Abstract - An analysis is undertaken to reveal the role that various processes in living and nonliving natureplay in the establishment of the chemical composition of the atmosphere and the temperature balance of theEarth. An inference is made that the biospheric mechanisms of CO2 removal from the atmosphere are insuf-ficient in the situation of the current anthropogenic impact and the existence of potentially dangerous CO2
sources in nonliving nature, which may be activated with the increase in the Earth’s average temperature. Itis shown that the sustainability of natural systems responsible for the maintenance of the chemical composi-tion of the atmosphere is itself impaired as the human activity destroys climate-forming biocenoses. Thiscan lead to an irreversible change in the Earth’s climate, with the result that the Earth’s average temperaturewould rise to 100–150°C and above. This will render life on the Earth (at least in its present form) impossi-ble. A radiative–adiabatic model of the greenhouse effect is constructed and used to make asymptotic esti-mates of the increase in the Earth’s average temperature with varying concentration of greenhouse gasesover a wide range. On the basis of this model, an integral model of the change in the Earth’s climate is con-structed, which takes into account the thermal inertia of the ocean and the aerosol pollution of the upper at-mosphere. It is demonstrated that an irreversible (catastrophic) change in the Earth’s climate (the green-house catastrophe) can take place in relatively near future - in 200–300 years.
Biophysics, Vol. 46, No. 6, 2001, pp. 1078-1088. Translated from Biofizika, Vol. 46, No. 6, 2001, pp. 1138-1149.
Institute of Cell Biophysics, Russian Academy of Sciences, Pushino, Moscow Region, 142290 Russia;
BIOPHYSICS Vol. 46 No. 6 2001
ROLE OF VARIOUS PROCESSESIN THE FORMATION OF THE CHEMICAL
COMPOSITION OF THE ATMOSPHEREAND THE TEMPERATURE BALANCE
OF THE EARTH
Carbon cycle. Insufficiency of the biologicalmechanisms îf CO2 removal. Figure 1 shows theamount of carbon (per cm2 of the Earth’s surface) invarious spheres of the Earth and the rate of its transferbetween the main regions of its occurrence in terms ofg = 10–6 g per cm2 per year [1].
Note a dramatic (several orders of magnitude)insufficiency of the biological mechanisms of CO2 re-moval from the atmosphere as compared to itsanthropogenic emissions. Although the total photo-synthetic production of organic substances is 8530g(in terms of carbon) and is much larger than the
anthropogenic CO2 emissions of 350 g, most of or-ganic carbon returns to the atmosphere in the form ofCO2 through respiration, decay, fires, etc. The differ-ence between the rate of biogenic CO2 fixation(through photosynthesis and the formation of carbon-ates) and the rate of release of CO2 fixed by photosyn-thesis (through respiration, fires, etc.) is small and isonly 8.8g, which is about 50 times lower than the rateof anthropogenic CO2 emissions to the atmosphere.Unfortunately, many works (especially popular sci-ence publications) compare the total photosyntheticproduction of organic substances and the anthropo-genic CO2 emissions, which creates the illusion of atrivial reversibility of the current changes in theEarth’s atmosphere.
The role of various biocenoses in the long-termCO2 removal from the atmosphere was analyzed.
BIOSPHERE AND EARTH’S CLIMATE: GREENHOUSE CATASTROPHE 1079
Fig. 1. Carbon cycle (g = 10–6 g per cm2 per year).
Atmosphere 0.125 g/cm2
Photosynthesis
8530 g7.7 g
Fires310 g
Respiration8220 g
Plants0.125 g/cm2
7.5 gBurning350 g
Crystalline schists2000 g/cm2
Carbonates2500 g/cm2
Basalts33 g/cm2
Coal and oil663 g/cm2
Animals0.015 g/cm2 Ocean
7.5 g/cm2
7.5 g
1.3 gJuvenile CO2
0.1 gMetamorphism
7.6 g
Contrary to the popular opinion that “the forest is the
lungs of the planet”, the role of forest biocenoses in
the long-term CO2 fixation proved to be extremely
small, because virtually all of the carbon fixed by
photosynthesis returns to the atmosphere in the form
of CO2 through respiration, decay of dying leaves andwood, and also forest fires.
The long-term CO2 removal from the atmo-sphere requires that much of the carbon fixed by pho-tosynthesis be inaccessible for oxidation. Such
BIOPHYSICS Vol. 46 No. 6 2001
1080 KARNAUKHOV
Fig. 2. Cause-and-effect diagram of the basic climate-forming processes.
