Challenging the Greenhouse Effect Specification and the Climate Sensitivity of the IPCC

Abstract

The greenhouse effect concept has been developed to explain the Earth’s elevated temperature. The prevailing theory of climate change is the anthropogenic global warming theory, which assumes that the greenhouse (GH) effect is due to the longwave (LW) absorption of 155.6 Wm-2 by GH gases and clouds. The actual warming increase to 33°C of the Earth’s surface temperature according to the present GH effect definition is the infrared downward LW radiation of 345.6 Wm-2 emitted by the atmosphere. The atmosphere’s temperature is the key element behind this radiation. According to the energy laws, it is not possible that the LW absorption of 155.6 Wm-2 by the GH gases could re-emit downward LW radiation of 345.6 Wm-2 on the Earth’s surface. In this study, the GH effect is 294.5 Wm-2, including shortwave radiation absorption by the atmosphere and the latent and sensible heating effect. This greater GH effect is a prerequisite for the present atmospheric temperature, which provides downward radiation on the surface. Clouds’ net effect is 1% based on the empirical observations. The contribution of CO2 in the GH effect is 7.3% corresponding to 2.4°C in temperature. The reproduction of CO2 radiative forcing (RF) showed the climate sensitivity RF value to be 2.16 Wm-2, which is 41.6% smaller than the 3.7 Wm-2 used by the IPCC. A climate model showing a climate sensitivity (CS) of 0.6°C matches the CO2 contribution in the GH effect, but the IPCC’s climate model showing a CS of 1.8°C or 1.2°C does not.

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*Corresponding author: E-mail: aveollila@yahoo.com;
Physical Science International Journal
22(2): 1-19, 2019; Article no.PSIJ.49095
ISSN: 2348-0130
Challenging the Greenhouse Effect Specification
and the Climate Sensitivity of the IPCC
Antero Ollila
1*
1
Department of Civil and Environmental Engineering (Emer.), School of Engineering, Aalto University,
Espoo, Otakaari 1, Box 11000, 00076 AALTO, Finland.
Author’s contribution
The sole author designed, analyzed, interpreted and prepared the manuscript.
Article Information
DOI: 10.9734/PSIJ/2019/v22i230127
Editor(s):
(1)
Dr. Lei Zhang, Winston-Salem State University, North Carolina, USA.
(2)
Dr. Mohd Rafatullah, Division of Environmental Technology, School of Industrial Technology, Universiti Sains Malaysia,
Malaysia.
(3)
Dr. Roberto Oscar Aquilano, School of Exact Science, National University of Rosario (UNR), Rosario, Physics Institute
(IFIR)(CONICET-UNR), Argentina.
Reviewers:
(1)
Peter Stallinga, University of Algarve, Portugal.
(2)
Bharat Raj Singh, APJ Abdul Kalam Technical University, India.
Complete Peer review History:
http://www.sdiarticle3.com/review-history/49095
Received 02 March 2019
Accepted 16 May 2019
Published 24 May 2019
ABSTRACT
The greenhouse effect concept has been developed to explain the Earth’s elevated temperature.
The prevailing theory of climate change is the anthropogenic global warming theory, which
assumes that the greenhouse (GH) effect is due to the longwave (LW) absorption of 155.6 Wm
-2
by
GH gases and clouds. The actual warming increase to 33°C of the Earth’s surface temperature
according to the present GH effect definition is the infrared downward LW radiation of 345.6 Wm
-2
emitted by the atmosphere. The atmosphere’s temperature is the key element behind this radiation.
According to the energy laws, it is not possible that the LW absorption of 155.6 Wm
-2
by the GH
gases could re-emit downward LW radiation of 345.6 Wm
-2
on the Earth’s surface. In this study, the
GH effect is 294.5 Wm
-2
, including shortwave radiation absorption by the atmosphere and the latent
and sensible heating effect. This greater GH effect is a prerequisite for the present atmospheric
temperature, which provides downward radiation on the surface. Clouds’ net effect is 1% based on
the empirical observations. The contribution of CO
2
in the GH effect is 7.3% corresponding to 2.4°C
in temperature. The reproduction of CO
2
radiative forcing (RF) showed the climate sensitivity RF
value to be 2.16 Wm
-2
, which is 41.6% smaller than the 3.7 Wm
-2
used by the IPCC. A climate
model showing a climate sensitivity (CS) of 0.6°C matches the CO
2
contribution in the GH effect,
but the IPCC’s climate model showing a CS of 1.8°C or 1.2°C does not.
Original Research Article

Ollila; PSIJ, 22(2): 1-19, 2019; Article no.PSIJ.49095
2
Keywords: Greenhouse effect; climate change; Earth’s energy balance; climate sensitivity; climate
model.
1. INTRODUCTION
The comprehensive article of Henderson and
Henderson-Sellers [1] starts the history of “the
greenhouse effect” with Fourier, Tyndall, and
Arrhenius and ends at the present time. The
definition of the GH effect emerged in the present
form and quickly stabilized in the beginning of the
twentieth century. Since that time, the
anthropogenic global warming (AGW) theory is
based on the increased GH effect caused by
rising concentrations of GH gases [2] and
recently by clouds. The important moment in the
climate change science was the establishment of
the Intergovernmental Panel on Climate Change
(IPCC) in 1988. In its first assessment report [3],
the GH effect was described to have been
caused by trace gases, which absorb terrestrial
radiation and re-emit radiation to the surface,
thereby increasing the temperature. In its fourth
assessment report [4], IPCC writes: “Much of this
thermal radiation emitted by the land and ocean
is absorbed by the atmosphere, including clouds,
and reradiated back to Earth. This is called the
greenhouse effect.”
In the report AR5 of IPCC [2], there is only one
sentence about the CO
2
contribution to the GH
effect: “Water vapour is the primary greenhouse
gas in the Earth’s atmosphere. The contribution
of water vapour to the natural greenhouse effect
relative to that of carbon dioxide (CO
2
) depends
on the accounting method but can be considered
to be approximately two to three times greater”
(p. 666). In a way IPCC seems to keep this
matter insignificant. The contribution of CO
2
is
essential, and the GH effect is a very profound
phenomenon in climate change science and can
be used to test the results of climate models.
The contributors of the GH effect according to
the published research studies are the absorbers
of longwave (LW) radiation, which are the main
GH gases and clouds. There are only a few
comprehensive studies on this subject [2-10].
The author has recognized three studies
applying all-sky conditions [7,8,10]. In these
studies, the percentages of three main
contributors vary: for water, they range from 38%
to 80.7%; for carbon dioxide (CO
2
) from 12.9% to
26%; and for clouds from 1% to 39%. It should
be noticed that in all studies above, the
percentages of GH factors have been calculated
from the LW absorption value, which varies from
125 Wm
-2
to 158.3 Wm
-2
[6-10].
The main objective of this study is to analyze the
GH contribution effects of different sky conditions
and new contribution effects that had not been
considered in the earlier studies. Energy fluxes of
different sky conditions are needed in the GH
effect analysis. Therefore, the Earth’s annual
mean energy budget has been updated.
2. EARTH’S ENERGY BALANCE
The author has updated the former energy
balance for clear, cloudy, and all-sky conditions
[11] utilizing the latest observed outgoing LW
radiation values [12] at the top of the atmosphere
(TOA) for clear sky and all-sky conditions during
2000–2010, Fig. 1. Some other flux value
updates are needed, and they have been
explained in detail along with the uncertainties
Table A1 of Appendix. The tables of Appendix
have been referred by using letter A and a
number.
Based on the observations [13-15] the cloud
base and top values, 1.6 and 4.0 km, have been
used. The absorption values below the cloud
cover depend on the surface temperatures of the
different skies [16]. The author has applied
average global temperature, pressure, and the
concentration profiles of GH gases of the year
2015. The Spectral Calculator application [17]
has been used for spectral analyses. The GH
gas concentrations have been modified from the
GH gas profiles of the Polar Summer of the
Spectral Calculator. The water profile has been
adjusted in such a way that the total precipitable
water (TPW) is 2.6 cm. In this application the
HITRAN line data version 2012 was available
[18] and the coefficients in the water continuum
model are also updated [19]. The calculations
have been carried out in such a way that the
absorption values of different skies can be
calculated below and above the cloud cover.
3. GREENHOUSE EFFECT
3.1 Greenhouse Effect Definitions
In addition to the IPCC’s definition, Hartmann
[20] summarizes the final details of the GH effect
in this way: “Most of this emitted infrared
radiation is absorbed by trace gases and clouds
in the overlying atmosphere. The atmosphere
also emits radiation, primarily at infrared
wavelengths, in all directions. Radiation emitted
downward from the atmosphere adds to the

