SCOPE 29 - The Greenhouse Effect, Climatic Change, and Ecosystems, Chapter 3, How Much CO2 Will Remain in the Atmosphere?

The atmospheric concentration of carbon dioxide is rising and is now 25% higher than during the first half of the last century, i.e. before the rapid expansion of agriculture and industry began. Fossil fuel combustion and changing land use (deforestation and expanding agriculture) have caused large emissions of CO₂ into the atmosphere. Since the continued rise of atmospheric CO₂ concentrations might lead to changes of the global climate, it is essential to be able to project future concentrations which may occur due to alternative future emission scenarios. Atmospheric CO₂ is exchanging with terrestrial vegetation and soils and with the oceans. For this reason the observed increase during the last hundred years is less than half of the total emissions during this same period. This chapter on the carbon cycle will serve as a basis for assessing likely future levels of atmospheric CO₂ concentrations.

During the last few decades considerable progress has been made in improving our understanding of the key features of the global carbon cycle. Rather detailed quantitative models have been developed. Many overviews of the carbon cycle have been published, e.g. Keeling (1973), Revelle and Munk (1977), Bolin et al. (1979), Broecker et al. (1980), Peng et al. (1983). It is not the purpose of this chapter to present an extensive synthesis of past research, but we shall restrict ourselves to those aspects of the global carbon cycle that are of importance for the determination of likely future atmospheric CO₂ concentrations.

3.2 CARBON IN NATURE

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. The biogeochemical cycle of carbon is necessarily very complex, since it includes all life forms on Earth as well as the inorganic transfers between and within the different carbon reservoirs. Being the most complex element cycle in nature, it has been most extensively studied and is better understood than other element cycles.

Figure 3.1 is a schematic diagram of the global carbon cycle, showing the major carbon reservoirs with which we will be concerned, i.e. the atmosphere, the terrestrial biosphere including soils, the hydrosphere, including marine life, and the lithosphere. The transfers between these reservoirs as well as some processes in their interior are also shown schematically. They will be analysed in more detail in the following.

Figure 3.1 Schematic diagram of the global carbon cycle. Approximate reservoir sizes are given in units of 10¹⁵ g C and fluxes between reservoirs in units of 10¹⁵ g C yr^-l, valid as of the early 1980s. Data from compilation by Bolin (1983) modified in accordance with most recent data (cf also Table 3.2). Although single numbers usually are given, there is considerable uncertainty about both reservoir sizes and fluxes. A complete balance is not achieved as later discussed in Section 3.7

We note first that the characteristic time scales which govern the carbon cycle range from millions of years for processes controlled by the movements in the Earth's crust, to days or even seconds for processes related to air-sea exchange and photosynthesis. We will limit the following discussion to time scales less than 20,000-30,000 years and in this time perspective we may disregard lithospheric processes except those of erosion, chemical denudation and sedimentation. The former two are controlled by the partial pressure of CO₂ in soil water, they release carbon into the atmosphere-biosphere- hydrosphere system and are balanced by sedimentation of carbon at the bottom of the sea (Broecker, 1973). The pre-industrial transfer of this kind was probably quite small, less than 0.5 10¹⁵ g C yr^-1, but may in spite of this be important in the analysis of changes from glacial to interglacial periods. Relative to the more rapid changes which have occurred during the last two centuries, however, these transfer processes are of secondary importance and accordingly we may largely limit our analysis to atmosphere-biosphere- hydrosphere interactions including the change of carbon content of soil due to changing land use.

There are more than a million known carbon compounds, thousands of which are vital to biological processes. Carbon atoms have nine possible oxidation states ranging from + IV to -IV. The most common state is that of complete oxidation, i.e. +IV, in CO₂ and CO₃^-2 (carbonate). The former constitutes more than 99% of the carbon in the atmosphere. About 97% of the carbon in the oceans is in the form of dissolved carbonate (H₂CO_3(aq), HCO₃_(aq)^-1 and CO_3(aq), and in the lithosphere carbonate exists as minerals (CaCO₃(s), CaMg(CO₃)², FeCO₃). In oxidation state + II, we find CO, a trace gas in the atmosphere, which is rather quickly oxidized to CO₂. Neutral carbon is present in the lithosphere in small quantities as graphite and diamond and in soil as charcoal. Assimilation of carbon by photosynthesis creates reduced carbon (CnH_2nO_n) which is present as biota, as dead organic matter in the soil and in the top layers of the sediments, as coal, oil and gas reserves at greater depths, and as highly dispersed reduced carbon in the lithosphere. Some gaseous compounds that contain reduced carbon (CH_x, particularly CH₄, i.e. methane) find their way into the atmosphere by further reduction due to anaerobic processes. Although there are thus several different gaseous carbon compounds formed by bacterial decomposition, we need only consider CO₂ in the present context, since the oxidation of these other gases proceeds rather quickly. Since methane is another greenhouse gas, the concentration of which also is changing, we need to analyse its budget in the atmosphere, which is done in Chapter 4. In the oceans there is a considerable amount of carbon in the form of dissolved organic carbon. The processes of oxidation of these compounds into carbonate ions are poorly known.

There are three carbon isotopes (from a total of seven) that are of importance in nature. Two are stable, ¹²C and ¹³C, one is radioactive, ¹⁴C, with a half-life of 5730 years.

The amount of ¹³C is expressed by the permille deviation (¹³C) of the ratio ¹³C/¹²C for the sample from a universally accepted standard (cf Craig, 1957b; Stuiver and Polach, 1977).

The abundance of ¹⁴C (¹⁴C) is expressed in terms of the deviation (in ‰) of the activity of the sample from that of the standard (National Bureau of Standards, normalized to ¹³C = -19‰), and corrected for radioactive decay since 1950. In geosciences the concept ¹⁴C is used and defined as follows. The ¹⁴C-atoms are subject to fractionation in processes of chemical reaction and transfer, due to the fact that a molecule containing ¹⁴C is heavier than one containing ¹³C or ¹²C. Since the weight difference between ¹⁴C and ¹²Cis twice that between ¹³C and ¹²Cthe fractionation of ¹⁴C is approximately twice that of ¹³C. By introducing a correction to the measured ¹⁴C value, which is twice the ¹³C fractionation, the ¹⁴C and ¹²C fields in nature to a first approximation can be compared without the need for considering the different effects of fractionation of ¹⁴C and ¹²C. Concentrations are therefore usually expressed in terms of ¹⁴C (see Stuiver and Polach, 1977; Wigley and Mueller, 1981).

The importance of the different carbon isotopes as observed in nature is related to the fact that the rates of transfer of carbon compounds and the equilibria of chemical reactions are dependent on the carbon isotope they contain. Accordingly, the distributions of the stable isotopes ¹²C and ¹³C in nature differ. The distribution of ¹⁴C in addition depends on the formation of ¹⁴C due to nuclear reactions between neutrons (formed by cosmic radiation) and nitrogen atoms in the atmosphere on one hand, and radioactive decay on the other. The different distributions of these three isotopes provide important information on key characteristics of the carbon cycle.

3.3 CARBON IN THE ATMOSPHERE

Accurate measurements of atmospheric carbon dioxide were begun by Keeling at Mauna Loa in 1957 (cf Bacastow and Keeling, 1981). This record as well as that from the South Pole are invaluable pieces of geophysical information that reveal several important features of the carbon cycle (Figure 3.2). The average atmospheric CO₂ concentration in 1984 was 343 ± 1 ppmv. Several other series of regular measurements have been begun since then. They confirm in principle the annual cycle of the atmospheric concentrations and the gradual increase with time as shown in Figure 3.2 but provide in addition information on the global variations of these features (cf Pearman and Hyson, 1980). We conclude from analysis of these records that the annual variations are primarily due to the regular variations of terrestrial photosynthesis, to a minor degree to the annual variations of sea surface temperature, which influence the solubility of CO₂ in sea water and thirdly to annual variations of photosynthesis in the sea. The steady increase of atmospheric CO₂ in the atmosphere is slightly larger in the Northern Hemisphere than in the Southern one, presumably due to the fact that the net emissions caused by human activities are located primarily in the Northern Hemisphere (see Keeling and Heimann, 1985). In addition there are small interannual variations, which are associated with variations of the general circulation of the atmosphere, e.g. the Southern Oscillation and the related variations of the equatorial ocean currents in the Pacific (El Niño). These variations of atmospheric CO₂ reflect features of the air-sea exchange of CO₂ which are of interest in the analysis of the global carbon cycle. Their quantitative interpretation is, however, uncertain. In the validation of models for the global carbon cycle the regular increase of atmospheric CO₂ as observed during the last 25 years is of fundamental importance.

Earlier measurements of atmospheric CO₂ (since the middle of the last century) were usually rather inaccurate and samples were not collected with necessary care and adequate consideration of representativeness. Wigley (1983) has concluded that the most likely value about 1870 was 270 ± 15 ppmv, primarily based on data from the Southern Hemisphere. Siegenthaler (1984) on the other hand points out that a careful selection of Northern Hemispbere data is more trustworthy and considers the most likely value in the 1880s to have been 285-290 ppmv. The uncertainty of these values is, however, still considerable.

Measurements of atmospheric concentrations of CO₂ have been extended about 30,000 years back in time by the analysis of air trapped in glacier ice (Delmas et al., 1980; Neftel et al., 1982). The mean concentration during the Holocene was about 270 ppmv, but values as low as about 200 ppmv have been recorded towards the end of the last glaciation. It has recently been possible to cover also the period 1750-1960 with such measurements (Neftel et al., 1985). Figure 3.3 shows that the values determined for samples from the 1950s agree well with the Mauna Loa data (cf Figure 3.2), while concentrations during 1750-1800 seem to have been about 280 ppmv, starting to rise slowly soon thereafter. Similar analyses by Raynaud and Barnola (1985) show systematically somewhat lower values and also slowly decreasing concentration from late medieval times until an increase due to man began about 250 years ago. For a more detailed discussion of previous work on this problem reference is made to WMO (1983). We shall here adopt the most likely value for the atmospheric CO₂ concentration to have been 275 ± 10 ppmv before the expansion of agricultural activities and the industrial revolution during the 19th century.

Figure 3.2 Concentration of atmospheric CO₂ at Mauna Loa Observatory, Hawaii. Dots indicate monthly averages determined from continuous from measurements. Based on data reported by Bacastow and Keeling (1981), supplemented by data from recent years supplied by personal communication

Figure 3.3 Atmospheric CO₂ concentrations measured in glacier ice formed during the last 200 years (Neftel et al., 1985)

The first measurements of the ¹³C-isotope in the atmosphere were made by Keeling in 1956 and similar measurements were repeated in 1978 (cf Keeling et al., 1979). The ¹³C abundance in atmospheric CO₂, ¹³C, was -7.0‰ in 1956 and -7.65‰ in 1978. The change during this period is shown by a dashed-dotted line in Figure 3.4.

Variations of ¹³C of atmospherjc CO₂ in the past can be inferred from measurements of ¹³C in wood from tree rings, which have been dated by using dendrochronology (see Figure 3.4 and Freyer, 1979; Freyer and Belacy, 1983; Stuiver et al., 1984). Isotopic fractionation occurs in the process of photosynthesis and the further transformation of the primary carbon compounds into cellulose (cf Francey and Farquhar, 1982; Farquhar et al., 1982).

Figure 3.4 Changes of ¹³C in tree rings and of atmospheric CO₂ relative to preindustrial conditions (1800-1850). The data points and squares and the continuous and dashed curves show measurements by Freyer (1979) using tree samples (see also Peng et al. 1983). The histograms are measurements on trees according to Stuiver et al. (1985), where the one drawn by solid lines shows results from trees on open sites. The dash-dotted line gives the change in the atmosphere 1956-1978 according to Keeling et al. (1979)

The ¹³C fractionation in the sequence of events is about 19‰ (for C₃ plants) resulting in ¹³C values for wood of about -26‰. If we assume that the fractionation is independent of the ¹³C value of CO₂ in the ambient air from which carbon is extracted, the observed change as a function of time can be taken as a measure of ¹³C changes of atmospheric CO₂. The data are, however, quite uncertain because of the influence of other environmental factors on the fractionation process, e.g. stress (Francey and Farquhar, 1982). By careful selection of samples we may, however, assume that the change of ¹³C in wood during the last few hundred years reflects a corresponding change of ¹³C in atmospheric CO₂. Recently ¹³C measurements of CO₂ trapped in glacier ice have also been reported (Friedli et al., 1984). These data show smaller changes during the last 200 years than most of the data from tree ring analyses (cf Figure 3.4). On the basis of the data available today the decrease of ¹³C in atmospheric CO₂ during the last 200 years seems to have been 1.0-1.5‰.

