Influence of Adiabatic Gravitational Compression of Atmospheric Mass on the Temperature of the Troposphere Citation: Thizon M. Influence of Adiabatic Gravitational Compression of Atmospheric Mass on the Temperature of the Troposphere. Ecol

Abstract

The temperature that the Earth's surface would have without the greenhouse effect, with an atmosphere completely transparent to infrared radiation, or even without an atmosphere at all, is generally estimated at-18°C. The greenhouse effect is estimated to induce a warming of 33°C to justify the surface temperature of +15°C. To explain this discrepancy, we examine, with the ideal gas law, to which the Earth's atmosphere obeys its normal conditions of pressure and temperature, the role that the adiabatic compression of the atmospheric mass subjected to gravity can play. The dimensional analysis of the ideal gas law demonstrates that compression of the atmosphere produces energy, which can be calculated in Joules. The temperature of the atmosphere near the Earth's surface is influenced by both its invariable atmospheric mass, solar irradiation and the greenhouse effect. This calls into question the commonly established Earth's energy budgets which consider almost exclusively radiative effects, and which deduce a back radiation attributed to the greenhouse effect which is abnormally high.

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Journal of Ecology and Environmental Sciences
JEAES | Volume 12| Issue 3|September, 2024 1
Influence of Adiabatic Gravitational Compression of
Atmospheric Mass on the Temperature of the Troposphere
Michel Thizon*
CNAM (National Conservatory of Arts and Crafts), Paris, France
Research Article
Received: 02-Aug-2024, Manuscript
No. JEAES-24-144291; Editor
assigned: 05-Aug-2024, PreQC No.
JEAES-24-144291 (PQ); Reviewed:
19-Aug-2024, QC No. JEAES-24-
144291; Revised: 26-Aug-2024,
Manuscript No. JEAES-24-144291
(R); Published: 02-Sep-2024, DOI:
10.4172/2347-12.3.003
*For Correspondence: Michel Thizon,
National Conservatory of Arts and
Crafts, Paris, France
E-mail: thizon.michel@orange.fr
Citation: Thizon M. Influence of
Adiabatic Gravitational Compression
of Atmospheric Mass on the
Temperature of the Troposphere. Ecol
Environ Sci. 2024;12:003
Copyright: © 2024 Thizon M. This is
an open-access article distributed
under the terms of the Creative
Commons Attribution License, which
permits unrestricted use, distribution,
and reproduction in any medium,
provided the original author and
source are credited.
ABSTRACT
The temperature that the Earth's surface would have without the
greenhouse effect, with an atmosphere completely transparent to infrared
radiation, or even without an atmosphere at all, is generally estimated at -
18°C. The greenhouse effect is estimated to induce a warming of 33°C to
justify the surface temperature of +15°C. To explain this discrepancy, we
examine, with the ideal gas law, to which the Earth's atmosphere obeys its
normal conditions of pressure and temperature, the role that the adiabatic
compression of the atmospheric mass subjected to gravity can play. The
dimensional analysis of the ideal gas law demonstrates that compression
of the atmosphere produces energy, which can be calculated in Joules. The
temperature of the atmosphere near the Earth's surface is influenced by
both its invariable atmospheric mass, solar irradiation and the greenhouse
effect. This calls into question the commonly established Earth's energy
budgets which consider almost exclusively radiative effects, and which
deduce a back radiation attributed to the greenhouse effect which is
abnormally high.
Keywords: Greenhouse effect; Temperature; Radiation; Atmospheric mass
INTRODUCTION
Earth temperature without atmosphere or greenhouse effects
Goody et al., estimated the solar energy available to heat, both directly
and indirectly, the earth and its atmosphere at an average of 224 W/m-2
[1]. Applying the Stefan-Boltzmann law they assumed that the Earth
radiates as a perfect black body in the infrared band at a temperature of
255.5 K (or min 17.6°C) for the effective emission temperature [2]. These
authors noted that this temperature is lower than the average
temperature of the Earth's surface and indicated that much of the
radiation to space must come from the atmosphere rather than from the
surface. Goody et al., arbitrarily assigned a value of 1 to the emissivity ε
for the calculation, while Jacquemoud assigned a value of 0.98 [3].

