Odekon M. Encyclopedia of paleoclimatology and ancient environments

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Energ y balance at the earth’s su rface

There has been little work to infer variations of surface heat

fluxes from geothermal data. Beltrami et al. ( 2000) estimated,

using an analytical approximation, the average heat flux into

the ground during the last 1,000 years, over a large region from

eastern and central Canada. Results indicated average heat flux

increases of 17.0 mWm

2

and 74.0 mWm

2

since 1,765 and in

the last 100 years, respectively. They also identified a cold per-

iod between 1,500 and 1,800, indicated by a negative subsur-

face temperature anomaly.

More recently, singular value decomposition inversion was

used to reconstruct surface heat flux histories from the heat

flux anomalies detected in the subsurface (Beltrami, 2001a).

In the Earth, the heat flux at any depth, ignoring the heat pro-

duction, can be expressed as the sum of the quasi steady-state

geothermal heat flux, q

, and the transient component,

ðz; t Þ :

qð z; t Þ¼q

þ Dq

ð z; t Þð9 Þ

If the surface heat flux history is modeled by a series of step

heat flux changes at the surface, the heat flux at the depth z

is given by:

ðz Þ¼ q

k ¼1

erfc

ﬃﬃﬃﬃﬃﬃ



 erfc

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

k 1



ð10Þ

ðt Þ¼q

; t

k 1

 t  t

; k ¼ 1 ; :::; K ; t

¼ 0 ð11Þ

The system of linear equations can be resolved by singular

value decomposition inversion in a similar fashion as for the

ground surface temperature reconstruction.

An analytical estimate of the heat flux history from geother-

mal data (Beltrami et al., 2000), used an approximation based

on fractional calculus (Wang and Brass, 1999). An equivalent

expression for the heat flux history for a semi-infinite, homoge-

neous medium subjected to a series of sudden changes of sur-

face temperature at any time between [ t

,t], where t is the

time at the moment of observation and t

is time before present,

is given by:

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

Dt kp

k ¼l þ1

½ð T

 T

k þ1

Þð

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

k  l



ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

k  l þ 1

Þð12Þ

Equation ( 12) is general and can be applicable to any time ser-

ies at any time scale as long as the initial surface heat flux is

zero, to avoid error accumulation in time (Beltrami, 2001b).

Observational results of Levitus et al. ( 2001) showed an

increase in observed ocean heat content of 18.2  10

J (over

the past half-century) and an increase in atmospheric heat

content 6.6  10

J, while the heat gained by the cryosphere

is around 8.1  10

J. From the analysis of geothermal data

Beltrami et al. (2002) estimated the heat gained by the litho-

sphere during the last half-century as 9.1  10

J. Recent

inversion of the same data set yielded 7.1  10

J for the

heat absorbed during the same time period (Beltrami, 2002a)

(Figure B13). These results are consistent with the idea that

the observed warming of the Earth during the last fifty years

has been global and affects all climate system components.

Further information on the latest developments in borehole cli-

matology can be found in Gonzalez-Rouco et al., 2008.

Hugo Beltrami and Daniela Nitoiu

Bibliography

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Inference from inversion. Geophys. Res. Lett., 28, 655–658.

Beltrami, H., 2001b. Surface heat flux histories from inversion of geother-

mal data: Energy balance at the Earth’s surface. J. Geophys. Res., 106,

21,979–21,994.

Beltrami, H., 2002a. Climate from borehole data: Energy fluxes and tem-

peratures since 1500. Geophys. Res. Lett., 29(23), 2111, doi: 10.1029 /

2002GL015702.

Beltrami, H., 2002b. Earth’s long-term memory. Science, 297, 206–207.

Beltrami, H., and Mareschal, J.C., 1991. Recent warming in Eastern

Canada inferred from geothermal measurements. Geophys. Res. Lett.,

18, 605–60.

Beltrami, H., and Mareschal, J.C., 1992. Ground temperature histories for

central and eastern Canada from geothermal measurements: Little Ice

Age signature. Geophys. Res. Lett., 19, 689–692.

Beltrami, H., Cheng, L., and Mareschal, J.C., 1997. Simultaneous inversion

of borehole temperature data for past climate determination. Geophys.

J. Int., 129,311–318.

Beltrami, H., Wang, J.F., and Bras, R.L., 2000. Energy balance at the

Earth’s surface: Heat flux history in eastern Canada. Geophys. Res.

Lett., 27, 3385–3388.

Beltrami, H., Smerdon, J., Pollack, H.N., and Huang, S., 2002. Continental

heat gain in the global climate system. Geophys. Res. Lett., 29, doi:

10.1029/ 2001GL014310.

Beltrami, H., Gosselin C., and Mareschal, J.C., 2003. Ground surface tem-

peratures in Canada: Spatial and temporal variability. Geophys. Res.

Lett., 30(10), doi: 10.1029 /2003GL017144.

Bullard, E.C., 1939. Heat flow in South Africa. Proc. R. Soc. London A.,

173, 474–502.

Carslaw, H.S., and Jaeger, J.C.,1959. Conduction of Heat in Solids, 2nd ed.

New York: Oxford University Press, 510pp.

Figure B13 (a) Global mean ground surface temperature history

(GSTH) from borehole temperature data. The dotted lines represent the

stability of the GSTH for a data noise level of 0.02



K. (b) Global mean

surface heat flux history (SHFH) for the same data set. The global

SHFH describes the energy balance history at the Earth’s surface for the

last 500 years.

BOREHOLE CLIMATOLOGY 105

Chisholm, T.J., and Chapman, D.S., 1992. Climate change inferred from

analysis of borehole temperatures: An example from western Utah.

J. Geophys. Res., 97, 14155–14176.

Grove, J.M., 1988. The Little Ice Age. London: Methuen, 498pp.

Gonzalez-Rouco, J.F., Beltrami H., Zorita E., and Stevens M.B. (2008).

Borehole climatology: A discussion based on contributions from

climate modelling, Climate of the Past Discussions, 4,81–110.

Huang, S., Pollack, H.N., and Shen, P.Y., 2000. Temperature trends over

the last five centuries reconstructed from borehole temperatures. Nature,

403, 756–758.

Jackson, D.D., 1972. Interpretation of inaccurate, insufficient, and inconsis-

tent data. Geophys. J. R. Astron. So., 28,97–110.

