The Global Carbon Cycle

11.1 Introduction

Although many elements are essential to living matter, carbon is the key element of life on Earth. The carbon atom’s ability to form long covalent chains and rings is the foundation of organic chemistry and biochemistry. The biogeochemical cycle of carbon is necessarily very complex, since it includes all life forms on Earth as well as the inorganic carbon reservoirs and the links between them. Despite being a complicated elemental cycle, it is extensively studied and to date, probably the best understood elemental biogeochemical cycle. The possibility of global climatic change brought about by the enhanced greenhouse effect of fossil fuel CO₂ in the atmosphere has also prompted much carbon-related research.

There exists a multitude of review articles and books about the carbon cycle available with varied degrees of detail and points of emphasis: e.g., Bolin (1970a,b); Keeling (1973); Woodwell and Pecan (1973); Woodwell (1978); Bolin et al. (1979); Revelle (1982); Bolin and Cook (1983); Degens et al. (1984); Warneck (1988); Watson et al. (1990); IPCC (1992); Siegenthaler and Sarmiento (1993); Sundqvist (1993); Schimel et al. (1995); and Heimann (1997) to name a few.

This treatment of the carbon cycle is intended to give an account of the fundamental aspects of the carbon cycle from a global perspective. After a presentation of the main characteristics of carbon on Earth (Section 11.2), four sections follow: 11.3, about the carbon reservoirs within the atmosphere, the hydrosphere, the biosphere and the lithosphere; 11.4, which covers some important fluxes between the reservoirs; 11.5, which gives brief accounts of selected models of the carbon cycle; and finally 11.6, describing natural and human-induced fluctuations in the carbon cycle. A recurring theme in this chapter will be to explore how mechanisms with different time scales in the carbon cycle influence the atmospheric cycle of CO₂. These time scales on which various components of the global carbon cycle interact with the atmosphere are indicated in Fig. 11-1. The reader should take note that the question of atmospheric CO₂ concentration, despite being of profound importance in today’s debate about human induced climate change, is only one detail of the global carbon cycle. Carbon is present everywhere and indeed most material motions and transformations are linked in one way or another to the global carbon cycle.

Fig. 11-1 Major reservoirs and fluxes of the global carbon cycle, including time scales. Numbers given are Pg C (1 Pg C = 10¹⁵ g C) Pg C/yr, respectively. (After Sundquist, 1993.)

The relevant time scales vary over many orders of magnitude, from millions of years (for processes controlled by the movement of the Earth’s crust) to days and even seconds for processes related to air-sea exchange and photosynthesis. Depending on the problem studied, models are usually constructed only to include processes that work on time scales judged to be relevant in the particular study. For example, most models used to study mankind’s perturbation of atmospheric CO₂ exclude the geologic processes working on time scales longer than 5000 years and only include those processes that actively respond to atmospheric changes on the decadal time scale. Although the CO₂ content in the atmosphere is modulated by changes in the exchange rates at the atmosphere-ocean and atmosphere-biosphere interface; the level of the CO₂ concentration in the atmosphere is ultimately determined by geologic processes occurring on very long time scales. The controlled erosion rate, together with volcanism, releases carbon from the lithosphere into the ocean-atmosphere-biosphere system. This is counteracted by the sedimentation rate of carbon in the deep oceans. The balance between these two processes determines the long-term CO₂ level in the atmosphere.

There are more than a million known carbon compounds, of which thousands are vital to life processes. The carbon atom’s unique and characteristic ability to form long stable chains makes carbon-based life possible. Elemental carbon is found free in nature in three allotropic forms: amorphous carbon, graphite, and diamond. Graphite is a very soft material, whereas diamond is well known for its hardness. Curiosities in nature, the amounts of elemental carbon on Earth are insignificant in a treatment of the carbon cycle. Carbon atoms have oxidation states ranging from +IV to –IV. The most common state is +IV in CO₂ and the familiar carbonate forms. Carbonate exists in two reservoirs, in the oceans as dissolved carbon in the forms of H₂CO₃(aq),, and, and in the lithosphere as solid carbonate minerals: CaCO_3(s), CaMg(CO₃)₂, FeCO₃. Carbon monoxide, CO, is a trace gas present in the atmosphere with carbon in oxidation state +II. Assimilation of carbon by photosynthesis creates the reduced carbon pools of the Earth. Reduced carbon is present with variable oxidation states that will be discussed further below. Methane, CH₄, is the most reduced form of carbon with an oxidation state of – IV.

11.2 The Isotopes of Carbon

There are seven isotopes of carbon (¹⁰C, ¹¹C, ¹²C, ¹³C, ¹⁴C, ¹⁵C, ¹⁶C) of which two are stable (¹²C and ¹³C). The rest are radioactive with half-lives between 0.74 s (¹⁶C) and 5726 years (¹⁴C). Only the stable isotopes and ¹⁴C (often referred to as “radiocarbon”) are included in this treatment of the carbon cycle.

The most abundant isotope is ¹²C, which constitutes almost 99% of the carbon in nature. About 1% of the carbon atoms are ¹³C. There are, however, small but significant differences in the relative abundance of the carbon isotopes in different carbon reservoirs. The differences in isotopic composition have proven to be an important tool when estimating exchange rates between the reservoirs. Isotopic variations are caused by fractionation processes (discussed below) and, for ¹⁴C, radioactive decay. Formation of ¹⁴C takes place only in the upper atmosphere where neutrons generated by cosmic radiation react with nitrogen:

The ¹⁴C content of the material in a carbon reservoir is a measure of that reservoir’s direct or indirect exchange rate with the atmosphere, although variations in solar also create variations in atmospheric ¹⁴C content activity (Stuiver and Quay, 1980, 1981). Geologically important reservoirs (i.e., carbonate rocks and fossil carbon) contain no radiocarbon because the turnover times of these reservoirs are much longer than the isotope’s half-life. The distribution of ¹⁴C is used in studies of ocean circulation, soil sciences, and studies of the terrestrial biosphere.

Fractionation is another major process responsible for creating inhomogeneities in the isotope distribution. Physical, chemical, and biological processes may be sensitive to the molecular weights of the molecules (atoms) involved. Thus exchanges between reservoirs can discriminate between different isotopes; for example when plants take up CO₂ they preferentially take up ¹²C, this makes organic carbon on average lighter than atmospheric carbon. The definition of δ used to describe variations in isotope composition was introduced in Chapter 5. For ¹³C, δ¹³C, in parts per thousand, ‰, is defined by

(1)

Here ¹³R_S is the ¹³C/¹²C ratio in the sample and ¹³R₀ is the ¹³C/¹²C ratio the accepted standard PDB (PeeDee belemnite, after a Cretaceous belemnite rock from the PeeDee formation in North Carolina). Craig (1957a) has determined R₀ to be 0.0112372.

The ¹⁴C content of a sample is described in a similar manner. The basis for ¹⁴R₀ is an oxalic acid standard of the US National Bureau of Standards normalized for ¹³C fractionation and corrected for radioactive decay since a reference date January 1, 1950 (Stuiver and Polach, 1977). The absolute value of ¹⁴R₀ is 1.176.10⁻¹² (Stuiver et al., 1981).

¹⁴C content is usually reported in Δ¹⁴C units. The Δ¹⁴C scale was originally defined by Broecker and Olson (1959). The reasoning behind introducing the scale is that all variations in ¹⁴C due to fractionation should be eliminated by correcting for the sample’s observed ¹³C/¹²C ratio relative to that of postulated average terrestrial wood. The wood is assumed to have a δ¹³C value of – 25‰ and fractionation for the ¹⁴C isotope is assumed to occur as the square of that for ¹³C for all processes. The approximate expression for Δ¹⁴C proposed by Broecker and Olsson (1959) is

(2)

Δ¹⁴C is used frequently in modeling, since no corrections for fractionation are necessary when modeling fluxes between reservoirs.