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According to Hansen, a solar irradiance of 1367 W/m-2 or generally accepted today 1361 W/m-2, but varying with solar
fluctuations, leads to a surface temperature of 255 K (or min 18°C), which induces a greenhouse effect of +33°C [4].
Cotton reported that the emission temperature is -19°C and the earth temperature is +14°C, which corresponds to a
global greenhouse effect of +33°C [5]. The global greenhouse effect is also estimated at +33°C [6-8].
Logically, at -18°C the surface of the earth without an atmosphere or with an atmosphere totally transparent to
longwave radiation and that plays no physical role, without any greenhouse effect, should be entirely frozen and
covered with frost over its entire surface. This would result in a high Albedo which could be on the order of 0.5 to 0.9
instead of an albedo of 0.30 or 0.29 generally accepted in its current state. In this situation, instead of the solar energy
absorbed by the surface reaching approximately 160 to 168 W/m-2 (Figure 1) this energy could be on the order of 70
W/m-2 [9-11]. The Stefan-Boltzmann formula yields a potential surface temperature of approximately -85°C [2]. Note that
at these temperatures the water vapor pressure above ice is infinitesimal and could only generate an infinitesimal
greenhouse effect. However, according to Nikolov et al., the effects linked to the atmosphere would bring
approximately 90°C and not 33°C to the surface at a temperature of 15°C [12,13]. This would suggest that the global
natural effect of atmosphere could be on the order of 90°C rather than the 33°C of the traditional purely radiative
approach as reported by almost all the authors.
Global mean energy budget of the Earth
Many authors have endeavored to establish an overall assessment of the energy flows to which the earth is subjected
to justify the surface temperature in an essentially radiative system. The Intergovernmental Panel on Climate Change
(IPCC) itself places great emphasis on this in each of its reports. The Figure 1 summarizes the values and differences
obtained while Table 1 summarizes the main authors who evaluated this earth assessment over a period of
approximatively twenty years.
Figure 1. Range of nine energy balances (minimum/maximum according to the authors).
Table 1. Global energy balance of the Earth according to the authors.
Year
Author
Incoming
radiation
(W/m2)
Absorbed
at surface
(W/m2)
Surface
radiation
(W/m2)
Back
radiation
(W/m2)
Evap+sensible
heat (W/m2)
2001
NASA [14]
342
168
390
324
102
2007
IPCC AR4 [15]
342
168
390
324
102
2008
Jacquemoud [3]
342
168
390
324
102

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2009
Trenberth et al.
[16]
341
161
396
333
97
2012
Stephens et al.
[17]
340
165
398
345
112
2012
Wild et al. [18]
340
161
397
342
105
2013
IPCC AR5 [19]
340
161
398
342
104
2015
Lackner et al.
[20]
342
168
390
324
102
2021
IPCC AR6 [21]
340
160
398
342
103
The dispersion and imprecision of the results do not allow the effect on surface temperature to be deduced with
sufficient accuracy. These budgets must be improved as noted by Lupo et al. [22].
Effect of atmospheric pressure
Few authors have mentioned the role that an atmospheric mass subject to gravity could play in temperature. We can
nevertheless cite Leroux [23] Jelbring [24], and Chilingar [25] but these authors evoke a potential role of atmospheric
pressure on a qualitative level without seeking to calculate and quantify the effects, probably given the difficulty of
integrating the atmosphere as a whole. Nikolov et al., clarify the role of atmospheric pressure for several planets,
through a complex semiempirical iterative approach [11].
Dimensional analysis of the ideal gas law PV=nRT
The ideal gas law PV=nRT is one of the most fundamental laws of physics and applies entirely to the lower troposphere
under its usual conditions of pressure and temperature. This universally accepted law, established in 1834 by Émile
Clapeyron, has been perfectly stable for nearly 200 years, which is the case for very few physical laws.
 P is the pressure (Pa);
 V is the volume of the gas (m3);
 n is the quantity of material (mol);
 T is the absolute temperature (K);
 R is the universal constant of ideal gases (8.314 J K−1 mol−1);
Dimensional analysis leads to:
R=PV/nT i.e., J K−1 mol−1=Pa.m3 K−1 mol−1 Hence J=Pa.m3=energy
The volume of air multiplied by the pressure to which it is subjected is considered energy (Joules). The atmosphere is
heated by compression due to the gravitational field to which it is subjected. Isolated in space, the Earth can only
exchange energy with space by radiation, but the atmospheric mass cannot radiate spontaneously since its
homonuclear constituents O2, N2, and Ar are passive and cannot radiate. The earth's surface is warmer and the
atmosphere cannot cool down on contact with it. The compression is thus adiabatic. The greenhouse gases contained
in the atmosphere at low levels, mainly H2O and CO2, are capable of radiating at long wavelengths but do not interact
radiatively with O2 and N2; additionally, they are under the influence of permanent terrestrial infrared radiation, which
they are capable of absorbing, and which is generated continuously from the solar energy received by the Earth's
surface.
The process includes the upward expansion, toward vacuum of the agitated molecules whose kinetic energy decreases
and therefore the pressure, which causes cooling with altitude. It is not due to a decrease in gravity which decreases
by less than 3/1000 at a 10 km altitude but of a struggle between gravity and the suction of the vacuum, until the