The observed changes are primarily due to low ¹³C values (-24 to -27‰) for the emissions of CO₂ into the atmosphere by deforestation, changing land use and by fossil fuel combustion but may also reflect natural variations of the carbon cycle. Fossil fuels have on the average the same ¹³C concentrations as wood, since they were formed from organic material buried in the ground. Although the measured ¹³C values for atmospheric CO₂ are uncertain, they are of importance for the calibration of global carbon cycle models as will be discussed in Section 3.6.4.

The amount of the ¹⁴C isotope on Earth depends on an approximate balance between the formation of ¹⁴C by cosmic radiation and radioactive decay. The quasi-steady global carbon cycle before the agricultural and industrial revolutions presumably maintained an approximately constant partitioning of ¹⁴C between the different carbon reservoirs in nature. The amount of ¹⁴C in the atmosphere at that time, as well as changes since then, can be used for analysis of the mechanisms that govern the global carbon cycle.

In the scale adopted for ¹⁴C (see Section 3.2.3) the value for atmospheric CO₂ in 1954 was close to 0 ‰, i.e. before any significant changes had been caused by the injections due to nuclear bomb testing, which had begun in 1952. Variations of ¹⁴C before that time can be determined by analysis of wood samples from tree rings. Careful measurements have been presented by Stuiver and Quay (1981) as shown in Figure 3.5. A marked decrease has apparently occurred since early last century amounting to approximately 25‰. It must be due primarily to the emission of ¹⁴C-free fossil CO₂, which has diluted the pre-industrial ¹⁴C content in atmospheric CO₂. Significant variations, of the order of 10‰, are also present in the record shown in Figure 3.5 and similarly during previous centuries. We do not understand adequately the reasons for their occurrence. In the later analysis we shall only make use of the general decrease observed since early last century.

Figure 3.5 Atmospheric D¹⁴C values derived from tree rings between 1820 and 1954. Single-year determinations are given, except for the 1890-1915 interval. The vertical bars denote one standard deviation. ¹⁴C levels during the period 1895- 1915 probably give an upper limit only. For details see Stuiver and Quay (1981). (The declining curve shows the model calculations by Peng et al. (1983); see further Section 3.6.4)

Since the first nuclear bomb tests in 1952 and 1954 very marked changes of the ¹⁴C values for atmospheric CO₂ have been observed. Measurements primarily by Nydal and Lövseth (1983) are displayed in Figure 3.6 and reveal the large injections of ¹⁴C in 1958 due to US Pacific tests and in 1961-1962 from Soviet tests. Since then very limited injections have been made. Initially most of the radioactive debris is transferred into the stratosphere. Since the exchange time between the stratosphere and the troposphere is several years, the declining concentrations in the troposphere from 1965 due to transfer from the atmosphere into the terrestrial biosphere by photosynthesis and into the oceans due to air-sea exchange are delayed by inflow from above. Obviously the observations shown in Figure 3.6 represent important data for testing models of the carbon cycle.

The mixing of tropospheric air is rather rapid. The westerlies at middle latitudes in the two hemispheres circle the Earth on the average in about a month, vertical overturning between ground level and the tropopause (at 12 to 16 km elevation) also takes about a month, north-south mixing within a hemisphere is accomplished in about three months and effective exchange between the two hemispheres takes about a year. In the present context we are concerned with processes of change over periods of several years, decades and centuries. We may therefore assume that the troposphere at any time is well mixed. The approximate validity of this assumption is borne out by the fact that the annual latitudinal averages of the atmospheric CO₂ concentration differ by merely 1.5-2.0 ppmv between high northerly and high southerly latitudes. The concentration in the Northern Hemisphere is larger than that of the Southern Hemisphere. Since this difference has been enhanced during the last few decades with increasing fossil fuel combustion, it seems likely that it is primarily due to the fact that about 90% of the present emissions from fossil fuel combustion take place in the Northern Hemisphere. The observed north-south gradient is in general accord with the rates of horizontal mixing of tropospheric air as deduced by other means. Although it may be necessary to consider the seasonal variations of the atmospheric CO₂ concentrations to account in more detail for the air-sea exchange, terrestrial photosynthesis and soil respiration, their inclusion into a global carbon cycle model is not crucial for our understanding of its long-term behaviour and for projecting likely future atmospheric CO₂ concentrations as a result of given emission scenarios.

Figure 3.6 Direct measurements of atmospheric ¹⁴C (surface data) during the period 1954 to 1981(upper set). Data 1954-1962 as compiled by Tans (1981) and 1962-1981 according to Nydal and Lövseth (1983). Data from the ocean surface (lower set) are from a few sites only and not representative for the oceans as a whole, see Figures 3.10-3.11

The exchange between the stratosphere and the troposphere is considerably slower than the transfer within the troposphere. Accordingly the seasonal variations of atmospheric CO₂ decrease rapidly above the tropopause. The upward trend as observed in the troposphere (see Figure 3.2) is considerably delayed in the stratosphere. Measurements by Bischof et al.(1980) reveal CO₂ concentrations about 7 ppmv lower at 36 km elevation than at tropopause level (at about 15 km). This is equivalent to a mixing time of 5-8 years between these two levels. In a detailed analysis of the increase of atmospheric CO₂ due to net emissions at the Earth's surface this delay should be accounted for. Since the observed lag is changing only slowly with time and since the storage capacity of the stratosphere is only about 15% of that of the troposphere, we may in the present context safely disregard this delayed transfer of CO₂ into the stratosphere.

When attempting to model the changes of ¹⁴C in the atmosphere during and after the injections due to nuclear bomb testing, account must be taken, however, of the fact that a major part was emitted into the stratosphere. A more detailed analysis of this transfer has been given by Machta (1972). In the present context stratosphere-troposphere transfer is not of prime concern.

3.4 AIR-SEA EXCHANGE

During pre-industrial quasi-steady state conditions more than 90% of ¹⁴C on Earth was present in sea water and bottom sediments (the latter containing merely a few per cent). An approximate balance was maintained between the transfer of ¹⁴C from the atmosphere to the sea and radioactive decay within the sea. By measuring the difference of ¹⁴C between atmospheric CO₂ and CO₂ dissolved in the surface layer of the sea, the global average of the gross exchange of CO₂ between the atmosphere and the sea can be determined (cf review by Bolin et al., 1981). The decrease of atmospheric ¹⁴C concentrations and increase of ¹⁴C in ocean surface water since the time of nuclear testing offers another possibility to determine the rate of gaseous exchange (Stuiver, 1980). Peng et al.(1979) have estimated the rate of gaseous exchange between the atmosphere and the sea by measuring the disequilibrium between 22b_Ra and 222_Rn due to the evasion of 222_Rn into the atmosphere. On the basis of these three methods the mean rate of gross exchange of CO₂ between the atmosphere and the sea at an atmospheric CO₂ concentration of 300 ppmv has been determined to be 18 ± 5 moles m^-2 yr^-l. This implies a mean residence time for CO₂ in the atmosphere before transfer into the sea of 8.5 ± 2 years.

Gas exchange across the air-sea interface varies across the ocean surface particularly depending on winds and waves. Since we do not know adequately the relative role of the physical processes of importance for the exchange, it has not been possible to determine the magnitude of these variations. However, the global CO₂ exchange between the atmosphere and the sea can be deduced reasonably well with global carbon cycle models calibrated against the global changes that have taken place in the past.

When CO₂ dissolves in sea water the molecule undergoes hydration reactions forming H₂CO_3(aq), which in turn dissociates into H + , HCO₃^- and CO₃^2-.For a detailed account of the chemical reactions and equilibria that establish themselves reference is made to Keeling (1973), Takahashi el al. (1980) and Baes (1982). The carbonate system is defined by total carbon or dissolved inorganic carbon (C = DIC); total borate (B); alkalinity (Alk = A), which describes the acid neutralizing capacity; acidity, pH; the partial pressure, P_CO₂ which in equilibrium with the atmosphere is equal to the atmospheric CO₂ pressure. For our present purpose we may consider B = const, the magnitude of which is well known. We can then deduce any two of the quantities that characterize the carbonate system, if the other two are known. The two usually chosen to describe the system are DIC and A. For the following discussion it is important to keep in mind that, if CO₂ is transferred to sea water, alkalinity remains unchanged, while on the other hand, the formation and decomposition of inorganic and organic compounds change both DIC and alkalinity, A.

(i) The solubility of CO₂ in sea water, and accordingly total carbon in equilibrium with a given atmospheric CO₂ concentration, is temperature dependent. The functional relationship is given in Figure 3.7.
(ii) The CO₂ exchange between gas phase and solution is buffered, the 'buffer' factor,, also called the 'Revelle' factor (Revelle and Suess, 1957), being given by

where indicates a finite change of the variable concerned. The variations of in the range of the key variables DIC and alkalinity observed in the ocean are shown in Figure 3.8.

Figure 3.7 CO₂ concentration in sea water (ppmv) as function of dissolved inorganic carbon (DIC) and temperature (assuming 35‰ salinity and 2.35 meq kg^-1 alkalinity (Holmen, 1985)

Figure 3.8 The buffer factor of sea water (at temperature of + 15 °C and salinity 35‰) as function of dissolved inorganic carbon (DIC) and alkalinity (A). For present concentrations in surface water, DIC = 2.05 mmol kg^-1, A = 2.30 meq kg^-1, = 10.6 (Holmén, 1985)

We note that the solubility and the buffer factor increase with decreasing temperature. Since the atmospheric CO₂ partial pressure does not change much from pole to equator, in the mean CO₂ is transferred from the atmosphere to the sea at high latitudes during winter and in the opposite direction at low latitudes, although there are significant deviations from this pattern due to the fact that upwelling also brings CO₂-rich water from deeper layers to the surface. The buffer factor is of the order of 10 and increases with increasing values for DIC. This implies that P_CO2 is sensitive to quite small changes of the amount of DIC in the water. The change of the atmospheric CO₂ concentration by about 25%, which has occurred during the last 100 years, has been associated with a change of DIC in the surface waters by merely 2-2.5% to maintain equilibrium. The storage capacity of the ocean for the excess atmospheric CO₂ is reduced by a factor

10, as compared with what might be expected at first sight when comparing reservoir sizes as shown in Figure 3.1. Exchange equilibrium between the atmosphere and the sea is established about ten times more quickly for total carbon than for the ¹³C and ¹⁴C isotopes.

3.5 CARBON IN THE SEA

As was shown in Figure 3.1, the oceans contain more than 50 times as much carbon in the form of DIC (38000 10¹⁵ g) as found in the atmosphere in the form of CO₂ (727 10¹⁵ g = 343 ppmv) in 1983. In addition significant amounts of dissolved organic carbon are present in the sea (cf below). The vertical distribution of DIC is not homogeneous, but concentrations are higher in the deep sea than in the surface layers (Figure 3.9). There is also a systematic change from rather low deep sea values in the Arctic Sea, to higher concentrations in the Atlantic Ocean, still higher values in the Antarctic Ocean and in the Indian Ocean and maximum values in the Pacific Ocean.

The vertical distribution of alkalinity is rather similar to that of DIC (Takahashi et al., 1981). The range of variations is, however, considerably smaller (about 30% of that of DIC) (see Figure 3.9).

It is interesting to note that the surface concentrations of DIC would be about 15% higher if the oceans were well mixed, which in turn would imply an atmospheric CO₂ concentration of about 700 ppmv. The maintenance of the vertical gradients of DIC (as well as alkalinity) in the oceans is crucial for the present atmospheric CO₂ concentrations, see further Section 3.5.2.

Marine life is almost exclusively restricted to the surface layers with intense photosynthesis in the photic zone and bacterial decomposition also taking place primarily in the top 100 m of the sea. Some dead organic matter largely in the form of faecal pellets, and so called macroflocs (Honjo, 1980), probably only about 10% of the primary production, reach deeper layers and perhaps 1% is deposited on the ocean floor. The total primary production in the sea is about 40 10¹⁵ g C yr^-1 (de Vooys, 1979) but the rate of photosynthesis per unit area has large variations from more than 0.5 9 C m^-2 day^-1 in areas of intense up-welling to less than 10% of this value in the desert regions of the ocean which are characterized by down-welling and lack of nutrients.

