N[rxa cos2

2n mAvAMAa cos <p dX

is the meridional transport of the absolute angular momentum in the atmosphere which is equal to the sum of the meridional transports of the planetary momentum (the first term on the right-hand side) and the relative momentum (the second term); (pAE — pAW) is the pressure difference on the west and east slopes of the ith mountain ridge; summation is carried out for all mountain ridges and other irregularities of the Earth's surface that cross the latitude belt in question; xx is the zonal component of tangential wind stress at the underlying surface; the remaining designations are the same.

Equation (2.6.3) describes the budget of the angular momentum in the zonal belt of unit meridional extension. To estimate the components of the budget we use observational data of the annual mean zonal wind velocity (Figure 2.16). The distinguishing feature of its distribution in the meridional

Ocean Velocity Distribution
80° S 60 40 20 0 20 40 SO H Figure 2.16 Annual mean latitude-altitude distribution of the zonal component of wind velocity (m/s), according to Peixoto and Oort (1984).

plane is the three-cell structure of the circulation in each hemisphere with two direct cells in the tropical and polar latitudes and one reverse cell in the temperate latitudes. It will be recalled that the direct cell of the circulation is the one with upwelling of warmer air and with downwelling of cooler air. On the other hand, in the reverse cell there is upwelling of cooler air and downwelling of warmer air. The direct cell of the circulation in low latitudes is usually referred to as the Hadley cell, and the reverse cell as the Ferrel cell.

It can be seen from Figure 2.16 that the zonal component of the wind velocity at low atmospheric levels is directed to the west (easterly trade winds) in low latitudes, and to the east (the westerlies) in temperate latitudes. Accordingly, the surface friction stress directed against the wind will be positive in the first case and negative in the second case. From this it follows that the atmosphere passes momentum to the Earth in low latitudes and obtains it from the Earth in temperate latitudes. But since, in accordance with Newton's third law, the Earth renders an equal and opposite (in direction) effect on the atmosphere, one can suggest that it is as a source of momentum for the atmosphere in low latitudes and a sink of momentum in temperature latitudes. The same can be said with regard to relative angular momentum. To confirm this we refer to Figure 2.17, which presents the results of calculations of the meridional distribution of the total surface torque due to both pressure and friction forces. This torque is thought to be positive if it tends to increase the eastward angular momentum of the atmosphere, that is, if, in the last term in Equation (2.6.3), the tangential wind stress is replaced by an equal, but opposite in direction, tangential stress of the underlying surface. According to Figure 2.16 the surface friction contributes to the transport of relative angular momentum from the underlying surface to the atmosphere in the tropics, and from the atmosphere to the underlying surface in temperate latitudes, and this direction of the transport probably remains constant throughout the year.

We note two more sources of relative angular momentum for the atmosphere: the regions of localization of the north and south polar cells of circulation. The appropriate radius of the latitude circle (the arm a cos q>) is small and this is why the relative angular momentum transferred from the underlying surface to the atmosphere is also small.

It has been found that the relative angular momentum is transferred from the underlying surface to the atmosphere in the tropics. Its subsequent fate is as follows: first it is carried by the ascending branches of Hadley cells into the upper tropospheric layers, then it is transported by the transient eddies into the midlatitudes, and here it is reduced to compensate for losses in the

relative angular momentum in the atmospheric planetary boundary layer due to friction.

It is known that the velocity Qa of solid rotation is equal to 464 m/s and is much larger than the relative wind velocity u. One might think that because of this the meridional transport of absolute angular momentum has to be determined mainly by the planetary momentum transport. But in the steady state the integral (over the atmospheric mass) meridional transport of absolute angular momentum does not depend on the planetary momentum transport, for, according to the law of conservation of mass, the integral zonal component of the wind velocity is identically equal to zero. In other words, the integral meridional transport of absolute angular momentum is determined solely by the transport of relative^angular momentum, and this in turn depends solely on the correlation [wAtfA] between the zonal and meridional components of the wind velocity. But because infinite accumulation of absolute angular momentum in temperate latitudes, as well as its infinite subtraction in the low latitudes, does not occur, the reverse (compensatory) transport of absolute angular momentum must exist. It is natural to assume that such transport is concentrated in the ocean. Let us check this possibility.

