SCOPE 13 - The Global Carbon Cycle

ABSTRACT

The earth's crust contains 65.5 x10²¹ g of C, equivalent to 0.27% of all rocks. One-quarter of this mass is non-carbonate carbon. Both forms of carbon have distinct ¹³ C ‰ values: carbonate-C in the region of 0‰, on the PDB scale, and non-carbonate-C in the region of 25‰ PDB. The original isotopic composition in the mantle must have been approximately 7‰ ¹³C PDB. The lithospheric part of the carbon cycle starts with the sedimentation of terrigeneous and planktonic material or the oceans. Consequent subduction, metamorphism, or uplifting add the sea sediments to the continental crust. Weathering and erosion finally return the material to the oceans or continental basins. All these fluxes are generally less than 10¹⁵ g C/year. The figure for the global river transport of inorganic carbon is one of the best known in the total carbon cycle, and is 0.45 x 10¹⁵ g C/year, with evidence of increasing rates caused by human interference. Most of the weathering on the continents involves dissolution of carbonates. The carbon dioxide used for this process from soil air is recharged upon precipitation of carbonates: there is no net sink by carbonate dissolution. The only net sink of atmospheric CO₂ through weathering occurs by destruction of silicates, which involves only 0.010.02 x 10¹⁵ g C/year.

13.1 INTRODUCTION

Models of rock cycles have been developed during the last few years (e.g. Garrels and Mackenzie, 1971, 1972; Garrels and Perry, 1974; Garrels et al., 1975). The main features of the cycles are: (i) sedimentation of carbonates and organic matter in oceans and in continental basins, (ii) subduction and uplift of the oceanic crust, and (iii) weathering and erosion of rocks exposed on the continents.

13.2 ROCK MASSES AND THEIR CARBON CONTENT

Table 13.1 compiles estimates for the masses of different rock reservoirs of earth, while Table 13.2 gives average composition of various rock types. The composition of the average igneous rock can also be taken as representative of the whole crust (Garrels and Mackenzie, 1972). Carbon analyses (Fuex and Baker, 1973) of granitic rocks (14 samples) yielded 450 ppm carbonate-C and 65 ppm non-carbonate-C, while unaltered basalts and peridotites (10 samples) yielded 0-620 ppm carbonate-C(an average of 106 ppm) and 49-460 ppm non-carbonate-C (an average of 101 ppm) (14 samples). In altered basalts the carbonate-C was much larger, between 0.23 and 2%.

Table 13.1a Masses of earth in 10²⁴ g (Garrels and Mackenzie, 1971, condensed from Table 1.4 and Figure 2.5. Reproduced by permission of W. W. Norton & Co., Inc., and by permission of the authors)

Table 13.1b Sediment masses in 10²⁴ g (altered after Garrels and Mackenzie, 1971, Table 3.4. Reproduced by permission of W. W. Norton & Co., Inc., and by permission of the authors)

The ratio of limestones, shales, and sandstones for post-Precambrian rocks is 20:65:15 and for Precambrian rocks 8:86:6; with a weight ratio of 1.3 between both compartments (excluding volcanic rocks), the ratio becomes 15:74:11 for all sedimentary rocks (Garrels and Mackenzie, 1971). In the steady-state sediment cycle model of Garrels and Mackenzie (1972) (see also Section 13.7), the ratio calculated from a river flux with the composition and quantity of present river loads is about 15:70:15, which is in accordance with the aforementioned values.

Table 13.1c Estimates of mass and lithologic properties of major sedimentary units* (Garrels and Mackenzie, 1971, Table 8.1. Reproduced by permission of W. W. Norton & Co., Inc., and by permission of the authors)

The total mass of sediments is estimated according to mean depths of sediments in oceans (between 1 and 2 km) and continents (around 2.7 km), mean porosity, and mean density. This total sediment mass is estimated by Garrels and Mackenzie (1971) (Table 13.1) to be 3.2 x 10²⁴ g with volcanic rocks, or 2.34 x 10²⁴ g without, while Li (1972) and Ronov and Yaroshevsky (1967) obtained a mass of 2.4 x 10²⁴ g; Garrels and Mackenzie (1972) and Garrels and Perry (1974) assume 2.5 x 10²⁴ g, which should include metamorphic rocks from sedimentary educts.

It is estimated that sediments contain 0.5% organic carbon by weight (Garrels and Perry, 1974). The figure for Precambrian rocks is lower: 0.3%. Modern sediments contain 0.8 to 0.9% by weight (Ronov, 1971).

With these figures at hand it is possible to take an inventory of carbon (Table 13.3, Figure 13.1): assuming a basaltic composition for the oceanic crust, and a mean thickness of 4 km (6 km average oceanic crust thickness, minus 2 km sediment cover), and a density of 3 g/cm³, we obtain 268 x 10⁶ km² x 4 km x 3 x 10¹⁵ g/km³ = 3.22 x 10²⁴ g; of this 106 ppm is carbonate-C = 0.34 x 10²¹ g, and 101 ppm non-carbonate-C = 0.32 x 10²¹ g.

Large differences in carbon content occur between altered and unaltered basalts. Alteration is due to local degassing processes which conduct volcanic gases into the crust. It is, however, very difficult to assess the amount of altered basalts, which could lead to an estimation of -the flux in the gaseous phase. This problem should be given more consideration and more carbon analyses are needed.

Table 13.2 Chemical analyses of `average rock' (in wt. %) (Garrels and Mackenzie, 1971, Table 9.1. Reproduced by permission of W. W. Norton & Co., Inc., and by permission of the authors)

Figure 13.1 The unbalanced rock cycle, compartment sizes, and flux rates as given in the text

Table 13.3 Masses of carbon in crustal compartments

In the following, a mean carbon content of 200 ppm C for the oceanic basaltic crust is assumed. Oceanic sediments have a given composition as outlined in Table 13.1c, with a mean CO₂ content of 4.36% or 1.18% carbonate-C. The total mass of carbon (Table 13.3) can be calculated from the corrected density and porosity as given in Table 13.1 c) for the hemipelagic and pelagic sediments. It is not specified in the quoted reference whether the analyses (Tables 13.1c and 13.2) include organic carbon. If it is included, the carbonate concentrations in marine sediments would be too low. By multiplying the total mass by 0.5% organic carbon, we obtain 6 x 10²¹ g of organic carbon in oceanic sediments.

