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Abstract
The widespread explanations of the greenhouse effect taught to millions of schoolchildren are misleading. The objective of this work is to clarify how
increasing CO
2
produces warming in current times. It is found that there are two contexts for the greenhouse gas effect. In one context, the fundamental
greenhouse gas effect, one imagines a dry Earth starting with no water or CO
2
and adding water and CO
2
. This leads to the familiar “thermal blanket”
that strongly inhibits IR transmission from the Earth to the atmosphere. The Earth is much warmer with H
2
O and CO
2
. In the other context, the current
greenhouse gas effect, CO
2
is added to the current atmosphere. The thermal blanket on IR radiation hardly changes. But the surface loses energy primarily
by evaporation and thermals. Increased CO
2
in the upper atmosphere carries IR radiation to higher altitudes. The Earth radiates to space at higher altitudes
where it is cooler, and the Earth is less able to shed energy. The Earth warms to restore the energy balance. The “thermal blanket” is mainly irrelevant to the
current greenhouse gas effect. It is concluded that almost all discussions of the greenhouse effect are based on the fundamental greenhouse gas effect, which
is a hypothetical construct, while the current greenhouse gas effect is what is happening now in the real world. Adding CO
2
does not add much to a “thermal
blanket” but instead, drives emission from the Earth to higher, cooler altitudes.
How Increased CO
2
Warms
the Earth-Two Contexts for
the Greenhouse Gas Effect
Donald Rapp*
1445 Indiana Ave., South Pasadena, CA 91030, USA
*Correspondence: Donald Rapp, 1445 Indiana Ave., South Pasadena, CA 91030, USA,
Email: drdrapp@earthlink.net
Mini Review
Article Information
Submitted: October 14, 2024
Approved: October 23, 2024
Published: October 24, 2024
How to cite this article: Rapp D. How Increased CO
2
Warms
the Earth-Two Contexts for the Greenhouse Gas Effect. IgMin
Res. October 24, 2024; 2(10): 854-859. IgMin ID: igmin259;
DOI: 10.61927/igmin259; Available at: igmin.link/p259
Copyright: © 2024 Rapp D. This is an open access article
distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is
properly cited.
Before attempting to deal with the question of how rising
CO
2
concentration affects the current Earth’s climate, it is
appropriate to irst discuss the Earth’s energy budget. The
exact values for each energy low are not important, but
the relative values are important to show which processes
dominate.
Finally, we provide an explanation of how adding CO
2
to the current atmosphere produces global warming in the
current atmosphere. The mechanism is not widely known and
is likely to be surprising to some. Warming does not occur by
increasing the thickness of the thermal blanket but instead
occurs by raising the altitude at which the Earth radiates to
space.
Solar energy input to the earth
Estimates of energy transfer in the Earth system were
made by Lindsey, Trenberth, et al. Wild, et al. and Stephens,
et al. [1-4]. In the manuscript that follows, the results of these
studies are interpreted and averaged to provide a rough
summary of the Earth’s energy budget. The exact values of
the various energy lows are not important in this study, but
their relative magnitudes are important to deine the major
mechanisms for energy low. These four references will be
referred to generically as “LTWS”. Godwin also reviewed these
Introduction
Background
Were it not for the Sun, the Earth would be a frozen hulk in
space. The Sun sends a spectrum of irradiance to the Earth, the
Earth warms, and the Earth radiates energy out to space. This
process continues until the Earth warms enough to radiate
about as much energy to space as it receives from the Sun,
reaching an approximate steady state. If for some reason, the
Earth is unable to radiate all the energy received from the Sun,
the Earth will warm until it can radiate all the energy received.