Figure 3.9 The mean vertical distribution of (a) alkalinity and (b) total dissolved inorganic carbon (DIC) in five regions of the world oceans. NA = North Atlantic, SA = South Atlantic, AA = Antarctic region (south of 45 OS), SP = South Pacific Ocean and NP = North Pacific Ocean. From Takahashi et al. (1981)

Photosynthesis is dependent on nutrients being available. Wherever light is adequate the nutrients are quickly used up. In particular, lack of nitrogen and phosphorus often limits the rate of primary production. At high latitudes, however, particularly in the Antarctic Ocean, the presence of rather high concentrations of both nitrogen and phosphorus in the surface waters clearly indicates that some other environmental factor, probably light, limits primary production (cf Knox and McElroy, 1984; Sarmiento and Toggweiler, 1984).

Primary production, both the formation of inorganic and organic compounds, obviously reduces the amount of DIC by direct uptake. The alkalinity on the other hand is affected differently. For each µmol of carbon that is used in the formation of organic tissue, alkalinity is increased by about 0.16 µeq, while it is decreased by 2 µeq if the carbon is used for CaCO₃ formation. The differences between the spatial distributions of DIC and alkalinity therefore implicitly contain information on the relative magnitudes of the formation and decomposition or dissolution of organic and inorganic particulate matter in the sea. The distribution of DIC as shown in Figure 3.9 may be interpreted to a first approximation as a quasi-steady state, but undoubtedly the increasing concentration of atmospheric CO₂ has induced a net CO₂ flux into the oceans, which in turn must have modified the pre-industrial distribution of DIC at upper levels in the sea. We shall later determine by indirect means how much the distribution of DIC in the oceans may have changed during the last 100 years.

The total amount of dissolved organic carbon (DOC) in the sea has been deduced from rather few measurements, and a value of about 1000 10¹⁵ g C is usually quoted (Williams, 1975). An unknown portion of this carbon pool may be of terrestrial origin. Gorshkov (1982) has proposed that a considerable amount of dissolved organic carbon is produced as excretion from zoo-plankton and that this process is enhanced when the CO₂ partial pressure in sea water increases. No observations to support this hypothesis have been presented and it is unlikely to occur.

Figure 3.10 Vertical distribution of ¹⁴C in the Atlantic Ocean (expressed in of ¹⁴C units,‰) along a section in the western basin. The values shown are for natural conditions, i.e. prior to influx of bomb-produced ¹⁴C. The thick dashed line shows the depth to which significant amounts of bomb ¹⁴C penetrated at the time of the GEOSECS survey in 1973. The analysis above this line is due to Broecker and Peng (1982) (data from Broecker et al., 1960 and Stuiver and Ostlund, 1980)

Figure 3.11 The increase of ¹⁴C in the western basin of the Altlantic Ocean (in ¹⁴C units, ‰) from the time of the first nuclear bomb tests in the middle of the 1950s until the time of the GEOSECS survey in 1973 (based on data from Broecker et al., 1960 and Stuiver and Östlund, 1980)

The distribution of ¹⁴C in dissolved inorganic carbon has been measured in all oceans during the GEOSECS expeditions 1972-1978. Figure 3.10 is an attempt to reconstruct the most probable pre-bomb distribution in the western basin of the North Atlantic. The GEOSECS data (Stuiver and Ostlund, 1980) have been used at the depths which bomb-produced tritium had not yet reached at that time (cf Figure 3.12), while the distribution at upper layers is based on measurements in 1957 by Broecker et al. (1960), cf Broecker and Peng (1982). The penetration of bomb-produced ¹⁴C during the period 1957-1973 can be determined as shown in Figure 3.11.

The time course of ¹⁴C in the surface layers of the oceans based on direct measurements can be deduced approximately from the data shown in the lower part of the graph in Figure 3.6. Measurements have also been made by using carbonate deposition in corals, which can be accurately dated (Druffel and Suess, 1983). Maximum ¹⁴C values seem to have been reached early in the 1970s. These variations should also be reproduced in efforts to model the carbon cycle and its change.

A limited number of analyses of ¹⁴C in dissolved organic carbon (DOC) in the sea, mostly from deep-water samples (Williams, 1975), are available. Considerably lower ¹⁴C values are found,

300 to

350‰, equivalent to an age of 3000-4000 years, which is the basis for the view that DOC primarily consists of refractory material. The easily degradable compounds (e.g. sugars, proteins) are quickly consumed in the surface layers by zoo- plankton and serve as an important energy source. We estimate that the turnover (oxidation) of DOC below the surface mixed layer is 0.2-0.4 10¹⁵ g C yr^-1 , which is about 5% of the total amount of reduced carbon (particulate and dissolved organic carbon) which is oxidized in these deeper layers of the oceans.

About 0.5 10¹⁵ g C yr^-1 is deposited on the ocean floor (Broecker and Takahashi, 1977), some of which is organic carbon and some CaCO₃. Organic carbon is the main energy source for organisms at the sea floor and only a small part is buried in organic form in the sediments, except in the coastal zone or on the continental shelves. In some limited regions (e.g. parts of the Baltic Sea) the oxygen content of the bottom water may be depleted, the rate of oxidation decreased and significant amounts of organic carbon buried. Regions of anoxic conditions have increased due to coastal pollution and the amount of organic matter withdrawn from the rapid turnover within the sea has probably increased in recent years. Estimates of the magnitude of these changes are not yet reliable, although some attempts to assess this sink have been made (Walsh et al., 1981).

Ocean water is supersaturated with respect to CaCO₃ above the surface of saturation, the lysocline, which is found at about 4000 m depth in the Atlantic Ocean and at merely about 1000 m in the Pacific Ocean. No appreciable dissolution of CaCO₃ takes place above the lysocline while dissolution reduces the net accumulation at greater depths and prevents it totally below the carbonate compensation depth. Since stirring of the sediments by bottom-living organisms (bioturbation) extends about 10 cm into sediment, an appreciable amount of carbon (

5,00010¹⁵ g C) in the form of CaCO₃ is in slow exchange with inorganic carbon in sea water, primarily at the depth of the lysocline (Broecker and Takahashi, 1977).

There are some measurements of ¹⁴C in ocean sediments (cf Broecker and Takahashi, 1977) showing a rather rapid decrease with depth, which fact represents a valuable measure of accumulation rate. This rate has changed significantly since the last glaciation, which fact should be considered in the analysis of possible changes of the carbon cycle that may have occurred in association with climatic variations. We also note that the total ¹⁴C inventory of the sediments is small in comparison with the atmosphere, the biosphere and the oceans, which permits us to restrict our theoretical analysis of the carbon cycle to these latter reservoirs.

Due to the CO₂-buffering (see Section 3.4.2) the change of DIC in sea water by CO₂ uptake, required to maintain equilibrium with an increasing atmospheric CO₂ concentration, is markedly reduced and a quasi-equilibrium between atmospheric CO₂ and sea water is established rapidly. The rate of turnover of the ocean primarily determines its role in the global carbon cycle.

The ocean surface layers are rather well mixed down to the upper boundary of the thermocline layer, i.e. down to a depth of about 75 m between about 45° N and 45° S (cf Bathen, 1972). Further polewards wintertime cooling creates mixing to considerably greater depths, which in limited areas and during short periods of time extends all the way to the bottom as is the case in the Greenland Sea and in the Weddel Sea. Furthermore, quasihorizontal large scale mixing brings cold surface water equatorwards into the thermocline layer at depths between about 100 and 1000 m along the density (isopycnic) surfaces from the regions of the major ocean currents at latitudes 45-55°, the Gulf Stream in the North Atlantic, the Kuroshio in the North pacific and the circumpolar Antarctic current. Vertical mixing across the isopycnic surfaces in the thermocline layer also takes place, but is restricted because of the prevailing stable stratification. Both processes are presumably of importance for the transfer of carbon in the sea.

The rate with which ocean surface water is mixed into deeper layers of the ocean was poorly known until both radioactive and stable tracers could be used for more precise estimates. The penetration of bomb-produced tritium into the thermocline region of the Atlantic and Indian Oceans has been analysed by Broecker et al. (1980) using estimates of tritium transfer from the atmosphere to the sea by Weiss and Roether (1980). From 1958-1962, when intense nuclear bomb testing took place, until 1972-1974, when the (GEOSECS) geochemical survey was undertaken, large amounts of tritium invaded the oceans. During this period of 10-15 years the average penetration depth (the total tritium inventory per unit area divided by the surface concentration) between 45º N and 45º S was 350-550 m, except in the equatorial upwelling region, where it was merely about 200 m. In polar regions, where mixing to great depth takes place, the invasion of tritium is much larger and gives important information on the rates of transfer as shown in Figure 3.12 (Östlund et al., 1976). The Transient Tracer Ocean Program (TTO) in 1982 reveals a further substantial advance of tritium-rich water downwards and equatorwards. Similar information on the characteristics of deep water formation in the North Atlantic has been obtained by analysis of chlorofluorocarbons in sea water (Bullister and Weiss, 1982). Since their gradual increase in the atmosphere is about the same over the entire globe, the source function for transfer from the atmosphere to the sea is much better known than that for tritium. Still, a quantitative interpretation of what these data mean with regard to the penetration of excess CO₂ into the deeper layer of the ocean is not yet possible because of inadequate data coverage.

Another more direct way of determining the CO₂penetration into the sea has been proposed by Brewer (1978). Water at the sea surface equilibrates with atmospheric CO₂ within about a year (disregarding seasonal variations). The amount of DIC established in the surface waters in this way is carried along as this water moves to deeper layers, but usually also increases in course of time because of decomposition and dissolution of detritus settling from the ocean surface layer. This latter increase can be computed, however , by considering the simultaneous increase of nutrients and alkalinity. No accurate determinations of the likely atmospheric CO₂ concentrations at the time of the deep water formation can be made in this way, but Brewer (1978) estimates that the DIC concentrations in the deep sea correspond to P_CO₂ values at the time of deep water formation between 240 and 280 ppmv. A series of similar computations was also presented by Chen (1982). All these results are, however, uncertain. It has not been possible to estimate the total CO₂ uptake by the sea since pre-industrial times.

As has been previously emphasized, the quasi-steady state distribution of DIC in the oceans represents an approximate balance between downward transfer due to the detritus flux and upward transfer by mixing and upwelling from deeper layers with greater DIC concentrations. In the discussion above we have considered the transfer of excess CO₂ into the deep sea being brought about by a decrease of the transfer upwards by mixing because of the CO₂-enriched ocean surface layers, but have simultaneously assumed that the detritus flux downward remains unchanged. The justification has been the fact that the primary production in the ocean surface layer is usually limited by lack of nutrients. It should be noted, however, that this is not necessarily so in the major upwelling areas on the south side of the Antarctic Circumpolar current in a latitude belt 55-60º S as has recently been emphasized by Knox and McElroy (1984), Sarmiento and Toggweiler (1984) and Siegenthaler and Wenk (1984). This circumstance indicates that there are other limiting factors for phytoplankton growth at these latitudes, e.g. incident radiation associated with the extension of sea ice to quite northerly latitudes during the austral spring and early summer. Conditions may have been quite different during other climatic regimes. Accordingly the carbon cycle may also have been different. Knox and McElroy (1984) have analysed some of these alternative possibilities and shown that they may have been characterized by different atmospheric CO₂ concentrations in balance with a lower DIC concentration in the surface layers as compared with present conditions. In the present context we note this particular feature of the oceanic component of the carbon cycle as a possible mechanism for enhanced downward flux of carbon, if a reduction of the extension of sea ice would occur as a result of warming at high latitudes. This represents a negative feedback between the carbon cycle and the climate system, i.e. increased atmospheric temperatures would enhance the CO₂ uptake by the oceans and reduce the rate of increase of atmospheric CO₂. A more precise assessment of the significance of this possibility has not been made. We note also that the lower CO₂ concentrations during the last ice age with more extensive sea ice coverage are opposite to what would be expected from the interactions described above.

Figure 3.12 Distribution of tritium in the western North Atlantic according to Östlund et al. (1976), in tritium units (defined as (T/H)^-18). Prebomb concentrations were below one tritium unit in surface layers and below 0.1 in the deep sea

It is commonly assumed in analyses of the likely future atmospheric CO₂ concentrations that the general circulation of the oceans will not change. However, it is clear that changes have occurred in the past. If a significant warming of the atmosphere were induced by the enhanced atmospheric CO₂ concentration, some change of the ocean circulation would most likely occur. Particularly the intermittent formation of deep water might be reduced, which in turn would probably decrease the role of the oceans for uptake of excess CO₂ from the atmosphere. Since we do not know much about likely changes of ocean circulation in response to climatic change, although some model experiments have been carried out, it does not seem meaningful to analyse further the possible implications with regard to the global carbon cycle. They may, however, be significant (see also Bolin, 1981, and Broecker, 1981).