First we write down the budget equation for absolute angular momentum in the zonal belt of ocean with unit meridional extension. By analogy with (2.6.3) we obtain

dt a dtp



is the meridional transport of absolute angular momentum in the ocean; (Poe — Pow) is the pressure difference at the east and west edges of continents, of mid-ocean ridges and other bottom undulations crossing the zonal belt in question; the tangential stress at the ocean bottom is assumed to be negligible compared to the tangential stress at the free ocean surface.

We compare estimates of the meridional transport of absolute angular momentum in the atmosphere and Jhe^ocean. Let^us assume that typical values of ratios of correlation terms [«a^a! and [«o^ol °f the mass of unit columns of the atmosphere and the ocean (mA and mQ), and of the extension of the atmosphere and the ocean in the zonal direction, are equal to 104, 3 x 10"3, and 2 respectively. Then 0(MMTJMMTo) « 102, that is, the meridional transport of the absolute angular momentum in the ocean is only 1% of that in the atmosphere, and, hence, it cannot compensate for the accumulation of the absolute angular momentum in the midlatitudes of the atmosphere.

Considering this fact, Equation (2.6.4) for the annual mean conditions is rewritten in the form

X (Poe — Pow)a cos <P dz + 2n[r°]a2 cos2 (p. (2.6.5)

This suggests that the torque of the frictional force at the ocean surface is balanced by the torque created by the pressure difference (difference of mean ocean level) at the eastern and western edges of the continents, and, therefore, in contrast to the atmosphere the redistribution of the absolute angular momentum in the ocean occurs in the zonal rather than in the meridional direction (Figure 2.17).

Thus, we have only one possibility: to close the cycle of absolute angular momentum by its meridional transport in the Earth's solid body. This accords with Oort (1985), who proposed the diagram (Figure 2.18) describing the


Figure 2.18 Schematic representation of the absolute angular momentum cycle in the ocean-atmosphere-lithosphere system, according to Oort (1985). The pressure and friction torques are designated by symbols 0>, 3~ respectively; index L indicates belonging to the land, index O indicates belonging to the ocean.


Figure 2.18 Schematic representation of the absolute angular momentum cycle in the ocean-atmosphere-lithosphere system, according to Oort (1985). The pressure and friction torques are designated by symbols 0>, 3~ respectively; index L indicates belonging to the land, index O indicates belonging to the ocean.

cycle of absolute angular momentum. The clarity of this diagram barely hides its shortcomings, related to difficulties of interpretation of the mechanism of absolute angular momentum transport in the Earth's solid body.

2.7 Carbon budget

The distinguished place of carbon among other chemical elements is determined first by the fact that carbon atoms, due to their electrical neutrality, easily interact with each other and with atoms of other elements, creating stable organic compounds and thereby producing a crucial effect on biological processes and on the life evolution on Earth. Moreover, carbon is included in the composition of such important (in the climatic sense) compounds as carbon dioxide whose role in the formation of the Earth's radiation is difficult to overestimate.

Carbon content. The carbon in the atmosphere is mainly present in the form of two stable compounds (carbon dioxide C02 and methane CH4) and of one unstable compound (carbon monoxide CO) which quickly oxidizes to C02.

The volume concentration of the first compound in January 1988 was 351 ppm, of the second one it was about 1.6 ppm, and of the third one it was about 0.1 ppm. It is clear that the carbon content in the atmosphere is almost completely determined by carbon dioxide.

Regular precise measurements of C02 concentration in the atmosphere were initiated during the International Geophysical Year (1957-1958) on Mauna Loa (Hawaii). During 1960-1963 the South Pole station (Antarctica) began operations, and today there are more than 30 stations for background monitoring of C02 - these stations being located far from industrial centres. Analyses of data from these stations indicate that atmospheric C02 concentration has marked seasonal variability arising from a phase shift in the process of formation (production) and disintegration (destruction) of the organic matter substance in terrestrial ecosystems. The maximum amplitude of seasonal variations (~ 8.2 ppm) have been recorded at Gold Bay (Alaska) located in the region of the boreal forests of North America, and in Eurasia. The maximum amplitude decreases to the north to about 3 ppm on Mauna Loa and 0.5-1.5 ppm in the Southern Hemisphere where the phase shift between production and destruction of the organic matter localized mainly in the forests of the tropical belt is low.

Large-scale spatial variations in the volume concentration of atmospheric C02 are less than local seasonal variations. Thus, the average values for eight years (1976 through 1983) of volume concentrations at two neighbouring stations, Mauna Loa and Kumutahi, located at 3397 and 3 metre heights respectively, differ from each other by only 0.4 ±0.3 ppm, and the average values for the same period at stations located in the northern and southern polar regions of the Earth differ by 3.2 ppm. Such relatively small spatial variability of the volume concentrations of atmospheric C02 is explained by rapid (compared with the time of renewal, see below) mixing of the atmosphere whose characteristic time scale (as shown in Table 1.1) does not exceed 106 s.