By subtracting total sediments and basaltic oceanic crust from the total crustal mass, we obtain the continental igneous mass. This mass (17.58 x 10²⁴ g) underlies the continents and their margins. With 450 ppm carbonate and 65 ppm non-carbonate carbon, the carbon content of igneous masses has been calculated as in Table 13.3.

The carbon content of the continental sediments can be calculated by taking the average sedimentary rock composition (Table 13.2) = 4.7% CO₂ = 1.28% C, multiplied by the mass of continental sediments. Similarly, organic carbon can be calculated by multiplying continental sediment mass by 0.5%.

The total carbon inventory in the crust amounts to almost 65.5 x 10²¹ g, of which 73% is carbonate carbon, while the rest is principally organic carbon. 

Estimates of carbon in rocks have been collected from various sources: Garrels and Mackenzie (1971, p. 250) estimated the total CO₂ in sediments neutralized by HCl to be 210 x 10²¹ g CO₂ = 57 x 10²¹ g C. This is more than the calculated yields for all sediments. Garrels et al. (1975, Fig. 28), and Garrels and Perry (1974, Table III) estimated the carbon mass as 5 x 10²¹ moles of CO₂ = 60 x 10²¹ g carbonate-C and 1 x 10²¹ moles= 12 x 10²¹ g organic-C of which ~1% is fossil fuel. Baes et al. (1976) calculated 30 x 10²¹ g carbonate-C down to a 4-km depth limit and 6.6 x 10²¹ g non-carbonate-C, of which 0.01 x 10²¹ g or 0.15% are fossil fuels. Reiners (1973, Fig. 1) quoted Bolin (1970), with only 20 x 10² ` g of total carbon in sediments plus 0.01 x 10²¹ g of fossil fuel carbon.

13.3 FORMS OF CARBON IN ROCKS

Carbon has nine possible oxidation stages, i.e. from +4 to 4. Most common is the +4 in CO₂ or CO^2-₃ (H₂ CO₃, or HCO₃). CO (+2) plays a role as a volcanic gas and in bacterial activity. Neutral carbon is present in the minerals graphite and diamond. Most non-carbonate-C is fixed as C_nH_2nO_n by photosynthesis. With the help of three adenosinetriphosphate and of two reduced pyridine nucleotides, five electrons reduce the carbon from the +4 stage to the 1 level.

Further reduction by certain bacteria or by inorganic processes can produce CH₄ (methane) as the most reduced form of carbon to occur.

13.3.1 Carbonates

Seventy-three per cent (Baes et al., 1976: 82%) of the crust-carbon is present as carbonates. Calcite (CaCO₃, Ca 9-fold-coordinated, trigonal scalenoedric, is capable of incorporating several % Mg into its lattice) and aragonite (CaCO₃, Ca 6-fold-coordinated, orthorhombic dipyramidal, is capable of taking up several % Sr into its lattice) are the dominant biogenic carbonates. Inorganically, calcite precipitates from solutions with Ca/Mg ratios larger than 1, if CO₂ pressure is favourable. With smaller Ca/Mg values, first Mg-calcite (up to 40 mol % Mg in solid solution), and then aragonite are precipitated. In very Mg-rich solutions, monohydrocalcite, hydromagnesite, and nesquehonite can form. Dolomite (CaMg(CO₃)₂, trigonal rhombohedric) is the third carbonate mineral of wide importance; it forms by early diagenetic disintegration of high-Mg-calcites. The same holds true for the rarer magnesite (MgCO₃) and huntite (CaMg₃ CO₃)₄ ). The Ca/Mg ratio has to be lower than 0.13 for the formation of dolomite, conditions normally found only in evaporative areas. Siderite (FeCO₃), an iron ore, is formed by metasomatic alteration of (CaCO_3, minerals, as well as in the absence of oxygen.

Figure 13.2 shows the percentage in volume of sedimentary rock as calculated for different periods of the earth's history. With increasing sediment depth and continental growth, volcanic rocks diminish and shales (lutites) dominate. The changing proportions of limestone and dolomite should also be noted. Magnesium today is either absorbed by clay minerals or deposited as high-Mg-calcite in shallow seas, while carbonate combines preferentially with calcium to form limestones. One of the reasons for this change is the fact that granitic continental crust tends to become more acidic. The weathering of feldspars dominates over the weathering of the more basic Mg-containing hornblendes and pyroxenes, which causes a five times larger Ca output to the rivers than that of Mg. Since the domination of land by plants in early -Phanerozoic times, more CO₂ has become available in soil, stimulating calcification in the oceans. Once the Mg/Ca ratio in the oceans (now about 5) has been lowered, calcite can be precipitated, both inorganically and organically, to form limestones.

Figure 13.2 Volume percentage of sedimentary rocks as a function of age. (Garrels and Mackenzie, 1971, Fig. 10.3. Reproduced by permission of Elsevier Scientific Publishing Co. and by permission of the authors.)

The isotopic composition of carbonates has changed only slightly during the earth's history (Figure 13.3) Veizer and Hoefs (1976) have collected almost 2000 ¹³ C analyses of limestones and dolomites. Permian carbonates have large ¹³C values. A decrease of 3‰ with increasing age occurred during Precambrian, as well as -Phanerozoic times. At the Precambrian -Phanerozoic boundary, a distinct 3‰ decrease seems to have taken place. As the ¹⁸O values in carbonates diminish considerably with increasing age, the carbonates are, in general, heavier in ¹³C at a certain ¹⁸O level in Precambrian times than in later ages.

Figure 13.4 depicts ¹³C values from different rocks, both carbonate ¹³C and the respective non-carbonate ¹³C figures. Differences in range between carbonates and igneous rocks are small compared to the difference with the non-carbonate carbon, with values between 30 and 20 ¹³C. By balancing sedimentary organic carbon with sedimentary carbonate carbon, Fuex and Baker (1973) deduce a mantle ¹³C of about 7‰.