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equilibrium which defines an adiabatic thermal gradient. Gravity nevertheless prevents air molecules from escaping
into space. Only some H2 molecules can reach the release speed.
MATERIALS AND METHODS
The ideal gas law allows us to determine the absolute temperature of the atmosphere. By calculating the equivalent
energy in Joules for the entire Earth's atmosphere from PV=nRT. We can also deduce the acquisition in °K compared
to that in the absence of atmosphere, via the thermal capacity of the air. It is not necessary to integrate the entire
atmosphere, which would present a certain difficulty, since we are looking for energy and temperature at zero altitude.
The troposphere can be compared to the mathematical entity that is a hollow ball with a diameter equal to the diameter
of the Earth. By a tight approximation, it is enough to carry out the calculations for the first 100 m of atmosphere
(Table 2), on the basis of indisputable known physical data.
 Surface area of the earth=5.101 × 1014 m2
 Volume with a thickness of 100 m of air=5.101 × 1016 m3
 Pressure at an altitude of 0=10.13 × 104 Pa
 Air 42.29 mol.m-3 at 0 m and 15°C
It is necessary to emphasize that the calculation is based on a final temperature of 15°C, at altitude zero. Temperature
which has therefore already integrated the existing greenhouse effect. The effect due to atmospheric mass which is
then calculated is nevertheless completely dissociated from the greenhouse effect.
Table 2. Data for an air layer 100 m thick. The left part is from U.S. Standard Atmosphere, according to The Engineering
ToolBox [26].
Altitude
(m)
Pressure (Pa)
Temp
(°C )
Density
(kg.m-3)
Temp.
(K)
Volume (m3)
Number of
moles (n)
Volumetric
heat
capacity (CJ
m-3 K-1)
0
10.13 × 104
15
1.225
288.1
5.101 × 1016
2.165 × 1018
1.25 × 103
5000
5.405 × 104
-17.47
0.7364
255.6
5.101 × 1016
*1.301 × 1018
-
10000
2.650 × 104
-49.9
0.4135
223.2
5.101 × 1016
*0.731 × 1018
-
15000
1.211 × 104
-56.5
0.1948
216.6
5.101 × 1016
*0.345 × 1018
-
Note: *n: Deduces from density
RESULTS
Heating of the atmosphere in °K by adiabatic compression
As a tight approximation, for 100 m of atmospheric thickness
Altitude 0 m
 PV=(10.13 × 104 Pa) (5.101 × 1016 m3)=5.167 × 1021 J
 Volumetric heat capacity of air C=1256 J m−3 K−1 (at 0 m, 15°C)
 For 5.101 × 1016 m3 of air; +1°K requires 1256 × 5.101 × 1016 J=6.41 × 1019 J
 5.167 × 1021 J/6.41 × 1019 J=80.7
 +80.7 K overheating due to pressure
Note: With an air layer of 200 m the precision is lower and leads to an overheating of 80.6 K