Ollila; PSIJ, 22(2): 1-19, 2019; Article no.PSIJ.49095
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Fig. 1. Earth’s energy balance and flux values (Wm-2) in all-sky conditions
warming of Earth’s surface by sunlight. This
enhanced warming is termed the greenhouse
effect.” In the present climate, the direct solar
insolation on the surface is 165 Wm
-2
and
downward LW radiation emitted by the
atmosphere is 345.6 Wm
-2
, showing the
magnitude of the GH effect.
The conclusion of the prevailing GH effect
definitions is this: the warming of the atmosphere
is caused mainly by GH gases and clouds that
absorb the LW radiation emitted by the Earth’s
surface. On the other hand, according to these
references, the real warming impact of the GH
effect is the same as the LW radiation emitted by
the atmosphere back to the Earth’s surface. LW
absorption in the atmosphere is only a pre-phase
in the process of transforming the absorption
energy into radiation energy emitted by the
atmosphere to the surface.
Thinking about the very basic feature of the GH
phenomenon, it does not matter how the
atmosphere warms up but the essential element
in the GH effect is the existence of the
atmosphere. Interesting enough, Swedish
meteorologist Nils Ekholm [21] used the term
“Greenhouse effect,” describing it in this way:
“The other is that the atmosphere, absorbing but
little of the insolation and the most of the
radiation from the ground, receives a
considerable part of its heat store from the
ground by means of radiation, contact,
convection, and conduction, whereas the earth’s
surface is heated principally by direct radiation
from the sun through the transparent air.” Ekholm
was not aware that most of the ground heat
originates from the GH effect (about 67.7%).
Otherwise, he was obviously the first to realize
that the atmosphere also receives energy from
sources other than the absorption of LW
radiation.
3.2 Shortwave Absorption and Longwave
Absorption Warming Effects
The Earth receives solar insolation of about 240
Wm
-2
and emits an energy flux with the same
magnitude into space. GH gases, aerosols and
clouds in the atmosphere absorb 75 Wm
-2
, and
thus, 165 Wm
-2
directly warms the surface. The
same kind of absorption by a magnitude of 155.6
Wm
-2
happens to LW radiation emitted by the
Earth’s surface. But according to climate change
scientists, there is a big difference in
transforming these absorption energies into
warming effects on the surface. In both cases,
the absorption energies must find ways to
increase surface temperature.
The temperature impact of SW absorption is
simply the magnitude of this absorption, 75 Wm
-
2
. Nobody has ever claimed that the whole
downward flux emitted by the atmosphere is due

Ollila; PSIJ, 22(2): 1-19, 2019; Article no.PSIJ.49095
4
to the SW absorption; the absorbed SW radiation
75 Wm
-2
is just a part of the downward LW
radiation 345.6 Wm
-2
emitted by the atmosphere.
According to the present practice, this is not a
mechanism in the LW absorption, but the
downward LW flux 345.6 Wm
-2
is totally due to
the LW absorption only. This goes against the
physical laws. SW and LW absorption/reradiation
processes in the atmosphere have no physical
difference.
3.3 Spectral Analysis Calculations
Absorption processes in the atmosphere can be
analyzed by spectral calculations. Applying the
average atmospheric conditions as defined in
Section 2, the total absorption flux calculated in
the troposphere is 303.31 Wm
-2
in the clear sky
conditions. The downward flux emitted by the
atmosphere can be calculated using the same
atmospheric conditions but no GH gas
concentrations. The result is 307.06 Wm
-2
,
having a 1.2% difference from the absorption flux
value. This result means that the downward LW
flux magnitude depends only on the temperature
of the atmosphere as it should be per Eq. (1) of
Planck because there is no LW flux radiating
from space to the Earth’s surface. Miskolczi [22]
depicts the downward LW flux and shows that it
is zero at the TOA, then it starts to sharply
increase in the troposphere and reaches the
maximum value at the surface following the
atmospheric temperature profile.
It is not a coincidence that the magnitudes of the
total absorption and downward radiation flux are
almost the same. Hundreds of simulations [22]
with different atmospheric structures showed that
these two fluxes are equal. Kirchoff’s radiation
law states that they are equal in radiation
balance conditions. The small differences are
well inside the uncertainty limits of the flux
observations.
The counter argument against the traditional
calculation basis of GH effect could be that
anyway the total absorption of LW radiation in
the atmosphere is totally due to the GH gases. It
is true but it is not the whole truth. The total
absorption value in the clear sky is 310.9 Wm
-2
and the reduction of the total absorption by
removing CO
2
from the atmospheric composition
would be 20.1 Wm
-2
. It means that the
contribution of CO
2
to the total absorption in clear
sky conditions would be only 6.5% and in all-sky
conditions even less. There is no essential
difference to the result of the traditional method
in Table 1.
One could ask, where is the impact of SW
absorption, latent and sensible heating, if the
total absorption of LW radiation is due to the GH
gases only? The absorption of GH gases
depends strongly on the temperature and also on
the pressure of the atmosphere. The impact of
these other elements of GH phenomenon have
their effects in this calculation method in their
contributions to the atmospheric temperature and
pressure profile. In all-sky conditions the sum of
the energy fluxes of latent heating, sensible
heating and SW absorption is 190.0 Wm
-2
and
the same of LW absorption by GH gases is 155.6
Wm
-2
. These figures show the portions what
these elements have in maintaining the
atmospheric temperature profile. It means that
the contribution of the LW absorption in
maintaining the temperature profile is
100*155.6/345.6 = 45.0%.
The observed atmospheric temperature profile is
normally used in calculating the total LW
absorption without considering the contributing
factors maintaining this profile. It may lead to the
wrong conclusion that the atmospheric
temperature profile is due to the LW absorption
by the GH gases only, which is not true.
3.4 Other Energy Fluxes Warming the
Lower Atmosphere
The GH effect is a physical-chemical
phenomenon in which the lower part of the
atmosphere warms up. Every object or matter
warmer than absolute zero emits radiation
always and at all wavelengths. Planck’s law
dictates that the Earth’s surface emits radiation
with detectable energy intensity from 3 to 100
µm:
E = ((8¶hc)/λ
5
) * 1/(e
(hc/(kTλ))
-1) (1)
Where E is the energy radiated per unit volume
by a cavity of a blackbody, h is Planck’s
constant, c is the speed of light, λ is the
wavelength, k is the Boltzmann constant, and T
is the absolute temperature. Planck’s law means
that the material in emitting radiation depends
only on the temperature of the atmosphere, and
it is not able to separate the warming effects of
different sources.

Ollila; PSIJ, 22(2): 1-19, 2019; Article no.PSIJ.49095
5
Fig. 2. Energy fluxes contributing to the greenhouse effect in all-sky conditions (Wm-2)
The present GH effect definition ignores other
sources that warm up the atmosphere. For
example, the SW radiation emitted by the Sun
and absorbed by the atmosphere is 75 Wm
-2
,
which is 31.3% of the total SW energy flux
absorbed by the Earth (Figs. 1 and 2). This
portion of SW radiation radiates on the surface
from the atmosphere and is part of the LW
radiation emitted by the atmosphere.
Thinking about the very basic feature of the GH
phenomenon, it does not matter how the
atmosphere warms up. Climate change scientists
have ignored the warming effect of SW
absorption by the atmosphere in calculating the
GH effect. It has been accepted as an energy
source in energy balance calculations, but not in
GH effect calculations.
Nowadays, we know quite exactly how much
energy the atmosphere receives as the
insolation, sensible heat, and latent heat. The
sum of these sources is 75.0+90.8+24.2 = 190.0
Wm
-2
, 22% greater in the all-sky conditions than
the LW absorption by GH gases and clouds
(155.6 Wm
-2
) – total absorption by the
atmosphere being 345.6 Wm
-2
. The LW
absorption according to Kiehl & Trenberth [7] is
only 125 Wm
-2
, because they have used an
atmospheric model containing only 50% absolute
water vapor found in the average global
atmosphere. This low LW absorption value is the
main reason for an unrealistically high CO
2
contribution (26%) of their study. In the updated
energy balance, the LW absorption is 155 Wm
-2
by Trenberth et al. [23]. The same value of
Schmidt et al. [8] is 155 Wm
-2
and the Stephens
et al. [12] 158.3 Wm
-2
.
There is no physical reason to leave these three
energy sources out of the GH effect calculations.
The first law of thermodynamics states that the
energy of an isolated system can be transformed
from one form to another but can be neither
created nor destroyed. According to its
temperature, the warmed-up matter of the
atmosphere emits LW radiations into all
directions, including the Earth’s surface. It has no
meaning as to how the matter has received and
maintained its temperature. It is true that only GH
gases can absorb LW radiation, but according to
the physical radiation law, every matter emits
thermal radiation above absolute zero
temperature according to its temperature. As
shown by the spectral analysis, the atmosphere
with the present temperature profile without any
GH gases would emit the same LW radiation
downward.