11.3 The Major Reservoirs of Carbon

11.3.1 The Atmosphere

Carbon is present in the atmosphere mainly as CO₂, with minor amounts present as CH₄, CO and other gases. The CO₂ content of the atmosphere is one of the best known quantities of the global carbon cycle. Accurate measurements were begun in 1957 (Keeling et al., 1976a,b; Bacastow and Keeling, 1981) with other groups following in the 1960s (Bischof, 1981) and 1970s (Pearman, 1981). One of the latest results of this research is shown in Fig. 11-2, which is a global picture of the variations in CO₂ as function of latitude. The seasonal variations have a 6-month phase shift between the two hemispheres. The amplitude of the seasonal variations varies with latitude. The largest variations (10–15 ppmv) are seen at high latitudes, north of 50°N northern hemisphere. In southerly high latitudes the amplitude is only about 1 ppmv and along the equator there are small seasonal variations. The greater amplitude in the northern hemisphere is consistent with the occurrence of photosynthesis by extensive seasonal forests in that hemisphere that consume CO₂ in the spring and summer and respirate it in the fall and winter. Another very obvious fact in the CO₂ record is the increasing concentration caused by mankind’s perturbation of the carbon cycle. This is mainly due to the combustion of fossil fuel, but carbon mobilized from carbon pools on land, mainly oxidation of phytomass and soil organic carbon, is also significant. The atmospheric CO₂ concentration at the end of 1997 was 365 ppmv at Mauna Loa. Estimates of the pre-industrial CO₂ content from recent ice-core results (Etheridge et al., 1996) converge towards values close to 280 ppmv. Fossil fuel emissions (Marland and Boden, 1991; Marland and Rotty, 1984; Marland et al., 1989; Rotty, 1981) are well known: the trade in coal and oil has considerable economic value and is therefore well documented. Assuming that all fossil fuel produced is oxidized within a few years from its removal from the ground, a good estimate of the total emissions can be made. During the past decades there has been an average observed airborne fraction of about 0.55. (The observed airborne fraction is defined as the observed CO₂ increase divided by the amount produced by fossil fuel combustion.) Since this quantity does not take any biospheric influences into account, it has limited value, although its use is widespread.

Fig. 11-2 Three-dimensional representation of the latitudinal distribution of atmospheric carbon dioxide in the marine boundary layer. The surface represents data smoothed in time and latitude. The Norwegian and Swedish flask sampling effort at Zeppelin Station is shown in the inset as flask monthly means. Data from the NOAA CMDL cooperative air sampling network were used. (Figure kindly provided by Dr Pieter Tans and Dr Thomas Conway of NOAA (CMDL).)

A recent development that has substantially raised our knowledge about the carbon cycle is the measurement of the O₂/N₂ atmospheric ratio (Heimann, 1997). Figure 11-3 shows the combined curves of CO₂ for Mauna Loa and South Pole as well as the recent development of data regarding the oxygen to nitrogen ratio in the air. We can note that there is a clear decline of the oxygen ration in the atmosphere consistent with the consumption of oxygen through combustion of fossil fuel. In Fig. 11-2 we saw that the seasonal variability of CO₂ is strongly dampened in the southern hemisphere; this is not true for atmospheric oxygen. To understand this one has to consider the carbonate chemistry in the oceans (see Section 10.4.2.5 of the previous chapter for an explanation of how dissolved inorganic carbon is dominated by carbonate and bicarbonate ions). Oxygen does not have the corresponding dissociation chemistry and will exchange freely between the surface waters and the atmosphere such that the seasonal cycle of oxygen in the surface waters is transferred into the atmosphere. The increase in CO₂ simultaneous with a decrease in oxygen is consistent with a carbon dioxide source from oxidation of highly reduced (organic) carbon (fossil fuels, biomass, or soil carbon). In Fig. 11-4 the combined usage of CO₂ and O₂ is utilized to calculate what reservoirs must have been changing in size to explain the trends of both gases during the past years. There has apparently been a substantial terrestrial sink active during the early 1990s. This is discussed more later in the chapter.

Fig. 11-3 Direct atmospheric measurements of the CO₂ concentration (left-hand scale) at Mauna Loa (Hawaii) and the South Pole station (Keeling et al., 1995) together with the concurrently observed decrease in atmospheric oxygen content (right-hand scale) at La Jolla, CA after 1989. (Taken from Heimann (1997) with permission from the Royal Swedish Academy of Sciences.)

Fig. 11-4 Globally and annually averaged oxygen versus CO₂ concentration from 1991 to 1994. The oxygen concentration is displayed as the measured O₂/N₂ ratio and expressed in “per meq” which denote the pm deviation from a standard ratio. The inset shows the directions of the state vector expected for terrestrial and oceanic uptake. The long arrow shows the expected atmospheric trend from fossil fuel burning if there were no oceanic and terrestrial exchanges. (Used with permission from Keeling et al. (1996). Nature 381: 218–221, Macmillan Magazines.)

There are a number of ways to estimate the pre-industrial atmospheric CO₂ content. The total emissions (from fossil fuel combustion) during the period 1850 to 1982 are estimated at 173 Pg C with an uncertainty of less than 10 Pg (1 Pg = 10¹⁵ g). Assuming a constant airborne fraction of 0.54, a pre-industrial atmospheric CO₂ content of 614 Pg (290 ppmv) is calculated (Bolin et al., 1981). This calculation does not take into account any biospheric emissions, nor is the assumption of a constant airborne fraction perfectly sound. Estimates of the pre-industrial CO₂ content based on the carbonate chemistry of “old” ocean (water that has yet to be contaminated by anthropogenic carbon emissions) give values ranging between 250 (Chen and Millero, 1979) and 275 ± 20 ppmv (Brewer, 1978). In a critical examination of CO₂ measurements performed in the 1880s, Wigley (1983) arrives at a CO₂ level around 260–270 ppmv. Finally, measurements of CO₂ content in air bubbles occluded in glacial ice from Antarctica and Greenland (Neftel et al., 1982; Barnola et al., 1983; Etheridge et al., 1996) give the least criticized data and indicate a value of 280 ±10 ppmv (see Fig. 11-5).

Fig. 11-5 CO₂ content of air bubbles trapped in glacial ice from Greenland and Antarctica, showing a pre-industrial concentration of ca. 280 ppmv.

Approximately 1% of the atmospheric carbon budget is maintained by methane (Ehhalt, 1974). Current global background levels of CH₄ are estimated at 1.7 ppmv, which corresponds to 3 Pg C (Blake and Rowland, 1988). Sources of methane are both natural and anthropogenic today. Important natural sources include fluxes from wetlands and enteric fermentation in wild animals (elephants and bison). Anthropogenic sources include rice paddies (to the extent they are placed in areas not previously part of natural wetlands), cattle (which have increased much more since the second world war than the decline in elephants and bison), coal mines, and leakage from gas fields (Crutzen, 1991; IPCC, 1990, 1992). Biomass burning is another substantial source of atmospheric methane. During the initial stages of burning there is usually an open flame in which essentially all carbon compounds are oxidized to CO₂. After the open flames have subsided there is, however, a long period of time when the remaining coals are fuming, releasing a multitude of less oxidized compounds (see Fig. 11-6) (Crutzen and Andreae, 1990; Hao et al., 1996; Levine, 1994). Leakages from gasfields in the Former Soviet Union (FSU) were notorious. During the 1990s the increase rate of atmospheric methane has decreased substantially probably to an extent due to infrastructure development in Russia combined with a general decrease in the gas extraction in FSU. The main sink for methane in the atmosphere is oxidation by the hydroxyl radical (·OH).

Fig. 11-6 Concentrations of gases in the smoke from an experimental fire of Trachypogon grass from Venezuela as a function of time and the stack gas temperature. The dotted line separates the flaming phase from the smoldering phase. Concentrations are in percent by volume for CO₂, in volume mixing ratios (ppm) for the other species (1% = 10 000 ppm). (Used with permission from Crutzen and Andreae (1990). Science 250: 1669–1678, AAAS.)

Oxidation of methane is one of the sources of atmospheric CO. Another internal source of importance is the oxidation of terpenes and isoprenes emitted by forests (Crutzen, 1983). Important are also biomass burning activities (Crutzen and Andreae, 1990; Hao et al., 1996; Levine, 1994). The carbon monoxide concentration in the atmosphere ranges from 0.05 to 0.20 ppmv in the remote troposphere (with considerable differences between the northern and southern hemispheres) which means that about 0.2 Pg of carbon is present as CO in the atmosphere.

Apart from CO₂, CH₄, and CO there are many gases containing carbon present in the atmosphere, terpenes, isoprenes, various compounds of petrochemical origin and others. We will not discuss them further, although some, like dimethylsulfide (DMS, (CH₃)₂S), are of great importance in the biogeochemical cycles of other elements. The total amount of atmospheric carbon in forms other than the three discussed is estimated at 0.05 Pg C (Freyer, 1979).

