SCOPE 13 - The Global Carbon Cycle

ABSTRACT

New data on fluctuations in atmospheric CO₂ content in past and present are summarized. The amount of CO₂ produced from fossil fuels since industrialization and from man's modifications of land biota is estimated by the use of carbon isotope techniques.

3.1 INTRODUCTION

Carbon dioxide is a trace gas in the earth's atmosphere which exchanges between various carbon reservoirs, particularly the oceans and the biosphere, and is produced in excess amounts largely due to fuel burning. Consequently, its atmospheric concentration shows temporal, local and regional fluctuations. Since the beginning of industrialization, its atmospheric concentration has increased. The 1974 mean concentration of atmospheric CO₂ was about 330 ppm (Baes et al., 1976), which is equivalent to 2574 x 10¹⁵ g CO₂ or 702.4 x 10¹⁵ g C, assuming 5.14 x 10²¹ g as the mass of the atmosphere and 29 as the mole weight of air (Man's Impact on the Global Environment, 1970). This value is significantly higher than the amount of atmospheric CO₂ in 1860, if the estimate of Bray (1959), that the atmospheric mixing ratio at the time was about 290 ppm (= 617.2 x 10¹⁵ g C), is accepted.

The consumption of CO₂ by photosynthesis on land (expressed in terms of net primary production) is about 120 x 10¹⁵ g dry organic matter/year, which is equivalent to about 54 x 10¹⁵ g C/year (Lieth and Whittaker, 1975). In a steady state, the consumption is balanced by oxidation of recently grown organic carbon in the respiration process. Only about 0.1% of the grown organic carbon within the land and oceanic cycle remains unoxidized, and is deposited to form new fossil carbon which amounts to about 0.07 x 10¹⁵ g C/year (Garrels et al., 1973). This deposition is approximately the same as the present annual average release of CO₂ from volcanoes, fumaroles, and hot springs and amounts to about (0.010.05) x 10¹⁵ g C/year (Baes et al., 1976). The burning of fossil fuels now releases CO₂ to the equivalent of about 5 x 10¹⁵ g C/year (Baes et al., 1976), which is about one-tenth of the natural production, but nearly two orders of magnitude greater than the rate of return to the fossil reservoir. The total reservoir of fossil carbon in forms suitable for exploitation has been estimated to be between 3 x 10¹⁸ g C (Johnson, 1975) and 10 x 10¹⁸ g C (Bolin, 1970). Recently, it has become evident that an additional input of non-fossil excess CO₂ into atmosphere, due to forest cutting, forest burning, soil management practices, etc., is of the same order of magnitude as the input of fossil fuel CO₂. At present, nearly 3 x 10¹⁵ g C/year of the excess CO₂ remains airborne. The missing part disappears to other carbon reservoirs. Based on the airborne fraction of fossil fuel CO₂ and the uncertainty of the input of non-fossil fuel CO₂ into the atmosphere, the net CO₂ uptake of the oceans may be between 2 and 8 x 10¹⁵ g C/year. The net uptake of the excess CO₂ by land biota, due to stimulation of photosynthesis by the enhanced CO₂ partial pressure, is questionable.

3.2 DIURNAL VARIATIONS IN ATMOSPHERIC CO₂

Variations in the atmospheric CO₂ content on land are mainly due to the exchange of CO₂ between vegetation and the atmosphere; a summary has been given, for example, by Lieth (1963) and by Baumgartner (1969). The processes in this exchange are photosynthesis and respiration. The consumption of CO₂ by photosynthesis of plants is largely controlled by light, and no photosynthesis can occur during the night. This consumption of CO₂ by the living plant material is balanced by a corresponding production of CO₂ during respiration of the plants themselves, and from decay of organic material, which occurs mainly in the soil through the activity of bacteria (soil respiration). The release of CO₂ from the soil depends on the type, structure, moisture, and temperature of the soil. The CO₂ concentration in soil air can be 1000 times higher than in air (Enoch and Dasberg, 1971).