Shift of temperature zones in Earth's lithosphere
Decrease in CO solubility2
in ocean water Increase in ocean water temperature
Decomposition of ocean sediments of methane hydrates
Deglaciation
Rearrangement of North Atlantic currents, onset of new Ice Age
Decrease in Earth`s albedo
Increase in Earth`s average temperature
Anthropogenic CO emissions2 Increase
in atmosphere CO2
concentration
Increase in atmospheric water vapor concentration
Anthropogenic aerosol emissions to upper atmosphere
Increasein climate humidity
Increase in bog area
Increase in productivity of bog biocenoses, acceleration of CO fixations through2
peat formations
Increase in tropical sea area
Increase in productivity of tropical sea biocenoses, acceleration of CO fixation2
through limestone formation
Bog drainingSea pollution by pesticides,
herbicides, and industrial waste; disturbance of bio- logical balance by fishing and seafood catching
Wars, nuclear tests, civil and military jet aviation
Burning of coal, oil, gas, and other mineral fuels (power, transport, heating, production)
NO
OS
PH
ER
E
LIV
ING
NA
TU
RE
BIO
SP
HE
RE
AT
MO
SP
HE
RE
HY
DR
OS
PH
ER
E
NO
NL
IVIN
G N
AT
UR
E
LIT
HO
SP
HE
RE Acceleration of decomposition
of carbonates CaCO =CaO+CO3 2
conditions take place only in bog biocenoses and trop-ical sea biocenoses (Fig. 2).
In bog biocenoses, dying plants fall into stand-ing water with an extremely low dissolved oxygencontent and are accumulated there with virtually nodecay (the partial anaerobic decay to form methanedoes not change the overall pattern). Partially decayedplant debris accumulated in bogs produce peat seams,from which lignite and coal deposits form.
Over the last 100 years, the total bog area on theEarth has been almost halved and continues to de-crease because of bog draining. Correspondingly, therate of CO2 removal from the atmosphere lowers.Note that bog draining is often accompanied by ex-tinction of endemic species adapted to live only underdefinite conditions of certain bogs located in a spe-cific climatic zone. Therefore, the restoration of thebog area is now associated not only with the difficultyof removing lands from agricultural use but also, insome cases, with the impossibility of restoring whole-some biocenoses.
In tropical sea biocenoses, the CO2 removalfrom ocean water, to which CO2 passes from the at-mosphere, occurs somewhat differently. Carbon diox-ide is used as a structural material by heterotrophicorganisms in the formation of calcareous shells andcoverings. Virtually all carbonates in the Earth’s crust(limestones, dolomites, marble, chalk, etc.) are ofbiogenic origin. Among the most important cli-mate-forming species are coral polyps and foramini-feral plankton (a total of about 80 species).
Unfortunately, the state of climate-forming trop-ical sea biocenoses has been studied poorly. There isfragmentary information on the death of coral reefs[2]. No systematic monitoring of the state of forami-niferal microplankton is performed, although one canassume that it is foraminiferal plankton that must beone of the components of the tropical sea biocenosisthat are most sensitive to ocean dumping of pesticidesand herbicides.
Since it seems unlikely that the rate of CO2 re-moval from the atmosphere by the biological mecha-nisms can increase more than 50-fold (to compensatefor the anthropogenic CO2 emissions), processes innonliving nature that affect the carbon dioxide con-centration were analyzed to find mechanisms thatmaintain the stability of the chemical composition of
the atmosphere and, consequently, the sustainabilityof the Earth’s climatic system as a whole.
Greenhouse catastrophe. Role of natural (non-anthropogenic) CO2 sources. Figure 2 presents acause-and-effect diagram of the basic climate-formingprocesses. The arrows indicate the cause-and-effectrelationships between processes: the solid arrowsshow the direct (stimulatory) effect and the dotted ar-rows represent the reverse (inhibitory) effect. Thecrisscrossed arrows indicate the cause-and-effect rela-tionships that existed in the past but were broken (orweakened) by the anthropogenic impact (dashed ar-rows).
