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Earth Sciences
2019; 8(6): 346-351
doi: 10.11648/j.earth.20190806.15
ISSN: 2328-5974 (Print); ISSN: 2328-5982 (Online)
On the Apparent Relationship Between Total Solar
Irradiance and the Atmospheric Temperature at 1 Bar on
Three Terrestrial-type Bodies
Author; Robert Ian Holmes PhD
Affiliation; Science & Engineering Faculty, Federation University, Ballarat, Australia
Email address:
r.holmes@federation.edu.au
To cite this article:
Robert Ian Holmes. On the Apparent Relationship Between Total Solar Irradiance and the Atmospheric Temperature at 1 Bar on Three
Terrestrial-type Bodies. Earth Sciences. Vol. 8, No. 6, 2019, pp. 346-351. doi: 10.11648/j.earth.20190806.15
Received: October 23, 2019; Accepted: December 18, 2019; Published: December 26, 2019
Abstract: It has been discovered that there appears to exist a close relationship between relative differences in total solar
irradiance and the atmospheric temperature, at a pressure of 1 bar, on all three terrestrial-type bodies which possess thick
atmospheres. The apparent relationship is through the quaternary root of total solar irradiance at 1 bar, and applies to the planetary
bodies Venus, Earth and Titan. The relationship is so close that the average surface atmospheric temperature of Earth can be
easily calculated to within 1 Kelvin (0.5%) of the correct figure by the knowledge of only two numbers, neither of which are
related to the Earth’s atmosphere. These are; the atmospheric temperature in the Venusian atmosphere at 1 bar, and the top-of-
atmosphere solar insolation of the two planets. A similar relationship in atmospheric temperatures is found to exist, through
insolation differences alone, between the atmospheric temperatures at 1 bar of the planetary bodies Titan and Earth, and Venus
and Titan. This relationship exists despite the widely varying atmospheric greenhouse gas content, and the widely varying albedos
of the three planetary bodies. This result is consistent with previous research with regards to atmospheric temperatures and their
relationship to the molar mass version of the ideal gas law, in that this work also points to a climate sensitivity to CO2 - or to any
other ‘greenhouse’ gas - which is close to or at zero. It is more confirmation that the main determinants of atmospheric
temperatures in the regions of terrestrial planetary atmospheres which are >0.1 bar, is overwhelmingly the result of two factors;
solar insolation and atmospheric pressure. There appears to be no measurable, or what may be better termed ‘anomalous’
warming input from a class of gases which have up until the present, been incorrectly labelled as ‘greenhouse’ gases.
Keywords: Climate Change, Global Climate Change, Global Warming, Greenhouse Gases, Greenhouse Effect,
Venus Temperature, Earth Temperature, Titan Temperature, Atmospheric Thermal Gradient
1. Introduction
It is known that all planetary bodies with thicker
atmospheres naturally set up a rising thermal gradient in that
part of the atmosphere, which is higher than a pressure of 0.1
bar, until that bodies’ surface is reached [1]. Previous works
[2-4, 14] have indicated that there may be a relationship
between total solar irradiance (TSI), atmospheric pressures
and planetary atmospheric temperature on bodies which
possess thick atmospheres. It is shown here that this
relationship appears to exist across all three terrestrial-type
bodies which possess thick atmospheres. If this relationship
proves to be robust, then it will present difficulties for several
current hypothesis with regards to what forms and causes
planetary atmospheric temperature. In particular, the idea that
greenhouse gases play a significant role in forming
atmospheric temperature, (15) and the idea that albedo plays a
significant role in forming atmospheric temperatures (22).
1.1. A Physical Law Must Be Universal
Whenever a hypothesis is used to explain the Earth’s
temperature, it must also take into account the universality of
the physical laws of nature. For instance, it must explain how
a similar gradient/enhancement appears in other planetary
atmospheres with widely varying levels of greenhouse gases
[1]. And must also explain, as shown here, how the
Earth Sciences 2019; 8(6): 346-351 347
atmospheric temperature at 1 bar, in all three terrestrial-type
bodies which possess thick atmospheres seem to be related to
the quaternary root of relative differences in total irradiation at
equal pressure, regardless of the very different albedos and
greenhouse gas percentages of these bodies.