Due to these processes, diurnal variations in the atmospheric CO₂ content on ground level will result. Typical measurements have been performed by Keeling (1958, 1961) for different areas. The diurnal range can be as great as 100 ppm. In regions of a fairly dense vegetation cover, the atmospheric CO₂ content increases from about 320 ppm at mid-day to almost 400 ppm during the night. The plots for the CO₂ content and ¹³ C are similar (Figure 3.1). The minimum concentrations and ¹³ C values of 7‰ during the day, however, have been attributed, not to any special effect produced by the vegetation, even though downward CO₂ fluxes exist, but to complete mixing with the free atmosphere. The increase during the night is the result of addition of plant and soil respiration CO₂ with a ¹³ C value in the range (2125)?. The pattern of the diurnal variation depends on the plant cover and the season. Only slight diurnal variations occur during winter and early spring, because of the absence of photosynthesis, which has been demonstrated, for example, by Clarke (1969) in rural air. The variation range becomes progressively smaller with the height of sampling, although the effect is recognizable, under certain conditions, as high as 150 m above ground (Huber, 1952; Chapman et al., 1954). Meteorological parameters can affect the diurnal pattern; some data are available describing the influence of combustion sources (Clarke and Facro, 1966).

Figure 3.1 Diurnal variation in the concentration and carbon isotopic ratio of atmospheric CO₂ in a coastal redwood forest of California, 1819 May 1955, Big Sur St. Pk. (Keeling, 1958. Reproduced by permission of Pergamon Press.)

Several CO₂ gradient measurements, very close to various crop canopies, are known (for references, see e.g. Verma and Rosenberg, 1976). Recently, intensive studies of CO₂ fluxes have been performed in agricultural (Verma and Rosenberg, 1976) and forest regions (Bischof and Odh, 1976), where the strongest sinks for CO₂ exist. The net daily CO₂ flux (in g CO₂ /m² ) downward in an agricultural region (Nebraska, U.S.A.), calculated from the downward daytime and upward nocturnal fluxes, is about 1012 in early June, 1820 in early August (maximum), 6-10 in September, and 15 in early October (Verma and Rosenberg, 1976). Similar studies, without flux calculations, have been published by Spittlehouse and Ripley (1977). Not only downward, but also upward fluxes have their maxima in summer; Woodwell and Dykeman (1966) have found spring and summer respiration rates in a forest to be 2 to 3 times higher than winter rates at the same temperature. 

3.3 SEASONAL AND LATITUDINAL VARIATIONS IN ATMOSPHERIC CO₂

Seasonal variations in the atmospheric CO₂ content, including samples at different altitudes, have been reported by Bischof and others (Bischof, 1960, 1962, 1965, 1970, 1971, 1973; Bischof and Bolin, 1966; Bolin and Bischof, 1970; Bolin and Keeling, 1963; Keeling et al., 1968). Analyses, of troposphere and lower stratosphere air samples, collected on aircraft flights in the northern hemisphere (Bolin and Bischof, 1970), show distinct seasonal variations, decreasing with increasing altitude, with maxima in spring and minima in the late summer (Figure 3.2). The amplitude of the seasonal variation amounts to about 6.5 ppm at 2 km altitude and 3.5 ppm in the uppermost part of the troposphere. The phase shift of the seasonal variation between these two levels is 2530 days. No variations at all, or only small ones, are found in the lower stratosphere, which demonstrates that the vertical exchange of CO₂ is damped by the tropopause. The amplitude of the seasonal variation in the lower stratosphere, at 1112 km altitude, is less than 1 ppm and the phase is delayed at least 1¹/₂ months as compared with the upper troposphere. Smaller space and time variations in tropospheric CO₂ have been reported by Pearman and Garratt (1973) in the southern hemisphere. Other measurements by the same authors (Garratt and Pearman, 1973) confirm these observations for air of oceanic origin, whereas CO₂ of continental (Australian) origin varies considerably with altitude over the first 2 km, related to land surface effects. Diurnal, seasonal and annual variations in atmospheric CO₂, similar to patterns of a nonlocal influenced atmosphere, have been detected even in the industrialized area of New York (Woodwell et al., 1973).

