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Atmospheric carbon dioxide and climate

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Atmospheric radiative fluxes are evaluated for the line-by-line model of spectral lines in considering the atmosphere as a weakly nonuniform plane layer and altitude profiles of its parameters are taken from the model of standard atmosphere. Concepts of molecular spectroscopy are combined with the local thermodynamic equilibrium for greenhouse gases and with information from HITRAN data base for parameters of radiative transitions. In addition, the energetic balance of the Earth allows one to determine the radiative flux from clouds. As a result, the algorithm is worked out for evaluation of the atmospheric radiative flux toward the Earth depending on its composition. We below concentrate on the change of atmospheric radiative fluxes as a result of doubling of the concentration of CO2 molecules. It is shown that the change of the global temperature in this case according to the above algorithm in 5-6 times exceeds that followed from climatological models which are based on old spectral data, rather than those from HITRAN data base. These codes ignore overlapping of spectral lines of atmospheric radiators.
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21
Journal of Atmospheric Science Research | Volume 02 | Issue 04 | October 2019
Journal of Atmospheric Science Research
https://ojs.bilpublishing.com/index.php/jasr
ARTICLE
Atmospheric Carbon Dioxide and Climate
Boris. M. Smirnov*
Joint Institute for High Temperatures RAS, Izhorskaya 13/19, Moscow 125412, Russia
ARTICLE INFO ABSTRACT
Article history
Received: 26 April 2020
Accepted: 12 May 2020
Published Online: 31 March 2020
Atmospheric radiative fluxes are evaluated for the line-by-line model of
spectral lines in considering the atmosphere as a weakly nonuniform plane
layer and altitude profiles of its parameters are taken from the model of
standard atmosphere. Concepts of molecular spectroscopy are combined
with the local thermodynamic equilibrium for greenhouse gases and with
information from HITRAN data base for parameters of radiative transitions.
In addition, the energetic balance of the Earth allows one to determine the
radiative ux from clouds. As a result, the algorithm is worked out for eval-
uation of the atmospheric radiative ux toward the Earth depending on its
composition. We below concentrate on the change of atmospheric radiative
uxes as a result of doubling of the concentration of CO2 molecules. It is
shown that the change of the global temperature in this case according to
the above algorithm in 5-6 times exceeds that followed from climatolog-
ical models which are based on old spectral data, rather than those from
HITRAN data base. These codes ignore overlapping of spectral lines of
Keywords:
Absorption coefcient
Cloud emission
Global temperature
Optical thickness

*Corresponding Author:
Boris. M. Smirnov,
Joint Institute for High Temperatures RAS, Izhorskaya 13/19, Moscow 125412, Russia;
Email: bmsmirnov@gmail.com
1. Introduction
The participation of the greenhouse effect in the en-
ergetic balance of our planet was understood two
hundred years ago [1,2]. Then atmospheric emission
in the infrared spectrum range increases the radiative ux
to the Earth and increases the global Earth’s temperature
which is the Earth’s surface temperature is averaged over
the globe and time. Three basic greenhouse components
are H2O and CO2 molecules, as well as water microdrop-
lets which constitute clouds.
Starting from the Arrhenius paper [3] in 1896, connec-
tion between the concentration of atmospheric carbon
dioxide and the Earth’s climate causes the main attention
to the greenhouse problem, especially, if this results from
the human activity. The contemporary version of infrared
(IR) atmospheric emission for outside radiation was pre-
sented in [4-6] that considers emission and absorption of
atmospheric molecules. Recently [7] the author formulated
the problem of IR atmospheric emission toward the Earth
with accounting for cloud radiation. We below consider
the theory of IR atmospheric radiation to the Earth and
connect its results with those of adjacent problems.
2. Methods
We now consider methods which allow us to compose
the algorithm to calculate the radiative flux from the at-
mosphere to the Earth. For the analysis of emission of
molecular components, it is necessary to modify the clas-
sical molecular spectroscopy which was constructed as
a direction of quantum mechanics at the beginning of 20
22
Journal of Atmospheric Science Research | Volume 02 | Issue 04 | October 2019
century (for example [8,9]). Classical molecular spectrosco-
py considers infrared radiation of molecules as transitions
between some vibration and rotation molecular states,
so that selection rules determine the connection between
initial and nal vibration and rotation states for radiative
transitions of a given molecule symmetry.