Ollila; PSIJ, 22(2): 1-19, 2019; Article no.PSIJ.49095
6
Climate change scientists have ignored the
warming effects of energy sources other than the
LW absorption by GH gases. In doing so, they
accept that the total LW radiation to the Earth’s
surface is 345.6 Wm
-2
and that it has been
caused solely by GH gases and clouds, which
absorb 155.6 Wm
-2
from the thermal radiation
emitted by the Earth’s surface. The result of this
interpretation is that the absorption by GH gases
and clouds have caused the Earth’s surface to
become 33°C warmer. This approach does not
consider a physical contradiction in that an
energy source of 155.6 Wm
-2
cannot create an
energy flux of 345.6 Wm
-2
, which has the real
warming effect on the Earth’s surface.
There are two options to resolve this problem.
We could specify that the GH effect is only a
portion of the total warming effect of the
atmospheric downward LW radiation: 33°C *
(155.6/345.6) = 14.9°C. This could not be the full
solution, however, because the total GH effect is
really the magnitude of the downward LW
radiation by the atmosphere, as specified by the
present GH effect term. Any energy flux warming
the atmosphere is thus an integral part of the
Earth’s GH effect.
3.5 The Greenhouse Effect of All
Contributing Factors
The Earth’s gross energy balance shows that the
all-sky atmosphere balance value is 585.6 W m
-2
because it includes the LW radiation 211.5 Wm
-2
emitted into space and the LW radiation 28.5
transmitted into space. The net energy absorbed
by the atmosphere is 585.6 – 211.5 – 28.5 =
345.6 Wm
-2
.
The author has calculated the GH effect using all
energy sources, including SW absorption and
latent and sensible heating. The GH gas
contributions have been calculated by removing
a GH gas in question from the atmospheric
model in the Spectral Calculator application [17].
One of the most essential features of our planet
is, that the oceans cover 70% of the surface area
and provide humidity into the atmosphere, which
plays the key role in the GH phenomenon.
The cloud absorption values for SW insolation
are 27.0 Wm
-2
and 17.8 Wm
-2
according to the
energy balance for cloudy and all-sky conditions.
The contributors of the SW absorption for the
clear sky case [24] are water 77.2%, ozone
19.5%, CO
2
2.3%, aerosols 1.9%, and methane
and nitrogen oxide 0.7%. Based on the energy
balance analysis, the overall absorption values
caused by LW absorption (Wm
-2
) only of different
skies are clear sky 128.1, cloudy sky 167.8, and
all-sky 155.6. The absorption effect of water in
different skies is the difference between the
overall GH absorption minus the sum of the GH
gas absorptions.
The absorption of SW radiation is caused by GH
gases, aerosols and by clouds. The results of the
all-sky conditions are summarized in Table 1.
The details of the SW and LW flux calculations
are in Appendix Tables A2-A6.
Table 1 shows the contributions of two different
approaches, which could be called a Net GH
effect and a Gross GH effect. The Gross GH
effect considers only the positive absorption
effects of clouds, but the Net GH effect considers
the real surface temperature effects of clouds
based on the observations. The results show that
water is the main contributor, consisting of a
vapor effect of 45.6% and a latent heating effect
of 30.8%, for a total of 76.4%. The contribution
effect of CO
2
is 7.3%. This low contribution
means that the total GH effect of the CO
2
concentration 400 ppm is only 2.4°C.
The major controversial contributor is the GH
effect of clouds. Most research studies [12,16,25-
29] show that cloud forcing has a negative
impact on the surface temperature, varying from
-17 to -30 Wm
-2
. Two often referenced studies
[7,8] show that clouds have a positive GH
contribution of +25%, and +39% in the GH effect.
These figures suggest that more cloudiness
means higher GH effect and thus higher surface
temperature. This is in direct conflict with the
general cloud forcing impact.
The reason for this conflict originates from the
two opposite effects of clouds on radiation.
Clouds reduce the incoming SW radiation effect
from 287.2 Wm
-2
in the clear sky to 240 Wm
-2
in
all-sky, and thus the change is -47.2 Wm
-2
. At the
same time, the GH effect increases from 128.1
Wm
-2
to 155.6 Wm
-2
, and thus the change is
+27.4 Wm
-2
. The net effect is cooling by -19.8
Wm
-2
.
If only the positive radiative forcing effects of
clouds are accounted for by increasing the GH
effect, it does not give the right response to the
surface temperature impact. This temperature
effect is the main reason to assess the GH effect:
what is the GH effect on the surface temperature
and what are the portions of individual

Ollila; PSIJ, 22(2): 1-19, 2019; Article no.PSIJ.49095
7
Table 1. Greenhouse effects according to individual contributors in all-sky conditions
(L is latent heating and T is sensible heating)
Contributor
SW
absorp.
Wm
-2
LW+L+T+
Clouds
Wm
-2
SW+LW+
L+T+Clouds
Wm
-2
Net
contrib.
%
Net
contrib.
°C
Gross
contrib.
%
Water 43.5 90.9 134.4 45.6 14.9 38.9
Latent heating 0.0 90.8 90.8 30.8 10.0 26.3
Sensible heating 0.0 24.2 24.2 8.2 3.0 7.0
Carbon dioxide
1.3
20.1 21.4 7.3 2.4 6.2
Ozone 11.0 6.9 17.9 6.1 2.0 5.2
Clouds 0.0 2.8 2.6 0.9 0.3 15.5
Methane & Nitrogen oxide 0.4 1.8 2.2 0.7 0.2 0.6
Aerosols 1.0 0.0 1.0 0.3 0.1 0.3
Total 57.2 237.5 294.5 100.0 33.0 100.0
contributors? There is a study by Ollila [10]
showing a very small positive cloud effect of 1%.
This is based on the emitted radiation values of
clear sky 394.1 Wm
-2
and all-sky 395.6 Wm
-2
[16]. These values correspond to the black
surface temperatures 15.6°C and 15.9°C, which
means that the all-sky surface temperature is
0.3°C higher than that of clear sky.
4. EFFECT ON CLIMATE CHANGE
MODELS
4.1 The Simple Climate Model of the IPCC
These results have an effect on the climate
change models. IPCC uses both ECS
(Equilibrium Climate Sensitivity) and TCS
(Transient Climate Sensitivity) concepts and
summarizes the differences in AR5, p. 1110 [2]:
“ECS determines the eventual warming in
response to stabilization of atmospheric
composition on multi-century time scales, while
TCR determines the warming expected at a
given time following any steady increase in
forcing over a 50- to 100-year time scale.” IPCC
has changed the TCS to TCR (Transient Climate
Response). On page 1112 of AR5, IPCC [2]
states that “TCR is a more informative indicator
of future climate than ECS.”
IPCC [2] has applied the radiative forcing (RF)
model and the positive water feedback as a
combination of
dT = λ*RF, (2)
where dT is the global surface temperature
change (K) starting from the year 1750 and λ is
the climate sensitivity parameter (K/(Wm
-2
). The
λ value is 0.5 K/(Wm
-2
) per IPCC [4]. The RF
value can be calculated according to the CO
2
concentration using Eq. (3) by Myhre et al. [30]. It
has been used by the IPCC as well as by
General Climate Models (GCMs)
RF = 5.35 * ln(C/280) (3)
where C is the CO
2
concentration (ppm). This
simple model is applicable to calculate the TCS
value as well as the temperature response for
the scenarios up to 1370 ppm CO
2
concentration. The simple model of Eq. (2) and
(3) gives a TCS value of 1.85°C. It can be
compared to the IPCC’s latest report AR5 [2],
which shows TCS between 1.0°C and 2.5°C,
meaning an average value of 1.75°C. AR5 [2] is
the average value of TCS/TCR of the 30 most
complicated GCMs, and the value is 1.8°C.
There is also the third TCR/TCS value calculated
by GCMs [2] in section 8.6.2.3 of the AR5: “It can
be estimated that in the presence of water vapor,
lapse rate and surface albedo feedbacks, but in
the absence of cloud feedbacks, current GCMs
would predict a climate sensitivity (±1 standard
deviation) of roughly 1.9°C ± 0.15°C.”
Considering these slightly different TCS values of
IPCC, the simple model is a justified model that
can be used to calculate the warming values of
different CO
2
and other GH gas concentrations.
AR5 [2] is the average λ value 1.0 K/(Wm
-2
) for
the ECS of 30 GCMs, which means that the
simple climate model according to Eq. (2) is
applicable to both TCR and ECS calculations. As
referenced above, in TCR calculations, λ
includes the feedback effects of water vapor,
lapse rate, and surface albedo. In the AR4, the
IPCC [4] writes: “The diagnosis of global
radiative feedbacks allows better understanding
of the spread of equilibrium climate sensitivity
estimates among current GCMs. In the idealized