Figure 3:2 Amplitude and phase shift of seasonal variations in atmospheric CO₂ at different altitudes, calculated from direct observations by harmonic analysis (Bolin and Bischof, 1970. Reproduced by permission of the Swedish Geophysical Society.)

The seasonal variations are the result of photosynthesis by land plants in summer, and respiration by land plants and soils throughout the year. They are also, perhaps to a lesser extent, the result of biological activity in surface ocean waters. The variations produced by vegetation are evidently far greater in the northern than in the southern hemisphere (Keeling et al., 1968). The CO₂ concentration varies by 10 ppm on the north coast of Alaska, by 6 ppm over the island of Hawaii (Pales and Keeling, 1965), and only by 1.5 ppm at the South Pole (Brown and Keeling, 1965). Earlier measurements of the atmospheric CO₂ content, as a function of latitude for each calendar month, have been summarized by Bolin and Keeling (1963) and are given in Figure 3.3. The observations have been explained in terms of a model in which there is a source of CO₂ in the tropics, an industrial source in the mid-latitudes of the northern hemisphere and sinks in the polar regions (Figure 3.4). From the natural sources, a net CO₂ transfer into the ocean of about 5.5 x 10¹⁵ g C/year in each hemisphere poleward of about 30^° latitude, and a net release of about 11 x 10¹⁵ g C/year in the tropical regions have been evaluated. The land vegetation north of 45^° N is responsible for a net CO₂ consumption of about 4 x 10¹⁵ g C during the vegetation period in the summer.

Based on relationships between the contents of oxygen, carbon dioxide, and phosphate in Pacific Ocean water, Postma (1964) has estimated that CO₂ escapes from sea-water within a broad band in the equatorial region, between approximately 20^° N and 20^° S. Smaller escape bands at higher latitudes will probably disappear, due to the progressive increase in the total atmospheric CO₂ content. Partial-pressure measurements of CO₂ in the world's major oceans, summarized by Keeling (1968), confirm that the surface waters of the Pacific and Atlantic Oceans in the equatorial belts are supersaturated in CO₂ with respect to air. Besides, seasonal variations of the CO₂ partial pressure in surface ocean waters exist, depending on temperature and nutrients (for references, see e.g. Skirrow, 1975).

Figure 3.3 Smoothed curves of the concentration of atmospheric CO₂, as a function of latitude for each calendar month (Bolin and Keeling, 1963. Reproduced by permission of the American Geophysical Union.)

Figure 3.4 Computed time average sources and sinks for CO₂ as a function of latitude. The units of ppm/year are averaged over the total air column (Bolin and Keeling, 1963. Reproduced by permission of the American Geophysical Society.)

The seasonal variations as a function of latitude and altitude, are summarized by Bolin and Keeling (1963) and Bolin and Bischof (1970); they are consistent with a characteristic vertical exchange time in the troposphere of about one month, and a horizontal exchange time between the northern and southern hemispheres of about one year. It has been pointed out (SCOPE Workshop, Ratzeburg 1977, Group 1 Report) that many more measurements should be carried out on the variability of atmospheric CO₂ in space and time, in order to detect the horizontal and vertical CO₂ transport in detail, and, possibly, to obtain information on the exchange of atmospheric CO₂ between land biota and the oceans.

