to establish the limits of temperature rise that can be achieved for specific variations in the controls used to calculate the global average temperature. Our analysis establishes that, for the current insolation and Bond albedo, the maximum temperature that can be achieved for a thermally radiant opaque atmosphere is a rise to 29°C. This global average temperature is achieved by a total blocking of the surface-to-space atmospheric window. In order to raise the global average atmospheric temperature to the expected value of 36°C for a putative Cretaceous hothouse world, it is therefore necessary to reduce the planetary Bond albedo. The lack of continental icecaps, and the presence of flooded continental shelves with epeiric seas in a global eustatic high stand sea level, is invoked as an explanation to support the modelling concept of a reduced global Bond albedo during the Cretaceous period. The geological evidence for this supposition is mentioned with reference to published sources.},
 year = {2020}
}

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TY  - JOUR
T1  - An Analysis of the Earth’s Energy Budget
AU  - Stephen Paul Rathbone Wilde
AU  - Philip Mulholland
Y1  - 2020/10/07
PY  - 2020
N1  - https://doi.org/10.11648/j.ijaos.20200402.12
DO  - 10.11648/j.ijaos.20200402.12
T2  - International Journal of Atmospheric and Oceanic Sciences
JF  - International Journal of Atmospheric and Oceanic Sciences
JO  - International Journal of Atmospheric and Oceanic Sciences
SP  - 54
EP  - 64
PB  - Science Publishing Group
SN  - 2640-1150
UR  - https://doi.org/10.11648/j.ijaos.20200402.12
AB  - In this paper we quantify and attribute by inspection the constituent elements of the power intensity radiant flux transmission for the atmosphere of the Earth, as recorded in the following two published sources; Oklahoma Climatological Survey and Kiehl and Trenberth. The purpose of our analysis is to establish the common elements of the approach used in the formulation of these works, and to conduct an assessment of the two approaches by establishing a common format for their comparison. By applying the standard analysis of a geometric infinite series feed-back loop to an equipartition (half up and half down) diabatic distribution used for the atmospheric radiant flux to all elements of the climate model; our analysis establishes the relative roles of radiant and mass-motion carried energy fluxes that are implicitly used by the authors in their respective analyses. Having established the key controls on energy flux within each model, we then conduct for the canonical model a series of “what-if” scenarios to establish the limits of temperature rise that can be achieved for specific variations in the controls used to calculate the global average temperature. Our analysis establishes that, for the current insolation and Bond albedo, the maximum temperature that can be achieved for a thermally radiant opaque atmosphere is a rise to 29°C. This global average temperature is achieved by a total blocking of the surface-to-space atmospheric window. In order to raise the global average atmospheric temperature to the expected value of 36°C for a putative Cretaceous hothouse world, it is therefore necessary to reduce the planetary Bond albedo. The lack of continental icecaps, and the presence of flooded continental shelves with epeiric seas in a global eustatic high stand sea level, is invoked as an explanation to support the modelling concept of a reduced global Bond albedo during the Cretaceous period. The geological evidence for this supposition is mentioned with reference to published sources.
VL  - 4
IS  - 2
ER  -

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