Lachenbruch, A.H., and Marshall, B.V., 1986. Changing climate: Geother-

mal evidence from permafrost in the Alaskan Arctic. Science, 234 ,

689–696.

Lanczos, C., 1961. Linear Differential Operators. Princeton, N.J: D. Van

Nostrand, 564pp.

Levitus, S., Antonov, J., Wang, J., Delworth, T.L., Dixon, K., and Broccoli, A.,

2001. Anthropogenic warming of the Earth’s climate system.

Science, 292, 267–270.

Menke, W., 1989. Geophysical Data Analysis: Discrete Inverse Theory, Int.

Geophys. Ser,. vol. 45, San Diego, CA: Academic Press, 289pp.

Shen, P.Y., and Beck, A.E., 1992. Paleoclimate change and heat flow den-

sity inferred from borehole temperature data in the Superior Province of

the Canadian Shield. Palaeogeogr. Palaeoclimatol. Palaeoecol. (Global

and Planetary Change Section), 98, 143–165.

Wang, K., and Brass, R.L., 1999. Ground heat flux estimated from surface

soil temperature. J. Hydrol. 216, 214–226.

Cross-references

Climate Variability and Change, Last 1,000 Years

Little Ice Age

106 BOREHOLE CLIMATOLOGY

CARBON CYCLE

Historical background of the carbon cycle

The discovery that plants use carbon dioxide for growth in sun-

light and return it to the atmosphere in darkness must have been

the first scientific observation of part of the carbon cycle. The dis-

covery of carbon dioxide as a gas that forms by fermentation and

burning of charcoal, under the name of spiritus silvestris,is

attributed to Jan Baptista (or Baptist) van Helmont, a man of

medicine, alchemy, and early chemistry in the then Spanish

Netherlands, in the first half of the 1600s (e.g., Graham, 1974).

Presentation of the first general scheme of the carbon and nitro-

gen cycles was attributed to the French chemist, Jean Baptiste

André Dumas, in 1841 (Rankama and Sahama, 1950, p. 535).

Dumas (1842) described the cycle of CO

consumption and

production by respiration, pointing to the sources of “carbonic

acid” in the air and soil where it forms from decomposition of

manure or organic fertilizers. He also pointed out that the Earth’s

primordial atmosphere must have contained all the carbon diox-

ide and nitrogen that has been taken up by living organisms.

As to the geochemical cycles, in 1875, several chapters on the

cycles of chemical elements appeared in a book on Earth history

by Friedrich Mohr, a professor at the University of Bonn, with

one short chapter on the carbon cycle among them (Mohr,

1875, pp. 397–398). The role of carbon dioxide as a gas warming

the atmosphere, in addition to the similar role of water vapor

that was known earlier, was demonstrated by Arrhenius (1896).

The formation of organic matter from carbon dioxide and water

under the action of light, the process known as photosynthesis,

has been studied since the later part of the 1700s, when molecular

oxygen was discovered to be part of the process and carbon diox-

ide was identified as a component of air. Short histories of suc-

cessive discoveries in photosynthesis since the late 1,700s to

the twentieth century have been published by several authors

(Gaffron, 1964; Meyer, 1964, p. 21; Bassham, 1974; Whitmarsh

and Govindjee, 1995). By the 1920s, the cycles of the chemical

elements that are involved in biological processes – carbon,

nitrogen, and phosphorus – and that are also transported between

soil, crustal rocks, atmosphere, land and ocean waters, and the

Earth’s interior were sufficiently well recognized. Alfred Lotka’ s

book, Elements of Physical Biology, published in 1925, includes

chapters on the cycles of carbon dioxide, nitrogen, and phos-

phorus that present a modern treatment of what are today called

the biogeochemical cycles (Lotka, 1925). The term biogeochem-

ical reflects the fact that biological, physical, and chemical

processes play important roles and interact with each other in

the carbon cycle. By 1950, the geochemical cycles of elements

in the Earth’s interior and on its surface became textbook mate-

rial, with the variable degree of detail in each cycle reflecting

the knowledge of the reservoir contents and inter-reservoir fluxes

at the time (Rankama and Sahama, 1950). Subsequent decades

produced the knowledge we have today of the different chemical

forms of carbon in the different compartments of the Earth, their

abundances, and flows, all of which make the global biogeo-

chemical cycle of carbon.

Structure of the carbon cycle

Geochemical or biogeochemical cycles of chemical elements are

usually represented by environmental reservoirs and material

flows or fluxes connecting them to each other. The structure of

the global carbon cycle is shown in Figure C1 and the masses

of carbon in the main environmental reservoirs are summarized

in Table C1. The inventory of the reservoirs represents the geo-

logic near-Recent, with atmospheric carbon given as the pre-

industrial concentration of CO

. Estimates of carbon masses in

other reservoirs are subject to variable and greater uncertainties.

The mass of carbon in land plants has been variably reported in

the range of 15–20% of the value given in Table C1, 700 Gt

C (1 gigaton or 1 Gt ¼10

g). Large variations in the estimated

global mass of peat and soil humus have also been reported in

the literature. Thus, the numbers in Table C1 should be viewed

as estimates for geologically recent time, and it should be kept

in mind that the masses of carbon in the individual reservoirs

have varied considerably throughout the Earth’ s history. The car-

bon cycle is usually divided into a deeper part, called the endo-

genic cycle, and the exogenic cycle that includes the surface

reservoirs of the sediments, oceanic and continental waters, land

and aquatic biomass, soils, and the atmosphere.

The biggest reservoir of carbon near the Earth’s surface lies

in past and present oceanic sediments. These include carbonate

rocks that comprise limestones, consisting mostly of the

mineral calcite (CaCO

), and dolomite rocks made predomi-

nantly of the mineral dolomite (CaMg(CO

)

); younger uncon-

solidated carbonate sediments on the ocean floor, composed to

a large extent of skeletal remains of marine organisms; and

organic matter in sediments that consists of many different orga-

nic compounds containing reduced carbon. Inorganic, oxidized

carbon in carbonates accounts for about 84% of the sedimentary

carbon mass, and the remaining 16% are in reduced organic

matter. Both inorganic (oxidized) and organic (reduced) carbon,

occurring in carbonate rocks and organic matter, make only

3.7 wt.-% of all the sediment preserved in the geologic record.