3.4 LONG-TERM INCREASE IN ATMOSPHERIC CO₂

Diurnal and seasonal variations are superimposed by a long-term increase in the atmospheric CO₂ content, which has already been considered in early investigations in connection with the increasing use of fossil fuels (Callendar, 1958; Bray, 1959; Slocum, 1955). Callendar considered that between 1900 and 1956 an increase in atmospheric CO₂ of about 12% occurred. Detailed knowledge of the trend, however, is lacking because of the absence of reliable atmospheric measurements for that period. Careful observations over the last two decades have established that a progressive increase in the atmospheric CO₂ concentration exists. Pales and Keeling (1965) have shown that over the period 1959 to 1963 the average CO₂ content of air sampled at Mauna Loa Observatory, Hawaii, increased at a rate of about 0.68 ppm/year. Measurements in the troposphere and the lower stratosphere in the northern hemisphere, by Bolin and Bischof (1970), covering the period 1963 to 1968, indicate an annual increase of 0.7 ± 0.1 ppm. Recently, the measurements of the atmospheric CO₂ at Mauna Loa Observatory, Hawaii, and at the South Pole from 1957 to 1971 have been summarized by Keeling et al. (1976a, b) (Figure 1.2, this volume). The data shows a higher and lower seasonal oscillation at Mauna Loa Observatory and at the South Pole, respectively, but nearly the same long-term increase of annual average CO₂ concentrations of 3.1%, from about 315.7 to 325.4 ppm at the South Pole, and of 3.4%, from about 316.1 to 326.8 ppm at Mauna Loa Observatory, over the 195971 period. The rate of increase, however, has not been steady. In the mid-1960s it declined; at the end of the last decade it accelerated to more than 1 ppm/year (see Table 3.3). Additional data for the 197274 period, from Keeling's CO₂ measurements at Mauna Loa Observatory, have been given by Baes et al. (1976), arriving at a CO₂ concentration of 330.7 ppm in 1974.

All CO₂ data are expressed in ppm of CO₂ in dry air, based on the 1974 manometric mole fraction scale, which is approximately 3 ppm higher than the formerly used CO₂ index scale (Keeling et al., 1976a). The conversion to the absolute manometric scale has become necessary, because the response of the commonly used infra-red CO₂ analysers depends on the instrument and the composition of the reference carrier gas (Bischof, 1975; Pearman and Garratt, 1975; Pearman, 1977).

3.5 AMOUNT OF CO₂ PRODUCED FROM FOSSIL FUELS AND CEMENT

It has been commonly assumed that the cause of the long-term CO₂ increase is mainly due to the industrial CO₂ production. Keeling (1973a) has estimated the industrial CO₂ production resulting from the burning of fossil fuels and kilning of limestone from 1860 to 1969. Revised data from 1960 to 1971, including the CO₂ production by flaring of natural gas, is given by Rotty (1973). This data (including that for the 197176 period; after Rotty, 1977) is summarized in Table 3.1. It has been shown graphically (Baes et al., 1976) that the annual industrial CO₂ production increases exponentially, with interruptions only during the periods of the two world wars and the great depression in the early 1930s. The fractions of CO₂ emissions from individual fuels and cement for selected years are calculated in Table 3.2, demonstrating the relative shift of different sources since industrialization. About one-half of the total industrial CO₂ has been produced in the last 20 years. The cumulative CO₂ production for the 1860-1974 period is about 136 x 10¹⁵ g C. This is 22% of the amount of CO₂ in the atmosphere in the late nineteenth century, assuming 290 ppm as the atmospheric mixing ratio at that time. The actual increase of atmospheric CO₂ from 290 to 330 ppm (1974 value) amounts to 13.8%, which means that about 63% of the industrial CO₂ output has remained airborne. In Table 3.3, the airborne fraction has been calculated from the latest direct measurements to a mean of 58%. The variations in the annual values show that the rate of the atmospheric CO₂ increase in both hemispheres is not strictly proportional to the rate of industrial CO₂ production. No systematic trend, however, is observed from 1957 to 1974, whether the airborne fraction is increasing or decreasing. Recently Newell et al. (1978) observed that variations in the airborne fraction are dependent mainly on temperature changes of the tropical Pacific ocean.