The analysis of processes in nonliving nature re-vealed no mechanisms of maintaining the stability ofthe chemical composition of the atmosphere (first ofall, with respect to the CO2 concentration). The foundnegative feedbacks between the CO2 concentrationand the Earth’s average temperature were either sim-ple damping (as, e.g., the thermal inertia of the oceanor the dissolution of an additional amount of CO2 inocean water with increasing CO2 concentration in theatmosphere) or relatively weak feedbacks (the temper-ature–humidity–albedo feedback). An unusual nega-tive feedback related to the rearrangement of NorthAtlantic currents can even lead to a temporary de-crease in the average temperature in Northern Europeand America (a peculiar kind of another Little IceAge) [3–5], but none of the revealed feedbacks is suit-able to be the global stabilizing factor.
But then it proved that there are a lot of pro-cesses in nature that implement a positive feedbackbetween the CO2 concentration and the Earth’s aver-age temperature. In essence, these processes are relatedto natural (nonanthropogenic) sources of CO2 emis-sions to the atmosphere, which are activated with theincrease in the Earth’s average temperature (Fig. 2).Of prime importance among such sources are the fol-lowing:
(1) An increase in the ocean water temperatureupon the change in the Earth’s average temperaturewill cause a decrease in the CO2 solubility in oceanwater. The excess of carbon dioxide will enter the at-mosphere. Since the amount of CO2 in ocean water isat least 60 times higher than that in the current atmo-sphere, this CO2 source is a great potential danger.
(2) Still larger amount of fixed CO2 is containedin the Earth’s crust (approximately 50 000 times
BIOPHYSICS Vol. 46 No. 6 2001
BIOSPHERE AND EARTH’S CLIMATE: GREENHOUSE CATASTROPHE 1081
larger than in the Earth’s atmosphere and about thesame as in the Venus’ atmosphere) in the form of car-bonate-containing rocks (limestones, dolomites, mar-ble, chalk, etc.). The decomposition of carbonatesboth due to a shift of temperature zones in the Earth’slithosphere upon the increase in the Earth’s averagetemperature and due to the human impact on theEarth’s crust (underground nuclear tests, drilling, etc.)can cause the release of enormous amounts of CO2 tothe atmosphere.
(3) Other potentially dangerous natural CO2
sources are ocean sediments of methane hydrates.Methane hydrates are stable only at high pressuresand low temperatures. An increase in the ocean bot-tom water temperature can lead to the decompositionof methane hydrates and the release of large amountsof methane and CO2 to the atmosphere (through themethane oxidation by methane-oxidizing bacteria andthe direct methane oxidation in the upper atmo-sphere). The amount of carbon in ocean sediments ofmethane hydrates is estimated at no smaller than10 000 Gt, which is more than ten times larger thanthe amount of carbon in the atmosphere.
(4) There is a very strong positive feedback be-tween an increase in the atmospheric water vapor con-centration and an increase in the Earth’s average tem-perature. Since water vapor is a greenhouse gas, anincrease in the water vapor concentration causes a fur-ther increase in the Earth’s average temperature.
As already noted, a common property of theabove potential natural CO2 sources is the strong posi-tive feedback between the CO2 concentration and theEarth’s average temperature, which can lead to an av-alanche-like increase in the CO2 concentration in theatmosphere even in a case of total abandonment of theuse of carbon-containing mineral fuels (coal, oil, gas).In circumstances of destruction of natural biosystemsinvolved in the CO2 removal from the atmosphere,this can cause an irreversible change in the chemicalcomposition of the atmosphere and, consequently, inthe Earth’s climate. The scenario of such irreversibleclimatic changes caused by the increase in the CO2
concentration was called the greenhouse catastrophe[6–10].
In crude summary, one can infer that, at present,there are no efficient mechanisms to limit the increasein the CO2 concentration in the atmosphere. The rela-tive stability of the climatic parameters is now duemainly to the inertia of the Earth’s climatic system,
specifically, due to the thermal inertia of the oceanand the existence of capacious reservoirs for green-house gases (the atmosphere, the ocean, and the bio-sphere).
In this context, it was of particular interest to es-timate the possible changes in the basic climatic pa-rameters and, first of all, the Earth’s average tem-perature.
RADIATIVE–ADIABATIC MODELOF THE GREENHOUSE EFFECT
Basing on the above, one can suppose that theincrease in the CO2 concentration in the atmospherewill continue in both near and distant future. This willnecessarily lead to an increase in the Earth’s averagetemperature.
Although the first reports on the possible role ofgreenhouse gases in the formation of the temperaturebalance of the Earth and other planets came out as farback as almost 150 years ago [11], the estimates ofthe dependence of the greenhouse effect on a changein the CO2 concentration still differ almost tenfold(!!!): the increment DT as the CO2 concentration inthe atmosphere is doubled is reported to be fromDT £ 1°C [12] to DT ³ 5°C (according to the Intergov-ernmental Panel on Climate Change (IPCC)). Thisdifference is largely because of the necessity of mak-ing additional assumptions in conventional radia-tive–convective models [13].