The carbon content in a unit atmospheric column is determined by the expression CA = (PclVcoJm^M where cA = i0~6(pCO2/p)qCO2 is the specific concentration of C02; qCOl = 106 x Pco2/ps is the volume concentration of C02; and pCOl and ps are the partial pressure of C02 and the atmospheric pressure at the sea level respectively; mA is the mass of a unit atmospheric column with unit cross-section; pc, pC02 and p are the molecular weights of carbon, carbon dioxide and air; the symbol A designates, as before, the operation of averaging over mass. According to this expression the carbon content in the atmosphere in January 1988 was 745 GtC (1 Gt = 109 t). For comparison, before the industrial revolution, that is, before 1860, it was equal to 594 GtC.

The dissolving of C02 in water is described by two expressions: C02 S C02 (diss) and C02 (diss) + H20 S H2C03 defining the hydration phenomenon and condition for the chemical equilibrium of carbonic acid H2C03. The dissolving takes several minutes and is determined by the equilibrium constant K0 = [H2C03]/[C02], where [C02] and [H2C03] are concentrations of dissolved carbon dioxide and dissolved carbonic acid. If the inorganic carbon content in the ocean were controlled only by this process then it would amount to 1% of its present value. In practice, carbon dioxide is not an inert gas like oxygen, nitrogen or like the noble gases such as argon, and this is why the dissolving of C02 in water is accompanied by a reaction with the substances of the Earth's crust and by the formation of other compounds which gradually accumulate in the ocean and, as a result, their concentrations become many times larger than the concentration of carbonic acid.

The major carbonic compound in the ocean is the bicarbonate ion HC03 . Its content as a percentage of the total amount of inorganic carbon in the ocean is about 95%. The bicarbonate ion is formed by the dissociation of carbonic acid when the proton is lost. This stage proceeds instantly and is described by the condition of chemical equilibrium H2C03 S HCOf + H + with dissociation constant = [HC03 ][H+]/[H2C03], where [HC03 ] and [H+] are the concentrations of bicarbonate and hydrogen ions.

The next stage is the dissociation of the bicarbonate ion and the formation of a carbonate ion CO\~. The appropriate condition for chemical equilibrium takes the form HC03 S C03~ + H+ and is determined by the dissociation constant K2 = [C0§"][H+]/[HC03 ], where [C03~] is the concentration of carbonate ions. The carbonate ion is the final product of the reaction of dissolved carbon dioxide with bases. Its concentration increases in the ocean until the solubility limit of calcium carbonate CaC03 is reached. The dissolving of CaC03 is described by the expression CaC03 S Ca2+ + CO2-, and the dissociation constant Ks is determined by the product of concentration of calcium ions [Ca2+] and carbonate ions [C03~] coexisting in equilibrium with one of two crystal forms of calcium carbonate: calcite and aragonite.

Let us define the total concentration cQ of inorganic carbon in the ocean as Cq = [C02] -I- [HCO3 ] + [CO2-]. Available data obtained by gas chromatography indicate (see Takahashi et al., 1981) that the total concentration of inorganic carbon at the ocean surface increases with latitude from 1900 ^imol/kg in the equatorial zone up to 2150 ^mol/kg at latitude 55°N and up to 2250 (imol/kg at latitudes 55-60°S. It also increases with depth, but only within the limits of the upper two-kilometre layer of the ocean. A decrease in the total concentration of inorganic carbon in the surface layer is explained by inorganic carbon consumption during the process of photo-synthetic activity of phytoplankton, and to some extent by C02 exchange with the atmosphere, while an increase in total concentration below 1000 metres is explained by the decomposition of falling residues of phyto- and zooplankton and by the oxidation of soft organics. According to Kobak (1988) the total content of inorganic carbon in the ocean amounts to 38 200 GtC. And 864 GtC of this, that is, slightly more than in the atmosphere, is in the upper 100-metre layer of the ocean.

Data for the last few years obtained from satellite images, aerophotography and ground-based studies have allowed us to establish (see Kobak, 1988) the fact that the total content of organic carbon in the terrestrial biota does not exceed 560 GtC. Note that 20 years ago it was estimated as 827 GtC. The causes of these discrepancies are the limited nature and inaccuracy of initial information on the specific (referred to unit area) content of carbon in forest ecosystems and the areas which they occupy.