Figure 13.3 Histogram of ¹³C for limestone and dolomites from various age groups. (Veizer and Hoefs, 1976, Fig. 5. Reproduced by permission of Pergamon Press Ltd., Oxford.)

13.3.2 Organic Carbon

Organic carbon differs from carbonate carbon not only in isotopic composition and oxidation number, but also in the multiplicity of its chemistry. An increasing number of papers have been published in the last few years, dealing with the biogeochemistry of fossil organic carbon compounds.

Bacterial destruction and chemical diagenesis account for at first a rapid and then a slower disintegration of the entrapped organic sediment particles. In the course of these processes, the metabolites which form and collect are very different from their parent substances. Crude oil, natural gas, and coal are some of the products now essential to our civilization.

Figure 13.4 Isotopic composition of carbon in different rocks. The composition of mantle carbon (7‰PDB) is based on estimates on the isotopic composition and relative amounts of the main crustal carbon reservoirs, and on the assumption of mantle degassing as the exclusive source of crustal carbon. (Fuex and Baker, 1973, Fig. 1. Reproduced by permission of Pergamon Press Ltd., Oxford.)

Alkanes occur in plants and sediments, often with a predominance of odd over even chain length. In carbonates and evaporite deposits, predominance of even over odd can occur, possibly due to dehydration and reduction of lipid acids and to alkaline evaporative environments (Welte and Waples, 1973). The isoprenoids, phytane and pristane, are present in almost all sediments.

Amino acids and sugars, basic components of all organic tissue, can be identified in sediments. Racemization of biogenic laevo amino acids into their dextro forms can be used as a geochronological tool.

Other classifications of organic matter are based on various extraction fractions (such as humic matter). Bituminous matter is generally called kerogen. Jackson and Moore (1976) have analysed rocks of various composition and of various ages for special kerogen properties and C, N, and P contents. C and N contents decreased in Phanerozoic times with increasing age, while the C content of cherts in prePhanerozoic times increased again. In general, the maturation process tends to remove the aliphatic and nitrogen-bearing compounds, causing an enrichment of condensed aromatic components. This leads to an inverse relation between total organic carbon and the ratio of aromatic to aliphatic kerogen carbon. The high organic carbon levels in the older cherts are interpreted as relics of the once higher CO₂ level in the primordial atmosphere, while the increase in Phanerozoic times is due to: (i) the increased sedimentation because of increased primary productivity; (ii) the increased reductivity in sediments; (iii) the change in the input pattern due to evolution (e.g., the appearance of faecal pellets from developing animals); and (iv) the longer time in maturation.

Kerogen is considered to be quite resistant to migration in the rocks, while lighter fractions, such as the alkanes, are considered as contaminations of younger meterial, especially in pre-Phanerozoic rocks (Smith et al., 1970).

Apart from the large isotopic difference of organic matter from carbonates, the ¹³C values increase with increasing intensity of metamorphosis (Hoefs and Frey, 1976), from 25‰ in the unmetamorphic and anchimetamorphic rocks to 10‰ in the amphibolite facies (heated up to about 500 ^°C).

13.4 SEDIMENTATION RATES IN OCEANS

13.4.1 Carbonates

Several approaches can be applied to obtain sedimentation rates (Broecker, 1974):

(1) By knowing the carbon difference between surface water and deep water, the mean depth of the deep water and the upwelling rate (200 cm/year calculated by ¹⁴C deficiency in the deep water), the rate can be calculated to be 2.5 g/cm² in a thousand years, of which 2.0 g are redissolved and 0.5 g is deposited on 20% of the oceanic bottom area protruding above the lysocline. In these areas the rate should then be 2.5 g/cm² per thousand years (Figure 13.5a).

(2) One can measure the carbonate content in dated cores. For those cores, taken from the 20% of areas with calcareous sediments, mean sedimentation rates of 0.90.8 g CaCO₃/cm² per thousand years have been established by this method. Distributed over the total ocean area, we obtain 0.20.16 g CaCO₃ /cm² per thousand years (Fig. 13.5b).

Figure 13.5 (a) Distribution of carbonate-rich oceanic sediments. (The Atlantic and Indian distributions are based on data obtained by Pierre Biscaye, K. Venkatarathnam, James Gardner, and Thomas Kellogg, all of Lamont-Doherty Geological Observatory, Karl Turekian, Yale University, and David Ellis, Oregon State University. The Pacific distribution is based on data compiled by A. P. Lisitzin from the U.S.S.R.). (Broeker, 1974, Fig. 2.2. From Chemical Oceanography by Wallace S. Broecker (© 1974 by Harcourt Brace Jovanovich, Inc. and reproduced with their permission)

(b) Actual rates of carbonate sedimentation (g/cm² 10³ year). (Broeker, 1974, Fig. 3.12. From Chemical Oceanography by Wallace S. Broecker (© 1974 by Harcourt Brace Jovanovich, Inc. and reproduced with their permission)

(3) The sedimentation rate of carbonates should, if the system is at steady state, be equal to the Ca runoff from the continents. With an average dissolved load of 15 ppm Ca, and a stream discharge of 0.376 x 10²⁰ g/year, we obtain a dissolved Ca flux of 0.564 x 10¹⁵ g/year, giving a minimum sedimentation of 1.41 x 10¹⁵ g CaCO₃/year or 0.169 x 10¹⁵ g C/year. Divided by the area of the ocean (362 x 10⁶ km²), the sedimentation rate is 0.39 g CaCO₃ /cm² per thousand years.

This third value is intermediate to the two figures calculated above. It does not take into account, however, the CaCO₃ brought in by suspension, nor does it take rapid sedimentation at river mouths and on continental shelfs into consideration. Broecker, for instance, calculates the percentage of detrital aluminosilicates reaching the open ocean as 6%.

By looking at these calculations, the average CaCO₃ sedimentation rate seems to stay between 0.5 and 0.2 g/cm² per thousand years. This gives us a carbonate carbon flux of 0.220.09 x 10¹⁵ g/year to the sediments. This is a net flux. Certainly, more carbonate is sedimentated, which in turn is redissolved from the sediment interface.