11.3.2 The Hydrosphere

Oceanic carbon is mainly present in four forms: dissolved inorganic carbon (DIC), dissolved organic carbon (DOC), particulate organic carbon (POC), and the marine biota itself. The marine biota, although it is a small carbon pool with a standing crop of about 3 Pg C (De Vooys, 1979) has a profound influence on the distribution of many elements in the sea (Broecker and Peng, 1982). Primary production in the photic zone is the major input of organic carbon in the oceans (Mopper and Degens, 1979). Labile (reactive) organic compounds are efficiently reoxidized in the mixed layer, whereas less than 10% of the primary production is distributed into the reservoirs of POC and DOC. Williams (1975) has used ¹⁴C techniques to determine the average age of deep water DOC to be 3400 years. The DOC is thus clearly older than the turnover time of water in the deep oceans (100–1000 years) indicating the persistent nature of the dissolved organic compounds in the seas.

A detailed characterization of DOC is difficult to make; a large number of compounds have been detected but only a small portion of the total DOC has been identified. Identified species include amino acids, fatty acids, carbohydrates, phenols and sterols. The amount of carbon in the oceans as DOC is estimated to 1000 Pg and the amount present as POC is about 30 Pg (Mopper and Degens, 1979).

DIC concentrations have been studied extensively since the appearance of a precise analytical technique (Dyrssen and Sillén, 1967; Edmond, 1970). The aquatic chemistry of CO₂ has been treated extensively; reviews can be found in Skirrow (1975), Takahashi et al. (1980), and Stumm and Morgan (1981). When CO₂ dissolves in water it may hydrate to form H₂CO₃(aq) which in turn dissociates to and. The conjugate pairs responsible for most of the pH buffer capacity in seawater are and B(OH)₃/ (with some minor contributions from silicate and phosphate). Although the predominance of at the oceanic pH of 8.2 actually places the carbonate system close to a pH buffer minimum, its importance is maintained by the high DIC concentration (≈2 mM). Ocean water in contact with the atmosphere will, if the air-sea gas exchange rate is short compared to the mixing time with deeper waters, reach equilibrium according to Henry’s Law.

Two further reactions to be considered are the ionization of water and the borate equilibrium:

(3)

In order to be able to solve for hydrogen ion concentration we define total borate (SB) and total carbon (ΣC ≡ DIC) as

represents the sum of CO₂(aq) and H₂CO₃. Alkalinity, a capacity factor, representing the acid neutralizing capacity of the aqueous solution, is given by the following equation (ignoring influences from some minor components like phosphate and silicate) (see also Chapter 5):

(4)

Given any two of the four quantities ΣC, Alk, pH,, the other two can always be calculated provided appropriate equilibrium constants are available (the equilibrium constants depend on temperature, salinity and pressure). Hydrogen ion concentration, for example, be calculated from Alk and ΣC with the equation

(5)

K₁ and K₂ are the dissociation constants for H₂CO₃. Alkalinity and ΣC are the analyzed values and ΣB is calculated from salinity. can then be calculated by

(6)

where K_H is the Henry’s Law constant for CO₂ described in Chapter 5. At the pH of ocean water (about 8) most of the DIC is in the form of and (Fig. 11-7) with a very small proportion being [H₂]. Although [H₂] changes in proportion to CO₂(g), the ionic forms changes little as a result of the various acid-base equilibria. This fact is responsible for the “buffer” factor (buffer here refers to buffering of CO₂ exchange) also known as the “Revelle” factor (Revelle and Suess, 1957). See Chapter 4 for an application of this factor. The buffer factor is defined by

Fig. 11-7 Distribution of dissolved carbon species in seawater as a function of pH. Average oceanic pH is about 8.2. The distribution is calculated for a temperature of 15°C and a salinity of 35‰. The equilibrium constants are from Mehrbach et al. (1973).

(7)

Figure 11-8 shows how, pH, and β are dependent on ΣC and Alk. Note that in Fig. 11-8 that organic carbon formation (or the opposite process, respiration) is moving parallel to the alkalinity in the diagram (apart from a small alkalinity change due to nitrate and phosphate uptake) axis whereas calcium carbonate formation represents a vector that decreases DIC by one unit for every two units of alkalinity (moles and equivalents respectively). For current atmospheric, prevailing temperature and salinity, β is about 14 in polar regions and about 10 in equatorial waters. The significance of β ∼ 10 is that for a 10% increase in atmospheric only a 1% increase in ΣC is necessary to reach a new equilibrium. The buffer factor’s large value is important since it greatly constrains the ocean’s ability to take up increases in atmospheric CO₂. Average DIC and Alk concentrations for the world oceans can be seen in Fig. 11-9. With an average DIC of 2.35 mmol/kg seawater and a world oceanic volume of 1370 × 10⁶ km³ the DIC carbon reservoir is estimated to be 37 900 Pg C (Takahashi et al., 1981). The surface waters of the ocean contain a minor part of the DIC 700 Pg C. Nevertheless, the surface waters play an important role as a means of communication between the atmosphere and the deep oceans. Although DIC is a large carbon reservoir with lively exchange with the atmosphere, its importance as a sink for anthropogenic CO₂ emission is restricted by several factors. The static uptake capacity of the seawater (solubility and “buffer” factor), the slowness of attainment of equilibrium between the ocean water and atmosphere, the ventilation of the deep ocean, and the oceanic sedimentation rate all impose constraints on the role of the oceans as a sink for atmospheric CO₂. The sluggish deep water formation rates essentially dictated by the fact that the oceans are heated from above which creates a very stable stratification creates a central bottleneck in the carbon cycle. Despite a very rapid exchange of carbon between the surface waters and the atmosphere the carbon is not transported away from the atmosphere. The turnover time of carbon dioxide in the atmosphere is short (a few years) but the ability of the carbon cycle to transport excess carbon (like anthropogenic releases of fossil fuel) away from the atmosphere is much longer (decades to hundreds of years). A significant consequence of this is that releases of CO₂ into the atmosphere will create a perturbation of the atmospheric concentration of CO₂ that will require hundreds of years to fully equilibrate.

Fig. 11-8 Isolines of pH (a), (b), and the Buffer factor (c) plotted as functions of DIC and alkalinity. The lines have been calculated for a temperature of 15°C and a salinity of 35‰. The equilibrium constants for K₁ and K₂ are from Mehrbach et al. (1973), K₀ from Hansson (1973) and B calculated from salinity according to the formula given by Culkin (1965).

Fig. 11-9 (a) The vertical distributions of alkalinity (Alk) and dissolved inorganic carbon (DIC) in the world oceans. Ocean regions shown are the North Atlantic (NA), South Atlantic (SA), Antarctic (AA), South Indian (SI), North Indian (NI), South Pacific (SP), and North Pacific (NP) oceans. (Modified with permission from T. Takahashi et al., The alkalinity and total carbon dioxide concentration in the world oceans, in B. Bolin (1981). “Carbon Cycle Modelling,” pp. 276–277, John Wiley, Chichester.)

Oceanic surface water is everywhere supersaturated with respect to the two solid calcium carbonate species calcite and aragonite. Nevertheless carbonate precipitation is exclusively controlled by biological processes, specifically the formation of hard parts (i.e., shells, skeletal parts etc.). The very few existing accounts of spontaneous inorganic precipitation of CaCO₃(s) (so-called “whitings”) come from the Bahamas region of the Caribbean (Morse et al., 1984).

The detrital rain of carbon-containing particles can be divided into two groups: the hard parts comprising calcite and aragonite and the soft tissue containing organic carbon. The composition of the soft tissue shows surprising uniformity, the average composition being (CH₂O)₁₀₆ (NH₃)₁₆PO₄ (see Chapter 10, Section 10.3.1). The average composition of the particulate matter (here a composite of organic and inorganic particles) settling through the water column and subsequently being dissolved in the deep ocean is given by P:N:C:Ca:S = 1:15:131:26:50 (Broecker and Peng, 1982) with a CaCO₃-C/Org-C ratio of 1:4. Calculating an average composition of the carbon that actually is deposited in sediments is more difficult since the areas of deposition are different for organic and inorganic carbon. More than 90% of the deposition of organic material takes place on the continental shelves; soft tissues falling into the deep oceans are consumed by heterotrophic organisms before isolation from the water column within the sediments.

The solubility of calcite and aragonite increases with increasing pressure and decreasing temperature in such a way that deep waters are undersaturated with respect to calcium carbonate, while surface waters are supersaturated. The level at which the effects of dissolution are first seen on carbonate shells in the sediments is termed the lysocline and coincides fairly well with the depth of the carbonate saturation horizon. The lysocline commonly lies between 3 and 4 km depth in today’s oceans. Below the lysocline is the level where no carbonate remains in the sediment; this level is termed the carbonate compensation depth.