In molecular spectroscopy, rates of radiative transitions
in molecules are expressed through the Einstein coeffi-
cients of these transitions. Spectra of molecules have the
discrete character, but spectral lines for each radiative
transitions are broaden due to interactions in gases where
radiative molecules are located. Contemporary molecular
spectroscopy is based on data banks, as HITRAN data
bank for molecules [10-13]. Then the rate of a given radiative
transition is expressed through four molecular parameters,
namely, ωj, the frequency of the center of a j-th transition,
Sj, the intensity of this transition that is proportional to the
rst Einstein coefcient, νj, the width of the spectral line,
and Ej, the excitation energy from the ground molecule
state to a lower transition state [11].
Considering the atmosphere as a weakly nonuniform
at gaseous layer located over the Earth surface, and com-
bining classical molecular spectroscopy with local thermo-
dynamic equilibrium at each point of this layer, one can
calculate the radiative uxes to the Earth for the line-by-
line model [14], i.e. for each frequency, at a given mixture
of emitted molecular gases and a given altitude prole for
the density of each greenhouse gas and the temperature.
In this case we use the model of standard atmosphere [15]
for the space distribution of carbon dioxide molecules and
water molecules. But this algorithm is suitable for any
space distribution of emitted components and is useful in
meteorological codes where atmospheric radiation may be
added to transport of mass, temperature and humidity. In
this case the altitude proles of the temperature and densi-
ty of radiative components are required also.
One can model atmospheric radiation toward the Earth
as emission of a at layer. If this gaseous layer is optically
thick and its temperature is independent of an altitude, the
partial radiative ux through its boundary is given by the
Planck formula
3
22
( ) (1)
4 exp 1
IT
cT
ω
ω
ω
π
=





(1)
If the optical thickness of the layer is restricted, the ra-
diative ux at a given frequency is given by [16]
() ()( ) (2)J T I T gu
ωωω
=
(2)
In this way the opaque factor
()gu
ω
is dened for a given
optical thickness
u
ω
of the layer according to formula [16]
11
00 0
( ) cos exp cos cos 1 exp , (3)
cos cos
u
u
u
g u d du d
ω
ω
ω
θ θθ
θθ



= = ⋅− −
 

 

∫∫ ∫
(3)
where
θ
is an angle between the direction of photon
motion and the boundary perpendicular. In the limit of
optically thick layer
1u
ω
>>
the opaque factor is
( )1gu
ω
=
,
and formula (2) is transformed in formula (1).
It is necessary to take into account that the temperature
varies, as an altitude is changed. For this one can divide
the troposphere in some layers with an identical tempera-
ture and account a nonuniformity of the layer by numeri-
cal evaluation, as it is made in [5]. In our approach [17,18] we
expand the total radiative ux over a small parameter and
reduce the radiative process to that of an equilibrium layer
with the temperature
of an effective layer that is locat-
ed at an altitude
, that is
( ) (4)T Th
ωω
=
(4)
In particular, in the case of an optically thick layer the
effective layer is dened such, that its optical thickness is
2/3 [17,18]
0
2
( ) ( ) (5)
3
h
u h k h dh
ω
ωω
≡=
(5)
Here
()kh
ω
is the absorption coefcient at a given fre-
quency and an indicated altitude. The procedure of deter-
mination of the radiative temperature
in a general case
is described in [7] in detail.
The above analysis relates to molecular components of
the atmosphere. Then, considering emission of molecules
to be noncoherent, we summarize radiative fluxes from
all the molecules and obtain the radiative temperature
for the total radiative ux of a molecular gas. The separate
problem is insertion in this scheme clouds or small atmo-
spheric particles that is absent in climatological codes.
Among models of cloud emission, we choose nally such,
that clouds on a certain altitude absorb infrared radiation
entirely. This means that the optical thickness of clouds
is high, and they emit infrared radiation. As a result, we
have for the radiative ux from the atmosphere [7]
[ ]
()() ()1 (),(6)
cl
J I T gu I T gu
ω ωω ω ω ω
= +−
(6)
where
cl
T
is the cloud temperature.