It is widely accepted that rising CO
2
concentration reduces
the ability of the Earth to radiate energy to space. In a dynamic
situation where the CO
2
concentration is continually increasing
with time, the Earth will continuously warm as it tries to
“catch up” to the effect of increasing CO
2
and reestablish a
steady state. It is a conundrum that while it is widely accepted
that rising CO
2
concentration produces global warming, the
exact mechanism by which warming is induced in the current
atmosphere by rising CO
2
is not widely understood. The
concept of a “thermal blanket” imposed by greenhouse gases
to warm the Earth has merit in some contexts but is mainly
irrelevant to the question of how adding CO
2
to the current
atmosphere produces warming.
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references, but he reached very different conclusions than are
reached in this manuscript [5].
LTWS is widely agreed that the average solar power
input to Earth is 341 W/m
2
. The solar irradiance in the upper
atmosphere is about 1,362 W/m
2
[6]. The LTWS models
hypothesize 1,362 W/m
2
of solar power impinging on a
column of the radius of the Earth (R) with the cross-sectional
area πR
2
, while the total area of the Earth is 4πR
2
, so the
average solar intensity on the Earth is (1/4) (1,362 W/m
2
).
That is how they might have derived 341 W/m
2
as the average
solar input to the Earth.
Based on LTWS, solar power input to Earth was interpolated
and averaged to be approximately distributed as follows:
Input to Earth: 341 W/m
2
Relected by the atmosphere (and returned to space) 79 W/m
2
Relected by the Earth’s surface (and returned to space) 23 W/m
2
Total injected into the Earth system = 341 – 79 – 23 = 239 W/m
2
Absorbed by the Earth’s lower atmosphere 76 W/m
2
Absorbed by the Earth’s surface 163 W/m
2
These inputs from the Sun to Earth are used as starting
points for analyzing energy low within the Earth system.
IR radiation
A fundamental law of physics states that all bodies emit a
spectrum of radiant power proportional to the fourth power
of their absolute temperature. A body at absolute temperature
T (K) emits power per unit area:
P = σ T
4
= 5.67 x 10
-8
T
4
(W/m
2
)
For example, a body at T = 280 K is said to emit 348 W/m
2
.
However, this law of physics is academic and not directly
applicable to real-world experience. In the real world, we
never have a single isolated body emitting radiation, instead,
we deal with pairs of bodies where the warmer one radiates
a net lux to the cooler one. (If you stand next to a body at
280 K, you don’t feel an incoming heat lux of 348 W/m
2
).
For example, if there is one body at 280 K and a second body
at 275 K, the warmer body will radiate through a vacuum
to the cooler body at a net of 24 W/m
2
. That is a real-world
parameter that can be measured. But the academic model
involves calculating the emission of the warm body as 348
W/m
2
and the emission of the cooler body as 324 W/m
2
, and
subtracting, the net transfer from the warm body to the cool
body is 24 W/m
2
. But the calculated values are academic
and cannot be measured in the real world with 348 W/m
2
in
one direction
and 324 W/m
2
in the opposite direction. Those
values are only of academic use to infer the measurable net of
about 24 W/m
2
. See the simple model in Figure 1 presented
here for illustration.
Next, consider the case where an IR-absorbing gas is placed
between the two radiating bodies as shown on the right side
of Figure 2. In the left side of the igure, there are two plates
radiating from one another through a vacuum with the warm
plate delivering a net of 215.7 W/m
2
to the colder plate. On
the right side of Figure 2, the space between the plates is illed
with an IR-absorbing gas. The molecules that absorb radiant
energy, reemit energy in all directions, including back toward
the hotter plate. The higher the density of gas, the less radiant
energy gets through to the cold plate. The actual amount of IR
radiation that reaches the colder plate depends on the opacity
of the IR-absorbing gas. In Figure 2; 25 W/m
2
was arbitrarily
inserted for illustration of a very opaque gas.
It should also be noted that the plates emit a characteristic
spectrum of IR wavelengths for their temperatures, and if the
IR-absorbing gas does not absorb a part of the spectrum, that
part of the spectrum will pass through the gas as easily as if it
were a vacuum.