The planetary average abundance of carbon in the Earth as

a whole is not well constrained because its abundance in the

lower mantle and core is not well known, but its abundance

in the Earth’s mantle is much lower than in the sediments,

0.008–0.015 wt.-%.

Oxidized carbon is the most abundant form at the Earth’s

surface where it occurs as carbon dioxide gas, dissolved carbo-

nate and bicarbonate ions, and carbonate ions in sedimentary

minerals. In addition to carbonate minerals, pure elemental car-

bon occurs in nature in two minerals, diamond and graphite.

Diamonds are a product of high temperature and pressure asso-

ciated with explosive volcanic rocks called kimberlites and

lamproites that formed in the mantle. Graphite deposits occur

in different forms: hydrothermal veins in igneous rocks where

Figure C1 Global biogeochemical cycle of carbon. Reservoirs on the Earth surface represent the exogenic cycle. Masses of the major reservoirs

given in Table C1. Mass units: 1 mol C ¼12.011 g C or 1 10

mol C ¼120 Gt C. From Mackenzie and Lerman (2006).

108 CARBON CYCLE

crystalline graphite precipitated from hot fluids, thermally

metamorphosed coal, and metamorphic rocks originally rich

in organic matter. Another form of carbon occurring in igneous

rocks is carbonatite, a rock made mostly of calcite, dolomite,

and iron-containing dolomite (ankerite). Carbonatites are be-

lieved to form in the mantle, at high pressures of CO

, and

extrude as volcanic rocks or intrude into the upper lithosphere

at the later stages of magmatic differentiation. The occurrence

of carbonatites is limited to small areas at about 330 locations

(Barker, 1997), and their total mass is very small in comparison

to the sedimentary limestones and dolomites.

On Earth, the biological origin of organic matter is indicated

by the abundance ratio of the two stable isotopes of carbon,

C: this ratio is lower in biologically-produced organic mat-

ter than in the source of CO

used in chemosynthesis or pho-

tosynthesis. However, organic compounds of non-biological

origin occur in a class of meteorites know as chondrites, among

which carbonaceous chondrites contain between 0.26 and

3.5 wt.-% carbon in organic compounds coexisting with alumi-

nosilicate minerals. This abundance of organic carbon in extra-

terrestrial materials may be compared with its abundance of

about 0.75 wt.-% in the entire preserved mass of sediments on

Earth. Fossil fuels – coal, petroleum, and hydrocarbon gases –

represent a very small part of the global reservoir of sedimentary

organic matter (Figure C1). Known reserves of fossil fuels (coal,

petroleum, and natural gas), recoverable with present-day tech-

nology, are estimated at about 800 Gt C or 7 10

mol C. Esti-

mates of total fossil fuel reserves are about 5,000 Gt C and,

additionally, 10,000 Gt C in methane-hydrate deposits on the

ocean floor and in the tundra, estimated within a range of a factor

of 10 smaller or greater (Kvenvolden, 1988; Kvenvolden and

Lorenson, 2001). These masses of fuel reserves and methane

hydrates make about 0.1 wt.-% of sedimentary organic carbon

(Figure C1). The mass of atmospheric carbon dioxide would

more than double if the known fossil fuels of 800 Gt C were

burned to their commercial exhaustion and there were no removal

of carbon dioxide from the atmosphere. A much greater potential

increase in atmospheric carbon dioxide is indicated by the

amounts of the estimated fuel reserves and methane hydrate.

The mass of carbon stored over the geologic history of the

Earth in sedimentary limestones, dolomites, and undecomposed

organic matter exceeds by a very large factor, about 100,000

the mass of carbon in atmospheric CO

at the present time.

Next in size is the carbon reservoir of the oceans or, more

generally, of the oceanic and continental surface and ground

waters that comprise most of the hydrosphere. The main form

of carbon in the global water reservoir is dissolved carbon

dioxide and its ionic species, and the generally less abundant

dissolved organic carbon from incomplete decomposition of

living and dead organic matter. These dissolved forms of car-

bon are usually denoted DIC, for dissolved inorganic carbon,

and DOC, for dissolved organic carbon. Dissolved inorganic

carbon (DIC) includes three aqueous species – CO

, HCO



2

– and, to a lesser degree, their complexes with metal ions

in solution. On the other hand, dissolved organic carbon

includes a great variety of organic compounds ranging in mole-

cular weight from light, simple organic acids to much heavier

and structurally more complex species. Besides the dissolved

forms of carbon, there are particles containing both inorganic

and organic carbon in continental and ocean waters. Particulate

inorganic carbon or PIC is mostly the grains of eroded carbo-

nate rocks and skeletons of calcareous organisms formed in

surface waters that sink to the ocean floor. Its organic counter-

part, particulate organic carbon or POC, consists of undecom-

posed cells, products of metabolic excretion by zooplankton

(fecal pellets), soft parts of dead organisms and organic matter

adsorbed on mineral-particle surfaces such as clays.

The total mass of carbon in the global oceans, consisting

mostly of DIC, is about 60 times greater than its atmospheric

mass (Table C1). The greater mass of DIC in the ocean

becomes either a source or sink of atmospheric carbon dioxide,

depending on environmental conditions (Sect. Running of the

carbon cycle).

In the atmosphere, carbon dioxide is the most abundant

of the carbon-containing gases. At present, it forms a volume

fraction 3.85 10

4

or 385 ppmv

of the atmosphere, increas-

ing at a rate of approximately 1.5 ppmv per year. Other gases,

such as methane (CH

) from natural sources or agricultural

activities, carbon monoxide (CO) and volatile organic com-

pounds mainly from industrial activities, and the most recent

emissions of the various chloro-fluoro-carbon compounds

(CFCs) used as refrigerant and spray-propellant gases are

believed to have a potentially much greater effect on atmo-

spheric temperature, stratospheric and tropospheric ozone, and

climate, despite their occurrences at concentrations much lower

than those of atmospheric CO

In the biosphere, land plants represent a major part of the

carbon in living organic matter. This very large and diversified

group includes predominantly photosynthetic plants ranging in

Table C1 Carbon masses in the major environmental reservoirs. From

data in Li (2001), Mackenzie (2002), Ver et al. (1999), and Walker (1977).