The variations in ¹⁴C seen in the deep oceans of the world (Fig. 11-10) show features created by radioactive decay. The radiocarbon distribution is an important tool for determining the replacement times of the deep oceans. Great care has to be taken when interpreting the ¹⁴C distribution to take into account mixing between waters of different origin. This is especially true in the Atlantic, since the degree of isotopic equilibrium reached between the air and surface waters is different in the two source areas of Atlantic deep water, the Arctic and Antarctic surface waters (Broecker, 1979). This complication makes the apparent ¹⁴C age in seawater not simply a measure of the time elapsed since isolation from the atmosphere but a complex blending of the effects of water-mass mixing and uneven degrees of isotopic equilibrium in the ocean.

Fig. 11-10 The Δ¹⁴C values of the cores of the North Atlantic, Pacific, and Indian Oceans deep waters. The oldest waters are encountered near 40°N in the Pacific Ocean. (Modified with permission from M. Stuiver et al. (1983). Abyssal water carbon-14 distribution and the age of the world oceans, Science 219, 849–851, AAAS.)

Care must also be taken to not confuse the ¹⁴C perturbation, e.g. from nuclear weapons testing with the ΔCO₂ perturbation lifetime. The former is largely due to fast isotopic exchange while the latter is controlled by a slower mass flux.

11.3.3 The Terrestrial Biosphere

Large amounts of carbon are found in the terrestrial ecosystems and there is a rapid exchange of carbon between the atmosphere, terrestrial biota, and soils. The complexity of the terrestrial ecosystems makes any description of their role in the carbon cycle a crude simplification and we shall only review some of the most important aspects of organic carbon on land. Inventories of the total biomass of terrestrial ecosystems have been made by several researchers, a survey of these is given by Ajtay et al. (1979).

Primary production maintains the main carbon flux from the atmosphere to the biota. In the process of photosynthesis, CO₂ from the atmosphere is reduced by autotrophic organisms to a wide range of organic substances. The complex biochemistry involved can be represented by the formula

(8)

Gross primary production (GPP) is the total rate of photosynthesis including organic matter consumed by respiration during the measurement period, while net primary production (NPP) is the rate of storage of organic matter in excess of respiration. There are two main routes taken to estimate the world NPP and standing phytomass. The first method is to classify the biosphere into ecosystems in which, from measurements of estimates, values for the primary productivity and phytomass are assigned. The alternative method is to use estimates made by prognostic models simulating the effects of environmental factors on productivity and phytomass.

The possible effects of increased atmospheric CO₂ on photosynthesis are reviewed by Goudriaan and Ajtay (1979) and Rosenberg (1981). Increasing CO₂ in a controlled environment (i.e., greenhouse) increases the assimilation rate of some plants, however, the anthropogenic fertilization of the atmosphere with CO₂ is probably unable to induce much of this effect since most plants in natural ecosystems are growth limited by other environmental factors, notably light, temperature, water, and nutrients.

Estimates of terrestrial biomass vary considerably, ranging from 480 Pg C (Garrels et al., 1973) to 1080 Pg C (Bazilevich et al., 1970). Bazilevich et al. attempted to estimate the magnitude of the biomass before mankind’s perturbation of the ecosystems. The latest work that undoubtedly had the most data available estimates the total terrestrial biomass, valid as of 1970, as 560 Pg C (Olson et al., 1983).

Terrestrial biomass is divided into a number of subreservoirs with different turnover times. Forests contain approximately 90% of all carbon in living matter on land but their NPP is only 60% of the total. About half of the primary production in forests yields twigs, leaves, shrubs, and herbs that only make up 10% of the biomass. Carbon in wood has a turnover time of the order of 50 years, whereas turnover times of carbon in leaves, flowers, fruits, and rootlets are less than a few years. When plant material becomes detached from the living, plant carbon is moved from the phytomass reservoir to litter. “Litter” can either refer to a layer of dead plant material on the soil or all plant materials not attached to a living plant. A litter layer can be a continuous zone without sharp boundaries between the obvious plant structures and a soil layer containing amorphous organic carbon. Decomposing roots are a kind of litter that seldom receives a separate treatment due to difficulties in distinguishing between living and dead roots. Average turnover time for carbon in litter is thus about 1.5 years, although caution should be observed when using this figure. For tropical ecosystems with mean temperatures above 30°C the litter decomposition rate is greater than the supply rate so storage is impossible. For colder climates NPP exceeds the rate of decomposition in the soil. The average temperature at which there is balance between production and decomposition is about 25°C. The presence of peat, often treated as a separate carbon reservoir, exemplifies the difficulty in defining litter. The total amount of peat is estimated at 165 Pg C (Ajtay et al., 1979). Figure 11-11 illustrates this very strongly. The tropics have an extremely high NPP but very little carbon in the soil; whereas all higher latitude areas have the opposite relationship. The dynamics of the carbon reservoirs is very different on either side of the balance isotherm. Also thought provoking is the fact that a very large proportion of the areas that are covered today with carbon-rich soils have appeared in areas covered by ice shields during ice ages; much of the carbon in these soils today has probably been deposited since the last glaciation. A climatic change that moves the balance isotherm polewards would most likely give rise to a net flux of carbon to the atmosphere from regions that today are close to balance or in carbon accumulation zones. The zones of soil carbon accumulation are also the zones most likely to experience growth limitation due to lack of nutrients since the continuous deposition of carbon will always retain some nutrients (e.g., N and P). Another observation regarding Fig. 11-11 is that land-use changes occurring today in the tropics mobilize carbon to the atmosphere by the decrease in standing biomass; the companion flux of soil carbon oxidized upon plowing of virgin land is much smaller than for opening new agricultural land in temperate regions. This is something that occurred in Europe and North America during the nineteenth century. Many of these lands are today being abandoned because of changes in agricultural practice; this gives rise to a net flux of carbon from the atmosphere to the standing biomass and soils (Sedjo, 1992). In the perspective of national carbon balances there are several complications; the net uptake today in temperate regions is only possible due to an early release of carbon due to land use changes. This illustrates two aspects of carbon exchanges and the terrestrial biosphere, the time scales of exchange can be long and simultaneously human behavior can alter the reservoirs rapidly upon change of human habits (see Fan et al., 1998).

Fig. 11-11 (a) Global distribution of carbon produced annually, in grams of dry matter/m² per year. (b) Global distribution of carbon preserved in soils, in kg/m². (Both figures from Box and Meentemeyer (1991), used with permission from Elsevier Publishers.)

There is a group of organic compounds in terrestrial ecosystems that are not readily decomposed and therefore make up a carbon reservoir with a long turnover time. There are also significant structural differences between the marine and terrestrial substances (Stuermer and Payne, 1976). The soil organic matter of humus is often separated into three groups similar in structural characteristics but with differing solubility behavior in water solutions. Humic acids, fulvic acids, and humin are discussed in Chapter 8. Schlesinger (1977) presented an assessment of the various carbon pools for temperate grassland soil (Fig. 11-12). The undecomposed litter (4% of the soil carbon) has a turnover time measured in tens of years, the 22% of the soil carbon in the form of fulvic acids is intermediate with turnover times of hundreds of years. The largest part (74%) of the soil organic carbon (humins and humic acids) also has the longest turnover times (thousands of years).

Fig. 11-12 Detrital carbon dynamics for the 0–20 cm layer of chernozem grassland soil. Carbon pools (kg C/m²) and annual transfers (kg C/m² per year) are indicated. Total profile content down to 20 cm is 10.4 kg C/m². (Reproduced with permission from W. H. Schlesinger (1977). Carbon balance in terrestrial detritus, Ann. Rev. Ecol. Syst. 8, 51–81, Annual Reviews, Inc.)

11.3.4 The Lithosphere

Although the largest reservoirs of carbon are found in the lithosphere, the fluxes between it and the atmosphere, hydrosphere, and biosphere are small. It follows that the turnover time of carbon in the lithosphere is many orders of magnitude longer than the turnover times in any of the other reservoirs. Many of the current modeling efforts studying the partitioning of fossil fuel carbon between different reservoirs only include the three “fast” spheres; the lithosphere’s role in the carbon cycle has received less attention.