At present, the variety of species of life on Earth is determined by its terrestrial inhabitants: angiosperms and insects. The last-mentioned group accounts for one million species. In the ocean the specific variety of fauna and flora is much less (about 30000 species of plants and about 160000 species of animals) and this is explained by the lower (than on the land) variability of ecologic and climatic conditions controlling species composition and density of the biota. The seaweeds are the major producers of organic matter in the ocean. There are about 30 000-35 000 known water-plant species and more than half of these dwell in the ocean.

The main mass of organic carbon in the ocean is contained in dissolved organic matter (DOM) representing the intermediate substances between living organisms and biogenous inorganic matter, and combining true solutions and colloids of organic carbon as well as particles with sizes from 0.45 through 1 |im. According to experimental data the mean concentration of DOM in the ocean is equal to 1.36 + 0.20 mg/1, which is equivalent to 1800-2000 GtC in the entire ocean volume.

Another form of existence of organic carbon in the ocean is suspended organic matter (SOM), including living cells of phyto- and zooplankton, residues of organisms, organic matter of skeleton formations, terrigenous and aeolian influx as well as precipitated, adsorbed from a solution and aggregated organic matter with particle sizes larger than 1 pm. The concentration of SOM in the ocean is much less than that of DOM and accounts for an average 53 + 26 (¿m/1. Its maximum values fall in high-productive regions, and its minimal values fall in low-productive regions and deep ocean layers. The total content of SOM in the ocean is estimated as 25.5 + 1.5 GtC.

About 50% of this is in depths of over 1000 m where bacterial activity is low and oxidation of organic matter is very slow. About the same amount of SOM (15-20 GtC) is not mineralized and gradually descends to the ocean bottom.

Finally, the third form of existence of carbon in the ocean is living organic matter. All present-day estimates of phyto- and zoomass are close to 3 GtC. Thus, estimates of the total content of DOM, SOM and living organics are related to each other as 100:1.4:0.15. This 'pyramid of mass' is caused by equilibrium of the production and destruction of organic matter in the ocean. In other words, it reflects the different stability (from the viewpoint of decomposition) of separate forms of organic matter.

The organic matter created in the process of vital functions by living organisms (primarily by plants and photosynthesizing organisms) is involved in rapid biological transformations and is also accumulated in relatively stable (in the sense of destruction) complexes forming soil organics on the land and water humus in the ocean. Affected by biochemical and chemical processes the organic residues are subjected to destruction with the result that part of the organic matter is transformed into mineral compounds (carbon dioxide, ammonia, nitrites and nitrates, etc.); the remaining part is converted into more stable (slowly oxidized) organic forms. This is why, for example, it is customary to classify all organic residues on the land in three groups: vegetable deciduosity and organic underlay (fallen leaves, dead parts of trees, bushes and grass cover); unstable biochemical compounds (incompletely modified vegetable residues, products of metabolism and newly formed humus matter); and stable biochemical compounds (humus, peat, sapropel, etc.) containing 84.2, 673 and 1346 GtC respectively. Thus, the total content of organic carbon in soil is equal to 2104 GtC, that is, it practically coincides with its value in the dissolved organic matter of the ocean.

The largest amount of soil carbon is concentrated in the boreal belt, and the least amount is concentrated in the polar zone of the land (35.1% and 6.5% of the total content respectively). Note, however, that the minimum content of the organic carbon in the polar belt is explained not by its low concentration, which is even higher than in the tropical, subtropical and subboreal belts but, rather, by the small area of the polar belt.

The organic matter in the ocean is also classified into stable and unstable groups, which, for the most part, have autochthonic (formed by living organisms) origin. The vertical variability for the unstable fraction is greater than for the stable fraction. Suffice it to say that the concentration of water humus in the ocean surface layer is equal to ~2.2 x 10"3gC/l, and at a scale of 3000 m it is equal to ~1.5 x 10~3gC/l, while the concentration of the unstable fraction, determined only by the vital function processes of zooplankton and bacteria, can differ by a hundred times within the limits of the ocean thickness.

Estimates of the carbon content in sedimentary deposits of the ocean and continents are rather approximate. The most recent estimates (see Budyko et al., 1985) attest that the sedimentary shell of the Earth contains 97.8 x 106 GtC, including 86 x 106 Gt of carbonate and 11.8 x 106 Gt of organic carbon.