For realization of formula (6), it is necessary to use
profiles for distribution of atmospheric radiators. As for
radiating molecules, this information follows from the
model of standard atmosphere or other similar sources.
But it is difcult to obtain the same information for clouds
consisting of water microdroplets because they are not
formed in motionless air. Therefore determination of the
DOI: https://doi.org/10.30564/jasr.v2i4.1838
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Journal of Atmospheric Science Research | Volume 02 | Issue 04 | October 2019
amount of condensed water in the atmosphere is problem-
atic.
In order to solve this problem within the framework of
the model of standard atmosphere, we add to the above
information the energetic balance of the atmosphere
which was composed at rst by NASA [19]. In particular,
the NASA data for the Earth’s energetic balance was pub-
lished in the author book [20] of 1975. Subsequently other
versions of the Earth’s energetic balance were represented
by World Meteorological Organization (WMO) [21,22]. But
these uxes coincide with previous ones within the limits
of a few percent.
The total flux of infrared radiation toward the Earth
integrated over frequencies must coincide with that fol-
lowed from the energetic balance of the Earth and its
atmosphere. This requirement allows one to determine the
position of clouds. In particular, for the model of the stan-
dard atmosphere, the effective altitude of cloud location
is approximately 3.4 km, and the effective temperature of
cloud emission is
266
cl
TK=
, whereas the temperature
of the Earth’s surface is equal
288
E
TK=
for this model.
Thus, the above scheme allows one to determine the pa-
rameters of the radiative ux from the atmosphere to the
Earth.
3. Results
We use the above scheme to determine various radiative
uxes of the atmosphere. The connection between direct
and reverse radiative processes is governed by the Kirch-
hoff law [23] or the principle of detailed balance for these
processes. This allows one to use the absorption coeffi-
cient
as the parameter of the absorption process in the
analysis of atmospheric emission. The absorption coef-
cient of molecules of a given type is given by
( ) (7)
j
j
j
k N S Ta
ω ωω
=
(7
Here N is the total number density of molecules of a giv-
en type,
j
S
is the intensity of the spectral line for a given
transition, and the distribution function of photons over
frequencies for air at atmospheric and nearby pressures is
determined for the impact mechanism of broadening of
spectral lines
( ) ( )
22
, (8)
2 /2
j
j
jj
a
ωω
ν
π ωω ν
=
−+


8
where
j
ω
is the frequency of the spectral line center, and
j
ν
is the spectral line width. Next, the intensity of spectral
lines is given in the HITRAN tables for a certain tempera-
ture. The transition to another temperature proceeds on the
basis of formula
( ) ( ) exp (9)
jj
j jo
o
ST ST TT
εε

=⋅−


(9)
Table 1. Radiative uxes of greenhouse atmospheric com-
ponents to the Earth and their contributions to the total
radiative ux absorbed by the Earth [7]
Component Flux, W/m2Portion, %
H2O-molecules 166 51
H2O-droplets (clouds) 96 29
CO2-molecules 58 18
CH4-molecules 4 1
N2O-molecules 3 1
Thus, these formulas with using the HITRAN data
allow us to determine the absorption coefcient and then
the atmospheric radiative fluxes to the Earth according
to a described scheme. The values of the radiative uxes
toward the Earth are presented in Table 1. In addition,
atmospheric molecules and clouds are sources of infra-
red emission in a different frequency range. According
to evaluations within the framework of this scheme [7],
approximately 95% of the radiative ux at frequencies be-
low 800cm-1 is created by water and carbon dioxide mole-
cules, while 84% of this ux at frequencies above 800cm-1
is due to water microdroplets of clouds.
Let us consider the greenhouse effect which consists
in change of the global temperature as a result of varia-
tion of the atmosphere content. Usually as the measure
of this effect is taken the doubling of the concentration
of CO2 molecules, and below we compare variations of
radiative fluxes as a result of this variation. We denote
by
J
the variation of the total radiative flux as a re-
sult of doubling of carbon dioxide concentration, and by
22
( ), ( ),
cl
J H O J CO J∆ ∆∆
the corresponding changes of
the radiative fluxes created by water molecules, carbon
dioxide molecules and clouds correspondingly. From the
denition of the total radiative ux the following equation
is fullled
22
( ) ( ) (10)
cl
J J H O J CO J∆ =∆ +∆ +∆
(10)
Table 2 contains the changes of these radiative uxes in
indicated frequency ranges.