Units: 1 mol C = 12.011 g C

Reservoir Mass of carbon

In grams C In moles C

Atmosphere

(at pre-industrial 280 ppmv) 5.94 10

4.95 10

CO (present) 1.24 10

4.42 10

(present) 4.82 10

3.01 10

Ocean

Dissolved inorganic (DIC) 3.74 10

3.11 10

Dissolved organic (DOC) 1 10

8.33 10

Particulate organic (POC) 3 10

2.50 10

Ocean biota 3 10

2.50 10

Land biota

Phytomass 7 10

5.83 10

Bacteria and fungi 3 10

2.50 10

Animals 1 to 2 10

1.25 10

Land

Soil humus 1.5 10

1.25 10

Reactive fraction of humus 2 10

Dead organic matter, litter, peat 2.5 10

2.08 10

Inorganic soil (CaCO

) 7.2 10

6 10

Sediments

Carbonates 6.53 10

5.44 10

Organic matter 1.25 10

1.05 10

Continental crust (layer 30 km thick) 2.58 10

2.14 10

Oceanic crust (layer 6.5 km thick) 9.20 10

7.66 10

Upper mantle (layer from 30 to 700 km) (8.9 to 16.6) 10

1.1 10

ppmv is parts per million by volume. In the atmosphere that is a mixture of

ideal gases at the total pressure P = 1 atm, concentrations of individual

gases in units of ppmv are also their partial pressures in units of 10

6

atm.

at a concentration of 370 ppmv has a partial pressure 3.70 10

4

atm.

CARBON CYCLE 109

size from short-lived unicellular organisms to trees whose life-

times average several decades. Forests are the main reservoir of

biotic carbon on land. In the ocean, most of the photosynthesiz-

ing organisms live in the upper layer of the oceans where suffi-

cient light is available, called the euphotic zone, of an average

thickness of 50 m, ranging up to about 200 m in very clear

water. These free-floating organisms are the phytoplankton,

and at least one group of the phytoplankton (coccolithophorids)

are important producers of calcium carbonate shells that have

made up a major part of the ocean-floor carbonate sediments

since the middle of the Mesozoic Era. Additional aquatic

photosynthesizers include the great variety of algae and bigger

plants rooted to the bottom, known as macrophytes. The ocea-

nic phytoplankton makes only a small fraction, about 0.5%, of

carbon in the global biota. However, oceanic plants have a

much shorter life cycle, about 20 days–1 month, than the land

plants that turn carbon over approximately every 10 years.

These differences account for the fact that flows of carbon

through the land and oceanic phytomass are not too different

(Table C4).

Carbon on the primordial earth

The Earth’s history in its early stages went from the formation

of the planet by accretion of a cloud of solid particles and gases

to its partial melting after accretion, which resulted in the struc-

tural separation of its major units – the inner and outer core, the

mantle and the lithosphere, and the crust. After the formation of

the Earth nearly 4.55 billion years ago, a long period of some

650–800 million years preceded the appearance of life, the first

fossil records of which are dated at 3.75–3.9 billion yr before

present (Mojzsis et al., 1996; Rosing, 1999). This time of pre-

biotic Earth, known in the geologic time scale as the Hadean

Eon, was a long period of environmental conditions very differ-

ent from those of later time, when photosynthetic organisms

emerged and modified greatly the Earth’s surface environment.

In this early, prebiotic stage of Earth history, when the tempera-

tures near the Earth surface were considerably higher than at

present, possibly near the 1,000



C of silicate melts, the lighter

chemical constituents of the Earth were separated or degassed

from the solids and melt, forming the fluid layer of the primor-

dial atmosphere. These volatile constituents became the major

components of the outer shell of the Earth that comprises its

atmosphere, hydrosphere, biosphere, and sediments.

The chemical elements and their compounds that escaped

from the molten or solid Earth interior by degassing and made

the primordial atmosphere are known as the volatiles (Rubey,

1951)orhyperfusibles (Poldervaart, 1955), mainly water

O), carbon (C), nitrogen (N), sulfur (S), and chlorine (Cl),

as listed in Table C2. Rubey (1951, 1955) and later investigators

who studied the balance of the volatiles at the Earth’s surface

demonstrated that their complete inventory includes some of

the same constituents that had been added to the Earth’s surface

by the weathering of igneous rocks and, in general, by transfer

of materials from the lithosphere to the oceans and sediments.

These amounts are small fractions of the total masses of volatiles

and the difference between the total and those derived from

igneous rocks is known as excess volatiles. The masses of H

C, N, S, and Cl in the present-day Earth’s surface environment

are approximately the masses of the volatiles on the primordial

Earth that became incorporated in the differentiated outer shells

of the cooler, later Earth. Water is the most abundant volatile

and its mass exceeds the masses of other volatiles by a factor of

30–300. The individual estimates of H

O and N, shown in

Table C2, agree within 10–15%, but there is a much greater var-

iation among the estimates of C, Cl, and S, attributable probably

to the differences in the estimated masses of sedimentary rock

salt, sulfates, sulfides, and the organic and inorganic carbon

reservoirs. The view that most of the volatiles on the Earth’s sur-

face had been released from the mantle by degassing rather than

remaining on the surface from an early stage of planetary accre-

tion has been discussed by several authors (Rubey, 1951; Walker,

1977; Li, 2000). Degassing was probably not uniform and for

such volatiles as carbon dioxide, water and perhaps sulfur, large

fractions may still remain in Earth’s upper mantle and possibly

deeper in its interior.

The five primordial volatile gases were likely to have been

O (v), CO

, HCl, and H

S, although a number of authors

have argued for different species of carbon, nitrogen, and sulfur

as components of the primordial atmosphere: methane (CH

)

instead of carbon dioxide (CO

), ammonia (NH

) instead of mol-

ecular nitrogen (N

), and sulfur dioxide (SO

) instead of the

reduced form of hydrogen sulfide (H

S). Concerning the main

chemical form of carbon in the early atmosphere, CO

rather than

is a thermodynamically stable species in the presence of

even very low concentrations of oxygen gas (O

), such as might

have existed in contact with magmatic silicate melts. For the

five volatiles to exist in a gaseous state, the temperature of the

atmosphere should have been sufficiently high to prevent their

condensation. Of the five, the highest critical temperature is that

of H

O, 374



C, and this may be taken as a representative

temperature of that stage of the early Earth before the volatiles

began to condense to liquid water and form an aqueous solution

of reactive and nonreactive gases. Although the time sequence

and rate of Earth’s cooling, the formation of the early oceans,

and the reactions between minerals and water that led to the

Table C2 Volatiles in primordial Earth’s surface environment (masses in grams of chemical species shown)