A modification of the carbon circulation in the sea might also occur, if the total amount of nutrients in the sea would increase. Assuming that photosynthesis still would be limited primarily by nutrients in the surface layers their concentrations would still be low and accordingly the vertical nutrient gradient enhanced between the surface layers and the deep sea. The vertical mixing of the sea would then transfer more nutrients to the sea surface, an increased photosynthesis would be maintained and associated with increased detritus flux to deeper layers. The vertical gradient of DIC would also be larger, the surface concentrations accordingly decreased and similarly the CO₂ partial pressure.

Broecker (1981) has analysed possible mechanisms of this kind (especially emphasizing the role of phosphorus) that may have been of importance during the transition from glacial to interglacial conditions. Their possible occurrence might explain the rather low atmospheric CO₂ concentrations that seem to have prevailed towards the end of the glacial epoch and the high concentrations during the warm period around 8000 BP (cf Section 3.3.1). Although the possible series of events proposed offers an interesting hypothesis, further analyses of data are necessary to show that the observed changes of atmospheric CO₂ during the last 20,000 years can be explained in this way. Nevertheless, the works by Broecker (1981), Knox and McElroy (1984), Sarmiento and Toggweiler (1984) and Siegenthaler and Wenk (1984) show that complex secondary effects may result, which in turn call for care when we later estimate likely changes l00 years into the future as a result of man-made emissions of CO₂ (see Section 3.8.4).

Both carbon and phosphorus are carried to the sea by rivers (cf Figure 3.1). Schlesinger and Melack (1981) and others have shown that the carbon flux is about 0.5 10¹⁵ g C^-1 but may be increasing due to intensified agriculture and forestry. Furthermore, in the light of the possible interdependence of the carbon and phosphorus cycles we estimate below the importance of man's increasing use of phosphorus as fertilizers in agriculture and forestry and as detergents in households and industry. The annual mining of phosphorus was about 13 10¹² g P in 1972 (Pierrou, 1976) and has presumably increased since then. At most 50% reaches the aquatic systems (lakes, rivers and the sea), probably significantly less, since part of the phosphorus used to fertilize farm land and forests is immobilized in the soils. It has been well established, however, that eutrophication of lakes and the coastal zones of the oceans has occurred because of nutrient release. Changes in the open sea cannot be seen because of the great variability of marine primary production. For an approximate calculation of the possible increased primary production in the aquatic systems we assume that 20-50% of the phosphorus input by man is used in the primary production of natural systems and that the organic matter produced in this way becomes part of the carbon cycle in the sea or is buried in the sediments. If we accept a Redfield mass-ratio C: P of 40 (Redfield, 1958), a withdrawal of 0.1-0.3 10¹⁵ g C yr^-1 from the atmosphere and the surface layers of the aquatic systems could result. This corresponds to 2-6% of the annual release of carbon to the atmosphere due to fossil fuel combustion at the time of the phosphorus mining estimate. This is a comparatively small but not insignificant sink that may have to be considered. Independent verification of its role is, however, desirable. Some of this carbon withdrawal might be accomplished by transfer of detrital matter to the deep sea along the continental slope as proposed by Walsh et al. (1981).

We obviously need a quantitative model to describe adequately how the distribution of carbon in the sea changes, when the atmospheric CO₂ changes due to anthropogenic emissions of CO₂ into the atmosphere. It is important that we are able to explain in this way past changes to develop confidence in projections for the future. Dynamical general circulation models of the oceans with proper inclusion of biological and chemical processes will in a long-term perspective represent the most satisfactory approach to such an analysis of the role of the oceans in the carbon cycle. So far few results of this kind are available. We shall therefore have to employ simple geochemical models which, however, are most useful in providing some important constraints on the rates of exchange and turnover of carbon in the sea.

We shall limit ourselves to a brief account of the historical development and primarily be concerned with the present status of the work in this field. Reference is made to Keeling (1973), Oeschger et al. (1975), Björkström (1979), Bolin et al. (1981), Bacastow and Börkström (1981), Hoffert et al. (1981), Killough and Emanuel (1981), Oeschger and Heimann (1983), Siegenthaler (1983), Peng et al. (1983), Emanuel et al. (1984) for more detailed presentations of the models developed.

The simplest model advanced is the two-box model consisting of a well- mixed surface layer and a well-mixed deep sea reservoir. Photosynthesis, detritus formation and dissolution are all assumed not to change and can therefore be ignored in the analysis. Such a model was first proposed by Craig (1957a), further developed by Bolin and Eriksson (1959) and analysed in detail by Keeling (1973). Although it still may be useful for analyses of the characteristic role of the sea in the carbon cycle, it is by now clear that this simple model cannot be used for quantitative projections (Bacastow and Björkström, 1981; Bolin et al., 1983). It is for example necessary to prescribe the thickness of the surface layer to be 400-600 m, as compared with an observed value of about 75 m, to obtain response characteristics of this model similar to those of more detailed models. It is thus not possible to identify model parameters with observed features of the real ocean.

Oeschger et al. (1975) proposed a box-diffusion model, which describes the world ocean in terms of a well-mixed surface layer (about 75 m deep) and a deep sea reservoir, within which vertical transfer is accomplished by eddy diffusion (see Figure 3.13a). The rate of air-sea exchange is given in accordance with measurements (Section 3.4.1) and the eddy diffusivity is assigned a value of 1.3 cm2 sec^-1, which yields a vertical distribution of ¹⁴C in approximate agreement with the observed global average (cf Section 3.5.3). Peng et al.(1983) have assigned a larger value, 1.6 cm² sec^-l, for the eddy diffusivity in the layer between 75 and 700 m (i.e. in the thermocline region) to reproduce the transfer in this layer as revealed by the penetration of tritium during the period 1957-1973. A reduction to 0.5 cm² sec^-1 below 700 m is then necessary to maintain balance, since also deep water formation (with a rate of 50 10⁶ m³ S^-¹ = 1.6 10¹⁵ g yr^-1) is considered in approximate accordance with observed conditions (see Section 3.5.5). This version of the model has been used by Peng et al. (1983) in their analysis of the global carbon cycle. A similar model has also been used by Goudriaan and Ketner (1984). We shall return to a more detailed analysis of its characteristics in Sections 3.7.1 and 3.7.2. Similar work has also been presented by Soviet scientists (cf Buettner and Zacharova, 1983).

Figure 3.13 Schematic diagram showing the basic characteristics of (a) the box- diffusion model with an upper well-mixed layer and the thermocline layer and the deep sea into which transfer exclusively takes place by vertical diffusion (Oeschger et al., 1975); (b) the box-diffusion model with polar outcrop in which transfer into the thermocline layer and the deep sea also is accomplished by quasi-horizontal (isopycnic) exchange from the regions of cold surface water in polar regions (Siegenthaler, 1983 )

An extension of this model to include the role of intermediate and deep water formation at high latitudes has been made by Siegenthaler (1983). The deep sea is described with the aid of a series of isopycnic layers that reach the ocean surface in polar regions within an area that constitutes about 10% of the total sea surface (cf Figure 3.13b). Both cross-isopycnic transfer as described in the box-diffusion model with the aid of vertical eddy diffusivity and quasi-horizontal transfer along the isopycnic surface between the sea surface at high latitudes and deeper layers of the ocean further equatorwards are thereby accounted for. As previously, the model is calibrated by prescribing appropriate values for eddy diffusivity and air-sea exchange to account for the steady distribution of ¹⁴C. To maximize the role of isopycnic exchange, horizontal mixing is assumed to be instantaneous whereby the ventilation of the deep sea becomes limited by the size of the area of deep water formation at high latitudes and the rate of air-sea exchange. Vertical (cross-isopycnic) turbulent transfer is accordingly decreased, the eddy diffusivity becoming 0.7 cm2 sec^-l. The model is still not able to reproduce the rather rapid penetration of bomb-produced ¹⁴C (Figure 3.11) into the thermocline region (cf Section 3.5.5), nor the observed increase of atmospheric CO₂ in the atmosphere as a result of known fossil fuel emissions (cf Section 3.2). Good agreement with reality is obtained by increasing the vertical eddy diffusivity to 1.7-2.5 cm² sec^-l, as obtained from a calibration using bomb-produced ¹⁴C. The observed vertical steady state distribution of ¹⁴C at greater depth is then not reproduced.

The models described above are quasi-linear. Their response to emissions depends on model characteristics (rates of air-sea exchange, vertical diffusion etc.) and the initial conditions assumed at the beginning of a time integration. The latter are, however, the result of past emissions. Because of the linearity of the system we may consider future changes as the sum of the response of the system at equilibrium to a given emission scenario and the decline of the initial state towards the new equilibrium state that would prevail without any future emissions (Oeschger and Heimann, 1983). The latter adjustment has been called 'the declining base line.

We first compute the model response to exponentially increasing emissions. A reasonable scenario is then one with an e-folding time of 22.5 years (cf Chapter 2). For the two-box model we assume the well-mixed surface layer to be 75 m (cf Section 3.5.5), the ¹⁴C value for the mixed layer to be -50‰ (cf Figure 3.10) and for the deep sea -160‰ (the approximate average for the deep sea in the Atlantic and Pacific Oceans) to determine the rate of water exchange between the mixed layer and the deep sea. We use the model parameters for the box-diffusion model as described above. Let us define the airborne fraction () of the emissions into the atmosphere to be the ratio between the increase in the atmosphere and the emissions (cf Section 3.7.3) and compute its asymptotic value when the models are perturbed by exponentially increasing emissions. The following values for are obtained (cf Bacastow and Björkström, 1981; Siegenthaler, 1983).

Two-Box model	0.80
Box-diffusion model, original version	0.67
Box-diffusion model, with polar outcrop	0.61
Box-diffusion model, with polar outcrop
and enhanced vertical eddy diffusivity	0.53

The differences noted are very significant, but depend markedly on the e-folding time chosen. Assuming rather an e-folding time of 50 years reduces for the two-box model to 0.75 and similarly for the other models. These response characteristics are brought out by some recent computations by Svenningsson (1985), although his results also depend on the fact that the initial conditions imposed do not correspond to a steady state. The box-diffusion model due to Siegenthaler (1983) is used with a vertical diffusivity necessary to account for the uptake of bomb-produced ¹⁴C. The model was integrated from a pre-industrial state until 1980 using estimates of past emissions due to fossil fuel combustion (Chapter 2) to provide initial conditions for integration into the future. Upper and lower bounds for future emissions as specified in Chapter 2 were prescribed and also an intermediate scenario. Although these emission scenarios were not exponential and the airborne fraction therefore changed slowly, the mean changes during the period 1980-2050 illustrate in principle the dependence of the airborne fraction on the rate of emissions, Table 3.1. The results are also compared with a similar computation by Siegenthaler (1983) using a scenario of rapidly increasing emissions.

It is obvious that the airborne fraction is markedly dependent on the rate with which the global carbon cycle is being disturbed. Although the model is simple, the general characteristics of the response as shown in Table 3.1 probably are valid.

The box-diffusion model of the oceans is undoubtedly useful for general analysis of the role of the oceans in the global carbon cycle. By consideration of the changes of the ¹³C isotopes as observed during the last few hundred years quantitative validation of the choice of model parameters can be done (cf Section 3.8.2). Nevertheless, it is desirable to make better use of the rich data base that describes the state and circulation of the oceans, i.e. measurements of temperature, salinity and currents. The increasing amount of data on the distribution of biochemical tracers in the sea (cf Broecker and Peng, 1982) should of course also be used systematically. Two approaches are being pursued to develop more detailed models, which can be carefully compared with available data.

Table 3.1 Airborne fraction of emissions when forcing the global carbon cycle using an exponential CO₂emission, Siegenthaler (1983), (1), and with selected emission scenarios during the period 1980 to 2050 (Svenningsson, 1985), (2)-(4 )

A general circulation model of the ocean developed on the basis of dynamical principles (Hasselmann, 1982) has been used for a first simulation of the transfer of carbon and ¹⁴C (Maier-Reimer, 1984). More development is, however, necessary to ascertain that the ocean circulation models describe the real ocean adequately and to include biological processes.