Table 2. Changes of radiative uxes from the standard
atmosphere to the Earth as a result of doubling of the
concentration of CO2 molecules in the infrared spectrum
range [7]. These changes are dened in the text and are
DOI: https://doi.org/10.30564/jasr.v2i4.1838
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Journal of Atmospheric Science Research | Volume 02 | Issue 04 | October 2019
expressed in W/m2
Frequency range, ∆ω ∆J (CO2 ) ∆J (H2 O) ∆Jcl ∆Jt
580 - 600
600 - 620
620 - 640
640 - 660
660 - 680
680 - 700
700 - 720
720 - 740
740 - 760
760 - 780
780 - 800
800 - 850
900 - 950
950 - 1000
1000 - 1050
1050 - 1100
0.96
0.81
0.63
0.15
0.18
0.21
0.12
0.64
1.07
0.56
0.25
0.15
0.20
0.76
0.18
0.37
-0.89
-0.74
-0.61
-0.14
-0.18
-0.20
-0.03
-0.05
-0.10
-0.02
-0.02
-0.03
0
-0.01
0
0
-0.04
-0.03
0
0
0
0
-0.03
-0.39
-0.68
-0.40
-0.17
-0.08
-0.16
-0.53
-0.13
-0.26
0.03
0.04
0.02
0.01
0
0.01
0.06
0.20
0.29
0.14
0.06
0.04
0.04
0.22
0.05
0.11
total 7.24 -3.02 -2.90 1.32
As it follows from Table 2, doubling of the concen-
tration of atmospheric carbon dioxide causes an increase
of the radiative ux due CO2 molecules by 7.2W/m2,
whereas radiative uxes due to water molecules and
water microdroplets decrease by 3.0W/m2 and 2.9W/m2
correspondingly, and the change of the total radiative ux
is 1.3W/m2. In addition, the contribution of 30% to the
change of the radiative ux due to CO2 molecules is creat-
ed by vibration transitions at wave lengths near 9.4µm and
10.6µm which are used in CO2 lasers. The contribution of
this frequency range to the total radiative ux due to car-
bon dioxide molecules is about 2%.
In addition to Table 2, we give in Figure1 the average
c
J
which is created by CO2 molecules at
frequencies below indicated ones and the corresponding
total flux
t
J
. These fluxes are defined according to for-
mulas
2
00
( ), ,
ct
J J CO d J Jd
ωω
ωω
= ∆ ∆= ∆
∫∫
(10)
where
2
()J CO
and
J
are dened in formula .
Figure 1. Change of the radiative uxes as a result of
doubling of the concentration of CO2 molecules up to an
indicated frequency due to emission of CO2 molecules
( )
c
J
and the change of the total radiative ux
( )
t
J
Figure 1 includes the frequency ranges which are
responsible for formation the ux changes under consid-
eration. The change of the radiative ux due to CO2 mole-
cules
c
J
is formed mostly (approximately 80%) inside
the absorption band of the CO2 molecule (mostly near
the boundary of this absorption band) that ranges from
580 cm-1 up to 760cm-1. The frequency range near the left
boundary of the absorption band of the CO2 molecule
does not give the contribution to the change of the total
radiative ux toward the Earth
t
J
because of a strong
absorption by water molecules at such frequencies. Hence,
an increase of the radiative flux due to carbon dioxide
molecules is compensated by the decrease of the radiative
ux due to water molecules at these frequencies.
One can transform the change of the total radiative ux
as a result of doubling of carbon dioxide concentration
2
1.3 W/mJ∆=
into the change of the global tempera-
ture
T
in the standard method through the climate sen-
sitivity [24] . As a result, one can obtain
(0.6 0.3) K (11)
T∆= ±
(11)
A large error results from a high sensitivity of this
change to variation of parameters. In addition, there is an
uncertainty in determination of shift of the cloud tempera-
ture as a result of an increase of the global temperature.