13.4.2 Organic Carbon

The sedimentation of organic carbon in the oceans (Figure 13.5c) is a complex process; in coastal areas, not only does continental runoff determine the amount of terrigenous plant matter introduced, but the kind, time, and amount of nutrients delivered also have a pronounced influence on the planktonic fixation of organic carbon. In the open ocean, planktonic production prevails, especially in upwelling zones and in deeper and nutrient-rich waters. In the Arctic zone, the plankton bloom occurs once during summer, while temperate climates sustain two blooms, a larger one in spring and a lesser one in autumn. In the equatorial seas, there is increased phytoplankton productivity during winter.

Suspension concentrations are higher in shelf areas; Lisitzin (1972) recorded 2-3 mg/1 as an average and 1.5 mg/l in the open ocean. An overall mean, both vertically and laterally, of one mg/1 was estimated, resulting in a global suspension mass of 1.37 x 10¹⁸ g. Half of this is stored in the Pacific and 16 x 10¹⁵ is annually exchanged by currents between the oceans.

Of this vast amount of particulate matter in the oceans, only part is carbon, and of this only very small fractions reach the ocean bottom and eventually stay there permanently (see Chapters 10 and 11, this volume). Garrels and Perry (1974) calculated the organic carbon flux by dividing the product of the total sediment mass (25000 x 10²¹ g) and an average organic carbon content of 0.5% by the product of the total annual sediment flux of 6.1 x 10¹⁵ g/year x 0.5% organic carbon to obtain 0.03 x 10¹⁵ g/year. Seibold (1974) estimated a flux value of 0.04 x 10¹⁵ g/year.

The sedimentation potential of the shallow seas alone, however, is considerably larger. With a shelf area of 93 x 10⁶ km² (Table 13.1a) an assumed average sedimentation rate of 0.05 cm/year, a porosity of 50%, a density of 2.3, and a carbon content of 3-4% by weight, an annual 0.3-0.4 x 10¹⁵ g C/year may be deposited (this volume, Group III, Report). In fact, eutrophication of coastal areas may be instrumental in the fixation of carbon and account for some of the missing industrial CO₂. The rates at which nitrogen and phosphorus are fixed and mined are 6 x 10¹² and 0.4 x 10¹² moles/year respectively. With a sediment C:N:P ratio of 150:15:1, eventually 60 x 10¹² moles or 0.72 x 10¹⁵ g of carbon may be fixed. This amount, incidentally, is equal to the missing industrial carbon not picked up by the ocean (1.6 x 10¹⁵ g) and not remaining in the atmosphere (2.4 x 10¹⁵ g) (Dahlem Konferenzen, 1977, Group Report `Man and the global nitrogen cycle'). It is obvious that the calculation falls short of reproducing the reality. Most of the phosphorus will not be available in a dissolved form, but will be fixed chemically to soil and agricultural products.

13.4.3 Sedimentation in Continental Basins

Of the 148.9 x 10⁶ km² continents, 14.1 x 10⁶ km² belong to the Antarctic and 33.6 x 10⁶ km² are central regions without drainage to the oceans. Excluding the Antarctic, which has runoff only in the form of ice, 75% of the total continents are peripheral and 25% central regions (Baumgartner and Reichel, 1975). Central areas are arid: 100.5 x 10¹⁸ g of H₂O fall as precipitation over the peripheral areas, while only 8.2 x 10¹⁵ g fall in central regions. This is a percentage ratio of 92 to 8 (with respect to total precipitation over the continents, excluding the Antarctic).

In peripheral areas 62.8 x 10¹⁸ g are evaporated and 37.8 x 10¹⁸ g discharged to the oceans. This gives a runoff coefficient (D/P) of 0.375 for peripheral regions. Central areas actually have no runoff, as all precipitation is eventually re-evaporated to the atmosphere, P = E = 8.2 x 10¹⁸ g/year. This evaporation occurs partly from the surfaces of closed lakes and salt pans of central basins. By assuming a similar runoff coefficient to that in peripheral areas, the flux of water into the closed lakes should have a maximal size of 8.2 x 0.375 = 3.075 (x 10¹⁸ g). This is 8% of the peripheral discharge.

Sediment transport by way of river flux may be relatively larger than in peripheral regions, due to: (i) the leaching of salt deposits often occurring in closed basins, and (ii) a high mechanical erosion resulting from sparse vegetation and from few, but violent, rain storms.

If we assume that less discharge is cancelled out by more erosion, the rate of erosion in continental basins may be estimated by multiplying the calculated runoff by the mean carbon loads established for peripheral areas (see Chapter 12, this volume, Table 12.1 b). The mean concentrations are:59.8 ppm HCO₃ , 3.28 dissolved organic carbon (DOC), and 1.76 particulate organic carbon (POC). The corresponding fluxes into continental basins are: 0.0362 x 10¹⁵ g HCO₃ -C, 0.01 x 10¹⁵ DOC, and 0.0054 x 10¹⁵ g POC per year.

The global mean for mechanical to chemical erosion is 4.7 (Garrels and Mackenzie, 1971, Table 5.1). The mean carbon content of the suspended sediment was calculated to be 0.96% (Garrels and Mackenzie, 1971, Table 4.11, recalculated). Multiplying the mean river salinity (111 ppm) by the total discharge from peripheral areas x 4.7 x 1%, we obtain a flux of 0.197 x 10¹⁵ g C suspended in the peripheral regions and (multiplying by 0.08) 0.0157 x 10¹⁵ g into central basins.

The sum for the total fluxes into continental basins is:

HCO3 C	0.036	x 1015 g/year
DOC	0.01	x 1015 g/year
POC	0.0054	x 1015 g/year
inorg. susp.C	0.016	x 1015 g/year
total C	0.067	1015 g /year

 The sedimentation rate is smaller, since roughly half of the HCO₃-C is given off to the atmosphere with the formation of CaCO₃, i.e., about 0.018 x 10¹⁵ g, and only part of the organic carbon is buried in the continental basin sediments because of rapid oxidation. The sedimentation rate should, therefore, be closer to 0.040.05 x 10¹⁵ g C/year.