In the sections that follow, the surface of the Earth can
be regarded as the warm plate and a high altitude in the
atmosphere can be regarded as the cold plate with gas in
between that absorbs most of the IR radiation and passes
some IR radiation.
The two contexts of the greenhouse effect
We are all aware of the widely discussed greenhouse effect
Figure 1: Radiant heat transfer between warm and cool bodies.
Figure 2: Radiant heat transfer from warm plate to cold plate separated by vacuum or
separated by IR absorbing gas.
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that warms the Earth as the concentration of greenhouse
gases increases. But just how does it work?
Here, we deine two contexts for greenhouse gas effects:
1) The fundamental greenhouse gas effect can be described
by a “gedanken experiment” in which one imagines
a dry Earth starting with no water or CO
2
and begins
adding water and CO
2
. The original atmosphere, lacking
water and CO
2
, will transmit IR radiation completely.
As a result, the Earth will be quite cool. As H
2
O and
CO
2
are added to the atmosphere, the transmission of
IR radiation from the Earth’s surface is increasingly
inhibited, and the Earth warms. As the Earth warms,
evaporation and thermals transmit more energy from
the Earth to the atmosphere. By the time H
2
O and
CO
2
levels reach current levels, the atmosphere is
almost opaque to IR radiation, and a “thermal blanket”
greatly reduces IR transmission from the Earth to the
atmosphere. The Earth cools primarily by evaporation
and thermals, and it is much warmer than if CO
2
and
water were absent. The notion of a “thermal blanket”
of IR absorbing gases warming the Earth has validity
in this context starting with a transmitting atmosphere
and adding greenhouse gases. However, once the
thermal blanket is established with ~ 400 ppm CO
2
,
adding more CO
2
has only a small effect on reducing IR
radiation from the surface.
2) The current greenhouse gas effect deals with the
question: How does the addition of CO
2
to the
atmosphere affect the global average temperature in
2024 and beyond, with CO
2
around 400+ ppm? It was
shown previously that starting with no water or CO
2
,
adding H
2
O and CO
2
to the atmosphere generates a
“thermal blanket” for radiation. But once that “thermal
blanket” is well established and the lower atmosphere is
very opaque to IR radiation, what is the effect of adding
even more CO
2
? Dufresne, et al. provide a detailed
technical analysis to show how the current greenhouse
effect works [7]. However, this reference is complex
and written for expert specialists in IR transmission
through the atmosphere. In the sections that follow, a
simpler, qualitative interpretation will be presented.
Energy budget of the earth
Energy transfer in the Earth system can take place by
thermal transfers (“thermals”) where winds carry warm air
up to colder regions, evaporation from the surface (removes
heat), and condensation in the atmosphere (deposits heat)
and radiation (further discussion follows).
After analyzing the data in the LTWS references (see
Section 1.2), a rough estimate of key energy lows per unit time
in the Earth system is given as follows. The exact numbers are
not critical; only their relative values are important for this
discussion.
Upward power low from the surface:
Thermals (warm air transported upward) 18 W/m
2
Evaporation from the surface and condensation in the
atmosphere 80 W/m
2
Radiation to the atmosphere 25 W/m
2
(note: some
estimates are as high as 50 W/m
2
)
Radiation through IR window to space 40 W/m
2
Total power from surface = 163 W/m
2
Received by the lower atmosphere:
Incoming solar irradiance absorbed 76 W/m
2
Thermals (from Earth) 18 W/m
2
Condensation 80 W/m
2
Radiation (from Earth) 25 W/m
2
Total = 199 W/m
2
Upper atmosphere:
Radiation (from Earth) through the window to space 40
W/m
2
Radiation from lower atmosphere 199 W/m
2
Total radiation emitted to space 239 W/m
2
Total power emanating from Earth to space = 239 + 79 +
23 = 341 W/m
2
These results can be visualized in Figure 3 which is based
on the references LTWS.