1.2. Applying the Stefan-Boltzmann Law of Isolated Bodies
to Planets with Atmospheres
It is known from the Stefan-Boltzmann law that the
radiating temperature of an isolated planetary body in space,
(one which possesses no atmosphere), varies with the fourth-
root of the power incident upon it [30]. And given that
previous works [1-4] have detailed that a principle factor in
determining atmospheric temperatures on planetary bodies
with thick atmospheres is atmospheric pressure, logic dictates
that these may be combined - initially at a standard for pressure
- for example, 1 bar.
2. Calculated vs Measured Temperatures
of the Three Planetary Bodies at 1 bar
If this hypothesised relationship proves to be true, and the
atmospheric temperature of a planetary body in space varies
with the quaternary root of relative TSI difference, it will mean
that the temperature of Venus at 1atm (Tv) should be found to
be the quaternary root of 1.91 times the temperature on Earth
at 1atm (Te). Note that Venus receives 1.91 times the solar
insolation of Earth [5]. Similarly, Earth’s average temperature
(Te) will be found to be the quaternary root of 0.52 times the
temperature on Venus at 1atm (Tv). Note that Earth receives
0.52 times the solar insolation of Venus [5]. For Titan, the only
other terrestrial-type body with a thick atmosphere, again; it
will mean that the temperature of Titan at 1atm (Tt) should be
the quaternary root of 0.01089 times the temperature on Earth
at 1atm (Te). Note that Titan receives 0.01089 times the solar
insolation of Earth [5].
Therefore;
x Te (1)
Venus
x Te (2)
Tv = 1.176 x 288
Tv = 339 Kelvin
Earth
x Tv (3)
Te = 0.850 x 340
Te = 289.1 Kelvin
Titan
x Te (4)
Tt = 0.323 x 288
Tt = 93 Kelvin
2.1. The Disappearance of ‘Albedo’ and the ‘Greenhouse’
Gas Effect
Logic perhaps dictates that the widely differing albedos and
‘greenhouse’ gas content must mean something for planetary
temperatures. Yet the temperatures at 1 bar, calculated from
other planets, using relative TSI alone, are surprisingly close
to the measured temperatures. These bodies are acting as
though here is no effect from the varying greenhouse gas
content, and no effect from the different planetary albedos.
Table 1. The calculated vs measured temperature of three terrestrial-type bodies at 1 atm.
Planet
Measured Temp
Relative TSI
Fourth Root TSI
Calculated Temp
Albedo
GHG %
Venus
340 Kelvin
1.91
1.176
339 Kelvin
77%
96.5%
Earth
288 Kelvin
0.523
0.850
289.1 Kelvin
30%
2.5%
Titan
85-90 Kelvin
0.01089
0.323
93 Kelvin
22%
2.7%
Figure 1. Greenhouse gas content and albedo vary widely across Venus, Earth and Titan.
2.2. Venusian & Titan Temperature at 1atm Is Accurately
Predicted by Relative TSI Alone
The Venusian lapse rate, perhaps surprisingly considering
the very different atmospheric conditions, is very similar to
Earth’s at 7.7 K/km but extends much higher, up to at least
50km [6]. A little below that height at 49km is where a
348 Robert Ian Holmes: On the Apparent Relationship Between Total Solar Irradiance and the Atmospheric
Temperature at 1 Bar on Three Terrestrial-type Bodies
pressure of 1atm is to be found and is where a temperature of
~340K has been measured [6-8] to prevail. The measured
temperature in the Venusian atmosphere cited here comes from
Venera’s 8, 9, 10, 11 and 12 and from the Pioneer Sounder at
1atm, averages 340K [12, 13, 20]. Titan data comes from
NASA, occultations and the Huygens lander [5, 10, 11, 23, 31,
32]. Earth data [5, 9, 16]. The temperature at 1atm on Venus,
divided by the fourth-root of the insolation difference, results
in 289.1K - a value very close to Earth’s average surface
temperature of 288K at 1atm. Yet Venus has a 96.5%
greenhouse gas atmosphere, compared to Earth’s at just 2.5%.
It’s hard to imagine atmospheres with such a differing
greenhouse gas content, yet there still remain very strong
similarities in the rate of the tropospheric thermal gradient and
as seen here, in the relative insolation-adjusted temperatures at
1atm. These measurements, relationships and the similarity of
the thermal gradients point strongly towards the existence of a
universal physical law which governs planetary atmospheric
temperatures - and one which does not take into account the
relative greenhouse gas contents; instead, this law clearly
operates as if greenhouse gases are not special.