Table 3.1  Annual* and cumulative industrial CO₂ production data from 1860 to 1976 (in units of 10¹⁵ g C/year)

Table 3.2Relative fractions* of CO₂ emissions from individual fuels and cement by years (in %)

All industrial production data is based on UN statistics. It has been pointed out (SCOPE Workshop, Ratzeburg 1977, Group 1 Report) that the uncertainty of the 1976 value of 5 x 10¹⁵ g C/year may be between +7 and -3%, because of possibly incorrect data for China, differences between production and consumption data, etc.

Table 3.3 Comparison between annual industrial output and increase of atmospheric CO₂. Calculation of the airborne CO₂ fraction (= ratio of the annual atmospheric CO₂ increase to the annual industrial output)

	Industrial		Atmospheric increase				Airborne
Year	output*		Mauna Loa†		South Pole†		CO2 fraction
	(ppm)		(ppm)		(ppm)
1957	1.10				1.09		:	0.99
1958	1.14				0.93		:	0.82
1959	1.20		0.89		0.82		0.74:	0.68
1960	1.27		0.68		0.72		0.54:	0.57
1961	1.25		0.86		0.65		0.69:	0.52
1962	1.32		0.46		0.61		0.35:	0.46
1963	1.40		0.60		0.61		0.43:	0.44
1964	1.48		0.62		0.62		0.42:	0.42
1965	1.55		0.67		0.67		0.43:	0.43
1966	1.63		0.78		0.74		0.48:	0.45
1967	1.65		0.88		0.84		0.53:	0.51
1968	1.76		1.89		0.98		1.07:	0.56
1969	1.86		1.32		1.13		0.71:	0.61
1970	2.00		1.04		1.32		0.52:	0.66
1971	2.06		1.15				0.56:
1972	2.14		2.19				1.02:
1973	2.27		0.54				0.24:
1957-70	20.60				11.73		:	0.57
1959-73	24.83		14.57				0.59:
							0.58 ±	0.14
*Output data from Table 3.1. 1 x 1015 g C is equivalent to 0.4698 ppm CO2
† The Mauna Loa data are calculated from the annual average values (Keeling et al., 1976a; Baes et al. 1976) as a mean between those for the cited and the next year. The South Pole data are calculated from the values for 1 July (Keeling et al., 1976b) as a mean between those for the cited and the next year.

3.6 AMOUNT OF NON-FOSSIL CO₂ PRODUCED DUE TO MAN'S MODIFICATIONS OF LAND BIOTA AND SOILS

The production of CO₂ from burning of fossil fuels is now estimated at 5 x 101 ⁵ g C/year. Recently, it has become evident that other anthropogenically produced CO₂ is of the same order of magnitude.

Bolin (1977) has estimated that clear-cutting and burning of forests in developing countries can produce an input of CO₂ into the atmosphere of at most 1.5 x 10¹⁵ g C/year, which is probably an overestimate, partly because not all of the living biomass burns, and partly because some of these areas become covered again by vegetation. A transfer in the opposite direction by plantation of new forests may be between 0.2 and 0.4 x 10¹⁵ g C/year. Increased use of wood for industrial purposes (logs, pulp wood, etc.) corresponds to 0.4 x 10¹⁵ g C/year, from which, however, possibly one-half goes into long-lasting structures. Burning of fuel wood may inject CO₂ into the atmosphere at a rate of 0.2-0.4 x 10¹⁵ g C/year. Cultivation of land by draining of bogs and marshes, and transfer of forest land into agricultural land may represent a net flux of about 0.10.5 x 10¹⁵ g C/year. From these rough figures, Bolin (1977) has estimated the total CO₂ net flux to the atmosphere to be (1.0 ± 0.6) x 10¹⁵ g C/year, which is 20% of the present CO₂ production by fossil fuel combustion.