As shown in Figure 3, incoming solar irradiance (341 W/
m
2
) is partly relected by the lower atmosphere back out to
Figure 3: Energy lows in the Earth's system. (Based on LTWS references).
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space (79 W/m
2
), partly relected by the Earth’s surface
back out to space (23 W/m
2
), partly absorbed by the lower
atmosphere (76 W/m
2
), and inally about 163 W/m
2
is
absorbed by the surface.
The Earth’s surface emits the 163 W/m
2
that it absorbs as
follows:
40 W/m
2
is radiated to space through a window in the
absorption spectra of H
2
O and CO
2
18 W/m
2
is transmitted by thermals to the lower
atmosphere
80 W/m
2
is transported to the lower atmosphere by
evaporated water
25 W/m
2
is the net radiative transfer from the surface to
the lower atmosphere through the optically thick CO
2
and H
2
O
(as visualized on the right side of Figure 2). (Note that some
references use a higher value).
Radiation from the Earth’s surface to the lower atmosphere
requires further discussion. The LTWS references show high
up and down radiation lows. For example, Trenberth, et al.
did not show radiation transfer between the Earth’s surface
as a simple 25 W/m
2
net radiative transfer from the surface
to the lower atmosphere. Instead, they showed 356 W/m
2
radiated upward from the surface and 333 W/m
2
of “back
radiation” from the atmosphere to the surface [2]. The igure
356 W/m
2
radiated upward from the surface corresponds to
the theoretical radiation from a blackbody at 281.5 K. The
claimed downward igure is dificult to explain. But both of
these igures are academic. What is happening is that the
warm Earth is radiating upward through an optically thick gas
of H
2
O and CO
2
absorbers, and the radiant transfer through
that thick gas is estimated to be only a mere ~25 W/m
2
. This
is the “thermal blanket” so often referred to in discussions of
global warming. The thermal blanket is real. But the problem
with so many discussions of the greenhouse effect is that
there is a preoccupation with radiant energy transfer between
the Earth and the atmosphere (which is “blanketed”) while
neglecting the more important transfers of energy to the
atmosphere by processes other than radiation.
The terms “lower atmosphere” and “upper atmosphere”
are deined next. Following Miscolczi, Figure 4 shows that the
demarcation between upper and lower atmospheres occurs at
an altitude of roughly 12 km above which H
2
O is frozen out
and the temperature roughly stabilizes [8]. Energy transfer in
the lower atmosphere takes place by conduction, convection,
and radiation. Energy transfer in the upper atmosphere takes
place primarily by radiation.
The lower atmosphere receives energy by absorption of
incoming solar irradiance, and thermals, evaporation, and
radiation from the Earth’s surface. In the upper atmosphere,
energy transfer is primarily by radiation, propagated by the
residual CO
2
concentration (water is frozen out). Over a range
of higher altitudes, the upper atmosphere radiates energy to
space.
The greenhouse effect
The greenhouse effect can only be fully understood by
comprehensive modeling of upward energy lows in the Earth
system. Excellent studies by Dufresne, et al. and Pierrehumbert
provide detailed physics [7,9]. Here, we interpret these results
qualitatively.
The Earth is surrounded by cold space. The Earth receives
solar radiation from the Sun, this energy is absorbed in the
atmosphere, at the surface, in the oceans, and clouds. The
Earth becomes warmer than its surroundings and radiates
energy away to space. This continues until the Earth radiates
about as much energy per unit of time as it receives from the
Sun. It then remains relatively stable thermally. If for any
reason, the Earth is unable to radiate all the energy per unit
time it receives, it will warm.
Within the Earth system of land, ocean, atmosphere, and
clouds, energy transfer is taking place continuously. There is
a net energy low upward toward higher altitudes. From the
surface of the Earth, much of the upward low of energy in
the lower atmosphere is through evaporation and convection.
The lower atmosphere is almost opaque to IR radiation due to
water vapor and CO
2
.