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8
situation that the climate response to a doubling
of atmospheric CO
2
consisted of a uniform
temperature change only, with no feedbacks
operating (but allowing for the enhanced
radiative cooling resulting from the temperature
increase), the global warming from GCMs would
be around 1.2°C.” This statement means that the
λ value 0.324 would give a warming value of
1.2°C for the RF value of 3.7 Wm
-2
due to the
CO
2
warming effects only.
4.2 Climate Sensitivity Parameter
According to the Earth’s Energy
Balance
The simplest calculation method of the climate
sensitivity parameter  is based on the total
energy balance of the Earth by equalizing the
absorbed and emitted radiation fluxes
SC(1-α) * (¶r
2
) = sT4 * (4¶r
2
), (4)
where SC is the solar constant (1361 Wm
-2
), α is
the total albedo of the Earth, s is the Stefan-
Boltzmann constant (5.6704*10
-8
), and T is the
temperature (K). The temperature value T can be
solved using
T = (SC * (1 – α) (4s))
0.25
, (5)
where T is the temperature corresponding to the
emitted longwave (LW) flux in the atmosphere.
The average albedo according to Table S1
values is (100.2 Wm
-2
) / (340.2 Wm
-2
) = 0.295.
Using this albedo value, the temperature T would
be -17.1°C (=255.4 K). According to Planck’s
equation, this temperature corresponds to an LW
radiation flux of 239.8 Wm
-2
, which is very close
to the actual observed outgoing longwave
radiation flux of 240.2 Wm
-2
used in the energy
balance calculations of this study. The most
common magnitude of the GH effect is 33°C,
which means that the surface temperature would
be 15.9°C, and this value is the same as the
black surface temperature of the surface emitted
radiation flux [16].
The term SC(1-α)/4 is the same as the net
radiative forcing (RF), and therefore, Eq. (4) can
be written as RF = sT
4
. When this equation is
derived, it will be d(RF)/dT = 4sT
3
= 4(RF)/T. The
ratio d(RF)/dT can be inverted, transforming it
into :
dT/(d(RF)) =  = T/(4RF) = T/(SC(1-α)) = 255.40 /
(1361 *(1-0.295)) = 0.264 K/(Wm
-2
). (6)
This λ value means that there is no water
feedback according to the Earth’s energy
balance analysis.
4.3 Reproduction of the Radiative Forcing
of Carbon Dioxide
The radiative forcing (RF) of CO
2
according to
Myhre et al. [30] has been reproduced applying
two simulation tools available in the network,
namely the Spectral Calculator [17] and the
Modtran [31]. The parameters and choices
applied in Modtran simulations are depicted in
Table A8. The atmospheric temperature and GH
gas profiles are the same as those specified in
the Earth’s energy balance calculations of
Appendix.
The spectral calculations have been carried out
from the surface to an altitude of 70 km. In these
calculations, a few iterations are needed in both
calculation tools in order to find the surface
temperature, which compensates the increased
absorption caused by a CO
2
increase (393 ppm,
560 ppm, and 1370 ppm) bringing the OLR flux
exactly to the same the OLR (outgoing LW
radiation) flux caused by a CO
2
concentration of
280 ppm. Because both the OLR change and the
temperature change are calculated at the same
time, the  value can be easily calculated. The
cloudy sky values are calculated using the
Modtran simulations, which show about a 30%
lower OLR change than the clear sky
simulations. This relationship has been used to
estimate the cloudy sky values of Spectral
Calculator simulations. The IPCC’s AR5 report
[2] summarizes that according to several studies,
the overall RF values in cloudy sky conditions
are 25% lower than the clear sky values on
average.
The results of the simulations carried out by the
Modtran and Spectral Calculator are summarized
in Table 2.
Myhre et al. [30] have concluded that the
absorption of solar radiation in the troposphere
yields a positive RF at the tropopause and a
negative RF in the stratosphere, contributing to a
net cooling effect of CO
2
absorption of -0.06 W m
-
2
for the concentration change from 280 ppm to
381 ppm. The absorption calculations of solar
radiation [10] in the atmosphere from 0 to 70 km
show a very small net warming effect of CO
2
increase. Therefore, the solar radiation warming
effects due to CO
2
concentration changes have
not been included in the RF calculations.

Ollila; PSIJ, 22(2): 1-19, 2019; Article no.PSIJ.49095
9
The logarithmic fitting gives the following
equation between RF values and CO
2
concentrations in Table 2:
RF = 3.12 * ln(C/280). (7)
The coefficient of correlation is 0.99987, showing
an almost perfect fit. The different results in
comparison to the equation (3) of Myhre et al.
[30] have been analyzed in the discussion
section.
A sensitivity analysis for  has been carried out.
Using the Spectral Calculator simulation, a CO
2
concentration of 393 ppm gives a  value of
0.230 K/(Wm
-2
) and 1370 ppm gives a  value of
0.269 K/(Wm
-2
). The OLR value 233 Wm
-2
gives
a  value of 0.270 K/(Wm
-2
), and the OLR value
240 Wm
-2
gives a  value of 0.265 K/(Wm
-2
).
According to Spectral Calculator analysis, the RF
value for a CO
2
concentration of 560 ppm is 2.16
Wm
-2
, CS is 0.576°C, and  is 0.267 K/(Wm
-2
).
Using a CO
2
concentration of 560 ppm in
Modtran simulations, the RF is 1.834 Wm
-2
, the
CS is 0.49°C, and  is 0.267 K/(Wm
-2
). The
variation of  is relatively small, but  is not
invariant. The Modtran calculation results are not
as accurate and reliable as the Spectral
Calculator results because the atmospheric
conditions of Modtran cannot be specified with
the same accuracy as in Spectral Calculator. The
final choice for the climate sensitivity parameter 
is 0.27 K/(Wm
-2
), and the (transient) climate
sensitivity can be rounded to 0.6°C.
4.4 Fitting the Simple Climate Models into
the Greenhouse Effect
In Fig. 3a, two cases have been depicted: a) a
red curve according to the TCS value of 1.2°C
representing the IPCC model for CO
2
warming
effects only and b) a green curve according to
equation (7), and λ value of 0.27 K/(Wm
-2
)
without positive water feedback. The direct
humidity measurements do not show the
constant relative humidity either [10].
The calculation basis of curves in Fig. 3a are on
the Eqs (2), (3), and (7) for CO
2
concentration
280 ppm onward. These CO
2
warming impact
curves have been adapted to give a total
warming value of 2.4°C caused by the CO
2
concentration of 400.9 ppm as shown in this
study. The warming change from CO
2
concentration 0 ppm to 280 ppm (dashed curves)
is based on the absorption decrease by spectral
calculations in Fig. 3b. The detailed numerical
values of the absorption and warming
calculations are in Table A7 of Appendix.
The general feature of absorption is that the
absorption rate change, i.e. the angle coefficient
of the absorption curve, diminishes with
increasing GH gas concentration. The absorption
Fig. 3. Warming effects of CO
2
according to the new greenhouse effect of CO
2
being 2.4°C in
2014 (400.9 ppm)
(a) CO
2
warming effects from 280 ppm onward are per a green curve, TCS = 0.6°C, and per IPCC
(2013), a red
curve, TCS = 1.2°C. (b) The absorption values of carbon dioxide, methane, and nitrogen oxide. The detailed
numerical values of the absorption and warming calculations are in Table A7 of Appendix