The drawback of early radiative models andlater radiative–convective models [13, 14] is the ne-cessity of detailed calculations of the radiative andconvective flows both in the atmosphere and in the at-mosphere–land–ocean system. Computational diffi-culties in solving the strongly nonlinear three-dimens-ional problem are due not only to the limited memoryand speed of present-day computers but also to theexistence of fundamental (nonalgorithmic) instabili-ties in the system under investigation. Simplificationof the problem, which is inevitable for such systems,leads to uncontrolled loss of accuracy of the finalresults.
The purpose of this study was to construct ananalytical model of the greenhouse effect that wouldgive reliable estimates within an accuracy of at least50% over wide ranges of the concentration of green-house gases and the Earth’s average temperature. This
BIOPHYSICS Vol. 46 No. 6 2001
1082 KARNAUKHOV
model was called the radiative–adiabatic model of thegreenhouse effect.
The main difference of this model from conven-tional radiative–convective models of the greenhouseeffect is that the role of convective phenomena is re-stricted to the formation of the so-called adiabatictemperature gradient T(z) in the lower, radiative atmo-sphere (the troposphere):
T z T z( ) = -0 Ag , (1)
where T0 is temperature on the surface of a planet(e.g., the Earth) and z is the altitude above the planet’ssurface.
This assumption can be considered justified,since the adiabatic temperature gradient, which is dueto vertical movements of air masses, depends weaklyon specific dynamic parameters of such movementsand, over a wide range of these parameters, is deter-mined by the physicochemical composition of the at-mosphere and the acceleration of gravity near theplanet’s surface:
g e e eA = = × » ×-g
C/ /
p
( . ) deg deg9 8 10 103 m km. (2)
Here, g is the acceleration of gravity (for theEarth, g = 9.8 m/s2), Cp is the specific heat at constantpressure of the gas phase of the atmosphere (for theEarth, Cp = 1.005×103 J/(kg deg)), and e is a coeffi-cient determined by the air humidity and the contentof water aerosols in the air. For dry air, e = 1. In thegeneral case, e is always smaller than 1 (tropical deserts)and, as a rule, larger than 0.6 (the equatorial belt). Theadiabatic gradient exists on all the planets of the solarsystem that have atmosphere and is sufficiently accu-rately described by expressions (1) and (2).
If the distribution of gases in the planet’s atmo-sphere is known and is ri(z) and if the spectral proper-ties of each of the greenhouse gases are also known(ai(n) are the spectral absorptivities (emissivities)),then one can readily write the expression for thepower spectrum of the thermal (long-wavelength) ra-diation of an atmospheric element located at a certainaltitude z into the surrounding space:
W z W n z A n zrad rad abs( , )~
( , ) ( , )n = . (3)
Here,
~( , ) ( ) ( )
exp( )
W n z a zh
ch
kT z
i
i
irad =
æ
èç
ö
ø÷å n r
p n
n
2 3
(4)
is the power spectrum of the “primary” radiation ofthe atmospheric element located at the altitude z and
A n z a di
i
i
z
abs ( , ) exp ( ) ( )= -ìíî
üýþ
å ò¥
h n r x x (5)
is the absorptivity of the overlying atmospheric lay-ers. The coefficient ai(n) characterizes both emissivityand absorptivity of the ith greenhouse gas (accordingto Kirchhoff’s radiation law), and h is a coefficient,which depends on the dimensionality of the model (ina three-dimensional spherically symmetrical (quasi-one-dimensional) case, one must additionally performintegration with respect to solid angle over the upperhemisphere). The function ri(z) describes the changein the density of the ith greenhouse gas with altitude.Under the assumption that the atmosphere is isother-mal, the density of most greenhouse gases varies withaltitude z according to the barometric formula
r rm
i izm g
kTz( ) exp= -
ìíî
üýþ
0 air H
eff
, (6)
where mair @ 29 is the average molecular weight of air,mH = 1.67×10–27 kg is the atomic weight of hydrogen,k is the Boltzmann constant, ri
0 is the density of theith greenhouse gas at sea level (on the planet’s sur-face), and Teff is the so-called effective atmospherictemperature.