Carbon sources and sinks. We have already said that the carbon content in the atmosphere is closely related to the vital function processes of the terrestrial biota and that carbon dioxide is practically the only (at present at least) source of it. The first experimental data confirming the existence of the relation between the atmospheric C02 content and the assimilating activity of plants were obtained in the early 1920s. The advent of optical-acoustic gas analysers in the 1950s and increased measurement accuracy opened up the possibility of studying the physical mechanism of C02 assimilation in vegetable communities and creating a quantitative theory of photosynthesis.

The intensity of carbon exchange between the atmosphere and vegetable communities is characterized by the pure primary production defined as the difference between the total primary production (the rate of organic matter formation) and losses by respiration (the rate of organic matter destruction under respiration) of autotrophs and heterotrophs. It will be recalled that autotrophs are organisms that assimilate the carbon of inorganic compounds, and heterotrophs are organisms that use organic matter. If the total primary production is higher than losses by respiration, the ecosystem serves as a carbon sink for the atmosphere; otherwise it represents a carbon source for the atmosphere. According to Kobak (1988) the total primary production of all forest, steppe and tundra vegetable communities is equal to 118.2 GtC/year.

Let us define losses by autotroph respiration as the difference between the total primary production and the rate of carbon photosynthetic assimilation, and losses by heterotroph respiration as the sum of the rate of organic matter mineralization in the upper soil layer and the rate of organic matter transformation into humus. According to Kobak (1988) the rate of carbon photosynthetic assimilation is 58.2 GtC/year, while the rate of organic matter mineralization and its transformation into humus is 41.4 and 2.5 GtC/ year. The rate of organic matter transformation into humus consists of two components characterizing the rate of formation of unstable (1.44 GtC/year) and stable (1.04 GtC/year) fractions of the soil humus. Using these estimates and those mentioned above we find that the pure primary production of the terrestrial biota, which is equal to the rate of photosynthetic assimilation minus the rate of organic matter mineralization, and of its transformation into humus must constitute 58.2 — 41.4 — 2.5 = 14.3 GtC/year. Hence, the terrestrial biota serves as the carbon sink for the atmosphere.

The flux of C02 into the atmosphere is not only due to respiration of the terrestrial vegetation, but also to so-called soil breathing (C02 emission from soil) representing the result of oxidation of soil organics by microorganisms and of respiration of vegetation roots. But because in the absence of other sources and sinks of carbon its withdrawal from the atmosphere through the process of photosynthesis can be balanced only by soil breathing, it has to be equal to the carbon photosynthetic assimilation, that is, 58.2 GtC/year. Part (41.4 + 2.5 = 43.9 GtC/year) of this value is determined by the destruction of mineralized organic matter and humus; the other part is determined by respiration of vegetation roots.

In contrast to terrestrial vegetable communities, in ocean ecosystems the carbon is not a factor which limits photosynthesis. One such factor is the intensity of short-wave solar radiation, which is not less than the limiting value of 2.08 W/m2 when photosynthesis stops. The depth appropriate for this value is called the light compensation depth. Above this depth the intensity of photosynthetic assimilation is greater than losses for respiration, and below this depth the reverse situation takes place where phytoplankton can exist only due to the organic matter which has been formed previously, that is, due to conversion to heterotrophic nutrition.

The other factor limiting photosynthesis is the presence of biogenous elements in sea water - nitrate NO3 and phosphate HPO4". Indeed, according to the Redfield formula

(CH20) j 06(NH3)! 6(H 3 P04) + 13802, describing the process of photosynthesis and its reverse process of destruction of organic matter, for every 106 moles of C02 expended for photosynthesis 16 moles of nitrate and 1 mole of phosphate are consumed. It follows, therefore, that the content of carbon, nitrogen and phosphorus in phytoplankton cells is in the ratio 106:16:1, and thus lack of nitrogen and phosphorus limits the intensity of carbon assimilation.