Major species Rubey (1951) Poldervaart (1955) Walker (1977) This entry

Excess volatiles Hyperfusibles Total volatiles From igenous rocks Excess volatiles Total volatiles on Earth surface

O 1.66 10

1.66 10

1.590 10

0.031 10

1.559 10

1.430 10

C 2.48 10

6.22 10

7.609 10

0.804 10

6.805 10

7.784 10

N 4.20 10

4.50 10

4.892 10

0.04 10

4.852 10

4.890 10

Cl 3.00 10

3.40 10

3.120 10

0.1 10

3.020 10

4.311 10

S 2.20 10

3.00 10

5.220 10

0.8 10

4.420 10

1.245 10

Volatiles total 1.721 10

1.768 10

1.707 10

0.041 10

1.667 10

1.568 10

From data in Li (2001) and other sources.

110 CARBON CYCLE

accumulation of dissolved solids in ocean water are known very

incompletely, the prebiotic atmosphere and ocean likely evolved

in three stages:

(1) A hot atmosphere where the five volatiles could occur as

gases.

(2) A cooler atmosphere after the water has condensed and

accumulated as a liquid on the Earth’s surface, and hydro-

gen chloride and hydrogen sulfide were removed from the

atmosphere by reactions with crustal rocks and transport of

the reaction products to the primordial ocean.

(3) An atmosphere where carbon dioxide and nitrogen

remained the two main constituents, and CO

also dis-

solved in the primordial hydrosphere and reacted with crus-

tal rocks.

After the Earth’s surface had cooled, and HCl and H

S were

removed from the atmosphere by dissolution in the early hydro-

sphere and chemical reactions with crustal rocks, the two remain-

ing main constituents of the atmosphere were CO

and N

Chemical neutralization of the chloride-ion from HCl and the sul-

fate-ion from the oxidized H

S by reactions with silicate rocks

would have added metal cations that doubled the salt content of

the primordial ocean relative to the present-day value (70–80 g

1

as compared to 35 g kg

1

now). At a limiting, hypothetical

case of no removal of CO

and N

from the atmosphere, the

atmosphere would have been almost pure carbon dioxide at a

concentration 97.4 vol.-% CO

with 2.6 vol.-% N

(the C and

N masses of total volatiles given in the last column of Table C2

correspond to 6.481 10

mol CO

and 0.175 10

mol N

The combined mass of CO

and N

in this atmosphere, covering

the Earth surface of 510 10

, would have generated an

atmospheric pressure of about 56 bar.

At a surface temperature of the Earth near 25–35



C, about

25% of the CO

could dissolve in ocean water, with around

75% remaining in the atmosphere. Because N

gas at these tem-

peratures is much less soluble in water than CO

, the remaining

atmosphere would have been 96.6 vol.-% CO

and 3.4 vol.-%

, with a total atmospheric pressure of about 40 bar. Dissolution

of a large mass of CO

in the primordial hydrosphere would have

resulted in very high concentrations of DIC in water, about 1 mol

Ckg

1

, in comparison to the present-day concentration in ocean

water of about 2 10

3

mol C kg

1

. Because DIC reacts with

-ions in solution, making CaCO

as calcite and/or aragonite

(Reaction (8) below), the solubility of CaCO

and the capacity of

the solution to remain supersaturated with respect to these miner-

als place a limit on the mass of CO

and calcium that can remain

in solution. For the removal of most CO

from the primordial

atmosphere, a mass of CaCO

comparable to its present mass

preserved in sediments might have formed during the first several

hundred million years of Earth’s prebiotic history

. The higher

concentrations of CO

in the primordial atmosphere, at the time

when the solar luminosity was some 25–30% lower than at pre-

sent, might have been responsible for the warming of the Earth’s

surface that kept it above freezing temperatures and enabled

the emergence of life. (See Archean environments; Atmospheric

evolution, Earth; Faint young Sun Paradox, this volume).

Running of the carbon cycle

The starting point of the carbon cycle is the Earth’s mantle,

from where it was degassed with other volatile elements in

the early stage of the formation of the Earth. The processes

of material exchange between the mantle and the Earth’s

surface belong in the endogenic cycle that operates on a much

longer time scale (10

–10

years) and they are much slower

than those among the surface reservoirs (Figure C1).

in the atmosphere dissolves in rain, on land, and in ocean

surface waters. It is also taken out of the atmosphere and surface

waters by photosynthesizing organisms. Residues of living

plants in part decompose to CO

and organic acids, and in part

they become organic matter of soils and sediments. The solution

of CO

in fresh water is mildly acidic and together with dissolved

organic acids reacts with crystalline rocks of the continental

crust, causing mineral dissolution and release of such major con-

stituents of river waters as the metals sodium, magnesium, potas-

sium, and calcium. Metal ions in rivers (Na

,Mg

, and Ca

balanced to a large degree by negatively-charged bicarbonate

(HCO



) ions, are transported to the ocean. The calcium carbo-

nate minerals, calcite and aragonite – both chemically the same

(CaCO

), but differing in their crystal structure – form in the

ocean either as skeletons secreted by marine organisms that

range in size from microscopic algae to large mollusks and

corals, or by inorganic precipitation. Calcites containing up to

about 15 mol-% Mg are formed by some groups of calcareous

algae in shallow-water sections of the ocean. This calcium carbo-

nate accumulates over large areas of the ocean floor in the form

of settling shells of phytoplankton and zooplankton or in struc-

tures built of algae and corals, called reefs, in the shallower

parts of the coastal zones. Aragonite and calcites rich in mag-

nesium do not last long in the geologic record and they are

transformed to calcite by recrystallization and/or dissolution

and reprecipitation. Dolomite accounts for approximately 40%

of the carbonate rock mass of the Phanerozoic Eon, the last 540

million years, but it is much less abundant, about 15%, in the

carbonates of the younger Tertiary (Wilkinson and Algeo,

1989). At present, the formation of dolomite is much more re-

stricted as, for example, in the highly saline coastal playas in

the Persian Gulf.