4. Discussions
We now analyze the above results. In spite of a low accu-
racy, the change of the global temperature due to doubling
of the atmospheric concentration of CO2 molecules (11)
differs dramatically from that obtained on the basis of cli-
matological computer codes [25]
(3.0 1.5) K (12)T∆= ±
(12)
We show the reason of this description. Climatological
codes are based on studies before a middle of 20 century
[3,26-28] when information about radiative parameters was
restricted. Then interaction between spectra of carbon di-
oxide molecules and other greenhouse components (water
molecules and clouds) was ignored. As a result, the change
of the radiative ux due to carbon dioxide molecules was
equated with the change of the total radiative ux from the
atmosphere. In reality, an increase of the carbon dioxide
concentration, which leads to an increasing radiative ux
due to CO2 molecules, causes simultaneously a decreasing
radiative ux owing to water molecules and water micro-
droplets of clouds. Under the contemporary atmosphere
content, the ratio of changes for the ux due to carbons
DOI: https://doi.org/10.30564/jasr.v2i4.1838
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Journal of Atmospheric Science Research | Volume 02 | Issue 04 | October 2019
dioxide and the total one is 5-6. Correspondingly, climato-
logical models with such computer codes give the change
of the global temperature which exceeds the real one in 5-6
times.
A certain contribution to the error of the global tem-
perature change (11) follows from model assumptions in
the scheme used. In order to estimate this error, we com-
pare in Table 3 values of change of the global temperature
T
for model approaches which are used by the author
in the course of construction of the above algorithm. The
rst model [29,30] where it is used the average absorption co-
efcient of water molecules and water microdroplets over
the total spectrum, and the average absorption coefcient
of carbon dioxide molecules over oscillations, the second
model [31,32] takes the same water parameters and the accu-
rate absorption coefcient is used. In the third model [33,34]
the accurate absorption coefcient of water molecules on
the basis of HITRAN data base is used, and the altitude
distributions for water molecules and water microdroplets
are taken identical. In the above scheme [8] we account for
clouds to be located starting from certain altitudes. The
values of ∆J coincide for these four approaches with the
accuracy of 20%.
Note one more peculiarity of Table 3. For first three
models we restrict by the frequency range below 800 cm-1
only, because this range gives the main contribution to the
total radiative ux due to CO2 molecules. But we convince
subsequently that the range of laser spectral lines above
900cm-1 gives the contribution of 30 % to the change of
the radiative ux due to CO2 molecules. Therefore we use
in Table 3 the factor 1.3 for results of rst three models.
Table 3. Change of the global temperature at doubling of
the carbon dioxide concentration
Model
T
, o
C References
1
2
3
4
0.5
0.4
0.5
0.6
[29, 30]
[31,32]
[33, 34]
[7]
The physical picture of evolution of the global tempera-
ture may be added by NASA monitoring of atmospheric
parameters. Careful measurements of the concentration
of atmospheric CO2 molecules in Mauna Loa observatory
(NASA) in Hawaii [35,36] show the variation of this value
from 316ppm up to 411ppm starting from 1959 up to now
[37,38]. Because this observatory is located far from sources
and absorbers of carbon dioxide, and a time of residence
of a CO2 molecule in the atmosphere is (4-5) years, these
measurements may be considered as the global variation
of the concentration of atmospheric carbon dioxide.
One more parameter of the atmosphere, that characteriz-
es its state as a whole, is the global temperature that is the
temperature of the Earth surface which is averaged both
over time and globe. The problem is that fluctuations of
global temperature at each point of the Earth as a result of
such averaging over time are measured in degrees. How-
ever, it is possible to reduce the uctuations in the case of
comparison of the temperature differences at the same point
and time of day and season, but in different years, and with
subsequent averaging. This concept [39] allows one to reduce
the temperature uctuations up to (0.1-0.2) K.
The change of the global temperature from 1985 up
to now, where the correlation is observed between the
change of the global temperature
T
and the change of
the concentration of atmospheric carbon dioxide, we have
[40-42]
(0.6 0.1) K (13)T∆= ±
(13)
In spite the temperature evolution for oceans and land,
as well as for the Northern and Southern Hemispheres,
are different [43], one can take (13) as the global tempera-
ture change for last 35 years. This leads the change of the
global temperature as a result of doubling of carbon diox-
ide concentration in the real atmosphere [44]
(2.5 0.3) K (14)T
∆= ±
(14)
Comparing this with formula, one can find that the
contribution to the change of the global temperature due
to accumulation of carbon dioxide in the contemporary
atmosphere is approximately 25%.