Bolin et al. (1983) have approached the problem of modelling the ocean within the context of the global carbon cycle by asking the inverse question: What steady state patterns of ocean circulation, turbulent transfer , primary productivity, decomposition of organic detrital matter and dissolution of biogenic carbonates are required to explain the observed quasi-steady distributions of temperature, salinity, total carbon (DIC), alkalinity, ¹⁴C, oxygen and phosphorus? In a first attempt a 12-box model of the oceans was employed, and realistic patterns of the transfer parameters were obtained. Verification against the transient changes that have occurred in recent years showed, however, that the spatial resolution still was inadequate to describe these satisfactorily. An analysis of the response characteristics of the model by using exponentially increasing emissions (e-folding time 22.5 years) as discussed above yielded a value for the airborne fraction = 0.74. This result further emphasizes that simple box models are inadequate for a more precise analysis of the role of the oceans in the carbon cycle.

Finally, it is of interest to determine the sensitivity of the equilibrium atmospheric CO₂ concentrations to variations of the rate of photosynthesis in the sea (cf Section 3.5.1). Viecelli (1984) has analysed this problem and found that a decrease of the rate of photosynthesis by one per cent would lead to an increase of the equilibrium atmospheric CO₂ concentration by 0.5-2.5%, i.e. 2-7 ppmv, and that the adjustment would lag the change of photosynthesis by merely a few years. The rather wide range of uncertainty could probably be narrowed by a more careful validation of the model against different isotopic data.

3.6 CARBON IN TERRESTRIAL BIOTA AND SOILS

During the last two decades many attempts have been made to determine the amount of carbon in terrestrial vegetation and the annual turnover in the form of gross primary production, respiration and detritus formation. The early survey by Bazilevich et al. (1970) presented estimates of the potential vegetation and primary production. Since some undisturbed grassland and forestland (about 10% of the total land surface) have been converted into farm land, particularly at middle latitudes in the Northern fiemisphere, the biomass given by Bazilevich et al. (1970), 108010¹⁵ g C, represents a considerable overestimate of present conditions. Whittaker and Likens (1975) in a later estimate considered the state of the terrestrial biosphere in about 1950 and did not include standing dead wood. They also used a different classification. Later studies based on more data indicate, however, that also their estimate of carbon in living matter, 827 10¹⁵ g C, most likely is an overestimate. Two studies by Duvigneaud (see Ajtay et al., 1979) and Olson et al. (1983) give more detailed consideration of the patchiness of existing biomes particularly within tropical ecosystems. They both derive a value of 560 10¹⁵ g C for the present (1970) carbon reservoir in the form of living terrestrial phytomass. An even lower value 445 ± 25 10¹⁵ g, has been obtained by Brown and Lugo (1982,1984). They base their classification on the Holdridge (1967) life zone concept, whereby a different method is used to generalize available measurements to estimates of the biomass for whole biomes (see also Section 3.6.2).

It is difficult to compare these estimates because of the different classification systems that have been used. Table 3.2 shows an attempt to interpret the compilations by Ajtay et al. (1979) and Olson et al. (1983) in terms of the classification employed by Whittaker and Likens (1975). Although this kind of projection is approximate, it illustrates very well the difficulties encountered in any analysis of the global distribution of ecosystems.

The biomass of the forest systems has probably been markedly overestimated by Whittaker and Likens (1975), particularly so for tropical forests. It now seems clear that secondary forests contain considerably less carbon than do the natural tropical forests and their area is larger than previously assumed. Many regions which have been considered to be covered by closed

Table 3.2 Area coverage, plant carbon and net primary production for major terrestrial ecosystems according to Whit taker and Likens (1975); (2) Ajtay et al. (1979); (3) Olson et al. (1983). The amount of carbon in soil is also shown following the classification by (2) Ajtay et al. (1979), and according to (4) Schlesinger (1977), based on the classification by Whit taker and Likens (1975)

Data from Whittaker and Likens (1975) have been directly reproduced. The data from Ajtay et al. (1979) 'Mangrove forests' have been included as tropical humid (rain) forest and 'forest plantation' as temperate and boreal forests. The classification used by Olson et al. (1983) deviates from the one used in the table. Their 'interrupted woods' have here been included in 'tropical, temperate or boreal forests' if classified as 'second woods and field mosaic. and 'Tropical savannah and woodland' has been included in 'Savannah' in the present table.

forests should rather be classified as partly closed. In summary, we can conclude that the amount of carbon in biota in tropical forests is 170±70 10¹⁵ g C, compared with 460 10¹⁵ g C given by Whittaker and Likens (1975).

The total amount of plant carbon and the net primary production are almost identical in the compjlations of Ajtay et al. (1979) and Olson et al. (1983), 560 10¹⁵ g C and 60 10¹⁵ g C yr^-1 respectively. Although the areas covered by forests and woodland (items (1) to (5)) differ considerably, both with regard to the distribution between biomes and total size, these two surveys yield almost the same total amounts of plant carbon (45010¹⁵ g C) and total net primary production (2410¹⁵ g C yr^-1 and 2810¹⁵ g C yr^-1), i.e. about 80% and 40-50% respectively of the global values. The average residence time for carbon in forest systems is 16-20 years, but the average age of trees is at least twice as large, since less than half of the net primary production is transformed into cellulose. The average residence time for carbon in plant material outside the forest systems is only about 3 years.

An attempt to analyse in some detail the amount of soil carbon distributed according to the ecosystem classification introduced by Whittaker and Likens (1975) has been given by Schlesinger (1977, 1984) and yields a total inventoryof 1515 10¹⁵ g C. The result is shown in the last column of Table 3.2. A similar analysis has also been given by Ajtay et al. (1979) yielding quite a different distribution between biomes although the total amount of soil carbon, 1636 10¹⁵ g C, is only marginally larger. Post et al. (1983) have based their estimates on Holdridge's (1%7) classification scheme and the integration to obtain a global inventory was obtained with the values shown in Figure 3.14. The result, 1395 10¹⁵ also agrees rather well with the other estimates. Buringh (1984) has approached the problem differently and used a classification scheme based on soil types. The value for the total amount deduced is, however, almost the same: 1477 10¹⁵ g C. The estimates by Bazilevich (1974) 1392 10¹⁵ g C (excluding peat), and particularly by Baes et al. (1976 ), 1080 10¹⁵ g C, are, on the other hand, somewhat lower. The agreement between these different total estimates is, however, adequate for our present purposes. The main uncertainty is due to poor assessments of the peatlands of the world.

Both the assessments given in Table 3.2, and particularly those by Ajtay et al. (1979), indicate slower rates of soil decay in cold climates reflected in larger accumulation of soil carbon (per unit area) in boreal forest and temperate grassland than in tropical ecosystems. It should be emphasized, however, that only a small amount (a few per cent or less) of the detritus received annually by the soil reservoir remains there for any appreciable

Figure 3.14 Contours of soil carbon density plotted in Holdridge's (1967) scheme for world life zone classification. The temperature and precipitation uniquely determine a life zone and associated vegetation (from Post et al., 1983). With knowledge about the area covered by the different vegetation classes the global inventory can be deduced

period of time. Most of the dead organic matter is oxidized into CO₂ within a few years. Schlesinger (1977) has emphasized that in chernozem grassland soil 98% of the litter has a turnover time of merely 5 months, but that the remaining 2% on the average stays in the soil 500-1000 years. This characteristic feature of the process of soil formation is also reflected in the fact that the ¹⁴C-age of soils at middle latitudes is a few hundred years to more than a thousand years.

The rate of decomposition of organic matter when virgin land is claimed for agriculture is, however, quite different. Vitousek (1983) is of the opinion that as much as 50% of the organic carbon in agricultural soil in North America may have been lost by oxidation, since it was claimed before or at the turn of the last century. A more detailed assessment of this problem will be given in the following section.

Considerable changes of the terrestrial ecosystems have occurred during the last 200 years due to man's rapidly expanding activities. When forests or grassland were converted into farmland, organic matter, i.e living matter in plants and dead organic matter in humus and soils, was oxidized and emitted as CO₂ into the atmosphere. Some elemental carbon may also have been buried in the soil in the form of charcoal (as residues from forest burning) and in this way withdrawn from the rapid circulation in the carbon cycle (Seiler and Crutzen, 1980).

The most detailed assessment of past and ongoing changes of the terrestrial ecosystems has been made by Moore et al.(1981), Houghton et al.(1983) and Houghton (1984). By using historical records on changing land use a dynamic book-keeping model has been formulated accounting for changes that follow on disturbance, i.e. changes of vegetation and soil and estimates of products removed from the field or the forest. The amounts of carbon in these different components change because of regrowth and decay, which vary with geographical region and vegetation type. The 14 ecosystems on land (cf Whittaker and Likens, 1975, Table 3.2) are considered separately and also their distributions between 10 geographical regions. In total 69 region-specific ecosystems are defined in this way. Six different kinds of disturbances are considered:

Characteristic response curves for carbon in vegetation and in soil for each of these disturbances and for all regions have been determined on the basis of available data regarding ecosystem behaviour. Figure 3.15 shows two examples of changes in response to clearing for agriculture. The model keeps track of area, age and carbon content as a function of time for each disturbed ecosystem based on historical records for the regions concerned. The use of fuel wood is also accounted for. Although computations were begun in 1700, the period until 1860 has been considered as a time of adjustment of the model and has not been used in the following analysis.

The results of this assessment of change are obviously dependent on the initial assumptions of the size of the areas covered by different ecosystems and upon the amounts of carbon per unit area that are assumed to characterize them, the rates and type of disturbances and their change over time following disturbance. The data compiled by Whittaker and Likens (1975) have been used and as we have seen in Section 3.6.1 these probably are overestimates, particularly for the tropics. The results are also sensitive to assumptions of whether virgin or secondary forests are being cut in deforestation. The estimates (Houghton et al., 1983) now seem too large (cf Detwiler et al., 1984). Until recently Soviet forests have been considered to be a net carbon sink. It seems now clear, however, that the opposite may rather be true. Forests at mid-latitudes elsewhere in the Northern Hemisphere, on the other hand, most likely contain more carbon now than earlier this century. A similar analysis has also been carried out by Richards et al.(1981), but was limited to CO₂ release due to conversion of land to agricultural uses. Their value for release of carbon since 1860, 62 10¹⁵ g C, therefore probably is a considerable underestimate.

Figure 3.15 Schematic diagrams of carbon content of living vegetation (upper graphs) and soils following harvest (a) in forests, (b) in forests transferred into farm land which later is abandoned (Moore et al., 1981)

Seiler and Crutzen (1980) have proposed that terrestrial carbon is withdrawn from rapid circulation in the global carbon cycle by the formation of charcoal in the burning of grassland and forests (0.8 ± 0.5 10¹⁵ g C yr^-1 ). This figure probably is a considerable overestimate because of the use of Whit taker and Likens's (1975) estimates of the carbon content in tropical ecosystems. It also seems possible that the amounts of charcoal formed in forest burning are overestimates, since the accumulation in regions of shifting cultivation would have to be considerably larger than observed, if their estimates were correct (cf Schlesinger, 1977).

Figure 3.16 Emissions of carbon to the atmosphere due to deforestation and changing land-useaccording to three different procedures for analysis of past data (from Houghton, 1984; Bolin et al., 1985) The solid line is based on biomass data from Whit taker and Likens 1975); the dotted line is based on tropical biomass derived from timber volumes reported by FAO (1981); the dashed line depends on another scenario for the transfer of forest land and grassland into agriculture

The historical records of changing land use are too uncertain to give a reliable picture of the change during the period for our consideration. Attempts have been made to relate land use changes to population changes (Revelle and Munk, 1977; Houghton et al.1983). Considerable uncertainty still remains. Figure 3.16 shows some patterns of change as deduced by various means. We conclude on the basis of the studies referred to above that the net CO₂ release to the atmosphere during the period 1860 to 1980 totalled (150 ± 50) 10¹⁵ g C and that the release in 1980 was in the range 1.6 ± 0.8 10¹⁵ g C yr^-1 (cf Bolin et al., 1985). These direct assessments will be compared later with results obtained with carbon cycle models.

It should be emphasized that the possible response of photosynthesis and decay in terrestrial ecosystems to increasing atmospheric CO₂ concentrations and emission of pollutants such as SO₂ and NOx, possibly both fertilizing and acidifying the soils, has not been considered in this context. It is likely that such secondary changes are significant but their magnitudes are poorly known (see further Section 3.6.4 and Chapters 9 and 10).