Ollila; PSIJ, 22(2): 1-19, 2019; Article no.PSIJ.49095
10
due to a GH gas follows also another general
rule of absorption, which is that increasing
concentration change from zero upward has the
strongest effect in the beginning. These features
can be noticed also in the absorption curves of
methane and nitrogen oxide. The starting phase
approximately follows the Beer-Lambert law,
which states that absorbance depends linearly
on the concentration and path length. When the
concentration increases, this relationship is no
longer valid. There is a very nonlinear
dependency from 20 to 100 ppm for CO
2
, and
thereafter the relationship is slightly nonlinear
after 280 ppm, which can be approximated by a
logarithmic relationship very well. The curve of
the model (TCS = 0.6°C) according to Eq. (7) of
this study shows a smooth feature of a warming
rate without a transition point at the 280 ppm.
Table 2. The radiative forcing and warming
values of different CO
2
concentrations
(reference level 280 ppm). The clear sky
values are calculated by spectral calculator
and cloudy skies by Modtran
Sky

OLR, Wm
-2

T, °C
CO
2
, 393 ppm
Clear 1.29 0.28
Cloudy 0.90 0.22
All-sky 1.03 0.24
CO
2
, 560 ppm
Clear 2.69 0.66
Cloudy 1.88 0.51
All-sky 2.16 0.56
CO
2
, 1370 ppm
Clear 6.29 1.60
Cloudy 4.39 1.23
All-sky 5.04 1.36
It should be noticed that these kind of absorption
calculations have been applied by many
researchers [7-10] to quantify the GH effects of
GH gases. The temperature effects based on the
absorption may differ slightly from temperature
effects calculated based on the outgoing LW
radiation change at the top of the atmosphere.
The absorption change curve shows reliably the
general features of the temperature change as
CO
2
concentration increases.
The absorption values of CO
2
as depicted in Fig.
3b, have been transformed into warming values
(dashed line curves) in Fig. 3a using conversion
factors. These factors have been calculated so
that the CO
2
absorption by concentration 280
ppm gives the same warming value as the curve
in question according to Eqs (2), (3), and (7).
The IPCC model (Eq. (3) and λ value 0.324
K/(Wm
-2
)) gives the TCS value 1.2°C. It cannot
be fitted into the general behavior of the CO
2
absorption. A red curve according to the IPCC
model TCS=1.2°C gives warming values that are
too high as illustrated in Fig. 3a, because the
warming rate change is not smooth at the
concentration of 280 ppm.
The dotted straight line in Fig. 3a illustrates an
utmost theoretical case that the temperature
growth rate would be linear from 0 to 280 ppm
matching the curve of the model TCS=1.2°C.
This straight line has the same angle coefficient
as the curve TCS=1.2°C in the point of 280 ppm.
This situation would violate the general rules of
absorption. There is no strong nonlinear part
from 20 ppm to 100 ppm, and the angle
coefficient of the absorption curve does not
diminish continuously with increasing CO
2
concentration.
IPCC [2] has estimated that the actual
temperature increment from 1880 to 2012 has
been 0.85°C, p. 5 of SPM. According to IPCC
(2013) the radiative forcing value for the same
time period has been 2.34 Wm
-2
, which gives
1.17°C warming being 37.7% greater than the
observed temperature. This is an empirical
observation that the IPCC model gives too high
warming values for CO
2
.
4.5 Positive Water Feedback or Not in the
Atmosphere
The climate models referred by the IPCC apply
positive water feedback as reported in AR5 [2,
p.207]: “In summary, radiosonde, GPS and
satellite observations of tropospheric water vapor
indicate very likely increases at near global
scales since the 1970s occurring at a rate that is
generally consistent with the Clausius-Clapeyron
relation (about 7% per degree Celsius) and the
observed increase in atmospheric temperature.”
This assumption of the Clausius-Clapeyron (C-C)
relation should also mean constant relative
humidity (RH).
The C-C equation provides the relationship
between the saturation water pressure and the
temperature. The atmosphere is not saturated
with water vapor, but RH varies globally between
35% and 80% depending on the altitude. There
is no scientific basis to apply the C-C relationship
to atmospheric conditions.
Fig. 4 depicts the satellite temperatures [32] and
absolute humidity trends [33] from 1979 to 2019.

Ollila; PSIJ, 22(2): 1-19, 2019; Article no.PSIJ.49095
11
Fig. 4. The satellite temperature and absolute humidity trends
It can be noticed that absolute humidity does not
follow temperature changes according to the C-C
relationship. For example, during 1982–2002, the
temperature has been steadily increasing, but
absolute humidity has a decreasing trend.
4.6 Validation of Calculations
Simple linear model according to equation (2)
has been used for calculating the warming
values of CO
2
changes. Because the emitted
radiation depends on the temperature according
to Planck’s law, which is nonlinear as presented
in equation (1), it can cause errors. Fig. 5 depicts
the surface temperature changes according to
RF changes from 0 to 5 Wm
-2
in both ways. Fig.
5 shows in an illustrative way that the error for
the potential RF changes in using linear model is
insignificant.
Fig. 5. The dependency of the surface temperature on the radiative forcing (RF) according to
spectral calculations and to linear relationship T = λ * RF

Ollila; PSIJ, 22(2): 1-19, 2019; Article no.PSIJ.49095
12
The synthesis analysis
by Stephens et al. [34]
shows an average value of 314.2 Wm
-2
in 13
independent observation-based studies for the
downward LW flux on the surface. The value of
the same flux of this study model is 310.9 Wm
-2
,
meaning a difference of 1.0%. The LW radiation
flux at TOA in the clear sky conditions according
to spectral calculations of this study is 265.3 Wm
-
2
. The same flux value based on the NASA
CERES satellite observations [12] from 2000–
2010 is 266.4 Wm
-2
. The difference is 0.4%.
These uncertainties are much smaller than the
uncertainties of the observed flux values. These
values mean that the atmospheric model of this
study used in the spectral calculations, describes
very accurately the radiation fluxes of the real
atmosphere.
The total absorption values of Gross GH effect
are 312.8 Wm
-2
for clear sky, 363.9 Wm
-2
for
cloudy sky, and 345.6 Wm
-2
for all-sky according
to spectral analysis method. The downward
radiation fluxes emitted by the atmosphere (also
close to empirical values) in the energy budget
calculation are 318 Wm
-2
, 359.8 Wm
-2
, and 345.6
Wm
-2
. The total absorption (including SW and
LW absorption) of all-sky 345.6 Wm
-2
is the sum
of the following contributors in Wm
-2
: water
134.4, latent heating 90.8, clouds 53.7, sensible
heating 24.2, CO
2
21.4, ozone 17.9, methane &
nitrogen oxide 2.2, and aerosols 1.0. It is not a
coincidence that the figures of the total
absorption and downward radiation flux are
almost the same as Kirchoff’s radiation law
states that they are equal in radiation balance
conditions. The small differences are well inside
the uncertainty limits of the fluxes. The LW
absorption by GH gases only cannot create the
emitted fluxes by the atmosphere.
The absorption values above the cloud cover for
different skies are the same. In the energy
balance analysis, the absorption values of clouds
in cloudy sky and all-sky conditions are 49.6
Wm
-2
and 37.8 Wm
-2
, and the spectral
calculations show the corresponding values to be
52.4 and 35.8 Wm
-2
. These differences of -2.8
and +2.0 Wm
-2
are well inside the uncertainty
values of individual flux values, which show a
typical uncertainty of ±7 Wm
-2
.
5. DISCUSSION
The reason for the small positive temperature
effect of 0.3°C of the all-sky situation in
comparison to that of the clear sky is in the
dynamic time delays of the atmospheric and
ocean/land processes. When the clear sky turns
into cloudy sky, changes in radiation fluxes
happen almost immediately, because the longest
time constant of the atmosphere is only about 2.7
days
[35]. The time constant of land is 1.04
months and of the ocean mixing layer 2.74
months
[35,36].
The major positive effect of the cloudy sky is due
to the cloud cover during the nighttime, which
radically reduces the cooling rate of the surface
in comparison to the clear sky. This means that
during the first few days, the temperature effect
of the cloudy sky is slightly positive, but
eventually the cloudy sky always results in a
lower surface temperature. In a real climate,
cloudiness fluctuates continuously from clear sky
to cloudy sky in relatively short periods of only a
few days. That is why during the changing sky
conditions, the all-sky generally gives a small
positive warming effect. At the same time, it
should be noticed, for example, that a long-term
(> 1 week) increased cloudiness always results
in a lower surface temperature [11].
The AGW theory emphasizes the role of CO
2
. In
this theory the contribution of CO
2
has been
considered higher than its contribution calculated
by the method of removing its impact in spectral
calculations. The basis for this increased effect is
that the atmosphere, if CO
2
were removed from
it, would cool and much of water vapor would
rain out. This would cause more raining, and this
would cause further cooling resulting even
glaciated snowball state [2]. Schmidt et al. [8]
have used the average value of minimum and
maximum effects of CO
2
absorption, which is an
“ad hoc” method without a clear scientific basis.
However, majority of CO
2
contribution studies
have applied the method of removing the GH gas
in question [7,9,10,21] in spectral calculations.
The spectral analysis method takes into
consideration the overlapping absorption
frequencies/wavelengths. That is why this
method shows what is the contribution of each
GH gas in the present climate in a precise way.
The RF values of CO
2
concentration changes
according to different research studies [30,37,38]
have been depicted in Fig. 6.
Because Myhre et al.’s [30] study does not show
the actual total atmospheric water vapor amount,
and because the applied atmospheric water
vapor profile is not accessible in the common
databases, it is impossible to find a reason
between the reproduction of this study (equation
[7]) and equation (3)). Shi [38] has used positive