13.5 FLUXES BETWEEN CRUSTAL COMPARTMENTS AND MANTLE 

13.5.1 Sea-floor Spreading and Subduction of Crustal Plates

If we assume that the lithosphere has been formed by continuous addition of mantle material, we can calculate the annual net flux of mantle material to the crust. The oldest known rocks in the crust are 3.8 x 10⁹ years old, and the formation of a first crust, now reworked in younger rocks, may have started 4.5 x 10⁹ years ago. The 24 x 10²⁴ g of Crustal rock should then have accumulated at a rate of 56 x 10¹⁵ g/year. If we assume that 0.27% of this is carbon, we obtain 0.140.16 x 10¹⁵ g/year delivered from the mantle. It will be extremely difficult to assess where this net flux occurs, as this rate is one of the minor ones encountered in the carbon cycle.

In determining the rate of sea-floor spreading, we are faced with difficulties. The arithmetic mean of spreading rates as calculated by Le Pichon (1968) is 2.3 cm/year. The length of the mid-ocean ridges is estimated to be 72 x 10³ km (Wunderlich, 1973). The thickness of the basaltic crust is 4 km (see Section 13.1); Hess (1962) assumes a thickness of 4.7 km. The volume gain per annum is then 6.6 km³ , or (density 3 g/cm³) 20 x 10¹⁵ g. Khan (1974) arrived at a figure of 170 km³ annually generated by sea-floor spreading. He did not state, however, how he derived this large rate, but he had obviously included in his calculation the peridotite layer below.

It is assumed that the subduction velocity has the same value as sea-floor spreading. This is not necessarily the case, since subduction troughs may selectively subduce those plates which have higher velocities. The length of the subduction troughs is in fact only 44 x 10³ km, as estimated by Livingstone (1973), and plate velocities seem to remain around 34 cm/year (Holmes, 1965). By taking the spreading rates as subduction rates, we obtain 4 km³ subduced annually, with the difference of about 3 km³ lifted up in mountain belts; or by taking the plate velocities of Holmes, we find 5.37 km³, which would just balance the generation by spreading. On the other hand, the annual flux from the mantle (56 x 10¹⁵ g) would amount to about 1.72 km³ , which could fill the difference between the first subduction rate and the rate of crustal generation at the ridges. But this may be a hasty conclusion, as there are other processes by which mantle material can exchange with the crust.

Pluming is one of these processes. The upward flux of material over hot spots in the mantle may be of a considerable size. For approximately 20 hot spots on earth (most of them are situated beneath oceanic crust), Khan (1974) assumes a total flux of about 6 km³ /year. Again, this flux occurs in the mantle and it is questionable as to how much material enters the crust. With a density of 3 g/cm³ and a carbon content of 200 ppm, the maximal flux may be 0.0012 x 10¹⁵ g C/year. By looking at the huge volcano chains which have erupted over hot spots (e.g. Hawaii chain), one may think of pluming as a significant flow of material to the crust.

Crust may not only be subduced, but also eroded by mantle convection under continents. Also, intrusions of mantle material, a possible source of energy and material for continental volcanism, may play a certain role. Estimates of the magnitude of these processes are, however, difficult to obtain.

13.5.2 Subduction of Oceanic Sediments

Oceanic sediments are derived from the continents. If their subduction recycled their material to the mantle, the flux to the mantle would be positive, or just balanced, and no net gain of crust would result (compare figures presented above). If, at 44 x 10³ km length, a 2-km-thick layer of oceanic sediment is subduced at a rate of 2.3 (34) cm/year, we obtain a flux rate of 2 (2.63.5) km³/year. With an average total carbon content of 1.68% for the sediments and a mean density of 2.14 (weighted mean for pelagic and hemipelagic sediments including dissolved mass of pore solution, recalculated from Garrels and Mackenzie, 1971, Table 8.1), the resulting carbon flux is 0.073 (0.0950.13) x 10¹⁵ g/year. Note that this is about the size of the carbonate sedimentation of the oceans (Figure 13.1). Several questions, however, remain when we assume a reflux of sediment material to the continents in this manner. The sediments cannot be subduced but should be folded, partly metamorphosed, and uplifted on to the margins of continents. But only parts of the subduction troughs are situated at continent rims (e.g. off western South America) and appreciable lengths are found in the open oceans. How much of this oceanic sediment material is recycled to the surface by the activity of volcanoes? Is the present plate structure representative for the entire length of earth history'?

13.5.3 Uplifting and Metamorphosis

If we assume that, eventually, all carbon deposited in the oceans returns to the continents, we can estimate the net uplift rate of this process. Continents have a mean height of 850 m above sea-level, and oceans a mean depth of 3800 m. The sedimentation rate is 0.260.12 x 10¹⁵ g C/year, which is lifted annually by 4650 m. This figure does not include the carbon in the inorganic suspended matter, which is mostly settled in epicontinental seas, on the shelf in shallow water, or on the continental margin in medium water depths. The figure does not include the sediments deposited in continental basins either (see Section 13.4.3), which has a mean uplift rate of only several hundred metres.

During subduction, and in the processes associated with uplifting, some of the sediments are buried so far below the surface that hydrostatic pressure and increased temperature will cause metamorphosis.

In Section 13.2 different figures for total sediment mass were quoted. Garrels and Mackenzie (1972) report 2.5 x 10²⁴ g as the total mass including metamorphic rocks and 2.3 x 10²⁴ g not including metamorphic rocks (1971). The difference of 0.16 x 10²⁴ should thus represent the mass of metamorphic rocks from sedimentary educts. The ratio of total sediment to metamorphic rocks is 16. One-sixteenth of the uplifted rock undergoes metamorphism, i.e., about 0.0160.008 x 10¹⁵ g C/year.

13.6 EROSION

13.6.1 Weathering

Before water, wind, or ice can transport material to the oceans or continental basins, physical and chemical weathering processes have to take place. Carbon, in the form of carbonic acid, is especially responsible for the chemical destruction of rocks. The principal mineral reactions involving carbonic acid are:

Ca(Mg)CO₃ + CO₂ + H₂O = Ca ²⁺ (Mg²⁺) + 2HCO₃

It should be noted that for every mole of new CO₂, one mole of rock-derived CO²₃ is transported. After reprecipitation of the carbonate, one mole CO₂ is released again.