Fossil fuel burning is an example of mankind’s ability to significantly alter fluxes between reservoirs. The burning of fossil fuel transfers carbon from the vast pool of reduced carbon in the lithosphere to the atmosphere, and hence to the biosphere, hydrosphere, soils and sediments. The elemental carbon reservoir is estimated from average carbon contents in different types of rocks, ranging from 0.9% elemental carbon in shales to 0.1% in igneous and metamorphic rocks (Kempe, 1979b) and the relative abundance of the rock types. The resulting estimate is 2 × 10⁷ Pg C (Hunt, 1972), a single reservoir several orders of magnitude larger than the sum of all reservoirs discussed so far. Of the 2 × 10⁶ Pg of recycled elemental carbon (recycled carbon has traveled at least once through the lithospheric cycle) in the lithosphere only 10⁴ Pg make up the economically extractable reserves of oil and coal. Most of the reduced carbon species in the Earth’s crust are highly dispersed and probably never will be used as fuels. The carbonate minerals distributed in sedimentary rocks represent a carbon reservoir that is even larger than the elemental carbon reservoir. About three-fourths of the carbon in the Earth’s crust is present as carbonates. Several forms exist; the dominant biogenic forms are calcite and aragonite. Both are stoichiometrically CaCO₃ but calcite has six-coordinated Ca atoms and is capable of substituting several percent Mg into its lattice. Aragonite has nine-coordinated Ca atoms and several percent Sr can be incorporated into its lattice. Both forms can precipitate depending on the Ca/Mg ratio in the solution; for the present ocean Mg-calcite or aragonite are precipitated. Dolomite (CaMg(CO₃)₂) is a carbonate mineral of wide importance formed by diagenetic disintegration of Mg-rich calcites. Formation of dolomite is slow today and largely confined to evaporitic settings (Holland, 1978). The invasion of land by plants 600 million years ago, at the beginning of the Phanerozoic era increased the availability of CO₂ in the soil. There was a marked decrease of dolomitic sediments and increase in limestone sediments coherent with the appearance of terrestrial vegetation (Fig. 11-13).

Fig. 11-13 Volume percent of sedimentary rocks as a function of age. (Modified with permission from A. B. Ronov (1964). On the post-Cambrian geochemical history of the atmosphere and hydrosphere, Geochemistry 5, 493–506, American Geological Institute.)

11.4 Fluxes of Carbon between Reservoirs

Carbon is released from the lithosphere by erosion and resides in the oceans ca. 10⁵ years before being deposited again in some form of oceanic sediment. It remains in the lithosphere on the average 10⁸ years before again being released by erosion (Broecker, 1973). The amount of carbon in the ocean–atmosphere–biosphere system is maintained in a steady state by geologic processes; the role of biological processes is, however, of profound importance for the partitioning of carbon between the “fast” reservoirs.

Chemical weathering of crustal material can both add and withdraw carbon from the atmosphere. This has been discussed in Chapter 8. The oxidation of reduced carbon releases CO₂ to the atmosphere,

whereas dissolution of carbonates is associated with uptake of CO₂:

Silicates also lead to uptake of CO₂. Weathering of a non-aluminum silicate like Mg-olivine may be written

An example of aluminosilicate weathering is the reaction of the feldspar albite to a montmorillonite-type mineral

In the weathering of carbonates, one mole of rock CO₂ is mobilized for each mole of atmospheric CO₂ consumed. The reverse reaction (sedimentation of carbonate in the oceans) will again release one mole equivalent of CO₂(g). For the weathering of silicates there is a 1:1 relationship between CO₂(g) consumed and produced, in contrast to the 1:2 relationship for carbonate weathering. Estimates of global erosion rates are based either on average river data (Livingstone, 1963; Kempe, 1979b) or on global material balance calculations performed by extrapolating the material balance from a well documented area to the world (Kempe, 1979b).

The freshwater cycle is an important link in the carbon cycle as an agent of erosion and as a necessary condition for terrestrial life. Although the amount of carbon stored in freshwater systems is insignificant as a carbon reservoir (De Vooys, 1979; Kempe, 1979a), about 90% of the material transported from land to oceans is carried by streams and rivers.

Pure water in equilibrium with atmospheric CO₂ has a pH of about 5.6 at ambient temperatures. Although rainwater pH is affected by other airborne species with acid-base characteristics (Charlson and Rodhe, 1982), calculating the flux of carbon carried from the atmosphere to the surface by pH 5.6 rainwater is a good approximation, if a bit large. According to the weathering reaction, half the bicarbonate in stream water originates in the atmosphere. Rainwater clearly is unimportant as source for this carbon. Air within soils is the major source of CO₂ taking part in weathering reactions with carbonates and silicates. Bacterial decomposition of organic material together with root respiration maintain high partial pressures of CO₂ in soil air ( Chapter 7 and Kempe, 1979a). Approximately 0.4 Pg C/yr are withdrawn from the atmosphere by weathering reactions, 0.1 Pg C/yr is released by oxidation of elemental carbon, yielding a net flux of 0.3 Pg C/yr from atmosphere to lithosphere (Holland, 1978). The importance of the presence of liquid water on the face of the Earth, despite the relatively small numbers indicated above, is of profound importance for the state of the planet. The process of precipitating carbonate minerals would probably not proceed without water; a consequence would then be that most of the carbon presently deposited in the lithosphere would be present as CO₂ in the atmosphere much like the atmospheres on Venus and Mars.

Garrels and Mackenzie (1971) calculated global river loads based on Livingstone’s (1963) data. From these figures Kempe (1979a) deduced a total flux of 0.84 Pg/yr with rivers where about half is in the form of DIC and the rest being approximately evenly distributed between PIC, DOC, and POC.

Kempe (1979b) also estimates the flux of carbon from the lithosphere to oceans from glacial erosion (0.033 Pg/yr), global dust production (0.06 Pg/yr) and marine erosion (0.0045 Pg/yr) to give a combined flux of 0.1 Pg/yr. Although there is a general consensus that geologic processes control the amount of carbon in the ocean-atmosphere system, the mechanisms are debated. Walker (1977) assumes a steady-state model where the weathering rate is dependent on the CO₂ partial pressures in the atmosphere. An increase in will give a higher weathering rate, which results in an increase of the cation content of the oceans. The increased cation concentration yields a higher precipitation rate of carbonates which removes carbon, thereby restoring the original balance. The long-term atmospheric carbon dioxide budget is thus governed by a volcanic source and consumption by the weathering of silicates. Volcanism does not depend on atmospheric, but weathering does. The equilibrium level of CO₂ is therefore determined by the demand that the weathering sink must just balance the volcanic source. Holland (1978) presents somewhat different arguments and deduces, from balance calculations, indications of a juvenile carbon flux from the Earth’s interior of 0.08 Pg C/yr.

The exchange of carbon between the terrestrial biosphere and atmosphere goes through two channels. CO₂ is the major route with CH₄ making up about 1% of the exchange. Methane is mainly produced by enteric fermentation by animals, and anaerobic production in paddy fields, freshwater lakes, swamps, and marshes. Ehhalt (1974) estimates an upper limit for the herbivore production of methane from an assumption that 10% of the dry plant matter produced on land is consumed by herbivores and the food to methane conversion ratio for cattle is valid for all herbivores (cattle have the highest measured ratio). The present upper limit is 0.17 Pg C/yr with a range down to 0.08 Pg C/yr. Interestingly, the increase in world cattle population since the early 1940s accounts for about 25% of this figure. Methane emissions to the atmosphere from freshwater lakes, swamps and marshes are in the range of 0.15–0.22 Pg C/yr. The total flux of methane to the atmosphere is thus 0.5 Pg C/yr.

Carbon monoxide emissions from the terrestrial biosphere are small, but forest fires produce 0.02 Pg C/yr. Degradation of chlorophyll is dying plant material seems to be the largest CO-producing mechanism at 0.04–0.2 Pg C/yr (Freyer, 1979).

The exchange of CO₂ between the atmosphere and terrestrial biota is one of the prime links in the global carbon cycle. This is seen by studying the variations of ¹³C in the atmosphere. Figure 11-14 presents atmospheric Δ¹³C for the years 1956 and 1978. The lines are consistent with addition or subtraction of CO₂ with a Δ¹³C of about – 27‰, which could be derived from either fossil fuel or plant CO₂. It cannot be oceanic because surface water DIC has a Δ ¹³C of about +2‰ (Kroopnick, 1980). This confirms that the annual variations are primarily due to exchange with the terrestrial biosphere, and not caused by seasonal exchange with the oceans. This result has now been further confirmed by the already mentioned O₂/N₂ measurements (Heimann, 1997 and Fig. 11-3).