3.6.4 Modelling Changes of Carbon Storage and Isotope Composition in Terrestrial Ecosystems

In order to analyse past changes of atmospheric CO₂ concentrations and to project future changes we need to formulate a dynamic model of the terrestrial ecosystems to be combined with a model for the role of the oceans in the carbon cycle. We wish to consider the anthropogenic impacts as described in the previous section, and we should include the possible enhanced growth due to the increasing CO₂ concentration in the atmosphere. We must also be able to account for the changes of isotopic composition that have occurred.

The change of carbon storage in terrestrial ecosystems as a response to environmental changes, particularly to increasing atmospheric CO₂ concentration, is poorly understood (cf Chapter 10) and only very simple and crude models have been advanced in attempting to determine its importance for past changes of the carbon cycle as observed. Keeling (1973) and later Revelle and Munk (1977) have proposed that the change of the rate of photosynthesis might be put proportional to a power, of the percentage increase of the atmospheric CO₂concentration and also to the amount of synthesizing matter. Further, the rate of plant matter death is usually assumed to be directly proportional to the amount of living matter, the proportionality coefficients being different for photosynthesizing matter (leaves, grass, etc.) and structural matter (wood). They are usually determined from crude estimates of turnover times for these components of the biomass. An increase of the net primary production is then gradually balanced by enhanced plant matter death and similarly decomposition of detrital matter. The total carbon storage increases slowly when atmospheric CO₂ concentrations increase. This approach to model the ecosystem response is not complete, since it ignores the role of important ecosystem characteristics. Although the rate of photosynthesis probably increases when atmospheric CO₂ increases, it does not necessarily follow that carbon storage in the form of biomass would also increase. The latter might to a considerable degree be determined by climate and by soil properties, particularly availability of nutrients. The turnover rate might primarily increase, but less so the biomass. Until more appropriate models of ecosystems have been validated, the inclusion of the CO₂ fertilization effect is hardly justified except in attempting to assess the general implications of such effects (see further Chapters 9 and 10).

Peterson and Melillo (1985) have attempted to estimate what the increase of CO₂ uptake might be as induced by CO₂ and nutrient fertilization. They conclude that at most 5%, i.e. 0.3-0.4 10¹⁵ g C yr^-1, of the net annual release to the atmosphere is being transferred into the terrestrial ecosystems by increased photosynthesis. It is not known if this will lead to increased storage in the long term or not.

As has been emphasized before the distributions of ¹³C and ¹⁴C and their changes due to anthropogenic disturbances give valuable information about the dynamic behaviour of the global carbon cycle. For their interpretation global models are required in which the terrestrial ecosystems are properly described. An early attempt of this kind was made by Machta (1972). He assumed that terrestrial ecosystems could be described by merely two compartments, 'long-term biosphere', containing 1000 10¹⁵ g C and having a characteristic adjustment time of 40 years, and 'short-term biosphere' containing about 60 10¹⁵ g C with a turnover time of 2 years. In the light of our present knowledge this simple model is not adequate. Revelle and Munk (1977) include the biospheric growth factor due to increase of atmospheric CO₂, but retain otherwise the main features of Machta's model.

Peng et al. (1983) use four reservoirs in direct exchange with the atmosphere as shown in Figure 3.17a. The exchange is formulated by first order processes and the mass (M) and characteristic exchange times (t) for the different terrestrial compartments are shown in the figure. As seen the total amount of plant carbon (640 10¹⁵ g C) is somewhat larger than the recent estimates given in Table 3.2, while the turnover times agree well. The soil carbon is considerably less than the assessments by Schlesinger (1977) and the turnover rate of soils does not depict the characteristic features described in Section 3.6.2. The penetration of ¹³C and ¹⁴C into the soil is too rapid in the model with the parameter values proposed.

A dynamically more correct model of the terrestrial ecosystems has been proposed by Emanuel et al. (1984), cf Figure 3.17b. Detritus and soil carbon are formed from plant material and a distinction is made between rapidly overturning detritus and a slow soil reservoir. The sizes and response characteristics of the three plant reservoirs as assumed by Emanuel et al. (1984) are almost identical to those used by Peng et al. (1983), while the model of Emanuel et al. (1984) permits a more realistic response of the uptake of ¹³C and ¹⁴C by the soil. The values chosen in these model experiments imply, however, rather small differences between their general characteristics.

Figure 3.17 Schematic diagrams showing simple models for the terrestrial biosphere according to (a) Peng et al. (1983), (b) Emanuel et al. (1984) and (c) Goudriaan and Ketner (1984). The biomass (in 10¹⁵ g C) and average turnover time for carbon (in years) are shown for the different reservoirs. In the last model average characteristics for the six ecosystems when considered simultaneously are shown

A considerably more elaborate model has been developed by Goudriaan and Ketner (1984 ); cf Figure 3.17c. Their assumptions regarding the main ecosystem structure are similar to those of Emanuel et al. (1984), but are more detailed. They distinguish between six different ecosystems (tropical forest, temperate forest, grassland, agricultural area, human area and tundra/semidesert, each one of them modelled according to the scheme shown in Figure 3.17c). The total amounts of litter, humus and stable humus/charcoal as assumed are quite different from the estimates given in the previous section. The assumption of 28 years average turnover time for humus furthermore represents a quicker response of the soils to external disturbances. Goudriaan and Ketner (1984) finally assume a very significantly enhanced impact on plant growth due to the increasing atmospheric CO₂ concentrations (the integration presented yields a biota uptake that is 2.0 10¹⁵ g C yr^-1 larger in 1980 than without CO₂ enhancement) and similarly a considerable withdrawal of carbon by charcoal formation (0.9 10¹⁵ g C yr^-1 in 1980) which together almost completely prevent an increase of CO₂ in the atmosphere due to biomass burning and changing land use. Data are not available that validate the model in these regards.

In applying models for terrestrial ecosystems such as those outlined above to changes in ¹³C and ¹⁴C isotope distributions it is essential that the fractionation in the assimilation process is dealt with properly. It is different depending on whether diffusion through the stomata or carboxylation is of prime importance in the rate determining process. This in turn is affected by climatic conditions, site characteristics, and varies in the course of the growing season. Peng et al. (1983) discuss in some detail the ¹³C records which are used in validating the model and select trees to obtain a homogeneous set. Stuiver et al. (1984) also emphasize the difficulty in obtaining a reliable data set. In modelling the process it is assumed that the fractionation in the assimilation process is consistent with the 19-20‰ difference observed between ¹³C for atmospheric CO₂ and that for wood. Fractionation of ¹⁴C is assumed to be twice that of ¹³C (cf also Section 3.2.3).

Finally, it should be emphasized that the models that have been described briefly above have not been tested against independent ecosystem data. As a matter of fact it is difficult to see how this could be done. The approach is rather to explore if global models, including a description of the terrestrial ecosystems as outlined, are consistent with data available for validation as described in early sections of this chapter .

3.7 GLOBAL CARBON CYCLE MODELLING

Most early attempts to model the global carbon cycle are inadequate because data on the sizes and response characteristics of the various reservoirs were not determined satisfactorily. Also data on changes of ¹³C and ¹⁴C were rarely used as additional checks on the validity of the treatment of the transfer of total carbon.

Machta (1972) adopted a 2-box model for the oceans and similarly a 2-box model for the terrestrial biota, thereby distinguishing between short-lived and long-lived biota. Only by assuming the surface mixed layer to be 300 m deep was reasonable agreement achieved with the observed increase of atmospheric CO₂ between 1957 and 1970.

Siegenthaler et al.(1978) combined the box-diffusion model (see Section 3.5.6) with a simple one-compartment model for the terrestrial biota. In their analysis they also analysed model predictions of ¹³C and ¹⁴C changes due to anthropogenic disturbances. Stuiver and Quay (1981) modelled the Suess effect, i.e. the decrease of ¹⁴C due to the emission of fossil CO₂, using a similar model. A more detailed analysis was later presented by Peng et al. (1983), in which case the diffusion model for the ocean was modified as described in Section 3.5.6 and a more detailed treatment of the terrestrial ecosystems as outlined in Section 3.6.4 was included.

Emanuel et al.(1984) also pursued the same problem. Although their treatment of the terrestrial ecosystems is somewhat more sophisticated, their model suffers from the fact that the oceans are described by merely two reservoirs. By assuming a rather deep surface mixed layer they, however , arrive at general conclusions similar to those deduced by Peng et al. (1983). The analysis by Goudriaan and Ketner (1984) differs in important respects with regard to the treatment of the terrestrial ecosystems. We shall return to their results after having considered the analyses by the others in some detail. It is important to emphasize that for the time being the following processes are not being considered adequately or not at all.

Peng et al.(1983) in their study begin by attempting to reproduce the ¹⁴C changes in the atmosphere that have been recorded in tree rings (cf Figure 3.5) before bomb-produced ¹⁴C was emitted into the atmosphere (cf also Oeschger et al., 1975). If we assume that the observed decrease of ¹⁴C is due to the emission of ¹⁴C free CO₂ from fossil fuel combustion, we can deduce these with due regard to the exchange with both terrestrial biota, soils and the oceans. The release of CO₂ to the atmosphere by deforestation and expanding agriculture (Section 3.6.3) may be ignored in this context, since ¹⁴C of living biota and soils is only slightly below the atmospheric value and since therefore the ¹⁴C content of the atmosphere is not significantly diluted. The solid curve in Figure 3.5 has been obtained by such model calculations. There is reasonable agreement with observations. We note, however, that significant variations of ¹⁴C during the 19th century are not reproduced (and could not be, because model computations necessarily yield a monotonically decreasing ¹⁴C concentration). The observed decrease in recent decades also seems more rapid than what the model yields. Some of the deviations may be due to variations in the rate of ¹⁴C production by cosmic rays (cf Stuiver and Quay, 1981).

Bomb-produced ¹⁴C emitted to the atmosphere after 1954 raised ¹⁴C for atmospheric CO₂ rapidly (Figure 3.6) and a considerable transfer into the terrestrial biota and the oceans occurred. We may compare the integrated flux to the ocean 1954-1973 as deduced by the model with the increase as observed by the GEOSECS measurements 1972-1974. The observed increase of ¹⁴C in surface water agrees within about 15% with computed values (cf Broecker et al., 1980). We may conclude that the ¹⁴C data are in general agreement with the global carbon cycle model developed by Peng et al. (1983), although the way the global ocean data have been averaged for validation has not been justified.

We may next ask the question: How much carbon must have been emitted into the atmosphere by fossil fuel combustion, deforestation and changing land use with known ¹³C concentrations (cf Section 3.3.2) to explain the observed ¹³C changes since early last century? Before considering this problem, it should be emphasized that in this way we can only determine the net exchange between the atmosphere and the terrestrial biosphere. The question was preliminarily analysed already by Siegenthaler et al. (1978) and Wagener (1978). Later Peng et al.(1983), Emanuel et al.(1984) and Stuiver et al.(1984) have used their somewhat different models to answer this question. Peng et al.(1983) use the ¹³C data given by Freyer (1979) and Freyer and Belacy (1983), which probably show too large changes (cf 3.3.2), and so do Emanuel et al.(1984). Stuiver et al.(1984) on the other hand employ their own data, which by and large agree with the direct measurements reported by Friedli et al.(1984). Figure 3.18 shows the total emissions and also those from forests and soils alone according to Peng et al. (1983), which have been obtained by subtraction of the fossil emissions. Peng et al. (1983) estimate the emissions from forests and soils during the last 120 years to 26010¹⁵ g C, while Emanuel et al.(1984) and Stuiver et al. (1984) in their calculations obtain 230 10¹⁵ g C and 150 10¹⁵ g C respectively, the last result being the most plausible one in the light of the discussion in Section 3.6.3. The Peng et al.(1983) model has the most efficient exchange with the oceans, which means more rapid equalization between the different reservoirs. Larger emissions are therefore needed to explain the observed ¹³C change in the atmosphere. Figure 3.18 further shows that release from deforestation and soils should have reached a maximum at the end of the last century, 2 10¹⁵ g C yr^-1, and then decreased to about 1 10¹⁵ g C yr^-1. Emanuel et al. (1984) do not find such a time course, and it is hardly supported by the direct estimates that were summarized in Section 3.6.3.