Mg₂ SiO₄ + 4CO₂ + 4H₂O = 2Mg²⁺ + 4HCO₃^- + H₄ SiO₄

is the equation expressing the weathering of a non-aluminous silicate (here the Mg-olivine forsterite). It should be noted that of 4 moles CO₂ used for weathering, only 2 moles will return to the atmosphere when carbonate precipitates.

2NaAlSi3 O8 + 2CO2 + 11 H2O
	= Al2 Sit Os (OH)4 + 2Na+ + 2HCO3 + 4H4 SiO4

This equation illustrates the alteration of a feldspar (here albite) into the residual clay mineral kaolinite. The solution becomes alkaline, and carbonates will only precipitate if Na₂(HCO₃)₂ is produced by strong evaporation.

If anorthite (CaAl₂Si₂O₈) is weathered together with 2CO₂ and 3H₂O, no dissolved silica, but only kaolinite, 1 mole Ca and 2 moles HCO₃ are formed. Upon precipitation of calcite, only half of the CO₂ is returned to the atmosphere.

Weathering of silicate minerals requires CO₂ and thus is an effective mechanism for the removal of CO₂ from the air.

13.6.2 Erosion Rates

Erosion rates can be calculated in two ways: the first is to collect as much river data as possible to estimate world erosion rate; the second is to take a well-documented area as representative and calculate from this value the global balance.

The first procedure was carried out by Livingstone (1963) for the chemical loads of rivers. His calculations have been revised and connected to the present waterbalance data of Baumgartner and Reichel (1975) in Kempe (Chapter 12, this volume). It has not been possible to revise the data on dissolved organic, particulate organic and suspended inorganic matter in the rivers. The only global calculations given for these loads are those by Garrels and Mackenzie (1971). The following river loads can be calculated:

HCO3-C	0.445	x 1015 g/year
DOC	0.123	x 1015 g/Year
POC	0.066	x 1015 g/year
inorg. susp. C	0.197	x 1015 g/year
total C	0.831	x 1015 g/year

 The average SiO₂ content in rivers is 13.l ppm (Livingstone, 1963) which is derived from the weathering of silicates. The main silicate occurring in igneous rocks is plagioclase (Na_{o.6 2} Ca_o.₃ 8 Al_{1. 3 8} Si_{2.6 2} O₈ ), a mixture of anorthite and albite, which weathers into almost equal moles of HCO₃ and SiO₂ moles/2 Na⁺ and moles/3 Ca²⁺.

The total SiO₂ river load amounts to (13.l x 10^-6 x 37.7 x 10¹⁸ g H₂O) 0.49 x 10¹⁵ g or 8.2 x 10¹² moles. 8.2 x 10¹² moles carbon is 0.l x 10¹⁵ g C, so about one-quarter of the HCO₃-C in the rivers stems from the weathering of silicates. Of this, one-third is balanced by Ca and can form carbonate, i.e., one-sixth of 0.1 x 10¹⁵ g returns to the atmosphere, one-sixth forms carbonates, which are removed from the system, i.e., annually 0.016 x 10¹⁵ g. Together with the HCO₃ C from the weathering of carbonates, we obtain the following balance (all units in 10¹⁵ g/year):

Of the rest, 0.05 x 10¹⁵ g is balanced by Na⁺ liberated by the silicates, while about 0.02 x 10¹⁵ g is not electrically balanced by cations and potentially increases the pH, if it is not removed by photosynthesis.

The sink for CO₂, removed from the system by silicate weathering, has the size of about 0.010.02 x 10¹⁵ g C/year.

Another estimate on the global erosion can be drawn from the calculations done by Degens et al. (1976, Table 4, Figure 7) for the tributary area of the Black Sea. The weighted means (sum of area times respective value/sum of area) for the total river loads into the Black Sea have been calculated (Table 13.4). The ratio of suspended load to dissolved load is 1.7/1. A total of 240 x 10¹² g stems from an area of 1.98 x 10⁶ km². Calculating for the total peripheral regions of the continents (100.9 x 10⁶ km²) we obtain a global erosion rate of 12.07 x 10¹⁵ g/year. This figure should include HCO₃C, POC, and suspended inorganic carbon, but not DOC. By assuming a carbon content of 3%, a little larger than that for mean crustal rock (because of the large concentrations of CO²₃ in the water), we obtain a flux of 0.36 x 10¹⁵ g C/year from the rivers to the oceans.

Although the calculation is based on only 1% of the peripheral areas of the continents, the close agreement between this figure and the one based on the world river load is striking. The Black Sea area appears to be a particularly attractive example, because the river systems discharging into the Black Sea are derived from a wide array of geomorphologic and climatic settings (Figure 13.6).

13.6.3 Erosion by Means Other than Running Water

The best figures available for transport by ice, marine erosion and dust are those published by Garrels and Mackenzie (1971, Table 4.11).

The glacial flux was calculated by using an estimate by Yevteyev (1959) of 0.69 km³ of mechanical ground rock, which is annually transported by ice from the Antarctic continent. The rock is assumed to have the composition of unaltered average crustal rock. The figures calculated may be revised with newer data for the

Table 13.4 Denudation in source area of Black Sea basin (Degens et al., 1976, Table 2. Reproduced by permission of Ecological Bulletins)

Figure 13.6 Oragraphic map of the Black Sea drainage area. (Degens et al., 1976, Fig 1. Reproduced by permission of Ecology Bulletins.)

ice flux from Antarctica: 1987 x 10¹⁵ g are given off to the surrounding oceans annually (Baumgartner and Reichel, 1975). The ice flux from Greenland is 390 x 10¹⁵ g, which is 16.4% of the sum from both areas. Garrels and Mackenzie assumed that only 10% stem from areas other than the Antarctic; this proportion would give a 6% increase of the fluxes, a total flux of 1.85 x 10¹⁵ g rocks, of which 1.78% is carbon, i.e., the carbon flux with glaciers amounts to 0.033 x 10¹⁵ g C/year.