Ollila; PSIJ, 22(2): 1-19, 2019; Article no.PSIJ.49095
13
Fig. 6. Radiative Forcing (RF) curves of carbon dioxide according to different research studies
[29,34,35] and this study
water feedback in his calculations, and his curve
is very close to the curve by Myhre et al. [30], but
if the RF values are multiplied by 0.5 to remove
the positive water feedback, the curve is very
close to the equation of this study.
6. CONCLUSION
The atmosphere emits LW radiation according to
its temperature, but the LW absorption 155.6
Wm
-2
is not capable of creating the observed
downward LW radiation of 345.6 Wm
-2
. Other
factors are needed in the GH effect to explain
this gap, and they are SW absorption by GH
gases and sensible and latent heating. These
fluxes disappear into the atmosphere in the
present GH effect definition, leaving no effect on
the atmospheric temperature and downward
radiation for these fluxes. Together, these four
factors perfectly explain the downward LW
radiation, which has the real warming effect on
the surface. The new GH effect definition
explains the radiation fluxes and elevated
surface temperature without contradicting the
physical laws. All four factors have an essential
role in maintaining the atmospheric temperature
profile, which defines downward LW flux
according to Planck’s law.
This study shows that the increase of 33°C is
due to the downward LW radiation effect of 294.5
Wm
-2
. This figure is not the same as the
observed downward LW radiation flux of 345.6
Wm
-2
emitted by the atmosphere because the
clouds simultaneously increase LW absorption
and decrease solar insolation. Additionally, all-
sky conditions prevail only during short time
periods, and the observed surface temperatures
do not correspond to the observed radiation
fluxes due to the long-time delays of the climate
system.
The contribution of CO
2
is only 7.3% in the GH
effect, which means that the sole CO
2
effect of
1.2°C or 1.8°C calculated by GCMs applied by
IPCC cannot be fitted into the total GH effect of
CO
2
. The value of 1.2°C is not in line with the
statement from the IPCC (2013 p. 666) stating
that “the contribution of water vapor to the natural
greenhouse effect relative to that of carbon
dioxide (CO
2
) depends on the accounting
method but can be considered to be
approximately two to three times greater.” This
means that the warming effect of CO
2
would be
between 1.8°C/2 = 0.9°C or 1.8°C /3 = 0.6°C,
which are much lower values than 1.2°C. The
author has no explanation for this discrepancy in
the IPCC values. The IPCC model including the
GH effect and feedbacks shows about 37.7% too
much surface warming at the end of 2012. The
climate model, which can be fitted into the total
GH effect, shows 0.3°C warming by CO
2
by
2017. Therefore, other forces are needed to
explain the major part of present warming.

Ollila; PSIJ, 22(2): 1-19, 2019; Article no.PSIJ.49095
14
If a climate model using the positive water
feedback were applied to the GH effect
magnitude of this study, it would fail worse than a
model showing a TCS value of 1.2°C. If there
were a positive water feedback mechanism in the
atmosphere, there is no scientific grounding to
assume that this mechanism would start to work
only if the CO
2
concentration exceeds 280 ppm,
and actually, the IPCC does not claim so.
The absolute humidity and temperature
observations show that there is no positive water
feedback mechanism in the atmosphere during
the longer time periods. According to the
reproduction of Myhre et al.’s [30] study, the RF
value for CO
2
concentration of 560 ppm is 2.16
Wm
-2
being 41.6% smaller than the original value
3.7 Wm
-2
. According to the two methods of this
study, the climate sensitivity parameter λ is 0.27
K/(Wm
-2
). It is about half of the λ value 0.5
K/(Wm
-2
) applied by the IPCC and the reason is
in water feedback. Based on these two findings,
the TCS is only 0.6°C.
COMPETING INTERESTS
Author has declared that no competing interests
exist.
REFERENCES
1. Henderson MDH, Henderson-Sellers A.
History of greenhouse effect. Progr Phys
Geography Earth and Environ. 1990;14:1-
18.
2. IPCC. The Physical Science Basis,
Chapter 8.1. Working Group I Contribution
to the IPCC Fifth Assessment Report.
Cambridge University Press, Cambridge;
2011.
3. IPCC. The Physical Science Basis,
Policymakers summary, Climate change,
The IPCC scientific assessment.
Cambridge University Press, Cambridge;
1990.
4. IPCC. The Physical Science Basis,
Chapter 1.5, Working Group I Contribution
to the IPCC Fourth Assessment Report of
the Intergovernmental Panel on Climate
Change. Cambridge University Press,
Cambridge; 2007.
5. Pierrehumbert RT. Infrared radiation and
planetary temperature. Phys Today.
2011;64:33-38.
6. Michell JFB. The “greenhouse” effect and
climate change. Rev Geophys.
1989;27:115-139.
7. Kiehl JT, Trenberth KE. Earth’s annual
global mean energy budget. Bull Amer
Meteor Soc. 1997;90:311-323.
8. Schmidt GA, Ruedy RA, Miller RL, Lacis
AA. Attribution of the present-day total
greenhouse effect. J Geophys Res.
2010;115,D20106:1-6.
9. Ollila A. The roles of greenhouse gases in
global warming. E&E. 2012;23:781-799.
10. Ollila A. Warming effect reanalysis of
greenhouse gases and clouds. Phys Sci Int
J. 2017;13:1-13.
11. Ollila A. Dynamics between clear, cloudy
and all-sky conditions: Cloud forcing
effects. J Chem Biol Phys Sc. 2013;4:557-
575.
12. Stephens GL, Wild M, Stackhouse Jr PW,
L’Ecuyer T, Kato S, Henderson DS. An
update on Earth’s energy balance in light of
the latest global observations. Nat Geosc.
2012;5:691-696.
13. Chernykh IV, Alduchov OA, Eskridge RE.
Trends in low and high cloud boundaries
and errors in height determination of cloud
boundaries. Bull Amer Meteor Soc.
2001;82:1941-1947.
14. Wang J, Rossow WB, Zhang Y. Cloud
vertical structure and its variations from a
20-yr global rawinsonde dataset. J Climate.
2000;13:3041-3056.
15. Kokhanovsky AA, Rozanov VV, Lotz W,
Bovensmann H, Burrows JP. Global cloud
top height and thermodynamic phase
distributions as obtained by SCIAMACHY
on ENVISAT. Int J Rem Sens. 2011;28:
836-844.
16. Zhang Y, Rossow WB, Lacis AA, Oinas V,
Mischenko MI. Calculation of radiative
fluxes from the surface to top of
atmosphere based on ISCCP and other
global data sets: Refinements of the
radiative model and the input data. J
Geophys Res. 2004;109:1149-1165.
17. Gats Inc. Spectral calculations tool; 2015.
Available:http://www.spectralcalc.com/info/
help.php
18. HITRAN. Harvard-Smithsonian Center for
Astrophysics, The HITRAN (high-resolution
transmission molecular absorption) data
base; 2018.
Available:https://www.cfa.harvard.edu/hitra
n/
19. Mlawer EJ, Payne VH, Moncet J-L,
Delamere JS, Alvarado MJ, Tobin DC.
Development and recent evaluation of the
MT_CKD model of continuum absorption.