In the present-day ocean, both the photosynthetically pro-

duced organic matter and calcium carbonate in surface waters

have their own subcycles. As organic matter settles into the de-

eper ocean, it undergoes oxidation that returns CO

to ocean

water (see Carbon dioxide, dissolved (ocean)). This process is

also known as the biological pump. Some of the respired

is transported back to the surface layer by water mixing,

but some of it is used in dissolution of CaCO

that rains down

from the surface. An increase in concentration of dissolved

makes seawater more acidic and brings it to a level of

undersaturation with respect to calcite and aragonite. Both of

these minerals dissolve in the deep ocean, and their rates of dis-

solution are sufficiently fast to return most of the CaCO

ocean water. Preservation of CaCO

in ocean-floor sediments

is limited in the present-day ocean to depths smaller than

approximately 3,500–4,000 m, which is a combined effect of

a higher concentration of dissolved carbon dioxide that lowers

the CO

2

-ion concentration, an increase in the solubility of cal-

cite with an increasing pressure, and a faster dissolution rate in

a solution that is farther away from saturation with respect to

the mineral. Over geologically long periods, much of the ocea-

nic CaCO

was preserved in sediments that became the sedi-

mentary cover of the present-day continents and some of it

was transported into the mantle by the process of seafloor

spreading and subduction of their margins in ocean trenches.

This subduction process is part of the endogenic cycle

(Figure C1) that breaks down CaCO

at high temperatures in

the mantle and returns CO

to the surface, mostly in gases

emitted by continental and oceanic volcanoes. The isotopic

CARBON CYCLE 111

composition of carbon in CO

in some of the volcanic emis-

sions suggests that it is a mixture of carbon originally from

the mantle and carbon from the Earth’s surface.

The organic matter of terrestrial plants becomes incorporated in

soils, where it is known as humus (a mixture of complex organic

humic and fulvic acids), and the residues of fresh-water and ocea-

nic plants are buried in sediments. Some of this organic matter

decomposes more slowly, producing CO

and organic acids. The

nutrient elements nitrogen and phosphorus return to soil water,

where they become available once more for new plant growth.

However, some fraction of this organic matter resists decomposi-

tion. This fraction becomes nearly permanently buried. Because

land is at a higher elevation than the ocean surface, there is a con-

tinuous transport of running water carrying dissolved material

and solid particles eroded from rocks, soils, and terrestrial organic

matter to the ocean. Particles containing organic carbon (POC)

are brought to the ocean where some of the POC decomposes.

thus produced by decomposition of terrestrial organic matter

isaddedtoCO

already present in ocean water.

In the ocean, atmospheric CO

dissolves in the surface water

layer, a few hundred meters thick, which is well mixed by

winds, and there it is used in photosynthetic production of

organic matter, in addition to the production of calcium carbo-

nate. The exchange of CO

between surface ocean water and

the atmosphere depends on such factors as the mass of CO

in the atmosphere; temperature, salinity, and chemical composi-

tion of ocean water; the production and respiration of organic

matter; and precipitation and dissolution of calcium carbonate

minerals. For example, greater biological production of organic

matter and its storage in sediments removes carbon dioxide

from the atmosphere-ocean system; weathering of old organic

matter in oceanic sediments exposed on land returns carbon

dioxide to the atmosphere; and formation of calcium carbonate

and its deposition in sediments removes carbon from the

atmosphere-ocean system, yet it also changes the relative

abundances of the three dissolved species of inorganic carbon

in ocean water (CO

, HCO



, and CO

2

) and by this it affects

the air-sea CO

exchange.

Net removal of carbon from ocean water by sedimentation of

undecomposed organic matter and calcium carbonate must be

balanced by inputs of carbon from other sources. One obvious

but limited source is dissolution of atmospheric CO

in ocean

water. Another important source is oxidation of carbon in organic

matter that was eroded from older sediments on land and that was

transported to the ocean. As atmospheric CO

is the source both

of organic matter stored on land and in oceanic sediments, and

the atmosphere and ocean water lose CO

by the formation of

CaCO

and its storage in sediments, this CO

source would have

been exhausted rapidly if it were not replenished. Replenishment

comes from oxidation of old organic matter that is disseminated

in sediments and more concentrated in black shales. Tectonic

processes that cause uplift of continental masses and mountain

building expose these older sediments to the atmosphere and to

weathering and erosion on the Earth’s surface, thereby providing

input of CO

to the atmosphere. Volcanic emissions also add or,

in part, return CO

to the atmosphere.

Main driving processes

Deep carbon cycle

Carbon dioxide is emitted from the Earth mantle through subaer-

ial volcanism, in the spreading zones and ridges on the ocean

floor, and from magmatic plumes and hot spots. The occurrence

of this chemically oxidized form of carbon in magmatic emis-

sions indicates that CO

is not just a product of carbon oxidation

at the Earth’s surface but has a much longer geologic history on

our planet. This view is consistent with the chemical thermody-

namic properties of carbon and oxygen that tend to combine

and form carbon dioxide, as in the reaction:

C þ O

Ð CO

ð1Þ

Over a wide range of temperatures, from those at the Earth’s

surface to those of molten silicate melts, chemical equilibrium

in Reaction (1) is strongly shifted to the right, producing very

high ratios of CO

to O

. At the relatively low temperature of

the Earth’s surface, many processes represented by Reaction

(1) do not go spontaneously from the left to the right, but

carbon can exist metastably in contact with the oxidizing atmo-

sphere for a very long time. Common examples of such occur-

rences are the pure forms of elemental carbon graphite

and diamond; less pure forms, such as the coal varieties anthra-

cite, and lignite; and fossilized organic compounds, such as

amber.

A shorthand notation of the endogenic cycle of carbon is the

chemical reaction between calcium carbonate carried into the

mantle by tectonic plate subduction and silica, which produces

calcium silicate minerals and carbon dioxide:

CaCO

þ SiO

Ð CaSiO

þ CO

ð2Þ

The reaction is generally known as the Urey reaction (Urey,

1952, pp. 148 and ff.), although J.J. Ebelmen was credited with

introducing it much earlier, in 1845 (Berner and Maasch,

1996). In Reaction (2), CaSiO

represents various calcium sili-

cate minerals that occur in igneous and metamorphic rocks.

SiO

occurs either in the melt or in igneous rocks that can react

with calcium carbonate. Reaction (2), going from left to right,

describes the conversions of carbonates to calcium silicate and

production of carbon dioxide during metamorphism. The reverse

reaction, from right to left, represents chemical weathering of

silicates in the continental crust by reactions with CO

, and the

final product CaCO

. This omits intermediate reactions that

involve Ca

, HCO



, and CO

2

ions in aqueous solution.