Fig. 11-14 Change in the relation between δ¹³C and concentration of atmospheric CO₂ over 22 years. Mean change is shown as a dashed line. Solid lines show mixing relations for 1956 and 1978. __ denotes inferred northern hemispheric means for 1956 and 1978. (Modified with permission from C. D. Keeling et al. (1979). Recent trends in the ¹³C/¹²C of atmsopheric carbon dioxide, Nature 277, 121–123, Macmillan Magazines.)

Many estimates of total terrestrial net primary production are available, ranging between 45.5 Pg C/yr (Lieth, 1972) and 78 Pg/yr (Bazilevich et al., 1970). Ajtay et al. (1979) have revised the various estimates and methods involved, they also reassess the classifications of ecosystem types and the extent of the ecosystem surface area using new data and arriving at a total NPP of 60 Pg C/yr. Gross primary production is estimated to be twice net primary production, i.e., 120 Pg C/yr. This implies that about 60 Pg C/yr are returned to the atmosphere during the respiratory phase of photosynthesis. It is well known that carbon dioxide uptake by plants follows daily cycles; most plants take up CO₂ during the day and emit it at night. These diurnal patterns give rise to large variations in close to the vegetation sites (Fig. 11-15). The diurnal cycles that produce local changes are superimposed on the yearly cycles that give the hemispheric variations seen in Fig. 11-2.

Fig. 11-15 Variation in the vertical distribution of carbon dioxide in the air around a forest with time of day. (Reprinted with permission from B. Bolin (1970). The carbon cycle. In “The Biosphere,” p. 51, W. H. Freeman, NY.)

The subsequent fate of the assimilated carbon depends on which biomass constituent the atom enters. Leaves, twigs, and the like enter litterfall, and decompose and recycle the carbon to the atmosphere within a few years, whereas carbon in stemwood has a turnover time counted in decades. In a steady-state ecosystem the net primary production is balanced by the total heterotrophic respiration plus other outputs. Non-respiratory outputs to be considered are fires and transport of organic material to the oceans. Fires mobilize about 5 Pg C/yr (Baes et al., 1976; Crutzen and Andreae, 1990), most of which is converted to CO₂. Since bacterial heterotrophs are unable to oxidize elemental carbon, the production rate of pyroligneous graphite, a product of incomplete combustion (like forest fires), is an interesting quantity to assess. The inability of the biota to degrade elemental carbon puts carbon into a reservoir that is effectively isolated from the atmosphere and oceans. Seiler and Crutzen (1980) estimate the production rate of graphite to be 1 Pg C/yr. River transport of organic carbon, estimated earlier as 0.1 Pg C/yr, brings the sum of non-respiratory outputs to 7 Pg C/yr. Total respiration should therefore be around 50 Pg C/yr. This figure is in agreement with estimates of soil respiration rates determined from compilations of ecosystem types and their measured soil respiration rates (Ajtay et al., 1979).

The exchange of carbon dioxide between ocean and atmosphere has been studied extensively, since the prevailing view is that fossil fuel derived CO₂ not remaining in the atmosphere has entered the oceans (Siegenthaler and Sarmiento, 1993). To appraise the ocean-atmosphere exchange we make use of the radiocarbon distribution in the oceans. All ¹⁴C is produced in the atmosphere, hence all radiocarbon in the oceans must have entered through the air-sea interface. Under a steady-state assumption the net influx of ¹⁴C must be balanced by the total decay within the oceans. Using our knowledge of the ¹⁴C distribution in the oceans (Fig. 11-10) and the radiocarbon decay constant for ¹⁴C we can calculate the flux of carbon by the following simple relations:

where F_ma is the flux from the ocean mixed layer to atmosphere, F_am is the flux from atmosphere to mixed layer, k is the ¹⁴C decay rate, R_a, R_m, and R₀ are the ¹⁴C ratios in atmosphere, mixed layer, and average ocean respectively, V₀ is the ocean volume, and C₀ an average DIC concentration of the oceans. Solving for F_am we obtain the following:

(9)

The gross flux of carbon from atmosphere to ocean is thus ca. 80 Pg C/yr. There are several complications with the above calculation. The isotopic ratios must be steady-state values, which are unavailable due to the changes resulting from atmospheric atom bomb testing. The few available pre-bomb measurements from the late 1950s (Broecker et al., 1960) together with Δ¹⁴C determinations in corals (Druffel and Linick, 1978) are invaluable tools for determining a steady state R_m value. Nevertheless, we must be aware of the great sensitivity of the flux estimate to the R_m value since F_am is dependent on the reciprocal of R_a – R_m, which is a small number. Equation (9) can be reformulated to include the variations of surface water and the variations of Δ¹⁴C in surface waters. Figure 11-16 shows latitudinal distributions of in the Atlantic and Pacific Oceans (Tans et al., 1990). Surface water Δ¹⁴C exhibits considerable variations with very low values in the Antarctic surface waters. This flux has also been constrained with ¹³C studies (Quay et al., 1992).

Fig. 11-16 Partial pressure of CO₂ in surface ocean water along the GEOSECS tracks: (a) the Atlantic western basin data obtained between August 1972 and January 1973; (b) the central Pacific data along the 180° meridian from October 1973 to February 1974. The dashed line shows atmospheric CO₂ for comparison. The equatorial areas of both oceans release CO₂ to the atmosphere, whereas the northern North Atlantic is a strong sink for CO₂. (Modified with permission from W. S. Broecker et al. (1979). Fate of fossil fuel carbon dioxide and the global carbon budget, Science 206, 409–418, AAAS.)

The two prime mechanisms of carbon transport within the ocean are downward biogenic detrital rain from the photic zone to the deeper oceans and advection by ocean currents of dissolved carbon species. The detrital rain creates inhomogeneities of nutrients illustrated by the characteristic alkalinity profiles (Fig. 11-9). The amount of carbon leaving the photic zone as sinking particles should not be interpreted as the net primary production of the surface oceans since most of the organic carbon is recycled within the photic zone; only about 10% settles as detritus (Bolin et al., 1979). There is considerable patchiness in the rate of oceanic primary production (Fig. 11-17) with high values in areas of intense upwelling, while areas of slow sinking motions (the subtropical gyres) show photosynthesis rates only one-tenth as large. De Vooys (1979) gives a thorough account of the many methods employed and uncertainties involved in estimating the net primary production of the aquatic environments. We adopt an estimate of total primary production of 50 Pg C/yr but note that the range of estimates is huge (15–126 PgC/yr).

Fig. 11-17 Distribution of primary production in the world oceans (Degens and Mopper, 1976).

If 10% of the total primary production settles as detrital material, about 5 Pg C leaves the photic zone annually. The CaCO₃ to organic carbon ratio in the detritus is usually taken as 1:4 (Broecker and Peng, 1982) which signifies a carbonate flux around 1 Pg C/yr. The inorganic/organic ratio can actually vary; Chen (1978) obtained ratios between 1:10 and 1:3 in a water column study. The detrital rain is balanced by a small river input of carbon and upwelling of deep water enriched in carbon from the decomposition of the detritus at depth. To balance the carbon budget of the photic zone, oceanic circulation must provide a net transport of about 5 Pg C/yr from deeper layers to the surface. Comparing Fig. 11-17 with a map of upwelling areas clearly shows that upwelling and primary production are coupled processes. We can also study Fig. 11-16 where the high values in equatorial regions are caused by the upwelling of carbon-rich and cold, deep water. This water is supersaturated with respect to atmospheric CO₂ when it upwells. This state enhanced further upon warming. The North Atlantic has low values caused by biological depletion of carbon and cooling of waters flowing northward (i.e., the Gulf Stream). The yearly circulation of carbon through the atmosphere from equatorial upwelling regions to high latitudes is around 0.01 Pg C/yr (Bolin and Keeling, 1963).

In a steady-state ocean the sediment deposition rate of a nutrient like phosphorus ought to be balanced by riverborne influx to the oceans; 1.5–4.0 Tg P are transported to the oceans by rivers (Richey, 1983). Assuming a C/P molar ratio of 106:1 in the sedimentary organic material, the corresponding carbon flux is in the range of 0.06 to 0.16 Pg C/yr. The sedimentation rate of organic material is also estimated from the total annual sedimentation rate of 6.1 × 10¹⁵ g/yr by applying an average organic carbon content of 0.5% (Kempe, 1979b), resulting in 0.03 Pg C/yr. Kempe (1979b) estimates inorganic sedimentation at 0.09–0.22 Pg C/yr based on an oceanic calcium balance calculation and the carbonate content in dated deep-sea cores.