If we attribute the heterotrophic nutrition of phytoplankton to secondary production and attribute the same for chemosynthesis, which uses the energy of chemical reactions as a source, then the photosynthetic assimilation of carbon will represent the pure primary production of the ocean biota. There are many of its estimates that have mainly been obtained using the radiocarbon method. The most reliable of these are within the limits 23-46 GtC/year. It has also been shown that 75% of the pure primary production occurs in the open ocean, 17.5% occurs on the continental shelf, 4% occurs in estuaries, and only 0.5% occurs in local upwelling zones. Information about the seasonal variability of the ocean biota production can be classified as very approximate. Everything we know about this reduces to the following: at low latitudes phytoplankton production does not change throughout most of the year, but at temperate latitudes it undergoes distinct seasonal variations, increasing in spring and decreasing in summer. The summer decrease is related to the facts that phytoplankton is grazed by herbivorous zooplankton, and particularly to the lack of biogenous elements whose influx from the deep layers is blocked by the abrupt thermocline in the base of the upper mixed layer. In autumn, when vertical mixing is enhanced and the seasonal thermocline degenerates, phytoplankton productivity increases again. At high latitudes one (summer) peak only of productivity is recorded. These presentations are supported by data from colour scanning of the ocean surface by satellites that allow recovery of the chlorophyll concentration in water.

Apart from the autochthonic mechanism of organic matter formation in the ocean (photosynthesis), there is another mechanism - the allochthonic mechanism characterized by the inflow of organic matter with river and underground run-off, and by the removal of suspended particles and aeolian matter containing organic carbon from the land. According to Kobak (1988) the intensity of such a source of organic matter in the ocean amounts to «1 GtC/year. In addition, the contribution of river run-off is 0.21 GtC/year, that of underground run-off is 0.06 GtC/year, that of suspended particles is 0.4 GtC/year and that of aeolian matter is 0.3 GtC/year.

Autochthonic and allochthonic inflows of organic matter are compensated by lifetime secretions of plants and animals, as well as by decomposition of secretions and remains of plants and animals due to heterotrophic organisms (bacteria). The resulting production of dissolved and suspended organic matter amounts to 1.08 and 1.0-3.0 GtC/year, respectively (see Kobak, 1988), which signifies that 2-5% of the pure primary production goes into solution and about the same amount is precipitated. The precipitating organic matter formed during the process of biochemical and chemical reactions is subjected to destruction and is then dissolved at a rate of 0.9-2.9 GtC/year, so that the accumulation of organic matter in sedimentary deposits does not exceed 0.1 GtC/year.

Carbon exchange at the ocean-atmosphere interface. As previously mentioned, among all carbon-containing atmospheric gases only C02 has a sufficiently high concentration. Therefore, carbon exchange at the ocean-atmosphere interface is determined by the carbon dioxide flux. The first estimates of time-space variability of C02 flux on the basis of direct measurements of C02 partial pressure difference in water and air were obtained in 1986 at the Lamont Doherty Geological Observatory of Columbia University (US). They were then revised by Ariel et al. (1991). As a result it was found that the equatorial zone of the ocean (10°N-10°S) is a carbon source for the atmosphere. Here, due to the strong upwelling which ensures export to the surface of deep waters rich in carbon and biogenes, and due to the low solubility of C02 in water (the latter is due to the high temperature), carbon transfer from the ocean to the atmosphere amounts to 0.14 GtC in the Atlantic Ocean, 0.05 GtC/year in the Indian Ocean, and 0.54 GtC/year in the Pacific Ocean. These differences are caused by the different intensity of the equatorial upwelling.

In the subtropical gyres of the Northern (10°N-40°N) and Southern (10°S-40°S) Hemispheres the picture is more varied: in the Northern Hemisphere the Pacific and Atlantic Oceans serve as a sink of carbon for the atmosphere, and the Indian Ocean serves as a source. The respective values are: —0.01, —0.19 and 0.05 GtC/year. In the subtropical gyres of the Southern Hemisphere the carbon transfer from the ocean into the atmosphere takes place in the Atlantic (0.04 GtC/year), that from the atmosphere into the ocean takes place in the Pacific ( — 0.20 GtC/year) and Indian (—0.21 GtC/year) Oceans. Similarly, carbon transfer from the ocean into the atmosphere occurs in the northern subpolar area of the Pacific Ocean (0.17 GtC/year), that from the atmosphere into the ocean occurs in the northern (—0.38 GtC/year) and southern (—1.39 GtC/year) subpolar areas and in the southern polar area (-0.83 GtC/year) of the Atlantic Ocean.

In general, as shown by Ariel et al. (1991), the ocean absorbs atmospheric carbon at a rate of —2.21 GtC/year. Here, as before, the negative values of the flux conform to carbon transfer from the atmosphere into the ocean, and positive values do so in the reverse direction. Note that the annual mean global average carbon flux at the ocean-atmosphere interface turned out to be different from zero, which it would be in the absence of any long-term disturbances. Some of the arguments put forward by Ariel et al. (1991) favour the anthropogenic origin of such an imbalance.