There are a number of greenhouse gases towhich the barometric formula (6) is fundamentally in-applicable. The concentration of some of these gases,e.g., ozone, depends on chemical reactions in the at-mosphere and varies with altitude in a complex way.The concentration of the others, among which is suchan important greenhouse gas as water vapor, is deter-mined by condensation and evaporation. The varia-tion of the water vapor concentration in the atmo-sphere is mainly governed by the ambient air temper-ature, which, in turn (according to the radiative–adia-batic model), linearly depends on the altitude z:
r r r gH O H O H O0 A
2 2 2( ) ( ( )) ( )z T z T z= = - . (7)
According to available estimates [4], the largest(95%) contribution to the thermal radiation of the Earthis made by the atmosphere, where the main role isplayed by two greenhouse gases, carbon dioxide CO2
and water vapor H2O. Therefore, virtually without lossof generality, basing on expressions (1)–(7), one canwrite the expression for the total power of the thermalradiation of the Earth into the surrounding space:
BIOPHYSICS Vol. 46 No. 6 2001
BIOSPHERE AND EARTH’S CLIMATE: GREENHOUSE CATASTROPHE 1083
W T dzd W T n zrad0CO
0rad
0CO
02 2( , ) ( , , , )r n r= =òò
= -òò dzdnh
ch
kT z
am g
kT
2 32
p n h
nn r
m
exp( )
( ) expCO0CO air H
e
2
ff
H O H O0 A
2 2z a T zæ
èç
ö
ø÷ + -
æ
èç
ö
ø÷ ´( ) ( )n r g (8)
´ - -æ
èç
öexp ( ) expa
kT
m g
m g
kTzCO
0CO eff
air H
air H
eff
2 2n rm
m
ø÷ - -
æ
èçç
ö
ø÷÷
¥
òa d Tz
H O H O0 A
2 2( ) ( )n xr g x .
The condition for the radiation balance in ther-modynamic equilibrium requires that the power of theradiation incident on the planet be equal to the powerof the radiation emitted by the planet:
WS
W Tinc rad0CO
02=
-= =
( )( , )
1
4
ar const, (9)
where the solar constant S and the albedo a of the
planet are assumed constant.
Thus, the condition that the power of the thermalradiation emitted by the planet into the surroundingspace is constant gives a formal analytical solution ofthe problem on the relationship between small incre-ments in the CO2 concentration and the Earth’s aver-age temperature:
dWW T
dW T
radrad rad
=¶
¶+
¶
¶
( , ) ( , )r
rr
r0CO
0
0CO 0
CO 0CO
02
2
2
2
TdT
00 º
º Þ = -¶
¶
¶
¶
é
ëê0 0dT
W T W T
T0
0CO
0
0CO
CO0
0
2
2
2rad rad( , ) ( , )r
r
r ù
ûúdr0
CO2 .
(10)
At first glance, it seems that one has to surmountgreat computational difficulties to obtain the final an-alytical expression for T0(r0
CO2 ). However, there ex-ists a special translation–dilatation group of transfor-mations of the parameters T0 and r0
CO2 under whichthe function Wrad(r0
CO2 , T0) is invariant:
~ ,~
ln( ).