At higher altitudes, the atmosphere is colder and thins
out, water vapor is frozen out, and convection no longer
occurs, and radiation becomes the dominant means of energy
transfer. IR radiation will be propagated if there is suficient
CO
2
. Radiation energy transfer will persist out toward a
high altitude until the CO
2
concentration diminishes. Each
CO
2
molecule that absorbs an IR photon can reradiate in all
directions, but in a thin atmosphere, some upward IR radiation
will be lost, and on a net basis, this allows the Earth to radiate
out to space. The presence of an IR transmitting/absorbing
Figure 4: Pressure, temperature, and relative humidity vs. altitude [8].
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gas (CO
2
) will allow energy transport to higher altitudes. The
highest altitude where there is enough thin gas to maintain
radiation is the region of the atmosphere that mainly radiates
energy outward to space. This is illustrated on the left side
of Figure 5. Figure 5 was created here to illustrate how the
predominant energy transfer mechanisms gradually change
to IR radiation at higher altitudes, and the presence of CO
2
carries the IR radiation to higher altitudes.
If the CO
2
content of the atmosphere is increased, there
will be a higher concentration of CO
2
molecules in the upper
atmosphere (at the same density), and IR radiant energy low
will persist up to a higher altitude. The region that radiates
to space will be at higher altitudes (where it is colder) and
by the radiation law, the Earth will not be able to radiate as
much energy per unit time. The Earth and the atmosphere will
warm until the region of emission is warm enough to radiate
all the solar input to Earth out to space. This is illustrated on
the right side of Figure 5.
As Lindzen pointed out, the lower atmosphere is opaque
to IR radiation, and the surface of the Earth loses heat by
convection, particularly cumulonimbus towers in the tropics
[10]. At higher altitudes, the density decreases signiicantly,
and IR transmission becomes the dominant means of energy
transfer. This region of the atmosphere can radiate energy
from the Earth to space. So, there is a lower atmosphere in
which energy is transferred mainly by convection, topped by
a higher atmosphere with decreasing density with altitude,
where IR transmission gradually becomes the main means of
energy transfer. The Earth loses energy by radiating from this
upper level.
Serious analysts of the current greenhouse gas effect agree
that warming is mainly due to the increased CO
2
extending the
region of radiative energy transfer in the upper atmosphere
to higher altitudes, resulting in the emission of energy from a
higher altitude where it is cooler [7,9]. The “thermal blanket”
imposed by a nearly IR-opaque lower atmosphere only
contributes about 10% to the current greenhouse gas effect [7].
Authors perspective and future research directions
It is widely believed that greenhouse gases warm the Earth
via an IR radiation “thermal blanket”. Yet, as we have shown,
the addition of more CO
2
to the atmosphere at present with
a CO
2
concentration > 400 ppm does not produce signiicant
warming by thickening the blanket. Instead, analysis indicates
that adding CO
2
to the present atmosphere raises the altitude
where the Earth radiates to space and that is the source of the
current greenhouse effect. It is my experience that > 99% of
all discussions of the greenhouse effect miss this important
point, and I suspect that even most climate scientists don’t
understand this. We have a situation where the majority of the
world believes that the greenhouse gas effect is warming the
world, and this poses a threat to humanity. The U.N. and many
of the world’s nations have taken steps at great cost and risk
to reduce future CO
2
emissions, yet they fail to understand the
underlying mechanism of the current greenhouse effect. The
proper understanding of the current greenhouse effect rests
on a few published papers [7,9,10]. These analyses need to
be expanded and developed further, and promulgated in the
literature, along with a more comprehensive understanding of
how factors other than greenhouse gases affect climate change.
Our policies should be based on a more solid foundation of
understanding of the underlying physics.
As the 21
st
century progresses, the Earth will likely warm
further primarily dependent on the levels of future CO
2
emissions, but other factors also enter into the total picture
(land use, solar variations, ocean currents, volcanoes, etc.).