Hampicke (Chapter 7, this volume) arrives at a figure of 1.54.5 x 10¹⁵g C/year.Adams et al. (1977) have concluded that the CO₂ produced from deforestation is essentially equal to the fossil fuel CO₂ production. Higher estimates by Woodwell et al. (1978) amount to net fluxes of 48 x 10¹⁵ g C/year from the terrestrial biomass. All this data is based on statistics. From model interpretation of ¹³C measurements in tree rings, Freyer (1978a) has calculated a present non-fossil CO₂ net flux of (3 ± 2) x 10¹⁵ g C/year, based on an airborne fraction of 58 ± 14% and 36%, respectively, referring to the fossil and total (fossil and non-fossil) CO₂ production. An airborne fraction of 36%, referring to the total net CO₂ production, follows from comparison of the author's ¹³C data and available ¹⁴C measurements in tree rings summarized by Damon et al. (1973).

The accumulated input of CO₂, due to man's modifications of land biota and soils, has been estimated by Bolin (1977) to be (70 ± 30) x 10¹⁵ g C. Hampicke (1977) has calculated an input of 100 x 10¹⁵ g C. From the ¹³C and ¹⁴ C records in tree rings, higher values of 120 x 10¹⁵ g C for the 18501950 period, and lower values of 70 x 10¹⁵ g C for the 18601974 period have been suggested by Stuiver (1978) and Freyer (1978a), respectively. Both Bolin (1977) and Stuiver (1978) have interpreted their non-fossil input data on the assumption of lower preindustrial CO₂ values (of 275 ppm and 260 ppm, respectively) than the commonly accepted one of 290 ppm. Freyer (1978a), on the other hand, arrives in his preliminary model calculations at a preindustrial CO₂ value of 295 ppm. Eriksson (1977) has even deduced from model considerations a preindustrial value of 303 ppm.

In all known models describing the carbon cycle to explain past and predict future levels of atmospheric CO₂ (Bolin and Bischof, 1970; Machta, 1972, 1973; Ekdahl and Keeling, 1973; Bacastow and Keeling, 1973; Keeling, 1973b; Oeschger et al., 1975), the biosphere is considered as a sink of CO₂ because of stimulation of photosynthesis by the enhanced CO₂ content. If, in fact, due to man's activities, the biosphere has been a source of CO₂ rather than a sink, with the same order of magnitude as the fossil fuel sources, the parameters of all models have to be altered. The question, as to whether the ocean, as the only major sink of CO₂, has withdrawn those large quantities of CO₂ which have not been airborne, still remains unresolved.

Table 3.4 Characteristics carbon isotope composition of atmospheric CO₂ in different air types

			[CO2]	[CO2]
	Geographic		minimum	maximum				No. of
Air type	location	Date	(ppm)	(ppm)	I(13C)	M	r	analyses	References
Forest	California,	1955-56	313	410	24.03	5372	0.99	66	Keeling
	Washington,								(1958, 1961)
	Virginia,
	Arizona (U.S.A.)
Mountain	California (U.S.A.)	1955-56	316	320	21.70	4625	0.56	29	Keeling (1958, 1961)
Desert	California,	1956	314	323	9.18	599	0.09	21	Keeling (1961)
	Arizona (U.S.A.)
Marine	Pacific coast (U.S.A.)	1955	310	326	17.95	3473	0.59	16	Keeling (1961)
	Pacific ocean
Continental	Heidelberg	1974-75	333	371	27.77	6678	0.99	15	Esser (1975)
Urban	(West Germany)
Continental	Schauinsland	1975	321	336	22.51	4872	0.94	16	Esser (1975)
non-urban	(West Germany)
Continental	different parts of	1974,	316	510	25.34	5738	0.99	33	Freyer and
non-urban,	North Rhine	1977							Wiesberg (1975)
incl. addition	Westphalia								Freyer (1978c)
of combustion	(West Germany)
gases
Total					-24.89	5640	0.99	196

3.7 CARBON ISOTOPE STUDIES OF ATMOSPHERIC CO₂  

Atmospheric carbon dioxide comprises the carbon isotope species ¹²CO₂, ¹³CO₂, and ¹⁴ CO₂ . The average abundance of the stable isotopes is ¹²C = 98.89% and ¹³C= 1.11%. The radioactive ¹⁴C isotope, which is produced in the upper atmosphere by interactions of cosmic-ray neutrons with nitrogen (¹⁴N(n,p)¹⁴C), forms only some 10^-10 % of the total. In nature the mean isotope composition can be altered by kinetic processes or isotope exchange reactions (for compilation of isotope effects of carbon, see e.g. Degens, 1969; Schwarcz, 1969; Hoefs, 1973). The radioactive ¹⁴C isotope decays (-decay), moreover, with a half-life of about 5700 years.