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Gravity compression results, to the Earth's surface, in 80.7°C of natural greenhouse energy equivalence, which means
that to reach 15°C the initial temperature without atmosphere would be -65.7°C, very different from the -18°C
admitted by radiative approaches for an inactive atmosphere.
Direct application of the ideal gas law T=PV/nR
 Altitude 0 m T=(10.13 × 104 × 5.10 × 1016)/(2.165 × 1018 × 8.314)=287.1 K (+14.0°C)
 Altitude 5,000 m T=254.9 K (-18.2°C)
 Altitude 10,000 m T=222.4 K (-50.7°C)
 Altitude 15,000 m T=215.3 K (-57.8°C)
The calculated values/actual values: At an altitude of 0 m; T=14.0°C (actual 15°C); Altitude of 5,000 m; T=-18.2°C
(actual -17.5°C); Altitude of 10,000 m; T=-50.7°C (actual -49.9°C); Altitude of 15,000 m; T=-57.8°C (actual -56.5°C)
Thermal gradient: Calculated 0-5 km=-6.44°C/km; 5-10 km=-6.50°C/km; 10-15 km=-1.42°C/km
The standard thermal gradient from 0 to 10 km is -6.49°C/km. The ideal gas law explains phenomena linked to
temperatures up to 10,000 m in altitude. Beyond that, the results diverge, and other factors and phenomena are
involved, like ozone and UV influence.
DISCUSSION
Without an atmosphere but with the same Albedo of 30%, the Earth's surface would be at a temperature of -65.7°C.
In reality, with total and reflective covering of ice and frost causing a high Albedo, and without greenhouse effect the
temperature would be lower. The ideal gas law applied here leads to an average global temperature of the atmosphere,
in the immediate vicinity of the surface, of approximately 14.0°C. The often-advanced value of +33°C for the
greenhouse effect, calculated by imagining the surface of the Earth as a perfect black body located in a vacuum and
considering only the radiative effects, is no longer justified or necessary to explain the earth's temperature 15°C at
ground level. The radiative forcing’s or greenhouse effects usually taken into consideration are therefore poorly
estimated and probably weaker than commonly accepted. Until recently, the radiative approach has been
implemented very generally as an inappropriate and imprecise simplification of a complex system that ignores the
influence of the atmospheric mass subjected to gravity, the effect of which is maximal at the surface.
Questioning and re-examinating the phenomena currently considered, particularly radiative phenomena, seems
inevitable for better control of the Earth's temperature in the context of climate forecasts. Goody et al., suggested that
infrared emissions to space emanate from within the atmosphere at -17.6°C [1]. This corresponds to a minimum
altitude of 5,000 m [26]. In 2020, Schildknecht reaches the same conclusion through a long demonstration of radiative
transfer: "radiative equilibrium from the earth's surface to an atmospheric level above approximately five kilometers"
[27]. It is necessary to better distinguish and quantify radiative phenomena according to the altitude at which they occur
and to characterize their possible influence in the form of a greenhouse effect, which appears more moderate than
what is usually estimated for the lower troposphere, where human life unfolds.
The calculations were carried out using the average global values of the U.S. Standard Atmosphere and led to an
average overall result. It is obvious that by applying the ideal gas law at such and such a latitude and at such or such
a time of year, with the corresponding values of air density, and therefore of the number of moles, the pressure
variation and variations in air humidity, the deduced temperature would be variable and local. Weather-related
atmospheric pressure variations can fluctuate naturally and commonly between 973 hPa and 1047 hPa [28]. This