Photosynthesis and respiration

Carbon is the main constituent of life on Earth. The main pro-

cess that converts carbon dioxide into the organic molecules in

cells of living plants is known as photosynthesis. Photosynth-

esis involves the chemical reduction of carbon, using the

energy of sunlight to make organic matter in plants; the subse-

quent decomposition of organic matter is oxidation of carbon,

also known as respiration or mineralization. These reactions

are summarized in Reaction (3).

The respiration of organic matter is a process driven by bac-

teria that utilize the energy stored in CH

O for their own meta-

bolism. The common form of photosynthesis is the reaction

between carbon dioxide and water that produces organic matter

and free oxygen gas:

þ2H

O  *

)

Gross photosynthesis

Respiration

OþH

OþO

ð3aÞ

or, in a shorter form

þ H

O Ð CH

O þ O

ð3bÞ

112 CARBON CYCLE

More generally, photosynthesis includes H

A as a chemical

compound where reduced A

2

transfers four electrons to oxi-

dized carbon in CO

, to form organic matter of composition

O and liberate 2A (Reaction (4)). Hydrogen sulfide, H

is such an H

A compound utilized by some photosynthetic

sulfur-oxidizing bacteria:

þ 2H

A *

)

Gross photosynthesis

Respiration

O þ H

O þ 2A ð4Þ

The difference between gross photosynthetic production and

respiration is net primary production, denoted NPP and

usually given in units of carbon mass stored in living biomass

in a unit of time (for example, mol C yr

1

). Reactions (3) and

(4) are also often written with all the reactants and products

multiplied by 6, giving the composition of organic matter as

, analogous to the sugar glucose. Organic matter pro-

duced by photosynthesis stores 470–490 kilojoules or 112–

117 kilocalories of energy per 1 mole of carbon (1 mol

C ¼12.011 g C; 1 kcal ¼4.184 kJ). When organic matter is

oxidized, energy is released.

In photosynthesis, free molecular oxygen (O

) is produced

from water. Respiration generally oxidizes less reduced carbon

than that produced by photosynthesis, which results in some

surplus CH

O and O

. This imbalance between photosynthesis

and respiration has been of major importance to life on Earth

because it enabled accumulation of molecular oxygen in the

atmosphere and storage of organic matter in sediments over a

period of perhaps the last 2 billion years or about one-half of

the Earth’s age of 4.6 billion years.

In addition to carbon, photosynthesizing organisms need

nitrogen, phosphorus, sulfur, and trace elements. Mean atomic

proportions of carbon, nitrogen, and phosphorus in photosynthe-

sizing planktonic organisms are C:N:P ¼106:16:1. The consis-

tency and limited variability of this ratio, originally described

by Redfield et al. (1963) and called the Redfield ratio since then,

extend to oceanic zooplankton and to the plankton of continental

waters. Oceanic phytoplankton uses nitrogen in the form of dis-

solved nitrate ions, NO



, and phosphorus in the form of one of

the dissolved phosphate ions, mostly HPO

2

. In solution, where

the positively and negatively charged ions must balance, nitrogen

and phosphorus used in the photosynthetic reaction can be

written as neutral acid molecules, HNO

and H

, instead

of the equivalent (NO



þH

) and (HPO



þ2H

). The photo-

synthetic reaction of aquatic photosynthesis, similar to Reaction

(4), is:

106CO

þ 16HNO

þ H

þ 122H

Ðð5Þ

ðCH

OÞ

106

ðNH

ðH

Þþ138O

In Reaction (5), both carbon in CO

and nitrogen in NO



are

reduced, and the mass of oxygen produced is greater than the

mass of carbon fixed in organic matter. In the absence of

nitrate, ammonia (NH

or NH

þOH



) may be utilized at least

by some of the phytoplankton species, and organic matter of

the same composition would be produced by a reaction with

16NH

instead of 16NO



þ16H

, then producing 106O

The Redfield ratio for land plants is less well constrained than

for the aquatic phytoplankton, and C:N:P atomic ratios for land

plants have been reported in a wide range from about 510:9:1

to 2057:17:1. Land plants are more efficient photosynthesizers

than marine organisms because they fix more carbon and

produce more oxygen for each atom of phosphorus consumed.

Higher land plants emerged in the Devonian Period that lasted

from about 365 to 410 Ma ago. For a plant of C:N:P atomic ratio

510:9:1, the photosynthesis reaction based on carbon dioxide,

nitrate, and phosphate, similar to Reaction (5), produces organic

matter and oxygen in the following proportions:

510CO

þ 9HNO

þ H

þ 519H

Ðð6Þ

ðCH

OÞ

510

ðNH

ðH

Þþ521O

In both Reactions (5) and (6), respiration or mineralization of

organic matter is the reverse reaction (from right to left) that

also consumes oxygen, but releases nitrogen and phosphorus

to the environment, where they become available for new bio-

logical production. This recycling of nutrient nitrogen and, in

particular, phosphorus is of major importance to biological pro-

ductivity because the ultimate source of most phosphorus is in

much slower leaching or dissolution from crustal rocks (see

Phosphorus cycle).

Carbon in the atmosphere and hydrosphere

In an atmosphere containing oxygen, carbon dioxide is the only

chemically stable form of carbon. More reduced carbon gases,

such as carbon monoxide (CO), methane (CH

), and volatile

hydrocarbons are eventually oxidized to CO

. Carbon dio-

xide dissolved in water reacts to produce bicarbonate and car-

bonate ions:

þ H

O Ð H

þ HCO



Ð 2H

þ CO

2

ð7aÞ

An increase in concentration or partial pressure of CO

in the

atmosphere results in its higher concentration in solution at

equilibrium, and this further reduces the concentration of the

carbonate ions and changes the relative proportions of the dis-

solved inorganic carbon species:

þ H

O þ CO

2

Ð 2HCO



ð7bÞ

A higher CO

concentration can make the solution undersatu-

rated with respect to CaCO

and cause dissolution, as shown

in the following reaction going from the right to the left:

2þ

þ 2HCO



Ð CaCO

þ H

O þ CO

ð8Þ

Reaction (8), proceeding from left to right, represents the for-

mation of calcium carbonate minerals. As the bicarbonate ion,

HCO



, is the main species of DIC in ocean water and continen-

tal freshwaters, its reaction with Ca

removes 1 mole of carbon

into sediments and produces 1 mole of CO

thereby restoring

the balance of the carbonate species.