The accepted unit of stable carbon isotope ratios (¹³C/¹²C) is the ¹³ C value, given in per mil deviation from a defined standard (PDB standard; ¹³C/¹²C = 1123.72 x 10^-5

Figure 3.5 Relation between carbon isotope ratio and concentration of atmospheric CO₂ in different air types from measurements summarized in Table 3.4 (Keeling, 1958, 1961: full squares; Esser, 1975: open circles; Freyer and Wiesberg, 1975, Freyer, 1978c: open squares). All ¹³C measurements have not been corrected for N₂O contamination (Craig and Keeling, 1963), which is at the most in the area of + 0.6‰

 Table 3.5 ¹³C values of industrial CO₂ by sources* and years (in ‰ against PDB) 

	13 C (PDB)
	Mean		Range
Source
Coal	24		19 to 29
Petroleum	27		22 to 32
Natural Gas	40		29 to 51
Limestone	4		1 to 7
Year
1860	24	.0
1900	24	.2
1920	24	.4
1940	25	.1
1950	25	.7
1960	26	.2
1965	26	.7
1970	27	.3
1975	27	.4
*13 C data of sources according to Schwarcz (1969)

Atmospheric CO₂ varies with concentration in its stable carbon isotope ratio. These variations are mainly due to the fact that fossil and non-fossil CO₂ are different in their ¹³C values from atmospheric background CO₂. The relationship between ¹³C values and the reciprocal of CO₂ concentrations ([CO₂] expressed in ppm CO₂ of dry air) can be described, assuming a mixture of two different isotopic CO₂ species, by the following equation (Keeling, 1958):

        ¹³C⁼M(1/[CO₂])+I(¹³C)

where M is an empirical constant. The ordinate section I(¹³C) of this linear equation gives the ¹³ C values of the fossil or non-fossil CO₂ addition to atmosspheric background CO₂. In Table 3.4, the coefficients I(¹³ C) and M have been calculated by the method of least squares, from all available ¹³C measurements of atmospheric CO₂ in different air types. It is apparent from the correlation coefficients r that the above equation fits extremely well the measurements in forest and continental air, in which increasing CO₂ concentrations are caused by non-fossil (respiration) and fossil CO₂, respectively. The obtained I(¹³C) values are in the usual range, with somewhat lower ¹³C content in fossil than in respiration CO₂. The correlation in mountain, desert, and marine air, on the contrary, is low, which may be partly due to the small variations in measured CO₂ concentrations. The least-square fit for the total of measurements is illustrated in Figure 3.5. An example of diurnal variations in CO₂ concentrations and ¹³C values is given in Figure 3.1.

According to Figure 3.5, the present mean ¹³C values of atmospheric CO₂ are in the range of (78)‰ (PDB). The ¹³C values of fossil (industrial) carbon from different sources are given in Table 3.5. The mean ¹³C value of industrial CO₂, calculated from the mean ¹³C values and contributions of sources (according to Table 3.2), has been changing with time; nevertheless, industrial CO₂ is marked, with respect to atmospheric CO₂, by a ¹³C deficit of about (1819)‰. Values of ¹³C of organic carbon from plant species, which are formed by the normal Calvin photosynthetic pathway (see Chapter 8, this volume), are in the same range as in coal (see e.g. Degens, 1969; Schwarcz, 1969; for ¹³C values in wood, see e.g. Freyer and de Silva, 1978). In contrast, other plant species formed by a different C₄ metabolic pathway have ¹³C values in the range of (1019)‰ (PDB). These plant species, mainly tropical grasses which are relatively rich in ¹³C, were first reported by Bender (1971) and Smith and Epstein (1971). They amount, however, at the most to 10-20% of the total land biota (Goudriaan, personal communication). Stuiver (1978) has estimated the C₄ species to only a few per cent. From these facts, it follows that the ¹³C values of fossil (industrial) and non-fossil (biospheric) CO₂ are nearly the same as observed in the I(¹³C) values calculated in Table 3.4.