11.5 Models of the Carbon Cycle

The descriptive account of the carbon cycle presented above is a first-order model. A variety of numerical models have been used to study the dynamics and response of the carbon cycle to different transients. This subject is an extensive field because most scientists modeling the carbon cycle develop a model tailored for their particular problem.

Box models have a long tradition (Craig, 1957b; Revelle and Suess, 1957; Bolin and Eriksson, 1959) and still receive a lot of attention. Most work is concerned with the atmospheric CO₂ increase, with the main goal of predicting global CO₂ levels during the next hundred years. This is accomplished with models that reproduce carbon fluxes between the atmosphere and other reservoirs on time scales of 10–100 years, but does not include deep ocean circulation or sedimentary phenomena in detail. To study changes over thousands of years, the whole oceans, terrestrial biota, and soils must be considered. Extension to even longer time scales must deal with all geologic processes. On the other hand, many processes simulated in the fossil fuel studies can then be omitted or treated as instantaneous.

Simple three-box models with the atmosphere assumed to be one well-mixed reservoir and the oceans described by a surface layer and a deep-sea reservoir have been used extensively. Keeling (1973) has discussed this type of model in detail. The two-box ocean model is refined by including a second surface box, simulating an “outcropping” (deep-water forming) polar sea (e.g., Keeling and Bolin, 1967, 1968), and to include a better resolution of the main thermocline (e.g., Björkström, 1979). The terrestrial biota are included in a simple manner (e.g., Bolin and Eriksson, 1959) in some studies; Fig. 11-18 shows a model used by Machta (1972) where the role of biota is simulated by one reservoir connected to the atmosphere with a time lag of 20 years.

Fig. 11-18 A four-box model of the global carbon cycle. Reservoir inventories are given in moles and fluxes in mol/yr. The turnover time of CO₂ in each reservoir with respect to the outgoing flux is shown in brackets. (Reprinted with permission from L. Machta, The role of the oceans and biosphere in the carbon dioxide cycle, in D. Dryssen and D. Jagner (1972). “The Changing Chemistry of the Oceans,” pp. 121–146, John Wiley.)

The inadequacy of the two-box model of the ocean led to the box-diffusion model (Oeschger et al., 1975). Instead of simulating the role of the deep sea with a well-mixed reservoir in exchange with the surface layer by first-order exchange processes, the transfer into the deep sea is maintained by vertical eddy diffusion. In its original formulation, the box-diffusion model assumed that the eddy diffusivity remained constant with depth. Siegenthaler (1983) further developed the diffusion model to include polar outcropping areas. The box-diffusion model is in widespread use: for example an ambitious attempt (Peng et al., 1983) to stimulate the changes in total carbon, ¹³C and ¹⁴C during the last hundred years uses a version of the Oeschger model combined with four boxes simulating the terrestrial system.

Box models and box-diffusion models have few degrees of freedom and they must describe physical, chemical, and biological processes very crudely. They are based on empirical relations rather than on first principles. Nevertheless, the simple models have been useful for obtaining some general features of the carbon cycle and retain some important roles in carbon cycle research (Craig and Holmén, 1995; Craig et al., 1997; Siegenthaler and Joos, 1992).

There has been a tremendous development of various types of prognostic models of the carbon cycle during the past decades with increased refinement of both oceanic processes (see Siegenthaler and Sarmiento, 1993; Sarmiento et al., 1992, 1998), terrestrial processes (Bonan, 1995a; Bunnell et al., 1977; Cao and Woodward, 1998; Collatz et al., 1992; Denning et al., 1996a, b; Dickinson et al., 1986; Dorman and Sellers, 1989; Foley et al., 1996; Knorr and Heimann, 1995; Law et al., 1996; Law and Simmonds, 1996; Nemry et al., 1996; Potter et al., 1993; Sellers et al., 1996a, b) and atmospheric transport calculations (Erickson et al., 1996; Fung et al., 1983; Heimann and Keeling, 1989; Heimann et al., 1989; Hunt et al., 1996; Six et al., 1996). Description of these models is beyond the scope of this volume, to describe but define the forefront of the modeling research today.

11.6 Trends in the Carbon Cycle

Throughout this chapter many of the arguments are based on an assumption of steady state. Before the agricultural and industrial revolutions, the carbon cycle presumably was in a quasi-balanced state. Natural variations still occur in this unperturbed environment; the Little Ice Age, 300–400 years ago, may have influenced the carbon cycle. The production rate of ¹⁴C varies on time scales of decades and centuries (Stuiver and Quay, 1980, 1981), implying that the pre-industrial radiocarbon distribution may not have been in steady state.

Measurements of CO₂ concentrations in air bubbles trapped in glacial ice (Berner et al., 1980; Delmas et al., 1980; Jouzel et al., 1993; Raynaud et al., 1993) show that atmospheric was about 200 ppmv toward the end of the last glaciation 20000 years ago (Fig. 11-19).

Fig. 11-19 Paleorecord of carbonaceous gases together with temperature. (After Jouzel et al., 1993.)

Today, fossil fuel combustion undoubtedly accounts for a significant portion of the anthropogenic emissions although it is rivaled by carbon mobilized by deforestation and land-use changes (Woodwell et al., 1983). The industrial revolution marked the onset of large-scale fossil fuel combustion in the early part of the 19th century. Around 1860 the emissions had reached 0.1 Pg C/yr (Fig. 11-20). The increase has been steady since that time although the rate of increase has changed during the past century. In 1860 essentially only coal was used; the use of oil began at the end of the 19th century followed by gas in the early decades of this century. Total fossil fuel emissions increased by 4% per year between 1860 and the beginning of the First World War, when fossil fuel consumption had reached 0.9 Pg C/yr (90% of which was coal). For the next 30 years (1914–1945) the yearly increase was about 1%, but after the Second World War the growth rate returned to 4%. Figure 11-21 shows the marked changes in fossil fuel use since 1973. In this period the annual rate of increase diminished to less than 2%, and striking changes in fuel mix occurred. Oil and gas use increased more rapidly than coal from the turn of the century to 1973 so that emissions from oil surpassed those from coal in the late 1960s.

Fig. 11-20 Rate of transfer of carbon to the atmosphere due to fossil fuel combustion according to Rotty (1981).

Fig. 11-21 Annual CO₂ emissions from each type of fossil fuel with growth rates (Rotty, 1981).

The projection of future emissions of fossil fuel CO₂ is subject to a number of uncertainties. The growth rate has already shown great variations and the reserves of fossil fuels are not accurately known. Estimates of reserves range between 5000 and 10 000 Pg C, much of which would be costly to exploit with present techniques.

The atmospheric CO₂ content increased by about 1 ppmv per year during the period 1959–1978 (Bacastow and Keeling, 1981) with the South Pole increase lagging somewhat behind the Mauna Loa (19.5°N,155.6°W) data. This difference is consistent with our knowledge of interhemispheric mixing times and the fact that most fossil fuel emissions occur in the northern hemisphere (see also Conway et al., 1994a).

In Fig. 11-22 (Heimann, 1997) the variability of the carbon cycle on interannual scales is shown. These processes still remain to be elucidated in detail but regional climate variability alters regional fluxes significantly. One can easily find indications of strong El Niño events in the record. El Niño has two main influences: one on the Pacific Ocean that is capped by warm water and thus a weaker source of atmospheric CO₂ from the upwelling waters, and the other being alterations of the temperature and precipitation fields in large areas. The latter proves to create a large flux of carbon to the atmosphere, mainly from drought stricken tropical regions (notably northeast Brazil). The effect on the terrestrial components typically overshadows the decreased oceanic source during El Niño events (Gaudry et al., 1987; Craig, 1998). Interannual variability in atmospheric CO₂ can also be induced by trends in global climate on other time scales; there are indications of changes in temperature and growing season during the latest decades (Bacastow et al., 1985; Conway et al., 1994b; Dai and Fung, 1993; Goulden et al., 1996, Keeling et al., 1995, 1996; Kindermann et al., 1996; Myneni et al., 1998). There are obviously many exciting questions regarding this issue that remain.