We also summarize the results of evaluations under
consideration. We represent the algorithm of calculation
of the radiative flux from a weakly nonuniform gaseous
layer toward its surface. This algorithm is used for calcu-
lation the radiative ux from the atmosphere to the Earth’s
surface for the model of standard atmosphere. We use a
local thermodynamic equilibrium for atmospheric air and
its molecular admixtures, as well as clouds which provide
a high optical thickness of the atmosphere and are located
at a certain altitude. In addition, we assume radiation to be
noncoherent, so that the radiative ux at a given frequen-
cy is a sum of uxes from individual radiators. As a result,
the total radiative ux at a given frequency is expressed
through the radiative temperature of molecular radiators,
the opaque factor for molecules and the effective altitude
of emitting clouds or the radiative temperature of water
microdroplets which constitute clouds. The cloud tem-
perature follows from the requirement that the total radia-
tive ux toward the Earth summarized over frequencies is
DOI: https://doi.org/10.30564/jasr.v2i4.1838
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Journal of Atmospheric Science Research | Volume 02 | Issue 04 | October 2019
equal to that from the Earth’s energetic balance.
In calculation the molecular radiative parameters, we
combine molecular spectroscopy with information fol-
lowed from HITRAN data base. This algorithm allows us
to determine the partial radiative flux at each frequency
and the contribution of each greenhouse component. The
contribution to the total radiative flux for the real (stan-
dard) atmosphere is 51% due to water molecules, 29% due
to water microdroplets (clouds), 18% due to CO2 mole-
cules, and 2% due to CH4 and N2O molecules. In addition,
98% of the ux of infrared radiation at wavelengths below
12.5 µm is created by H2O and CO2 molecules, whereas
85% of the radiative ux at wavelengths above 12.5 µm is
due to clouds.
If the concentration of atmospheric CO2 molecules is
doubled without a change the other atmospheric param-
eters, the change of the radiative ux to the Earth due to
CO2 molecules is 7.2 W/m2, whereas the change of the
total radiative flux with accounting for screening fluxes
from other components is 1.3 W/m2 that corresponds to
the global temperature change of 0.6 ± 0.3 K. Usually
climatological models do not account for the interaction
between greenhouse that leads components to a six times
larger temperature change. One can compare the latter val-
ue with results of NASA programs for the analysis of evo-
lution of the carbon dioxide concentration and the global
temperature. From this it follows that doubling of the con-
centration of atmospheric CO2 molecules is accompanied
by the change of the global temperature according to (14).
Thus, in the real atmosphere only a forth part of the global
temperature change occurs due to variation of the con-
centration of CO2 molecules results from the greenhouse
effect involving these molecules.
5. Conclusion
In this paper we apply the algorithm [7] for evaluation of
atmospheric radiative uxes toward the Earth to the prob-
lem of the change of the global temperature as a result
of doubling of carbon dioxide concentration in the atmo-
sphere. This algorithm includes the combination of ther-
modynamics and molecular spectroscopy of atmospheric
air with usage the contemporary data for radiative IR tran-
sitions in molecules from HITRAN data base within the
framework of the line-by-line model, as well as the ener-
getic balance of the Earth and its atmosphere for radiative
fluxes of clouds. Though we apply this algorithm to the
global temperature on the basis of the model of standard
atmosphere, it may be applied to the analysis of radiative
uxes from a local atmosphere if altitude proles of the
atmospheric temperature and number densities of green-
house components are known. In this paper we take this
algorithm for evaluation of the global temperature due to
doubling of the carbon dioxide amount in the atmosphere.
The main conclusion of the above analysis is the impor-
tance of interaction between greenhouse components (H2O
and CO2 molecules, water microdroplets of clouds), since
elementary radiators of the atmosphere are simultaneously
absorbers. Hence, an increase of the amount of one green-
house component which leads to growth of the radiative
flux due to this component, causes simultaneously the
screening for radiation of other components, i.e., the radi-
ative ux owing to other components decreases. This fact
was not taken into account in rst studies of this problem
[3,26-28] because of restricted information about radiative tran-
sitions in molecules, though it was discussed [27,28].