Ollila; PSIJ, 22(2): 1-19, 2019; Article no.PSIJ.49095
15
Phil Trans Ser A Math Phys Eng Sc.
2012;370:2520-25.
20. Hartmann DL. Global Physical Climatology,
Elsevier Science, USA; 2015.
21. Ekholm N. On the variation of the climate
of the geological and historical past and
their causes. Quart J Royal Meteor Soc.
1901;27:1-62.
22. Miskolczi FM. Greenhouse effect and IR
radiative structure of the Earth’s
atmosphere. Int J Environ Res Public
Health. 2010;7:1-27.
23. Trenberth KE, Fasullo JT, Kiehl JT. Earth’s
global energy budget. Bull Amer Meteor
Soc. 2009;90:311-324.
24. Ollila A. Clear sky absorption of solar
radiation by the average global
atmosphere. J Earth Sc Geotech Eng.
2015;5:19-34.
25. Ohring G, Clapp PF. The effect of changes
in cloud amount on the net radiation at the
top of the atmosphere. J Atm Sc.
1980;37:447-454.
26. Harrison EF, Minnis P, Barkstrom BR,
Ramanathan V, Cess RD, Gibson GG.
Seasonal variation of cloud radiative
forcing derived from Earth radiation budget
experiment. J Geophys Res. 1990;95:
18687-18703.
27. Ardanuy PE, Stowe LL, Gruber A, Weiss
M. Shortwave, longwave, and net cloud-
radiative forcing as determined from
Nimbus 7 observations. J Geophys Res.
1991;96(D10):18537-18549.
28. Loeb HG, Wielicki BA, Doelling DR, Smith
GL, Keyes D, Kato S, Manalo-Smith N,
Wong T. Toward optimal closure of the
Earth's top-of-atmosphere radiation budget.
J Climate. 2009;22:748-766.
29. Raschke E, Ohmura A, Rossow WB,
Carlson BE, Zhang Y-C, Stubenrauch C,
Kottek M, Wild M. Cloud effects on the
radiation budget based on ISCCP data
(1991 to 1995). Int J Clim. 2005;25:1103-
1125.
30. Myhre G, Highwood EJ, Shine KP, Stordal
F. New estimates of radiative forcing due to
well mixed greenhouse gases. Geophys
Res Lett. 1998;25:2715-2718.
31. Berk A, Bernstein LS, Robertson DC.
Modtran. A moderate resolution model for
lowtran 7; 2017.
Available:http://forecast.uchicago.edu/Proje
cts/modtran.orig.html
32. UAH MSU dataset; 2019.
Available:https://www.nsstc.uah.edu/data/
msu/v6.0/tlt/uahncdc_lt_6.0.txt
33. NCEP/NCAR Reanalysis; 2019.
Available:https://www.esrl.noaa.gov/psd/cg
i-bin/data/timeseries/timeseries1.pl
34. Stephens GL, Wild M, Stackhouse Jr PW,
L’Ecuyer
T, Kato S, Henderson
DS. The
global character of the flux of downward
longwave radiation. J of Climate.
2011;25:2329-2340.
35. Kauppinen J, Heinonen JT, Malmi PJ.
Major portions in climate change: Physical
approach. Int Rev Phys. 2011;5:260-
270.
36. Stine AR, Huybers P, Fung IY. Changes in
the phase of the annual cycle of surface
temperature. Nature. 2009;457:435-441.
37. Hansen J, Gung I, Lacis A, Rind D,
Lebedeff S, Ruedy R, Russell G, Stone P.
Global climate changes as forecast by
Goddard Institute for Space Studies, Three
Dimensional Model. J Geophys Res.
1998;93:9341-9364.
38. Shi G-Y. Radiative forcing and greenhouse
effect due to the atmospheric trace gases.
Science in China (Series B). 1992;35:217-
229.

Ollila; PSIJ, 22(2): 1-19, 2019; Article no.PSIJ.49095
16
APPENDIX
The energy balance calculation bases are explained, and the values are depicted in Table A1. The
detailed values of SW absorption for all-sky conditions are in Table A2, and the values of LW
absorption in Table A3. The absorption flux values of the Gross GH effect for different skies are
tabulated in Tables A4–A6. The absorption and warming values of different carbon dioxide, methane
and nitrogen oxide concentrations are shown in Table A7.
Earth’s energy balance
The energy flux values in Table A1 are based on six different methods as marked
1-6
:
- The direct observations
1
- Equation F
all-sky
= 0.34*F
clear sky
+ 0.66*F
cloudy sky
based on the average cloudiness of 66%
2
- Spectral calculations
3
- Energy balance requirements for surface, atmosphere, and TOA
4
- Adding or subtracting fluxes
5
- Four different calculation basis
6
as explained below:
1) SW flux reflected by the air in the cloudy sky (Rp). Reflected flux has been assumed to be
dependent upon the amount of air molecules. The amount of air mass above the average cloud top (4
km) is 62% of the total air mass. Because the reflected radiation by air cannot take place in or below
clouds, the Rp flux of the cloudy sky can be estimated to be 0.62*23 Wm
-2
= 14.4 Wm
-2
.
2) SW absorption by a clear sky in cloudy and all-sky conditions (Sb). There are no measured or
calculated values available for SW fluxes absorbed by a clear sky in cloudy and all-sky conditions.
The author has calculated these fluxes using an iteration method. Two iterations were needed and
only the final results are represented in the flux table. The Sx represents the downward flux, which is
calculated by subtracting reflection fluxes with Rc and Rp values from SWin. The clear sky
absorption-% = 100 * Sb/Sx = 100 * 69/317 = 21.77. This percentage has been used in calculating the
air absorption for cloudy and all-sky conditions, and the values are clear sky = 52.3 and cloudy sky =
57.2.
3) Absorbed flux by clouds (Sr) from the reflected flux by surface (Rs). The Sc values can be
calculated as differences between the Si values and Sb values, which produce the values Sc = 24.7
for cloudy sky and Sc = 16.3 for all-sky. The cloudy sky absorption-% = 100 * Sco/Sxo = 100 *
24.7/240.4 = 10.28%, and all-sky absorption-% = 100 * Sca/Sxa = 16.3/262.5 = 6.2%. Using these
absorption-% values, the absorption fluxes Sr of reflected flux Rp can be calculated. The results for
cloudy sky are Sr = 2.3 and for all-sky Sr = 1.5. The calculated values for Rc, Rp, and Ra can be
checked by calculating the reflected fluxes at TOA and that their sum is the same as the measured
values Rt for different skies.
4) Sensible heating (T) and latent heating (L) values are based on three calculation bases utilizing an
iteration procedure: a) the sum of T+L must match the balance value of the “surface out,” b) the
relationship between the T values of clear sky/cloudy sky is the same as Ss values of clear sky/cloudy
sky, and c) the relationship between the L values of clear sky/cloudy sky is the same as the “surface
out” balance values of clear sky/cloudy sky.
The pseudo flux values of Ss are the effective values of SW radiation absorbed by the surface. They
are pseudo values because Earth can never reach the real balance for incoming SW radiation flux on
the surface. This is due to the long dynamic delays of the ocean and the land.