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corresponds to a fluctuation in surface air temperature within a range of 5°C, in accordance with the values of the
U.S. standard atmosphere and the ideal gas law.
CONCLUSION
The temperature on the surface of the earth is mainly determined by the action of gravity on the atmospheric mass,
which is an immutable fact on a scale of millennia. Climatic variations are the result of lesser phenomena. The solar
influence is felt during the day by the direct radiation received, mainly when the sun is at its zenith, and the balance
is modified by direct thermal exchanges between the sunny surface and the air in contact. The earth's surface and the
upper layers of the atmosphere radiate permanently towards space by emitting infrared radiation day and night, thus
restoring the overall balance. Surface infrared radiation is probably less intercepted in the lower troposphere by
greenhouse molecules than is usually thought, thus explaining the surface temperature. However, there is an
atmospheric dynamic, in particular through the water cycle, by evaporation-condensation, but whose overall energy
balance is zero. Air mass movements and convection contribute to the overall dynamics, mainly due to the rotation of
the Earth and the alternations between the presence and absence of solar radiation. Astronomical fluctuations in
sunshine, surface phenomena such as ocean currents, El Niño or La Niña phenomena, extreme weather phenomena
or even volcanic eruptions, as well as other factors that are probably poorly characterized, lead to variations in surface
temperature that nevertheless remain relatively damped due to the stabilizing effect of the invariable atmospheric
mass subject to gravity.
AUTHORS' CONTRIBUTIONS
All the author has contributed in manuscript calculations, writing the manuscript, and composition of figures and
tables.
REFERENCES
1. Goody RM, et al. Atmospheric radiation: Theoretical basis. Oxford University Press 1989.
2. Stefan Boltzmann Law. M=σεT4 i.e. T=(M/σε)0,25; M to W/m-2; Stefan-Boltzmann constant σ=5.670374 ×
10-8 W m-2 K-4 ; emissivity ε ≤ 1
3. Jacquemoud S. Teledetection et geophysique spatiale. University of Paris Diderot 2008.
4. Hansen JD, et al. Climate impact of increasing atmospheric carbon dioxide. Science. 1981;213:957-966.
5. Cotton DJ. Planetary Core and Surface Temperatures. Scientific Research. 2013.
6. Schmidt GA, et al. The attribution of the present day total greenhouse effect. J Geophys Res. 2010;115:D20.
7. Wallace JM, et al. Atmospheric science: An introductory survey. Elsevier. 2006;2:92.
8. Lacis AA, et al. The role of long-lived greenhouse gases as principal LW control knob that governs the global
surface temperature for past and future climate change. Tellus B. 2013;65:19734.
9. Wuttke S, et al. Measurements of spectral snow Albedo at Neumayer, Antarctica. Ann Geophys.
2006;24:7-21.
10. Robinson DA, et al. Albedo of a dissipating snow cover. 1984;1626-1634.
11. Dirmhirn I, et al. Some characteristics of the Albedo of snow. JAMC. 1975;375-379.
12. Volokin D, et al. On the average temperature of airless spherical bodies and the magnitude of Earth’s
atmospheric thermal effect. SpringerPlus. 2014;3:723.
13. Nikolov N, et al. New insights on the physical nature of the atmospheric greenhouse effect deduced from an
empirical planetary temperature model. Environment Pollution and Climate Change. 2001;1:112.
14. Schmidt LJ. Clouds in the balance. Langley Research Center DAAC.

Journal of Ecology and Environmental Sciences
JEAES | Volume 12| Issue 3|September, 2024
7
15. IPCC WGI AR4. Climate Change 2007: Working Group I: The Physical Science Basis. 2007.
16. Trenberth KE, et al. Earth's global energy budget. BAMS. 2009;90:311-323.
17. Stephens G, et al. An update on Earth's energy balance in light of the latest global observations. Nature
Geosci 2012;5:691-696.
18. Wild M, et al. The global energy balance from a surface perspective. Clim Dyn. 2012;40:3107-3134.
19. IPCC WGI AR5. Climate Change 2013: The Physical Science Basis. 2013.
20. Lackner M. Geoengineering for Climate Stabilization. Handbook of Climate Change Mitigation and Adaptation.
2015.
21. IPCC Sixth Assessment Report WGI AR6. The Earth’s Energy Budget, Climate Feedbacks and Climate
Sensitivity. 2021.
22. Lupo A, et al. Global climate models and their limitations. Climate change reconsidered II: Physical Science.
2013;9:148.
23. Leroux M. Dynamic Analysis of Weather and Climate. John Wiley & Sons, Publishers.1996.
24. Jelbring H. The “Greenhouse effect” as a function of atmospheric mass. Energy and Environment.
2003;14:351-356.
25. Chilingar GV, et al. Do increasing contents of methane and carbon dioxide in the atmosphere cause global
warming? ACS. 2014;4:819.
26. The Engineering ToolBox. U.S. Standard Atmosphere vs. Altitude.
27. Schildknecht D. Saturation of the infrared absorption by carbon dioxide in the atmosphere. Int J Mod Phys E.
2020;34:30.
28. Federal Office of Meterology and Climatology Meteoswiss. Atmospheric pressure.