r cr
g c
0CO
0CO
0
2 2=
= +
üýþT T H0 0 A
(11)
Here, gA = eg/Cp » 8 deg/km is the (Earth-)aver-age adiabatic gradient and H0 = kT/(mairmHg) is the al-titude at which the air density decreases by a factor ofe. Therefore, actually, the application of this group al-most immediately yields the analytical expression forthe differential greenhouse effect (furthermore, theexpression is directly obtained in an integral form forarbitrarily large changes Dr0
CO2 in the carbon dioxideconcentration):
DD
T H=+æ
èç
ö
ø÷ »g
r r
r0
0CO
0CO
0CO
2 2
2ln
» ×+æ
èç
ö
ø÷59 K 0
CO0CO
0CO
2 2
2ln
r r
r
D. (12)
This result allows a simple and vivid interpreta-tion, which demonstrates the physical meaning of thetranslation–dilatation symmetry (11) for the powerWrad(r0
CO2 , T0) (8) of the thermal radiation of theplanet. Indeed, one can readily see that transforma-tions (11) are in essence equivalent to the followingchange of variables in expression (8):
¢ = +
¢ = +
üýþ
z z H
H
0
0
ln ,
ln ,
c
x x c(13)
which can be interpreted as a shift of the basic charac-teristics of the atmosphere along the altitude axis bythe quantity
H H0 00CO
0CO
0CO
2 2
2ln lnc
r r
r=
+æ
èç
ö
ø÷
D. (14)
To test the validity of the expressions derived,the radiative–adiabatic model was used to evaluatethe greenhouse effect on the Venus. Such an applica-tion of the model is quite correct, because in con-structing this model, no additional assumptions weremade that would restrict the applicability of thismodel to the Earth’s atmosphere only. Indeed, it isknown that the CO2 density near the Venus’ surface ismore than five orders of magnitude higher than that
BIOPHYSICS Vol. 46 No. 6 2001
1084 KARNAUKHOV
near the Earth’s surface (r0VCO2 /r0E
CO2 ×1.2×105). Fromthis fact, one can easily calculate the altitude H0V atwhich the CO2 density in the Venus’ atmosphereequals the CO2 density in the Earth’s radiative atmo-sphere. Under the assumption that the atmosphere isisothermal, H0V » 75 km. Knowing the adiabatic gra-dient in the Venus’ atmosphere (g V
A = 8.9 deg/km),one can estimate the absolute value of the greenhouseeffect at
DT H0V 0V K= =g VA 670 . (15)
The really observed greenhouse effect on theVenus is DT = 500 K, which is only 25% lower thanthe calculated value. Such an accuracy can be re-garded as a success in view of such large differencesin the CO2 concentrations (105), the albedos, andother physicochemical parameters between the Earthand Venus’ atmospheres.
Moreover, the radiative–adiabatic model allowedone to analyze the error in the main result (12). Thiserror is an inevitable consequence of the simplifica-tions made. One can easily show that the maximal es-timated error in the result for the Earth does not ex-ceed 37% of the differential greenhouse effect:
DD
T » ± ×+æ
èç
ö
ø÷59 22K 0
CO0CO
0CO
2 2
2ln
r r
r. (16)
This error is due to the neglect of the contribu-tion of the Earth’s surface to the total thermal radia-tion of the Earth, the dependence of the Earth’salbedo on the Earth’s average temperature, the differ-ence of the really observed adiabatic gradient in theEarth’s atmosphere from its average, and the contri-butions of “minor” greenhouse gases. One can dem-onstrate that taking into account the nonisothermalcharacter of the Earth’s atmosphere and also the lati-tudinal distributions of the temperature and the hu-midity over a wide range only insignificantly affectsthe final result.
At the same time, the differential greenhouse ef-fect caused by the anthropogenic increase in the CO2
concentration in the Earth’s atmosphere is estimatedby the radiative–adiabatic model at
DT ( % ) ( . )30 15 5 6× = ±CO K2 , (17)
where 30% is the said anthropogenic increasethroughout the industrial stage of the development ofthe human civilization. This estimate not only ex-ceeds estimates made in other works but also is al-most ten times greater than the really observed
increase in the Earth’s average temperature for thelast 300–400 years. However, there is no contradic-tion here at all. The estimates made by the radia-tive–adiabatic model are asymptotic; i.e., they do nottake into account the thermal inertia of the Earth’s cli-matic system, first of all, the thermal inertia of theocean, which decreases the rate of change in theEarth’s average temperature. It will be shown belowthat taking into account the thermal inertia of theocean not only ensures agreement between the theo-retical and observed values of the resultant increase inthe Earth’s average temperature but also gives a de-tailed representation of the real temperature variationin the XX century.
MODEL OF THE CHANGE IN THE EARTH’SCLIMATE WITH REGARD
FOR THE THERMAL INERTIAOF THE OCEAN AND THE AEROSOL
POLLUTION OF THE UPPER ATMOSPHERE
An integral model describing the dynamics ofthe Earth’s average temperature with regard for theresults obtained by the radiative–adiabatic model ofthe greenhouse effect can be written as
dT t
dt
( )=
137
t
r
rin0
0CO
0CO AK
2
2T
tT t T t+ ×
æ
èç
ö
ø÷ - -
é
ëê
ù
ûúln
( )( ) ( )D .
(18)
Here, T(t) is the time variation of the Earth’s av-
erage temperature; tin is the relaxation time of theEarth’s climatic system, which is determined by thetotal thermal inertias of the ocean, glaciers, and land;
T0 and r0CO2 are the initial (preindustrial) values of the
Earth’s average temperature and the CO2 density, re-
spectively; r0CO2 (t) is the time variation of the CO2
density; and DTA(t) is the time variation of the ther-mal forcing due to the aerosol pollution of the upperatmosphere (the stratosphere).