Future energy demand will increase signiicantly and the
world will try to reduce emissions through expanded use of
renewable sources. Since the U.N. baseline year of 2015, global
annual CO
2
emissions increased by about 6% despite the
expansion of renewable energy usage. The people of the Earth
will face a long, dificult challenge to reduce CO
2
emissions in
the 21
st
century. The global average temperature will rise as
cumulative emissions increase [11]. Expanded use of nuclear
power and consumption of natural gas will be necessary but
probably not suficient. Natural gas should be a vital part of
any plan to transition to low emissions since it emits 2H
2
O
for each CO
2
when it is burned. Yet, the Internet is rife with
reports on US President Biden’s “War on Natural Gas” – a giant
step backward in the attempt to reduce global warming.
Finally, a major unknown in the matter of climate change is
the question of what are the impacts on human life at any level
Figure 5: Qualitative sketch to show radiation is dominant at the highest altitude.
By adding CO2 to the atmosphere, radiative energy transport is carried to a higher
altitude where it is colder, reducing the radiant power emitted by the upper
atmosphere.
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of CO
2
concentration in the atmosphere. There is a tendency
for politicians, media, and even climate scientists to attribute
every storm, every drought, every lood, and every heat wave
in 2024 to increased CO
2
. Pielke published numerous papers
and weekly postings on his website that analyze current
impacts against historical impacts, taking proper allowance
for demographic and inancial differences between the
present and the past, and generally, he inds these claims to be
spurious. This does not mean that impacts due to greenhouse
gases won’t occur. It just means that we have not observed
them yet [12].
Conclusion
There are two different contexts for discussion of the effect
of greenhouse gases on the Earth’s climate.
In one context, one can imagine an Earth with no water vapor
or CO
2
in the atmosphere. This Earth can radiate effectively to
space and is relatively cold. As water vapor and CO
2
are added
to the atmosphere, the IR-opacity of the atmosphere increases
and the Earth system warms. The greenhouse gases act as a
“thermal blanket” to warm the Earth by impeding upward
IR radiation. This is labeled the fundamental greenhouse gas
effect. However, once the thermal blanket is established,
adding more CO
2
has only a minimal effect on the thermal
blanket, and reduced upward IR radiation from the surface
does not produce signiicant warming. This is referred to by
Dufresne, et al. [7] as the “saturation paradox”.
In the other context, we are concerned with the effect of
adding more CO
2
to the current atmosphere where the CO
2
concentration is already 400+ ppm, and the thermal blanket
is already in place, restricting upward IR-radiation. This
is labeled the current greenhouse gas effect, and it is quite
different from the fundamental greenhouse gas effect. In the
current atmosphere, energy transfer from the Earth to the
atmosphere is primarily by evaporation and thermals, and
IR-radiant energy transfer is signiicantly impeded by an
almost opaque lower atmosphere. The “thermal blanket” is
in place, but it doesn’t change much as CO
2
is added to the
atmosphere. Adding CO
2
to the current atmosphere slightly
increases the opacity of the lower atmosphere but this is of
little consequence. In the upper atmosphere, CO
2
is the major
means of energy transport by IR radiation. The greatest effect
of adding CO
2
to the current atmosphere is to extend the
upward range of IR-radiant transmission to higher altitudes.
The main region where the Earth radiates to space is thereby
extended to higher altitudes where it is colder, and the Earth
cannot radiate as effectively as it could with less CO
2
in the
atmosphere. The Earth warms until the region in the upper
atmosphere where the Earth radiates to space is warm enough
to balance incoming solar energy.
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How to cite this article: Rapp D. How Increased CO
2
Warms the Earth-Two Contexts for the Greenhouse Gas Effect. IgMin Res. October 24, 2024; 2(10):
854-859. IgMin ID: igmin259; DOI: 10.61927/igmin259; Available at: igmin.link/p259