Fig. 11-22 (a) Interannual fluctuations of the growth rate of atmospheric CO₂ determined from the average of the seasonally adjusted records of the Mauna Loa and South Pole stations (see Fig. 11-3). (Data from Keeling et al., 1995.) The dashed line is the growth rate that would result from an atmospheric balance which takes into account the documented CO₂ inputs from fossil fuel and changes in land use together with the uptake rates computed by an ocean and a terrestrial model. (b) Anomalous, presumably climate driven CO₂ source as implied by the difference between the solid and dashed line shown in part (a). (Both parts taken from Heimann (1997), with permission from the Royal Swedish Academy of Sciences.)

Fossil fuel emissions alter the isotopic composition of atmospheric carbon, since they contain no ¹⁴C and are depleted in ¹³C. Releasing radiocarbon-free CO₂ to the atmosphere dilutes the atmospheric ¹⁴C content, yielding lower ¹⁴C/C ratios (“the Suess effect”). From 1850 to 1954 the ¹⁴C/C ratio in the atmosphere decreased by 2.0 to 2.5% (Fig. 11-23) (Suess, 1965; Stuiver and Quay, 1981). Then, this downward trend in ¹⁴C was disrupted by a series of atmospheric nuclear tests. Many large fission explosions set off by the United States with high emission of neutrons took place in 1958 in the atmosphere and the Soviet Union held extensive tests during 1960–1963. Figure 11-24 shows the atmospheric Δ¹⁴C trend during recent years. The two superpowers have ceased performing atmospheric bomb tests, which resulted in the spike-like injections of ¹⁴C in the early 1960s. The further fate of these spikes in the global biogeochemical cycle has proven to be an unintentional but valuable tool when deducing carbon fluxes between reservoirs.

Fig. 11-23 Comparison between the Peng et al. (1983) model-derived Suess effect curve (solid line) and the observed ¹⁴C/¹²C trend (points) for atmospheric CO₂ as reconstructed by Stuiver and Quay (1981) from measurements of tree rings. (Reproduced with permission from W. Broecker et al. (1983). A deconvolution of tree ring based δ¹³C record, J. Geophys. Res. 88, 3609–3620, American Geophysical Union.)

Fig. 11-24 Carbon-14 in the troposphere and the ocean surface water 1962–1981. ¹⁴C values for ocean surface water during this period range from 0–15% with no trend over time. (Modified with permission from R. Nydal and K. Lövseth (1983). Tracing bomb ¹⁴C in the atmosphere, J. Geophys. Res. 88, 3621–3642, American Geophysical Union.)

Agriculture has the explicit goal of harvesting organic matter and no accumulation of carbon in agricultural ecosystems is to be expected. It is important to recognize that an increased carbon fixation rate is not equivalent to an increased storage of carbon. Carbon accumulation in ecosystems is determined by the balance between net primary production and heterotrophic respiration, changes in both must be considered in the search for the missing carbon.

Eutrophication by the release of nitrogen and phosphorus in various forms could contribute significantly to the biotic storage of carbon. Anthropogenic releases of N and P correspond to the fixation of 9.6 and 17.6 Pg C/yr, respectively, if all N and P released was stored as trees in forests (Houghton and Woodwell, 1983). Most of the released nutrients are not available to be stored as wood, consequently the increased storage is probably much smaller than the potential value. Houghton and Woodwell (1983) conclude after considering eutrophication and other alterations of the environment that there is little evidence for an increased storage of carbon in the ecosystem of the Earth. This picture has later been modified; at least regionally there are likely increases of growth due to release of nutrients (McGuire et al., 1992, 1997; Schimel et al., 1996).

The terrestrial biota seem unable to take up much of the excess CO₂. In fact, a careful assessment of the impact of deforestation and land-use changes indicate that the terrestrial biota has been a considerable source of CO₂ during the past century (Bolin, 1977; Woodwell et al., 1983). A complex effort to deduce mankind’s impact on terrestrial biota using a bookkeeping model based on historical records on land use in all parts of the world (Moore et al., 1981; Houghton et al., 1983; Woodwell et al., 1983) gives the curves in Fig. 11-25. Woodwell et al. (1983) arrive at a carbon release in 1980 of 1.8 to 4.7 Pg C/yr from deforestation, which is comparable to the 5 Pg released from fossil fuels. Freyer and Belacy (1983) constructed a ¹³C/¹²C record from tree-ring studies (Fig. 11-26). Using a global carbon cycle model with box-diffusion model for the oceans and a simple four-box model for soil and land-biota, Peng et al. (1983) make use of this record of δ¹³C changes in the atmosphere to deduce the CO₂ contribution from forest and soils. The CO₂ emissions arrived at for 1980 are about 1.5 Pg C/yr, similar to the minimum values of Woodwell et al. (1983), but the trends during the past century differ significantly (Fig. 11-27). There are numerous indications that the terrestrial biosphere has significant interannual variability that creates variability in the atmospheric CO₂ concentration.

Fig. 11-25 Release of carbon from the biota and soils globally according to various estimates. The fossil fuel flux is from data of Rotty. (Modified with permission from G. M. Woodwell et al. (1983). Global deforestation: Contribution to atmospheric carbon dioxide, Science 222, 1081–1086, AAAS.)

Fig. 11-26 Decade-averaged Δ¹³C data of Northern hemisphere tree ring records from 1750–1979 and 7th-degree polynomial fit of the data. The vertical extension of blocks represents 95% confidence limits of the mean. The open circles give the ¹³C change of –0.65% in atmospheric CO₂ observed from 1956 to 1978 by Keeling et al. (1979). (Adapted from Peng et al., 1983.)

Fig. 11-27 Contrast between the ¹³C/¹²C derived forest-soil CO₂ scenario obtained from Peng et al. (1983) with that based on land use and stored carbon response functions obtained by Houghton et al. (1983). (Reproduced with permission from W. Broecker et al. (1983). A deconvolution of tree ring based δ¹³C record, J. Geophys. Res. 88, 3609–3620, American Geophysical Union.)

The role of carbon dioxide in the Earth’s radiation budget merits this interest in atmospheric CO₂. There are, however, other changes of importance. The atmospheric methane concentration is increasing, probably as a result of increasing cattle populations, rice production, and biomass burning (Crutzen, 1983). Increasing methane concentrations are important because of the role it plays in stratospheric and tropospheric and because it is important to the radiation budget of the world.

As we have seen, civilization is altering the global carbon cycle in several ways. Even though our knowledge of the most relevant processes in the carbon cycle has increased considerably, it remains limited. Figure 11-1 summarizes the carbon cycle as described in this chapter. There are a number of central observations to point out regarding this figure. The amount of fossil fuel still remaining is sufficient to increase the atmospheric CO₂ content many-fold. The amount of carbon stored in soils and standing biomass is small compared to the fossil fuel reserves; it is sometimes argued that the planting of trees could decrease the impact of our fossil fuel releases. Even if we double the standing biomass (an unrealistic vision since most land is needed for food production) the amount of carbon stored will be small compared to the total amount of fossil fuel available. Most of the terrestrial biosphere and soil carbon reservoirs are easily changed on short time scales; even if there can be net storage during a decade (what seems to be the case during the 1990s) this carbon can very rapidly return to the atmosphere. Because the transport of carbon into the deep oceans is a slow process, release of CO₂ to the atmosphere will perturb the atmospheric concentration for several centuries even if emissions cease. We must also note that the airborne fraction observed during the past decades might very well change as a response to climatic change; for example if the ocean surface becomes warmer there will be an increased stability of the water column yielding a slower transport of water the abyss as well as a decreased solubility of carbon dioxide in the water. Both these effects thus make the oceans less prone to taking up the excess CO₂. Revisiting Fig. 11-19 we can also note that the observed perturbations during the past 200 years are extreme compared to the observed variations that have occurred during the past 200000 years; CO₂ has increased from a pre-industrial global-mean value of about 280 ppmv to today’s (December 1998) value of 366 ppmv. The climate system will undoubtedly respond to these dramatic changes in radiative forcing although the details of the response remain uncertain. The use of fossil fuels thus passes a potential climate change problem onwards to coming generations; if the climatic impacts of the enhanced greenhouse effect prove to create severe difficulties for mankind or nature centuries will be required to repair the atmosphere. Despite the uncertainties regarding the climatic impacts (IPCC, 1990, 1992; Kattenberg et al., 1996) of the enhanced greenhouse effect this feature of the carbon cycle remains as a fundamental argument to avoid using fossil fuels whenever possible and actively seeking alternatives for the future.