Note that, in expression (18), the temperatureforcing
DT tt
( ( )) ln( )
rr
r0CO 0
CO
0CO
2
2
2K= ×
æ
èç
ö
ø÷37 , (19)
due to the greenhouse effect is estimated using the co-efficient corresponding to the lower limit of the confi-dence interval (16).
BIOPHYSICS Vol. 46 No. 6 2001
BIOSPHERE AND EARTH’S CLIMATE: GREENHOUSE CATASTROPHE 1085
The time variation r0CO2 (t) of the CO2 density
from the beginning of the industrial age to the presentday is well approximated by the exponential functionof time:
r rt0
CO0CO pr
CO
2 2
2
( ) . exptt t
= +-æ
èç
ö
ø÷
æ
èç
ö
ø÷1 0 3 , (20)
where tpr is the year 2000 and tCO2@ 45 years, which
corresponds to the annual increase in the CO2 emis-sions by 2.25%. Possible measures to limit the CO2
emissions to the atmosphere may lead to replacementof the exponential increase in the CO2 concentrationby a linear increase therein. Let us consider three sce-narios of the increase in the CO2 concentration in theEarth’s atmosphere:
(1) the exponential increase in the CO2 concen-tration persists (expression (20)),
(2) the CO2 emissions are stabilized in the year2000 at the 2000 level (the increase in the CO2 con-centration becomes linear), and
(3) the CO2 emissions are stabilized in the year2100 at the 2100 level.
The importance of taking into account the aero-sol pollution of the upper atmosphere (the strato-sphere) for estimating the change in the Earth’s aver-age temperature was noted as early as 1974 byBudyko [15]. Later, interest in this problem has con-siderably grown in connection with investigation ofthe “nuclear winter” phenomenon [16].
Let us describe the anthropogenic aerosol pollu-tion of the upper atmosphere by the following function
DD
T tT
( ) =0 before the year 1939,
before in the yeaA r 1939 and after.
ìíî
(21)
That is, it assumed that the anthropogenic aero-sol pollution of the upper atmosphere does not takeplace before 1939, jumped in 1939, and remains un-changed until now.
This assumption is justified by the fact that car-bon black aerosols (which are most optically active)can arrive at the stratosphere only as a result of theformation of a tropospheric channel¾ a powerful up-ward airflow transferring aerosol particles immedi-ately to the stratosphere (as being condensation nu-clei, aerosols entering the lower troposphere are quiterapidly washed down from the atmosphere by rains).
Before 1939, carbon black and dust particles ar-rived at the stratosphere only due to natural processes,such as volcanic eruptions. After 1939, the situationhas changed. During the World War II, fires in towns,oil storage facilities, etc., created conditions for theformation of tropospheric channels and the arrival ofcarbon black aerosols in the atmosphere. After theend of the World War II, the main source of the aero-sol solution of the stratosphere became atmosphericnuclear tests and, after their prohibition, civil flightsin the tropopause. Indeed, carbon black particles
BIOPHYSICS Vol. 46 No. 6 2001
1086 KARNAUKHOV
Fig. 4. Results of modeling for the period 1600–2050.Total increment in the Earth’s average temperature ascompared with the preindustrial age (1600–1700) ac-cording to the constructed model is 1.3 K, which agreeswell with paleoclimatic data obtained by analysis of themountain glaciation dynamics and some other methods.
Fig. 3. Results of modeling the increase in the Earth’s av-erage temperature in the period 1900–2010. Points repre-sent observed data. Note a good agreement between theobserved data and the modeling results.
1.4
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forming in the fuel combustion in airplane jet enginesdirectly enter the stratosphere.
Thus, the step form of DTA(t) as a function oftime seems to be quite justified. Unfortunately, avail-able information is insufficient to estimate the DTA
value, as well as to directly calculate the relaxationtime tin of the Earth’s climatic system, because thisrequires, in fact, a total reconstruction of the three-dimensional pattern of ocean currents.
Thus, the model involves two free parameters, tin
and DTA, whose values are fitted by collating the mod-eling results with the real temperature trend Tobs(t) inthe instrumental observation period (1900–2000). Byminimizing the root-mean-square deviation betweenthe observed [17] and theoretical temperatures:
( ( ) ( )) mint
i i
i
T t T t=
å - =1900
20002
obs , (22)
one can make numerical estimates of the parametersthat characterize the inertia of the Earth’s climaticsystem (tin » 200 years) and the thermal forcing dueto the aerosol pollution of the upper atmosphere(DTA » 5 K). Note that the relaxation timetin » 200 years is here a “renormalized” value, whichtakes into account that two greenhouse gases, CO2
and H2O, are considered.