In particular, the analysis on the basis of information
of fties [27,28] gave that overlapping of spectra of H2O and
CO2 molecules leads to a decrease of the global tempera-
ture by 20%. The above evaluations on the basis of infor-
mation from HITRAN data base show that this change is
in 5-6 times. Unfortunately, some climatological codes do
not account for this fact and suggest strongly heightened
values of the change of the global temperature due to an
increasing amount of carbon dioxide in the atmosphere.
Just these values are used in the Paris agreement of 2015
on climate [45]. We above determine the above change of
the global temperature according to which the greenhouse
effect due to CO2 molecules is approximately 25% of the
total change of the global temperature under contempo-
rary atmospheric conditions. As it follows from this, the
basis of the Paris climatic agreements [45] is wrong.
It would note indicate the danger of a wide propaganda
about the role of carbon dioxide in the future climate. In
particular, the propaganda of European media in interest
of some financial groups convinces European habitants
that the most danger in futures follows from injection of
carbon dioxide in the atmosphere as a result of combus-
tion of fossil fuels. Indeed, a contemporary increase of
the carbon dioxide amount in the atmosphere is a result
of human activity which changes the carbon equilibrium
between the atmosphere, land and oceans. The careful
investigations are required, as the above NASA programs
for atmospheric carbon dioxide and global temperature,
which allow one to understand a real state of affairs in or-
der to conserve our planet for the man.
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DOI: https://doi.org/10.30564/jasr.v2i4.1838
... Therefore, the change in the radiative flux ∆ c due to CO 2 molecules is taken in climatological models instead of the change in the total radiative flux ∆, and the error in the change of the global temperature under these conditions is exceeded by five times. This results from neglecting the absorption of emitted radiative fluxes by water molecules and water microdroplets of clouds by added CO 2 molecules [51,52]). This large difference follows also from a general conclusion for a plane gaseous layer with a low temperature gradient [51,52]). ...
... This results from neglecting the absorption of emitted radiative fluxes by water molecules and water microdroplets of clouds by added CO 2 molecules [51,52]). This large difference follows also from a general conclusion for a plane gaseous layer with a low temperature gradient [51,52]). Indeed, if we have a layer of a constant temperature and of a high optical thickness, where the emission is created by several components, this layer emits as a blackbody with the gaseous temperature. ...
... In this evaluation as well as previous evaluations, we have a contradiction with the results of climatological models in the analysis of the Earth's greenhouse effect, according to which the increase in the global temperature differs by five times. We show [51,52], so the large difference results from ignoring, in climatological models, the Kirchhoff law [50], according to which radiators are simultaneously the absorbers. In this case, we take the change in the radiative flux created by CO 2 molecules as the change of the total radiative flux. ...
Article
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The “line-by-line” method is used for the evaluation of thermal emission of the standard atmosphere toward the Earth. Accounting for thermodynamic equilibrium of the radiation field with air molecules and considering the atmosphere as a weakly nonuniform layer, we reduce the emission at a given frequency for this layer containing molecules of various types to that of a uniform layer, which is characterized by a certain radiative temperature Tω, an optical thickness uω and an opaque factor g(uω). Radiative parameters of molecules are taken from the HITRAN database, and an altitude of cloud location is taken from the energetic balance of the Earth. Within the framework of this model, we calculate the parameters of the greenhouse effect, including the partial radiative fluxes due to different greenhouse components in the frequency range up to 2600 cm−1. In addition, the derivations are determined from the radiative flux from the atmosphere to the Earth over the concentration logarithm of greenhouse components. From this, it follows that the observed rate of growth of the amount of atmospheric carbon dioxide accounts for a contribution of approximately 30% to the observed increase in the global atmosphere during recent decades. If we assume that the basic part of the greenhouse effect is determined by an increase in the concentration c(H2O) of water atmospheric molecules, it is approximately dlnc(H2O/dt)=0.003 yr−1. This corresponds to an increase in the average moisture of the atmosphere of 0.2%/yr.