Time of carbon renewal. The features, mentioned above, of the natural (not subjected to anthropogenic impacts) carbon cycle, together with the times of carbon renewal, are summarized in Table 2.4. Let us turn our attention to the following three facts. Firstly, the natural carbon cycle is closed in the atmosphere, ocean and biosphere, but it is not closed in the lithosphere, and thus in the climatic system as a whole. This is due to disregarding the interaction between the sedimentary shell, formed by sedimentary and volcanic rocks, and deep earth layers: during this process organic carbon accumulation on the ocean bottom in the form of carbonate sediments, that is, a net flux carbon from the biosphere to the lithosphere has to be compensated for by emission of volcanic carbon dioxide from the deep earth layers into the atmosphere and ocean.

Secondly, in accordance with the data presented in Table 2.4, the age of most ancient sediments and deposits of the ocean and continents, if estimated as the ratio between the carbon content and the characteristic rate of accumulation or erosion, should not exceed 100 million years. In other words, throughout the geological history of the Earth the sedimentary rocks must have been renewed repeatedly.

At first sight, this result contradicts the known facts and, in particular, the discovery of sedimentary rocks at the entrance to the Ameralik-Fjord (western Greenland) aged 3.8 billion years. This contradiction is explained by the variability of rates of sedimentary accumulation in the ocean and of erosion on the continents and thereby by the impossibility of applying present-day values to other geological periods. Let us recall in this connection the decrease in accumulation of carbonate sediments in the Medium and Late Carboniferous (346-232 million years ago), or the so-called interruptions in the sedimentary deposition sequence (intervals when there was no sediment accumulation) with recurrence changing from 40-60% at the beginning to 70-76% at the end of the Eocene Period (58-37 million years ago). As to the rate of continental erosion, this can be judged from variations in the mean ocean level characterizing the base of continental erosion. The most significant increase of 300-350 m in erosion over the last 570 million years, accompanied by the abrupt decrease in the export of terrigenous material into the ocean, occurred in the late Cretaceous Period (100-67 million years ago). This event and the ocean transgression which caused it had their origins in tectonic processes giving rise to the convergence of the African and Eurasian continents and the degeneration of the Tethys Ocean.

One should keep in mind the rather approximate character of estimates of the carbon accumulation rate in sedimentary depositions, and, most of all, the fact that the age of the most ancient sedimentary depositions in the ocean is determined by plate tectonics with characteristic time scales of «150 million years, and on the continents it is determined by the duration of

existence of granite sheets with characteristic time scales of «4 billion years. Therefore, the data in Table 2.4 do not contradict those for silt sediments discovered in the composition of ancient formations.

The third circumstance which should be particularly emphasized is the different renewal times for separate components of the carbon cycle. Indeed, as one can see from Table 2.4, the carbon renewal time is 0.1 year, and less for the ocean biota; about one year for plant deciduosity and organic underlayer; about ten years for the atmosphere, terrestrial biota and suspended organic matter in the ocean; hundreds, or even thousands, of years for the inorganic carbon content in the ocean, dissolved organic matter and soil humus; and, finally, hundreds of millions of years for sediments in the ocean and on the continents. Such a diversity of renewal times serves as the basis for the separation of three subcycles in the carbon cycle: the mobile subcycle, describing the processes of organic matter transformation and carbon circulation in the ocean-atmosphere system with time scales of about 103 years and less; the geochemical subcycle describing the processes of interaction between sea-water and carbonate sediments with time scales of about 104-105 years; and the geological subcycle, describing processes of organic matter burial and metamorphism, and of mantle outgassing with time scales of about 106 years and more.

We are interested in processes with time scales under 103 years. This restriction is equivalent to fixing slow (with time scales over 103 years) carbon subcycle characteristics. In this case the budget equation for the carbon in the atmosphere-ocean-biosphere-lithosphere system takes the form where cA and cQ are specific concentrations of inorganic carbon in the atmosphere and ocean; cLB (see below), cOB, and cL are specific concentrations of organic carbon in the terrestrial and ocean biota and in the lithosphere; CA = mAcA and CG = m0c0 are the inorganic carbon content in the atmospheric and ocean columns with unit cross-section; COB = mQcOB, CLB = mLcLB and CL = mLcL are the same but for inorganic carbon in the ocean and terrestrial biota and in the lithosphere; Q°s is the carbon flux (gas exchange) at the ocean-atmosphere interface; Q£B and QcB are the intensities of inorganic dCJdt + V mAvAcA = -<2°s - Q™, dCJdt + V-i=Q2S-Q2\ dCOB/dt + V mA vACqB = <2c® - Qc,

carbon sources and sinks in the atmosphere and ocean referred to the unit area; <2¿B is the intensity of carbon exchange between fast components of the terrestrial biota and the lithosphere normalized to the unit area; Qq and are the intensities of organic carbon exchange between fast and slow components of the carbon cycle in the lithosphere and the ocean normalized in an analogous way; all other designations are the same.