This result is consistent with previous research [3] with
regards to atmospheric temperatures and their relationship to
the molar mass version of the ideal gas law, in that this work
also points to a climate sensitivity to CO - or to any other so-
called ‘greenhouse’ gas - which is close to or at zero. It is more
confirmation that the main determinants of atmospheric
temperatures in the regions of terrestrial planetary
atmospheres which are >0.1 bar, is overwhelmingly the result
of two factors; solar insolation and atmospheric pressure.
There appears to be no measurable, or what may be better
termed ‘anomalous’ warming or cooling input in these regions
from a class of gases which have up until the present, been
apparently incorrectly labelled as ‘greenhouse’ gases.
‘Anomalous’ meaning an effect outside of the contributions
from their three basic properties of density, pressure and molar
mass; in short, as far as it is possible to measure, there is no
such thing as a special class of ‘greenhouse’ gases.
Figure 2. Temperatures at 1 atm are accurately predicted by TSI alone across these three bodies.
3. Implications for the ‘Greenhouse
Effect’ of ‘Greenhouse’ Gases
If this relationship between TSI alone and planetary
temperatures at 1 bar proves to be real, it will have important
implications for the very existence of the so-called
‘greenhouse effect’ as it has been proposed by the
intergovernmental panel on climate change and others [15, 19,
21, 22]. The data shows that the ‘greenhouse gas’
concentration varies widely from the low 2.7% and 2.5% [5,
9-11] for Titan and Earth respectively, to the very high 96.5%
for Venus; the implication must be that there cannot be any
special warming effect from the so-called ‘greenhouse’ gases.
This result adds and contributes to considerable other evidence
[2-4, 14, 17, 18, 24-29], that there is no sign of any 'greenhouse
effect' from ‘greenhouse’ gases on any of these three bodies.
TSI and a thermal gradient / thermal enhancement set up by
auto-compression [2, 3] and convection alone appear to be the
main drivers which establish planetary atmospheric
temperatures on these bodies.
Additionally, if the quaternary root of relative differences in
TSI at the equal atmospheric pressure of 1 atm does indeed
predict temperature irrespective of albedo, then the means by
which planetary atmospheric temperatures are presently
calculated, which include albedo, will have to be revised.
3.1. Average Temperature of Earth’s Surface Can Be
Accurately Calculated - from Venus
The relationship between a resultant atmospheric
temperature at 1 bar and the atmospheric pressure / relative
TSI combination means that Earth’s average surface
temperature can be easily and accurately calculated by
measuring just two input factors; the temperature of the Venus
atmosphere at 1 bar, and the relative distances of these planets
from the Sun (i.e. the relative TSI of Earth and Venus).
Thus;
x Te
(5)
Earth Sciences 2019; 8(6): 346-351 349
Kelvin
This temperature of the Earth’s surface, derived from Venus,
is within 0.4% of the correct figure. The same calculation -
using Titan’s atmospheric temperature at 1 bar and its relative
TSI, to arrive at an estimate of the Earth’s surface temperature,
is not quite as accurate as this but is still within a few percent
of the correct temperature. The reason for the discrepancy
could be due to Titan’s atmospheric temperature at 1 bar being
measured less often and being less well known than the
Venusian atmospheric temperatures. However, it could not be
due to an anomalous effect from Titan’s ‘greenhouse’ gas
content, unless those ‘greenhouse’ gases somehow cause a
slight cooling. Note that Titan has a far greater atmospheric
greenhouse gas content (in global warming potential terms)
[10, 31, 32] than Earth has.
A calculation from formula 1, using Earth or Venus as inputs,
results in a predicted Titan 1 bar temperature of 93 Kelvin. The
surface temperature on Titan, measured by the Cassini probe
has been shown to vary between 90 Kelvin at the poles and 94
Kelvin at the equator (31, 32). However, the surface pressure
on Titan is 1.45 bar; and given the thermal gradient known to
exist there, [1] the temperature at 1 bar is expected to be
somewhat lower, in the range 85 - 90 Kelvin. An investigation
into the reasons for this slight discrepancy between predicted
and measured temperatures at 1 bar is outside the scope of this
work.