The modeling results are presented in Figs. 3–6(in all the figures, along the abscissa is the incrementin the Earth’s average temperature as compared withthe preindustrial age (the year 1600)).
One can readily see that the resultant increase inthe Earth’s average temperature can amount to tensand hundreds of degrees (even if the anthropogenicCO2 emissions are stabilized). Note that Fig. 6 pres-ents an “optimistic” variant of the change in theEarth’s average temperature. Firstly, this is becausethe modeling uses the asymptotic estimate (19) of thegreenhouse effect that corresponds to the lower limitof the confidence interval (16). And secondly, themodel does not as yet take into account the positivefeedbacks between the temperature and the CO2 con-centration in the atmosphere, which can lead to an av-alanche-like increase in the CO2 concentration in theatmosphere and still more greatly narrow the timelimits for the conditions appropriate for the existenceof life and the human civilization on the Earth.
CONCLUSION
The results of this work suggested an unprece-dented danger related to the increase in the Earth’saverage temperature because of the greenhouse effect.
The irreversible change in the Earth’s climatecan be prevented only by taking a complex of mea-sures, such as:
BIOPHYSICS Vol. 46 No. 6 2001
BIOSPHERE AND EARTH’S CLIMATE: GREENHOUSE CATASTROPHE 1087
Fig. 6. Results of modeling the change in the Earth’s av-erage temperature for the period to the year 4000 (1) ifthe current increase in the CO2 concentration in the atmo-sphere persists and if the anthropogenic CO2 emissionsare stabilized at the (2) 2000 or (3) 2100 level.
Fig. 5. Prediction of the increase in the Earth’s averagetemperature for the period to the year 2100 (1) if the cur-rent increase in the CO2 concentration in the atmospherepersists and (2) if an international convention of stabili-zation of the anthropogenic CO2 emissions to the atmo-sphere at the 2000 level comes into effect. The modelingresults (the increase in the temperature by 5–8 K by theyear 2100 as compared with the current value) agree sat-isfactorily with the results of other studies.
10
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0
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(1) environmental measures, first of all, controland conservation of climate-forming biocenoses (in-cluding the use of cryoconservation methods);
(2) limitation and, in the future, total abandonmentof recovery and burning of mineral fuels (coal, oil, gas);
(3) “conversion of the power industry”¾ a grad-ual transition to renewable energy sources (hydro,wind, and solar power), including wood to be usedboth as firewood and as a raw material for organicfuel production;
(4) measures aimed at increasing the area (andbiomass) of forests to fix the excess of CO2 in the at-mosphere (for a while) and to extend the range of rawmaterials used in the “forest power” industry;
(5) artificial removal of CO2 from the atmo-sphere, e.g., by burial of carbon-containing waste, in-cluding household garbage; and
(6) control of the solar radiation incident on theEarth by constructing spaceborne shields in thenear-Earth space for protecting the Earth from a partof the solar radiation.
Of course, these measures are far from equiva-lent both in the strength of their effect on the climateand in the funds required for their implementation.However, in my opinion, only their simultaneous exe-cution will prevent dramatic consequences of thechange in the Earth’s climate.
The necessity to choose the optimal strategy us-ing incomplete information and to simultaneouslyperform a wide range of studies and also the insuffi-ciency of time and material resources extremely com-plicate the planning of measures required to stabilizethe Earth’s climate.
At the same time, with regard for the extremedegree of danger of the current change in the Earth’sclimate, the humankind (first of all, industrially devel-oped countries) must as soon as possible agree to pur-sue a coordinated policy in this field and to allocatenecessary funds both for conducting full-scale investi-gations and for taking a complex of measures aimedat stabilizing the Earth’s climate.
S.P. Kapitsa, A.V. Byalko, V.V. Burdyuzha, G.S. Go-litsin, V.I. Moroz, L.V. Ksanfomaliti, V.V. Smolyani-nov, and also V.N. Karnaukhov and E.V. Karnaukhovfor fruitful discussions and help in work.
REFERENCES
1. Bol’shaya sovetskaya entsiklopediya (The Great SovietEncyclopedia), Moscow: Sovetskaya Entsiklopediya,1973.