Figure 3.18 Emissions of carbon dioxide into the atmosphere due to deforestation and changing land use, derived from tree ring based atmospheric ¹³C concentrations (see Figure 3.4). The result is obtained by deducting the fossil fuel CO₂ input history (also shown) according to Rotty (1981) from the total emissions computed using the carbon cycle model developed by Peng et al.(1983)

Having in this way deduced approximately the total emissions as a function of time, we may finally analyse the past changes of atmospheric CO₂ concentrations that the models predict if subject to such external disturbances. It is useful to impose the constraint on the solution that concentrations in 1957 agree with the Mauna Loa observations, i.e. 315.5 ppmv (cf Section 3.3.1). Peng et al. (1983) deduce CO₂ concentrations early last century to have been 243 ppmv and Emanuel et al.(1984) derive an even lower value (235 ppmv), both well below the most plausible value of 275 ± 10 ppmv (see Section 3.3.1). Also the increase between 1958 and 1979 is more rapid in the models (27 ppmv for Peng et al.(1983)) than the observed value (21 ppmv). Stuiver et al.(1984) do not present a computation of this kind, but it is questionable if agreement with the data would be achieved unless the emissions from forests and soils during recent decades as summarized in Section 3.6.3 were reduced significantly.

The carbon cycle model developed by Goudriaan and Ketner (1984) yields quite different results because of the uptake due to CO₂ fertilization of the terrestrial ecosystems and charcoal formation. In spite of the fact that the emissions due to deforestation and expanding agriculture during the period 1860-1980 are assumed to have been considerably larger than given in Section 3.6.3, the net global decrease during this period is small (totally only 15 10¹⁵ g C while the atmospheric CO₂ concentration only increases from 290 to 339 ppmv). The model has not been tested against ¹³C and ¹⁴C changes in the way Peng et al.(1983) and Emanuel et al.(1984) have done, nor are the assumptions about the response characteristics of the terrestrial ecosystems supported by independent data. Although it is of interest to explore the implications of different carbon cycle models in this manner, the model presented by Goudriaan and Ketner (1984) cannot be used with confidence for projections of future changes of atmospheric CO₂ concentrations.

It is difficult to explain the discrepancies between the different models without rather extensive sensitivity analyses which are not available, although they might be explained, if the observed changes of ¹³C in the atmosphere during the last 120 years are overestimates of the real changes. It should be emphasized, however, that no detailed verification of the carbon cycle models has been made. They have rather been tested with regard to changes of integral properties as revealed by the temporal changes in the atmosphere and the well-mixed surface layer of the oceans. The verification of the ocean sub model using basic oceanographic data (cf Section 3.5.6) might clarify the role of the oceans, which obviously would be of great help in trying to resolve the remaining inconsistencies of the present global carbon models, often referred to as the problem of 'the missing sink '. Some maintain that the emissions due to deforestation and changing land use have been considerably overestimated, while others are of the opinion that the processes listed in Section 3.7.1, which mostly have not been included, must not be ignored.

Before a discussion of how to make use of the carbon-cycle models to assess likely future atmospheric CO₂ concentrations as a result of given emission scenarios, it is useful to express past changes in terms of the so-called airborne fraction. A comparison with the projections of future atmospheric concentration presented by Nordhaus and Yohe (1983) then also becomes possible (cf also Section 3.5.6).

First it is important to distinguish clearly between total airborne fraction (), which is the ratio between increase of CO₂ in the atmosphere (CO₂)_a and total emissions to the atmosphere (CO₂)_tot^:

and marginal airborne fraction (am), which has traditionally been defined as the ratio between increase of CO₂ in the atmosphere and emissions of CO₂ due to fossil fuel combustion ( CO₂)_ff:

The latter concept is useful when comparing model computations of the ocean response to emissions (usually a scenario of fossil fuel emissions, cf Section 3.5.6) without the complicating influence of changes of the terrestrial biosphere. The total airborne fraction, however, determines the rate of CO₂ increase in the atmosphere and is useful in predicting likely future CO₂ concentrations in the atmosphere.

Many projections of future atmospheric CO₂ concentrations have been based on simple extrapolations of past changes (cf WMO, 1981; Nordhaus and Yohe, 1983) usually assuming the most likely future value of to be about 50%. We therefore first estimate the value of in the past on the basis of available measurements and choose to do so for the two periods 1860-1980 and 1958-1982 (cf Bolin et al., 1985).

Fossil fuel emissions are well known (Chapter 2) and so are recent changes in atmospheric CO₂ concentrations. We do not know accurately pre-industrial atmospheric concentrations nor the emissions due to deforestation and changing land use. It is important to assess the uncertainty of past values for due to these uncertainties. Figure 3.19 shows the range of values obtained depending on the atmospheric CO₂ concentrations in 1860 and the net emissions from the terrestrial biosphere since then due to deforestation and changing land use. Accepting the ranges to have been 275 ± 10 ppmv and (150 ± 50) 10¹⁵ g C we find = 43⁺¹⁷_-11. Also for the period 1958-1982 the net emissions from forests and soils due to man's impact are uncertain. Figure 3.20 shows the dependence of on the magnitude of these emissions. Accepting a value 1.6 ± 0.8 10¹⁵ g G yr^-1 (cf Section 3.6.3) we obtain = 39⁺⁷_-5. The most plausible estimates are below the commonly accepted value of 50%, although not excluded in the former case.

We may also compute the airborne fraction that the global carbon cycle models yield, in response to the external disturbances as described above. It should be recalled that the models by Peng et al. (1983) and Emanuel et al. (1984) consider the oceans to be the only net sink for the anthropogenic emissions into the atmosphere, which on the other hand is not the case in the model of Goudriaan and Ketner (1984). Already the sensitivity analyses described in Section 3.5.6 show that it is unlikely that the airborne fraction would be less than 50% in the former cases. As a matter of fact the result obtained by Peng et al. (1983) implies = 49% for the period 1860-1980 while that obtained by Emanuel et al. (1984) is 55%. The comparatively small value obtained in the former study means that the modifications of the ocean model by changing the vertical eddy diffusivity and considering deep water formation separately have increased the ocean uptake capacity. Emanuel et al. (1984) have chosen a value for the depth of the mixed layer (

300 m) which is considerably larger than in reality, and which decreases and improves the agreement between model behaviour and observed changes. Goudriaan and Ketner (1984) obtain a value of about 0.3. The reasons for this small value are the assumptions of enhanced growth due to the increasing atmospheric CO₂ concentrations and charcoal formation. As previously pointed out (Section 3.6.3), it is questionable if these processes are dealt with quantitatively in an adequate way.

Figure 3.19 The average airborne fraction of CO₂ emissions into the atmosphere 1860-1980 as dependent on the emissions due to deforestation and changing land use and pre-industrial atmospheric CO₂ concentrations. Fossil fuel emissions are assumed to have been as reported by Rotty (1981)

Figure 3.20 The average airborne fraction 1958-82 as dependent on the emissions due to deforestation and changing land use during this period. Change of atmospheric CO₂ assumed in accordance with Bacastow and Keeling (1981) and fossil fuel emissions as given by Rotty 1981)

3.8 PROJECTIONS OF FUTURE ATMOSPHERIC CO₂ CONCENTRATIONS

It has been common in the past to estimate future atmospheric CO₂ concentrations by simply assuming that the airborne fraction of projected emissions remains constant. Usually a value of 50% has been assumed. On the basis of an assumption that emissions will increase to 13.6 10¹⁵ g C yr^-1 in 2025 the first joint ICSU/UNEP/WMO CO₂ assessment (WMO, 1981) estimated in this way that atmospheric CO₂ concentrations would reach a value between 410 and 490 ppmv in 2025. Net emissions of 50 10¹⁵ g C from the terrestrial ecosystems were assumed also to occur during this period.

A similar approach has been used by Nordhaus and Yohe (1983). It should be noted, however, that their definition of the airborne fraction is different from the one used here because of the inclusion of a seepage factor to account separately for the slow absorption of atmospheric CO₂ into the deep oceans. Furthermore, the values quoted in their paper, 38, 47, and 59% for the low, medium, and high cases respectively, are incorrect and were in reality about 10% higher (personal communication). On the basis of their published graphs showing the total emissions and associated increases of atmospheric CO₂ concentrations for the period 1975-2100 (their Figures 2.3 and 2.4) we compute that the airborne fraction (as defined here), which they have used implicitly during this period, rather is between 55 and 75%, much above what now seems reasonable. Nordhaus and Yohe (1983) have not considered future emissions due to deforestation and changing land use. Further, the airborne fraction depends on the rate of CO₂ emissions into the atmosphere in another way than implied by their formulation of the oceanic uptake. Although their approach is of considerable methodological interest, the results of their computations cannot be used directly for projections of future atmospheric CO₂ concentrations.

It was concluded in Section 3.7.3 that present models for the global carbon cycle are unable to account fully for past changes. Although we thus are not yet able to use such models explicitly for more precise projections of future changes of atmospheric CO₂ concentrations as a result of given emission scenarios, they are useful as a guide in the following discussion. It is important to consider possible reasons for model discrepancies (cf Section 3.7.1). We shall analyse in turn

It is possible that the increase of atmospheric CO₂ in the past has been limited by these (and possibly other) processes. We assess qualitatively their role and whether it is likely that they will increase or decrease in the future.

It is difficult to assess what these processes and their possible changes will mean with regard to future atmospheric CO₂ concentrations. On the basis of the results obtained from carbon cycle modelling and the discussion above we conclude: If emissions increase rapidly, e.g. by about 2% per year (or more), it seems likely that the airborne fraction will increase above its present value of approximately 40% (cf Section 3.5.6 ). For a more modest rate of emission increase, e.g. 1% or less, it seems more plausible that the airborne fraction remains unchanged, while it may decrease significantly if emissions remain constant or decrease. Although these conclusions are approximate and uncertain, we will make use of them in our final projections.

A number of projections of likely future CO₂ concentrations have been made by using the carbon cycle models described above (Budyko, 1972; Keeling and Bacastow, 1977; Siegenthaler and Oeschger, 1978; Laurmann and Spreiter, 1983; Oeschger and Heimann, 1983). Although they represent good first approximations, most of them overestimate changes of atmospheric CO₂ concentrations as a result of likely past emission scenarios. We shall here give a plausible range of the increase of future atmospheric CO₂ concentrations by consideration of these model computations and their deficiencies and also on the basis of simple estimates using the concept of airborne fraction.

Future CO₂ emissions due to fossil fuel combustion were discussed in some detail in Chapter 2, where a 'lower bound' (LB) and an 'upper bound' (UB) scenario were defined (cf Figure 2.10). They were determined on the basis of the large number of scenarios of this kind that have been presented in recent years and in addition subjective judgements of what seems possible in the light of other constraints (political, social, logistic, etc.) that usually have not explicitly been considered in the models used for such projections. We shall adopt these two bounding scenarios for the assessment of future atmospheric CO₂ concentrations. Although it is questionable to extend such projections beyond 2050, we shall do so for later comparison with corresponding analyses by Nordhaus and Yohe (1983). We simply assume that for the UB scenario emissions will continue to increase linearly with unchanged rate, while constant emissions of 2 • 10¹⁵ g C yr^-1 will characterize the LB scenario during the latter part of the 21st century.

We also need some plausible projections of likely future emissions from terrestrial ecosystems. In a long-term perspective it seems clear that they will be of less importance than those due to fossil fuel burning, for the simple reason that these carbon pools are limited. Some further reduction of the tropical forests seems likely, but the total storage of carbon as living matter in these ecosystems is merely 170 ± 80 • 10¹⁵ g C (cf Table 3.1). The biomass of ecosystems at higher latitudes on the other hand is presently not changing much. The further exploitation of forests for timber and pulp may lead to reduction of organic carbon in the soils, but probably not to the same extent as is the case when forest soil is being transformed into farm land.

In the light of (1) past changes of the terrestrial ecosystems due to man's exploitation of land for his needs, (2) (the total amounts of carbon in these systems and (3) the rates of present changes, it seems plausible to assume that an additional amount of the same magnitude may be transferred to the atmosphere in the period 1980-2100 as was emitted before 1980, i.e. approximately 1-2 • 10¹⁵ g C yr^-1 or totally 120-240 • 10¹⁵ g C for this period. As will be seen this assumption is not crucial for our final conclusions. Accordingly we add 2.0 • 10¹⁵ g C yr^-1 to the UB and 1.0 • 10¹⁵ g C yr^-1 to the LB scenario.