Ollila; PSIJ, 22(2): 1-19, 2019; Article no.PSIJ.49095
17
Table A1. Earth’s energy balance for clear, cloudy, and all-sky conditions (Wm
-2
)
SW radiation budget
Clear
Cloudy
All-sky
Uncertainty
SW total radiation from the sun SWin
340.2
1
340.2
1
340.2
1
±0.1
Total reflected SW rad. = Rc+Rp+Ra Rt
53.0
1
119.3
1
100.2
1
±2
SW flux reflected by clouds Rc 0.0
1
85.4
5
60.3
4
±10
SW flux reflected by air Rp 23.2
4
14.4
6
17.4
2
±10
SW flux downwards Sx = St-Rc-Rp Sx 317.0
5
240.4
5
262.5
5
±10
SW absorption by clear sky Sb 69.0
3
52.3
6
57.2
6
±10
SW absorption of Sx flux by cloudy sky Sc 0.0
1
24.7
4
16.3
2
±5
Sw insolation (Sx) absorbed by atmosphere Si 69.0
3
77.0
5
73.5
5
±10
Reflected flux (Rs) absorbed by clouds Sr 0.0
1
2.3
6
2.3
6
±0.5
Total absorption of SW rad. absorbed by atm. Sa 69.0
3
79.3
5
75.0
5
±10
SW radiation downwards to surface Sd 248.0
5
163.4
5
189.0
5
±10
SW radiation reflected by surface Rs 29.8
1
21.8
1
24.0
1
±3
Reflected Rs flux into space. Ra = Rs-Sr Ra 29.8
1
19.5
5
22.5
5
±3
SW radiation absorbed by surface Ss
218.2
5
141.6
5
165.0
5
±6
Net SW radiation = St - Rt NSR 287.2
5
220.9
5
240.0
5
±0.4
SW rad. absorbed by clouds & surface ASR
287.2
5
220.9
5
240.0
5
±0.4
Surface in:
SW radiation absorbed by surface (pseudo) Ss 197.0
4
149.3
2
165.0
1
±6
Downward radiation emitted by atmosphere Ed 318.0
3
359.8
2
345.6
1
±9
SFC-balance
515.0
5
509.1
5
510.6
5
±10
Surface out:
Sensible heating T 29.4
6
22.2
6
24.2
4
±7
Latent heating L 91.5
6
90.5
6
90.8
2
±10
LW radiation emitted by surface Es 394.1
3
396.4
3
395.6
3
±5
SFC-balance
515.0
5
509.1
5
510.6
5
±10
Atmosphere in:
SW absorption by clear sky Sb 69.0
3
52.3
6
57.2
6
±10
Total SW absorption by cloudy sky Sa 0.0
1
79.3
5
17.8
5
±6
Sensible heating T 29.4
6
22.2
6
24.2
4
±7
Latent heating L 91.5
6
90.5
6
90.8
2
±10
LW radiation absorbed by atmosphere Aa 310.9
3
396.4
3
367.1
3
±10
LW radiation transmitted from surface to space Et 83.2
3
0.0
3
28.5
3
±6
ATM-balance
584.0
5
588.4
5
585.6
5
±10
Processes inside the atmosphere:
LW rad. absorbed by GH gases below clouds Ag 107.5
3
109.3
3
108.9
3
±7
LW radiation emitted by GH gases at cloud bottom
Eg 203.4
5
287.1
5
258.2
5
±7
LW radiation absorbed by clouds or GH gases Ac 11.7
4
49.6
4
37.8
4
±7
LW radiation emitted by cloud top altitude Ec 191.7
5
237.5
5
220.4
5
±4
LW rad. absorbed by GH gases above clouds Au 8.9
3
8.9
3
8.9
3
±3
Total absorption by GH gases At 128.1
5
167.8
5
155.6
5
±7
Atmosphere out:
LW radiation emitted by GH gases at TOA
Eu
182.8
5
228.6
5
211.5
5
±12
Downward radiation emitted by atmosphere Ed 318.0
3
359.8
2
345.6
1
±9
LW radiation transmitted from surface to space Et 83.2
3
0.0
3
28.5
3
±4
ATM-balance
584.0
5
588.4
5
585.6
5
±10
TOA:
LW radiation emitted by GH gases at TOA Eu 182.8
5
228.6
5
211.5
5
±12
LW radiation transmitted from surface to space Et 83.2
3
0.0
3
28.5
3
±6
OLR
266.0
1
228.6
5
240.0
1
±0.4

Ollila; PSIJ, 22(2): 1-19, 2019; Article no.PSIJ.49095
18
Table A2. SW absorption fluxes for clear, cloudy, and all-sky conditions (Wm
-2
) by spectral
analysis method
SW absorption
Clear sky
Cloudy sky
All-sky
Water 52.4 39.8 43.5
Carbon dioxide 1.6 1.2 1.3
Ozone 13.2 10.0 11.0
Methane & Nitrogen oxide 0.5 0.4 0.4
Aerosols 1.3 1.0 1.0
Clouds 0.0 27.0 17.8
Total absorption 69.0 79.3 75.0
Table A3. LW absorption fluxes for clear, cloudy, and all-sky conditions (Wm
-2
) by spectral
analysis method
LW absorption
Clear sky
Cloudy sky
All-sky
Water
98.8
86.8
90.9
Carbon dioxide 20.1 20.1 20.1
Ozone 7.2 6.8 6.9
Methane & Nitrogen oxide 2 1.7 1.8
Aerosols 0 0 0.0
Clouds 0 54.4 35.9
Total absorption 128.1 169.8 155.6
Table A4. Gross greenhouse effect in all-sky conditions (Wm
-2
) by spectral analysis and
energy balance method (L = Latent heating, T = Sensible heating)
SW
Wm
-2
LW+L+T
Wm
-2
SW+LW+L+T
Wm
-2
Contribution
%
Contribution
°C
Water 43.5 90.9 134.4 38.9 12.83
Latent heating 0.0 90.8 90.8 26.3 8.67
Clouds 17.8 35.9 53.7 15.5 5.13
Sensible heating 0.0 24.2 24.2 7.0 2.31
Carbon dioxide 1.3 20.1 21.4 6.2 2.04
Ozone 11.0 6.9 17.9 5.2 1.71
Methane & Nitrogen oxide
0.4 1.8 2.2 0.6 0.21
Aerosols 1.0 0.0 1.0 0.3 0.10
Total 75.0 270.6 345.6 100.0 33.00
Table A5. Gross greenhouse effect in clear sky conditions by spectral analysis and energy
balance method (L = Latent heating, T = Sensible heating)
SW
Wm
-2
LW+L+T
Wm
-2
SW+LW+L+T
Wm
-2
Contribution
%
Contribution
°C
Water 52.4 98.8 151.2 48.3 15.95
Latent heating 0.0 91.5 91.5 29.3 9.65
Clouds 0.0 0 0.0 0.0 0.00
Sensible heating 0.0 29.4 24.2 7.7 2.55
Carbon dioxide 1.6 20.1 21.7 6.9 2.29
Ozone 13.2 7.2 20.4 6.5 2.15
Methane & Nitrogen oxide
0.5 2 2.5 0.8 0.26
Aerosols 1.3 0.0 1.3 0.4 0.14
Total 69.0 249 312.8 100.0 33.00

Ollila; PSIJ, 22(2): 1-19, 2019; Article no.PSIJ.49095
19
Table A6. Gross greenhouse effect in cloudy sky conditions (Wm
-2
) by spectral analysis and
energy balance method (L = Latent heating, T = Sensible heating)
SW
Wm
-2
LW+L+T
Wm
-2
SW+LW+L+T
Wm
-2
Contribution
%
Contribution
°C
Water 39.8 86.8 126.6 34.8 11.48
Latent heating 0.0 90.5 90.5 24.9 8.21
Clouds 27.0 54.4 81.4 22.4 7.38
Sensible heating 0.0 22.2 24.2 6.7 2.19
Carbon dioxide 1.2 20.1 21.3 5.9 1.93
Ozone 10.0 6.8 16.8 4.6 1.52
Methane & Nitrogen oxide
0.4 1.7 2.1 0.6 0.19
Aerosols 1.0 1.0 0.3 0.09
Total 79.4 282.5 363.9 100.0 33.00
Table A7. The absorption change caused by the concentration changes of carbon dioxide,
methane, and nitrogen oxide in the average global atmosphere conditions
Carbon dioxide
Methane
Nitrogen oxide
ppm
dE, Wm
-2
dT, °C
ppm
dE, Wm
-2
dT, °C
ppm
dE, Wm
-2
dT, °C
0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
25 10.69 1.19 1.77 0.89 0.09 0.31 0.86 0.09
35 12.26 1.36 7.26 1.77 0.19 1.32 2.04 0.21
50 13.32 1.48 10.00 2.04 0.21 3.32 3.35 0.35
100 15.44 1.72 15.49 2.47 0.26 5.32 4.28 0.45
200 18.35 2.04 50 3.96 0.42 10.32 5.90 0.62
280 19.80 2.20 100 5.07 0.53 25.00 8.15 0.86
379 20.51 2.28 139 5.65 0.59 58.32 10.94 1.15
410 21.40 2.38 200 6.35 0.67 100 13.07 1.37
560 23.01 2.56 379 7.77 0.82 200 14.99 1.57
800 24.92 2.77 1400 11.37 1.19 310 15.20 1.60
Table A8. Parameters and choices applied in Modtran simulations
Parameter
Value
Tropospheric ozone 28 ppb
Stratospheric ozone scale 1
Water vapor scale 1.2384
Ground temperature offset 1 °C (T= 288.2 K)
Holding fixed Water vapor pressure
Locality Subarctic summer
Clear sky No clouds or rain
Cloudy sky Cumulus cloud base 0.66 km, top 2.7 km
Altitude 70 km
_________________________________________________________________________________
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provided the original work is properly cited.
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