Dissolution of calcium carbonate by reaction with dissolved

represents the process of chemical weathering of lime-

stones and silicate rocks on land, where they are exposed to

atmospheric precipitation and groundwater containing elevated

concentrations of CO

from respiration of organic matter in

soils. The reaction of CO

with water that produces the bicar-

bonate and carbonate ions, the reactions of the latter with cal-

cium, and the relatively low solubility of CaCO

minerals

at the Earth’s surface conditions are the factors behind the

abundance of limestones and dolomites that once formed as

oceanic sediments and became part of the continental crust

and land surface.

CARBON CYCLE 113

Isotopic fractionation

In photosynthesis, plants use the lighter carbon isotope,

C, in

preference to the heavier isotope,

C. This biological fractiona-

tion is a non-equilibrium process and results in marine and most

terrestrial organic matter having a lower

C ratio than the

atmospheric source. This difference, expressed as d

C(%)

(see Carbon isotopes, stable), amounts to organic matter being

about 20–25% lighter than the value of d

C ¼7% of CO

the present-day atmosphere. The land plants in the metabolic

group C

that accounts for 85–95% of the present-day plant spe-

cies, have an average d

C 27%, with a range from 21

to 35% (O’Leary, 1988). A group of geologically younger land

plants, the C

plants, is characterized by a smaller isotopic frac-

tionation, 9to20%, with an average d

C 13%. This

metabolic pathway is only several million years old and it is

believed to have evolved in response to lower atmospheric CO

concentrations. The third and smallest metabolic group, the

CAM (crassulacean acid metabolism) plants, has carbon isotope

fractionation values that extend from those of the C

to C

plants.

In the ocean, the spread of d

C values for different groups of

planktonic and benthic plants is considerable: 10 to 22%

for algae and macrophytic plants, and 18 to 31% for plank-

ton. Values of 20 to 21% are considered a representative

average for marine plankton.

In the system of CO

gas, DIC, and CaCO

(calcite), isoto-

pic fractionation at equilibrium between pairs of species is con-

siderably smaller than in biological processes, as shown by the

fractionation values in Table C3.

Equilibrium fractionation factor, a, is usually written in the

d notation of the two species exchanging their

C and

For the exchange between aqueous HCO



and gaseous CO

the fractionation factor is, with the d values taken as fractions:

HCO



ðaqÞCO

ðgÞ

CÞ

1 þ d

ð9Þ

It should be noted that in the preceding notation the fractiona-

tion factor a is the quotient of the isotopic ratio in the aqueous

phase to the ratio in the gaseous phase. As long as d is much

smaller than 1 and a is close to 1, the approximations ln (1 þd)

 d and ln a  a – 1 are used in Equation (9), giving logarith-

mic and linear forms of a:

ln a

HCO



ðaqÞCO

ðgÞ

¼ d

 d

ð10aÞ

HCO



ðaqÞCO

ðgÞ

 1 ¼ d

 d

¼ 9:6

to 7:9

ð10bÞ

The preceding shows that the equilibrium fractionation is the

difference between the d

C values of the two species. The

bicarbonate ion in solution, as the main species of DIC, is iso-

topically heavier than CO

gas by 7.9% (at 25



C) to 9.6%

(at 5



C) (Table C3). Isotopic fractionation of carbon between

calcite and the bicarbonate ion in solution, as in Reaction (8),

is small at Earth surface temperatures, where the d

C of calcite

differs from HCO

–

by 0.1 to +0.9% (Table C3). For this rea-

son, changes in the isotopic composition of carbon in lime-

stones through geologic time, such as those shown in

Figure C2a, are considered as representative of the isotopic

composition of DIC in ocean water, from which the rates of

biological production and storage of organic carbon are esti-

mated for different geologic periods.

Carbon fluxes

On the Earth’s surface with a climate and vegetation cover

similar to those of pre-industrial times, the biggest carbon

fluxes are those of net primary production (NPP) on land and

in the ocean (Table C4 ). In Recent time, NPP on land recycles

atmospheric CO

every 9 years:

Recycling time ¼

mass

NPP

4:95  10

mol C

5:25  10

mol C yr

1

¼ 9:4yr

Residence time of carbon in the individual reservoirs is a mea-

sure of the carbon cycle dynamics. Changes in reservoir sizes

and fluxes in the geologic past produced great changes in the

residence times of carbon in the different reservoirs. In parti-

cular, changes in atmospheric carbon dioxide and density of

vegetation cover of land, discussed in the next section, were

likely to result in changes in the residence times. The near-

Recent mean residence time of carbon in land vegetation, from

Table C3

C equilibrium fractionation between species shown as 1 and 2 in gaseous phase (g), aqueous solution (aq), and calcite (cal).

Notation of the fractionation factor a

is given in Equations (9)–(10). Temperature T is in Kelvin

No. Species and phase lna

or a

– 1, as shown T range (a

– 1)  10

(%)

12 (



C) 5



C25



1CO

(aq) CO

(g) a

– 1 ¼0.373/ T + 0.00019

0–60 1.1 1.1

2 HCO



(aq) CO

(g) a

– 1 ¼9.552/ T – 0.02410

5–125 9.6 7.9

3 HCO



(aq) CO

(aq) a

– 1 ¼9.866/ T – 0.02412

5–125 10.7 9.0

4CO

2

(aq) CO

(g) lna

¼8.886/ T – 0.02225

0–100 9.7 7.6

5 CaCO

(cal) HCO



(aq) lna

¼–4.232/ T + 0.0151

0–35 0.1 0.9

6 CaCO

(cal) HCO



(aq) 25 0.90.2

7 CaCO

(arag) HCO



(aq) 25 1.80.2

Equation fitted by Mook et al. ( 1974) to data of Vogel et al. (1970).

Mook et al. (1974), as recalculated by Friedman and O’Neil (1977, fig 27).

Mook et al. (1974).

Regression fit to data of Thode et al. (1965, Table III).

Equation based on data of Salomons and Mook (1986, Table 6-2A) (Clark and Fritz, 1997).

Rubinson and Clayton (1969).

114 CARBON CYCLE