We first produce scenarios for future atmospheric CO₂ concentrations by simply applying fixed airborne fractions in the future assuming a value 50% for the UB scenario, while we present two alternatives for the LB scenario, namely 40% and the lower projections obtained by using the Siegenthaler model (cf Section 3.5.6 and Svenningsson, 1985). The computed atmospheric CO₂ concentrations until 2100 are shown in Figure 3.21 (heavy solid lines). It should be emphasized that the buffer factor gradually will increase, when atmospheric CO₂ concentrations increase and so will the airborne fraction. The assumed value of 50% will therefore be too small when CO₂ concentrations reach well above 600 ppmv, i.e. in the UB scenario towards the end of the next century. For comparison we also reproduce in Figure 3.21 the future changes as computed by Nordhaus and Yohe (1983) and show the 95th, 50th and 5th percentiles of the set of scenarios they deduce (dashed lines). See further the legend to Figure 3.21.

Figure 3.21 Scenarios for future atmospheric CO₂ concentrations. UB is based on emissions from fossil fuel combustion according to the upper bound given in Chapter 2, from terrestrial sources being constant at a level of 2 10¹⁵ g C yr^-1 and the airborne fraction of the total emissions being 50%; correspondingly LB is based on the lower bound fossil fuel emissions, terrestrial emissions being 10¹⁵ g C yr^-1 and the airborne fraction 40%. In the case of LB* the assessment of atmospheric CO₂ concentration was based on the carbon cycle model developed by Siegenthaler (1983) with enhanced uptake by the intermediate ocean waters (Svenningsson, 1985). NY 95, 50 and 5 are 95th, 50th and 5th percentiles of the atmospheric CO₂ concentration as given by Nordhaus and Yohe (1983), NY 95^* and NY 5* are the corresponding scenarios if using 50% and 40% airborne fractions respectively rather than the computations presented by the authors. For the year 2025 the previous UNEP/WMO/ICSU assessment is shown (WMO, 1981). Pre-industrial concentration (275 ppmv) and twice that value (550 ppmv) are also shown

We notice that the modified CO₂ concentrations using Nordhaus and Yohe (1983) emission scenarios are considerably lower than those that appeared in their original publication. The range of future CO₂ concentrations deduced on the basis of the UB and LB scenarios are still lower and also below the previous ICSU/UNEP/WMO assessment for the year 2025. Further the LB emissions beyond 2050 (totally 3.0 • 10¹⁵ g C yr^-1) only increase the atmospheric concentrations very slowly to about 370 ppmv in 2100, if a carbon cycle model is used rather than assuming a fixed airborne fraction (Svenningsson, 1985). The UB scenario on the other hand yields 580 ppmv in 2050 and about 900 ppmv in 2100.

A comparison of these simple extrapolations using different airborne fractions and projections with the aid of carbon cycle models reveals that the results depend more on the emission scenarios that are used than the particular response of the natural carbon cycle that forms the basis for the projections. When attempting to assess the consequences of different emission strategies, model computations are indispensable (cf Section 3.8.4). We also need improved models to interpret future changes of the carbon cycle and to improve projections and the design of emission strategies. For the time being we conclude that it seems quite unlikely that doubling of the atmospheric CO₂ concentration would occur before the middle of the next century and it may not even take place before the end of the next century.

Before closing this section it is important to recall briefly the basis for the UB and LB emission scenarios (cf Section 2.5). Although a number of scenarios have appeared that are well above the former one, it was concluded that these seem unlikely because of limited accessibility of coal reserves, lack of readily available water in the mining areas, constraints of terminal development and resource distribution issues and general environmental problems in addition to those directly related to the CO₂ issue. The LB scenario, on the other hand, although technically feasible, requires sustained efforts to reduce energy demands in most sections of society and a gradual expansion of other energy sources (solar, wind, biomass, nuclear). Still lower emission scenarios have been proposed, but seem unrealistic.

It is of interest to attempt to outline the emission strategies that are necessary in order not to exceed certain prescribed atmospheric CO₂ concentrations in the future. The problem may become of particular importance if it becomes possible to ascribe a climatic change to the emissions of CO₂or other greenhouse gases (cf Chapters 4 and 6). To analyse this question it is necessary to employ a carbon cycle model, since we cannot prescribe the airborne fraction of the emissions. Although available carbon cycle models still are deficient, an approximate idea of the necessary constraints on emissions can be obtained by using the model developed by Siegenthaler and Oeschger (1978) and Siegenthaler (1983), cf Svenningsson (1985).

As referred to in the preceding section atmospheric concentrations will not exceed about 400 ppmv in a foreseeable future if the emissions decrease to about 3 10¹⁵ g C yr^-1 during the next 65 years and thereafter are kept constant at that level. On the other hand, emissions according to the UB scenario would yield such high atmospheric CO₂ concentrations by 2020-2030 that unrealistically rapid reductions of the emissions thereafter would be necessary in order not to exceed 550 ppmv later during the century, e.g. a doubling as compared to pre-industrial conditions.

We next design two intermediate emission scenarios for the next 40-50 years: (a) continuation of the present (1973-1983) modest increase by about 1.5% per year and (b) a break of the present trend by reducing the increase to somewhat less than 0.5% per year. This latter scenario is similar to the one developed by Goldemberg (see Chapter 2.4). Different rate development assumptions were tested during the remainder of the next century to identify the effects of various policies on atmospheric CO₂ concentrations. Gas and oil reserves, as known today, were used up to depletion after 2030 modelled by a decreasing part of a logistic function. Coal rise was given to produce a smooth curve of total fossil fuel rise. Two ceilings towards the end of the next century of 430 and 540 ppmv were chosen, i.e. about 60% and 100% above pre-industrial conditions.

Figure 3.22a shows the necessary reductions of fossil energy use for the scenario (a) after 2030 in order not to exceed 540 ppmv, while the 430 ppmv ceiling necessarily will be exceeded. The distribution of the use of oil, gas and coal as a function of time is also given. With the low scenario case (b ) there is considerable freedom as to what path to choose after 2020 even if the ceiling is placed at 430 ppmv (Figure 3.22b). There is even room for a modest expansion of coal utilization after 2020 lasting until late next century to replace the depleted oil and gas reserves. We show also in Figure 3.22b the results of a similar computation by Siegenthaler and Oeschger (1978), in which case a simpler ocean model (Oeschger et al., 1975) was used. The different concentration scenarios are in principle about the same.

Figure 3.22 Development of fossil energy use (thin solid line, left scale) and atmospheric CO₂ concentrations, based on the Siegenthaler (1983) model of the global carbon cycle (heavy solid line, right scale). The short-dashed line shows the energy contribution by coal combustion, dotted line is that due to oil combustion and long-dashed line gas combustion. (a) Comparatively high CO₂ emission scenario until 2030 and thereafter the decline necessary not to exceed atmospheric CO₂ concentrations of 540 ppmv. (b) Low CO₂ emission scenario until 2020 and thereafter one possible emission scenario which yields atmospheric CO₂ concentrations not exceeding 430 ppmv (Svenningsson, 1985). The dash-dotted curve is a similar scenario produced by Siegenthaler and Oeschger (1978) in which case CO₂ concentrations were not permitted to rise by more than 50% above the pre-industrial level ..

3.9 CONCLUSIONS

ACKNOWLEDGEMENT

The preparation of this chapter has benefited greatly by the viewpoints from the participants in the expert group meeting on the carbon cycle and the projection of future concentration of atmospheric CO₂ held in Stockholm, 28 November-2 December, 1983: W.S. Broecker, D. Lal, B. Moore, V. Siegenthaler, and M. Whitfield.

Most valuable and detailed comments on a first draft of this paper have been received from J. Goudriaan, H. Oeschger, U. Siegenthaler, and J.D. Woods.

They have led to some significant modifications and I am grateful for having been able to take advantage of the views and information forwarded.

I am also grateful for numerous suggestions for modifications by: M.I. Budyko, W. Böhme, E. Degens, W. Ellsaesser, H.L. Ferguson, R.M. Gifford, V.A. Gorbachev, V.G. Gorshkov, I.G. Gringof, M.R. Kiangi, D. Lal, H. Landsberg, J.A. Laurmann, A.S. Monin, B. Moore, G. Preining, A. Rebello, G. deQ. Robin, R. Rotty, E. Salati, G. White, M. Whitfield, M.M. Yoshino.

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	3.1 INTRODUCTION
	3.2 CARBON IN NATURE
		3.2.1 Time Scales and Scope of the Treatise
		3.2.2 Key Chemical Compounds and Reactions
		3.2.3 Carbon Isotopes
	3.3 CARBON IN THE ATMOSPHERE
		3.3.1 Atmospheric CO₂
		3.3.2 The ¹³C Content of Atmospheric CO₂
		3.3.3 The ¹⁴C Content of Atmospheric CO₂
		3.3.4 Mixing in the Atmosphere
	3.4 AIR-SEA EXCHANGE
		3.4.1 Rate of Transfer
		3.4.2 Chemical Buffering
	3.5 CARBON IN THE SEA
		3.5.1 Total Carbon and Alkalinity
		3.5.2 Photosynthesis, Decomposition and Dissolution of Biogenic Material
		3.5.3 ¹⁴C in the Sea
		3.5.4 Ocean Sediments
		3.5.5 Transfer Processes Within the Sea
		3.5.6 Modelling the Role of the Oceans in the Carbon Cycle
	3.6 CARBON IN TERRESTRIAL BIOTA AND SOILS
		3.6.1 Carbon in Biota and the Rate of Primary Production
		3.6.2 Carbon in the Soil
		3.6.3 Changes of the Amount of Carbon in Terrestrial Ecosystems
		3.6.4 Modelling Changes of Carbon Storage and Isotope Composition in Terrestrial Ecosystems
	3.7 GLOBAL CARBON CYCLE MODELLING
		3.7.1 Model Features
		3.7.2 Simulation of Past Changes
		3.7.3 The Concept of Airborne Fraction
	3.8 PROJECTIONS OF FUTURE ATMOSPHERIC CO₂ CONCENTRATIONS
		3.8.1 Using the Concept of Airborne Fraction for Extrapolation
		3.8.2 The Use of Carbon Cycle Models
		3.8.3 Estimates of the Range of Future Atmospheric CO₂ Concentrations
		3.8.4 Emission Strategies
	3.9 CONCLUSIONS
	ACKNOWLEDGEMENT
	3.10 REFERENCES

3	How Much CO₂ Will Remain in the Atmosphere ?
	The Carbon Cycle and Projections for the Future
	B. BOLIN


	Emissions		Average	Average
	(10¹⁵ g C yr^-1)		annual increase	airborne
			of emissions (%)	fraction (%)
	1980	2050

(1)			4.4	53
(2)	6.2	20	1.7	45
(3)	6.2	10	0.7	38
(4)	6.2	2	-1.6	21


	Area (10¹² m²)			Plant carbon (10¹⁵g C)			Primary prod. (10¹⁵g C yr^-1)			Detritus, soil (10¹⁵g C)

	(1,4)	(2)	(3)	(1)	(2)	(3)	(1)	(2)	(3)	(2)		(4)

(1) Tropical rain forest	17.0	10.3	12.0	344	193	164	16.8	10.5	9.3	82			288
(2) Tropical seasonal	7.5	4.5	6.0	117	51	38	5.4	3.2	3.3	41
forest
(3) Temperate forest	12.0	7.0	8.2	174	88	65	6.7	4.6	4.9	72		161
(4) Boreal forest	12.0	9.5	11.7	108	96	127	4.3	3.6	5.7	135		247
(5) Woodland,	8.5	4.5	12.8	23	24	57	2.7	2.2	4.6	72		59
shrubland interrupted woods
(6) Savannah	15.0	22.5	24.6	27	66	49	6.1	17.7	10.7	264		63
(7) Temperate grassland	9.0	12.5	6.7	6	9	11	2.4	4.4	2.6	295		170
(8) Tundra, alpine	8.0	9.5	13.6	2	6	13	0.5	0.9	1.8	121		163
(9) Desert, semidesert	18.0	21.0	13.0	6	7	5	0.7	1.3	0.9	168		104
(10) Extreme desert	24.0	24.5	20.4	0	1	0	0.0	0.1	0.5	23		4
(11) Cultivated land	14.0	16.0	15.9	6	3	22	4.1	6.8	12.1	128		111
(12) Swamps, marshes	2.0	2.0	2.5	14	12	7	2.7	3.3	3.6		225	145
and coastal land
(13) Bogs and peatland		1.5	0.4		3	1		0.7	0.2
(14) Lakes and streams	2.0	2.0	3.2	0	0	1	0.4	0.4	0.4	0		0
(15) Human areas		2.0			1			0.2		10

Total	149.0	149.3	151.1	827	560	560	52.8	59.9	60.6	1636		1515

	(CO₂)_a
=
	(CO₂)_tot

	(CO₂)_a
_m=
	(CO₂)_ff