Even more difficult to obtain is the estimate of the material eroded by waves and currents along the coasts. Garrels and Mackenzie (1971) assume a flux of 0.25 x 10¹⁵ g, which would supply an additional amount of carbon of 0.0045 x 10¹⁵ g/year to the oceans.

The atmospheric dust settling over the oceans was assessed by Garrels and Mackenzie (1971) - assuming five dust storms annually to be 0.3/g³ cm ² on 1% of the ocean. Annually, 0.054 x 10¹⁵ g of material settle into the oceans (average sediment content of 1.78% C assumed), which gives a carbon transport of 0.001 x 10¹⁵ g/year. Slowly settling tropospherc dust also reaches the sea. The average dust concentration in the air is 10^-12 cm³ /cm³. With a density of 2.5 g/cm³, a troposphere density of 1.223 x 10^-3 g/cm³, and a mass of 51.3 x 10²⁰ g, the troposphere contains an average of 0.0105 x 10¹⁵ g of dust with a mean residence time of about one year. 0.0074 x 10¹⁵ will settle over the ocean, of which about 0.000 13 x 10¹⁵ g is carbon. The total dust flux from the continents through the atmosphere to the oceans amounts, then, to 0.0011 x 10¹⁵ g C/year.

Duce (1977) has reviewed existing data on organic carbon in aerosols (Table 13.5). His analyses suggest that the mean organic carbon content of particles in the marine environment stays at approximately 5 pg/m³ at surface conditions and around 1.5 µg/m³ in non-urban continental areas. It is interesting to note that 80% of the carbon in ocean areas is associated with particles less than 1 µm in diameter. This implies that the POC is not derived from the sea, as experiments with air bubbles in sea-water show that the carbon ejected with sea spray is bound mainly to the larger particles. Duce suggests, therefore, that the small particles form by reactions between land-derived gaseous compounds. This would also explain the apparently large residence time of these small particles, which only seems large, as the emission of small particles is supplemented by volatile hydrocarbons, derived from plants. Table 13.5 also gives the POC emissions, as estimated by Duce. A total of 0.056 x 10¹⁵ g is emitted annually, of which about 50% is believed to be anthropogenic and 50% natural. About 25% stems from oceanic sources and the rest is land-derived. These figures do not include inorganic carbonate carbon in dust, so that the total atmospheric particulate carbon budget seems to be at least 50 times larger than estimated by Garrels and Mackenzie (see above).

In addition to the continent-derived dust, cosmic dust also enters the atmosphere. Garrels and Mackenzie (1971) quoted Wasson et al. (1967), who presented a flux rate of 10^-7 g/cm² year; multiplied by the surface of Earth (510 x 10⁶ km²), a total of 5.1 x 10¹¹ g enters the atmosphere (Garrets and Mackenzie obtained 5.1 x 10¹² g, which is obviously a mistake in calculation).

Table 13.5 POC in troposphere (condensed from unpublished material by Duce, 1977, by permission of the author)

Measurements taken from the Apollo project on the Moon gave dust flow values of 4 x 10^-9 g/cm² year (quoted in Cailleux, 1976). The total flux to the Moon (Moon surface 37.95 x 10⁶ km²) is then 1.5 x 10⁹ g/year. The surfaces and the gravitational constants of Moon and Earth relate by 0.0744 and 0.167 respectively. Both Moon and Earth collect all dust which comes across their way through space. The cross-sections of the path pipes of Moon and Earth relate to one another like the squares of the gravitational constant. Consequently, the flux of cosmic dust to Earth must be 6² = 36 times that of the Moon. This gives a total flux of 5.465 x 10¹⁰ g/year or 1.07 x 10^-8 g/cm² year. These values are one order of magnitude lower than those by Garrels and Mackenzie.

Of all meteorites, 86% are chondrites; the remainder consists of achondrites, stony iron, and iron meteorites. The chondrites have been extensively investigated for their carbon content, which amounts to 0.04% (Gibson et al., 1971). 2% of the chondrites are carbonaceous chondrites, which have a mean carbon concentration of 1.32% (mean of 44 analyses, Gibson et al., 1971); Masses of meteorites and carbon content are shown in the following table:

13.6.4 Changes in Erosion Rates

Man's activity on this planet has caused disturbances in many of the natural processes. Erosion is clearly one of them. Due to agricultural activities, suspension loads of rivers have increased. It is, however, very difficult to assess the rate of this increase.

Recently, the varve-counting technique allowed a first insight into the magnitude of man's interference. Sediment cores in the Black Sea and in Lake Van (eastern Turkey) were dated by varve-counting. In the case of the Black Sea (Figures 13.6, 13.7) (Degens et al. 1976), sedimentation rates during Roman times remained at about 4 cm/1000 years, increasing to values twice as high in early, and thrice as high in late medieval times. Only in the last two hundred years has sedimentation slowed down again to a factor of two, principally as a consequence of soil conservation in the U.S.S.R. In the case of Lake Van (Kempe, 1977), the sedimentation rate increased from 5 cm/ 1000 years to three times the value within the last 800 years.

Detailed records of hydrochemical parameters of rivers are available only from industrialized countries, with more regular sampling being carried out since the Second World War. Only recently have computer carbonate equilibrium models (Kempe, 1975) made it possible to determine exact CO₂ pressure curves. The parameter with the greatest influence on the PCO₂ is the pH, which has been monitored regularly in Germany, for instance, since the early 1950s. Figure 13.8 gives an evaluation of 2000 water samples from the Elbe River at Hamburg (analyses by the Hamburger Wasserwerke, from 1954). After computing the PCO₂, monthly and annual averages were calculated for temperature and alkalinity. Both PCO₂ and alkalinity show an increase during the period sampled. The correlation coefficient for PCO₂ with time is 0.14 and for alkalinity 0.47.

Figure 13.7 Sedimentation rate versus varve model ages in a core from the Black Sea (Degens et al., 1976, Fig. 2. Reproduced by permission of Ecological Bulletins.)