Let us integrate Equation (2.7.1) over the whole of the Earth's surface, Equations (2.7.2) and (2.7.3) over the ocean surface and Equations (2.7.4) and (2.7.5) over the land surface, and then sum them up. As a result we obtain the equality

3({Ca} + {C0}/0 + {C0B}/0 + {CLB}/L + {CL}fL)/dt = -{Q2}fo ~ {6c}/l>

representing the law of carbon conservation on time scales of the order of 103 years or less.

Similarly, integration of Equations (2.7.1)-(2.7.5) over longitude and their consequent addition yields

2na cos <p S([CA] + [C0]/ó + [COB]/ó + [Clb]/L + [QJ/D/df

+ 8(MCTa + MCT0 + MCTL)/a d<p = -2na cos (p(VQ^]f'0 + iQhlfi),


'2n mLvLcLa cos (p dX, o are the meridional carbon transports in the ocean, atmosphere and lithosphere.

A rough estimate of MCTA and MCT0 can be obtained if we turn to (2.7.7) and assume that ([ô£]/o + LQhlfi) = 0> MCFL = 0. Considering that the meridional carbon transport in the atmosphere and ocean has to vanish at the pole, we obtain, on average for the year (MCTA 4- MCT0) = 0, that is, the annual mean meridional carbon transport in the atmosphere and ocean must balance each other. Let us recollect, then, that the ocean serves as a carbon source for the atmosphere at low latitudes and as a carbon absorber at high latitudes, and that the intensity of the annual mean carbon exchange between the ocean and the atmosphere in the equatorial zone accounts for

~0.8 GtC/year. Hence, the annual mean meridional carbon transport is directed from low latitudes to high latitudes in the atmosphere, and in the reverse direction in the ocean. In addition, since the ratios of masses and zonal extensions of the atmosphere and ocean are equal to 3 x 10"3 and 2 respectively, then, all things being equal, the typical value of the meridional carbon transport across the unit length of a latitude circle in the atmosphere has to be two orders greater than in the ocean. To convert relative units into absolute units we note that in the pre-industrial epoch, when sources and sinks of atmospheric C02 counterbalanced each other on average for the year, the meridional transport of C02 in the atmosphere amounted to 3-6 GtC/year.

Small-scale ocean-atmosphere interaction

3.1 Surface atmospheric layer

The surface atmospheric layer is a layer within the limits of which the vertical fluxes of momentum, heat and moisture remain approximately constant in height. Let us expand this definition.

We examine the averaged (in terms of the Reynolds conditions) equation of motion for the horizontal velocity vector v. With the statistically homogeneous (in the horizontal direction) velocity field it takes the form where p is the atmospheric pressure; x is the horizontal vector of the tangential wind stress; p is the air density; d/dt and V are the operators of the total derivative and of the horizontal gradient; the axis z is directed vertically upward; k is the unit vector directed along the z-axis.

The first two terms on the right-hand side of Equation (3.1.1) describing, respectively, the effects of the Coriolis force and of the force of the horizontal pressure gradient, are the main terms. Considering that they balance each other, then assuming that fu0 (here u0 is the characteristic wind velocity scale; / is the Coriolis parameter) is an upper estimate of the third term on the right-hand side of (3.1.1) and that the change of vector x/p in the vertical direction is 0.2|t|/p we obtain the following inequality for the thickness h1 of the layer of approximate constancy of vertical momentum flux: hl >0.2 (|t|/p)(/m0)_1, from which with \x\/p = 0.1 m2/s2, u0 = 10m/s, and / = 10"4 s-1 the estimate of hx > 20 m is derived.

The estimate of the thickness h2 of the layer of approximate constancy of vertical heat flux H can be obtained from the averaged heat budget equation which, in the absence of water vapour transitions, and radiative sources and p dz p dv di p dz p

sinks of heat, is written as

0 0

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