Figure 3.6 Decrease of atmospheric radiocarbon ¹⁴ C (Suess effect) expressed as percentage deviation from the AD 1890 wood standard, according to a smoothed-trend curve of tree-ring measurements (Damon et al., 1973), theoretical model estimations (Baxter and Walton, 1970), and model analysis of ¹³C tree-ring data on the assumption of a time-constant airborne fraction (= 36%) referred to the total atmospheric CO₂ input (Freyer, 1978a)

Predicted or measured ¹³C variations in atmospheric CO₂ have encouraged some authors to analyse ¹³C variations in tree rings for detection of past atmospheric CO₂ variations. Recently, these measurements have been summarized by Stuiver (1978), who has used his own data and that of Freyer and Wiesberg (1974a, b), and of Rebello and Wagener (1976), for estimations of the past biospheric CO₂ source. Freyer (1978a, b) has found detailed ¹³C measurements in tree rings that the ¹³C shift within the 196074 period fits the expected ¹³C decrease, calculated from the Mauna Loa data of Keeling et al. (1976a) according to Figure 3.5, extremely well. The author has used this coincidence for preliminary calculations of the past atmospheric CO₂ increase, which are evaluated from a ¹³C decrease of about 2‰ within the 18601974 period. The relationship of Figure 3.5 is valid only for short-term CO₂ variations; the question, however, exists as to whether this relationship is applicable to a long-term CO₂ increase.

The ¹³C values of fossil and non-fossil CO₂ can hardly be distinguished. Their ¹⁴C content, however, is completely different. Non-fossil CO₂ has nearly the same ¹⁴C content as atmospheric CO₂, whereas in fossil CO₂ the ¹⁴C isotope is decayed. The dilution of the atmospheric ¹⁴CO₂ content by fossil CO₂ (the so-called Suess effect) was first proposed and measured by Suess (1955). All available ¹⁴C measurements performed in tree rings have been summarized by Damon et al. (1973). The proposed theoretical dilution has been calculated by Baxter and Walton (1970). Recently, Freyer (1978a) has used this ¹⁴C data, in connection with his preliminary past atmospheric CO₂ concentrations, for calculations of the airborne CO₂ fraction referred to the total fossil and non-fossil CO₂ input. The resulting function, which is evaluated to an airborne fraction of 36%, together with the data of the former authors, is given in Figure 3.6. From critical analyses of ¹⁴C tree-ring measurements, Keeling (1973b) has derived a somewhat lower Suess effect of 2.8% for 1954 as those shown in Figure 3.6. Oeschger et al. (1975) in their model calculations even assume a Suess effect of as low as 2.2% for 1954.

From the mid-1950s the ¹⁴ C record can no longer be used because of increased ¹⁴C levels, by about a factor of 2, due to nuclear-bomb tests (for the record of the bomb peak ¹⁴C in tree rings, see e.g. Cain and Suess, 1976). This ¹⁴C increase has been utilized, however, as tracer of the airsea and inter-sea exchange of CO₂ in different studies. A summary has been given recently by Skirrow (1975).

It has been pointed out (e.g. World Meteorological Organization, 1977; SCOPE Workshop, Ratzeburg 1977, Group 1 Report) that past atmospheric CO₂ variations can be recognized only by isotopic studies of fixed atmospheric carbon dioxide in the form of tree rings.

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