Figure 13.8 Alkalinity, PCO₂, temperature, and runoff of the Elbe River at Hamburg. PCO₂ and annual means calculated according to data kindly provided by the Hamburger Wasserwerke

Regression analysis yields an average alkalinity increase of 0.011 meq/l and of log 0.003 PCO₂ per year. It has not yet been established how much of this increase can be attributed to the rise in atmospheric CO₂ concentration, or to other factors such as an increased erosion through land management practices, or an enhanced respiration activity within the river due to an increased organic carbon load. Organic carbon in the Elbe has been monitored only for the last 3 years (Figure 13.9). The trend cannot yet be appraised because of a strong seasonal variability. If, on the other hand, the decaying of organic particulate pollution is responsible for the increasing inorganic carbon load in the Elbe, we should expect a strong correlation between the discharge volume and the CO₂ pressure; at low water levels the pollution tends to concentrate, thus causing a larger PCO₂. No connection between these parameters can be seen in the curves of the annual averages as given in Figure 13.8.

The rivers Rhine, Danube, Inn, Elbe, Weser, and Ems in Germany were investigated for transported bulk matter (Kempe et al., 1977) using data from the International Hydrological Decade during 1966--73 (Bundesanstalt für Gewässerkunde 1969-77). Both total suspended matter (TSM) and total dissolved matter (TDM) show strong dependencies with runoff (Figures 13.10 and 13.11). The concentration of TSM increases with discharge volume, probably due to higher water velocities, while the concentration of TDM decreases due to a dilution effect. Total transport increases for both TSM and TDM with volume. Since Central Europe in the years 196673 observed a marked decline in water discharge (Figure 13.12, compare also Figure 13.8), it is difficult to assess time-dependent trends. Partial correlation analysis reveals, however, a trend of decreasing suspension load. Calculating the correlation of TSM load with time, while keeping the runoff volume constant, the coefficient becomes 0.38. Considering again the large number of samples involved, this gives evidence of a sinking suspension load. The reasons for this behaviour in German rivers may be due to: (i) the building of sewage plants, (ii) enhanced channellization to diminish bank erosion, or (iii) reforestation.

No data are available on the carbon content of the TSM, or of the TDM, which is derived from evaporation residues and not from the sum of total chemical analyses. 

The total erosion in Central Europe is around 0.1 mm/year and the ratio TSM/TDM is about 0.13. The global mean of this ratio is 4.7, indicating a large surplus of suspended matter; 80% of this is discharged by South East Asian rivers alone.

13.7 MODELS OF THE SEDIMENTARY ROCK CYCLE 

 Garrels and Mackenzie (1972) have computed a quantitative model of the sedimentary rock cycle. The carbon fluxes of this model have been redrawn in Figure 13.13.

The model is based on the assumption that no exchange with the crystalline parts of the crusts takes place and that the composition of the dissolved and suspended river loads has not changed significantly with time. The rock reservoir was partitioned into an older compartment, with a mean residence time of 600 million years, and a new reservoir, with a residence time of 150 million years. The total model residence time obtained was 413 million years, which is close to estimates given by other authors.

Figure 13.9 Dissolved plus particulate organic carbon (TOC), Elbe River at Hamburg. Data kindly provided by the Hamburger Wasserwerke

Figure 13.10 Suspension freight and suspension concentration versus runoff volume from the rivers Rhine, Ems, Weser, Elbe, Danube, and Inn, 196673. (Kempe et al., 1977. Reproduced by permission of the authors.)

It is of interest that the model results in a crust composition of 70% shales, 15% sandstones, and 15% limestone, which is close to other estimates of the average sediment composition (see Section 13.2).

Approximately 20% of the carbon is used for weathering silicates, which is not restored to the atmosphere by carbonate precipitation in the ocean, but through a net surplus of oxidation over photosynthesis in the sea. The total flux out of the oceans assumed in this way is 0.09 x 10¹⁵ g C/year. The residence time of carbonate carbon in the model is 380 million years.

These models show that it is possible to model the complex rock cycle with quite simple assumptions. The authors themselves stress, however, that many questions remain unsolved and that the model does not necessarily display the natural processes, but rather what the constructors thought these natural processes to be. Nevertheless, they may be of great help in understanding the relations of fluxes and compartments between different elements and reservoirs.

Figure 13.11 Dissolved freight and dissolved concentration versus runoff volume from the rivers Rhine, Danube, and Inn, 1966-73. (Kempe et al., 1977. Reproduced by permission of the authors.)

Figure 13.12 Mean of runoff volume (solid curves) for the rivers Rhine, Ems, Weser, Elbe, Danube, and Inn, 1966-73, in comparison to their total suspended load (hatched curve) and the mean of the runoff volume for the rivers Rhein, Donau, and Inn only in comparison with their dissolved load. (Kempe et al., 1977. Reproduced by permission of the authors.)

Figure 13.13 The carbon cycle as calculated by a quantitative model of the sediment rock cycle by Garrels and Mackenzie (1972). The model is based on a total material flux of sediments out of the oceans (without H₂O) of 6.1 x 10¹⁵ g/year, of which 3.21 x 10¹⁵ g are elements other than oxygen. Total rock mass is 2.5 x 10²⁴ g expressed as oxides, inorganic C (C_i) given as CO₂ and organic C (C_o) as CH₂O. Fluxes are net exchanges only

13.8 CONCLUSIONS

Most of the flux rates and pool sizes presented in this chapter will be subject to continuous improvement with the growing body of geochemical data. This particularly concerns data on the oceanic crust. It is emphasized that additional carbon analyses will only cause a limited improvement in the accuracy of the average concentration figures.

Much more data are needed on man's impact upon rates of weathering and erosion. The interpretation of the sediment records in lakes and coastal basins in correlation to past meteorological, hydrological, and chemical data may reveal changes induced by man.

A comparison between the flux rates in the natural rock cycle with those caused by the burning of fossil fuel indicates that burning of fossil fuels will release carbon in an amount ten times that liberated by erosion. It is for this reason that no potential sinks for the `missing carbon' in our atmosphere presently exist in the rock cycle. It is only the long-term effect, where rocks exercise control on atmospheric and oceanic carbon.

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