Chapter
Change of the radiative flux from the atmosphere to the Earth’s surface as a result of a change of the atmosphere composition is evaluated within the framework of the above model for standard atmosphere which uses the line-by-line method and parameters for radiative transitions of atmospheric molecules from the HITRAN data bank. Interaction between optically active molecules of the atmosphere through the radiation field is governed by the Kirchhoff law according to which atmospheric radiators are simultaneously absorbers. As a result, the change $$\Delta$$ in the radiative flux from the atmosphere to the Earth due to change in the concentration of molecules of a certain types differs from the change $$\Delta ^\prime$$ of the radiative flux created by molecules of this type. The ratio $$\Delta ^\prime /\Delta$$ of the above radiative fluxes is equal, three for water molecules, five for CO$$_2$$ molecules, two for CH$$_4$$ molecules, 1.5 for N$$_2$$O molecules and one for O$$_3$$ molecules. The simplification in universal climatological models, where the interaction between optically active components is neglected, the Kirchhoff law is ignored, i.e., the values $$\Delta$$ and $$\Delta ^\prime$$ assume to be identical in these models. Applying the above analysis to the real atmosphere, we find the change of the global temperature is $$(0.6 \pm 0.3)$$ as a result of doubling of the concentration of CO$$_2$$ molecules. On the basis of this analysis and observed evolution of the real atmosphere, one can obtain that an observed change in the concentration of CO$$_2$$ molecules leads to the change in the global temperature that is one third of the observed change. Assuming the other part of the global temperature change results from the change of the concentration c(H$$_2$$O) of water molecules, one can obtain for the rate of its change $$d \ln c(\text {H}_2\text {O})/\text {d}t =0.003\,\text {year}^{-1}$$. This corresponds to the rate of the change of the atmosphere moisture $$\eta$$ as $$d\ln \eta /\text {d}t=0.002$$, and this change conserves the stability of the real atmosphere more 100 year.
Chapter
The “line-by-line” method is used for evaluation of thermal emission of the standard atmosphere toward the Earth. Accounting for thermodynamic equilibrium of the radiation field with air molecules and considering the atmosphere as a weakly nonuniform layer, we reduce emission at a given frequency for this layer that contained molecules of various types to that of a uniform layer which is characterized by a certain radiative temperature $$T_\omega$$, an optical thickness $$u_\omega$$ and an opaque factor $$g(u_\omega )$$. Radiative parameters of molecules are taken from the HITRAN database, and an altitude of cloud location is taken from the requirement of coincidence of the total radiative flux from such evaluation with that followed from the energetic balance of the Earth. As a result of this evaluation for the contemporary atmosphere, we find that the radiative flux due to H$$_2$$O molecules equals $$165\,\mathrm{W}/\mathrm{m}^2$$, the flux of $$94\,\mathrm{W}/\mathrm{m}^2$$ is created by clouds, the radiative flux due to CO$$_2$$ molecules is $$61\,\mathrm{W}/\mathrm{m}^2$$, CH$$_4$$ molecules create a flux of $$4\,\mathrm{W}/\mathrm{m}^2$$, and the flux $$4\,\mathrm{W}/\mathrm{m}^2$$ is due to N$$_2$$O molecules. In addition, approximately 95% of the radiative flux at frequencies below $$800\,\mathrm{cm}^{-1}$$ is created by H$$_2$$O and CO$$_2$$ molecules, while $$84\%$$ of this flux at frequencies above $$800\,\mathrm{cm}^{-1}$$ is due to water microdroplets of clouds. It is shown that an increase of the concentration of one component which leads to an increasing radiative flux due to this component causes simultaneously to decreasing radiative flux due to other components because of overlapping of their spectra that corresponds to the Kirchhoff law. In particular, doubling of the concentration of atmospheric carbon dioxide gives an increase of the radiative flux due to this component by $$7.2\,\mathrm{W}/\mathrm{m}^2$$, whereas radiative fluxes due to water molecules and water microdroplets decrease by $$3.0\,\mathrm{W}/\mathrm{m}^2$$ and $$2.9\,\mathrm{W}/\mathrm{m}^2$$ correspondingly, i.e. the change of the total radiative flux is $$1.3\,\mathrm{W}/\mathrm{m}^2$$. This fact is not taken into account in some climatological models. Interaction of infrared radiation with water microdroplet and its pass through clouds is analyzed on the basis of the Mie model according to which a droplet is characterized by a sharp boundary. It is shown that stratus clouds, rather than cumulus ones, partake mostly in greenhouse phenomena of the Earth’s atmosphere.
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