3.2. Predictions of Atmospheric Temperatures Become
Possible
A further consequence - again if this simple relationship
holds between relative TSI and atmospheric temperatures at 1
atm - is that atmospheric temperature predictions become
possible. For example, a prediction of the 1 atm temperature
of Earth at double (Td) its current distance from the Sun can
easily be made;
Earth x2
x Te (6)
Td = 0.707 x 288
Td = 204 Kelvin
4. Consistent with Previous Research
The insolation-related correlation in temperature data from
1atm points towards there being no significant (or anomalous)
warming from the ‘greenhouse’ gases present and is consistent
with previous [3, 4, 14, 29] research. The previous work by
Holmes [3] reveals that a ‘greenhouse gas effect’ caused by
‘greenhouse gases’ effectively does not exist in planetary
troposphere’s (the regions of terrestrial atmospheres which
are >10kPa). A thermal gradient and a surface thermal
enhancement do exist - but these are attributed to auto-
compression / convection and not specifically to any
anomalous input from ‘greenhouse’ gases. The final
conclusions of that research can be summarized thus;
Postulates;
• The Ideal Gas Law is correct.
• The same external conditions such as insolation and auto-
compression prevail.
4.1. Why the Ideal Gas Law Is Inconsistent with Anomalous
Warming from a Greenhouse Gas Effect
For a ‘greenhouse effect’ caused by ‘greenhouse gases’ to
occur in a convecting atmosphere (one of >10kPa), a large
anomalous change must happen in the density, the pressure or
both.
No anomalous changes of this magnitude have been
detected in any planetary atmospheres. In fact, anomalous
changes of this nature are forbidden by the ideal gas law and
its derivatives like the molar mass version, because they treat
all gases equally. The molar mass version of the ideal gas law
accurately determines - and allows - an atmospheric
temperature to be determined based only on a gas constant and
three gas properties; namely pressure, density and molar mass.
No reference to the radiative properties of a gas are needed or
included. Therefore, it can be said that different concentrations
of gases at the same or at different times can provide the same
temperature or different temperatures.
However – the same concentrations of gases cannot
provide different temperatures at different times.
The formula T = P M / R ρ which is derived from the ideal
gas law, forbids it. This fact presents a terminal conflict with
the greenhouse gas hypothesis, as it is presented by the IPCC*
[15].
4.2. Why There Is a Terminal Conflict Between the Ideal
Gas Law and the IPCC’s Reports
*The reason for the terminal conflict is because it is stated
in all IPCC reports that there exists a time delay to reach
‘equilibration’, due to the nature of the greenhouse gas effect
resulting in what the IPCC calls the ECS (Equilibrium Climate
Sensitivity) climate sensitivity to CO being in the range of
1.5C - 4.5C. The IPCC reports state that if there was a sudden
doubling in the atmospheric greenhouse gas CO, the
greenhouse gas effect from this would operate slowly, causing
an eventual ~3c of warming over centuries to millennia.
Therefore, the IPCC’s claim is that since the IPCC’s climate
sensitivity range is 1.5C - 4.5C, the temperature must rise
significantly over time, with the same prevailing atmospheric
gas concentrations, and there would be no rapid equilibration,
as the ideal gas law and it’s derivative, the molar mass version,
demand. This represents the terminal conflict between the
IPCC's description of the ‘greenhouse gas effect’ and way the
molar mass version of the ideal gas law operates. The ideal gas
law is a pillar of gas thermodynamics and physics and cannot
be lightly discounted in favor of a wholly hypothetical
warming from ‘greenhouse gases’ such as CO, which has
never actually been empirically detected or quantified in the
real atmosphere.
350 Robert Ian Holmes: On the Apparent Relationship Between Total Solar Irradiance and the Atmospheric
Temperature at 1 Bar on Three Terrestrial-type Bodies
5. Conclusion
The temperature of the atmospheres at 1 bar (101.3kPa) of
all three of the terrestrial-type planetary bodies with thick
atmospheres, despite the large differences between them both
in atmospheric greenhouse gas content and albedo (Figure 1),
appears to relate almost exclusively to the quaternary root of
relative differences in TSI (Figure 2). This seems to point to
the main determinants of planetary atmospheric temperatures
of terrestrial-type bodies which possess thick atmospheres,
being atmospheric pressure and TSI, not albedo and
greenhouse gas content.
If this relationship proves to be a real feature of planetary
atmospheric physics, it will have far-reaching effects for how
albedo and ‘greenhouse’ gas content are treated when
calculating atmospheric temperatures in the future. The
relationship tends to add to previous work that indicates the
likelihood of a very low or a zero, climate sensitivity for CO2
[2-4,14,17,18,24-29].
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